Handbook of Thin Films, Five-Volume Set

Preface Thin film materials are the key elements of continued technological advances made in the fields of electronic, photonic, and magnetic devices. The processing of materials into thinfilms allows easy integration into various types of devices. The thin film materials discussed in this handbook include semiconductors, superconductors, ferroelectrics, nanostructured materials, magnetic materials, etc. Thin film materials have already been used in semiconductor devices, wireless communication, telecommunications, integrated circuits, solar cells, lightemitting diodes, liquid crystal displays, magneto-optic memories, audio and video systems, compact discs, electro-optic coatings, memories, multilayer capacitors, fiat-panel displays, smart windows, computer chips, magneto-optic disks, lithography, microelectromechanical systems (MEMS) and multifunctional protective coatings, as well as other emerging cutting edge technologies. The vast variety of thin film materials, their deposition, processing and fabrication techniques, spectroscopic characterization, optical characterization probes, physical properties, and structure-property relationships compiled in this handbook are the key features of such devices and basis of thin film technology. Many of these thin film applications have been covered in the five volumes of the Handbook of Thin Film Devices edited by M. H. Francombe (Academic Press, 2000). The Handbook of Thin Film Materials is complementary to that handbook on devices. The publication of these two handbooks, selectively focused on thin film materials and devices, covers almost every conceivable topic on thin films in the fields of science and engineering. This is the first handbook ever published on thin film materials. The 5-volume set summarizes the advances in thin film materials made over past decades. This handbook is a unique source of the in-depth knowledge of deposition, processing, spectroscopy, physical properties, and structure-property relationship of thin film materials. This handbook contains 65 state-ofthe-art review chapters written by more than 125 world-leading experts from 22 countries. The most renowned scientists write over 16,000 bibliographic citations and thousands of figures, tables, photographs, chemical structures, and equations. It has been divided into 5 parts based on thematic topics: Volume 1: Volume 2: Volume 3: Volume 4: Volume 5:

Deposition and Processing of Thin Films Characterization and Spectroscopy of Thin Films Ferroelectric and Dielectric Thin Films Semiconductor and Superconductor Thin Films Nanomaterials and Magnetic Thin Films

Volume 1 has 14 chapters on different aspects of thin film deposition and processing techniques. Thin films and coatings are deposited with chemical vapor deposition (CVD), physical vapor deposition (PVD), plasma and ion beam techniques for developing materials for electronics, optics, microelectronic packaging, surface science, catalytic, and biomedical technological applications. The various chapters include: methods of deposition of hydrogenated amorphous silicon for device applications, atomic layer deposition, laser applications in transparent conducting oxide thin film processing, cold plasma processing in surface science and technology, electrochemical formation of thin films of binary III-V compounds, nucleation, growth and crystallization of thin films, ion implant doping and isolation of GaN and related materials, plasma etching of GaN and related materials, residual stresses in physically vapor deposited thin films, Langmuir-Blodgett films of biological molecules, structure formation during electrocrystallization of metal films, epitaxial thin films of intermetallic compounds, pulsed laser deposition of thin films: expectations and reality and b"-alumina single-crystal films. This vol-

vii

viii

PREFACE ume is a good reference source of information for those individuals who are interested in the thin film deposition and processing techniques. Volume 2 has 15 chapters focused on the spectroscopic characterization of thin films. The characterization of thin films using spectroscopic, optical, mechanical, X-ray, and electron microscopy techniques. The various topics in this volume include: classification of cluster morphologies, the band structure and orientations of molecular adsorbates on surfaces by angleresolved electron spectroscopies, electronic states in GaAs-A1As short-period superlattices: energy levels and symmetry, ion beam characterization in superlattices, in situ real time spectroscopic ellipsometry studies: carbon-based materials and metallic TiNx thin films growth, in situ Faraday-modulated fast-nulling single-wavelength ellipsometry of the growth of semiconductor, dielectric and metal thin films, photocurrent spectroscopy of thin passive films, low frequency noise spectroscopy for characterization of polycrystalline semiconducting thin films and polysilicon thin film transistors, electron energy loss spectroscopy for surface study, theory of low-energy electron diffraction and photoelectron spectroscopy from ultra-thin films, in situ synchrotron structural studies of the growth of oxides and metals, operator formalism in polarization nonlinear optics and spectroscopy of polarization inhomogeneous media, secondary ion mass spectrometry (SIMS) and its application to thin films characterization, and a solid state approach to Langmuir monolayers, their phases, phase transitions and design. Volume 3 focuses on dielectric and ferroelectric thin films which have applications in microelectronics packaging, ferroelectric random access memories (FeRAMs), microelectromechanical systems (MEMS), metal-ferroelectric-semiconductor field-effect transistors (MFSFETs), broad band wireless communication, etc. For example, the ferroelectric materials such as barium strontium titanate discussed in this handbook have applications in a number of tunable circuits. On the other hand, high-permittivity thin film materials are used in capacitors and for integration with MEMS devices. Volume 5 of the Handbook of Thin Film Devices summarizes applications of ferroelectrics thin films in industrial devices. The 12 chapters on ferroelectrics thin films in this volume are complimentary to Volume 5 as they are the key components of such ferroelectrics devices. The various topics include electrical properties of high dielectric constant and ferroelectrics thin films for very large scale integration (VLSI) integrated circuits, high permittivity (Ba, Sr)TiO3 thin films, ultrathin gate dielectric films for Si-based microelectronic devices, piezoelectric thin films: processing and properties, fabrication and characterization of ferroelectric oxide thin films, ferroelectric thin films of modified lead titanate, point defects in thin insulating films of lithium fluoride for optical microsystems, polarization switching of ferroelecric crystals, high temperature superconductor and ferroelectrics thin films for microwave applications, twinning in ferroelectrics thin films: theory and structural analysis, and ferroelectrics polymers Langmuir-Blodgett films. Volume 4 has 13 chapters dealing with semiconductor and superconductor thin film materials. Volumes 1, 2, and 3 of the Handbook of Thin Film Devices summarize applications of semiconductor and superconductors thin films in various types of electronic, photonic and electro-optics devices such as infrared detectors, quantum well infrared photodetectors (QWIPs), semiconductor lasers, quantum cascade lasers, light emitting diodes, liquid crystal and plasma displays, solar cells, field effect transistors, integrated circuits, microwave devices, SQUID magnetometers, etc. The semiconductor and superconductor thin film materials discussed in this volume are the key components of such above mentioned devices fabricated by many industries around the world. Therefore this volume is in coordination to Volumes 1, 2, and 3 of the Handbook of Thin Film Devices. The various topics in this volume include; electrochemical passivation of Si and SiGe surfaces, optical properties of highly excited (A1, In)GaN epilayers and heterostructures, electical conduction properties of thin films of cadmium compounds, carbon containing heteroepitaxial silicon and silicon/germanium thin films on Si(001), germanium thin films on silicon for detection of near-infrared light, physical properties of amorphous gallium arsenide, amorphous carbon thin films, high-Tc superconducting thin films, electronic and optical properties of strained semiconductor films of group V and III-V materials, growth, structure and properties of plasma-deposited amorphous hydrogenated carbon-nitrogen films, conductive metal oxide thin films, and optical properties of dielectric and semiconductor thin films.

PREFACE

ix

Volume 5 has 12 chapters on different aspects of nanostructured materials and magnetic thin films. Volume 5 of the Handbook of Thin Film Devices summarizes device applications of magnetic thin films in permanent magnets, magneto-optical recording, microwave, magnetic MEMS, etc. Volume 5 of this handbook on magnetic thin film materials is complimentary to Volume 5 as they are the key components of above-mentioned magnetic devices. The various topics covered in this volume are; nanoimprinting techniques, the energy gap of clusters, nanoparticles and quantum dots, spin waves in thin films, multi-layers and superlattices, quantum well interference in double quantum wells, electro-optical and transport properties of quasi-two-dimensional nanostrutured materials, magnetism of nanoscale composite films, thin magnetic films, magnetotransport effects in semiconductors, thin films for high density magnetic recording, nuclear resonance in magnetic thin films, and multilayers, and magnetic characterization of superconducting thin films. I hope these volumes will be very useful for the libraries in universities and industrial institutions, governments and independent institutes, upper-level undergraduate and graduate students, individual research groups and scientists working in the field of thin films technology, materials science, solid-state physics, electrical and electronics engineering, spectroscopy, superconductivity, optical engineering, device engineering nanotechnology, and information technology, everyone who is involved in science and engineering of thin film materials. I appreciate splendid cooperation of many distinguished experts who devoted their valuable time and effort to write excellent state-of-the-art review chapters for this handbook. Finally, I have great appreciation to my wife Dr. Beena Singh Nalwa for her wonderful cooperation and patience in enduring this work, great support of my parents Sri Kadam Singh and Srimati Sukh Devi and love of my children, Surya, Ravina and Eric in this exciting project.

Hari Singh Nalwa Los Angeles, CA, USA

About the Editor

Dr. Hari Singh Nalwa is the Managing Director of the Stanford Scientific Corporation in Los Angeles, California. Previously, he was Head of Department and R&D Manager at the Ciba Specialty Chemicals Corporation in Los Angeles (1999-2000) and a staff scientist at the Hitachi Research Laboratory, Hitachi Ltd., Japan (19901999). He has authored over 150 scientific articles in journals and books. He has 18 patents, either issued or applied for, on electronic and photonic materials and devices based on them. He has published 43 books including Ferroelectric Polymers (Marcel Dekker, 1995), Nonlinear Optics of Organic Molecules and Polymers (CRC Press, 1997), Organic Electroluminescent Materials and Devices (Gordon & Breach, 1997), Handbook of Organic Conductive Molecules and Polymers, Vols. 1-4 (John Wiley & Sons, 1997), Handbook of Low and High Dielectric Constant Materials and Their Applications, Vols. 1-2 (Academic Press, 1999), Handbook of Nanostructured Materials and Nanotechnology, Vols. 1-5 (Academic Press, 2000), Handbook of Advanced Electronic and Photonic Materials and Devices, Vols. 1-10 (Academic Press, 2001), Advanced Functional Molecules and Polymers, Vols. 1-4 (Gordon & Breach, 2001), Photodetectors and Fiber Optics (Academic Press, 2001), Silicon-Based Materials and Devices, Vols. 1-2 (Academic Press, 2001), Supramolecular Photosensitive and Electroactive Materials (Academic Press, 2001), Nanostructured Materials and Nanotechnology-Condensed Edition (Academic Press, 2001), and Handbook of Thin Film Materials, Vols. 1-5 (Academic Press, 2002). The Handbook of Nanostructured Materials and Nanotechnology edited by him received the 1999 Award of Excellence in Engineering Handbooks from the Association of American Publishers. Dr. Nalwa is the founder and Editor-in-Chief of the Journal of Nanoscience and Nanotechnology (2001-). He also was the founder and Editor-in-Chief of the Journal of Porphyrins and Phthalocyanines published by John Wiley & Sons (1997-2000) and serves or has served on the editorial boards of Journal of Macromolecular Science-Physics (1994-), Applied Organometallic Chemistry (1993-1999), International Journal of Photoenergy (1998-) and Photonics Science News (1995-). He has been a referee for many international journals including Journal of American Chemical Society, Journal of Physical Chemistry, Applied Physics .......

Letters, Journal of Applied Physics, Chemistry of Materials, Journal of Materials Science, Coordination Chemistry Reviews, Applied Organometallic Chemistry, Journal of Porphyrins and Phthalocyanines, Journal of Macromolecular Science-Physics, Applied Physics, Materials Research Bulletin, and Optical Communications. Dr. Nalwa helped organize the First International Symposium on the Crystal Growth of Organic Materials (Tokyo, 1989) and the Second International Symposium on Phthalocyanines (Edinburgh, 1998) under the auspices of the Royal Society of Chemistry. He also proposed a conference on porphyrins and phthalocyanies to the scientific community that, in part, was intended to promote public awareness of the Journal of Porphyrins and Phthalocyanines, which he founded in 1996. As a member of the organizing committee, he helped effectuate the First International Conference on Porphyrins and Phthalocyanines, which was held in Dijon, France

xix

xx

ABOUT THE EDITOR in 2000. Currently he is on the organizing committee of the BioMEMS and Smart Nanostructures, (December 17-19, 2001, Adelaide, Australia) and the World Congress on Biomimetics and Artificial Muscles (December 9-11, 2002, Albuquerque, USA). Dr. Nalwa has been cited in the Dictionary of lnternational Biography, Who's Who in Science and Engineering, Who's Who in America, and Who's Who in the World. He is a member of the American Chemical Society (ACS), the American Physical Society (APS), the Materials Research Society (MRS), the Electrochemical Society and the American Association for the Advancement of Science (AAAS). He has been awarded a number of prestigious fellowships including a National Merit Scholarship, an Indian Space Research Organization (ISRO) Fellowship, a Council of Scientific and Industrial Research (CSIR) Senior fellowship, a NEC fellowship, and Japanese Government Science & Technology Agency (STA) Fellowship. He was an Honorary Visiting Professor at the Indian Institute of Technology in New Delhi. Dr. Nalwa received a B.Sc. degree in biosciences from Meerut University in 1974, a M.Sc. degree in organic chemistry from University of Roorkee in 1977, and a Ph.D. degree in polymer science from Indian Institute of Technology in New Delhi in 1983. His thesis research focused on the electrical properties of macromolecules. Since then, his research activities and professional career have been devoted to studies of electronic and photonic organic and polymeric materials. His endeavors include molecular design, chemical synthesis, spectroscopic characterization, structure-property relationships, and evaluation of novel high performance materials for electronic and photonic applications. He was a guest scientist at Hahn-Meitner Institute in Berlin, Germany (1983) and research associate at University of Southern California in Los Angeles (1984-1987) and State University of New York at Buffalo (1987-1988). In 1988 he moved to the Tokyo University of Agriculture and Technology, Japan as a lecturer (1988-1990), where he taught and conducted research on electronic and photonic materials. His research activities include studies of ferroelectric polymers, nonlinear optical materials for integrated optics, low and high dielectric constant materials for microelectronics packaging, electrically conducting polymers, electroluminescent materials, nanocrystalline and nanostructured materials, photocuring polymers, polymer electrets, organic semiconductors, LangmuirBlodgett films, high temperature-resistant polymer composites, water-soluble polymers, rapid modeling, and stereolithography.

List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins.

FREDERICK OJO ADURODIJA (161) Inorganic Materials Department, Hyogo Prefectural Institute of Industrial Research, 3-1-12 Yukihira-cho, Suma-ku, Kobe, Japan

VICTOR EROKHIN (523) Fondazione El.B.A., Corso Europa 30, Genoa, 16132 Italy

PIERANGELO GRONING (219) Department of Physics, University of Fribourg, Fribourg, CH- 1700 Switzerland

MICHAEL HUTH (587) Institute for Physics, Johannes Gutenberg-University Mainz, 55099 Mainz, Germany

u M. KOZLOV (261,559) Department of Physics, National Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine

HIDEYA KUMOMI (319) Canon Research Center, 5-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0193, Japan

CHU KUN KUO (675) Ceramic Engineering Research Group, Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada

MARKKU LESKEL)[ (103) Department of Chemistry, University of Helsinki, FIN-00014 Helsinki, Finland

PATRICK S. NICHOLSON (675) Ceramic Engineering Research Group, Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada YVES PAULEAU (455) National Polytechnic Institute of Grenoble, CNRS-UJF-LEMD, B.P. 166, 38042 Grenoble Cedex 9, France

S. J. PEARTON (375,409) Department of Materials Science and Engineering, University of Florida, Gainesville, Florida, USA

L. PERALDO BICELLI (261,559) Dipartimento di Chimica Fisica Applicata del Politecnico, Centro di Studio sumProcessi Elettrodici del CNR, 20131 Milan, Italy

MIKKO RITALA ( 103) Department of Chemistry, University of Helsinki, FIN-00014 Helsinki, Finland

LEONID R. SHAGINYAN (627) Institute for Problems of Materials Science, Kiev, 03142 Ukraine

xxi

xxii

LIST OF CONTRIBUTORS

FRANK G. SHI (319) Department of Chemical and Biochemical Engineering and Materials Science, University of California, Irvine, California, USA R. J. SHUL (409) Sandia National Laboratories, Albuquerque, New Mexico, USA

WILFRIED G. J. H. M. VAN SARK (1) Debye Institute, Utrecht University, NL-3508 TA Utrecht, The Netherlands

Handbook of Thin Film Materials Edited by H.S. Nalwa

Volume 1. DEPOSITION AND PROCESSING OF THIN FILMS Chapter 1. Methods of Deposition of Hydrogenated Amorphous Silicon for Device Applications Wilfried G. J. H. M. van Sark Chapter 2.

Atomic Layer Deposition Markku Leskelgi

Chapter 3.

Laser Applications in Transparent Conducting Oxide Thin Films Processing Frederick Ojo Adurodija

Chapter 4.

Cold Plasma Processes in Surface Science and Technology Pierangelo Gr6ning

Chapter 5.

Electrochemical Formation of Thin Films of Binary III-V Compounds L. Peraldo Bicelli, V. M. Kozlov

Chapter 6.

Fundamentals for the Formation and Structure Control of Thin Films: Nucleation, Growth, Solid-State Transformations Hideya Kumomi, Frank G. Shi

Chapter 7.

Ion Implant Doping and Isolation of GaN and Related Materials S. J. Pearton Plasma Etching of GaN and Related Materials S. J. Pearton, R. J. Shul

Chapter 8. Chapter 9.

Residual Stresses in Physically Vapor-Deposited Thin Films Yves Pauleau Chapter 10. Langmuir-Blodgett Films of Biological Molecules Victor Erokhin Chapter 11. Structure Formation During Electrocrystallization of Metal Films V. M. Kozlov, L. Peraldo Bicelli Chapter 12. Epitaxial Thin Films of Intermetallic Compounds Michael Huth Chapter 13. Pulsed Laser Deposition of Thin Films: Expectations and Reality Leonid R. Shaginyan

Chapter 14. Single-Crystal/~"-Alumina Films Chu Kun Kuo, Patrick S. Nicholson

Volume 2. CHARACTERIZATION AND SPECTROSCOPY OF THIN FILMS Chapter 1. Classification of Cluster Morphologies Nan Li, Martin Zinke-Allmang Chapter 2.

Band Structure and Orientation of Molecular Adsorbates on Surfaces by Angle-Resolved Electron Spectroscopies P. A. Dowben, Jaewu Choi, Bo Xu

xxiii

xxiv

CONTENTS OF VOLUMES IN THIS SET Chapter 3.

Superhard Coatings in C - B - N Systems: Growth and Characterization Arun K. Sikder, Ashok Kumar

Chapter 4.

ATR Spectroscopy of Thin Films Urs Peter Fringeli, Dieter Baurecht, Monira Siam, Gerald Reiter, Michael Schwarzott, Thomas Biirgi, Peter Briiesch

Chapter 5.

Ion-Beam Characterization in Superlattices Z. Zhang, J. R. Liu, Wei-Kan Chu

Chapter 6.

In Situ and Real-Time Spectroscopic Ellipsometry Studies: Carbon Based and Metallic TiNx Thin Films Growth S. Logothetidis

Chapter 7.

In Situ Faraday-Modulated Fast-Nulling Single-Wavelength Ellipsometry of the Growth of Semiconductor, Dielectric, and Metal Thin Films J. D. Leslie, H. X. Tran, S. Buchanan, J. J. Dubowski, S. R. Das, L. LeBrun

Chapter 8.

Photocurrent Spectroscopy of Thin Passive Films E Di Quarto, S. Piazza, M. Santamaria, C. Sunseri

Chapter 9.

Electron Energy Loss Spectroscopy for Surface Study Takashi Fujikawa

Chapter 10. Theory of Low-Energy Electron Diffraction and Photoelectron Spectroscopy from Ultra-Thin Films Jiirgen Henk Chapter 11. In Situ Synchrotron Structural Studies of the Growth of Oxides and Metals A. Barbier, C. Mocuta, G. Renaud Chapter 12. Operator Formalism in Polarization-Nonlinear Optics and Spectroscopy of Polarization-Inhomogeneous Media L L Gancheryonok, A. V. Lavrinenko Chapter 13. Secondary Ion Mass Spectrometry and Its Application to Thin Film Characterization Elias Chatzitheodoridis, George Kiriakidis, lan Lyon Chapter 14. A Solid-State Approach to Langmuir Monolayers, Their Phases, Phase Transitions, and Design Craig J. Eckhardt Chapter 15. Solid State NMR of Biomolecules Akira Naito, Miya Kamihira

Volume 3. FERROELECTRIC AND DIELECTRIC THIN FILMS Chapter 1. The Electrical Properties of High-Dielectric-Constant and Ferroelectric Thin Films for Very Large Scale Integration Circuits Joseph Ya-min Lee, Benjamin Chihming Lai Chapter 2.

High-Permittivity (Ba, Sr)TiO3 Thin Films M. Nayak, S. Ezhilvalavan, T. Y. Tseng

Chapter 3.

Ultrathin Gate Dielectric Films for Si-Based Microelectronic Devices C. Krug, L J. R. Baumvol

Chapter 4.

Piezoelectric Thin Films: Processing and Properties Floriana Craciun, Patrizio Verardi, Maria Dinescu

Chapter 5.

Fabrication and Characterization of Ferroelectric Oxide Thin Films Jong-Gul Yoon, Tae Kwon Song

CONTENTS OF VOLUMES IN THIS SET Chapter 6.

Ferroelectric Thin Films of Modified Lead Titanate J. Mendiola, M. L. Calzada

Chapter 7.

Point Defects in Thin Insulating Films of Lithium Fluoride for Optical Microsystems Rosa Maria Montereali

Chapter 8.

Polarization Switching of Ferroelectric Crystals Lung-Han Peng

Chapter 9.

High-Temperature Superconductor and Ferroelectric Thin Films for Microwave Applications F~lix A. Miranda, Joseph D. Warner, Guru Subramanyam

Chapter 10. Twinning in Ferroelectric Thin Films: Theory and Structural Analysis S. Pamir Alpay Chapter 11. Ferroelectric Polymer Langmuir-Blodgett Films Stephen Ducharme, S. P. Palto, V. M. Fridkin Chapter 12. Optical Properties of Dielectric and Semiconductor Thin Films L Chambouleyron, J. M. Marffnez

Volume 4. SEMICONDUCTOR AND SUPERCONDUCTING THIN FILMS Chapter 1. Electrochemical Passivation of Si and SiGe Surfaces J. Rappich, Th. Dittrich Chapter 2.

Epitaxial Growth and Structure of III-V Nitride Thin Films Dharanipal Doppalapudi, Theodore D. Moustakas

Chapter 3.

Optical Properties of Highly Excited (A1, In) GaN Epilayers and Heterostructures Sergiy Bidnyk, Theodore J. Schmidt, Jin-Joo Song

Chapter 4.

Electrical Conduction Properties of Thin Films of Cadmium Compounds R. D. Gould Carbon-Containing Heteroepitaxial Silicon and Silicon/Germanium Thin Films on Si(001) H. JOrg Osten

Chapter 5.

Chapter 6.

Low-Frequency Noise Spectroscopy for Characterization of Polycrystalline Semiconductor Thin Films and Polysilicon Thin Film Transistors Charalabos A. Dimitriadis, George Kamarinos

Chapter 7.

Germanium Thin Films on Silicon for Detection of Near-Infrared Light G. Masini, L. Colace, G. Assanto

Chapter 8.

Physical Properties of Amorphous Gallium Arsenide Roberto Murri, Nicola Pinto

Chapter 9.

Amorphous Carbon Thin Films S. R. P. Silva, J. D. Carey, R. U. A. Khan, E. G. Gerstner, J. V. Anguita

Chapter 10. High- Tc Superconductor Thin Films B. R. Zhao Chapter 11. Electronic and Optical Properties of Strained Semiconductor Films of Groups IV and III-V Materials George Theodorou Chapter 12. Growth, Structure, and Properties of Plasma-Deposited Amorphous Hydrogenated Carbon-Nitrogen Films D. E Franceschini Chapter 13. Conductive Metal Oxide Thin Films Quanxi Jia

xxv

xxvi

CONTENTS OF VOLUMES IN THIS SET

Volume 5. NANOMATERIALS AND MAGNETIC THIN FILMS Chapter 1. Nanoimprint Techniques Hella-C. Scheer, Hubert Schulz, Thomas Hoffmann, Clivia M. Sotomayor Torres Chapter 2. The Energy Gap of Clusters Nanoparticles, and Quantum Dots Klaus Sattler Chapter 3. Electronic States in GaAs-A1As Short-Period Superlattices: Energy Levels and Symmetry Weikun Ge, Jian-Bai Xia Chapter 4. Spin Waves in Thin Films, Superlattices and Multilayers Zhang Zhi-Dong Chapter 5. Quantum Well Interference in Double Quantum Wells Zhang Zhi-Dong Chapter 6. Electro-Optical and Transport Properties of Quasi-Two-Dimensional Nanostructured Materials Rodrigo A. Rosas, Ratil Riera, Jos~ L. Marfn, Germdn Campoy Chapter 7. Magnetism of Nanophase Composite Films D. J. Sellmyer, C. P. Luo, Y. Qiang, J. P. Liu Chapter 8. Thin Magnetic Films Hans Hauser, Rupert Chabicovsky, Karl Riedling Chapter 9. Magnetotransport Effects in Semiconductors Nicola Pinto, Roberto Murri, Marian Nowak Chapter 10. Thin Films for High-Density Magnetic Recording Genhua Pan Chapter 11. Nuclear Resonance in Magnetic Thin Films and Multilayers Mircea Serban Rogalski Chapter 12. Magnetic Characterization of Superconducting Thin Films M. R. Koblischka

List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins.

A. BARBIER (527) CEA/Grenoble, Ddpartement de Recherche Fondamentale sur la Matibre Condensde SP2M/IRS, 38054 Grenoble Cedex 9, France

DIETER BAURECHT (191) Institute of Physical Chemistry, University of Vienna, Althanstrasse 14/UZA II, A- 1090 Vienna, Austria

PETER BRflESCH (191) ABB Management Ltd., Corporate Research (CRB), CH-5405 Baden-Dattwil, Switzerland and Departement de Physique, Ecole Polytechnique, Federale de Lausanne (EPFL), PH-Ecublens, CH- 1015 Lausanne, Switzerland

S. BUCHANAN (331) Waterloo Digital Electronics Division of WDE Inc., 279 Weber St. N., Waterloo, Ontario, N2J 3H8, Canada

THOMAS BURGI (191) Laboratory of Technical Chemistry, Swiss Federal Institute of Technology, ETH Zentrum, CH-8092 Ztirich, Switzerland

ELIAS CHATZITHEODORIDIS (637) IESL/FORTH, Crete, Greece

JAEWU CHOI (61) Center for Advanced Microstructures and Devices, Louisiana State University, Baton Rouge, Louisiana, USA WEI-KAN CHU (231) Department of Physics, Texas Center for Superconductivity, University of Houston, Houston, Texas, USA

S. R. DAS (331) Institute for Microstructural Sciences, National Research Council, Ottawa, Ontario, K1A 0R6, Canada P. A. DOWBEN (61) Department of Physics and Astronomy and the Center for Materials Research and Analysis, Behlen Laboratory of Physics, University of Nebraska, Lincoln, Nebraska, USA F. DI QUARTO (373) Dipartimento di Ingegneria Chimica dei Processi e dei Materiali, Universit~ di Palermo, Viale delle Scienze, 90128 Palermo, Italy

J. J. DUBOWSKI (3 31) Institute for Microstructural Sciences, National Research Council, Ottawa, Ontario, K1A 0R6, Canada

xxiii

xxiv

LIST OF CONTRIBUTORS

CRAIG J. ECKHARDT (685) Department of Chemistry, Center for Materials Research and Analysis, University of Nebraska-Lincoln, Lincoln, Nebraska, USA URS PETER FRINGELI ( 191) Institute of Physical Chemistry, University of Vienna, Althanstrasse 14/UZA II, A- 1090 Vienna, Austria

TAKASHI FUJIKAWA (415) Graduate School for Science, Chiba University, Chiba 263-8522, Japan I. I. GANCHERYONOK (597) Department of Physics, Belarusian State University, E Skariny av. 4, Minsk 2220080, Belarus

J[IRGEN HENK (479) Max-Planck-Institut ffir Mikrostrukturphysik, Halle/Saale, Germany

MIYA KAMIHIRA (7 3 5) Department of Life Science, Himeji Institute of Technology, 3-2-1 Kouto, Kamigori, Hyogo 678-1297, Japan

GEORGE KIRIAKIDIS (637) IESL/FORTH, Crete, Greece

ASHOK KUMAR (115) Center for Microelectronics Research, College of Engineering, University of South Florida, Tampa, Florida, USA A. V. LAVRINENKO (597) Department of Physics, Belarusian State University, F. Skariny av. 4, Minsk 2220080, Belarus

L. LEBRUN (3 31 ) Institute for Microstructural Sciences, National Research Council, Ottawa, Ontario, K1A 0R6, Canada

J. D. LESLIE (3 31 ) Department of Physics, University of Waterloo, Waterloo, Ontario, N2L 3G 1, Canada NAN LI (1) Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, N6A 3K7, Canada

J. R. LIU (231) Department of Physics, Texas Center for Superconductivity, University of Houston, Houston, Texas, USA S. LOGOTHETIDIS (277) Aristotle University of Thessaloniki, Physics Department, Solid State Physics Section, GR-54006, Thessaloniki, Greece

TADEUSZ LUTY (685) Institute of Physical and Theoretical Chemistry, Technical University of Wroctaw, Wroctaw, Poland IAN LYON (637) Manchester University, England C. MOCUTA (527) CEAdGrenoble, D6partement de Recherche Fondamentale sur la Mati~re Condens6e SP2M/IRS, 38054 Grenoble Cedex 9, France

XXV

EIZI MORIKAWA (61) Center for Advanced Microstructures and Devices, Louisiana State University, Baton Rouge, Louisiana, USA

AKIRA NAITO (735) Department of Life Science, Himeji Institute of Technology, 3-2-1 Kouto, Kamigori, Hyogo 678-1297, Japan S. PIAZZA (373) Dipartimento di Ingegneria Chimica dei Processi e dei Materiali, Universit~ di Palermo, Viale delle Scienze, 90128 Palermo, Italy

G. RENAUD (527) CEA/Grenoble, D6partement de Recherche Fondamentale sur la MatiSre Condens6e SP2M/IRS, 38054 Grenoble Cedex 9, France

GERALD REITER (191) Institute of Physical Chemistry, University of Vienna, Althanstrasse 14/UZA II, A- 1090 Vienna, Austria

M. S ANTAMARIA (373) Dipartimento di Ingegneria Chimica dei Processi e dei Materiali, Universith di Palermo, Viale delle Scienze, 90128 Palermo, Italy MICHAEL SCHWARZOTT (191) Institute of Physical Chemistry, University of Vienna, Althanstrasse 14/UZA II, A- 1090 Vienna, Austria

MONIRA SIAM (191) Institute of Physical Chemistry, University of Vienna, Althanstrasse 14/UZA II, A- 1090 Vienna, Austria

ARUN K. SIKDER (115) Center for Microelectronics Research, College of Engineering, University of South Florida, Tampa, Florida, USA C. SUNSERI (373) Dipartimento di Ingegneria Chimica dei Processi e dei Materiali, Universith di Palermo, Viale delle Scienze, 90128 Palermo, Italy H. X. TRAM (331) Department of Physics, University of Waterloo, Waterloo, Ontario, N2L 3G 1, Canada

BO Xu (61) Department of Physics and Astronomy and the Center for Materials Research and Analysis, Behlen Laboratory of Physics, University of Nebraska, Lincoln, Nebraska, USA Z. ZHANG (231) Department of Physics, Texas Center for Superconductivity, University of Houston, Houston, Texas, USA

MARTIN ZINKE-ALLMANG (1) Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, N6A 3K7, Canada

List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins.

S. PAMIR ALPAY (517) Department of Metallurgy and Materials Engineering, University of Connecticut, Storrs, Connecticut, USA I. J. R. B AUMVO L ( 16 9) Instituto de Ffsica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509-900, Brazil M. L. CALZADA (369) Instituto Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049 Madrid, Spain I. CHAMBOULEYRON (593) Institute of Physics "Gleb Wataghin," State University of CampinasmUNICAMP, 13073-970 Campinas, Sao Paulo, Brazil FLORIANA CRACIUN (231) Istituto di Acustica "O.M. Corbino," Consiglio Nazionale delle Ricerche, 00133 Rome, Italy MARIA DINESCU (231) National Institute for Lasers, Plasma and Radiaton Physics, Institute of Atomic Physics, Bucharest, Romania

STEPHEN DUCHARME (545) Department of Physics and Astronomy, Center for Materials Research and Analysis, University of Nebraska, Lincoln, Nebraska, USA S. EZHILVALAVAN (99) Department of Electronics Engineering and Institute of Electronics, National Chiao-Tung University, Hsinchu, Taiwan, Republic of China V. M. FRIDKIN (545) Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow 117333, Russia

C. KRUG (169) Instituto de Ffsica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509-900, Brazil

BENJAMIN CHIHMING LAI (1) Department of Electrical Engineering and Institute of Electronics, Tsing-Hua University, Hsinchu, Taiwan, Republic of China

JOSEPH YA-MIN LEE (1) Department of Electrical Engineering and Institute of Electronics, Tsing-Hua University, Hsinchu, Taiwan, Republic of China

xxi

xxii

LIST OF CONTRIBUTORS J. M. MARTINEZ (593) Institute of Mathematics and Computer Science, State University of Campinas--UNICAMP, 13083-970 Campinas, $5o Paulo, Brazil J. MENDIOLA (369) Instituto Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049 Madrid, Spain FI~LIX A. MIRANDA (481) NASA Glenn Research Center, Communication Technology Division, Cleveland, Ohio, USA ROSA MARIA MONTEREALI (399) ENEA C.R. Frascati, Applied Physics Division, 00044 Frascati (RM), Italy M. NAYAK (99) Department of Electronics Engineering and Institute of Electronics, National Chiao-Tung University, Hsinchu, Taiwan, Republic of China S. P. PALTO (545) Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow 117333, Russia LUNG-HAN PENG (433) Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, Republic of China

TAE KWON SONG (309) Department of Ceramic Science and Engineering, Changwon National University, Changwon, Kyungnam 641-773, Korea

GURU SUBRAMANYAM (481) Department of Electrical and Computer Engineering, University of Dayton, Dayton, Ohio, USA T. Y. TSENG (99) Department of Electronics Engineering and Institute of Electronics, National Chiao-Tung University, Hsinchu, Taiwan, Republic of China

PATRIZIO VERARDI (231) Istituto di Acustica "O.M. Corbino," Consiglio Nazionale delle Ricerche, 00133 Rome, Italy JOSEPH D. WARNER (481) NASA Glenn Research Center, Communication Technology Division, Cleveland, Ohio, USA JONG-GUL YOON (309) Department of Physics, University of Suwon, Hwaseung, Kyung-gi-do445-743, Korea

List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins. J. V. ANGUITA (403) Large Area Electronics Group, School of Electronics, Computing and Mathematics, University of Surrey, Guildford, United Kingdom G. ASSANTO (327) Department of Electronic Engineering and National Institute for the Physics of Matter INFM RM3, Terza University of Rome, Via della Vasca Navale 84, 00146 Rome, Italy SERGIY BIDNYK (117) Center for Laser and Photonics Research and Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA

J. D. CAREY (403) Large Area Electronics Group, School of Electronics, Computing and Mathematics, University of Surrey, Guildford, United Kingdom L. COLACE (327) Department of Electronic Engineering and National Institute for the Physics of Matter INFM RM3, Terza University of Rome, Via della Vasca Navale 84, 00146 Rome, Italy CHARALABOS A. DIMITRIADIS (291) Aristotle University of Thessaloniki, Department of Physics, Thessaloniki 54006, Greece

TH. DITTRICH (1) Technische Universitiit, Mtinchen, Physikdepartment E16, Garching 85748, Germany

DHARANIPAL DOPPALAPUDI (57) Boston MicroSystems Inc., Woburn, Massachusetts, USA D. E FRANCESCHINI (649) Instituto de Ffsica, Universidade Federal Fluminense, Avenida Litor~nea s/n, Niter6i, RJ, 24210-340, Brazil E. G. GERSTNER (403) Large Area Electronics Group, School of Electronics, Computing and Mathematics, University of Surrey, Guildford, United Kingdom R. D. GOULD (187) Department of Physics, Thin Films Laboratory, School of Chemistry and Physics, Keele University, Keele, Staffordshire ST5 5BG, United Kingdom QUANXI JIA (677) Los Alamos National Laboratory, Superconductivity Technology Center, Los Alamos, New Mexico, USA

GEORGE KAMARINOS (291) LPCS, ENSERG, 38016 Grenoble Cedex 1, France

xxi

xxii

LIST OF CONTRIBUTORS

R. U. A. KHAN (403) Large Area Electronics Group, School of Electronics, Computing and Mathematics, University of Surrey, Guildford, United Kingdom

G. MASINI (327) Department of Electronic Engineering and National Institute for the Physics of Matter INFM RM3, Terza University of Rome, Via della Vasca Navale 84, 00146 Rome, Italy

THEODORE D. MOUSTAKAS (57) Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

ROBERTO MURRI (369) Department of Mathematics and Physics, INFM and University of Camerino, Via Madonna delle Carceri, 62032 Camerino, Italy

H. JORG OSTEN (247) Institute for Semiconductor Physics, (IHP), Frankfurt D-15236, Germany NICOLA PINTO (369) Department of Mathematics and Physics, INFM and University of Camerino, Via Madonna delle Carceri, 62032 Camerino, Italy

J. RAPPICH (1) Hahn-Meitner Institut, Abteilung Silizium-Photovoltaik, Berlin D- 12489, Germany

THEODORE J. SCHMIDT (117) Center for Laser and Photonics Research and Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA S. R. P. SILVA (403) Large Area Electronics Group, School of Electronics, Computing and Mathematics, University of Surrey, Guildford, United Kingdom JIN-JOO SONG (117) Center for Laser and Photonics Research and Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA

GEORGE THEODOROU (625) Department of Physics, Aristotle University of Thessaloniki, 540 06 Thessaloniki, Greece B. R. ZHAO (507) Institute of Physics, Chinese Academy of Sciences, Beijing, China

List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins. GERMAN CAMPOY (207) Departamento de Investigati6n en Ffsica, Universidad de Sonora, Hermosillo, Sonora, Mexico RUPERT CHABICOVSKY (375) Institute of Industrial Electronics and Material Science, Vienna University of Technology, A- 1040 Vienna, Austria

WEIKUN GE (99) Department of Physics, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong, China HANS HAUSER (375) Institute of Industrial Electronics and Material Science, Vienna University of Technology, A- 1040 Vienna, Austria THOMAS HOFFMANN (1) IMEC vzw, SPT Optical Lithography, Heverlee (Leuven), Belgium

M. R. KOBLISCHKA (589) Experimentalphysik, Universit~it des Saarlandes, D-66041 Saarbrticken, Germany J. P. LIU (337) Department of Physics and Institute for Micromanufacturing, Louisiana Tech University, Ruston, Louisiana, USA C. P. L u o (337) Behlen Laboratory of Physics and Center for Materials Research and Analysis, University of Nebraska, Lincoln, Nebraska, USA JOSE L. M A R ~ (207) Departamento de Investigati6n en Ffsica, Universidad de Sonora, Hermosillo, Sonora, Mexico ROBERTO MURRI (439) INFM, Dipartimento di Matematica e Fisica, Universith di Camerino, 62032 Camerino, Italy MARIAN NOWAK (439) Silesian Technical University, Institute of Physics, 40-019 Katowice, Poland GENHUA PAN (495) Centre for Research in Information Storage Technology, Department of Communication and Electronic Engineering, University of Plymouth, Plymouth, Devon PL4 5AA, United Kingdom NICOLA PINTO (439) INFM, Dipartimento di Matematica e Fisica, Universit~ di Camerino, 62032 Camerino, Italy Y. QIANG (337) Behlen Laboratory of Physics and Center for Materials Research and Analysis, University of Nebraska, Lincoln, Nebraska, USA

xxi

xxii

LIST OF CONTRIBUTORS KARL RIEDLING (375) Institute of Industrial Electronics and Material Science, Vienna University of Technology, A- 1040 Vienna, Austria RAIJL RIERA (207) Departamento de Investigati6n en Ffsica, Universidad de Sonora, Hermosillo, Sonora, Mexico

MIRCEA SERBAN ROGALSKI (555) Faculdade de CiSncias e Tecnologia, Universidade do Algarve, Gambelas, 8000 Faro, Portugal

RODRIGO A. ROSAS (207) Departamento de Ffsica, Universidad de Sonora, Hermosillo, Sonora, M6xico KLAUS SATTLER (61) Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii, USA

HELLA-C. SCHEER (1) Microstructure Engineering, Department of Electrical and Information Engineering, University of Wuppertal, 42097 Wuppertal, Germany

HUBERT SCHULZ (1) Microstructure Engineering, Department of Electrical and Information Engineering, University of Wuppertal, 42097 Wuppertal, Germany D. J. SELLMYER (337) Behlen Laboratory of Physics and Center for Materials Research and Analysis, University of Nebraska, Lincoln, Nebraska, USA CLIVIA M. SOTOMAYOR TORRES (1) Institute of Materials Science, Department of Electrical and Information Engineering, University of Wuppertal, 42097 Wuppertal, Germany JIAN-BAI XIA (99) Department of Physics, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong, China and Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

ZHANG ZHI-DONG (141, 169) Shenyang National Laboratory for Materials Science and International Centre for Material Physics, Institute of Metal Research, Academia Sinica, Shenyang 110015, People's Republic of China

Chapter 1 METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON FOR DEVICE APPLICATIONS Wilfried G. J. H. M. van Sark Debye Institute, Utrecht University, NL-3508 TA Utrecht, The Netherlands

Contents 1.

2.

3.

4.

5.

6.

7.

8.

9.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Historical Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 3

1.2. Material Aspects of Hydrogenated Amorphous Silicon . . . . . . . . . . . . . . . . . . . . . . Research and Industrial Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Reactor Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Scale-Up to Systems of Industrial Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. ASTER, a Research System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physics and Chemistry of P E C V D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Plasma Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Plasma Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasma Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. 1D Fluid Discharge Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. 2D Fluid Discharge Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Particle-in-Cell D{scharge Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasma Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Optical Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Electrostatic Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Mass Spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relation between Plasma Parameters and Material Properties . . . . . . . . . . . . . . . . . . . . . . . 6.1. External Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Internal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deposition Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Surface Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Solubility of Hydrogen in Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Elimination of Hydrogen from a-Si:H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. Dangling-Bond and Weak-Bond Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modifications of P E C V D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. V H F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Chemical Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3. RF Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hot Wire Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1. General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3. Material Properties and Deposition Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4. Deposition Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 8 8 9 10 11 14 14 15 18 21 21 30 33 39 39 40 42 51 53 53 55 63 64 65 65 67 67 68 73 74 76 76 77 78 79

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films ISBN 0-12-512909-2/$35.00

Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

2

VAN SARK 10. ExpandingThermal PlasmaChemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . 10.1. GeneralDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. ExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. MaterialProperties and Deposition Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4. DepositionModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1. SolarCells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. ThinFilm Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3. LightSensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4. ChemicalSensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5. OtherApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. I N T R O D U C T I O N This chapter describes the deposition of hydrogenated amorphous silicon (a-Si:H) and related materials by employing a low-temperature, low-density plasma. The method basically is a special form of chemical vapor deposition (CVD), which is known as plasma-enhanced chemical vapor deposition (PECVD) or plasma CVD. Essentially, silane gas (Sill4) is excited by a radiofrequency (RF, 13.56 MHz) plasma, which causes silane molecules to dissociate. Subsequently, dissociation products are deposited on heated substrates and form a layer. Most research and industrial reactor systems consist of two parallel electrodes in a stainless steel chamber. Because of the relative ease of depositing a-Si:H uniformly over large areas, the original parallel plate geometry with RF excitation frequency is commonly used in industry, and has not changed much over the past two or three decades [ 1-13]. Material and device optimization is mostly done empirically, and so-called device quality a-Si:H layers having excellent uniformity are made by PECVD. Nevertheless, several modifications have evolved since the first demonstration of deposition of a-Si:H, such as the use of higher excitation frequencies [from VHF (50-100 MHz) up to the gigahertz range], the use of remote excitation of the plasma, plasma beams, and modulation of the plasma in time or frequency. Even methods without the assistance of a plasma have evolved, such as the hot-wire CVD (HWCVD) method. The material properties of layers deposited in a PECVD reactor strongly depend on the interaction between the growth flux and the film surface. Therefore, a central theme in this chapter is the relation between material properties and deposition parameters. Considering the plasma as a reservoir of species, we can distinguish neutrals, radicals, and ions, which can be either positive or negative. In a typical RF discharge, which is weakly ionized, the neutral species are the most abundant, having a concentration of about 1016 cm -3, while the concentrations of radicals and ions are only about 1014 and 101~ cm -3, respectively. The energies of these species may differ considerably. The neutrals, radicals and ions within the plasma are not energetic at all (below 0.1 eV). The ions that reach substrates and reactor walls are much more energetic (1-100 eV). This can have enormous consequences for the ef-

79 79 80 81 82 82 82 86 87 88 89 91 92 92

fect of species on a growing film. For example, the amount of energy that is present in the plasma amounts to 1013 eV/cm 3 for radicals and 1012 eV/cm 3 for ions. This shows that although ions are much less present in the plasma, their effect may be comparable to that of radicals. In this chapter we will treat the common RF PECVD method for a-Si:H deposition, with emphasis on intrinsic material. First, a short introduction on the material properties of hydrogenated amorphous silicon is given. Subsequently, details are given on experimental and industrial deposition systems, with special emphasis on the UHV multichamber deposition system A S T E R (Amorphous Semiconductor Thin Film Experimental Reactor) at Utrecht University [14, 15]. This is done not only because many experimental results presented in this chapter were obtained in that system, but because in our opinion it can also be seen as a genetic multichamber deposition system. Then, a thorough description of the physics and the chemistry of the discharge is presented, followed by plasma modeling and plasma analysis results. Subsequently, relations will be formulated between discharge parameters and material properties, and models for the deposition of a-Si:H are presented. In further sections extensions or adaptations of the PECVD method will be presented, such as VHF PECVD [ 16], the chemical annealing or layer-by-layer technique [ 17], and modulation of the RF excitation frequency [ 18]. The HWCVD method [ 19] (the plasmaless method) will be described and compared with the PECVD methods. The last deposition method that is treated is expanding thermal plasma CVD (ETP CVD) [20, 21 ]. Other methods of deposition, such as remote-plasma CVD, and in particular electron cyclotron resonance CVD (ECR CVD), are not treated here, as to date these methods are difficult to scale up for industrial purposes. Details of these methods can be found in, e.g., Luft and Tsuo [6]. As all these methods are used in research for improving material properties with specific applications in mind, a summary of important applications for which a-Si:H is indispensable is given in the last section. It will be clear throughout this chapter that it is biased toward research performed at or in collaboration with the research group at the Debye Institute at Utrecht University. However, numerous references to other work are presented in order to put this research in a much broader perspective.

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON For further reading one may find excellent material in the (edited) books by (in chronological order) Pankove [1], Tanaka [2], Street [3], Kanicki [4, 5], Luft and Tsuo [6], Bunshah [7], Bruno et al. [8], Machlin [9, 10], Schropp and Zeman [11], Searle [12], and Street [13].

1.1. Historical Overview The research on amorphous semiconductors in the 1950s and 1960s was focused on the chalcogenides, i.e. materials containing group VI elements (sulfur, selenium, and tellurium), such as As2Se3. These glasses are formed by cooling from the melt, their structure being similar to oxide glasses. Of particular interest was the relation between disorder of the structure and its electronic properties. This still is a question not fully answered; see for example Overhof in his Mott Memorial Lecture [22]. Amorphous silicon (and germanium) was prepared in those days by thermal evaporation or sputtering (see e.g. [23]). This unhydrogenated material was highly defective, which inhibited its use as a semiconductor. Research on incorporating hydrogen as a passivating element was pursued by introducing hydrogen in the sputtering system, which indeed improved the electronical properties [24-26]. In 1965 it was discovered that deposition of amorphous silicon employing the glow discharge technique yielded a material with much more useful electronic properties [27, 28]. The deposition occurs on a moderatedly heated substrate (200-300~ through reactions of gas radicals with the substrate. At that time the infrared absorption bands of silicon-hydrogen bonds present in the deposited material were observed, but they were not recognized as such. Some years later, Fritsche and coworkers in Chicago confirmed that a-Si produced from a glow discharge of Sill4 contains hydrogen [29, 30]. A recent personal account of the early years in amorphous silicon research shows the struggle to reach this conclusion [31 ]. Spear and co-workers in Dundee succeeded in improving the electrical properties, and finally, in 1975, a boost in research activities occurred when it was shown that a-Si:H could be doped n- or p-type by introducing phosphine (PH3) or diborane (B2H6) in the plasma [32]: a range of resistivity of more than 10 orders of magnitude could be reached by adding small amounts of these dopants. The achievement of Spear and LeComber [32] immediately paved the way for practical amorphous silicon devices. In fact, it is argued that the research field became "polluted by the applications" [33]. Carlson and Wronski at RCA Laboratories started in 1976 with the development of photovoltaic devices [34]. The first p - i - n junction solar cell was reported by the group of Hamakawa [35, 36]. In 1980, Sanyo was the first to market devices: solar cells for hand-held calculators [37]. Also, considerable research effort was directed towards amorphous silicon photoconductors for application in photocopying machines and laser printers [38, 39]. The a-Si:H photoconductor is, amongst other materials, used as the light-sensitive component in the electrophotographic process. The first field effect transistors were also reported [40--42] at about this time. These thin film devices take advantage of the

3

capability to deposit and process a-Si:H over large areas. It took only a few years before these thin-film transistors (TFTs) were utilized in active matrix liquid crystal displays (AMLCDs) by various companies. Active matrix addressing can also be used in printer heads. Combining the photoconductive properties and the switching capabilities of a-Si:H has yielded many applications in the field of linear sensor arrays, e.g., 2D image sensors and position-sensitive detectors of charged particles, X-rays, gamma rays, and neutrons [43-47].

1.2. Material Aspects of Hydrogenated Amorphous Silicon 1.2.1. Atomic Structure

Hydrogenated amorphous silicon is a disordered semiconductor whose optoelectronic properties are governed by the large number of defects present in its atomic structure. The covalent bonds between the silicon atoms in a-Si:H are similar to the bonds in crystalline silicon. The silicon atoms have the same number of neighbors and on average the same bond lengths and bond angles. One can represent the disorder by the atom pair distribution function, which is the probability of finding an atom at a distance r from another atom. A perfect crystal is completely ordered to large pair distances, while an amorphous material only shows short-range order. Because of the shortrange order, material properties of amorphous semiconductors are similar to their crystalline counterparts. Amorphous silicon is often viewed as a continuous random network (CRN) [48, 49]. In the ideal CRN model for amorphous silicon, each atom is fourfold coordinated, with bond lengths similar (within 1% [50]) to that in the crystal. In this respect, the short-range order ( 0.22) the material mainly consists of chains of Sill2 bonds, and the material density is much lower. Berntsen et al. [84, 85] have separated the effect of hydrogen content and bond-angle variation. The structural disorder causes broadening of the valence and conduction bands and a decrease of the bandgap by 0.46 eV. Hydrogenation to 11 at.% results in an independent increase of the bandgap with 0.22 eV. For undoped a-Si:H the (Tauc) energy gap is around 1.6-1.7 eV, and the density of states at the Fermi level is typically 1015 eV -1 cm -3, less than one dangling bond defect per 107 Si atoms. The Fermi level in n-type doped a-Si:H moves from midgap to approximately 0.15 eV from the conduction band edge, and in p-type material to approximately 0.3 eV from the valence band edge [32, 86].

1.2.5. Metastability An important drawback of a-Si:H is its intrinsic metastability: the electronic properties degrade upon light exposure. This was discovered by Staebler and Wronski [87, 88], and is therefore known as the Staebler-Wronski effect (SWE). This effect manifests itself by an increase in the density of neutral dangling bonds, Ndb, upon illumination, according to Ndb(t) C~ G~ 1/3, where G is the generation rate and t the illumination time [89]. The excess defects are metastable; they can be removed by annealing the material at temperatures above ~ 150~ for some hours. The presence of these excess defects in concentrations up to 1017 cm -3 leads to a reduction of free cartier lifetime, and hence to a lower conversion effiency for solar cells. The SWE is an intrinsic material property; it is also observed in very pure a-Si:H, with an oxygen concentration as low as 2 x 1015 cm -3 [90]. At impurity concentrations above 1018 cm -3 a correlation between SWE and impurity level has been established [91 ]. The hydrogen concentration, the bonding structure of hydrogen in the silicon network, and the disorder in the silicon network together affect the SWE. It has been long assumed that the origin of the SWE was local. Stutzmann et al. [89] have proposed a model in which photogenerated charge carriers recombine nonradiatively at weak silicon-silicon bonds

(e.g., strained bonds). The release of the recombination energy can be used to break the bond, and the two dangling bonds thus formed are prevented from recombining by the passivation of one of the bonds by a back-bonded hydrogen atom. Recent experimental results contradict the local nature of this model. Electron spin resonance (ESR) experiments have revealed that there is no close spatial correlation between the presence of hydrogen and light-induced dangling bonds [92]. Further, it has been found that the rate of dangling-bond creation is independent of temperature in the range of 4 to 300 K [93]. As hydrogen is immobile at 4 K, diffusion can be ruled out. The SWE has been found to depend on the hydrogen microstructure. The amount of hydrogen bound to silicon in the dilute phase, i.e., monohydride bonds, determines the saturated density of metastable defects [94]. In addition, only in regions of low hydrogen density have light-induced defects been found in ESR experiments [92]; it may well be that in these regions only monohydride bonds up to the solubility limit of 2--4% of hydrogen in silicon [69, 95] are present. The presence of clustered hydrogen (high microstructure parameter R*) leads to faster defect creation kinetics [96, 97]. These and other observations have led to the realization that the SWE extends over large regions, because configurational defects are transported over long distances. Branz proposed the hydrogen collision model [98]: the defect-creating recombination takes place at a S i - H bond, and the recombination energy is used to lift the hydrogen to a mobile energy level. The mobile hydrogen atom diffuses interstitially through the material. This mobile hydrogen atom is represented by a mobile complex of a Si--H bond and a dangling bond [99]. As the complex diffuses through the silicon network, it breaks one S i - S i bond after another, but each broken bond is re-formed after the complex has passed it. If two mobile hydrogen complexes collide, an immobile metastable two-hydrogen complex is formed. The net result is that two dangling bonds are created that are not spatially correlated to hydrogen atoms.

1.2.6. Alloys The glow discharge technique is especially suitable for controlling various material properties by introducing other precursor gases in the plasma. As was first demonstrated by Anderson and Spear, incorporation of carbon or nitrogen in a-Si:H resuits in material with a large bandgap [ 100]. A linear relation between bandgap and carbon fraction xc in a-SiC:H has been reported [101,102]: Eg = 1.77+2.45xc. On the other hand, by diluting the plasma with germane (GeH4), material is obtained with small bandgaps [103]: from 1.7 eV (a-Si:H) to 1.0 eV (a-Ge:H). Here also a linear relation between bandgap and Ge fraction (XCe) has been reported [104], in which in addition the hydrogen fraction XH is included: Eg = 1.6 + XH -- 0.7XGe. The incorporation of elements as carbon, nitrogen, or germanium, however, leads to material with a low mobility and lifetime of charge carriers. This would limit the application of these alloys, and a large research effort has been undertaken to find ways around this problem.

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

7

,

4.0 0.3

A

A z~

_

(a)

3.0 r

0.2

A

A

2.0

A

1.0 0.0

,

I

q

,

0.2

,

,

,

0.4

,

0.6

,

,

0.8

1.0

Fig. 2. The dependence of the carbon fraction x = [C]/([Si] + [C]) on the gas-flow ratio r = [CH4]/([SiH4] + [CH4]) for films deposited in the ASTER system [AST1 (filled circles) and AST2 (filled triangles)] and for films deposited in a similar system (ATLAS) [ATL1 (open circles) and ATL2 (open triangles)]. (From R. A. C. M. M. van Swaaij, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1994, with permission.)

The addition of an extra feedstock gas (GeH4 or CH4) in large quantities (compared to dopant gases) adds an extra degree of freedom to the already complex chemistry of the discharge. It is therefore even more complicated to relate material properties to deposition conditions [ 105]. As an example, GeH4 is less stable than Sill4 in the glow discharge, and Ge is preferentially deposited from SiH4-GeH4 mixtures: even a low GeH4 fraction in the gas results in a high Ge fraction in the solid. Moreover, optimum conditions for a-Si:H deposition (low power density) cannot be translated simply to a-Ge:H deposition, in which case high power density is required to obtain good-quality material [106]. The deposition of a-SiGe:H requires elaborate fine tuning of deposition parameters. Other possibilities have been pursued to improve the properties of a-SiGe alloys, such as the use of strong dilution of SiH4-GeH4 mixtures with hydrogen [107], and the use of fluorinated reactants such as SiF4 [ 108]. Modulation of the discharge (see also Section 8.3) has been demonstrated to increase the amount of Ge in the alloy by a factor of 2-10, depending on discharge conditions, compared to a continuous discharge [ 109]. As Sill4 is less stable than CH4, a low C fraction in the solid is obtained for a high CH4 fraction in the gas. This is illustrated in Figure 2, which shows the dependence of the carbon fraction x = [C]/([Si]+[C]) on the gas flow ratio r = [CH4]/([SiH4]+ [CH4]) for films deposited in the A S T E R system and a system with a similar reactor (ATLAS) [101, 102, 110]. These films were deposited in the so-called low-power deposition regime [ 111, 112], which is defined as the regime in which the applied power density is lower than the threshold power density required for the decomposition of methane [112]. In this regime the deposition of films is dominated by the decomposition of silane and is not dependent on the methane concentration

(b)

oAz~ o

,

1.0 O0

r

I

A

~'~ 2.0 r,9 0.0

,

3.0

0.1

0.0

I

,

o,c~

50 4.0 ~9'

~

3 09

o

9

A

A

E.0

1.0 0.0 0.0

.

.

.

.

.

0.1

0.2

. 0.3

x Fig. 3. Absolute atomic concentrations in units of l022 at./cm3, determined by ERD, RBS, and optical reflection and transmission spectroscopy, of (a) hydrogen, (b) carbon, and (c) silicon as a function of the carbon fraction x. Results are presented for the series AST1 (filled circles), AST2 (filled triangles), ATL1 (open circles), and ATL2 (open triangles). (From R. A. C. M. M. van Swaaij, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1994, with permission.)

[ 111, 112]. Incorporation of carbon results from chemical reactions between methane molecules and silane species that are created by the plasma. The deposition rate in this regime is almost independent of the gas flow ratio r, provided the gas in the reactor is not depleted in the discharge [ 101, 102, 113]. The dependence of the absolute atomic concentration of hydrogen, silicon, and carbon on the carbon fraction is shown in Figure 3 [101,102]. The atomic concentrations were determined by using elastic recoil detection (ERD) and Rutherford backscattering spectrometry (RBS) [114]. The most striking observation is the rapid increase of the hydrogen concentration upon carbon alloying (Fig. 3a), which can be ascribed to the incorporation of CHn groups in the material during deposition [112, 115]. It can be inferred from the data that up to a carbon fraction of about 0.1, three hydrogen atoms are incorporated per carbon atom. Above x = 0.15 the rate Jof increase of the hydrogen concentration becomes smaller. For higher x-values the hydrogen concentration even tends to decrease. In Figure 3b and c the absolute atomic concentrations of carbon and silicon, respectively, are shown as a function of the carbon fraction. As expected, the carbon concentration

8

VAN SARK

Table I.

Selected Properties of Device Quality Hydrogenated Amorphous Silicon Films

Property

Symbol

Value

Unit

Optical bandgap (Tauc)

1.8

eV

Optical bandgap (cubic)

Eg Eg

1.6

eV

Refractive index

n

4.3

Absorption coefficient (600 nm)

ct600

4 x 104

cm-1

Urbach energy

E0

50

meV

Dark conductivity

ad

10-10

~- 1cm- 1

Photoconductivity (AM1.5)

aph

10 -5

S2-1 cm -1

Activation energy

EA

0.8

eV

Mobility-lifetime product

# z600

10 -7

cm 2 V - 1

Hydrogen content

CH

8-12

%

Microstructure factor

R*

0-0.1

HWHM of TO Raman peak

F/2

33

cm -1

Intrinsic stress

ai

400-500

MPa

Defect density

Ns

1015

cm -3 e V - 1

increases upon alloying. In contrast, the silicon content decreases rapidly, which implies that the material becomes less dense. As it was reported that the S i - S i bond length does not change upon carbon alloying [ 116], it thus can be inferred that the a-SiC:H material contains microscopic voids, which is in agreement with small-angle X-ray scattering (SAXS) resuits [62]. Much more can be said about Ge and C alloying, but that is not within the scope of this chapter. We refer to the books by Kanicki [5] and Luft and Tsuo [6].

1.2.7. Device Quality Characteristics Over the past decades the term device quality has come to refer to intrinsic PECVD hydrogenated amorphous silicon that has optimum properties for application in a certain device. Of course, depending on the type of device, different optimum values are required; nevertheless the properties as listed in Table I are generally accepted, e.g. [6, 11]. Many of these properties are interrelated, which has to borne in mind when attempting to optimize only one of them. Optimum properties for p- and n-type doped a-Si:H have been identified [6, 11]. For p-type doping boron is used as the dopant element. Due to alloying with silicon, the bandgap is reduced. This can be compensated by adding carbon. Typically silane (Sill4), methane (CH4), and diborane (B2H6) are used, with silane and carbon in about equal amounts and diborane a factor of thousand lower. This yields p-type material with Eg : 2.0 eV, EA "- 0.5 eV, ad = 10 -5 f2 -1 cm -1, and or600 = 104 c m - 1. Adding phosphine (PH3) to silane in the ratio 0.025:1 yields n-type material of good quality: Eg = 1.8 eV, EA = 0 . 3 eV, aa = 10 - 3 f2 - 1 c m - 1 , and or600 = 4 • 10 4 c m - 1 .

2. RESEARCH AND INDUSTRIAL EQUIPMENT 2.1. General Aspects. A plasma deposition system usually consists of several subsystems, each providing different functions [117]. The gas handling system includes process gas storage in high-pressure cylinders, mass flow controllers to measure and control the different gases to the reactor, and tubing. The vacuum system comprises pumps and pressure controllers. The plasma reactor is operated between 10 -4 and 10 Torr. 1 A much lower background pressure, in the ultrahigh vacuum (UHV) range (10 -9 mbar), is often required to ensure cleanliness of the process. High-vacuum rotary pumps are used in combination with turbomolecular pumps [ 118]. The deposition setup as shown in Figure 4a is the central part of the most commonly used planar diode deposition system. The power to the reactor system is delivered by means of a power supply connected to the reactor via appropriate dc or RF circuitry (matchboxes). Power supplies can consist of generator and amplifier combined in one apparatus, with a fixed RF frequency. More flexible is to have an RF generator coupled to a broadband amplifier [119, 120]. Using the planar diode geometry, p-i-n devices have been made in single-chamber reaction systems, either with [121] or without load lock [122]. In such single-chamber systems cross-contamination occurs. After deposition, small amounts of (dopant) gases will remain in the reactor due to adsorption on the walls. If no load lock is used, water vapor and oxygen are also adsorbed upon sample loading. These residual gases will desorb during subsequent depositions and may be built in as impurities in the amorphous layer [123, 124]. Additionally, the desorption of gases after a deposition may cause contaminated interfaces, e.g., a graded boron concentration profile may be present in the first monolayers of the/-layer of a p+-i interface [125, 126]. Contaminated interfaces combined with (too) high impurity levels in the layers lead to worse electrical properties of the layer [127, 128], which results in low efficiency of solar cells. By using a multichamber system [ 129], exchange of residual gases between successive depositions will be strongly decreased, and very sharp interfaces can be made. Furthermore, the use of a load-lock system ensures high quality of the background vacuum, and thus low levels of contaminants in the bulk layers. Multichamber reactor systems have been used for the fabrication of solar cells, and considerable improvements in energy conversion efficiency have been achieved [ 130, 131 ]. Most of the gases used are hazardous: they can be corrosive, flammable, explosive, and/or highly toxic. Silane is pyrophoric; the dopant gases diborane, phosphine, and arsine are extremely toxic, with TLV (threshold limited value) values in the low parts-per-million range. Therefore extreme care has to be taken 1Throughout this chapter the torr, millibar, and pascal are used as units of pressure, according to the original data rather then converting the first two to the SI unit. Note than 1 Pa = 0.01 mbar = 0.0076 Torr = 7.6 mTorr.

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

9

ity do not always take geometric causes into account. This has prompted the development of a standard type of reactor, the GEC (Gaseous Electronics Conference)reference cell [133]. Nevertheless generalizations on the effect of process parameters on material quality have been made. For an overview see, e.g., Luft and Tsuo [6].

2.2. Reactor Configurations

potential diagram

I Vdc

0

Vpl

(b) Fig. 4. Schematic representation (a) of a parallel-plate, capacitively coupled RF-discharge reactor, with unequal-size electrodes. The potential distribution (b) shows the positive plasma potential Vpl and the negative dc self-bias voltage Vdc.

in dealing with these gases. One generally installs, flow limiters (between the valve of the supply cylinder and pressure regulator, to prevent excessive gas flow in case of breakdown of the regulator), cross-purge assemblies [in order to purge the regulators and prevent release of the gas when exchanging (empty) gas cylinders], scrubbers or diluters to avoid above-TLV levels at the exhaust, detectors mounted at several critical locations, etc. More on safety issues can be found in, e.g., the proceedings of the 1988 Photovoltaic Safety Conference [132]. In the design of the reactor chamber one needs to address issues such as electrode geometry, gas flow patterns, heater design, and reactor volume (discharge and discharge-free regions). Hot walls will influence the gas temperature and the gas phase chemistry. Electrode size and electrode spacing as well as dark-space shields directly influence the discharge properties. Asymmetry introduces a bias, which may be controlled externally. Also the driving frequency is an important parameter. Over the years many reactor designs have been developed. Studies on the effects of process parameters on material qual-

Diode reactors can be powered by an RF or dc electric field. In case of RF excitation the deposition typically is on the grounded electrode. As the combined area of grounded electrode and reactor walls usually is larger than the area of the powered electrode, a dc self-bias is developed, as shown in Figure 4b. The potential drop at the powered electrode is much larger than at the grounded electrode. The powered electrode is more negative with respect to ground, and therefore is often called the cathode. The grounded electrode then is the anode. For a dc glow discharge, the potential distribution is similar to the one shown for the RF discharge in Figure 4b. In both cases ion bombardment at the cathode is larger than at the anode. Due to this, deposition of films on the cathode or anode leads to different microstructural properties. Deposition rates at the cathode are usually higher than at the anode. Films deposited at the cathode are dense, but also stressed. Anodic films are more porous. In dc discharges one sometimes uses a mesh positioned above the cathode, which has the same potential as the cathode [ 134]. Ions are thus slowed down by gas phase collisions in the region between mesh and cathode, and much better material is obtained [135]. Moreover, the mesh acts as a screen for reactive radicals. The SiH2 radical has a large sticking probability, and it will stick to the mesh easily. As a consequence, the SiH2 radical will be filtered out, and Sill3 will dominate the deposition. The resulting material quality has been shown in RF triode discharges to have been improved [ 136-139]. Planar triode RF discharges used in research generally are asymmetric; the area of the powered electrode is much smaller than the area of all grounded parts taken together (the grounded electrode may be just a small part of the grounded area). The dc self-bias therefore is large. One can reduce the asymmetry by confining the discharge with a grounded mesh [ 140, 141 ] or wall [142]. Such confinement also allows for a higher power density in the discharge, which leads to enhanced deposition rates. An external magnetic field has also been used to confine the plasma [143]. An arrangement where electromagnets are located under the cathode is known as the controlled plasma magnetron method [ 144]. The diffusion of electrons to the walls is prevented by the magnetic field between cathode and anode. This results in an increase in electron density, and consequently in a faster decomposition of silane and a higher deposition rate. At a deposition rate of 1 nm/s, device quality material is obtained [144]. In addition, a mesh is located near the anode, and the anode can by biased externally, both in order to confine the plasma and in order to control ion bombardment.

10

VAN SARK

Hot reactor walls are sometimes used as a means to increase the density of the films that are deposited on the walls. This reduces the amount of adsorbed contaminants on the walls, and leads to lower outgassing rates. A hot wall is particularly of interest for single-chamber systems without a load-lock chamber. Material quality is similar to the quality obtained with a cold reactor wall [ 145]. Other configurations that are used include an concentric electrode setup in a tubular reactor, where the discharge still is capacitivily coupled. Also, inductive coupling has been used, with a coil surrounding the tubular reactor [ 146, 147].

2.3. Scale-Up to Systems of Industrial Size A plasma process that has been demonstrated to yield good quality materials in the laboratory will one day need to be scaled up to a technology that can produce the materials in larger sizes and larger quantities. Such a transfer is not straightforward, and many technological difficulties will have to be overcome before a scaled-up process is commercially viable. A plasma process is characterized by many parameters, and their interrelations are very complex. It is of paramount importance to understand, at least to a first approximation, how the plasma parameters have to be adjusted when the geometrical dimensions of the plasma system are enlarged. Especially of use in scaling up systems are scaling laws, as formulated by Goedheer et al. [148, 149] (see also Section 3.2.2). In general, the substrate temperature will remain unchanged, while pressure, power, and gas flow rates have to be adjusted so that the plasma chemistry is not affected significantly. Grill [ 117] conceptualizes plasma processing as two consecutive processes: the formation of reactive species, and the mass transport of these species to surfaces to be processed. If the dissociation of precursor molecules can be described by a single electron collision process, the electron impact reaction rates depend only on the ratio of electric field to pressure, E / p , because the electron temperature is determined mainly by this ratio. The mass transport is pressure-dependent, because the product of diffusion constant and pressure, Dp, is constant. Hence, preservation of both plasma chemistry and mass transport is obtained by keeping both E and p constant during scale-up. As the area of the scaled-up reactor is larger (typically about 1 m 2) than its laboratory equivalent (1-100 cm2), the total power or current supplied to the discharge must be enlarged in order to keep E constant. For a parallel plate reactor the power simply scales linearly with the area increase, while for other configurations this will not be a simple relation, because the plasma is not confined between the electrodes. Note that changing the area ratio of grounded to powered electrode will affect the dc self-bias voltage and the ion bombardment. The gas flow rate is the only external parameter that needs adjustment. It should be scaled up so that the average flow velocity is identical for laboratory- and industrial-scale reactors. Alternatively, one can keep the average residence time constant, which is defined as rr = p V / Q , with V the volume of the reaction zone and Q the total mass flow rate. The residence time is a measure of the distance over

which the reactive species diffuse in the reaction zone. With the pressure constant, the requirement of constant residence time scales the gas flow rate proportionally to the reaction volume. The scale-up from a small to a large plasma reactor system requires only linear extrapolations of power and gas flow rates. However, in practice, the change in reactor geometry may result in effects on plasma chemistry or physics that were unexpected, due to a lack of precise knowledge of the process. Fine tuning, or even coarse readjustment, is needed, and is mostly done empirically. A critical issue in scaling up a process is the uniformity in deposition rate and material quality. In general, once the deposition rate is constant within 5% over the whole substrate area, the material properties also do not vary much. After fine-tuning the power and gas flow rates, operators still may face in homogeneity issues. These can be caused by local changes in temperature, RF voltage, and gas composition, due to various causes. As an example, it has been reported that improper attachment of the substrate to the grounded electrode results in a local decrease of the deposition rate [ 150, 151 ]. Low contamination levels are readily achieved in laboratory scale UHV systems. Very high costs inhibit the use of UHV in industrial scale systems, however, so another, "local-UHV" approach has been proposed, viz. the plasma box reactor [152]. The substrate is mounted in a box, which is surrounded by a shell, which is pumped to a low pressure. The process pressure in the box is maintained by a throttle valve. As the pressure in the box is larger than the pressure in the surrounding shell, contaminants diffuse outwards and the incorporation of contaminants in the deposited layer is low. Schropp and Zeman [ 11 ] have classified current production systems for amorphous silicon solar cells. They argue that costeffective production of solar cells on a large scale requires that the product of the deposition time needed per square meter and the depreciation and maintenance costs of the system be small. Low deposition rates must be accompanied by low costs. The costs requirement is the main drive for ongoing investigations into the question how to increase the deposition rates while maintaining device quality material. Current production system configurations can be divided into three classes: (1) singlechamber systems, (2) multichamber systems, and (3) roll-to-roll systems [ 11 ]. In single-chamber systems there is no transport of substrates under vacuum conditions, which makes the system simple, but contamination levels may be relatively high. The addition of a load lock lowers contamination levels and requires only a linear transport mechanism. During the deposition process temperature and geometry cannot be changed easily, but changes are required for different layers in the solar cell. Substrates are loaded consecutively, and for every substrate a complete pumpdown and heating are needed. The actual deposition time is much smaller than the total processing time. A higher throughput can be achieved by loading substrates in cassettes, as is general practice in the semiconductor industry. The investment is considered low, but so is the flexibility of the system.

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON Industrial scale multichamber systems offer many of the advantages that are characteristic of laboratory-scale systems. Typically, the deposition of each layer in a solar cell is performed in a separate chamber, and process parameter optimizations can be done for each layer individually. However, this high flexibility comes with high investment costs. Two types of multichamber systems can be distinguished, the cluster configuration and the in-line configuration. The cluster configuration is more or less an enlarged copy of a laboratory-scale system, and offers the greatest flexibility. Transport and isolation chambers can be shared by many deposition chambers, and, depending on the actual configuration, production can be continued even while some reactors are down. A cassette of substrates (batch) can be processed completely automatically, which increases throughput of the production system. The in-line configuration consists of deposition chambers that are separated by isolation chambers [153]. The layer sequence of a solar cell structure prescribes the actual sequence of deposition chambers. The flexibility is much less than with a cluster configuration, and costs are generally much higher, but the throughput can also be much larger. In an in-line system the substrates can move while deposition takes place, which leads to very uniformly deposited layers, as uniformity of deposition is required only in one dimension (perpendicular to the moving direction). In the roll-to-roll configuration the substrate consists of a continuous roll, e.g. stainless steel [154], SnO2:F-coated aluminum [155], or plastic [156-158], which is pulled through a sequence of deposition chambers.

2.4. ASTER, a Research System As a large part of the experimental and simulation results given in this chapter were obtained with or specifically calculated for the UHV multichamber deposition system A S T E R (Amorphous Semiconductor Thin Film Experimental Reactor) at Utrecht University [14, 15], it is described in this section. It also is a more or less genetic parallel plate multichamber research system. Similar commercially available multichamber equipment has been developed and described by Madan et al. [159]. It has also been installed at Utrecht University and is named Process Equipment for Amorphous Silicon Thin-Film Applications (PASTA). The A S T E R system is intended for use in research and consists of three identical plasma reactors, a spare chamber, and a load lock, all having the same outer dimensions. These chambers are connected radially via gate valves to a central transport chamber, in which a transport system or robot arm is located. All chambers are made of stainless steel, and all seals with valves, windows, gas-supply lines, and measuring devices are Conflat connections, ensuring that the vacuum will be of UHV quality. The A S T E R system was completely designed and partly built in-house; the chambers and transport arm were manufactured by Leybold companies. A schematic drawing is shown in Figure 5, which illustrates the situation around 1990 [14, 15]. The spare chamber was designed first to

;')a,k

11

/

I

JJ37,'i

Fig. 5. Schematicrepresentation of the ASTER deposition system.Indicated are: (1) load lock, (2) plasma reactor for intrinsic layers, (3) plasma reactor for p-type layers, (4) plasma reactor for n-type layers, (5) metal-evaporation chamber (see text), (6) central transport chamber, (7) robot arm, (8) reaction chamber, (9) gate valve, (10) gas supply, (11) bypass, (12) measuring devices, and (13) turbomolecularpump.

be used as an evaporation chamber, with which it was possible to evaporate contacts without exposing the sample to air. This was stopped for practical reasons. It was used then as a chamber where samples could be parked, to enhance productivity. As research shifted in the direction of plasma analysis, this fourth chamber was retrofitted with a quadrupole mass spectrometer [160]. After having built a separate system for plasma analysis in which the mass spectrometer was integrated [ 161 ], the fourth chamber now is in use for deposition of silicon nitride. The central transport chamber is an 80-cm-diameter stainless steel vessel, and is pumped by a 1000-1/s turbomolecular pump, which is backed by a small (50 l/s) turbomolecular pump to increase the compression ratio for hydrogen, and by a 16m3/h rotating-vane pump. UHV is obtained after a bake-out at temperatures above 100~ (measured with thermocouples at the outside surface) of the whole system for about a week. A pressure in the low 10 -11-mbar range is then obtained. With a residual gas analyzer (quadrupole mass spectrometer, QMS) the partial pressures of various gases can be measured. During use of the system, the pressure in the central chamber is in the low 10-1~ range due to loading of samples. Water vapor then is the most abundant species in the chamber. The robot arm can transport a substrate holder for substrate sizes up to 10 • 10 cm 2. The arm can both rotate and translate, and is driven mechanically by two external dc motors, one for each movement. The translation mechanism was specially designed for fast transport of the samples. The mechanism is based on an eccentrically moving hinge joint, much like a stretching human arm, and it combines high speed with a shock-

12

VAN SARK

free start and stop of the movement. It takes only 4 s to translate the substrate holder from the transport arm to the outermost position in the reaction chamber. A gear transmission inside the transport chamber is used to decrease the torque to be applied to the feedthroughs. WSe2 is used as lubricant for the gear wheels. The arm position is measured by potentiometers. The position of the arm in angular direction is reproducible to within 0.03 ~ of the preset position. A clear advantage of the central transport chamber is that a sample can be transported to the reaction chambers in any arbitrary sequence, without breaking the vacuum in the reaction chambers. Due to the very low pressure in the central chamber, the vacuum in the reaction chambers in fact is improved when a gate valve is opened. After a complete stretch of the robot arm, the substrate holder can be taken off the arm by a lift mechanism and clamped to the upper (grounded) electrode. Experienced operators are able to manually remove a substrate holder from one chamber and deliver it to any other within 30 s, including the time needed to open and close the gate valves. Automatic control by means of a programmable logic controller, coupled to a personal computer, only slightly shortens this transfer time. Because of the large heat capacity of the 12-mm-thick titanium substrate holder and the short transfer time, the cooling of the sample is limited to a few degrees. Fast transport and a low background pressure in the central chamber ensure that clean interfaces are maintained. Transport at 10-10 mbar for 30 s will give rise to a surface contamination of only about 0.01 monolayer of oxygen. New substrates are mounted on the substrate holder, which then is loaded in the load-lock chamber, which subsequently is evacuated down to 10-6-10 -7 mbar with a 150-1/s turbomolecular pump in combination with a 25-m3/h rotating vane pump. In this chamber the substrates are preheated to the desired temperature for the deposition, and at the same time they can be cleaned by dc argon sputtering. Usually the heating time (about 1 h) is much longer than the pumpdown time (less than 10 min). The substrate is transferred to the central chamber by a sequence of operations: opening the gate valve, translating the arm, lowering the substrate holder with the lift mechanism, retracting the arm (with the substrate holder), closing the gate valve. The pumping capacity of the central chamber is such that the 10-1~ background pressure is reestablished within 10 s after closing the gate valve. Each plasma reactor consist of a reaction chamber, an individual pumping unit, pressure gauges, and a dedicated gassupply system with up to four different gases, according to the layer type to be deposited. Residual gas exchange is prevented by the separation of the pumping units, as well as by the presence of the central chamber. The background pressure in the plasma reactors is lower than 10 -9 mbar, with partial pressures of water vapor and oxygen lower than 10 -1~ mbar, as a result of the capacity of the pumping unit, which is a 360-1/s turbomolecular pump backed with a 40-m3/h rotating-vane pump. The process pressure typically is between 0.1 and 0.5 mbar. This can be accomplished by closing the gate valve between reaction chamber and pumping unit (9 in Figure 5). The chamber

then is pumped only via the bypass (11 in Figure 5), in which a butterfly valve regulates the process pressure. A vertical cross section of the reaction chamber is shown in Figure 6. The inside diameter of the chamber amounts to 200 mm. The diameters of the grounded and powered electrodes are 180 and 148 mm, respectively, with a fixed interelectrode distance of 36.5 mm. The interelectrode distance has also been changed to 27 mm, and recently a modified powered electrode assembly has been retrofitted, with which it is possible to vary the interelectrode distance from 10 to 40 mm from the outside, i.e., without breaking the vacuum [ 162]. With process pressures in the range of 0.1-0.6 mbar the product of pressure and interelectrode distance, pL, may range from about 0.1 to 6 mbar cm. In practice, p L values are between 0.4 and 1.5 mbar cm, i.e., around the Paschen law minimum (see Section 3.2.4). The lower electrode is coupled via a H-type matching network to a 13.56-MHz generator. This network provides power matching between the RF power cable (50 f2) and the plasma. Power levels are between 1 and 100 W, or between 6 and 600 mW/cm e, using the area of the powered electrode. The substrate holder is positioned face down (6 in Figure 6) on the upper electrode; thus deposition is upward, which prevents dust formed in the plasma from falling onto the substrate. The plasma is confined between the powered and the grounded electrode and the reactor walls, which in addition can be watercooled. The substrate temperature can be varied up to about 500~ by means of fire rods in the grounded electrode. The temperature is regulated by a temperature controller, which measures the temperature with a thermocouple, also mounted in the upper electrode. The actual substrate temperature deviates from the temperature set by the controller, due to heat losses in the system. Therefore the actual substrate temperature has been measured by thermocouples on the substrate over a wide range of controller temperatures, and a calibration graph is used. Throughout this chapter, the actual substrate temperature is given. The appropriate gas mixture can be supplied to the center of the reactor (4 in Fig. 6) via holes in the lower electrode (2 in Fig. 6), and is pumped out through the space between substrate electrode and the reactor wall to the exhaust (5 in Fig. 6). Alternatively, the gas mixture can be supplied horizontally, parallel to the electrodes, through a flange in the reactor wall, positioned between the electrodes (perpendicular to the plane of the cross section in Fig. 6, not shown). In this case, the gas is pumped out at the opposite side of the supply. The volume of the reactor is about 10 1. At a typical process pressure of 0.2 mbar and a total gas flow rate of 60 sccm, the average residence time of molecules in the reactor amounts to about 1.3 s. Different gases experience different conductances towards the pump. The conductance is a combined result of the manually adjustable butterfly valve in the bypass line and the pumping system. This results in gas-dependent pressures for identical gas flows, as the flow Q is related to pressure p and conductance Cgas as Q - pCgas. In Figure 7 the pressures of

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

13

I I t T

I

I

...

~

...._..-,---"

~

5

-6

._.....--.........---

..._ . . - --.-

J

Fig. 6. Vertical cross section of the reaction chamber. Indicated are: (1) the grounded electrode, (2) the RF electrode, (3) the dark space shield, (4) the gas supply, (5) the gas exhaust, (6) the position of the sample holder during deposition, (7) the position of the sample holder when loaded, and (8) the lift mechanism.

40

'

I

'

I

'

I

'

I

'

I

'

I

pure argon, silane, and hydrogen are shown as a function of flow rate [163]. The setting of the butterfly valve was the same for all cases. As can be seen, the conductance for hydrogen is about a factor of 2-3 larger than for argon and silane. From the fact that the rate d p / d Q = C -1 decreases with increasing flow, it is inferred that the flow of the gases leaving the reactor is a mixed laminar-molecular (Knudsen) flow [118]. As a consequence of gas-dependent conductances, the composition of a gas mixture may differ from the one expected on the basis of flow ratios. As an example, the partial pressures (measured with a QMS) of a range of silane-hydrogen mixtures at a total flow of 30 sccm is shown in Figure 8a as a function

'

Ar 30

/o

t~

o/

20

o/~ 10

0

0

10

20

a0 40 Flow Q (sccm)

so

60

70

Fig. 7. The pressure p as a function of flow rate Q for different gases (Ar, Sill 4, H2) at one and the same setting of the pressure regulating butterfly valve in the bypass (11 in Fig. 5). (Redrawn from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

of the silane flow fraction rQ = OsiH4/(OsiH4 + QH2)[163]. A flow of hydrogen yields a lower pressure (about 3 times lower) than the same flow of silane; cf. Figure 7. The actual partial pressure ratio rp -~ PSiH4/(PSiH4 -F PH2)for these mixtures is shown in Figure 8b. It is clear that equal flow rates of different gases (in this case hydrogen and silane) do not lead to

14

VAN SARK 6O

'

I

'

I

'

I

'

I

1.0

'

Total 50 ~ " 0.8

g 40

~

o.6

k--

30

--~ o.4

L..

n

20

Q. 0.2

10

0 0.0

,

I

0.2

.

I

,

0.4

I

0.6

i

l

'

0.8

Silane flow fraction

re

(a)

0.0 0.0

0.2

0.4

0.6

0.8

Silane flow fraction

1.0

re

(b)

Fig. 8. (a) The total and partial pressures p and (b) the partial pressure ratio rp of silane and hydrogen in a silane-hydrogen mixture, at different flow ratios rQ. The total flow rate is 30 sccm. (Adapted from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

equal partial pressure ratios. This is important when comparing experimental and simulation data. Each of the reaction chambers has its own gas supply system, consisting of two channels 3-5 m in length. It also includes a nitrogen purge system. One channel is connected to a gas manifold for three types of gases; the other channel is connected to a single gas bottle. With this configuration it is possible to supply the reaction chamber with either a continuous flow of different gases or a mixture of gases, which may change rapidly during deposition (cf. chemical annealing [164, 165]). The gases are connected via pressure regulators to the supply channels. They can be switched to go via a mass flow controller to the reaction chamber or to go to a drain, which is continuously purged with argon and pumped with an 8-m3/h rotating-vane pump. When the pressure in the drain or the exhaust lines is too high, a safety exhaust is opened with a much larger diameter than the regular exhaust line from the reaction chamber. Nitrogen is available for pressurizing the system, and also is used to dilute the exhaust lines from the reaction chambers, to ensure below-TLV values on the roof of the building. If one needs to clean a reaction chamber, a separate channel with N F 3 is available. Etching with a N F 3 discharge has been found to reduce considerably the amount of Six Hy compounds adsorbed on the wall [166]. In the plasma reactor dedicated for intrinsic material deposition (2 in Fig. 5), only hydrogen and silane are used, along with argon. A mixture of trimethylboron (5% TMB in H2), Sill4, and methane (CH4) is used in the p-plasma reactor (3 in Fig. 5). Diborane can also be used. A mixture of phosphine [PH3 (1% in H2)] and Sill4 is used in an n-plasma reactor (4 in Fig. 5). All

gases are of 6.0 quality (99.9999% pure) if available from manufacturers, and otherwise as pure as possible. The low background pressure (10 -9 mbar) together with the purity of the gases used ensures a low concentration of contaminants. Amorphous silicon films made in the intrinsic reactor have been analyzed by using ERD, which is available in our laboratory [ 114]. The determined oxygen content in these films typically is lower than 3 • 1018 cm -3, which is somewhat lower than the values required for obtaining device quality films reported by Morimoto et al. [ 167]. It goes without saying that safety is very important in working with such a setup. A risk analysis has been performed. Safe operation procedures have been formulated. Personnel have been trained to work safely with the setup, which includes exchanging gas bottles using pressurized masks. Interlocks are installed, as well as emergency switches. Emergency power is available in case of power failures. Gases are stored in gas cabinets that were designed and installed with assistence of gas manufacturers. All valves in the gas-supply lines are normally closed valves: if compressed air (6 bar) is not available, all valves are by definition closed. Valves for nitrogen supply are normally open valves. Gate valves are double-action valves: compressed air is needed to either open or close the valve.

3. PHYSICS AND CHEMISTRY OF PECVD 3.1. General Introduction A plasma can be defined as a partially ionized, quasineutral gas, consisting of about equal numbers of positive and neg-

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON ative charges, and a different number of un-ionized neutral molecules. An external source of energy is needed to sustain the plasma for a sufficiently long time. The simplest and most widespread method that is used is the electrical discharge, dc or RF. High electric fields applied at millibar pressures yield nonequilibrium plasmas: free electrons are accelerated to 1-10 eV, while ions and neutrals have low energy (0.1 eV). These hot electrons initiate chemical reactions through collisions with the cold neutrals. Therefore, processing temperatures can be much lower than in thermal CVD, which has tremendous consequences for the applicability of PECVD. Without PECVD modern-day electronic chips would never have been possible. For general references see, e.g., Bruno et al. [8], Grill [117], Chapman [ 134], and Ricard [ 168]. This section treats the plasma physics and plasma chemistry of the typical silane-hydrogen RF discharge, with occasional examples that employ a somewhat higher excitation frequency. Electrical characterization of the discharge is followed by an analysis of the silane chemistry. An appropriate set of gas phase species is presented, which are then used in the modeling of the plasma. A comparison is made between modeling results and experimental work in ASTER. Extension to 2D modeling is presented as well. Plasma analysis is essential in order to compare plasma parameters with simulated or calculated parameters. From the optical emission of the plasma one may infer pathways of chemical reactions in the plasma. Electrical measurements with electrostatic probes are able to verify the electrical properties of the plasma. Further, mass spectrometry on neutrals, radicals, and ions, either present in or coming out of the plasma, will elucidate even more of the chemistry involved, and will shed at least some light on the relation between plasma and material properties. Together with ellipsometry experiments, all these plasma analysis techniques provide a basis for the model of deposition.

3.2. Plasma Physics 3.2.1. Plasma Sheath A schematic layout of a typical parallel-plate RF-discharge system is depicted in Figure 4a. The RF power is capacatively coupled to the discharge between the two electrodes. Silane is introduced between the electrodes, and reaction products and unreacted gas are pumped away from the reactor. The substrate onto which a-Si:H is deposited is mounted on the grounded (top) electrode (anode). The RF voltage V(t) = VRF sin wt is applied to the cathode, with co/27r = 13.56 MHz. This particular frequency had been chosen because radiating energy at this frequency would not interfere with communications [ 134]. However, higher harmonics do, and one should be careful to design proper shielding. Accelerated electrons in the applied electric field ionize gas molecules, and in these ionization processes extra electrons are created. In the steady state the loss of charged particles is balanced by their production. Due to their much lower mass,

15

electrons move much faster than ions. As a result, charge separation creates an electric field, compensating the diffences in electron and ion velocities. The potential in the central region, or bulk plasma, is slightly positive with respect to the electrodes, due to the small surplus of positive ions. The time-averaged potential profile is shown in Figure 4b. As ions cannot follow the oscillations in the applied electric field, it is this profile that ions experience. The bulk plasma is characterized by a constant potential, Vpl. In both sheaths (regions between plasma bulk and the electrodes), the ions experience a potential difference and are accelerated towards the electrodes. This leads to energetic ion bombardment of the electrodes. Electrons are expelled from the sheaths, so all ionization and dissociation processes must occur in the plasma bulk. Plasma light, resulting from emission from excited molecules, is emitted only from the plasma bulk; the sheaths are dark. The electrons follow the oscillations in the electric field, and experience the time-dependent plasma potential. Due to the capacitor through which the RF power is coupled to the electrodes, no dc current flows through the plasma. The ion and electron currents towards each of the electrodes balance each other over one RF period. In most systems the substrate electrodes are larger than the powered electrodes. This asymmetric configuration results in a negative dc self-bias voltage Vdc on the powered electrode. Without that, the difference in electrode areas would result in a net electron current per RF period [134, 169]. It has been shown that the ratio of the time-averaged potential drops for the sheaths at the grounded (Vsg) and the powered electrode (Vsp) are inversely proportional to a power of the ratio of the areas of the two electrodes (Ag, Ap) [134, 170-172]: Vsg =(A.__~_p)n

Vsp

\Ag]

with

l

[]

O

..O- - .. n"

O

0.2

:..."

0.02

Si2H8

0 o.

o

~ i ~D

~i i D

1:

s

.:

i m mD

~i D

D'D. D ....D

0.4

0.2

a-7' transition 0.0

,

0

i

10

,

,

20

,

,

,

30

Total pressure (a)

i

40

,

i

0.00

50

(Pa)

,

0.0 0

I

10

,

I

20

,

I

,

30

Total pressure (b)

I

40

i

I

50

(Pa)

Fig. 17. (a) The relative pressures (i.e., the ratio of the partial pressure to the total pressure) of H2, Sill4, and Si2H 6, and (b) the deposition rate, as a function of total pressure at an RF frequency of 50 MHz and a plasma power of 5 W. Other discharge settings are given in Table IV. Modeling results are in dotted lines and open symbols, experimental data in solid lines and filled symbols. Note the sudden increase at 30 Pa, i.e., the transition from the cx- to the y~-regime. (Compiled from G. J. Nienhuis, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

and the resulting discharge impedance. Agreement, therefore, is not expected between experimental and modeling results. Tendencies, however, will be clear from the results. Another important problem to address is the regime in which the discharge is operating, whether the c~ (dust-free) regime or the yt-regime, where dust plays an important role in the discharge [244] (see Section 6.1.6). Dust particles consist of large clusters of Si and H atoms, and are negatively charged by attachment of free electrons. They can be considered as an additional wall surface. Consequently, the free electron density decreases. In order to maintain the discharge, i.e., the amount of ionization, the average electron energy has to increase. This also leads to an enhanced dissociation of Sill4 and thus to a larger radical production. Generally, at low pressures and at low power levels the discharges operate in the a-regime. At a certain critical pressure, which depends more or less upon the other discharge parameters, the discharge makes a transition from the c~- to the )/t-regime. The modeling does not take dust effects into account. The discharge settings used are interesting, because at increasing total pressure the discharge regime is changed from ot to )/t, at a critical pressure of about 30 Pa. 4.1.10.1. Pressure Variation

In Figure 17 are shown the effects of total pressure on the relative pressures (i.e., the ratio of the partial pressure to the total pressure) of silane, hydrogen, and disilane (Fig. 17a) and on the

deposition rate (Fig. 17b). The RF frequency is 50 MHz, and the plasma power is 5 W. The relative pressure of hydrogen slowly increases, and the relative pressure of silane slowly decreases, both in model as well as in experiment. This is caused by an increase in silane depletion at higher total pressures, which resuits from a higher power dissipation by the electrons. At 16 Pa the fraction of dissipated power that is used to heat electrons is 79%, at 50 Pa this increases to 97%. This increase leads to a higher dissociation rate of silane, and explains the increased depletion. The relative pressure of disilane increases as a function of total pressure, due to the increased production of radicals, which is a result of increased dissociation of silane, as well as to the shorter gas volume reaction times and longer diffusion times to the walls, which result from increasing the pressure. Below 30 Pa the trends agree between model and experiment. The model slightly underestimates the silane partial pressure, by about 10%, and overestimates the hydrogen pressure by about 6%. Possible causes for this discrepancy are the simple 1D geometry of the model, the assumed relation between plasma power and source power, and the approximation for the pumping by using an average residence time. The discrepancy for the disilane data might be explained e.g. by questioning the dissociation branching ratio of silane. Layeillon et al. [ 195, 196] have discussed this, and conclude that dissociation of silane should result in a larger fraction of Sill3. At about 30 Pa, the experimental deposition rate (Fig. 17b) clearly shows a sudden increase, which is not revealed by the

28

VAN SARK 12

'

'

i

_.._2_'.,_' _~_ exp

,

i

0.5

1.2

10

-

...El .........[] .... ,1~'"

1.0

.'"

0.4

H2

[]-D.... t~ 12.

~

- - I I - - exp " [] .... m o d e l

.... [] ........ A ........ O---- m o d e l

=

n

.,"

.......0 .............[] .........[] .........[] m m ~ m m

~ -mm

8

o~

0.8 Zk AI~'~"~'~.&~&________A

E v

r"

0.3

.....-A .............A .........Z~.........Z~ to

6

0.6

Sill 4

r'l"

I,....

c .0

..............................- :'2 12.

4

0.4

0.2

O Q..

.~'"

D



0.1

Si2H e 0.2

,

I

,

20

I

40

RF-frequency

,

I

,

60

I

0.0

8(

(MHz)

(a)

0.0

,

0

t

,

20

I

40

RF-frequency

,

i

,

60

I

80

(MHz)

(b)

Fig. 18. (a) The partial pressures of H2, Sill4, and Si2H 6 and (b) the deposition rate, as a function of RF frequency at a total pressure of 16 Pa and a plasma power of 5 W. Other discharge settings are given in Table IV. At these settings the discharge is in the c~-regime. Modeling results are in dotted lines and open symbols, experimental data in solid lines and filled symbols. (Compiled from G. J. Nienhuis, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

model. In addition, the partial pressure of silane decreases (and of hydrogen increases). These features have been observed in other experiments as well [245-248], and are caused by the transition from the c~- to the )/t-regime.

4.1.10.2. RF Frequency Variation In Figure 18 are shown the effects of RF frequency on the partial pressures of silane, hydrogen, and disilane (Fig. 18a) and on the deposition rate (Fig. 18b). The total pressure is 16 Pa, and the plasma power is 5 W. The discharge is in the c~-regime. Both model and experiment show the same tendency: the dissociation of silane increases as a function of RF frequency. This can be explained following the arguments from Heintze and Zedlitz [236]. They found that the power dissipated by the ions in the sheaths decreases with increasing RF frequency. This is confirmed by the modeling results: at 13.56 MHz about 50% of the power is used for the acceleration of the ions, whereas at 80 MHz this is reduced to about 15%. Hence, at higher RF frequencies more power is used for the heating of electrons, which in turn leads to a higher dissociation of silane. As a result, more hydrogen and silane radicals are produced, and more molecular hydrogen is formed. A saturation is observed when all power is consumed by the electrons. The experimentally found linear increase of the deposition rate as a function of frequency is not seen in the modeling resuits that show saturation; see Figure 18b. The linear increase has also been measured by others [119, 120, 249], up to an RF frequency of 100 MHz. Howling et al. [250] have measured this

linear relationship, while taking special care that the effective power is independent of frequency. A possible explanation for the difference in tendencies of the deposition rate between experiment and model is that in the model the surface reaction and sticking coefficients of the radicals are taken to be independent of the discharge characteristics. In fact, these surface reaction coefficients may be influenced by the ions impinging on the surface [251 ]. An impinging ion may create an active site (or dangling bond) at the surface, which enhances the sticking coefficient. Recent experiments by Hamers et al. [163] corroborate this: the ion flux increases with the RF frequency. However, Sansonnens et al. [252] show that the increase of deposition rate cannot be explained by the influence of ions only. The discrepancy may also be caused by the approximations in the calculation of the EEDE This EEDF is obtained by solving the two-term Boltzmann equation, assuming full relaxation during one RF period. When the RF frequency becomes comparable to the energy loss frequencies of the electrons, it is not correct to use the time-independent Boltzmann equation to calculate the EEDF [253]. The saturation of the growth rate in the model is not caused by the fact that the RF frequency approaches the momentum transfer frequency Vme [254]. That would lead to less effective power dissipation by the electrons at higher RF frequencies and thus to a smaller deposition rate at high frequencies than at lower frequencies. Another possible explanation is the approximation that the vibrationally excited silane molecules are treated in the model

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON --I

30

'-~-A, ~ --~exp

'

' [ ] ........ A ........ ,,

8

,-l-a oE

O3 E

6 I

E 5 Lr~ s--

0

I

I

mbor mbor mbor mbor mbor mbor mbar mbor

I

H2 i

4

3

"1:9

o

I

>,,

9

c

I

-o- 0.50 -o-- 0.35 -O--- 0 . 5 0 0.25 -~- 0.20 ---m- 0 . 1 5 0.10 0.05

c -o

4

cO

o

9

2 0

0

,5 10 15 20 2.5 ,30

Power (W) (a)

t

5

10

1,5 20

i

25

,30

Power (W) (b)

Fig. 30. Electron (a) and ion (b) density as a function of power for different pressures in the case of a hydrogen discharge.

as the deposited amorphous silicon layer on the tip was sufficiently photoconductive. For typical silane discharge conditions values for Te are found to be between 2 and 2.5 eV. Electron densities are around 1 x 109 cm -3 [296]. Probe measurement in the ASTER system failed due to strong distortions of the probe current, even after following cleaning procedures.

5.3. Mass Spectrometry Mass spectrometry is used to obtain information on the neutral and ionic composition of the deposition discharge. Three modes of sampling are commonly used: analysis of discharge products downstream, line-of-sight sampling of neutrals, and direct sampiing of ions from the discharge. Mass spectrometry is a simple method to measure and quantify neutral species in a silane discharge, although calibrations are required. For ionic species, mass spectrometry is the only method available. A quadrupole mass filter is a proven instrument that is essential in mass spectrometry of low-pressure discharges.

5.3.1. Analysis of Neutrals The analysis of the neutral gas composition in a discharge yields useful information on the mechanisms and kinetics of silane dissociation. However, it should be borne in mind that with mass-spectrometric analysis one only detects the final products of a possibly long chain of reactions. The partial pressures of the stable neutral molecules in the discharge (silane, hydrogen, disilane, trisilane) can be measured

by a quadrupole mass spectrometer (QMS). The QMS usually is mounted in a differentially pumped chamber, which is connected to the reactor via a small extraction port [286]. In the ASTER system a QMS is mounted on the reactor that is used for intrinsic material deposition. The QMS background pressure (after proper bake-out) is between 10 -12 and 10 -]3 mbar. The controllable diameter in the extraction port is adjusted so that during discharge operation the background pressure never exceeds 10-11 mbar. The gas that enters the QMS is ionized by electron impact at a factory-preset electron energy of 70 eV (or 90 eV), and subsequently mass-analyzed. The ion currents at different mass-to-charge ratios (m/e) need to be converted to partial pressures by careful calibrations, as reported by Hamers [ 163]. Gas X is admitted to the reactor and the corresponding pressure p is measured, as well as the ion current I at a specific ratio m/e = # x of the gas, e.g., for argon m/e - 40 amu/e. The background signal at the same m/e -- # x that results from residual gases in the QMS chamber is subtracted from the measured ion current. The calibration factor Vx is defined as the ratio between the corrected ion current and the reactor pressure. Calibrations are performed typically at three pressures before and after measurements on the discharge, as the sensitivity of the channeltron in the QMS may rapidly change. The calibrations are performed with hydrogen, argon, silane, and disilane, with the main contributions at m/e = 2, 40, 30, and 60 amu/e, respectively.

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON 1.5

13.5

E 1.0 r-

9.0

(3 i,,_

I

0.6

E t3 o

43

I

I

I

Si2H6

O

n

I

~ - 0.4

g o_

~"3

Q-

I1~

I

,,. ,,. i

11~'I

r-

.s

a

o 0.5

4.5 ~ ~

s

e~

-6 ~ o.2

Si3H8

0

0.0

I

I

I

I

I

10

20

30

40

50

0.0

p (Po) Fig. 31. The deposition rate and the corresponding silane depletion as a function of the total process pressure. Other conditions are 50 MHz, 30:30 Sill4 :H2. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

In the deposition of a-Si:H the dissociation of the process gas silane leads to the formation of hydrogen, disilane, trisilane, higher-order silanes, and a solid film. Silane is depleted. From the consumption of silane, one may estimate the deposition rate of the solid film. The difference in the silane partial pressure between the discharge-on and the discharge-off state is often used as an indication of the amount of silane that is depleted [298-300]. However, the relative change in pressure in general is not equal to the relative change in flow, due to gasdependent conductances [ 163, 301] (see also Section 2.4). For example, in the A S T E R deposition system equal partial pressures of silane and hydrogen are observed for a flow ratio of silane to hydrogen of about 1.25. Hence, another way of determining the silane depletion is used [163, 301 ]. First, the partial pressures of silane and hydrogen are measured in the dischargeon state. Subsequently, the discharge is switched off, and the silane and hydrogen flow rates are adjusted so that the same partial pressures as in the discharge-on state are reached. These flow rates then are the flow rates of silane and hydrogen that leave the reactor in the discharge-on state. The silane depletion A aSiH4 is the difference between the admitted silane flow rate and the flow rate of silane that leaves the reactor when in the discharge-on state. Additionally, an estimate can be made of the deposition rate, under the assumptions that all depleted silane is used for the deposition (no large amount of higher-order silanes or dust is formed). Also the deposition is assumed to occur homogeneously over the surface of the reactor. The estimated deposition rate is r~ st -- A O s i H 4 / k 8 TOpAr, with p the atomic density of the amorphous silicon network (5 • 1022 cm-3), To the standard temperature (300 K), and Ar the reactor surface (0.08 m2). This yields an estimated deposition rate of 0.11 nm/s per sccm Sill4 depletion [163]. In Figure 31 the deposition rate is compared with the corresponding silane depletion as a function of process pressure for a silane-hydrogen discharge at 50 MHz and 10 W. For these conditions the or-? ,~ transition occurs at 30 Pa: the deposition rate is increased by a factor of 4,

0.0

I

I

I

I

I

10

20

30

40

50

p (po) Fig. 32. The partial pressures of disilane and trisilane. The dashed line is an extrapolation of the disilane partial pressure in the or-regime. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

whereas the depletion is increased only by a factor of 2. The fight-hand axis is scaled using the value 0.11 nm/s-sccm. In the or-regime the deposition rate is underestimated, whereas in the y'-regime it is overestimated. This is in part due to the assumed uniformity of deposition. In the u-regime the deposition rate at the center of the substrate is lower than at the edges; in the y1-regime this is reversed. Moreover, from the low dc bias voltages observed in the y1-regime it is inferred that the discharge is more confined. The partial pressures of disilane and trisilane are shown in Figure 32, for the same process conditions as in Figure 31. Both partial pressures increase as a function of pressure. Around the ct-y' transition at 30 Pa the disilane partial pressure increases faster with increasing pressure, as can be seen from the deviation from the extrapolated dashed line. The disilane partial pressure amounts to about 1% of the total pressure, and the trisilane partial pressure is more than an order of magnitude lower. Apparently, in the y~-regime the production of di- and trisilane is enhanced. Not only the silane depletion, but also the hydrogen production can be used to obtain information on the reaction products of the decomposition process. In Figure 33 the silane depletion and the corresponding hydrogen production are shown for a number of experiments, with process parameters such as to cover both the or- and the y~-regime [ 163, 301 ]. A clear correlation exists. In addition, the solid line in Figure 33 relates the hydrogen production and silane depletion in the case that only a-Si:H is formed with 10 at.% H, i.e., a-Si:H0.1 and H2. The dashed line represents the case where 30% of the silicon from the consumed amount of silane would leave the reactor as disilane, instead of being deposited as a-Si:H0.1. The data can well be explained by these two cases. In fact, they are an indication that part of the consumed silane leaves the reactor with a larger amount of H per Si atom than a-Si:H, which may be caused by the formation of higher silanes and/or powders.

44

VAN SARK 30

I

1

I

I

I

I

I

t

~ , 25 E

--

//

/--

+

(..) 09 c 0 D

-o 9

20

15

5.3.2. Analysis of Radicals

0_ c9

T

with others [201,309, 310]. The abstraction reaction H + Sill4 --~ Sill3 + Sill3 explains the large production of Sill3 radicals in this case. The discrepancy as reflected in the hydrogen production (either H or He) cannot be resolved solely by massspectrometric data.

5

.L

0 0

I

I

1

2

4

6

1

1

8 10 S;lane depletion ( s c c m )

I

I

12

14

Fig. 33. The depletion of silane and the corresponding production of hydrogen for several process conditions, covering both the c~- and the y'-regime. The solid line represents the case where all the consumed silane is converted into a-Si:H0.1 and 1.95H2. The dashed line represents the case where 30% of the consumed silane is converted into disilane instead of being deposited. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

Mass-spectrometric research on silane decomposition kinetics has been performed for flowing [298, 302-306] and static discharges [197, 307]. In a dc discharge of silane it is found that the reaction rate for the depletion of silane is a linear function of the dc current in the discharge, which allows one to determine a first-order reaction mechanism in electron density and temperature [302, 304]. For an RF discharge, similar results are found [303, 305]. Also, the depletion and production rates were found to be temperature-dependent [306]. Further, the depletion of silane and the production of disilane and trisilane are found to depend on the dwell time in the reactor [298]. The increase of di- and trisilane concentration at short dwell times ( Ei, and Ea ~ Ei + E A - - B , where E A - - B is the energy of the A--B bond [311 ]. When the electron energy is larger than Ea, the dissociative ionization process dominates, because the density of the molecule AB is much larger than that of the radical A. When the electron energy has a value between Ei and Ea, then only the radicals are ionized, and one is able to determine the radical density. In silane discharges, one observes the following: when the discharge is off, the mass spectrometric signal at role = 31 amu/e (SiH~-) as a function of electron energy is due to dissociative ionization of Sill4 in the ionizer of the QMS, with an ionization potential of 12.2 eV [312]. The signal with the discharge on is due to ionization of the radical Sill3 plus the contribution from dissociative ionization of silane (the ions from the discharge are repelled by applying a positive voltage to the extraction optics of the QMS). The appearance potential of the Sill3 radical is 8.4 eV [312], and therefore a clear difference between discharge on and off is observed. The corresponding threshold energies for Sill2 are 11.9 and 9.7 eV (these four numbers are also given by Kae-Nune et al. [311 ], as 12.0, 8.0, 11.5, and 9.0 eV, respectively). The net radical contribution to the ion signal is given by [311] A I ( A + ) - - (/on - lbg -- lions) -- ( / o f f - / b g )

nSiH4,on nSiH4,off

(38)

where/on (loft) is the signal when the discharge is on (off), Ibg the background signal, and lions the signal due to ions (which should be zero). The factor nSiH4,on/nSiH4,off takes account of the depletion of the density of Sill4, which can be obtained from the ratio lon/loff at high electron energies. The concentration of radical SiHx can be expressed as [311 ]

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

found that the Sill3 radical is the most abundant one, with a concentration varying between 1.8 x 1011 and 3.2 • 1011 cm-3. The Sill2 radical concentration was about a factor of 20 lower. Both radical concentrations increase with increasing power. From the radical concentrations it is possible to derive the radical flux to the surface:

10a

105 104

~SiHx -- nSiHx

8 Io2

~.,(S,H~--- S~H3*)"

IO t

ioo

45

7

11

9

10

ii

I2

13

I4

15

16

17

Eieearonenergy(eV) Fig. 34. Measured and fitted curves for the ionization of the Sill 3 radical. [From P. Kae-Nune, J. Perrin, J. Guillon, and J. Jolly, Plasma Sources Sci. Technol. 4, 250 (1995), 9 1995, Institute of Physics, with permission.]

IJSiHx

flSiHx

4

1 -- flSiHx/2

where 1JSiHx is the thermal velocity (= ~/8kBT/srm) of the radical SiHx, /TSiHx the surface reaction probability (see also Fig. 14 in Section 4.1.6). The quantity/7 is the adsorbed fraction of radicals, which either stick (sticking probability SSiHx) or recombine as Sill4 or Si2H6 and go to the gas phase (recombination probability YSiHx). By definition,/7 = s -4- 7/. An amount r = 1 - / 7 is reflected from the surface directly. The contribution of radical SiHx to the total deposition rate follows from SSiHx

MSi

Rd,SiHx -- ~SiHx flSiHx NAPa-Si:H

n(SiHx) = C Q(SiH4 --+ Sill +, E2 > Ea) n(SiH4) I(SiH +, E2 > Ea)

1 X

[E~ <Eo

E 1 - E 1 J Ei--E1t II

f

AI (Sill +, E) Q(SiHx ~ Sill +, E)

dE (39)

where I (Sill +, E2 > Ea) is the signal due to dissociative ionization of Sill4, A I (Sill +, E) the net radical signal [Eq. (38)], Q(SiH4 --+ Sill +, E2 > Ea) the electron impact cross section for the dissociative ionization of Sill4, Q(SiHx ~ Sill +, E) the electron impact cross section of the ionization of the radical SiHx, and C a geometrical correction factor. Clearly, the knowledge of the electron impact cross sections is essential for the exact determination of the radical densities. Kae-Nune et al. [311] have used data for deuterated methane radicals (CD3 and CD2 [313]) to determine Q(SiH3 ~ Sill +, E) and Q(SiH2 --+ Sill +, E) by scaling. The value of Q(SiH Sill +, E) is determined by taking the average of Q(SiH2 Sill +, E) and the measured Q(Si ~ Si +, E) [314]. In Figure 34 the measured SiH~- signal is compared with fitted curves for radical and dissociative ionization [311 ]. Nowadays, a commercially available QMS system (Hiden EQP300) is used by many groups, with which detection of radicals, and also of ions (see Section 5.3.3), is possible [315]. Kae-Nune et al. [ 198, 217, 311 ] have mounted this QMS system in the grounded electrode of their parallel plate PECVD reactor. Neutral (and ionic) species are sampled from the discharge via a 0.3-mm-diameter hole in the grounded electrode. Twostage differential pumping ensures a low background pressure (< 10 -6 Torr) in the ionization chamber of the QMS. With this setup a series of measurements was taken in which the power was varied from 5 to 30 W. The pressure was low, 0.06 Torr, while the temperature was 250~ The SiHx (0 < x < 3) radical densities near the surface were measured as a function of effective power delivered to the discharge. It was

(40)

(41)

where NA is Avogadro's number, MSi the molar mass of silicon, and Pa-Si:H the mass density of a-Si:H (2.2 g/cm3). For Sill3 Matsuda et al. have determined/7 and s [137]: f l S i H 3 - - 0.26 and SSiH3 : 0.09. For Sill2, Sill, and Si large/7 and s ~ /7 are assumed, viz.,/Tsin2 = ssin2 = 0.8 [311],/7sin = SSiH = 0.95 [316], and/Tsi = ssi = 1 [311]. Using these values for/7 and s, Kae-Nune et al. [311 ] have determined the contribution of radicals to the deposition rate. At low power levels, the deposition rate can fully be accounted for by the Sill3 and Sill2 radicals in a 60 : 40 ratio. At high power levels the other radicals also become important. At their highest power level of about 50 mW/cm 2, the sum of all radical contributions to the deposition rate is only 65%, indicating that dimer and trimer radicals, as well as ions, also contribute to the deposition. Using the same threshold ionization mass spectrometry setup, Perrin et al. [317] have measured the temporal decay of radical densities in a discharge afterglow. From these experiments the coefficient/7 for the radical Sill3 has been determined to be 0.28, which is in agreement with already known results from other (indirect) experimental approaches [ 136, 137, 318]. For the Si2H5 radical/7 is determined to be between 0.1 and 0.3. The coefficient/7 for atomic hydrogen on a-Si:H lies between 0.4 and 1, and is thought to represent mainly surface recombination to H2.

5.3.3. Analysis of lons Detection of ions from a discharge is done by direct sampling through an orifice. In order to extract the ions collisionlessly the dimensions of the sampling orifice should be smaller than the sheath thickness; they are typically of the order of 100 #xm. Moreover, the detected ions and their energies are representative of the plasma bulk situation only when the sheath is collisionless, i.e., at low pressures [286]. One generally is interested in the interaction of ions with a growing surface; hence normal operating pressures are used.

46

VAN SARK

In RF discharges of silane, SiH~- usually is the most abundant ion, but others (Sill +, and Sin H+ with 1 < n < 9) also are present [319]. The relative abundance of Sill + ions increases with increasing pressure, while that of Sill + decreases [319]. The ionization cross section of SiH~- is higher than that of SiH~- [320], but Sill + is lost via the reaction SiH~- + Sill4 --+ SiH~- + Sill3 [305]. At pressures lower than 0.1 Torr SiH~becomes the dominant ion. The ion clusters (SieH +, Si3H + . . . . ) are also present, and larger clusters (positive and neutral) can be formed through reactions with silane molecules. Negative ions have been detected [321 ], which are thought responsible for the powders in the discharge [322]. Ion energy distributions (IEDs) are measured by several groups [323-326]. The reliability of IEDs depends strongly on the knowledge of the transmission function of the instruments, which most likely is energy-dependent. Improper adjustment of the various potential levels throughout the instruments can result in "ghost" structures in the IED, and they reflect the physics of the instrument rather than of the discharge. Hamers et al. [161, 163] have presented a method to determine the proper transmission function of an electrostatic lens system of a commercially available ion energy and mass spectrometer, the Hiden EQP [315]. This system is used by many groups to study plasmas [160, 198, 311,321,327,328]. It is very versatile with respect to the control of voltages on the many electrostatic lenses. The EQP is mounted in a plasma reactor identical to the ones in ASTER; see Figure 35. The plasma is generated between the two parallel electrodes. In the grounded electrode, where normally the substrate is placed for the deposition of a-Si:H, a small orifice is located to sample particles that arrive from the discharge. The orifice is made in a 20-tzm-thick stainless steel foil, and has a diameter of 30 #m. The foil is integrated in a stainless steel flange. The ratio of the thickness of the foil to the diameter of the orifice results in a physical acceptance angle of 55 ~ with respect to the normal to the electrode. The small size of the orifice compared to the sheath thickness and the mean free path of the particles in the plasma ensures that the orifice does not influence the discharge [323]. Using this orifice in deposition plasmas leads to deposition of a-Si:H on the surface of the orifice, but also on its inner sides, thereby narrowing the sampiing diameter. This can be observed by monitoring the pressure rise in the mass spectrometer during experiments. Typically, a 50% reduction in orifice area takes 3 h. The a-Si:H film on the orifice then needs to be etched away, which is done e x s i t u by a KOH etch. The design of the instrument, together with the pumping capacity, ensures a low background pressure (< 10 -9 mbar). Under process conditions the pressure directly behind the orifice is about a factor of 105 lower than the process pressure; in the mass filter, even a factor of 106. The mean free path of particles that have entered the EQP therefore is several meters. The ion optics (IO in Figure 35) consists of a number of electrostatic lenses, which direct the sampled ions through the drift

DE QMF

/

f

CD

TMP

ESA DT --I0

PR

L"

""

'

:--I

MN Fig. 35. Vertical cross section of the reaction chamber equipped with the mass spectrometer system. Indicated are: QMF, the quadrupole mass filter; ESA, the electrostatic analyzer; CD, the channeltron detector; DE, the detector electronics; DT, the drift tube; IO, the ion optics; TMP, the turbomolecular pump; PR, the plasma reactor; and MN, the matching network.

tube (DT) to the electrostatic analyzer (ESA). The ESA transmits only those ions with a specific energy-to-charge ratio Epass. An ESA has a constant relative energy resolution AE/Epass. Because this ESA operates at a constant Ae, the pass energy Epass is constant. Here, ~Spass = 40 eV, and Ae = 1.5 eV (FWHM). The measurement of IEDs requires that sampled ions be decelerated or accelerated to this pass energy. This is also done in the ion optics part. The other very important function of the ion optics is to shape the ion beam. Voltages on the various lenses should be set to avoid chromatic aberration, which causes energy-dependent transmission of ions in the instrument, and as a result erroneous IEDs [161, 163]. The correct lens settings have been found by simulations of ion trajectories in the EQP using the simulation program SIMION [329]. In addition, an experimental method to find the correct settings has been presented [161,163]. The acceptance angle depends on the lens settings and on the ion energy. Low-energy ions are deflected more towards the optical axis than high-energy ions, which results in a larger acceptance angle. The acceptance angle varies between about 6 ~ and 1~ for ion energies between 1 and 100 eV [161, 163].

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON For lower energies the acceptance angle can reach values above 20 ~, which causes drastic increases of the low-energy part of the measured IED. The measured ion energy distributions are affected by the processes that ions experience during their passage through the plasma sheath. In a collisionless situation, the lED is solely determined by the RF modulation of the plasma potential. The extent to which an ion will follow these modulations depends on its mass. Electrons are able to follow the electric field variations instantaneously, while ions experience a time-averaged electric field. The energy of an ion that arrives at the electrode depends on the value of the plasma potential at the time that the ion entered the sheath. Hence, the ion energy is modulated in much the same way that the plasma potential is modulated. Many ions arrive at the electrode with energies close to the extreme values of the harmonically varying voltage, and this results in a saddle structure in the lED, in which the two peaks reflect the minimum and maximum plasma potential [134]. The heavier the ion, the more it experiences a time-averaged plasma potential, and the narrower the saddle structure is. Elastic collisions and chemical reactions in the sheath lead to a broad angular distribution of the ion velocity at the electrode. Examples for SiH~- and Sill + are the H - abstraction reactions SiH~- + Sill4 --+ Sill4 + SiH~-[330] and SiH~- + Sill4 --+ SiH~- + Sill3 [331]. Due to the small acceptance angle of the EQE these processes are only in part reflected in the IED [ 163, 332]. 5.3.3.1. Charge E x c h a n g e

Much more important for the shape of the IED are charge exchange processes. In a charge exchange process an electron is exchanged between a neutral and an ion. In the plasma sheath a charge exchange between a neutral of thermal energy and a fast ion leads to the formation of a thermal ion and a fast neutral. These newly created thermal ions are accelerated towards the electrode, and the kinetic energy that they gain depends on the phase in the RF period and their position at the time of creation. This leads to distinct peaks in the lED, and the origin of these peaks can be explained as follows [325]. Electrons respond to the RF modulation and move to and from the electrodes. The movement of the electron front is a function of the phase r in the RF period. When an ion is created (by a charge exchange process) behind the electron front, i.e., in the plasma bulk, it will not experience an electric field. Once the electron front moves inward to the plasma bulk, the ion will be accelerated to the electrode. Depending on the place of creation x, the ion will be able to reach the electrode before the electron front is at the position of the ion again. Once in the plasma bulk, the ion will not be accelerated until the electron front moves inward again. This may be repeated several times. Wild and Koidl [325] have presented a description of the origin of the maxima in IEDs. They argue that these maxima only occur if the ion energy at the electrode is independent of the phase r and the position x of creation of the newly formed ion. Two conditions are to be met: d e ~ d e = 0 and d e / d x = 0. As shown by Wild and

47

Koidl [325], the energy e varies between Emin and Emax, and for every x, the values of emin, emax, and er fulfill the condition d e ~ d e - 0. Further, er exhibits a series of extrema as a function of x, and at these extrema is alternately equal to Emin and Emax. At these extrema both conditions are met, and a saddle structure is observed in the lED. In addition, ions that arrive with the mean energy of the saddle structure have reached the electrode after an integer number of periods. Thus, ions in successive charge exchange saddle structures have needed an increased number of periods to reach the electrode, on average. Hamers has very nicely illustrated this by performing Monte Carlo simulations of charge exchange processes [163], using a time- and position-dependent electric field, which is calculated from the sheath model as described by Snijkers [333]. About 300,000 Sill + ions were followed. The ion density at the electrode was 3 x 108 cm -3, the plasma potential 25 V, and the excitation frequency 13.56 MHz. The main saddle structure is found to be around 25 V (23-27 V). In the IED four charge exchange peaks are clearly distinguished, at about 2, 7.5, 14, and 19 eV. From a comparison with the transit time, i.e. the time an ion needs to cross the sheath, it is clear that the peaks in the IED correspond to ions that needed an integer number of periods to cross the sheath. The first peak at 2 eV corresponds to ions that needed one period, and so on. In general, ions in charge exchange peak p needed p periods to cross the sheath. The energy position e p of the peak and the corresponding number p of periods of time T are used by Hamers et al. [ 163, 332] to reconstruct the time-averaged potential profile V (x) in the sheath. An ion that arrives with energy ep at the electrode has a velocity that follows from 89 v 2 - ep - e V (x). With v = d x / d t one derives

s07 Xp

m/2 Ep - e V ( x )

dx -

s0

dt - pT

(42)

where X p is the mean position of creation of the ions that arrive at the electrode with energy e p. The unknown V (x) now is found by further assuming that V (x) can be represented by a parabolic function [328, 333]. A parabolic potential profile corresponds to a constant (net) charge carrier density n as a function of distance x in the sheath, according to - V 2 V = V 9E -- e n / e o . The electric field E ( x ) in the sheath then is a linear function of x" enx

(43)

E ( x ) -- - E o + E0

with E0 the electric field at the electrode (x - 0). Integrating E(x) from the electrode (V - 0) over a distance x gives the potential V(x)-

en Eox + ~x

2

(44)

2e0

The sheath thickness ds is found from the position where the electric field vanishes: ds - e o E o / ( e n ) . Here the potential is equal to the time-averaged plasma potential Vpl. We then find,

48

VAN SARK

with Eq. (44), for the electric field at the electrode ;;

/ 2en Vpl Eo = -V ~o

;

;

10

9 '

.

. '

; ;;: '

-

(45) 5

and for the sheath thickness

0 15

ds = J2~0Vpl V

(46)

10

en

Rewriting Eq. (44) yields

5 u')

V(x)- %l

(47)

'q" 0

10

Substitution of V(x) in Eq. (42) and solving for ~p then yields

>,,,

-2

(.f) E

(48)

E

The energy position Ep of peak p in the IED of an ion with mass m is seen to be dependent on the plasma potential Vpl, the

Silane-argon discharges are very illustrative, for no less than four different ions have charge exchange maxima in their ion energy distribution. In Figure 36 IEDs are shown that were measured in a plasma that was created in a mixture of 13 sccm Ar and 13 sccm Sill4, at a pressure of 0.1 mbar. The applied RF frequency was 13.56 MHz, at a power of 10 W. The dc self-bias voltage that developed was - 1 3 5 V. The substrate temperature was 250~ At least the first six peaks in the IED of Ar + and the first five peaks in the lED of SiH~-

0 15

5 0 15

1~

,s{, Ecos(, 'e n

5.3.3.2. Silane-Argon Discharges

5

10

RF period T, and the ion plasma frequency O)i - - v/e2n/(mE.o). Equation (48) can be used to determine the (net) charge carrier density in the sheath and the time-averaged potential Vpl from measured IEDs. The mean position Xp follows from combining Eq. (47) and Eq. (48):

In silane discharges several ions are observed to be involved in a charge exchange process, and therefore maxima in their ion energy distribution at distinct energies are observed. The charge carrier density and the plasma potential that result from the fit of the lED allow for the quantification of the related parameters sheath thickness and ion flux. This method has been be used to relate the material quality of a-Si:H to the ion bombardment [301,332]; see also Section 6.2.3. In the following, IEDs measured in silane-argon and silanehydrogen discharges are shown, and Vpl and n are determined from fitting the data using Eq. (48). In fact, Vpl is determined from an IED that is not affected by collisions in the sheath; this is the case for Si2H~-, where only one peak is observed in the IED. It should be noted that in general the width of the saddle structure is smaller than the energy resolution (1.5 eV) of the instrument, and therefore cannot be distinguished.

0 15

t

5

0 0 Fig. 36.

5

10 15 20 Ion Energy (eV)

25

30

The measured ion energy distributions of (a) Ar +, (b) Sill +,

(c) SiH~-, (d) H~-, and (e) Si 2H4+ from a SiHn/Ar plasma. The conditions are 13 sccm Sill4, 13 sccm Ar, 13.56 MHz, 10 W, 0.2 mbar, 250~ Vdc = --135 V. The dotted lines in (a), (b), (c), and (d) indicate the position of the first 10 charge exchange peaks based on a plasma potential of 21.8 V and a charge carrier density n of 1.66 x 108 cm -3. The dotted line in the lED of Si2H~- (e) indicates the value of the plasma potential. Note the different scaling factors of the various IEDs. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

can clearly be discerned. From the IED of Si2H+ (Fig. 36e) a time-average plasma potential Vpl of 21.8 + 0.3 V is derived. Using now only one fitting parameter, i.e., the charge carrier density n, all distinct peaks in the IEDs of Ar +, SiH~-, Sill +, and H~- can be fitted with Eq. (48). Performing the fit yields n -- (1.66 4- 0.05) • 108 cm -3. The energy positions are fitted well, as can be seen by comparing the data in Figure 36 with the dotted vertical lines. The sheath thickness as calculated from Eq. (46) is 3.81 4- 0.05 mm. The first charge exchange peak in the Ar + I E D originates at a distance of 100 # m from the electrode, as calculated from Eq. (49). The sixth peak, which is still visible, originates at a distance of about half the sheath thickness from the electrode. It is observed that the SiH~- ion is the most abundant ion, see Figure 36b. The peak around 23 V is the main saddle structure and is asymmetric due to collision processes. Sill + (see Figure 36c) exhibits a 5 times lower peak intensity. The first five charge exchange maxima in the IED of Sill + (Fig. 36c)

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON are clearly visible. The IED intensity is about 5 times lower than for SiH~-. Although the Sill + ion is the main product of dissociative ionization of Sill4 [320], the measured IED intensity of SiH~- is always larger. The H - transfer reaction causes Sill + to be more abundant than Sill +. Also, in the lED of Ar + (Fig. 36a) about six of the charge exchange maxima are clearly visible. The broad overall IED shows that many ions underwent a charge exchange reaction in the sheath. Even H + (Fig. 36d) IEDs can be measured. The low intensity is due to the low partial pressure of hydrogen (it is created by silane dissociation only), and to the fact that the ionization potential of hydrogen is, like that of argon, higher than that of silane. Therefore the number of created hydrogen ions will be small. The maximum in the IED at 11 eV is the first charge exchange maximum of H~-. The energy of this maximum is always somewhat lower than the energy of the fourth charge exchange maximum in the SiH~- IED. This is due to the almost four times higher plasma frequency of the H~- ion (m/e 2 amu/e) than that of the SiH~- ion ( m / e - 30 amu/e). The H + saddle structure is broader than the saddle structures of the other ions, due to the larger ion plasma frequency of H~-. The ions with an energy larger than 25 eV are part of the highenergy side of the main saddle structure. Si2H+ is an ion that is created in the plasma by polymerization reactions. Several pathways may lead to this ion. The first pathway is the dissociative ionization of Si2H6 that is formed in a radical-neutral reaction. The second pathway is the direct formation in the ion-molecule reaction [192] Sill + + Sill4 --+ Si2H+ + H2.

5.3.3.3. Silane-Hydrogen Discharges

The IEDs of several ions in a typical silane-hydrogen plasma are shown in Figure 37. The plasma was created in a mixture of 26 sccm Sill4 and 24.5 sccm He, at a pressure of 0.2 mbar. The applied RF frequency is 13.56 MHz, at a power of 10 W. The self-bias voltage that developed was - 1 1 8 V. The substrate temperature was 250~ The discharge is in the ct-regime. The IEDs of H + and Sill + show distinct peaks. The positions of the peaks are again described with the plasma potential, as deduced from the SieH + lED, and the charge carder density n. The value for Vpl is 23.8 + 0.2 V, and the value for n is (1.11 4- 0.04) x 108 cm -3. The sheath thickness is 4.88 4- 0.10 mm. Under these and under most other conditions, the Sill + lED shows no distinguishable charge exchange maxima. The measured intensity in the SiH~- IED again is higher than that in the Sill + I E D . There are two distinct peaks at low energies in the Sill + lED, and such peaks are observed in most Sill + IEDs. Their energy positions cannot be explained by charge exchange processes. The intensity in the H + IED is higher than in the silane-argon plasma, simply because the partial pressure of hydrogen in this silane-hydrogen mixture is higher.

49

15 10

5 0

15 Sill 2 10

T

03 5

O v ,r'-

~

0

>" 15 03 C 10

- H 2 + 20x

(c)

c --

5

0

,5-Si2H4

+ 4x

10-

_ _~.~

50~

.... ~ 0

5

10 Ion

Fig. 37.

15 20 Energy (eV)

25

30

The ion energy distributions of (a) SiH~-, (b) Sill +, (c) H +, and (d)

Si2H~- from a SiH4-H2 plasma. The conditions are 26 sccm Sill4, 24.5 sccm H 2, 13.56 MHz, 10 W, 0.2 mbar, 250~ Vdc = -118 V. The dotted lines in (b) and (c) indicate the position of the first 10 charge exchange peaks based on a plasma potential of 23.8 V and a charge carder density n of 1.11 x 108 cm -3. The dotted line in the l i D of Si2H4+ (d) indicates the value of the plasma potential. Note the different scaling factors of the various IEDs. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

Charge exchange maxima are in general pronounced in the Sill + lED in discharges at 13.56 MHz. The successive charge exchange peaks tend to overlap each other at higher frequencies. The IED of H + exhibits charge exchange peaks that are still well separated at higher frequencies due to the almost four times higher ion plasma frequency of H~- than that of Sill +. Very different IEDs can be observed in discharges that are operated in the F'-regime and that contain powder. The discharge, in this case, is created in a mixture of 30 sccm Sill4 and 30 sccm He at a pressure of 0.60 mbar. The RF frequency is 13.56 MHz, and the applied power is 33.7 W. The dc self-bias voltage is -32.5 V. The substrate temperature is 250~ The measured IEDs are shown in Figure 38. The plasma potential is determined from the IED of SieH +, and is 49.2 -4- 0.5 V, which is about twice the value in discharges operated in the u-regime. The charge carder density is (9.94-0.3) x 108 cm -3. The sheath thickness is 2.34 4- 0.05 mm. The peaks in both the SiH~- (Fig. 38a) and the SiH~(Fig. 38b) lED are well separated, and the intensity in the region between the charge exchange peaks is relatively low. The

50

VAN SARK Table VI.

Property

Sheath Properties of an Argon-Silane and Two Silane-Hydrogen Discharges a

Ar/SiH 4

H2/SiH 4 (c~)

H2/SiH 4 (y')

Unit

Vpl

21.8 + 0.3

23.8 i 0.2

49.2 + 0.5

n

1.66 4- 0.05

1.11 + 0.04

9.9 -t- 0.3

V

ds

3.81 4- 0.05

4.88 4- 0.10

2.34 4- 0.05

mm

108 cm -3

E0

11.4 4- 0.2

9.8 + 0.2

42.0 • 0.8

kV/m

Fmax

1.93 4- 0.05

1.35 4- 0.04

17.3 4- 0.7

10 TMm -2 s -1

6.7 4- 0.2

5.2 4- 0.2

136 + 4

(EF)max

W m -2

aot and ?" regimes; plasma potential Vpl, charge carrier density n, sheath thickness ds, electric field at the electrode E 0, ion flux rmax, and ion energy flux (eF)max. Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.

,

,

i

7.s Sill3 5.0

.

,

+

,

,

,

2x

.

,

(o)

.

.

high-power, high-pressure discharge (y'-regime) has a twice larger plasma potential, a twice smaller sheath distance, a four times larger electric field E0, and a much larger ion flux and ion energy flux (see Section 6.2.2) than the discharge in the c~-regime.

2.5

5.3.3.4. Charge Exchange Reactions

0

7 ,.sISiH + 2

I,N

.

0 9--

.

( )

5X .

b

.

.

5.0

,

The charge exchange reactions between Ar and Ar + and between H2 and H~- are well known [325,328]" Ar +(f) + Ar (t) ~

,ll

V

-

(t)

H ~ (~ + H 2 -+

Ar (t) + m r +(t)

H~O+ H 2

+(t)

(50) (51)

2.5

2

c:

0

i

I

i

i

I

I

50

60

7.5

5.0

2.5

0 0

10

20 30 40 Ion Energy (eV)

Fig. 38. The ion energy distributions of (a) SiH~-, (b) SiH~-, and (c) Si2H~from a SiH4-H2 plasma in the ?"-regime. The dotted lines in (a), (b), and (c) indicate the position of the first 10 charge exchange peaks based on a plasma potential of 49.2 V and a charge carrier density n of 9.9 x 108 cm -3. Note the different scaling factors of the various IEDs. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

IED of Si2H]- also shows charge exchange maxima on the lowenergy side of the lED, as well as an asymmetrical main saddle structure around 50 eV. The sheath characteristics of the argon-silane and the two silane-hydrogen discharges of which the IEDs were shown above are summarized in Table VI. The sheath characteristics of the 10-W silane-argon discharge and the 10-W silanehydrogen discharge in the or-regime are rather similar. The

where (f) and (t) denote a fast ion or neutral and an ion or neutral with thermal energy. These reactions are called symmetrical resonant charge exchange reactions, as they occur between an ion and the corresponding neutral. The ionization energies of hydrogen (15.4 eV) and argon (15.8 eV) are higher than those of silane (11.6 eV) and disilane (9.9 eV). Therefore, ion-molecule reactions of H~- or Ar + with silane or disilane will result in electron transfer from silane to the ion [190], which leads to dissociative ionization of silane. These known asymmetric charge exchange reactions result in Sill + (0 < x < 3) ions with thermal energy in the sheath; see Table VII [334, 335]. The charge exchange of H + with Sill4 is a major loss process for the hydrogen ions in typical silane plasmas. The cross sections of these asymmetric charge exchange reactions are in general lower than the cross sections of resonant charge exchange processes [134]. For comparison, the cross section of the Ar+-Ar charge exchange reaction is 4 • 10 -15 cm 2, about one order of magnitude larger than the reactions listed in Table VII. The total cross section of charge exchange reactions between Ar + and Sill4 is much smaller than the total cross section of charge exchange reactions between H + and Sill4. The discharge in which the charge exchange peaks of Si2H~are observed is in the ),'-regime. A considerable amount of silane will be depleted and gas phase polymerizations occur, which means that Si2H6 is likely to be present in large quantities. Therefore, Hamers et al. [235] have suggested that Si2H6

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON Table VII.

Charge Exchange Reactions of Ar + and H + with Sill4 a cr (10 -16 cm 2)

Reaction Ar + + Sill 4 -+ Ar + Si + + 2H 2

0.2

Ar + + S i l l 4 - - + A r + S i H + + H 2 + H

0.3

Ar + + Sill 4 --+ Ar 4- Sill2+ + H 2

0.4

Ar + + Sill4 -+ Ar + Sill + + H

2

H~- + Sill 4 --+ H 2 -t- Si + + 2H 2

2

H + + S i l l 4 --+H 2 + S i l l + + H 2 + H

2

H2+ + Sill4 --->H 2 + Sill + + H2

11

H~- + Sill4 -+ H 2 + SiH~- + H

34

a The cross sections cr for reactions with Ar + are determined at thermal energies of the reactants [334]" the cross sections for reactions with H~- are determined at a kinetic energy of the reactants of 1 eV [335]. (Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

of a semiinfinite medium [336]"

(

H + -t- S i 2 H 6 --+ H2 q- S i 2 H + q- H89

(52)

5.4. Ellipsometry Another in situ technique that is used to study deposition in real time is ellipsometry. This optical technique is noninvasive and does not perturb the discharge. In ellipsometry one measures the amplitude and phase of the refected light from a surface. Spectroscopic ellipsometry (SE) allows for the wavelength-dependent measurement of the dielectric function of the material, at submonolayer sensitivity [336]. Spectroscopic phase-modulated ellipsometry (SPME) gives the possibility of fast data recording, and therefore is exploited for kinetic studies of the deposition of a-Si:H [337]. Spectroscopic ellipsometry is a very sensitive tool to study surface and interface morphology in the UV-visible range. The use of IR light allows for the identification of S i - H bonding configurations [338]. Polarization modulation can be done by rotating the polarizer, as is done in rotating-element ellipsometers [339], or by using photoelastic devices [337]. Data acquisition nowadays is fast, which makes real-time measurements of film and interface formation possible: a full spectrum ranging from 1.5 to 5 eV can be measured in less than a second [340-342]. In a typical ellipsometry experiment a sample is irradiated with polarized light, which subsequently is reflected from the sample surface and detected after passing an analyzer. The ratio p of complex reflectances for perpendicularly (s) and parallelly (p) polarized light usually is represented as follows: rn

p = ~ = tan 9 exp(i A)

(53)

rs

with rp and rs the complex reflectances for p- and s-polarized light, and 9 and A two convenient angles. This ratio can be related directly to the complex dielectric function 6 -- 61 + i 62 in the special case of light incident at an angle q~ on the surface

(54)

In case of multilayer structures much more complex expressions result. In the IR one usually presents spectroellipsometric measurements using the optical density D -- ln(~/p), where ~ refers to the substrate before deposition of a film [343]. The presence of a vibrational mode (rocking, bending, stretching) of a silicon-hydrogen bond, for instance, is revealed by a peak at the corresponding energy of that mode in the real part of D versus energy (in cm -1). The contribution of a specific vibration mode to the dielectric function of the film is estimated from the Lorentz harmonic-oscillator expression [344]" - ~

is involved in the charge exchange reaction where Si2H + is created:

[1

~ - s i n 24~ l + t a n 2q5 l + p

51

+

F o92 - o02 - i Fw

(55)

with w0 the frequency of the mode, F its oscillator strength, and F a damping constant. The oscillator strength can be expressed as F -- w2 (~0 - ~oo), where ~0 and Eoo are the high- and lowfrequency dielectric constants, respectively. The vibration mode of a chemical bond will show up as a maximum or minimum in the real part of D versus energy, depending on the dielectric function of the substrate. The interpretation of ellipsometric data is based on the description of the optical properties of the material under study. Effective-medium theories (EMTs) are widely used for this purpose, as they can be applied when materials are heterogeneous and when the size of inhomogeneities is small compared to the wavelength of the light, so that scattering of light can be neglected. In a-Si:H the presence of voids will have an effect on the dielectric function. Also, during deposition the surface will roughen more or less, depending on deposition conditions, which will have a perturbing effect on the polarization of the incident light. An optical model of a substrate with an a-Si:H film could consist of a substrate, an a-Si:H film with voids, and a surface layer of a-Si:H with a large number of voids, which reflects the surface roughness. The general form that is used in EMTs to describe the dielectric function e of an a-Si:H layer with a certain fraction of voids is given by [345] 6=

6a6v -Jr-Krh (fara -+- fvrv)

K~h + (faro + rosa)

(56)

where x is the screening parameter [x = ( I / q ) - 1 and 0 < q < 1], 6h is the host dielectric function, 6a and fa are the dielectric function and volume fraction of the a-Si:H component, and 6v and fv are the dielectric function and volume fraction of the void component. Several approximations can be made. At the end of the seventies Aspnes et al. [346] found that the Bruggeman approximation provided the best description for the data available. Recently Fujiwara et al. [345], with new spectroellipsometric data, confirmed this fact. The Bruggeman approximation [61] defines 6h - - 6. For spherical inclusions q -- 1/3, i.e., tc -- 2, and the dielectric function is isotropic. For

52

VAN SARK

the effect of voids present in the a-Si:H layer we further simplify Eq. (56) by taking ev = 1, and substituting fa = 1 - f v . In a real-time spectroellipsometric measurement in which the kinetics of a-Si:H deposition is studied, trajectories are recorded in the A-qJ plane at various photon energies between 2 and 4 eV. These trajectories can be simulated and fitted to models that represent the growing a-Si:H layer. Canillas et al. [347] have made a detailed study of the deposition of the first few layers of a-Si:H on a NiCr/glass substrate. Similar results are obtained for a c-Si substrate. They have proposed several models to explain the data. One possible model is the h e m i s p h e r i c a l nucleation model, which describes a hexagonal network of spherical a-Si:H nuclei located at an average distance d between them. The growth is represented by an increase in the radii of the nuclei until the nuclei make contact. This results in an a-Si:H layer with a large void fraction, of fv = 0.39 [286]. From the start of the deposition (fv = 1) to the point where the nuclei make contact (fv = 0.39), the dielectric function is calculated using the Bruggeman EMT, and a A - ~ trajectory can be simulated. In another model, the columnar nucleation model, columns of a-Si:H material start to grow from the initial hexagonal network, where the growth is represented by an increase in column radius and height. Again, fv is calculated, and the dielectric function can be deduced from that. A further refinement is that the columns coalesce, and form a dense layer, with a layer of a certain thickness on top, which consists of free standing columns. This extra layer, typically 5 nm in thickness, represents the roughness, and increases with film thickness for typical deposition conditions. A recent study supports the concept of coalescing 3D islands of a-Si:H [340]: directly from the start of the deposition, the thickness of the surface roughness layer increases to 2 nm. At that thickness the islands start to combine into a continuous layer, and the thickness of the surface roughness layer decreases to remain constant at 1.5 nm. Andfjar et al. [246] have used SE to study the effects of pressure and power on the properties of a-Si:H. In their system the ct-/I transition occurs just above 0.2 mbar at a power of 10 W. They found that the density of the material is decreased on going from the ct- to the yl-regime, as is deduced from the decrease in the imaginary part of the dielectric function E2. Collins et al. [342] have used SE to study the effects of hydrogen dilution. On native oxide c-Si substrates they have found that the thickness of the roughness layer is nearly constant at 1.5-2 nm in the case of deposition with pure silane, for a total deposited layer thickness up to 1000 nm. At a dilution factor R = [H2]/[SiH4] of 10, the thickness of the roughness layer decreases from 1.5 to just below 1 nm. In case of R = 20, a similar decrease is observed (with a minimum of 0.3 nm at a bulk layer thickness of 20 nm), but followed by a steep increase to 4.5 nm at a bulk layer thickness of 100 nm, which is consistent with the formation of a microcrystalline film. At values above R = 25, the deposited layer is microcrystalline. These deposition experiments have also been carried out starting on a 300-nm-thick a-Si:H film, prepared with R -----0. Here, the amorphous-to-microcrystalline transition, as evidenced by

the steep increase of the thickness of the roughness layer, occurs at 200 nm for R -- 15 and at 60 nm for R -- 30. Based on these observations, a phase diagram was constructed, showing the amorphous-to-microcrystalline transition as a function of the bulk layer thickness and the dilution factor R. The importance of this phase diagram lies in the fact that a deposition process that is close to the amorphous-to-microcrystalline transition yields material that has excellent optoelectronic properties [348-352]. Spectroscopic ellipsometry has also been applied in the characterization of compositionally graded a-SiC:H alloys [353], where the flow ratio z - [CH4]/([CH4] + [Sill4]) was varied during deposition. The analysis of the SE data on the graded layer prompted the development of a new four-medium model, which consists of the ambient, a surface roughness layer, an outer layer, and the pseudo-substrate. A virtual interface approximation is applied at the interface between outer layer and pseudo-substrate. This model gives the near-surface carbon content and the instantaneous deposition rate, as well as the thickness of the roughness layer. Besides a-Si:H-a-SiC:H interfaces, also p - i interfaces have been characterized, which is possible because the dielectric function changes at the interface [354, 355]. The use of IR in SE allows for the investigation of hydrogen incorporation in a-Si:H. The identification of vibrational modes in nanometer thin films is difficult, due to the weak signals. Nevertheless, Blayo and Drrvillon have shown that monohydride and dihydride bonding configurations can be discerned in 0.5- to 1-nm-thick a-Si:H layers [338], using IR phasemodulated ellipsometry (IRPME). In in situ IRPME studies the real part of D is presented in the stretching mode region of the IR, i.e., 1900-2200 cm -1. Three stretching modes can be revealed in this range, typically around 2000, 2100, and 2160 cm -1, corresponding to Sill, Sill2, and Sill3 bonding configurations. From the evolution of the Sill- and the Sill2 stretching mode with increasing deposited thickness, it was found [356] that the deposited layer is built up from two layers. The bottom layer contains Sill bonds, and linearly increases in thickness with deposition time. The top layer has a nearly constant thickness of 1-2 nm, and contains SiH2 bonds. At the start of the deposition a layer consisting of Sill2 is formed, and its thickness increases with time. At a thickness of about 1 nm, another layer between substrate and the SiH2-containing layer is formed, which contains Sill. The deposition proceeds as the thickness of this latter layer increases with time. Attenuated total reflection IR spectroscopy has revealed that SiH2 and Sill3 surface modes are present even before the SiH2-containing layer is formed [340]. The position of the Sill and SiH2 stretching modes varies with the thickness of the deposited layer. In the first few monolayers the Sill peak shifts upwards by about 20 cm -1, as a result of the very high hydrogen content [340]. At the end of the coalescence phase, the Sill peak is at 1995 cm -1, and its position does not change any more. The substrate used was c-Si with a native oxide layer. In contrast, another study shows an increase in the Sill peak position from 1960 to 1995 cm -1, to-

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON gether with an increase in the Sill2 peak position from 2060 to 2095 cm -1, for thicknesses of the deposited layer between 0 and 500 nm [344]. Moreover, these shifts depend on the deposition temperature and on the substrate. These findings were related to the change in disorder as a function of deposited thickness. The disorder, characterized by the width of the Raman TO peak, decreased with increasing thickness.

R

t-

._o

Luft and Tsuo have presented a qualitative summary of the effects of various plasma parameters on the properties of the deposited a-Si:H [6]. These generalized trends are very useful in designing deposition systems. It should be borne in mind, however, that for each individual deposition system the optimum conditions for obtaining device quality material have to be determined by empirical fine tuning. The most important external controls that are available for tuning the deposition processs are the power (or power density), the total pressure, the gas flow(s), and the substrate temperature. In the following the effects of each parameter on material properties will be discussed.

6.1.1. Plasma Power When the plasma power (density) is increased, the deposition rate is increased monotonically up to the point where the gas flow rate becomes the limiting factor [81,357] (see Figure 39). This deposition rate increase comes with a number of disadvantages, including poor film quality and powder formation. At low power levels a large part of the Sill4 remains undissociated [303], and the corresponding films contain only silicon monohydrides, inferred from FTIR measurements. At high power levels the Sill4 is strongly dissociated, and the films contain a large amount of Sill2 [358]. The microstructure parameter R* is high. The high power levels also lead to columnar microstructure, which is accompanied by high spin densities [359, 360]. Experimental results obtained in ASTER show similar trends, as is shown in Section 6.2.3. The electrical properties (dark conductivity and photoconductivity) are reported to first decrease and then increase upon increasing power [361]. The optical bandgap increases with increasing power, due to the increase of the hydrogen content [63, 82, 362, 363]. However, at very high power levels, microcrystalline silicon is formed [364], which causes the hydrogen content (and, consequently, the bandgap) to decrease. As a result of the deterioration of film properties with increasing power levels, to obtain device quality material the use of low power is required, albeit with a concomitant low deposition rate. Increasing the deposition rate without altering the device quality material properties is a large research challenge.

m

(/1 0 Q. "13

rate

6. RELATION BETWEEN PLASMA PARAMETERS AND MATERIAL PROPERTIES 6.1. External Parameters

53

power density

Fig. 39. Schematic representation of the influence of power density and flow rate on the deposition rate. [After A. Matsuda, J. Vac. Sci. TechnoL A 16, 365 (1998).]

6.1.2. Total Pressure The deposition rate as a function of total pressure shows two different dependences. In the low-pressure, or supply-limited, regime the deposition rate is proportional to the pressure, while in the power-limited regime it is constant [365]. At low pressure the film quality is not good. The supply of Sill3 radicals, needed for high quality films, is depleted easily, and Sill2 and Sill radicals can reach the substrate. Moreover, ion bombardment may be too severe. Therefore, higher pressure levels are required. Usually the operating pressure (in combination with electrode distance and power lever) is set so that one works just above the Paschen curve (see Section 3.2.4). The pressure should not be too high, otherwise gas-phase polymerization occurs [55]. These yellow powders (which turn white upon oxygen exposure) are to be avoided, as they increase the downtime of deposition systems due to clogging of the pumps. At normal working pressures it has been found that the hydrogen content and dihydride content increase with the pressure [81 ].

6.1.3. Gas Flow The gas flow rate is usually presented as a deposition parameter; however, it is much more instructive to report the gas residence time [6], which is determined from the flow rate and the geometry of the system. The residence time is a measure of the probability of a molecule to be incorporated into the film. The gas depletion, which is determined by the residence time, is a critical parameter for deposition. At high flow rates, and thus low residence times and low depletion [303], the deposition rate is increased [357, 365] (see Figure 39) and better film quality is obtained, as is deduced from low microstructure parameter values [366].

6.1.4. Hydrogen Dilution The addition of a hydrogen flow to the silane flow often is used to improve the material quality of the deposited film. Moderate hydrogen dilution of silane (0.15 < [SiHa]/([SiH4] + [H2]) < 1) has been found to yield a lower optical bandgap, a

54

VAN SARK

lower activation energy, a lower total hydrogen content, a lower microstructure factor, and a higher photoresponse [ 15, 82, 367369]. Unfortunately, also the deposition rate is reduced. Device quality material is obtained for values of [Sill4]/([Sill4] + [H2]) between about 0.3 and 0.7. Moreover, an improvement of the uniformity of deposition over a 10 x 10-cm 2 substrate area has been found as well [370]" for [SiH4]/([SiH4] -k- [H2]) - 1/3 the variation in thickness amounted to only 1.5 %. In the intermediate regime of hydrogen dilution (0.05 < [SiH4]/([SiH4] + [H2]) < 0.15) the hydrogen content increases again, as well as the bandgap, while the microstructure factor remains low [369]. In this regime wide-bandgap a-Si:H can be obtained with better optoelectronic properties than a-SiC:H. Highly diluted silane ([SiH4]/([SiH4] + [H2]) < 0.05) causes the deposited films to be crystalline rather than amorphous, due to selective etching of strained and weak bonds by atomic hydrogen [371,372]. Interestingly, using hydrogen dilution to deposit a-Si:H films "on the edge of crystallinity" [ 154, 349] resulted in improved material stability. These materials are also referred to as polymorphous silicon (pm-Si) [373,374]. The admixture of a small amount of silane to a pure hydrogen plasma drastically changes the plasma potential, the dc self-bias voltage, and the charge carrier density. Hamers [163] has found a doubling of the carrier density by changing [SiH4]/([SiH4] + [H2]) from 0 to 0.1. The dc self-bias becomes more negative by 25%, and the plasma potential is lowered by about 10-15 %. For fractions from 0.1 to 0.5 these parameters remain about constant. The parameters change again when [SiH4]/([SiH4] + [H2]) is larger than 0.5.

i

25

'

i

i

i

'

A A1 D A2

20

.d 15

!

(a)

-

9

A3

9

P1

v

Z

= I0

-..% 0

,

I

,

I

,

I

'

I

,

I

(b)

0.9 0.7 0.5 0.3

0.1 I

37

9

9 (c)

36

7 I~ 35 o

c~ F.-,

34

33 ,

6.1.5. Substrate Temperature The substrate temperature is a very important deposition parameter, as it directly affects the kinetics of ad- and desorption of growth precursors, surface diffusion, and incorporation. Actual substrate temperatures may differ from substrate heater setpoints. Calibration of temperature readings is needed, so as to report the correct substrate temperature. The deposition rate is nearly independent of temperature, while the total hydrogen content, the microstructure parameter, and the disorder decrease with increasing temperature [375]; see also Figure 40 [84, 85]. As a consequence, the optical bandgap decreases as well. An optimum deposition temperature around 250~ exists, such that the material contains only Sill bonds. At higher temperatures the hydrogen evolution from the film causes lowering of the hydrogen content, and leads to higher defect densities. The photoconductivity and photoresponse also have an optimum value around 250~ 6.1.6.

e-y'

Transition

As was shown above, the properties of the discharge will change with process parameters such as the process pressure, the RF power, and the excitation frequency. Two different plasma regimes can be distinguished: the c~- and the y'-regime [184, 244-246, 248]. In the transition from the or-regime to

I

1 O0

,

I

,

200 Ts

I

300

i

I

400

,

I

500

(~

Fig. 40. The influence of deposition temperature on (a) the hydrogen concentration, (b) the microstructure parameter, and (c) the Raman half width F/2. The labels A and P refer to the ASTER and the PASTA deposition system. Series A1 was prepared from a SiH4-H2 mixture at 0.12 mbar. Series A2 and A3 were deposited from undiluted Sill4 at 0.08 and 0.12 mbar, respectively. Series P1 was deposited from undiluted Sill4. (From A. J. M. Berntsen, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

the F'-regime a change occurs in plasma properties. This includes the plasma impedance, the optical emission from the plasma [184], and the dc self-bias voltage at the powered electrode [245] in a reactor with electrodes of unequal size. An increase in the deposition rate of the film and a change of the film properties is observed near the transition from the or- to the y'-regime [245]. As an example, Figure 41 shows the deposition rate as a function of pressure, for various hydrogen dilution ratios [376]. It can be seen that higher hydrogen dilution pushes the c~-y' transition away, as it were. Other examples are shown in Figure 46 and Figure 64. The transition is assumed to be initiated by the formation of larger particles in the gas phase [246, 322]. Negative ions [377] are trapped in the plasma bulk, and recombine with silane radicals to become large negative ions (or small clusters). The charge of these particles can

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON 0.6

0.5

'

I

'

I

'

I

'

I

'

I

In view of the above, instead of avoiding powder formation regimes in discharges, careful powder management involving optimization of the ratio of radicals and silicon nanoparticles arriving on the substrate has been proposed [379].

.H2:SiH4dilution r a t i o --'--0:1 higher m / / m - - - ~ ~ - --o-1:2 dilution~/ jj.m......~ .

o4

/,

,--

--A--

"-'~

"

,2,

i

0.0

-v.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

o

// ~

1.~~

--V--

,

0.0

6:1 8:1

--zx--

"~ 0.3 -

o

/

4:1

.

.

.

.

~.

.

I

0.4

,

55

I

0.8

,

I

1.2

,

I

1.6

~

I

2.0

pressure (mbar)

Fig. 41. The deposition rate as a function of deposition pressure for different ratios of hydrogendilution (0:1 < H2 : Sill4 < 10: 1). The depositiontemperature was 240~ the Sill4 flowwas 600 sccm, and the excitation frequency was 13.56 MHz. The arrowindicates increasing hydrogendilution. The e-regime is below the dotted line, the yt above it. [After R. B. Wehrspohn, S. C. Deane, I. D. French, I. Gale, J. Hewett, M. J. Powell, and J. Robertson, J. Appl. Phys. 87, 144 (2000).]

fluctuate, and can become positive. The clusters coalesce, and when the size of the coagulates is sufficiently large the charge builds up and remains negative. They grow further by deposition of a-Si:H on their surface. These particles are often referred to as powder or dust [378]. Due to the large amount of negative charge (up to hundreds of electrons) on them, the free electron density drops. Therefore, the electron temperature has to increase in order to sustain the discharge. The discharge becomes more resistive, causing more efficient power coupling into the plasma [322]. Most of these phenomena are observed in discharges with the conventional 13.56-MHz excitation frequency, but they can also be observed at higher excitation frequencies [301 ]. Interestingly, it has been argued that nanoparticulate formation might be considered as a possibility for obtaining new silicon films [379]. The nanoparticles can be crystalline, and this fact prompted a new line of research [380-383]. If the particles that are suspended in the plasma are irradiated with, e.g., an Ar laser (488 nm), photoluminescence is observed when they are crystalline [384]. The broad spectrum shifts to the red, due to quantum confinement. Quantum confinement enhances the bandgap of material when the size of the material becomes smaller than the radius of the Bohr exciton [385, 386]. The broad PL spectrum shows that a size distribution of nanocrystals exists, with sizes lower than 10 nm. Moreover, it was found that incorporation of nanoparticles about 8 nm in diameter in a-Si:H led to improved properties, the most important one being enhanced stability against light soaking and thermal annealing [387]. A later study revealed a typical crystallite size of 2-3 nm, with a hexagonal close-packed structure [388]. Diamond structures can also be observed [389]. Hence the name polymorphous silicon is justified.

6.1.7. Other Deposition Parameters Depending on the flow pattern in the reactor, the depletion of gases can cause nonuniform deposition across the surface of the substrate. As is depicted in Figure 4, the gas usually is introduced at the top of the cylindrically symmetric reactor, and it flows into (and out of) the discharge region from the sides. Many other configurations exist, e.g., a radial flow reactor, where the gas flow is introduced underneath the powered electrode, and pumped away through the center of this electrode. A reverse radial flow reactor, where the gas flow is introduced from the center of the powered electrode and pumped away at the sides, has also been proposed [ 117, 370]. The best solution to overcome depletion is to inject the gas directly via a showerhead at the grounded electrode [173]. Meiling et al. [82] have investigated the effect of electrode shape. They found that in the case of a ring electrode, less dense material with a larger bandgap was obtained than in the case of a flat-plate electrode. In addition, the ring electrode induces an extra nonuniformity in thickness, as a result of the nonuniform electric field between the powered and the grounded electrode. Further, the area ratio of grounded to powered electrode in the case of the ring electrode is much higher, which yields higher dc bias voltages and higher ion bombardment energies. Hence, a ring electrode should not be used. Many different substrates are used for a-Si:H deposition. Usually Coming 7059 glass [390] and crystalline silicon are used for materials research, as both have similar thermal expansion coefficients to a-Si:H. Devices are mostly made on glass coated with transparent conductive oxide (TCO). As TCO coatings one uses indium tin oxide (ITO), fluorine-doped tin oxide (SnO2 :F), and zinc oxide (ZnO). Ion bombardment may lead to the reduction of the ITO coating [391 ], while ZnO-coated glass is much more resistant to this. Polymer films have been used as substrates for flexible solar cell structures. They require lower deposition temperatures than glass or stainless steel. It has been found that various material properties are thickness-dependent. Raman experiments show a dependence on the type of substrate (glass, c-Si, stainless steel, ITO on glass) and on the thickness (up to 1/~m) of the films [392, 393]. Recent transmission electron microscopy (TEM) results also show this [394]. This is in contrast to other results, where these effects are negligible for thicknesses larger than 10 nm [395, 396], as is also confirmed by ellipsometry [397] and IR absorption [398] studies. 6.2. Internal P a r a m e t e r s

6.2.1. The Role of lons There are many effects possible due to the interaction of ions with a surface during deposition, e.g., the enhancement of

56

VAN SARK 0.08

0.8

'

,

'

i

'

i

'

S in a-Si:H 0.06

0.6

" -

8 ~0.04

~

0.4

0

lOeV ....

0.02

50 eV

"

0.2

0.00

0.0 0

20

40

60

80

d e p t h (A)

(a)

-

0

i

5

,

10

"

"

'r . . . . . 15

20

d e p t h (A)

(b)

Fig. 42. Simulated depth distributions of (a) hydrogen and (b) silicon ions incident on a-Si:H with energies of 10 and 50 eV. Note the difference in depth scale. Simulations were performed with TRIM92.

adatom diffusion, ion-induced desorption, displacement of surface or subsurface atoms, sticking or subsurface trapping of the ions, sputtering, and implantation in subsurface layers (subplantation). Light and slow ions are able to excite Sill surface bonds vibrationally, which may enhance the surface migration or desorption of weakly physisorbed species, such as Sill3. For the nonmobile chemisorbed species, such as Sill2, to be desorbed, a higher ion mass and/or energy is needed. At the same time, however, this may cause subplantation and resulting collision cascades or thermal spikes, which will lead to local defects and poor electronic properties [ 173]. Several views exist on the exact processes that occur during the deposition of a-Si:H. Ganguly and Matsuda [399] explain the growth of a-Si:H using a surface diffusion model, in which ions are ignored. Perrin [211] has formulated a model of the RF discharge in which, also, ions are not thought to be of importance to the growth. On the other hand, Vep[ek et al. [400] introduce the term ion-induced dehydrogenation, and Heintze and Zedlitz [249, 280] show the importance of ion fluxes in plasmas, which are excited with very high frequency (VHF) electrode voltages. In addition, molecular dynamics studies of low-energy (10 eV) particle bombardment on crystalline silicon surfaces show surface dimer bond breaking [401 ] and the formation of interstitials [402], among other effects. Few measurements are available on the ion energies and fluxes in the sheath of a discharge under typical deposition conditions [280, 403-405]. The influence of ion bombardment on defect density [405], mobility [404], and electronic properties [403,406] has been reported. The dependence of stress on the ion bom-

bardment has been suggested by many authors [284, 376, 407, 408]. In the field of PECVD of amorphous or diamondlike carbon, it is assumed that ions are of prime importance for the formation of dense material [409]. Others also stress the importance of ion bombardment on film properties [410--412]. In addition, in electron beam deposition of amorphous silicon it was shown that the formation of microvoids is inhibited when Ar + assistance is used during deposition [413]. It was found that the energy per atom is the decisive parameter instead of the ion/atom ratio. Supplying 12 eV per Ar + ion is sufficient for annihilation of all microvoids. As a further example, calculation of projected ranges of low-energy particles in a solid can be performed with the Monte Carlo simulation program TRIM (transport of ions in matter) developed and supplied by Ziegler et al. [414]. The results of simulations with TRIM92 (TRIM Version 1992) of hydrogen and silicon ions incident on a-Si:H (CH = 0.1) with energies of 10 and 50 eV, respectively, are presented in Figure 42. The projected ranges of hydrogen (1 nm at 10 eV, 2.5 nm at 50 eV) are much larger than those of silicon (0.3 nm at 10 eV, 0.75 nm at 50 eV). Clearly, these low-energy ions influence the surface and subsurface layers of the deposited film. It is difficult to isolate the effect of ion bombardment on material properties. An external bias can be applied to the discharge in an attempt to study the effect of varying acceleration voltages over the sheath. However, this modifies the whole potential profile, and consequently the discharge chemistry. Conclusions drawn from such experiments obviously are misleading. It has been demonstrated in a multipole discharge

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON ,

150

i

-(o)

i

.

i 9 i "..." i ~..:"

E E

~

,

.

100

.

i

,

-

i

.:. :":". 9 :".'"

i i i

to E

u

57

,

50

c-

effect is clearly demonstrated in Figure 43: the thickness (deposition rate) is enhanced by about a factor of two just behind the aperture. The deposition conditions were chosen to yield good quality material. From geometrical modeling it was found that under these discharge conditions the contribution of ions to the deposition was 10% [419], which confirms the estimate from Kae-Nune et al. [311 ].

I

0 150

I I

(b)

i i

.I

i

6.2.2. T h e I o n F l u x

i ..: ":,.

In order to study the influence of ions on the deposition process, a reliable quantification of the ion flux and energy is imperative. This flux cannot be determined directly from the detected number of ions in an IED as measured by means of QMS, for three reasons [332]. First, the orifice size decreases during subsequent measurements due to deposition of a-Si:H on the edges of the orifice. Second, due to the limited acceptance angle of the mass spectrometer system, only a fraction of the ions that arrive at the substrate is actually detected. This fraction depends on the type and number of interactions that an ion experiences while traversing the sheath, and also on the ion species itself. In addition, this implies that the mean kinetic energy of the impinging ions cannot be determined. Third, the ion flux from a typical silane plasma consists of many different ions. All ions must be taken into account in the quantification of the ion flux. Another approach is needed [163, 301,332], and one follows from the definition of the ion flux V, i.e. the product of the density of the ions ni and their mean velocity Vi" F -- ni-vi. The contribution of electrons to the time-averaged charge carrier concentration at the electrode n can be neglected, as the electron current towards the electrode is peaked in a very short time during the RF period. We thus have n i - n. A further assumption is that there are no collisions in the sheath. As a result of this, the velocity ~i is equal to the maximum velocity, Vmax, that the ions gain. The value of Vmax follows from the time-averaged plasma potential e Vpl" 1)max -" v/2e Vpl/m, with the average mass of the ions. If the ions reach the electrode without collisions in the sheath, the IED will show a distinct peak at eVpl; see e.g. the IED of SizH + in an c~-silane discharge (Figure 37). The maximum ion flux Fmax at the electrode is thus estimated to be

I

E E

~

O3 O3

100

E

u

50

t'-"

'.":""

i

I

i

9

i i

. . . "'"

i I

-500

I

:

I

i

0

500

-'~.........--

x (micrometer) Fig. 43. Measuredand simulated thickness profiles on the substrate behind the slit for a film deposited under discharge conditions that typically yield good material properties: (a) along the length of the slit, (b) across the slit. The vertical dashed-dotted lines indicate the boundaries of the apertures. The dotted lines represent the measuredprofiles, the solid lines the simulated profiles. The dashed lines are the simulated deposition profiles of the radicals. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.) at low pressure (

--

..2

~1

10

0 3-

t

i

i

t

i

0

0 0.6

(b) E

~2

-

&

0.2

1-

t

3O -

i

I

0.0

(C)

(f)

4.4

y,

-•.E20

_

4.2

2:::) ,eL

4.0 10

3.8 0 0

i

i

10

20

i

.,30 P (W)

i 40

i 50

0

.30 P (W)

Fig. 44. Plasma parameters as deduced from the IEDs and material properties as a function of power delivered to the SiH4-Ar discharge at an excitation frequency of 50 MHz and a pressure of 0.4 mbar: (a) the plasma potential Vpl (circles) and dc self bias Vdc (triangles), (b) the sheath thickness ds, (c) the maximum ion flux Fmax, (d) the growth rate rd, (e) the microstructure parameter R*, and (f) the refractive index n2 eV. (Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

the ions (and the flux) is overestimated by at most a factor of two. Also, the ion kinetic energy flux overestimates the real energy flux if collisions take place in the sheath. However, in many collisions the kinetic energy is distributed over the different particles. For instance, in a charge exchange process, the original ion is neutralized, but retains its kinetic energy. The newly formed ion will gain the energy that the neutralized ion would have gained in the rest of the trajectory. The two particles will transport the total amount of kinetic energy corresponding to the plasma potential to the surface [ 163]. In order to express the importance of the ions to the growth process quantitatively, two related quantities can be defined: the fraction of arriving ions per deposited atom, Ri, and the kinetic energy transferred by ions per deposited atom, Emax. These quantities are used in ion-beam-assisted deposition in order to relate material properties to ion flux and energy [421]. Their definition is Ri :

Emax =

rmax prd (EF)max

prd

(59) (60)

where the number of deposited atoms per unit time and per unit area is prd, with p the atomic density of the amorphous network (5 • 1022 cm -3) and rd the growth rate.

6.2.3. Relation between Ion Flux and Material Quality A systematic study of the role of the ions in the deposition process and their influence on the quality of the layers has been performed by Hamers et al. [163,301,332] in the ASTER deposition system. More specifically, a study has been made on the relation between the plasma parameters and the material properties in both the or- and the yt-regime at typical deposition conditions. Here, the results for power and pressure variation are summarized. Details can be found elsewhere [163, 301, 332]. First, results on power variation are described, for two different discharges: (1) a silane-hydrogen discharge in the powder-free u-regime, and (2) a silane-argon discharge in both the c~- and the powder-producing y1-regime. The process conditions of the series in silane-hydrogen are an excitation frequency of 13.56 MHz, a pressure of 0.20 mbar, gas flows of 30 sccm Sill4 and 30 sccm H2, and a substrate temperature of 250~ The power was varied between 5 and 20 W. It was found that the absolute magnitude of the dc selfbias voltage increases linearly with increasing power, and the trend of the ion flux is similar (0.8 x 1018 m -2 s -1 at 5 W, and 2.1 x 1018 m -e s -1 at 20 W). This linear relationship between Vdc and growth rate had been observed earlier [15, 151,422], and in practice can even be used as a calibration curve. The

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON i

|

w

h

i_.

|

(o)

0.40

0.50 0.20 0.10

0.00

I

I

10> ~)

6 E

LJ

2 0 0

I

I

10

20

'1 i

'

I

I

I

50

40

50

L_

4

(b)

'

8-

59

P (w) Fig. 45. (a) The ratio of the ion flux to the deposition flux, R i , and (b) the ratio of the energy flux to the deposition flux, Emax, as a function of power delivered to the SiH4-Ar discharge at an excitation frequency of 50 MHz and a pressure of 0.4 mbar. (Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

plasma potential was 22.7 V at 5 W and was only 3 V higher at 20 W. In this series only two films were deposited, one at 10 W and one at 15 W. The refractive index in both cases was 4.33, representative of good material. The fractions of arriving ions per deposited atom, Ri, as defined in Section 6.2.2, are 0.26 and 0.20, respectively, while the kinetic energy transferred by ions per deposited atom, Emax is about 5 eV in both cases. The process conditions of the series in silane-argon are an excitation frequency of 50 MHz, a pressure of 0.40 mbar, gas flows of 30 sccm Sill4 and 60 sccm Ar, and a substrate temperature of 250~ The power is varied between 3 and 50 W. Plasma parameters deduced from measurements of the IED and material properties are shown in Figure 44 and Figure 45. The discharge changes from the u-regime to the ),t-regime around 10 W, which can best be observed by the decrease of the dc selfbias and an increase in sheath thickness (see Figure 44a and b). The bias is very low in the y~-regime, typically between - 2 and - 1 V, indicative of a more symmetrical discharge. The plasma potential increases with increasing power and tends to saturate at the highest powers. Visual inspection of the discharge shows that the optical emission from the plasma becomes brighter and more homogeneously distributed on going from the ct- to the yl-regime. In the ct-regime the emission intensity is highest at the boundary between plasma bulk and sheaths. The growth rate, plotted in Figure 44d, increases with increasing power, which is ascribed to the higher degree of dissociation in the discharge. The growth rate reaches a maximum around 30 W, and decreases somewhat at higher powers: the growth rate then is limited by the flow rate. It has been estimated that about 60% of the silane is used for deposition [163];

the rest may well (partially) partake in the processes that lead to the creation of powder. This yellow powder is always observed in the reactor after experiments performed in the yf-regime. It is always found outside the plasma confinement, and never on the substrate. At the transition from the ct- to the yl-regime the enhancement of the growth rate (Fig. 44d) is larger than the change in ion flux (Fig. 44c), as shown in Figure 45a, where Ri is plotted. An Ri-value of 0.25 or larger is commonly found in the ctregime, whereas Ri is typically 0.10 or lower in the y~-regime. In addition, the amount of kinetic ion energy per deposited atom, Emax, shows a minimum of about 2 eV between 10 and 20 W; see Figure 45b. The microstructure parameter is low in the material deposited at the lowest power (Fig. 44e); it increases rapidly with increasing power up to 20 W, and then decreases again with further increasing power. The opposite holds for the refractive index (Fig. 44f), although that is less clear. A high value of the microstructure indicates a large fraction of S i - H 2 bonds in the material, corresponding to an open material structure and a low refractive index. From a comparison between the behavior of the microstructure parameter R* (Fig. 44e) and the ion kinetic energy per deposited atom, Emax (Fig. 45b), it can be concluded that a oneto-one relation appears to exist between the relative strength of the ion bombardment, expressed in terms of Emax, and the microstructure parameter. This has also been suggested by others [246, 422]. Both the dark conductivity and the photoconductivity of the sample deposited at 40 W have been measured. The photoconductivity has been measured under AM 1.5 conditions. The dark conductivity and photoconductivity of the material deposited at 40 W are 1 x 10-10 and 1.2 x 10 - 4 ~ - 1 c m - 1, respectively. These values are indicative of good electronic properties, such as a low defect density and a high carrier mobility. The improvement of electrical properties of the deposited films at high RF power densities has also been reported by Nishikawa et al. [361]. The influence of power variation on the material properties is in agreement with the trends observed by Andfijar et al. [246], who studied the c~-g t transition in pure silane discharges at 13.56 MHz. Further, this has also been observed for pure silane discharges at 50 MHz by Meiling et al. [423]. The c~-y' transition can also be induced by changing the process pressure. At low pressures the discharge is in the c~-regime. At a certain pressure it changes to the gt-regime on increasing the pressure by only 0.02-0.04 mbar. The experiments presented here span a pressure range from 0.08 to 0.5 mbar, and, as above, plasma properties that are deduced from IED measurements are compared with material properties. The other process conditions are an excitation frequency of 50 MHz, a power level of 10 W, gas flows of 30 sccm Sill4 and 30 sccm H2, and a substrate temperature of 250~ Data are summarized in Figure 46 and Figure 47. The self-bias voltage decreases quite rapidly in magnitude with increasing pressure, as shown in Figure 46a. The plasma potential slowly increases with pressure

60

VAN SARK 9

4O

,

.~

.

,

.

.

.

.

40

18 3O

2o~

20

>-

10 0 4

12 I

I

I

I

I

0

I

-(b)

I

I

I

0.2

I

_"5

I

(f)

0.4

E E3

~'A" 6 E

~-- 14

10

I

0.0

I

5OO

-

n~

.

250

O

0

v

i_ 4

9

.

-250 I

I

I

I

I

_(d) n.

I

I

I

I

I

4.4

1.0

). 4.2 4.0

0.5

3.8

0.0

0.1

0.2

0.3 p (tabor)

0.4

0.5

i

i

0.1

0.2

i

0..3 p (tabor)

i

i

0.4

0.5

Fig. 46. Plasma parameters as deduced from the IEDs and material properties as a function of process pressure of a SiH4-H2 discharge at an excitation frequency of 50 MHz and a power of 10 W: (a) the plasma potential Vpl (circles) and dc self-bias Vdc (triangles), (b) the sheath thickness ds, (c) the maximum ion flux Fmax, (d) the growth rate rd, (e) the hydrogen content, (f) the microstructure parameter R*, (g) the internal stress ~r, and (h) the refractive index n 2 eV. (Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

up to a pressure of 0.20 mbar and decreases towards the highest pressures (Fig. 46a). As both dc self-bias and plasma potential decrease, Vrf will also decrease [ 134]. Such a decrease has been measured by others [ 184, 245]. The sheath thickness falls from around 3 to 2 mm at around 0.2 mbar (Fig. 46b). The ion flux (Fig. 46c) is rather constant in the region up to 0.2 mbar, whereas it is nearly doubled on the high-pressure side. A slight decrease of the ion flux in the c~-regime has been observed in 13.56-MHz discharges by Roca i Cabarrocas [403]. The growth rate increases by about a factor of 4 upon a pressure change from 0.2 to 0.3 mbar (Fig. 46d). The fraction Ri is shown in Figure 47a to be around 0.25 in the c~-regime, whereas it drops to about 0.10 at pressures higher than 0.3 mbar, because the deposition rate increases a factor of 2.5 more than the ion flux. Since the plasma potential decreases with increasing pressure, the ions arriving at the film surface are expected to have a lower energy per ion in the y'-regime than in the a-regime. This is clearly seen in Figure 47b, where Emax changes from about 5 eV at pressures below 0.3 mbar to about 2 eV at the higher pressures. As can most clearly be seen in Figure 46d, the ot-y t transition occurs at a pressure of about 0.3 mbar for these experimental conditions. The impedance of the plasma, as well as the optical emission from the plasma, changes on going through

the transition. The depletion of Sill4 during deposition was already shown and compared with the deposition rate in Figure 31. The effect of the c~-y' transition on the partial pressures of disilane and trisilane was already presented in Figure 32 (see Section 5.3.1). The amount of silicon in these higher-mass neutral species is only about 5% of the total amount of silicon in Sill4, as can be concluded from the measurements of the partial pressures of these gases. The transition however effects the production of these higher silanes. The increase of the partial pressures is larger than the increase in depletion. This means that the amount of these higher silanes produced per consumed quantity of silane increases at the higher pressures. The material properties are also affected on going through the c~-y' transition. The hydrogen content is about 12% up to 0.2 mbar, and increases to over 16% at higher pressures (Fig. 46e). The increase in the hydrogen content occurs at a lower pressure than the increase in deposition rate, much like the behavior of the ion flux. The microstructure parameter is lower than 0.1 up to a pressure of 0.3 mbar, and is around 0.3 above this pressure (Fig. 46f). The internal stress in the layers is about 500 MPa compressive at low pressures, changes to a tensile stress around 0.3 mbar, and remains tensile at 200 MPa at higher pressures (Fig. 46g). The refractive index is around 4.30 up to a pressure of 0.3 mbar, but decreases towards the high-

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON |

61 |

|

4.4

0.40 g

~ L_9

030

> 4.2

E 0.20 _

o O I

L...

4.0

0.10 i

0.00

I

I

I

3.8

I

v

9

I

'

(b)

8

9

I

0.6

10 >

(o)

2

O.4

6 E

w

-'6 0.2

4

o

.2 t i

0.1

i

0.2

I

0.3 p (mbar)

i

I

0.4

0.5

0

A i

i

i

5

10 E,.,.,o,, (eV)

15

20

Fig. 47. (a) The ratio of the ion flux to the deposition flux, Ri, and (b) the ratio of the energy flux to the deposition flux, Emax, as a function of process pressure of a SiH4-H2 discharge at an excitation frequency of 50 MHz and a power of 10 W. (Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

Fig. 48. Materialproperties as functions of Emax at 250~ (a) refractive index n2 eV, and (b) microstructure parameter R*. The closed circles represent pure silane and silane-hydrogen plasmas. The open circles refer to silane-argon plasmas. Lines are to guide the eye. (Adapted from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

est pressures (Fig. 46h). In summary, the material becomes of poorer quality at higher pressures. The gt-regime is associated with the formation of particulates in the plasma [322]. However, these particles are assumed not to be incorporated in the film and thus not to be the direct cause of the different material properties. In the presented range of pressure variation, Hamers [ 163] also has studied the influence of the substrate temperature on the plasma and the material. It was found that in the temperature range of 200 to 300~ the trends of the bias voltage, the plasma potential, and the growth rate as functions of pressure all are the same, while the absolute magnitude depends on the temperature. The trends in material properties are similar to the ones reported above: at a temperature of 200~ the material quality is worse than at higher temperatures. The c~-Vt transition occurs at a lower pressure than at a temperature of 250~ This has been observed before [248]. In all the experiments reported here it is observed that the value of Ri is rather constant at a value of 0.25 in the c~-regime, whereas in the v'-regime it typically amounts to 0.10. In other words, if all the Si atoms that originate from ions contribute to the deposition, the contribution of ions to the deposition in the c~-regime is 25%, and in the y~-regime 10%. The observation that these values are rather constant in each regime strongly indicates that the deposition rate is limited by the ion flux. In an attempt to relate ion bombardment to material structure it is very illustrative to correlate the refractive index n2 eV and the microstructure parameter R* with the kinetic ion energy per deposited atom, Emax. The data presented above for various discharges (pure silane, silane-argon, and silane-hydrogen) at

a temperature of 250~ are thus summarized in Figure 48. It is very clear that the structural properties of the layers are poor (small n2 eV and large R*) for small Emax. The structural properties improve rapidly with increasing Emax up to a value of about 5 eV. All samples with Emax below 5 eV are deposited in the g'-regime. Above 5 e V a dense network with only a small fraction of S i - H 2 bonds is produced. The structural properties do not change further with increasing Emax. The role of the substrate temperature can be inferred from a plot of n2 eV and R* versus Emax at the three temperatures mentioned: 200, 250, and 300~ (see Figure 49). At a substrate temperature of 200~ the refractive index is lower at every Emax than at a substrate temperature of 250~ Further, the threshold at which dense material is obtained is observed to be a few electron volts higher than at 250~ The refractive index at 300~ is high and independent of Emax. The microstructure parameter R* as a function of Emax behaves similarly for material deposited at 200 and at 250~ At 300~ the value of R* is less than 0.1 and independent of Emax. It is noteworthy to show the relation between the internal stress and Emax as a function of temperature (Fig. 50). The stress is linearly dependent on Emax (between 1 and 7 eV) with a slope of about 175 MPa/eV for material deposited at 200 and at 250~ For the 300~ data series this relation is shifted upwards by about 600 MPa, and at values of the stress larger than about 1000 MPa (Emax was about 4.5 eV) the deposited layers started to peel off from the silicon substrate directly after exposure to air. In summary, the ion bombardment clearly is needed to create or promote a dense amorphous network at temperatures up to 250~ At higher

62

VAN SARK ,

4.4

--

4.2

--

,

,

(o) 9

>

I

i--.--

~

~

J

.... .......-'""

A

...a~ ....... ..........~"

t"

4.0 .....

&

,3.8

I

I

I

300~

9

250~

0

200~ I

&

_

(b)

0.40 2

0.30

A

A

o.2o

o 0.10 (..)

ooo

": 0

i , ,,o 2

4 6 Emo, (eV)

!

8

10

Fig. 49. Material properties as function of Emax at three temperatures: (a) refractive index n 2 eV, and (b) microstructure parameter R*. Lines are to guide the eyes. (Adapted from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.) I

800

..-~

400

.

i....i ~ --

.~ ..

9

200

&..-"

"" ..1~"

600 o rl

I

200~ o 250~ 9 300~

_ 9

..

..

_,,..9

..~~

0"]

E~ .~-'"

-200 -

9..-'~ + ,"

0

A"

I

I

I

I

2

4

6

8

10

Emo,, (eV) Fig. 50. Internal stress as a function of Emax at three temperatures, for the pressure series in Figure 46 in the SiH4-H2 discharge running at an excitation frequency of 50 MHz and a power of 10 W. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

temperatures energetic ion bombardment results in too high intrinsic stress.

6.2.4. lon-Surface Interactions The different processes in which the ions might well be involved at the surface can be indentified on the basis of their chemical reactivity at the surface and the amount of energy they transport towards the surface. It is assumed that Sill3 radicals are responsible for the production of deposition sites at the hydrogen-covered surface when no ions are present [ 138]. If ions contribute to the depo-

sition process, a higher deposition rate has been reported; see e.g. [419]. The fraction of arriving ions per deposited silicon atom varies between 0.1 and 0.3, depending on the discharge regime (see Section 6.2.3). Assuming equal sticking probabilities of ions and radicals (0.3 for the Sill3 radical [192]), up to about 10% of the deposition is attributed directly to the ions. This value has also been found by Kae-Nune et al. [311 ]. On the other hand, ions can penetrate into the subsurface layers, and hence their sticking probability will be closer to one. In addition, direct incorporation of ions in the amorphous network can only partly explain the increase in deposition rate. The creation of deposition sites by the ions possibly is of greater importance. It has been suggested that a direct relation between the ion flux and the deposition rate exists, if the availability of deposition sites is the limiting factor in the deposition process [236, 400, 424]. Also, partial dissociation of a polyatomic ion upon impact may occur [412, 425-427]. The dissociation of a hydrogencontaining ion may lead to the production of more than one hydrogen atom per ion. These atoms create molecular hydrogen and dangling bonds upon reaction with hydrogen bonded to the surface. The probability y of the recombination process of atomic hydrogen has been estimated to be between 0.4 and 1 [317]. In discharges operating in the y'-regime large particles consisting of several ions are present, in contrast to discharges in the c~-regime. In both regimes the same relative amount of ions contributes to the deposition, as is deduced from the measured amount of radicals that contribute to the deposition, which is regime-independent [317]. These larger ions in the y'-regime are thought to create more deposition sites per arriving ion than the smaller ions in the c~-regime [163]. This results in a smaller number of ions per deposited atom in the yCregime. The kinetic ion energy flux, (•l-')max, which is typically 20 W m -e [163, 301], will raise the substrate temperature by only a few degrees. Therefore, the influence of ions will be limited to the vicinity of impact. Furthermore, typical ion energies are below the sputtering threshold of silicon [ 134]. Enhancement of surface diffusion of the growth precursors is considered as one of the beneficial effects of ion bombardment [246, 428]. The potential energy of ions, which is released when the ion is neutralized, is typically 10 eV. This energy can be a substantial fraction of the total energy transferred. The release of this ionization energy is sufficient to excite atoms into excited electronic states, thereby weakening their bonds and enhancing their mobilities [429]. The influence of ion bombardment on the structure of deposited materials has been studied by Mtiller [428, 430] by performing molecular dynamics calculations on ion-assisted vapor phase growth of nickel. Nickel, of course, is very different from hydrogenated amorphous silicon, but the resemblance of the two deposition processes and some material properties is remarkable. In both cases, the growth precursors stick to the surface or diffuse along the surface, and the material can have a columnar-like structure or a structure with voids. Ion bombardment during the deposition of Ni promotes the formation of a dense film. The ion energies and fluxes in the molecular

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON dynamics studies were similar to those in typical a-Si:H deposition conditions. Two important processes modify the structure of the nickel film, viz., forward sputtering and diffusion enhancement of surface species. Similar processes are likely to occur in a-Si:H deposition. In the deposition of amorphous germanium by ion-assisted electron-beam evaporation, it was also found that a kinetic energy of about 5 eV per deposited atom is needed to produce a dense amorphous germanium network, irrespective of the amount of kinetic energy of the ions: the effect of five ions with 20 eV was the same as that of one ion of 100 eV [431]. These two additional examples clearly indicate the beneficial role that ion bombardment apparently has on the density of the deposited film. In the formation of a hydrogenated amorphous silicon network, the presence of the bonded hydrogen must be taken into account, as it was shown in the preceding that both the hydrogen content and the microstructure parameter are influenced by the ion bombardment. The high value of the microstructure parameter and the concomitant low density of the material for low values of Emax at 250~ (Fig. 48) indicate that the cross-linking is not sufficiently fast to create a dense network. This cross-linking process is activated by the locally released energy of chemisorption [432, 433], and involves the temperature-activated evolution of H2 from the surface. Hydrogen desorption due to cross-linking, which is known to occur from thermal desorption measurements [434], starts to become important at temperatures higher than 300~ At this temperature a drastic change in the importance of ion bombardment for achieving a dense network was observed (see Fig. 49). At lower deposition temperatures the cross-linking during the deposition is temperature-limited and the kinetic energy of the ions is needed to achieve cross-linking. If the amount of ion kinetic energy is insufficient, cross-linking will be incomplete and will result in an open network structure with a large amount of S i - H 2 bonds. At larger values of the ion kinetic energy the cross-linking is stimulated and a dense network is formed. Ion bombardment rather than the temperature induces crosslinking, as the microstructure parameter, the stress, and (to a lesser extent) the refractive index have the same dependence on Emax at both 200 and 250~ At 300~ the thermally activated cross-linking process is becoming important. Tensile stress can be related to the presence of voids in the material. The large microstructure parameter at low Emax is indicative of voids. A kinetic energy of the ions of 20 eV is typically enough to implant some of these ions a few monolayers below the surface of the growing film [400]. The extra Si atoms deposited in the layer at this depth will cause a compressive stress. Light hydrogen ions, which are less abundant than e.g. SiHf ions, penetrate deeper into the material (see also the TRIM simulation results in Fig. 42). The stress in the films deposited at 200 and 250~ depends similarly on Emax. At these temperatures the ion energy is needed to densify and to crosslink the network. At a temperature of 300~ the stress is much higher, which is explained by the fact that the ions reach an already dense network and some will be implanted, resulting in excess-stress in the material.

63

7. DEPOSITION MODELS A conceptual view of the processes that occur in PECVD of a-Si:H has been given by Perrin [173] and is shown in a slightly adapted form in Figure 51. Primary gas phase reactions are electron-impact excitation, dissociation, and ionization of the source gas molecules (Sill4), thereby producing radicals and positive and negative ions. Secondary reactions in the gas phase between (charged) molecules and radicals produce other species. Diffusion of reactive neutral species leads to material deposition. Positive ions are accelerated to the substrate and bombard the growing film. Negative ions are confined in the bulk of the discharge, which can lead to particulate formation. On the surface, species diffuse to growth sites and contribute to the film after sticking to the underlying material. Also, surface species recombine with other species and desorb from the surface (see also Fig. 14). Subsurface reactions are the release of hydrogen from this hydrogen-rich layer and the relaxation of the silicon network. Nowadays, it is generally accepted that device quality a-Si:H is obtained under PECVD conditions where the Sill3 radical is the predominant growth precursor [123, 137, 192]. At typical deposition temperatures and pressures the a-Si:H surface is almost completely terminated by hydrogen atoms. The Sill3 radical is thought to physisorb on this hydrogenterminated surface before it is incorporated into the film [ 136, 137, 317, 435-438]. The excess hydrogen is eliminated from the hydrogen-rich (40-50%) subsurface, so as to form "bulk" a-Si:H with a hydrogen content of about 10%.

solid

bulk a-Si:H subsurface reactions: H2 release/Si relaxation ~IL [ surface reactions, precursor diffusion [

plasma

--' /

3 ~ - ~ ~ ~ ~

C

sheath

""1

.............................................................................................................

plasma bulk

~

. I

.

(

~1

I

confinement I Jr .............. '"

~

~

. ...........................................................

}

gas reactions and diffusion

~r SiH4 H2

e + SiH4

pump Sill4 H2 Si2H6

t

electrical power driving frequency

Fig. 5 l. Schematicrepresentation of the processes occurring in a SiH4-H2 discharge and the various particles present in the energy and material balances. [After J. Pen'in, in "Plasma Deposition of Amorphous Silicon-Based Materials," (G. Bruno, P. Capezzuto, and A. Madan, Eds.), Chap. 4, p. 177. Academic Press, Boston (1995).]

64

VAN SARK

Robertson has summarized the three recent classes of models of a-Si:H deposition [439]. In the first one, proposed by Ganguly and Matsuda [399,440], the adsorbed Sill3 radical reacts with the hydrogen-terminated silicon surface by abstraction or addition, which creates and removes dangling bonds. They further argue that these reactions determine the bulk dangling bond density, as the surface dangling bonds are buried by deposition of subsequent layers to become bulk defects. The second class of models was formulated by Winer [441] and Street [442, 443]. Here the notion that hydrogen atoms are more mobile than silicon atoms forms the basis of the model. The silicon network is fixed up to a temperature near the crystallization temperature (650~ Hydrogen is mobile above a temperature of about 200~ and its motion allows for the interconversion of defects, weak bonds, and strong bonds. These processes occur in the subsurface layer, and surface processes are not explicitly included. In this model, the optimum deposition temperature is the one at which hydrogen atoms can diffuse one atomic spacing as to remove the weak bonds. After deposition, the weak bond distribution can only be changed irreversibly while the defect distribution can be changed reversibly, as described by the defect pool models [444-446]. In the third class of models, computer simulations try to fully incorporate all processes in the discharge, the interaction of species created in the discharge with the wall (i.e., the substrate), and the network formation [190, 191,232, 447-449]. These models to date do not treat the formation of disorder or defects, but aim at the understanding of the deposition rate, hydrogen content, and other macroscopic properties in relation to the discharge conditions (see also Section 4). Robertson has combined and extended the first and second classes of models [439] by focusing on the origin of weak bonds. A surface adsorption model is used to describe surface coverage of the silyl radical Sill3. Then, the processes that cause hydrogen to be expelled from the subsurface layer lead to the formation of weak bonds, which are frozen in. The dangling bond defects arise from these weak bonds by the defect pool process. In the following, a description is given of the Robertson deposition model (details can be found in [439,450]).

7.1. Surface Adsorption On the hydrogen-terminated surface, the surface species are mainly =-Sill, but at lower temperature ( 400~ characterized by an apparent activation energy of about 1.6 eV, and a low-temperature regime (Ts < 250~ with an apparent activation energy of about 0.15 eV. Various hydrogen elimination processes are summarized in Figure 53 [439]. In the high-temperature regime it is most likely that hydrogen is eliminated to form H2 at the surface, with an activation energy of 2.1 eV (Fig. 53a). This is similar to H evolution from crystalline silicon [439, 458]. At intermediate temperatures (250~ < Ts < 400~ the elimination of hydrogen occurs via diffusion of atomic hydrogen towards the surface with an activation energy of 1.5 eV to recombine as H2, i.e., the standard effusion process [459-461 ]. This is described with the hydrogen density of states (HDOS) diagram [442, 443,446, 459,462]; see Figure 53b. The HDOS diagram displays the energy of a hydrogen atom in a-Si:H compared to that of a free hydrogen atom in vacuum. A hydrogen bound as S i - H has an energy of - 3 . 3 eV with respect to the vacuum level, while a

hydrogen at a S i - S i bond center (BC in Fig. 53b) has an energy of about - 1 eV. In a-Si:H hydrogen is more stable at the bond center of a weak bond, which is represented as a tail in the HDOS below - 1 eV. In the HDOS there exists a mobility edge (HM), above which the hydrogen states form a percolation path. Hydrogen diffusion occurs by excitation from #H to HM. The difference #H -- HM amounts to 1.5 eV which is less than 2.2 eV, but much larger than the apparent activation energy of 0.15 eV. Robertson proposed that the local bond rearrangement close to the surface can account for this low activation energy [439]. It is assumed that hydrogen exists largely in pairs, analogous to the H~ in crystalline silicon [463]. This H~ consists of two Si--H bonds in the same direction [464, 465]. It can undergo a local rearrangement with one hydrogen atom passing through two bond center positions, at a cost of 1 eV [245]. Another local rearrangement is possible in which the H passes through the bond center to combine with the other hydrogen atom to form the interstitial molecule He (Figure 53c). The Si--Si bond center site is the transition state of the reaction. As hydrogen is more strongly bound at a weak S i - S i bond than at a normal S i - S i bond [466, 467], the energy barrier is lowered. As a consequence, the elimination of hydrogen to form He is eased in the presence of weak bonds. An alternative hydrogen elimination process has been proposed by Severens et al. [432, 468]. They argue that hydrogen can be eliminated by a cross-linking step [469] immediately after a physisorbed Sill3 radical has chemisorbed on a surface dangling bond. This cross-linking probability is thermally

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON activated, but due to the energy released at the chemisorption of Sill3 (about 2 eV), the activation is quite low [432]. If this cross-linking process does not occur immediately after chemisorption, it is assumed that hydrogen is incorporated into the film. An activation energy of 0.15 eV is deduced from fitting hydrogen incorporation data [468]. A detailed description of the local bond rearrangement has been derived [439], using the concept of the HDOS with a lowenergy tail that corresponds to the H present at weak S i - S i bonds. The width of this tail is 2Evo, i.e., twice the width of the valence band tail in the electronic density of states, which in turn is about equal to the Urbach energy E0 [442, 443]. The HDOS then is [439]

No e x p ( E - E s ) N(E) = 2Ev-----~ 2Evo

(67)

with Es at the top of the HDOS, i.e., the energy barrier for rearrangement of the ideal H~ (1 eV). The rearrangement occurs by activation of H to a state E in the tail. The reaction rate in atoms per unit surface area is the product of this HDOS, the MaxwellBoltzmann factor, and an attempt frequency Vl (~ 103 s-l), and is expressed in the low-temperature regime as [439]

(Es)

VlkBT exp RT = 2Evo 2Evo

(68)

The values obtained from this equation compare well with the experimental values of Evo as a function of temperature.

7.3.2. Athermal Reactions Next, athermal, plasma-driven hydrogen elimination reactions are considered. Ions play an important role in the deposition. They can account for 10-25% of the total deposition rate [301, 311 ], depending on the regime of the discharge. Moreover, the energy that they carry to the (sub)surface [163] can be used to overcome energy barriers (see also Section 6.2.1). Ions penetrate the film and eliminate hydrogen by displacing hydrogen atoms from subsurface Si--H bonds. They subsequently recombine as hydrogen molecules and effuse back to the surface (see Fig. 53d). The displacement yield Yo is given by the modified Kirchin-Pease equation YD = Ei/2ED, where Ei is the ion energy and ED the displacement energy [412]. Here, Eo is equal to the S i - H bond energy, i.e., 3.3 eV. In the c~-regime the contribution of ions to the deposition rate is 25% [301], and a typical average ion energy is 10 eV (see Section 6.2.1). This gives a displacement yield Yo of about 40% of the deposition rate. This illustrates the beneficial role of ions in improving the material quality [284, 301,358, 417, 470]. For the )/'-regime about 10% of the ions contribute to the deposition rate, and typical average ion energies are 20-30 eV [301]. This gives a displacement energy Yo of about 30-45% of the deposition rate. In this regime average ion energies are larger than the bulk displacement energy of silicon of 22 eV [285, 376], which degrades the material quality. It is this athermal dehydrogenation process that reduces the excess weak-bond density associated with a high polymeric

67

content, rather than ions' densifying the material by removing polymeric SiHx groups. Low energy ions are especially effective at dehydrogenation because the displacement energy Ed is low. This favors the use of VHF PECVD reactors, where the ion energies are much lower and the ion densities much higher than at 13.56 MHz. Further, atomic hydrogen in hydrogen-diluted discharges can contribute to abstraction of surface and subsurface hydrogen [471 ]. The atomic hydrogen reduces the fraction of higher SiHx groups [466]. Only a small amount is incorporated directly [472]. Atomic hydrogen does not reduce the surface hydrogen content below 50%, because this would result in surface dangling bonds that would be passivated by incident hydrogen [472, 473]. Atomic hydrogen can also diffuse into the a-Si:H with an activation energy of 0.4-0.7 eV [461 ], which allows subsurface hydrogen abstraction. However, this would be less important at low temperatures, due to the considerable activation energy.

7.4. Dangling-Bond and Weak-Bond Density The hydrogen elimination processes described above create the distribution of weak bonds. The dangling-bond distribution is formed from this by interconversion from weak bonds to dangling bonds. For substrate temperatures above the hydrogen equilibration temperature of 200~ hydrogen is mobile, and the defect pool operates. This allows the weak-bond and dangling-bond distributions to equilibrate [439]. At temperatures below 200~ hydrogen motion is inhibited, and equilibration should not be possible. Nevertheless, Stutzmann [474] reported that the dangling-bond density as a function of temperature shows the the same behavior as the weak-bond density, for all temperatures. This suggests that a defect pool of sorts operates below 200~ in the surface layer [439]. It is assumed that a large athermal, plasma-driven hydrogen flux is present in the hydrogen elimination zone at temperatures below 200~ which mediates the equilibration of the danglingbond and weak-bond distributions. The dangling-bond density and weak-bond density thus remain linked in the elimination zone by a largely temperature-independent relationship, given by the defect pool [445,446]. The dangling-bond density in the elimination layer becomes the bulk defect density as the layer is buried deeper and becomes frozen in. This proposed process allows the weak-bond density to determine the dangling-bond density at all temperatures [439].

8. MODIFICATIONS OF PECVD Of the great number of possible and reported modifications, in this section only the most important ones are described, viz., the use of higher excitation frequency (VHF), the use of gas flow modulation (known as chemical annealing or layer-by-layer deposition), and the use of RF modulation.

68

VAN SARK

8.1. VHF

8.1.1. General Deposition of hydrogenated amorphous silicon employing the VHF PECVD technique (typical frequency range 20-110 MHz) has been reported to yield an increase in deposition rate by one order of magnitude over the conventionally used frequency of 13.56 MHz [ 16, 146,250, 280], without adversely affecting material quality [183, 280, 475]. This is of great importance for lowering the production cost of a-Si:H solar cells. The explanation of the VHF influence on the deposition rate is still a topic of discussion. It has been proposed theoretically that the high-energy tail in the EEDF is increased with an increasing ratio w/v of the excitation frequency to the energy collision frequency [276, 476]. This leads to an increased ionization rate [ 146, 250, 280]. However, mass spectrometry resuits on the decomposition of silane as a function of frequency show that the increase of the deposition rate cannot solely be attributed to the enhancement of radical production [ 119, 120]. It has also been found or deduced that the flux of ions towards the surface is increased with increasing frequency [146, 183, 279, 284] while at the same time the ion energy is decreased. This low-energy, high-flux ion bombardment enhances surface mobilities of adsorbed species. It was shown in Section 6.2.3 that a kinetic energy of 5 eV per deposited atom is needed to produce good quality a-Si:H [301 ]. Because the wavelength of the RF signal is of the order of the substrate dimensions (3 m at 100 MHz), it can be expected that uniform deposition is more difficult at these high frequencies [477]. In fact, a practical optimum frequency around 60-70 MHz is used [478, 479], which provides a good compromise between high deposition rate and attainability of uniform deposition. Further, the use of a distributed RF electrode network where all nodes have identical amplitude and phase improves the homogeneity of deposition [480].

8.1.2. Optimization of Deposition Conditions A change of excitation frequency prompts for optimization of other deposition parameters, such as pressure, power, and geometry. Chatham and Bhat have shown that the maximum of Sill* emission at 414 nm is shifted towards lower pressure upon increasing the frequency [ 146]. This means that the maximum in radical production also shifts to lower pressure. Experimental results obtained in the ASTER deposition system corroborate this [247]. A 20-fold increase in deposition rate was reported for an increase in frequency from 13.56 to 100 MHz [119, 120]. Here the electrode distance was about 4 cm, while the pressure was 0.12 mbar. A reasonable thickness uniformity was observed. For a smaller electrode distance (2.7 cm) higher pressures are needed in order to maintain good homogeneity in thickness. This is demonstrated in Figure 54, where the conditions to obtain a homogeneity deviating less than 5% over a 10 x 10-cm 2 area are presented. The power density in this case was 57 mW/cm 2. The shaded area represents the process

Fig. 54. Optimumvalues for pressure and frequency for uniform (thickness variation v 20 "6. >

'i 15-

10 0

I

I

I

I

I

10

20

30

40

50

60

p (Pa) Fig. 56. The plasma potential as a function of pressure for a frequency of 30, 50, and 65 MHz. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

(a) .

"~ ,,l=,a

9=

.

.

.

.

i

.

.

.

"~ ,ff o7 ,ff

0.4

3.0 .~ 2.5

;

0.6

9 ~=-,I

o

.

1.2 _l 13.56 MHz 9 30 MHz 9 40 MHz 1.0 -o 50 MHz zx 60 MHz best fit 0.8 -

-

9

2.0 1.5

9

I

9 9 -A []

0.0

9-

(b) .

.

.

.

.

.

I

i

,

|0 4

o

,

10 5

p f2/3 (mbar/s2/3) (b) Fig. 55. (a) Deposition rate as a function of pressure at various frequencies. The shaded area shows the 5% uniformity conditions. (b) Best fit of deposition rate versus p f2~3, clearly showing the c~-V f transition.

151,488] revealed that the value of ds is constant for the conditions where pw 1/2 is constant [487]. The deposition rate as a function of pressure at various frequencies and at a power density of 57 mW/cm 2 is shown in Figure 55a. The shaded area represents the conditions for which uniform deposition is observed. At all frequencies the deposition rate at low pressure is lower than at high pressure by a factor of 5 to 6. This effect is well known, and it is explained by the transition from the oe- to the yf-regime of the plasma [245]. It follows from the figure that the transition region shifts to lower pressure with higher frequencies. Fitting the deposition rate as a function of the scaling parameter pa fb shows that a good fit is obtained for a = 1 and b = 2/3; see Figure 55b. This holds for all frequencies. The same behavior has been found for the plasma potential [163]. As is illustrated in Figure 56, the plasma potential slightly increases in the low-pressure c~-regime, but clearly decreases with increas-

I

-

iF-

1.0

.g o.5 0.0

I

_

o

-~ 0.2

I

113 m W / c m 2 57 m W / c m 2 28 m W / c m 2 Chatham & Bhat

--El B

~ _ _ -r-+ - - k - -~t G - - -A- m - - -

I

20

I

......a

I

I

40 60 80 frequency (MHz)

I

100

120

Fig. 57. Deposition rate as function of frequency at optimum pressure at each frequency (see Fig. 54) at three power densities. Also shown are data by Chatham and Bhat [146].

ing pressure at all three frequencies. The pressure at which the plasma potential starts to decrease occurs at a lower pressure at the higher frequencies. The rapid increase of deposition rate as a function of frequency, as reported in the literature, e.g. [ 16, 119, 120, 280, 475], is observed in the c~-regime. In or near the y'-regime the enhancement in deposition rate as a function of frequency is not pronounced. This is illustrated in Figure 57 by results at three power densities. Chatham and Bhat's data [ 146] also show only a slight increase with frequency. In Figure 58 optical and structural material properties are shown. The refractive index at 2.07 eV (600 nm), n2.07 eV, decreases with increasing applied RF power P, and is more or less independent of the frequency (Fig. 58a). The absorption coefficient at 2.07 eV behaves similarly. Values are around 2 to 3 x 104 cm -1. The cubic bandgap Eg increases with power, and is also not dependent on frequency (Fig. 58b). The hydro-

70

VAN SARK

4.5 4.4

c,,I

=

4.3 4.2 4.1 4.0 3.9

'

"

1.70

28 m W / c m z : 57 m W / c m 2 113 mW/cm2, A 8,.

_11 L - - " | -

1.65

.

:..

.+

~

n

i

i

A

0.6 0.4

II

15 10

i

l

i

9

.

.

.

9

.

.

28 mW/cm22 9 57 m W / c m 9 113 m W / c m 2 Ak

"- -,

"4........ ~t. . . . . . . . . . . . . . . . . "J'

=

i

3O 40 50 60 70 80 frequency (MHz)

28 m W / c m 2 57 m W / c m 2 1~ mw/cm2 A

.

A v

(b) i

40 50 60 70 80 frequency (MHz) .

A

1.60

A i

.

A

..It ...... i / ~.''---I---Ir

" - - - I

(a) i

A

i._

|

Ar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

.

...................

.~_ e~ "

O 28 m~g;/cm 2 " 9 57 m W / c m 2 Ik 113 m W / c m 2

>

@

30

2O

'

I o.o I

"

.

0.2 (c) n

30

a r i

n

I

i

0.0

i

n

i

i

i

3O 40 50 60 70 80 frequency (MHz)

40 50 60 70 80 frequency (MHz)

Fig. 58. (a) Refractive index n2.07eV, (b) cubic bandgap Eg, (c) hydrogen content CH, and (d) microstructure parameter R* as function of frequency at optimum pressures (see Fig. 54) at three power densities.

gen content CH increases from 13 at.% at low power to 19 at.% at high power, again being nearly independent of frequency (Fig. 58c). The microstructure parameter R* increases with power, with only a slight dependence on frequency (Fig. 58d). The character of the intrinsic stress is changed from compressive (about 600 MPa) at low power to tensile (100 MPa) at high power. Only a slight influence of frequency is observed, and the dependence on power is much clearer. Small-angle X-ray spectroscopy (SAXS) data show that voids are absent in the samples deposited at low power densities [66]. For higher powers voids are observed, and there appears to be a sudden change between 27 and 58 mW/cm 2. Electrical data are shown in Figure 59 as a function of deposition rate for all frequencies, using the relation between deposition rate and power density as depicted in Figure 54. Both dark conductivity and photoconductivity decrease exponentially with increasing deposition rate. The data in this range of deposition rates can be fitted with O'd = 9 x 10 - 1 2 e x p ( - 1.5rd) and aph = 8 • 10 -6 exp(--0.5rd), with Od and aph expressed in ~2-1 cm -1, and rd in nanometers per second. Consequently the photoresponse %h/ad increases with deposition rate as about 106 exp(rd). Activation energies amounted typically to 0.7-1.0 eV. From thermally stimulated conductivity (TSC) measurements [489-492] a midgap density of states (DOS) of 1.5 x 1016 cm -3 eV -1 is determined. The product/zr at 300 K is 9 x 10 -5 cm 2 V -1. Both DOS a n d / z r are independent of frequency. Summarizing the results, it is clear that most of the material properties are not strongly dependent on frequency in the range

10-4

i

u

i

i

.... ~

10 -6 10 -8

-

> 10 -9 10-

_

...................... " .... "~5~ff~ ........... - - , - o .................. c r l

30 40 50 65 80

[] 99

"~ 10-12 o 0.0

MHz MHz MHz MHz MHz

....

oo 9 n_ 9

O

C,9

10-14

i

photo

9

A~ I

0.5

I

9 I

dark I

1.0 1.5 2.0 deposition rate (nm/s)

I

2.5

Fig. 59. Darkconductivity (ad) and photoconductivity (O'ph) as functions of deposition rate for all frequencies.

of 30 to 80 MHz. The effect of power density is much more important. The material deposited at the lowest power is of device quality. Using larger power densities results in less dense material. This can be inferred from the decrease of the refractive index and the increase of the microstructure parameter, in combination with the increase in hydrogen content. Perrin et al. [245] have shown that the increase in deposition rate is more pronounced above a certain threshold power density. This power density is close to the lowest power density

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

15 C'4

E rj E 9

L)

-

'

.

10 5-

.

.

.

~

20 18

Vo~ - 0.82 V

~

FFJSC-m A 18"2 0.67 /cm2=

.~~ ~ 16

Eff.= 10.0%

~

0 ...................................................................... f...................

,,

-5

E

. J,c

.

.

o

o

. ,~

71

.

1.0 0.9

(a)

Vo~ ~ ~

0.8~.

14

0.7

12

0.6

10

0.5 0.3 0.4

Eft.

-10 -15

-

i

-

I

-0.2

:

0.0

I

~

I

I

0.2 0.4 0.6 V o l t a g e (V)

0.8

'o

|

1.0

6

'o 8'o ,'o

0

1

!

|

|

|

(b)

0.8 o~,,~ r

~ in the experiments shown here. The deposition rate is probably the main parameter causing the observed difference between the low-power and high-power material and the deterioration of layers at higher power levels. This confirms the known observation that in general, the quality of material deposited in the y'-regime is worse than in the c~-regime [245]. The presented material quality results are similar to results reported by others [119, 120, 280, 475], although those frequency series were obtained in the or-regime at constant low pressures. Here, good quality homogeneous layers were deposited at the ot-y ' transition region. Especially the low power results compare well with results by others. The intrinsic material fabricated at the frequencies reported above was incorporated in p+-i-n + solar cells [493]. The pand n-layer were prepared by the conventional 13.56-MHz discharge. The device quality films indeed yield good solar cells, of 10% efficiency, as is shown in Figure 60. This cell is manufactured with a 500-nm-thick/-layer made at 65 MHz with a power density of 42 mW/cm 2, resulting in excellent properties. The deposition rate still is 2-3 times higher than at the conventional 13.56 MHz; 0.2-0.5 nm/s versus 0.1-0.15 nm/s [494]. Similar results were reported by Jones et al. [495]. The effects of power density on the material quality are also reflected in the cell quality, e.g. the efficiency. Figure 6 l a shows a decrease in efficiency with increasing power density or deposition rate. This is also seen in the spectral response measurements (Fig. 61b). A shift in the red from long (700 nm) to shorter (650 nm) wavelength is observed if one compares cells deposited at low and high power densities. This can be explained by the fact that the material is less dense, with a higher hydrogen content, yielding a larger bandgap. The observed decrease in the blue part of the curve as a function of power density may well be due to changes in the p-i interface, which are induced by a different ion bombardment condition. The differences in material properties are also reflected in the degradation behavior of the cells. Figure 62 shows the nor-

4

Power density (mW/cm 2)

I

Fig. 60. Current-voltage characteristics of a solar cell made at 65 MHz and 42 mW/cm 2. The dashed line indicates the maximum-power point.

0

o.6

= 0.4

i

"~"

"1.

-

-

x. x

-.

4,,,a

28 m W / c m 2_ '\'"~i"-.~"'\ '.,',.\ 0.2 ............ 57 m W / c m 2 ....... 113 m W / c m 2 '-~'..N....~ 0.0 400 500 600 700 800 wavelength (nm) Fig. 61. Solar cell performance parameters as functions of power density for cells made at 65 MHz: (a) Jsc, efficiency, Voc, and fill factor (FF); (b) spectral response. i

i

i

i

i

i

I

1.0 r ~

~. 0.8 9-N E 0

Z

0.6

i

_-28mW/cm 2 2 - - o- 42 m W / c m --*-- 57 m W / c m 2 0.4 - - - a - 113 m W / c m 2 I

10 -2

I

10 -1

I

"~-.,~ -" "' ~ "-..N

~k.

-

-- -0

~'~'I~---Z~

...

I

1 10 Time (h)

I

I

102

103

Fig. 62. Normalized solar cell efficiency as a function of illumination time for different power densities as obtained by continuous illumination of 1000-W/m 2 AM1.5 light. The initial efficiencies of the four cells were 9%, 10%, 8%, and 6% for 28-, 42-, 57-, and 113-mW/cm 2 power density, respectively.

malized efficiencies as a function of illumination time. The efficiencies of the cells with the/-layer deposited at low power densities stabilize at around 60% of their initial value, while the cells with the/-layer deposited at high power densities stabilize at 40%. This correlates with the hydrogen content of the /-layers, which is around 12% and 19% for the low and the

72

VAN SARK

3O

120

>~ 20

80

10

40

0.4

_

(d)

_

///~_

~< ~'~ o.2

I

0

I

0.0 0.6

~,.4 E

I

I

(e)

0.4

.u" 0.2

(b)

-

I

0.0

I

(c)

4.4

- (f) db,

~'4

4.2 I-

4.0

L 2

3.8 i

0

30

frequency

i

50 (MHz)

i

70

0

30

frequency

i

50 (MHz)

70

Fig. 63. Plasma parameters as deduced from the IEDs and material properties as a function of excitation frequency of the SiH4-H2 discharge at a power of 10 W and a pressure of 0.16 mbar: (a) the plasma potential Vpl (circles) and dc self-bias Vdc (triangles), (b) the sheath thickness ds, (c) the maximum ion flux Fmax, (d) the growth rate r d, (e) the microstructure parameter R*, and (f) the refractive index n 2 eV. (Compiled from E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)

high power densities (see Fig. 58) and which is indicative for the low-density material at obtained at these high power densities. Also a frequency dependence was observed, especially in Voc, which was not expected from the material study. As only the deposition conditions of the i-layers are varied, a change at the p-i interface must be responsible for the change in Voc. The lower value of Voc at low frequency was attributed to the difference in ion bombardment at the p-i interface [493].

8.1.3, DischargeAnalysis In the ASTER deposition system, experiments have been carried out in which the excitation frequency was varied between 13.56 and 65 MHz [169]. The other process conditions were kept constant at a power of 10 W, a pressure of 0.16 mbar, gas flows of 30 sccm Sill4 and 30 sccm H2, and a substrate temperature of 250~ As in Section 6.2.3, plasma properties that are deduced from lED measurements are compared with material properties in Figure 63. The IEDs of SiH~- at four frequencies are shown in Figure 64. The plasma potential is about 25 V (Figure 63a). This value of the plasma potential is typical for the silane plasmas in the asymmetric capacitively coupled RF reactors as used in the

ASTER deposition system, and is also commonly found in argon or hydrogen plasmas [ 170, 280, 327]. From the considerable decrease of the dc self-bias with increasing frequency (Figure 63a) it is inferred that the potential drop over the sheath of the grounded electrode (Vpl) and the one over the sheath of the powered electrode (Vpl - - V d c ) , become comparable in magnitude. Hence, the discharge is becoming more symmetric with increasing frequency. In contrast, Heintze and Zedlitz [236] also presented data on the plasma potential as function of frequency in silane plasmas: the plasma potential varies from about 27 V at 35 MHz to about 20 V at 180 MHz. Moreover, Dutta et al. [284] used a symmetric capacitively coupled RF reactor and estimated the plasma potential in their system from the applied voltage at the powered electrode. A decrease of the plasma potential from 45 V at 13.56 MHz to only 15 V at 70 MHz is observed. This difference in behavior is thought to be solely due to the different reactor geometries. The charge carder density in the sheath increases by a factor of 3 on increasing the excitation frequency from 13.56 to 65 MHz. As a consequence, the sheath thickness ds decreases from 4.4 mm at 13.56 MHz to 2.8 mm at 65 MHz (Fig. 63b), which results in a reduced number of collisions in the sheath.

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

10

only increased by a factor of 1.5, while the deposition rate on the electrodes increased by nearly an order of magnitude. From the constant depletion, assuming a homogeneous deposition throughout the reactor, a frequency-independent deposition rate of 0.44 nm/s is deduced [163]. At 13.56 MHz the observed deposition rate is a factor of 3 lower, whereas at 65 MHz the measured deposition rate equals the estimated value of 0.44 nm/s. This suggests that the increased deposition rate at higher frequencies, as measured at the center of the grounded electrode, is partly due to a more homogeneous deposition profile throughout the reactor at higher frequencies [ 163, 280]. This suggestion is further supported by the fact that the discharge is more symmetric at higher frequencies, as deduced from the low dc self-bias at high frequencies.

13.56 MHz

5

18 30 MHz

I

m ~r~

0

58 50 MHz

>., e

8.2. Chemical Annealing

25

~

c c

lO8 65 MHz

50

0_._ 0

10 20 Ion energy (eV)

73

30

Fig. 64. The ion energy distributions of Sill + at several frequencies. (From E. A. G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands,

1998, with permission.)

This is nicely illustrated in Figure 64, where the IEDs of Sill + are shown for several frequencies. Clearly, the contribution of low-energy ions decreases upon increasing the frequency. The increase in the deposition rate rd (Fig. 63d) corresponds to the increase in the ion flux (Fig. 63c): the fraction of arriving ions per deposited atom, Ri, is constant at about 0.25. Such observations have also been reported by Heintze and Zedlitz [236], who furthermore suggested that the deposition rate may well be controlled by the ion flux. The kinetic ion energy per deposited atom, Emax, is also constant and amounts to about 5 eV. As was shown in Section 6.2.3, the material quality as reflected in the refractive index n2 eV (Fig. 63e) and the microstructure parameter R* (Fig. 63f) is good: n2 eV is around 4.25, and R* is low (

I

I

"

-

" - -

-

5012_ -

~,'.a..,~._

O& 1 0 0 0 0

r

[

w

...--. . . . .

~ m

0

O-

3.0

la

I

_[

t

I

I

I

I

I

I

$t/

Ik-i

-- ]

..--..-

...... I I

I

010

,

/

-

6 0 D.---.---.._

L

w

I

5001

I

1

I!

I b

5100

I

E

2,0

100_.

0

1

,..-- 5 0 1 0 d p~

1.0

!'

ID ID ID ID ID ID ID ID II

200

,~, II

"''0 9

5000

Z I

0,0 0.0

I

I

I

0.9

I

1 .8 x

I

"I"~

I

2.7

(crn)

Fig. 67. The development in time of (a) the average electron energy and of (b) the density of electrons between the electrodes in the case of a 50-MHz plasma and a modulation frequency of 5 kHz. The RF electrode is located at x = 0, and the grounded electrode at x = 2.7 cm. The numbers near the curves in both graphs represent the number of RF cycles. One RF cycle _ 20 ns. The plasma is turned off at cycle 0, turned on at cycle 5000, and turned off again at cycle 10,000. [From A. C. W. Biebericher, J. Bezemer, W. E van der Weg, and W. J. Goedheer, Appl. Phys. Lett. 76, 2002 (2000), 9 2000, American Institute of Physics, with permission.]

and the overshoot of the rates cover only a small fraction of the modulation period. In other words, the discharge is in a quasi steady state with respect to the applied power, and the deposition rate is only slightly above the corresponding deposition rate at cw conditions. As the modulation frequency increases, the overshoot becomes more important, which leads to an increase in deposition rate. When the period of the modulation becomes shorter than the decay time of the electron density, the power is distributed over too many electrons to yield considerable heating. The heating becomes less, and less of the radicals is produced, as is shown in Figure 66a. It is therefore concluded that an optimum in the modulation frequency exists, which corresponds to the decay time of the electron density. From Figure 67b it can be inferred that this optimum should be around 100 kHz, as at 200 cycles the electron density is reduced to 1/e of its value at cycle 0, i.e., the lifetime is 200 RF cycles, or 4/zs. Another beneficial effect of modulation of the discharge is the observed improvement of uniformity of deposition. At cw discharge conditions that normally result in thickness variations

of 70%, modulation lowers the variation to about 10% [519]. This was attributed to the fact that, as a result of modulation, reactions are not confined to the sheaths, and radicals are produced in the entire volume between the electrodes. Madan et al. [515] have presented the effect of modulation on the properties of the material (dark conductivity and photoconductivity) and of solar cells. They also observe an increase in deposition rate as a function of modulation frequency (up to 100 kHz) at an excitation frequency of 13.56 MHz, in their PECVD system [ 159]. The optimum modulation frequency was 68 kHz, which they attribute to constraints in the matching networks. Increasing the deposition rate in cw operation of the plasma by increasing the RF power leads to worse material. Modulation with a frequency larger than 60 kHz results in improved material quality, for material deposited with equal deposition rates. This is also seen in the solar cell properties. The intrinsic a-Si:H produced by RF modulation was included in standard p-i-n solar cells, without buffer or graded interface layers. For comparison, solar cells employing layers that were deposited under cw conditions were also made. At a low deposition rate of about 0.2 nrn/s, the cw solar cell parameters are: Voc = 0.83 V, Jsc = 15.8 mA/cm 2, FF = 0.67, and r / = 8.8% (at AM1.5 illumination conditions). Solar cells produced with the intrinsic layer deposited at 68-kHz modulation frequency are of the same quality: Voc = 0.81 V, Jsc = 17.1 mA/cm 2, FF = 0.63, and r / = 8.7%. Biebericher et al. [519] report that beyond a modulation frequency of about 40 kHz in their 50-MHz discharge the material is slightly worse than at standard cw conditions. However, they argue that due to the enhancement in deposition rate, lower partial pressures of silane can be used, which results in more efficient silane consumption. Indeed, they have shown that lowering the gas flows by a factor of 3 leads to a reduction in deposition rate of only a factor of 1.5 at 100-kHz modulation frequency [520]. Clearly, the efficiency of silane consumption is of great importance in production.

9. H O T W I R E C H E M I C A L

VAPOR DEPOSITION

9.1. General Description

The hot wire chemical vapor deposition (HWCVD) method was introduced as early as 1979 by Wiesmann et al. [521]. The principle of HWCVD is based on the thermal decomposition of silane at a heated tungsten (or tantalum) filament, foil, or grid. At temperatures of 1400-1600~ the silane is decomposed into a gaseous mixture of silicon and hydrogen atoms. Matsumura [522-524] further developed HWCVD, but termed it catalytical CVD (CTL-CVD); for he showed that the decomposition of silane at a heated tungsten filament is a catalytic process. The use of a much higher pressure (>0.1 mbar) than the one Wiesmann et al. used (< 5 x 10 -4 mbar) led to a high deposition rate (0.5 nrn/s) [521 ]. Doyle et al. showed that the silicon atoms deposited on the filament are then thermally evaporated onto the substrate, which is located within a few centimeters of the filament; hence the term evaporative surface decomposition [525].

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON At the same time, thermal and catalytic dissociation of silane and hydrogen lead to the generation of hydrogen atoms at the filament surface [526]. Device quality a-Si:H made by HWCVD (as they termed it) was first reported by Mahan et al. [19, 527]. They obtained a-Si:H with hydrogen concentrations as low as 1%. Deposition rates as high as 5 nm/s [528] and 7 nm/s [529] have been achieved for a-Si:H of high quality. In order to obtain device quality material it was shown by Doyle et al. [525] that the radicals that are generated at the filament (atomic Si and atomic H) must react in the gas phase to yield a precursor with high surface mobility. Hence, the mean free path of silane molecules should be smaller than the distance between filament and substrate, dfs. Too many reactions between radicals and silane molecules, however, result in worse material. In fact, optimal film properties are found for values of pdfs of about 0.06 mbar-cm [530, 531 ]. The combination of high deposition rate and the ability to produce device quality material is of particular interest for solar cell production and TFT fabrication [532-535]. Further, the low hydrogen content was expected to yield improved stability against light-induced degradation [527], as the StaeblerWronski effect is related to the hydrogen content in the material (see also Section 1.2.5). This was demonstrated by Crandall et al. [536], who incorporated an HWCVD-deposited layer in solar cells, and observed reduced degradation upon light soaking as compared to devices with a conventional PECVD layer. In these hybrid solar cells only the intrinsic layer was made by HWCVD; all other (doped) layers were deposited by PECVD. Wang et al. [537] have reported solar cells that were completely made using HWCVD. HWCVD-deposited a-Si:H layers have also successfully been used as the semiconductor layer in inverted-staggered TFTs [538, 539]. Moreover, it was demonstrated that these TFTs have excellent electrical properties, they do not suffer from a shift of the threshold voltage upon prolonged application of a gate voltage and these HWCVD TFTs are stable [538,540]. In a TFT, the metastable character of a-Si:H manifests itself as a reversible threshold-voltage shift, upon prolonged application of gate voltage (see Section 11.2). Dilution of silane with hydrogen leads to the formation of polycrystalline silicon films (poly-Si:H) that still contain a small amount (~ 1.7 v

LU 1.6-

A A

1.5-

.4

z~

A 9

PECVD samples HWCVD samples

i

.,.

0

1'0

1'5

20

[HI (at.%) Fig. 69. Relation between the optical bandgap (Tauc convention) and the hydrogen content in a-Si:H deposited by HWCVD (closed circles) and PECVD (open triangles). (From K. E Feenstra, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998, with permission.)

ronment in the immediate vicinity of the filament will become depleted of silane. The generation of deposition precursors (and also the deposition rate) is limited by the silane supply. Above a certain flow, the dissociation reaction rate is the limiting factor, and as a consequence the deposition rate will remain constant upon a further increase of the silane flow. Dilution of silane with hydrogen to moderate amounts (0.75 < [SiH]4/([SiH4] + [He]) < 1) is not expected to have a large influence on material properties, as even in the pure silane case a large amount of atomic hydrogen is present. Every Sill4 molecule dissociates to give four H atoms [525]. Also, the mean free path of the atomic H is larger than that of Si, being about 8 cm at 0.02 mbar [531], and consequently all hydrogen will reach the substrate. It is found that the deposition rate depends linearly on the dilution fraction, as it depends on the partial pressure of silane. Significant changes in the refractive index, the hydrogen content, the microstructure parameter, and electrical properties are observed for values of [Sill4]/([Sill4] + [He]) lower than about 0.3-0.4. A closer look at these data reveals that moderate hydrogen dilution slightly improves the dark conductivity and photoresponse, whereas dilution fractions smaller than 0.3-0.4 lead to deterioration of the material. Similar trends were also observed by Bauer et al. [550] and Molenbroek et al. [528,530]. The common linear dependence of the bandgap on the hydrogen content as observed for PECVD-deposited material is not observed for HWCVD-deposited material. A large dataset is shown in Figure 69, in which the relation between bandgap and hydrogen content is compared for HWCVD- and PECVD-deposited material [531]. It is seen that the bandgap of HWCVD-deposited material follows a similar behavior, as a function of hydrogen content, to that of PECVD-deposited material, for values of the hydrogen content of 7% and higher: the bandgap varies between 1.7 and 1.85 e V [531]. The bandgap of PECVD-deposited materials decreases to 1.5 eV

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON Table IX. Exothermic Gas Phase Reactions in the HWCVD Process, Their Enthalpies, and Their Rates [192], Estimated for Typical Operating Conditions Chemical reaction

Enthalpy (eV)

Reaction rate (cm 3 s - 1 )

H + Sill 4

~

Sill 3 + H 2

-0.54

2.68 • 10 -12

H + Sill 3

--+ S i l l 2 + H 2

-1.46

2 • 10 -11

Sill3 + Sill3

--+ Sill 4 + Sill 2

-0.91

1.5 • 10 -10

Si + Sill 4

--+ Si2H 2 + H 2

-0.34

3.5 • 10 -10

-0.4/-0.05

2 • 10 -10

Si2H2 + Sill4 ~ Si3H 4 + H 2

at a hydrogen concentration of 2%, whereas the bandgap of HWCVD-deposited material remains unchanged at 1.7 eV, even at hydrogen concentrations of 1%. This difference in behavior is due to the difference in the number of voids present in the material. A large number of voids reduces the effective density of the material, and increases the average S i - S i bond distance. As a result, the bandgap remains high. Crandall et al. [71 ] found that the number of voids increased with decreasing hydrogen content in HWCVD-deposited material. This observation is also supported by small-angle X-ray scattering (SAXS) [551] and nuclear magnetic resonance (NMR) [552] data.

9.4. Deposition Model The deposition mechanism in HWCVD of a-Si:H can be divided into three spatially separated processes. First, silane is decomposed at the tungsten filament. Second, during the diffusion of the generated radicals (Si, H) from the filament to the substrate, these radicals react with other gas molecules and radicals, and new species will be formed. Third, these species arrive at the substrate and contribute to the deposition of a-Si:H. The filament material acts as a catalyzer in the silane decomposition process. This is clear by comparing the S i - H bond energy (3-4 eV) in silane with the thermal energy at the filament temperature of 2000~ (0.25 eV): they differ by an order of magnitude. The dissociation of silane proceeds in two steps [525]. First, the silane reacts with the tungsten to form a tungsten silicide WxSiy at the surface of the filament. Hydrogen atoms leave the surface before they can recombine to form molecular hydrogen. Subsequently, the silicon atoms evaporate from the surface, which is an activated process with an activation energy of 3.6 eV [525]. At a filament temperature of about 1700~ the silane decomposition rate and the evaporation rate balance each other. For lower temperatures a tungsten-silicon alloy is formed on the filament. A fraction of the generated radicals react with gas molecules before they are able to reach the substrate directly. This fraction depends on the process pressure. A number of reactions may take place, and only the exothermic ones are listed in Table IX, as endothermic reactions are not very likely to occur. As can be seen in Table IX, the Si and H radicals are highly reactive with silane. Most reactions will occur with the omnipresent silane. Quantum chemistry computations, confirming the findings of Molenbroek et al. [530], have shown that the reaction of

79

Si with Sill4 proceeds via insertion of Si into the Sill4 to form Si2H4, followed by a rearrangement of the thus formed species and the elimination of H2, which yields Si2H2 [553]. An increasing amount of Sill3 will be created via the reaction of H with Sill4 upon increasing the pressure. As a product of the reaction Sill3 + Sill3, Sill2 is created which at higher pressures may polymerize further to Si3H4. Holt et al. [554] have performed Monte Carlo simulations to study gas phase and kinetic processes in HWCVD. They showed that under the conditions for obtaining device quality material Sill3 is the most abundant species at the substrate. At a pressure of about 0.08 mbar the fluxes of Sill3, SizH2, and Si to the substrate were calculated to be 5 • 1017, 1 x 1016, and 5 • 1013 cm -2 s -1 , respectively. The HWCVD deposition process is more or less the same as for PECVD, and was described in Section 7. Important differences between the two is the absence of ions, and the limited number of different species present in the gas phase, in the former. At low pressure atomic Si is the main precursor. This yields void-rich material with a high microstructure factor. Increasing the pressure allows gas phase reactions with Si and H to create more mobile deposition precursors (Sill3), which improves the material quality. A further increase leads to the formation of higher silanes, and consequently to a less dense film. Using threshold ionization mass spectrometry and in situ ellipsometry, Schrrder and Bauer [555] have shown that the Si2H4 radical may well be the species responsible for deposition, rather than Sill3 as in PECVD. This larger and less mobile precursor is thought to be the cause of the observed differences in the deposition conditions required in HWCVD and PECVD to obtain device quality material.

10. EXPANDING T H E R M A L PLASMA CHEMICAL

VAPOR DEPOSITION 10.1. General Description The expanding thermal plasma chemical vapor deposition (ETP CVD) technique has been developed in the group of Schram [20, 556] and has been used for the deposition of several materials, such as hydrogenated amorphous silicon [21] and carbon [557], and even diamond [558]. The technique is a remote-plasma deposition method. The generation of the plasma, the transport of the plasma, and the deposition are geometrically separated. In remote-plasma CVD the substrate holder is not a necessary electrode for the plasma. The absence of direct plasma contact with the substrate allows for better control of ion bombardment, which is advantageous. Also, the properties of the plasma can be varied independently, which makes optimization of the whole process simpler. An argon-hydrogen plasma is created in a dc thermal arc (cascaded arc) operated at high pressure (~ 0.5 bar) [556, 559, 560] (the cascaded arc is also employed in IR ellipsometry, providing a well-defined source of intense IR radiation; see Section 5.4 [343]). As the deposition chamber is at much lower pressure (0.1-0.3 mbar), a plasma jet is created, expanding into

80

VAN SARK

Fig. 70. Cross-sectionalview of a expanding thermal plasma deposition reactor. (Courtesy of M.C.M. van de Sanden, EindhovenUniversity of Technology, Eindhoven,The Netherlands.)

the deposition chamber. Near the plasma source silane is injected, and the active plasma species dissociate the silane into radicals and ions. These species can deposit on the substrate, which is positioned further downstream. The main advantage of this technique is the very high deposition rate that can be obtained for the different materials. However, this high deposition rate may not always be compatible with good material quality. A large effort has been made and has resulted in the deposition of good-quality a-Si:H at deposition rates as high as 10 nm/s [432, 561,562].

10.2. Experimental Setup The ETP CVD setup is schematically shown in Figure 70. It consists of a thermal plasma source, a cascaded arc, and a low-pressure deposition chamber [563,564]. The cascaded arc consists of three cathodes, a stack of ten copper plates with a central bore of 4 mm, and an anode plate with a conical nozzle [556]. The length of the cascade is about 10 cm. All parts are water-cooled. Pure argon or an argon-hydrogen mixture is introduced into the arc. The argon flow is varied between 1800 and 6000 sccm, and the hydrogen flow between 0 and 1200 sccm. The arc pressure is between 0.4 and 0.6 bar. The dc discharge is current-controlled. The arc current and voltage are 30-75 A and 45-120 V, respectively. Typical arc plasma parameters are a electron density and temperature of 1016 cm -3 and 1 eV [565], respectively. The deposition chamber is a cylindrical vessel with a diameter of 50 cm and a length of 80 cm. At about 5 cm from the arc outlet, silane can be introduced via an injection ring (7.5-cm diameter) that contains eight holes of 1-mm diameter each. The distance between arc outlet and substrate is 38 cm.

The substrates are heated via the substrate holder, of which the temperature can be controlled between 100 and 500~ Samples can be loaded via a load lock equipped with a magnetic transfer arm. The substrate can be optionally RF-biased. A residual gas analyzer (QMS) and an ellipsometer complete the setup. The typical pressure is in the range of 0.15-0.5 mbar. The deposition chamber has a volume of 1801. During processing it is pumped by a stack of two Roots blowers and one forepump (total pumping capacity is about 1500 m3/h); otherwise it is pumped by a turbo pump (450 l/s), with which a base pressure of 10 -6 mbar is reached. As a result of the large pressure gradient between arc and deposition chamber the plasma expands supersonically from the nozzle into the deposition chamber. After a stationary shock front at about 5 cm from the nozzle, the plasma expands subsonically. As a consequence, the electron density and temperature are drastically reduced [566]. In this downstream region the plasma is recombining, much as in an afterglow plasma. The low electron temperature in the region where the silane is introduced implies that electron-induced reactions are ineffective for the ionization and dissocation of silane. It is found that the admixture of H2 to Ar in the arc is the cause of the strong reduction in the ion and electron density [567]. For pure Ar, the ion density is 1013 cm -3, and consists mainly of Ar +. At high H2 flows (1800 sccm), the ion density is about 4 x 101~ cm -3, and is mainly H +. At low hydrogen flows, ArH + is the most aboundant ion. The reason for this drastic change in density is that fast molecular processes become an important recombination channel for the ions [560, 568]. The atomic H concentration increases from about 2 x 1011 cm -3 at low (240 sccm) H2 flow to about 2 x 1012 cm -3 at high (1800 sccm) H2 flow. The arc

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON changes basically from an argon ion source to an atomic hydrogen source on going from pure argon to admixture of a large amount of hydrogen.

81

o~ 100 tO

E

10.3. Material Properties and Deposition Conditions The deposition rate is found to be independent of the deposition temperature, for low (0.3 nm/s) to high (30 nm/s) rates [472, 473]. The deposition rate and the silane consumption increase with increasing partial pressure of silane [569]. A higher arc current yields a higher silane depletion and deposition rate [563]. The bond-angle distortion, as determined from Raman spectroscopy measurements, varied between 8.3 ~ at low deposition rate and 9.1 o at high deposition rate [570], indicating a slightly increased disorder. The incorporated amount of hydrogen depends on the deposition temperature. The hydrogen content decreases with increasing temperature. For films deposited at a high rate, the hydrogen content always is higher than for the films that were deposited at a low rate. The hydrogen content varies from 60 at.% at a deposition temperature of 100~ to 10 at.% at a deposition temperature of 400~ for high-rate deposited films. The corresponding values for low-rate deposited films are 22 at.% (100~ and 5 at.% (400~ The microstructure factor also decreases with increasing temperature. The refractive index increases with increasing temperature [468]. Both dark conductivity and photoconductivity show an increase with increasing temperature, and have a maximum at 400--450~ [571 ] of 4 x 10 -6 and 10 -9 f2-1 cm- 1, respectively. The deposition rate and the silane consumption decrease sharply by a factor of about four upon adding 60-120 sccm hydrogen to pure argon in the arc, as in shown in Figure 71a. Further addition of hydrogen does not influence these parameters much [569, 572]. Similar effects are observed for the refractive index, microstructure factor, activation energy, and dark conductivity and photoconductivity: adding a small amount of hydrogen leads to a large change, which is saturated upon further hydrogen admixture. Using ion and threshold ionization mass spectrometry (TIMS), Langmuir probe measurements, and cavity ring down absorption spectroscopy (CRDS), the influence of hydrogen admixture on the film growth precursors has been investigated [567, 569, 573]. For the argon-hydrogen plasma, it was found that electron temperature and ion fluence decrease with increasing hydrogen flow. At low hydrogen flow the electron temperature is 0.3 eV, whereas at high hydrogen flow it is 0.1 eV. The ion fluence is decreased from about 120 sccm at low hydrogen flow to about 4 sccm at high flow. Adding silane to the argon-hydrogen plasma leads to the formation of large, hydrogen-poorpositive silicon ions [567]. With increasing flow the cluster size increases; in fact, the higher silane clusters SinH + (n > 5) are much more abundant than the lower silane clusters. The total ion flux towards the substrate scales linearly with the silane flow, while it decreases with increasing hydrogen flow. The maximum contribution of the cationic clusters to film deposition ranges from 4% to 7%

tO

O

10

10

o~

S inl l

(b)

t-

m

§

-+-t

{]) 0 Wl-.l tO

[]

~

.a

10

Sill3

(c)

9

TIMS CRDS

I,...,

tO

O

10

(d) T T

I 0.1

CRDS T Sill

T

_ I -

200

T

T

I

400 H 2 flow

T I

600

800

1000

(sccm)

Fig. 71. The influence of hydrogen admixture on (a) the silane consumption, and the contribution of (b) SinH+, (c) Sill3, (d) Sill and Si to the deposition, as measured by TIMS and CRDS. (From W. M. M. Kessels, Ph.D. Thesis, Technische Universiteit Eindhoven, Eindhoven, the Netherlands, 2000, with permission.)

for varying silane flows, and from 5% to 9% for varying hydrogen flows (Fig. 7 lb), and is nearly independent of both the silane and the hydrogen flow [567]. As a consequence, the contribution of neutral species to the deposition is more than 90%, and consists mainly of Sill3. This contribution increases from about 20% at low hydrogen flow to about 90% at intermediate hydrogen flow, and remains constant with further increase (Fig. 71c). A contribution of Sill2 larger than 0.1% could only be measured at zero hydrogen flow, and amounted to about 5%. Other radicals, viz., Sill and Si, contribute about 2% and 0.2%, respectively, to the deposition (Fig. 71 d), irrespective of hydrogen flow. The optimized conditions for the deposition of good-quality a-Si:H have been found to be: an argon flow of 3300 sccm, a hydrogen flow of 600 sccm, a silane flow of 600 sccm, an arc current of 45 A, an arc voltage of 140 V, an arc pressure of 0.4 bar, a process pressure of 0.2 mbar in the downstream region, and a substrate temperature of 400~ [571,572]. At this high deposition temperature the hydrogen content is 6-7 at.%. Consequently the (cubic) bandgap is low, 1.51 eV. Also, the microstructure factor still is nonzero, viz. 0.2, and what is more, the dark conductivity is a factor of 10 higher than needed for

82

VAN SARK

device quality material. The electron drift mobility is somewhat smaller than usual for device quality films, but the hole drift mobility is one order of magnitude larger. The activation energy, Urbach energy, and defect density are 0.75 eV, 50-55 meV, and 1016 cm -3.

10.4. Deposition Model Kessels has summarized the information on the reactive species emanating from the Ar-H2-operated cascaded arc [571], and has formulated a global reaction scheme. For a hydrogen flow between 0 and 120 sccm, the dissociation of silane is governed by dissociative charge transfer of Ar + with Sill4, which generates Sill + (n < 3)ions: Ar + + Sill4 --+ Ar + Sill + + 9... Then, as the electron density is high, these reactions are quickly followed by dissociative recombination reactions with electrons, which generates Sill + (m < 2) radicals: Sill + + e - --+ SiHm + --'. These highly reactive radicals react with silane molecules, forming polysilane radicals: SiHm + Sill4 --+ Si2Hp + " - . When the electron density is decreased as a result of the dissociative recombination reactions, ion-molecule reactions between silane ions and silane will become significant as well. These reactions (Sill + + Sill4 --+ Si2H + + ..-) lead to sequential ion-Sill4 reactions (SipH + + Sill4 --+ Sip+ill + + 9..), which generate cationic clusters (up to SiloH + have been observed). At a hydrogen flow larger than 300 sccm the ion fluence from the arc is greatly reduced. Reactions with atomic H emanating from the arc now are more effective. The dissociation of silane is governed by hydrogen abstraction, which generates the Sill3 radical (H + Sill4 ~ H2 + Sill3). The small flow of H + from the arc is responsible for a charge exchange reaction with silane, which creates Sill + (n < 3), which initiates sequential ionmolecule reactions as above. The deposition of good-quality a-Si:H using ETP CVD is a result of the dominant presence of the Sill3 radical under conditions of high hydrogen flow in the cascaded arc. The deposition process itself is more or less the same as for PECVD, and was described in Section 7. An important difference between the ETP CVD and the PECVD process is the absence of ions with considerable energy (> 1 eV) and the larger number of cationic clusters in the former. Nevertheless, good-quality a-Si:H is deposited at high rates.

11. APPLICATIONS The first practical device demonstrating the use of a-Si:H as a photovoltaic material was the 2.4%-efficient solar cell reported by Carlson and Wronski [34]. Since then, interest in a-Si:H has been growing rapidly, more or less prompted by the many possible applications. It is used in solar cells and optical sensors based on the photovoltaic effect. Especially the possibility of uniform large-area deposition has been exploited in a-Si:H thin film transistors (TFTs) that are used in controlling active-matrix liquid crystal displays (LCDs). The high photoconductivity and

fast photoresponse of a-Si:H is of great importance for use in large-size linear image sensors. A selection of applications is presented in the following subsections: solar cells, TFTs, light sensors (visible, IR, X-ray), and chemical sensors. Also, light-emitting devices, in particular utilizing erbium incorporation in a-Si:H, are presented. Finally, electrostatic loudspeakers in which an a-Si:H film is incorporated are described. Details of various applications described here, as well as many other applications, can be found in the excellent edited books [4, 5, 11, 13,574].

11.1. Solar Cells

11.1.1. Operation Principle The operation principle of a solar cell is based on charge separation. Photogenerated electrons and holes must be spatially separated in order to contribute to the net current of the device. Charge separation is done by an internal electric field. In crystalline semiconductors this can be achieved by stacking a p-type doped material on an n-type doped material. The internal field at the p-n junction prevents the recombination of photogenerated electrons and holes. Once separated, however, recombination may occur, and is an important loss process in a solar cell [575]. In amorphous semiconductors a p-n junction hardly shows photovoltaic action. Photogenerated electrons and holes cannot diffuse over long distances, as the defect density in p- and n-type doped material is high. Therefore an undoped (intrinsic) layer has to be introduced between the p- and the nlayer, with a thickness smaller than the mean free path of the slower carriers, viz. the holes. In the presence of an electric field the drift length is the mobility-lifetime product times the electric field: )~mfp : # r E [576]. With typical values of # r and E the mean free path usually exceeds by far the thickness of the solar cell, and virtually all photogenerated carriers can be collected. However, under certain operating conditions, field-free regions in the/-layer may exist, and the collection efficiency is decreased because the diffusion lengths of the carriers are much smaller than the thickness of the solar cell [ 11,577]. The p and n layers provide the built-in potential but do not contribute to the collection of carriers. Therefore these layers need to be only as thick as the depletion layer (5-20 nm), as any additional thickness will unnecessarily decrease the collection efficiency by absorbing light. The intrinsic layer should be as thick as possible to absorb the maximum fraction of photons, but the depletion width at operating conditions of about 1 # m sets an upper limit. Typically, one uses a thickness of 500 nm. A schematic cross-section of a p-i-n a-Si:H solar cell [11 ] is shown in Figure 72a. In this so-called superstrate configuration (the light is incident from above), the material onto which the solar cell structure is deposited, usually glass, also serves as a window to the cell. In a substrate configuration the carrier onto which the solar cell structure is deposited forms the back side of the solar cell. The carrier usually is stainless steel, but flexible materials such as metal-coated polymer foil (e.g. polyimid) or a very thin metal make the whole structure flexible [ 11 ].

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON

83

When Rs 90%), large bandgap (> 3.5 eV), and low sheet resistance (< 10 f2/Fq). Tin oxide is made by atmospheric CVD, which inherently produces a native texture. Zinc oxide and ITO, both made by sputtering or evaporation, usually are fiat. Zinc oxide can be etched by HC1 to produce a rough surface [11]. Both tin oxide and zinc oxide are chemically resistant. ITO can be made chemically resistant by adding a thin titanium oxide layer as a protective coating [582]. Zinc oxide has a high contact resistance with doped a-Si:H, which can be circumvented by using a microcrystalline doped layer [583]. Absorption in the p-layer can be reduced by using an a-SiC:H alloy with a bandgap of about 2 eV [584]. Carbon profiling within the p-layer further improves the window properties [585]. An intentionally graded p-i interface (buffer layer) 10 nm in thickness enhances the spectral response in the blue [125,494, 586], which can be attributed to a reduced interface recombination. The properties of the i-n interface and the n-layer are not critical, as long as the conductivity is high. Introducing a TCO layer between n-layer and metal back contact enhances the light trapping even further. Absorption mainly is enhanced in the long-wavelength region [587]. The optimum thickness is found to be 70 nm [588].

84

VAN SARK

Fig. 73. Schematiccross section of a triple-junction a-Si:H substrate solar cell on stainless steel (a), and the corresponding schematicband diagram (b). (FromR. E. I. Schroppand M. Zeman, "Amorphousand Microcrystalline Silicon Solar CellsmModeling, Materials and Device Technology,"Kluwer Academic Publishers, Boston, 1998, with permission.) In the substrate configuration the stainless steel carrier is coated with a Ag-ZnO bilayer in order to enhance the back reflection of the back contact; see Figure 73 [ 11 ]. An increase in Jsc of about 50% was achieved by Banerjee and Guha [589] by using a textured Ag-ZnO bilayer, which further enhances the optical path length and consequently the absorption. As at this stage no a-Si:H has been deposited, there are virtually no restrictions on the process temperature. After depositing the n-layer, a similar i-n buffer layer can be deposited as in p-i-n cells. Bandgap profiling, i.e., increasing the bandgap towards the top p-layer, is much easier for n-i-p structures, as here simply decreasing the deposition temperature during deposition automatically yields a larger bandgap [ 11 ]. In superstrate p-i-n cells, deposition of the/-layer is from the pto the n-layer. In this case, a decrease in the bandgap is achieved by increasing the temperature during deposition, which may not always be desirable for the already deposited p-layer and p-i interface. Another advantage is that the most critical top layers are deposited last. The transparent top contact is deposited last of all, which imposes restrictions on the process temperature. Thermally evaporated ITO and ZnO deposited by metal-organic CVD (MOCVD) are most suitable. At a typical thickness of 70 nm the ITO serves as a good antireflection coating as well. Due to t h e somewhat high sheet resistance, a metal (Ag) grid is necessary to reduce the series resistance [ 11 ].

11.1.3. Multiple-Junction Solar Cells The performance of a-Si:H can be improved by stacking two (or more) cells with different optical bandgaps on top of each

other; see Figure 72b [11]. In such a tandem solar cell, the larger-bandgap material, of which the top cell is made, collects the high-energy photons, while the lower-energy photons are collected in the lower cell. While theoretical efficiencies of single-junction a-Si:H solar cells are around 15%, values above 20% are calculated for multijunction cells. A two-terminal (top and bottom contact) double-junction cell consisting of a top cell with a bandgap of 1.75 eV and a bottom cell with a bandgap of 1.15 eV is predicted to have a conversion efficiency of 21%, while a triple stack of 2.0-, to 1.7-, 1.45-eV cells is predicted to have an efficiency of 24% [590]. In the latter cell carbon alloying of a-Si:H would make the top cell, and germanium alloying the bottom cell. However, due to high defect densities present in a-SiC:H and a-SiGe:H, other ways of obtaining good-quality high- and low-bandgap material have been developed. Dilution of Sill4 with hydrogen in the regime 0.05 < [SiH4]/([SiH4] + [H2]) < 0.15 yields material of better optoelectronic properties than a-SiC:H [369], and is therefore used for the top cell (Fig. 72b). Hydrogen dilution also improves the quality of a-SiGe:H alloys [369]. An a-SiGe:H bottom cell must be designed to operate at long wavelengths, with relatively weakly absorbed light. The concept of bandgap grading at the p-i interface, as in a-Si:H cells, has been demonstrated to be inappropriate for a-SiGe:H cells [591]. Several bandgap profiles were investigated. The best solar cell performance was obtained for a bandgap that first decreased but then increased; see also Zimmer et al. [592]. A triple junction structure based on 1.79-, 1.55-, and 1.39-eV materials [593] was reported to have an initial efficiency of 14.6% and a stabilized (see Section 11.1.4) efficiency of

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON 12.1% [154]. In these series-connected structures the open circuit voltage is the sum of the Voc'S of the individual cells (here Voc = 2.3 V), while the currents are matched to be equal in all cells: Jsc = 7.56 mA/cm 2. The fill factor is 0.7 [154]. A schematic cross section of such a triple-junction p - i - n a-Si(Ge):H solar cell structure in the substrate configuration is shown in Figure 73 [ 11 ], together with the corresponding band diagram. This band diagram shows the intricate bandgap profiling scheme that is needed to obtain these high-efficiency solar cells. A critical part in the structure of multijunction solar cells is the n - p junction that separates the individual cells. Here, electrons that are generated in the top cell (Fig. 72b) flow to the n - p junction, where they must recombine with holes from the bottom cell. As a result of the very high doping levels used, recombination takes place via tunneling. When the recombination rate is not balanced with the supply of carriers, space-charge accumulation will occur, which negatively influences the electric field in the adjacent cell that has the highest generation rate [ 11 ]. Often one of the layers of the tunnel junction is microcrystalline [594]. Another important issue in multijunction cells is current matching. The individual currents must exactly balance; otherwise a loss in efficiency occurs. A current mismatch can be easily revealed by measuring the spectral response [595]. If the currents are matched, then the quantum efficiency is fiat over a wide range of wavelengths. If one of the cells is limiting the current, then the observed quantum efficiency is not fiat, and in fact is the quantum efficiency of the current-limiting cell. Empirical optimization of the thicknesses of the individual cells within the structure is to be combined with computer modeling. A comprehensive model is required in which an optical and an electrical model of a-Si:H are integrated [11]. Since such a model contains about 100 input parameters for a single-junction solar cell, a careful calibration procedure is needed to extract input parameters from measured layer properties [596, 597]. Current matching in tandem cells has been investigated using a model that not only well describes recombination via tunneling but also takes into account the optical enhancement due to the textured TCO [598]. It was found that for an a-Si:H-a-Si:H stack the optimum thickness of the bottom cell amounted to 300 nm, while for an a-Si:H-a-SiGe:H stack it amounted to 150 nm. The optimum thickness of the top cell was 50 and 60 nm for the a-Si:H-a-Si:H and the a-Si:Ha-SiGe:H stack, respectively [ 11,598].

11.1.4. Stability Illumination of solar cells causes a reduction of efficiency and fill factor, as a result of light-induced creation of defects (Staebler-Wronski effect, Section 1.2.5). This reduction is halted after several hundred hours of illumination. The reduction is correlated with solar cell thickness. A large intrinsic layer thickness leads to a large reduction of efficiency and fill

85

factor compared to a small intrinsic layer thickness. The solar cell properties can be completely recovered by annealing at about 150~ The open circuit voltage and short circuit current decrease only slightly. Material properties cannot always be correlated with degradation behavior [493, 495, 599, 600]. Lee et al. [600] have shown the degradation kinetics of cells in which the intrinsic layer was deposited by highly diluting the silane. A clear correlation was observed between the decrease in efficiency and the increase of/zr. Another example that demonstrates a correlation between degradation behavior and material quality was shown in Figure 62. Here the normalized cell efficiency as a function of illumination time was depicted for solar cells, where the intrinsic layer is deposited at different discharge power levels [493]. At the lower power levels the efficiency stabilizes at about 60% of its initial value, whereas at the higher power levels it stabilizes at 40%. This has been attributed to the fact that at the higher power densities the density of the material is lower and the hydrogen content is higher. As a result of the creation of defects, trapping of electrons or holes is enhanced. Thus, the created defects reduce the product lzr, which depresses charge collection and solar cell efficiency. The charge collection length, i.e., the average distance that a carrier travels before it is trapped, is defined as dc = lzr Vbi/d, with Vbi the built-in voltage (typically around 1.2 V [3]) and d the thickness of the cell. An empirical relationship between fill factor and charge collection length dc was reported by Faughnan and Crandall [601 ]: F F - 0.35 + 0.15 l n ( - ~ )

(70)

Smith et al. [602] have derived the dependence of FF on illumination time. They combined the empirical relationship between FF and dc [Eq. (70)] with the time dependence of the defect density (Ndb(t) CC G~ 1/3 [89]) and the relation between/zr and defect density (Ndb CC 1//zr [3]). They arrived at

FF(t) -- FFi - ~ log ~/

(71)

where F F i is the initial FF, k a kinetic constant for degradation, and ti the initial time. Their data were fitted with FF i = 0.68 and k = 0.25. Catalano et al. [603] have introduced the device thickness into an empirical time dependence of the efficiency:

0 - - 0 i [ 1"1- g log(t~.)]

(72)

where 0i is the initial efficiency, and K a rate constant. The removal of defects was found to be a temperature-activated process [604] represented by K = K' exp(Ea/ksT), where K I is a constant increasing with the thickness (cx d~ and EA an activation energy (0.2 eV [603]). At 35~ Eq. (72) can be rewritten as [603]

[

17 = rli 1.1 - 0.165d ~

(t)l ~

(73)

86

VAN SARK

From the increase of the rate constant with thickness it is clear that thick cells will degrade deeper than thin cells. However, because the initial efficiency increases with thickness, an optimum thickness of 200-300 nm is found [577]. The degradation of solar cell properties can be circumvented by proper device design [ 11 ]. The parameter of interest here is the electric field profile after degradation, which should be optimized for carrier collection. A thinner intrinsic layer combined with enhanced light confinement leads to a higher electric field after degradation. Also, bandgap profiling may assist the carrier transport in the low-field region that is present in the intrinsic layer after degradation [605]. Further hydrogen dilution during deposition of the intrinsic layer has been reported to improve the stability [606]. Individual cells in multijunction cells are more stable, due to their reduced thickness compared to single-junction cells. Moreover, as the amount of light that is absorbed in the bottom cell is reduced and as the degradation rate is reduced at lower light levels, the stability is improved [606]. Therefore the multijunction cell is expected to be more stable than a singlejunction cell of the same thickness, which indeed has been demonstrated [577,606-608]. Outdoor operating temperatures of solar cells are around 60~ At this temperature significant annealing of defects occurs [606], and the stability is better than at 25~ Interestingly, seasonal measurements of the performance of solar cells show that the efficiency is higher in summer than in winter [609], which was attributed to annealing of defects [610]. However, it was subsequently reported that these seasonal effects are due to the spectral differences in summer and winter, rather than the increased operating temperature in summer [611, 612]. The research effort in many laboratories around the world on the optimization of laboratory-scale (1-cm 2 area) cells has led to the development of large-area (1 m 2) solar cell modules with an efficiency exceeding 10% [613, 614]. In a module individual cells can be connected in series or parallel, depending on the desired output voltage and current. Details on this topic can be found elsewhere, e.g., [11,157, 577, 607,615,616]. 11.2. Thin Film Transistors

11.2.1. Operation Principle The most common a-Si:H TFT structure is the so-called inverted staggered transistor structure [40], in which silicon nitride is used as the gate insulator. A schematic cross section is shown in Figure 74. The structure comprises an a-Si:H channel, a gate dielectric (SiNx), and source, drain, and gate contacts. The operation principle of these TFTs is identical to that of the metal-oxide-semiconductor field-effect transistor (MOSFET) [617, 618]. When a positive voltage VG is applied to the gate, electrons are accumulated in the a-Si:H. At small voltages these electrons will be localized in the deep states of the a-Si:H. The conduction and valence bands at the SiNx-a-Si:H interface bend down, and the Fermi level shifts upward. Above a certain threshold voltage Vth a constant proportion of the electrons will be mobile, and the conductivity is increased linearly

Fig. 74. Schematiccross section of an inverted staggered TFr structure.

with VG - Vth. As a result the transistor switches on, and a current flows from source to drain. The source-drain current ISD can be expressed as [619] ISD = #FECG ~

(VG -- Vth)

--

VD

(74)

where #FE is the effective carrier or field-effect mobility, Ca the gate capacitance, VD the drain voltage, and W and L the channel width and length, respectively. Saturation of the source--drain current occurs when d JsD/dVD = 0, and it is then expressed as W ISD,sat- #FECG~-~(VG- Vth)2

(75)

The maximum current in the on state is about 10 -4 A, while the current at VG - - 0 is 10 -11 A, which shows the large dynamic range. The threshold voltage is around 1 V, typically, a n d / z ~ can amount to 1 cmZV -1 s -1 [618]. At the interface of the nitride (Eg -- 5.3 eV) and the a-Si:H the conduction and valence band line up. This results in band offsets. These offsets have been determined experimentally: the conduction band offset is 2.2 eV, and the valence band offset 1.2 eV [620]. At the interface a small electron accumulation layer is present under zero gate voltage, due to the presence of interface states. As a result, band bending occurs. The voltage at which the bands are flat (the flat-band voltage V ~ ) is slightly negative.

11.2.2. Stability TFTs are not perfectly stable. After prolonged application of a gate voltage, the threshold voltage starts to shift. Two mechanisms can account for this [621]. One is the charge trapping of electrons in the nitride, where the silicon dangling bond is the dominant electron trap. When electrons are transferred from the a-Si:H to the nitride, they can be trapped close to the interface, and a layer of fixed charge results. This fixed charge QF reduces the charge induced in the a-Si:H, and the transfer characteristic shifts by an amount Q F/CG. In the second mechanism deep defect states are created by the breaking of strained or weak S i - S i bonds. Electrons are trapped in these states and act as fixed negative charges, which results in band bending. This gives a decrease in source-drain current or a positive shift

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON of Vth of several volts. It has been found that the time dependence of the threshold current follows a stretched exponential behavior [622]:

t AVth= (Vth(CX:~)- Vth(0))[(exp(--~0) 3 ) - 1 ]

(76)

where Vth(C~) and Vth(0) are the threshold voltages at infinity and at t -- 0, respectively. The factor/3 has been related to the time-dependent (cx t ~-1) hydrogen diffusion coefficient in a-Si:H [623,624]. HWCVD-deposited a-Si:H layers incorporated in invertedstaggered TFTs have been reported to result in stable behavior of the T F r [538,539]. The threshold voltage does not shift upon prolonged application of a gate voltage. It has been suggested that not only the H content but also the H bonding structure is responsible for the difference in metastable character for PECVD and HWCVD layers [94, 96, 97,625]. Another disadvantageous phenomenon in TFTs is the photoconductivity of a-Si:H [626]. Electrons and holes are photogenerated and recombine at the back surface (gate insulator). The photocurrent reduces the on/off ratio of the TFT. Illumination, however, cannot always be avoided, e.g., in active matrix displays. A way of circumventing this is to make the a-Si:H as thin as possible.

87

plates is controlled by the voltage on the pixel electrode. Nematic liquid crystals consist of rod-shaped molecules that align themselves parallel to an applied electrical field. When no field is present, they align themselves according to the surfaces in between which they are contained. By orienting the crystals, a change in polarization of the light passing through the crystals can be achieved. In this way, the crystals act as light switches. The voltage on the pixel electrode is controlled by the transistors. These act as switches that pass the voltage on their source to the drain, which is, the pixel electrode. When the gate is switched off, the pixel electrode is electrically isolated from the source, and the information remains on the pixel electrode. An n • m matrix of source and gate lines is able to address n • m pixels. This allows for high-definition large-area television displays. As an example, a 640 • 480 pixel display with three subpixels for each color consists of over one million transistors. Active matrix addressing can also be used in printer heads [628] and linear sensor arrays [629]. a-Si:H TFTs are used to address a linear array of output or input transducers, respectively. In the linear sensor array, a-Si:H photodiodes are used.

11.3. Light Sensors 11.3.1. Linear Arrays

11.2.3. Fabrication The TFTs are made on transparent glass substrates, onto which gate electrodes are pattemed. Typically, the gate electrode is made of chromium. This substrate is introduced in a PECVD reactor, in which silane and ammonia are used for plasma deposition of SiNx as the gate material. After subsequent deposition of the a-Si:H active layer and the heavily doped n-type a-Si:H for the contacts, the devices are taken out of the reactor. Cr contacts are evaporated on top of the structure. The transistor channel is then defined by etching away the top metal and n-type a-Si:H. Special care must be taken in that the etchant used for the n-type a-Si:H also etches the intrinsic a-Si:H. Finally the top passivation SiNx is deposited in a separate run. This passivation layer is needed to protect the TFT during additional processing steps. The thickness of the active layer is about 100-300 nm, while the source--drain distance (channel length) amounts to a few micrometers. The channel length is determined by the current requirements and usually exceeds 10/zm. Other manufacturing schemes as well as altemative structures are described elsewhere [619, 621]. Technology developments for the next generation TFTs that are to be used for high-resolution displays have been summarized by Katayama [627].

11.2.4. Application in Active Matrix Displays One of the most important applications of TFTs is in active matrix addressing of liquid crystal displays (AMLCD) [619, 621 ]. The light transmission of a liquid crystal between two glass

Linear arrays of a-Si:H photodiodes are widely used in optical page scanning applications such as fax machines and document scanners [630]. The large linear dimension of the array (as wide as the page to be scanned) allows a much simpler design. No optics are needed for image size reduction, which is required when a CCD camera is used as the detecting element. The matrix addressing is similar to that in AMLCD technology, but confined to one dimension. For each pixel a p - i - n photodiode is connected to a transistor. During illumination of the pixel, charge is transferred to the bottom electrode, and accumulates when the TFT is off. Upon switching on of the TFT, the charge will flow out and can be read by external electronic circuitry. In this way, the sensor integrates the signal during the time that it is not addressed. Readout times are very short in comparison with accumulation times.

11.3.2. Photoreceptors a-Si:H photoconductors can be used as the light-sensitive components in electrophotographic or xerographic processes [39, 631, 632]. In contrast with conventional materials such as AseSe3, CdS, or ZnO, a-Si:H is nontoxic and provides a hard surface. Typically, a three-layer structure is used on top of a glass substrate: n-a-Si:H/i-a-Si:H/a-SiC:H. The electrophotographic process consists of a number of steps [633]. First, the photoconductor is charged in the dark via a corona discharge. Then the photoconductor is illuminated by projecting the image to be copied onto the surface. In the areas that are exposed to light the material becomes conductive and charge flows to the substrate. The nonilluminated parts

88

VAN SARK

still contain charge. The photoconductor then is moved under a bias electrode, and an electric field is present in the gap between electrode and charged surface. Now, liquid toner (ink) is introduced in this gap, and the pigment particles from the toner drift to the surface of the photoconductor due to the electrostatic force. The last step is the transfer of the toner to paper, where it is fused by heat or pressure to make the image permanent. A charged photoconductor discharges slowly in the dark, as is evident from the small decrease in time of the surface voltage. The discharge during illumination is much faster. When the discharge is not complete, a small residual voltage remains on the surface. A low dark current is required, which limits the dark photoconductivity of a-Si:H to 10-12 f2-1 cm- 1. The residual voltage can be minimized by optimizing the/xr of the material. The purpose of the n-type doped a-Si:H layer is to prevent injection of charge from the substrate into the photoconductor. Thus it serves as a blocking layer. Injection of surface charge into the photoconductor is prevented by the surface blocking layer. The a-SiC:H is of low quality, with a high midgap density of states. Surface charge will be trapped in these midgap states. The corona discharges produces oxygen ions and ozone, which may react with the photoconductor [634]. As a means to circumvent possible degradation of the surface layer, an extra, protective thin layer was proposed, with high carbon content [101, 635, 636]. This would reduce silicon-oxygen reactions at the surface. Excellent electrophotographic characteristics have been obtained with a thin device comprising a 0.1-/zm-thick n-type a-Si:H layer, a 1.0-/zm intrinsic a-Si:H layer, a 0.1-/zm undoped a-SiC0.1 :H layer, and a 0.014-/zm undoped a-SiC0.3 :H layer [ 101 ].

bottom n-i-p junction. A change in polarity and value of the voltage selects the color that can be detected. The operation of the device is based on adjusting the photocurrent detection in the middle n-i-n junction. A TCO/p-i-n-i-p/TCO/p-i-n/metal stack has been designed as a three-color sensor [643, 644]. An extra contact is made to the middle TCO. With appropriate bandgaps the peak detection is at 450, 530, and 635 nm for the blue, green, and red, respectively. An active matrix of two-color a-Si:H photodetectors has been reported [645], where a n-i-p-i-n switching device is stacked on a two-color p-i-n-i-p structure.

11.3.5. IR Sensor The absorption values of a-Si:H in the IR are much higher than of c-Si, due to transitions between extended states and deep levels. The IR sensitivity increases with increasing defect density. However, as the collection efficiency decreases drastically with increasing defect density, photodiodes cannot be used. Another approach is based on the change in photocapacitance due to IR radiation. A structure similar to a p-i-n a-Si:H solar cell has been used as an infrared detector [646]. The intrinsic layer in fact is a so-called microcompensated layer with very low concentrations of boron and phosphorus, but with a high defect density. In this layer the IR sensitivity is enhanced, due to transitions between extended states and hole traps. The increase in trapped charge modifies the electric field in the device, which is observed as a change in capacitance. A high responsivity is observed between 800 and 1400 nm, as well as between 3500 and 4500 nm.

11.3.3. Position Sensor An a-Si:H-based position sensor consists of an intrinsic film sandwiched between two transparent conductive electrodes [637]. Two line contacts on the top are perpendicular to two on the bottom. When a light spot is incident on the device, carriers are generated, and a photocurrent flows to the contacts. The contacts form resistive dividers, so that from the ratio of the photocurrents the lateral position relative to the top or bottom contacts can be determined. The top contacts give the x-position, and the bottom contacts the y-position. A p-i-n diode has been used on glass and on polyimid as a position-sensitive detector [638, 639]. The position of an incident light spot is measured by means of the lateral photovoltage.

11.3.4. Color Sensors Similar to multijunction solar cells are color detectors, which have been designed to detect two [640, 641 ] or three [642-644] colors. A so-called adjustable threshold color detector (ATCD) consists of an a-Si:H-a-SiC:H p-i-n-i-p-i-n stack [642]. This ATCD discriminates between the three fundamental colors, red, green, and blue. As a result of proper thickness and bandgap design, the blue is absorbed in the top p-i-n junction, the green in the middle n-i-n junction, and the red in the

11.3.6. X-Ray Sensor High-energy radation can be imaged with a-Si:H, either directly or via a converter [3]. A thick film is required for direct detection, due to the weak interaction of the radiation with the material. A converter usually is a phosphor, which emits in the visible, and thin a-Si:H films are needed. X-rays with an energy up to 100 keV eject the electrons from the inner atomic core levels to high levels in the conduction band. The emitted electrons create electron-hole pairs due to ionization. These pairs can be detected in the same way as in p-i-n photodiodes. X-ray imagers consist of a phosphor in direct contact with the surface of an array of a-Si:H photodiodes. The device is a matrix-addressed array, in which each imaging pixel consists of a photodiode and a TFT [647-649]. These X-ray imagers are very suitable for static and dynamic imaging in medical diagnosis. 11.4. Chemical Sensors

11.4.1. pH ISFET An ion-sensitive field effect transistor (ISFET) with a reference electrode is similar to a MOSFET, with the gate exposed to

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON an electrolyte. Selected ion concentrations can be measured. The threshold voltage of an ISFET depends on the potential of the electrolyte-insulator surface, which in turn is dependent on temperature and on the pH of the electrolyte. The threshold voltage has been found to shift down linearly by about 0.5 V on going from pH 7 to pH 1 [650]. Also, a drift of the gate voltage in time is found; it is small (1 mV/h) for low pH and large (7 mV/h) for high pH [651 ]. This is related to a small temporal change in capacitance of the insulator [652].

11.4.2. Hydrogen Sensor A metal-insulator-semiconductor (MIS) device where palladium is used as the metal is sensitive to hydrogen. This sensitivity is a result of dissociation of hydrogen on the Pd surface, which induces an interface dipole layer that changes the barrier height and dark diode current (reverse bias current) [653]. Using a MIS structure with a-Si:H, i.e., glass/Cr/n-a-Si:H/ i-a-Si:H/SiOx/Pd, Fortunato et al. [654] reported that the presence of 400 ppm of hydrogen leads to an increase of the reverse current of this device by three orders of magnitude. When these devices are illuminated during operation, 400 ppm of hydrogen induces a shift of the open circuit voltage to lower values. Hence, these photochemical sensors can operate as a gas sensor either in the dark or under illumination.

11.5. Other Applications

11.5.1. Loudspeakers The capability of depositing a-Si:H uniformly over large areas has been of special interest for application in electrostatic loudspeakers, where the a-Si:H layer is suitable for the retention layer on the vibrating foils in the loudspeaker. One aims at obtaining a large-area thin film that can be either positivily or negatively charged by applying a high voltage, but at the same time can hold large surface charge densities that do not displace laterally. Here, the high photosensitivity is not important, and in fact should be quenched for proper operation. Electroacoustic transducers can be divided into electrodynamic and electrostatic transducers. The most commonly used loudspeakers convert electrical energy to acoustical energy by electrodynamical means: driving an electromagnetic coil that activates a diaphragm. At low frequencies, however, the diaphragm acts as a high-pass filter, with a cutoff frequency that depends on the diameter of the diaphragm. The mechanical construction of large-area loudspeakers adversely influences the amplitude and phase behavior, especially at high frequencies. These drawbacks usually are overcome by using different-size loudspeakers for different frequency ranges. The electrostatic loudspeaker is used for high-end sound reproduction. The operation principle of an electrostatic loudspeaker is illustrated in Figure 75. Essentially, the electrostatic loudspeaker is a capacitor with air as the dielectric. One of the electrodes is a thin, electrically conducting foil (a in Fig. 75), and the other is a perforated flat fixed plate (b in Fig. 75) that

89

..._

. . . . . . . .

Fig. 75. Schematicdrawing of an electrostatic loudspeaker: a, thin flexible foil coated with a-Si:H (or graphite); b, perforated flat fixed plates.

also is conductive. The electrodes are oppositely charged by a high voltage, 5 kV. Sound is produced by superimposing audiofrequency voltages that drive the movement of the foil [655]. The following issues need to be addressed. The amplitude of the foil motion should be very small to avoid nonlinear distortion. A large-area foil therefore is used. Further, the electrical force between the electrodes can be as large as 20 kV/cm, which may lead to electrical breakthrough. Another issue is the presence of an electric field component over the surface of the foil, as a result of clamping the foil to the edges of the support. This field will vary with the amplitude of the foils, which leads to charge displacements and associated power dissipation. This effect especially may be present at low frequencies, where amplitudes are large. The thin film should meet the following requirements. Areas in excess of 1 m 2 need to be deposited continuously, reproducibly, and homogeneously. The use of plastic foils sets a limit to the deposition temperature. The thin film should be capable of holding large surface charge concentrations, and have a large lateral resistivity. It should be mechanically stable, capable of accommodating mechanical deformations, and resistant to humidity. Usually, the foils are coated with a graphite layer as the semiconducting thin film. However, these layers are frequently unstable, and suffer from charge discplacement effects, which eventually lead to electrical breakdown [656]. Prototype electrostatic loudspeakers where the graphite is replaced by a-Si:H have been made, where a Mylar foil (area 10 • 10 cm 2, thickness 6 / z m ) is used [657]. Deposition of the a-Si:H layer was carried out in the ASTER deposition system. Uniform deposition (standard deviation of thickness, 1.5%) was achieved by diluting the Sill4 with H2 with Sill4 : H2 = 1:2 [370]. The deposition was at room temperature. The hydrogen content amounted to 18 at.%, and the bandgap was 1.81 eV. The dark conductivity and AM1.5 photoconductivity were 7.5 x 10 -9 and 1.8 x 10 -8 f2-1 cm-1, respectively. In practice the film would not be exposed to light. The frequency reponse characteristics of the foil with a-Si:H were measured in the range from 2.9 Hz to 5.46 kHz, by making use of generated pink noise with a continuous energy distribution. In Figure 76 the frequency response characteristics of the a-Si:H-coated foil are compared with those of a conventional graphite-coated foil of the same area. It can be concluded from this figure that the output of the a-Si:H-coated loudspeaker is lower than that of the graphite-coated one from 60 Hz upwards. In spite of the lower efficiency in this range, the a-Si:H-coated loadspeaker outperforms the graphite-coated one in the low range (10-60 Hz). The response is more extended towards low

90

VAN SARK

Fig. 76. Frequencyresponsecharacteristics of a conventional, graphite-coated diaphragm (bar graph) and an a-Si:H-coated diaphragm (line graph).

frequencies, and the cutoff behavior (dB/octave) also seems improved. The frequency response is stable, even after prolonged application of low-frequency signals. The improvement was attributed to the reduced power dissipation at low frequencies due to the absence of charge displacement currents at the surface of the a-Si:H coated foil [657].

11.5.2. Erbium in a-Si:H

Erbium, one of the rare-earth materials, has been very important in the development of optical communication technology in the past decades. The trivalent erbium ion (Er 3+) has an incomplete 4 f shell, which is shielded from the outside by 5s and 5p shells. Due to this, in erbium-doped materials a sharp optical transition from the first excited state to the ground state of Er 3+ is observed, which occurs at an energy of 0.8 eV. The corresponding wavelength is 1.54 #m, which is of great importance in that standard silica-based optical fibers have the highest transparency at this wavelength. Indeed, Er-doped silica optical fibers have been demonstrated to operate as optical amplifiers at 1.54 #m [658, 659]. Planar amplifiers in which Er-doped channel waveguides are manufactured on a planar substrate have also been demonstrated [660]. These are of particular importance in that they can be integrated with other waveguide devices on a single chip. If efficient light emission from Erdoped silicon were possible, integration of optical and electrical functions on a single silicon chip would be within reach. Due to the small emission and absorption cross sections of Er 3+, a high Er density is needed to reach reasonable values of optical gain. Typically Er densities are between 0.1% and 1.0% (1019-1020 Er/cm3). These values are far beyond the equilibrium solubility limits of Er in silicon. Therefore, nonequilibrium methods have to be used, such as ion implantation. Er implantation in crystalline silicon leads to amorphization, and additional annealing (600~ is required to recrystallize the silicon. Optical activation of the Er may even require subsequent annealing at higher temperatures. Impurities such as oxygen or carbon have been found to enhance the luminescence. More can be found in the reviews on Er in silicon that have been published by Polman [661] and Priolo et al. [662, 663].

In this sub-subsection, the Er doping of amorphous silicon is discussed. The problem of limited solubility of Er in crystalline silicon has been circumvented. However, the electrical properties of pure a-Si are poor compared to c-Si. Therefore, hydrogenated amorphous silicon is much more interesting. Besides, the possibility of depositing a-Si:H directly on substrates, i.e., optical materials, would make integration possible. Both low-pressure chemical vapor deposition (LPCVD) [664] and PECVD [665, 666] have been used to make the a-Si:H into which Er is implanted. In both methods oxygen is intentionally added to the material, to enhance the luminescence. The a-Si:H is deposited on Si(100) by LPCVD from Sill4 and NeO at 620~ with hydrogen and oxygen contents of 10% and 31%, respectively. The a-Si:H layer was 340 nm thick. Erbium was implanted at 500 keV to a dose of 1 • 1015 Er/cm e. The peak concentration of Er at a depth of 150 nm was 0.2%. Upon annealing at 400~ room-temperature photoluminescence is observed [664], with the characteristic Er 3+ peak at 1.54 #m. Temperature-dependent luminescence measurements in the range from 77 to 300 K show quenching of the peak luminescence by only a factor of 3. In the case of to Er-implanted crystalline silicon, this quenching is 10-100 times larger. Moreover, the luminescence intensity for the amorphous material is higher over the whole range of measured temperatures. Luminescence lifetime measurements reveal a doubleexponential decay, with lifetimes around 160 and 800/zs, independent of temperature in the range of 77-300 K. This behavior differs from the lifetime quenching as observed for oxygen- or nitrogen-codoped c-Si, where the lifetime is quenched by one to nearly three orders of magnitude [667, 668]. This has been attributed to nonradiative deexcitation of excited Er 3+ that occurs at higher temperatures and depends on the bandgap of the material [669]: the larger the bandgap, the less quenching should be observed. Indeed, the large bandgap of the LPCVD a-Si:H (about 2 eV) seems to inhibit quenching. With PECVD a-Si:H is deposited on a Coming glass substrate from Sill4 at 230~ employing the PASTA deposition system described by Madan et al. [ 159]. The hydrogen and oxygen contents were of 10% and 0.3 %, respectively. The presence of this background concentration of oxygen probably was due to postponed maintenance; however, it was advantageous for this particular experiment. The a-Si:H layer was 250 nm thick. Erbium was implanted at 125 keV to a dose of 4 • 1014 Er/cm e. The peak concentration of Er at a depth of 35 nm was 0.2%. In some samples additional oxygen was implanted at 25 keV to a dose of 7 • 1015 Er/cm e, which resulted in an oxygen peak concentration of 1.7%, which overlapped the Er depth profile. Upon annealing at 400~ room-temperature photoluminescence is observed [665,666], with the characteristic Er 3+ peak at 1.54 /xm, as shown in Figure 77. The inset shows the behavior of the peak intensity as a function of annealing temperature. Temperatures between 300 and 400~ clearly are optimum annealing temperatures. Both the as-implanted samples and the samples annealed at 500~ show no erbiumrelated luminescence. In order to remove irradiation-induced

METHODS OF DEPOSITION OF HYDROGENATED AMORPHOUS SILICON 1.0

. . . .

I

. . . .

I

I

I

. . . .

I

I

I

. . . .

I

. . . .

I

'

'

'

'

A

I

~

0.8

Ol

N.

0

',-,'0.6

hlgh-O

c:

A'--"A

"~

m r

(!.) rm

0.4

0

high-O

"

..J

o..

o

/

,oo2oo~oo4oo5oo

/

0.2

0.0

-

\\ Iow-O

.

1.55

,

9

.

I

. . . .

1.4.0

I

.

1.45

,

.

.

I

1.50

.

,

.

.

I

1.55

,

,

~

,

I

1.60

9

,

i

91

Incorporation of Er during deposition of a-Si:H has also been achieved using molecular beam epitaxy [675], magnetronassisted decomposition of silane [676], PECVD with a metalorganic source of solid erbium (tris(2,2,6,6-tetramethyl-2,5heptadionato)Er(III) [677, 678] and tris(hexafluoroacetylacetate)Er(III). 1,2-dimethoxyethane [679]), electron cyclotron resonance PECVD in combination with sputtering of erbium [680], and catalytic CVD combined with pulsed laser ablation [681 ]. Explanations of the quenching behavior seem to be dependent on the sample preparation technique; recently, however, a comprehensive energy transfer model based on a F6rster mechanism (resonant dipole coupling [682]) has been proposed [683].

i

1.65

Wavelength (jzm) Fig. 77. Room-temperature photoluminescence spectra of Er-implanted PECVD a-Si:H, annealed at 400~ The implantation energy and dose were 125 keV and 4 • 1014 Er/cm 2, respectively, which resulted in peak concentration of 0.2 at.%. "Low-O" and "high-O" denote a peak oxygen concentration in a-Si:H of 0.3 and 1.3 at.%, respectively. The inset shows the 1.54-/zm peak intensity as a function of annealing temperature, for both oxygen concentrations. [From J. H. Shin, R. Serna, G. N. van den Hoven, A. Polman, W. G. J. H. M. van Sark, and A. M. Vredenberg, Appl. Phys. Lett. 68, 697 (1996), 9 1996, American Institute of Physics, with permission.]

effects, high annealing temperatures are needed; however, that increases the outdiffusion of hydrogen. Temperature-dependent luminescence measurements in the range from 77 to 300 K show quenching of the peak luminescence by a factor of about 15. Similar behavior is observed in the lifetime quenching [665, 666]. As the band gap of the PECVD a-Si:H is about 1.6 eV, nonradiative deexcitation of Er may occur at elevated temperatures. The amount of quenching lies in between that of c-Si and LPCVD a-Si:H, just like the bandgap. Electroluminescent devices were made to demonstrate the possible application of these a-Si:H materials. Er-doped p-n diodes in c-Si show electroluminescence, both in forward and reverse bias [670-672]. Under forward bias the electroluminescence signal is attributed to electron-hole recombination, which results in excitation of the Er 3+. Under reverse bias, in particular beyond the Zener breakdown, the erbium is excited by impact excitation by hot electrons that are accelerated across the junction. Incorporated in a device, the LPCVD a-Si:H material shows electroluminescence only in reverse bias [673]. The mechanism is similar to the one described for c-Si. The PECVD a-Si:H material was incorporated in a p-i-n solar cell structure, with a thickness of the intrinsic layer of 500 nm (see Section 11.1). Oxygen was coimplanted at 80 keV (3.2 • 1015 O/cm 2) and at 120 keV (5.5 • 1015 O/cm2), which resulted in a roughly constant oxygen concentration of 1.0% in the Er projected range in the middle of the intrinsic a-Si:H layer. Electroluminescence is observed under forward bias [674].

11.5.3. Miscellaneous

Photodiode arrays have been used as retinal implants [684]. These arrays of p-i-n diodes are fabricated on a thin titanium layer bonded to a glass plate. The total thickness of this flexible structure is 1.5 #m. The microphotodiode array (MPDA) is used to replace photoreceptors (rods and cones) that have become defective due to disease. Near-field optical microscopy (NSOM) [685, 686] has been used as a tool for nanolithography on the submicron length scale. Here, the fiber optic probe is used as a light source to expose a resist by scanning the surface. Dithering (oscillating the probe tip parallel to the surface) is needed to keep a constant probe-sample distance. As NSOM is not diffraction-limited, it is in principle possible to generate features with smaller dimensions (< 100 nm [687,688]) than those that are achievable with far-field optical lithography. Patterning of a-Si:H involves oxidizing the surface by local removal of hydrogen passivafion. The thus formed oxide layer is the mask for subsequent etching. Herndon et al. [689] have reported on NSOM patterning of PECVD a-Si:H in open air, by using an Ar ion laser as the light source. Subsequent etching in a hydrogen plasma revealed an etch selectivity of 500:1. The feature widths are found to be dependent on the dither amplitude A monolithic, amorphous-silicon-based, photovoltaic-powered electrochromic window has been reported by Gao et al. [690]. A thin, wide-bandgap a-SiC:H n-i-p solar cell on top of a glass substrate is used as a semitransparent power supply. An electrochromic device consisting of LiyWO3/LiA1F4/V205 is deposited directly on top of the solar cell. The operation principle is based on the change of optical absorption by inserting and extracting Li + in and out of the WO3 film. A prototype 16-cm 2 device is able to modulate the transmittance of the stack by more than 60% over a large part of the visible spectrum.

12. C O N C L U S I O N In this chapter the deposition of a-Si:H by PECVD has been described. The chapter covers material as well as discharge issues. It tries to relate material and discharge properties in various ways. Plasma modeling provides a means to study in detail

92

VAN SARK

the physical and chemical processes that occur in the plasma. The presented models show a high degree of sophistication, but from the comparison with experimental data it is clear that especially the deposition model needs improvement. Also, a full 2D model most probably is not needed, as differences between 1D and 2D modeling results are not very large. Plasma analysis reveals information on the products of chemical processes, and can be used to good effect as a feedback to plasma modeling. The role of ions has been thoroughly illustrated, and the important result that ion bombardment with moderate energy is beneficial for material quality has been quantified. The many modifications to the conventional RF PECVD method show that one still is trying to find methods that will in the end lead to improved material properties. This is especially the case for the intrinsic metastability of a-Si:H. In this respect, the stable material that is obtained at discharge conditions "at the edge of crystallinity" is very promising. Also, the quest for higher deposition rates while at least maintaining device quality material properties shows the industrial drive behind the research. Faster deposition allows for more solar cells to be produced in the same time. In the three deposition methods PECVD, HWCVD, and ETP CVD one can see certain similarities. In one region in the reactor system, the generation of growth precursors takes place. For PECVD this occurs in the discharge bulk, for HWCVD at and around the wire, and for ETP CVD in the vicinity of the expanding beam. A transport region exists where precursors are transported to the substrate. For HWCVD and ETP CVD this region is between wire/source and substrate. For PECVD this region is the sheath. The third region is the deposition region, in all cases the substrate. Looking at these techniques from this perspective, one can conclude that the deposition mechanism of a-Si:H is universal. The best material quality is obtained when the Sill3 radical is abundantly present. In the last part of this chapter a summary was given of some applications. These are the driving force for the large research effort that continues. From these applications and the many more that were not treated here, it will be clear that a-Si:H is a material that is omnipresent and contributes greatly to our wellbeing.

Acknowledgments It goes without saying that the work presented here could not have been done without the help and support of many people. First, many thanks go to John Bezemer, my supervisor, who taught me all there is to know about plasma deposition of a-Si:H, and now enjoys his retirement. Second, I gratefully acknowledge the colleagues with whom I performed and discussed numerous deposition and plasma analysis experiments: Hans Meiling, Edward Hamers, Stefania Acco, Martin van de Boogaard, Arjan Berntsen, Ernst Ullersma, Ren6 van Swaaij, Meine Kars, Gerard van der Mark, and students Renre Heller, Remco van der Heiden, Pieter van de Vliet, Micha Kuiper,

Tjitske Kooistra, Jan-Wijtse Smit, Edward Prendergast, Tom Thomas, and Lenneke Slooff. Further, I would gratefully like to thank the following persons for various types of continuous support during my active time of research on a-Si:H deposition: Wim Arnold Bik, Frans Habraken, Arjen Vredenberg, Dirk Knoesen, Wim de Kruif, Albert Polman, Gerhard Landweer, Jeroen Daey Ouwens, Kees Feenstra, Maarten van Cleef, Jatindra Rath, Wim Sinke, Bert Slomp, Jeike Wallinga, Karine van der Weft, Ruud Schropp, and Werner van de Weg, who headed the group for over a decade. I very much enjoyed the fruitful collaboration with Wim Goedheer and his group--Gert Jan Nienhuis, Peter Meijer, and Diederick Passchier--at the FOM Institute for Plasmaphysics "Rijnhuizen;' and thank him for supplying me with published and additional data used in the section on plasma modeling. Also, the biannual Dutch meetings on solar cell research always allowed for many discussions with colleagues from Eindhoven Technical University (Daan Schram, Gijs Meeusen, Richard van de Sanden) and Delft Technical University (Miro Zeman, Wim Metselaar). Further I thank Hans Gerritsen and Gijs van Ginkel for allowing and stimulating me to write this chapter. And last but not least, I thank my wife Joni, son Guido, and daughter Sophie for the enormous joy they give me every day. Parts of the work presented here were financially supported by the Netherlands Agency for Energy and the Environment (NOVEM), the Foundation for Fundamental Research on Matter (FOM), the Royal Netherlands Academy of Art and Sciences (KNAW), the Netherlands Technology Foundation (STW), and the Netherlands Organization for Scientific Research (NWO).

REFERENCES 1. J. I. Pankove, Ed., "Hydrogenated Amorphous Silicon, Semiconductors and Semimetals, Vol. 21, Parts A-D,' Academic Press, Orlando, FL, 1984. 2. K. Tanaka, Ed., "Glow-Discharge Hydrogenated Amorphous Silicon." KTK Scientific Publishers, Tokyo, 1989. 3. R.A. Street, "HydrogenatedAmorphousSilicon" Cambridge Solid State Science Series. CambridgeUniversityPress, Cambridge, U.K., 1991. 4. J. Kanicki, Ed., "Amorphous and Microcrystalline Semiconductor Devices--Optoelectronic Devices." Artech House, Norwood,MA, 1991. 5. J. Kanicki, Ed., "Amorphous and Microcrystalline Semiconductor Devices--Materials and Device Physics." Artech House, Norwood,MA, 1992. 6. W. Luft and Y. S. Tsuo, "HydrogenatedAmorphousSilicon Alloy Deposition Processes." Marcel Dekker, New York, 1993. 7. R. E Bunshah, Ed., "Handbook of Deposition Technologies for Films and Coatings--Science, Technologyand Applications." Second Edition. Noyes Publications, Park Ridge, NJ, 1994. 8. G. Bruno, P. Capezzuto, and A. Madan, Eds., "Plasma Deposition of Amorphous Silicon-Based Materials." Academic Press, Boston, 1995. 9. E. S. Machlin, "Materials Science in Microelectronics--the Relationships between Thin Film Processing and Structure." Giro Press, Crotonon-Hudson, NY, 1995. 10. E. S. Machlin, "Materials Science in Microelectronics--Volume 2, The Effects of Structure on Properties in Thin Films." Giro Press, Croton-onHudson, NY, 1998.

METHODS

OF DEPOSITION

OF HYDROGENATED

11. R. E. I. Schropp and M. Zeman, "Amorphous and Microcrystalline Silicon Solar Cells--Modeling, Materials and Device Technology." Kluwer Academic Publishers, Boston, 1998. 12. T.M. Searle, Ed., "Properties of Amorphous Silicon and its Alloys, EMIS Datareview Series, No. 19." IEE, London, 1998. 13. R.A. Street, Ed., "Technology and Applications of Amorphous Silicon." Springer-Verlag, New York, 2000. 14. C. A. M. Stap, H. Meiling, G. Landweer, J. Bezemer, and W. E van der Weg, "Proceedings of the Ninth E.C. Photovoltaic Solar Energy Conference, Freiburg, ER.G., 1989" (W. Palz, G. T. Wrixon, and P. Helm, Eds.), p. 74. Kluwer Academic, Dordrecht, 1989. 15. H. Meiling, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1991. 16. H. Curtins, N. Wyrsch, and A. V. Shah, Electron. Lett. 23, 228 (1987). 17. H. Shirai, J. Hanna, and I. Shimizu, Japan. J. Appl. Phys. 30, L881 (1991). 18. J. T. Verdeyen, L. Beberman, and L. Overzet, J. Vac. Sci. Technol. A 8, 1851 (1990). 19. A. H. Mahan, J. Carapella, B. P. Nelson, R. S. Crandall, and I. Balberg, J. AppL Phys. 69, 6728 (1991). 20. G. M. W. Kroesen, D. C. Schram, and M. J. F. van de Sande, Plasma Chem. Plasma Proc. 10, 49 (1990). 21. G. J. Meeusen, E. A. Ershov-Pavlov, R. F. G. Meulenbroeks, M. C. M. van de Sanden, and D. C. Schram, J. Appl. Phys. 71, 4156 (1992). 22. H. Overhof, J. Non-cryst. Solids 227-230, 15 (1998). 23. J. Tauc, Ed., "Amorphous and Liquid Semiconductors." Plenum, New York, 1974. 24. A. J. Lewis, G. A. N. Connell, W. Paul, J. R. Pawlik, and R. J. Temkin, "Tetrahedrally Bonded Amorphous Semiconductors," AIP Conference Proceedings, Vol. 20 (M. H. Brodsky, S. Kirkpatrick, and D. Weaire, Eds.), p. 27. American Institute of Physics, New York, 1974. 25. E.C. Freeman and W. Paul,. Phys. Rev. B 18, 4288 (1978). 26. W. Paul and H. Ehrenreich, Phys. Today 38 (8), 13 (1985). 27. H. E Sterling and R. C. G. Swann, Solid State Electron. 8, 653 (1965). 28. R. C. Chittick, J. H. Alexander, and H. E Sterling, J. Electrochem. Soc. 116, 77 (1969). 29. A. Triska, D. Dennison, and H. Fritzsche, Bull. Am. Phys. Soc. 20, 392 (1975). 30. H. Fritzsche, "Proceedings of the 7th International Conference on Amorphous and Liquid Semiconductors" (W. E. Spear, Ed.), p. 3. CICL, Edinburgh, 1977. 31. H. Fritsche, Mater. Res. Soc. Proc. Symp. 609, A17.1.1 (2000). 32. W. Spear and P. LeComber, Solid State Commun. 17, 1193 (1975). 33. I. Solomon, Mater. Res. Soc. Proc. Symp. 609, A17.3.1 (2000). 34. D.E. Carlson and C. R. Wronsld, Appl. Phys. Lett. 28, 671 (1976). 35. H. Okamoto, Y. Nitta, T. Yamaguchi, and Y. Hamakawa, Sol. Energy Mater. 3, 313 (1980). 36. Y. Hamakawa, Mater. Res. Soc. Proc. Symp. 609, A17.2.1 (2000). 37. Y. Kuwano, T. Imai, M. Ohnishi, and S. Nakano, "Proceedings of the 14th IEEE Photovoltaic Specialists Conference, San Diego, 1980," p. 1408. IEEE, New York, 1980. 38. I. Shimizu, T. Komatsu, T. Saito, and E. Inoue, J. Non-cryst. Solids 35 & 36, 773 (1980). 39. S. Oda, Y. Saito, I. Shimizu, and E. Inoue, Philos. Mag. B 43, 1079 (1981). 40. P. G. LeComber, W. E. Spear, and A. Ghaith, Electron. Len. 15, 179 (1979). 41. A. J. Snell, K. D. MacKenzie, W. E. Spear, P. G. LeComber, and A. J. Hughes, J. Appl. Phys. 24, 357 (1981). 42. M. J. Powell, B. C. Easton, and O. F. Hill, Appl. Phys. Lett. 38, 794 (1981). 43. R.L. Weisfield, J. Non-cryst. Solids 164-166, 771 (1993). 44. S.N. Kaplan, J. R. Morel, T. A. Mulera, V. Perez-Mendez, G. Schlurmacher, and R. A. Street, IEEE Trans. Nucl. Sci. NS-33, 351 (1986). 45. T. C. Chuang, L. E. Fennel, W. B. Jackson, J. Levine, M. J. Thompson, H. C. Tuan, and R. Weisfield, J. Non-cryst. Solids 97 & 98, 301 (1987). 46. L.E. Antonuk, C. E Wild, J. Boundry, J. Jimenez, M. J. Longo, and R. A. Street, IEEE Trans. Nucl. Sci. NS-37, 165 (1990).

AMORPHOUS

SILICON

93

47. C. van Berkel, N. C. Bird, C. J. Curling, and I. D. French, Mater. Res. Soc. Symp. Proc. 297, 939 (1993). 48. W.H. Zachariasen, J. Am. Chem. Soc. 54, 3841 (1932). 49. D.E. Polk, J. Non-cryst. Solids 5, 365 (1971). 50. M.A. Paesler, D. E. Sayers, R. Tsu, and J. G. Hernandez, Phys. Rev. B 28, 4550 (1983). 51. D. Beeman, R. Tsu, and M. E Thorpe, Phys. Rev. B 32, 874 (1985). 52. R.A. Street, Phys. Rev. Lett. 49, 1187 (1982). 53. N. E Mott, Philos. Mag. 19, 835 (1969). 54. W.M. Arnold Bik, C. T. A. M. de Laat, and E H. P. M. Habraken, NucL Instrum. Methods Phys. Res. B 64, 832 (1992). 55. M.H. Brodsky, Thin Solid Films 40, L23 (1977). 56. G. Lucovsky, R. J. Nemanich, and J. C. Knights, Phys. Rev. B 19, 2064 (1979). 57. H. Shanks, C. J. Fang, L. Ley, M. Cardona, E J. Demond, and S. Kalbitzer, Phys. Status Solidi B 100, 43 (1980). 58. A.A. Langford, M. L. Fleet, B. P. Nelson, W. A. Lanford, and N. Maley, Phys. Rev. B 45, 13367 (1992). 59. W. Beyer and M. S. Abo Ghazala, Mater. Res. Soc. Symp. Proc. 507, 601 (1998). 60. A.H. Mahan, P. Raboisson, and R. Tsu, Appl. Phys. Lett. 50, 335 (1987). 61. D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935). 62. A. H. Mahan, D. L. Williamson, B. P. Nelson, and R. S. Crandall, Sol. Cells 27, 465 (1989). 63. H. Meiling, M. J. van den Boogaard, R. E. I. Schropp, J. Bezemer, and W. E van der Weg, Mater. Res. Soc. Symp. Proc. 192, 645 (1990). 64. M. J. van den Boogaard, S. J. Jones, Y. Chen, D. L. Williamson, R. A. Hakvoort, A. van Veen, A. C. van der Steege, W. M. Arnold Bik, W. G. J. H. M. van Sark, and W. E van der Weg, Mater. Res. Soc. Symp. Proc. 258, 407 (1992). 65. M. J. van den Boogaard, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1992. 66. S. Acco, D. L. Williamson, W. G. J. H. M. van Sark, W. C. Sinke, W. E van der Weg, A. Polman, and S. Roorda, Phys. Rev. B 58, 12853 (1998). 67. A.H. Mahan, D. L. Williamson, B. P. Nelson, and R. S. Crandall, Phys. Rev. B 40, 12024 (1989). 68. P.C. Taylor, in "Semiconductors and Semimetals" (J. I. Pankove, Ed.), Vol. 21 C, p. 99. Academic Press, Orlando, FL, 1984. 69. S. Acco, D. L. Williamson, P. A. Stolk, F. W. Saris, M. J. van den Boogaard, W. C. Sinke, W. E van der Weg, and S. Roorda, Phys. Rev. B 53, 4415 (1996). 70. S. Acco, W. Beyer, E. E. Van Faassen, and W. E van der Weg, J. AppL Phys. 82, 2862 (1997). 71. R. S. Crandall, X. Liu, and E. Iwaniczko, J. Non-cryst. Solids 227-230, 23 (1998). 72. S. Acco, D. L. Williamson, S. Roorda, W. G. J. H. M. van Sark, A. Polman, and W. F. van der Weg, J. Non-cryst. Solids 227-230, 128 (1998). 73. P.J. Zanzucchi, C. R. Wronski, and D. E. Carlson, J. Appl. Phys. 48, 5227 (1977). 74. G.D. Cody, B. Abeles, C. Wronski, C. R. Stephens, and B. Brooks, Sol. Cells 2, 227 (1980). 75. J. Tauc, in "Optical Properties of Solids" (E Abel6s, Ed.), Chap. 5, p. 277. North-Holland, Amsterdam, the Netherlands, 1972. 76. R.H. Klazes, M. H. L. M. van den Broek, J. Bezemer, and S. Radelaar, Philos. Mag. B 45, 377 (1982). 77. T. Tiedje, J. M. Cebulka, D. L. Morel, and B. Abeles, Phys. Rev. Lett. 46, 1425(1981). 78. K. Pierz, B. Hilgenberg, H. Mell, and G. Weiser, J. Non-cryst. Solids 97/98, 63 (1987). 79. K. Pierz, W. Fuhs, and H. Mell, Philos. Mag. B 63, 123 (1991). 80. N. Maley and J. S. Lannin, Phys. Rev. B 36, 1146 (1987). 81. R.C. Ross and J. Jaklik, J. Appl. Phys. 55, 3785 (1984). 82. H. Meiling, W. Lenting, J. Bezemer, and W. E van der Weg, Philos. Mag. B 62, 19 (1990). 83. R.S. Crandall, Sol. Cells 24, 237 (1988). 84. A.J.M. Berntsen, W. E van der Weg, P. A. Stolk, and E W. Saris, Phys. Rev. B 48, 14656 (1993).

94 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102.

103. 104. 105.

106.

107. 108. 109. 110.

111. 112. 113. 114. 115. 116. 117. 118. 119.

120.

VAN SARK A.J.M. Berntsen, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1993. W.E. Spear and P. G. LeComber, Adv. Phys. 26, 811 (1977). D.L. Staebler and C. R. Wronski, Appl. Phys. Lett. 31,292 (1977). D.L. Staebler and C. R. Wronski, J. Appl. Phys. 51, 3262 (1980). M. Stutzmann, W. B. Jackson, and C. C. Tsai, Phys. Rev. B 32, 23 (1985). T. Kamei, N. Hata, A. Matsuda, T. Uchiyama, S. Amano, K. Tsukamoto, Y. yoshioka, and T. Hirao, Appl. Phys. Lett. 68, 2380 (1996). C. C. Tsai, J. C. Knights, R. A. Lujan, W. B. B. L. Stafford, and M. J. Thompson, J. Non-cryst. Solids 59 & 60, 731 (1983). S. Yamasaki and J. Isoya, J. Non-cryst. Solids 164-166, 169 (1993). P. Stradins and H. Fritzsche, Philos. Mag. B 69, 121 (1994). C. Godet, P. Morin, and P. Roca i Cabarrocas, J. Non-cryst. Solids 198200, 449 (1996). J. Daey Ouwens and R. E. I. Schropp, Phys. Rev. B 54, 17759 (1996). S. Zafar and E. A. Schiff, Phys. Rev. B 40, 5235 (1989). C. Manfredotti, E Fizzotti, M. Boero, P. Pastorino, P. Polesello, and E. Vittone, Phys. Rev. B 50, 18046 (1994). H.M. Branz, Solid State Commun. 105,387 (1998). R. Biswas, Q. Li, B. C. Pan, and Y. Yoon, Mater Res. Soc. Symp. Proc. 467, 135 (1997). D.A. Anderson and W. E. Spear, Philos. Mag. 35, 1 (1977). R. A. C. M. M. van Swaaij, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1994. R . A . C . M . M . van Swaaij, A. J. M. Berntsen, W. G. J. H. M. van Sark, H. Herremans, J. Bezemer, and W. E van der Weg, J. Appl. Phys. 76, 251 (1994). J. Chevallier, H. Wieder, A. Onton, and C. R. Guarnieri, Solid State Commun. 24, 867 (1977). S. Wagner, V. Chu, J. P. Conde, and J. Z. Liu, J. Non-cryst. Solids 114, 453(1989). C. M. Fortmann, in "Plasma Deposition of Amorphous Silicon-Based Materials" (G. Bruno, P. Capezzuto, and A. Madan, Eds.), Chap. 3, p. 131. Academic Press, Boston, 1995. W. Paul, S. J. Jones, E C. Marques, D. Pang, W. A. Turner, A. E. Wetsel, P. Wickboldt, and J. H. Chen, Mater Res. Soc. Symp. Proc. 219, 211 (1991). A. Matsuda and K. Tanaka, J. Non-cryst. Solids 97, 1367 (1987). G. Bruno, P. Capezzuto, G. Cicala, and E Cramarossa, J. Mater Res. 4, 366 (1989). G. Bruno, P. Capezzuto, M. Losurdo, P. Manodoro, and G. Cicala, J. Noncryst. Solids 137&138, 799 (1991). H. Herremans, W. Grevendonk, R. A. C. M. M. van Swaaij, W. G. J. H. M. van Sark, A. J. M. Berntsen, W. M. Arnold Bik, and J. Bezemer, Philos. Mag. B 66, 787 (1992). M. P. Schmidt, I. Solomon, H. Tran-Quoc, and J. Bullot, J. Non-cryst. Solids 77-78, 849 (1985). I. Solomon, M. P. Schmidt, and H. Tran-Quoc, Phys. Rev. B 38, 9895 (1988). M.N.P. Carrefio, I. Pereyra, M. C. A. Fantini, H. Takahashi, and R. Landers, J. Appl. Phys. 75,538 (1994). W. M. Arnoldbik and E H. P. M. Habraken, Rep. Prog. Phys. 56, 859 (1993). M.L. Oliveira and S. S. Camargo, Jr., J. Appl. Phys. 71, 1531 (1992). E Evangelisti, J. Non-cryst. Solids 164-166, 1009 (1993). A. Grill, "Cold Plasma in Materials Fabrication--from Fundamentals to Applications." IEEE Press, Piscataway, NJ, 1994. J. E O'Hanlon, "A User's Guide to Vacuum Technology." Second Edition. Wiley, New York, 1989. J. Bezemer, W. G. J. H. M. van Sark, M. B. vonder Linden, and W. E van der Weg, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy Conference, Amsterdam, the Netherlands, 1994" (R. Hill, W. Palz, and P. Helm, Eds.), p. 327. H.S. Stephens & Associates, Bedford, U.K., 1994. J. Bezemer and W. G. J. H. M. van Sark, "Electronic, Optoelectronic and Magnetic Thin Films, Proceedings of the 8th International School on Condensed Matter Physics (ISCMP), Varna, Bulgaria, 1994," p. 219. Wiley, New York, 1995.

121. M. B6hm, A. E. Delahoy, F. B. Ellis, Jr., E. Eser, S. C. Gau, E J. Kampas, and Z. Kiss, "Proceedings of the 18th IEEE Photovoltaic Specialists Conference, Las Vegas, 1985," p. 888. IEEE, New York, 1985. 122. C.R. Dickson, J. Pickens, and A. Wilczynski, Sol. Cells 19, 179 (1986). 123. K. Tanaka and A. Matsuda, Mater Sci. Rep. 2, 139 (1987). 124. F. Jansen and D. Kuhman, J. Vac. Sci. Technol. 6, 13 (1988). 125. W.Y. Kim, H. Tasaki, M. Konagai, and K. Takahashi, J. Appl. Phys. 61, 3071 (1987). 126. A. Catalano and G. Wood, J. Appl. Phys. 63, 1220 (1988). 127. Y. Kuwano, M. Ohnishi, S. Tsuda, Y. Nakashima, and N. Nakamura, Japan. J. Appl. Phys. 21, 413 (1982). 128. R. A. Street, J. Zesch, and M. J. Thompson, Appl. Phys. Lett. 43, 672 (1983). 129. M. Ohnishi, H. Nishiwaki, E. Enomoto, Y. Nakashima, S. Tsuda, T. Takahama, H. Tarui, M. Tanaka, H. Dojo, and Y. Kuwano, J. Non-cryst. Solids 59/60, 1107 (1983). 130. S. Nakano, S. Tsuda, H. Tarui, T. Takahama, H. Haku, K. Watanabe, M. Nishikuni, Y. Hishikawa, and Y. Kuwano, Mater Res. Soc. Symp. Proc. 70, 511 (1986). 131. S. Tsuda, T. Takahama, M. Isomura, H. Tarui, Y. Nakashima, Y. Hishikawa, N. Nakamura, T. Matsuoka, H. Nishiwaki, S. Nakano, M. Ohnishi, and Y. Kuwano, Japan. J. Appl. Phys. 26, 33 (1987). 132. W. Luft, Ed., "Photovoltaic Safety," AIP Conference Proceedings, Vol. 166. American Institute of Physics, New York, 1988. 133. P. J. Hargis, Jr., K. E. Greenberg, E A. Miller, J. B. Gerardo, J. R. Torczynski, M. E. Riley, G. A. Hebner, J. R. Roberts, J. K. Olthoff, J. R. Whetstone, R. J. Van Brunt, M. A. Sobolewski, H. M. Anderson, M. E Splichal, J. L. Mock, E Bletzinger, A. Garscadden, R. A. Gottscho, G. Selwyn, M. Dalvie, J. E. Heidenreich, J. W. Butterbaugh, M. L. Brake, M. L. Passow, J. Pender, A. Lujan, M. E. Elta, D. B. Graves, H. H. Sawin, M. J. Kushner, J. T. Verdeyen, R. Horwath, and T. R. Turner, Rev. Sci. Instrum. 65, 140 (1994). 134. B. Chapman, "Glow Discharge Processes--Sputtering and Plasma Etching." Wiley, New York, 1980. 135. A. Gallagher, Mater Res. Soc. Symp. Proc. 70, 3 (1986). 136. J. Perrin, Y. Takeda, N. Hirano, Y. Takeuchi, and A. Matsuda, Surf. Sci. 210, 114 (1989). 137. A. Matsuda, K. Nomoto, Y. Takeuchi, A. Suzuki, A. Yuuki, and J. Perrin, Surf. Sci. 227, 50 (1990). 138. A. Matsuda and K. Tanaka, J. Appl. Phys. 60, 2351 (1986). 139. T. Ichimura, T. Ihara, T. Hama, M. Ohsawa, H. Sakai, and Y. Uchida, Japan. J. Appl. Phys. 25, L276 (1986). 140. T. Hamasaki, M. Ueda, A. Chayahara, M. Hirose, and Y. Osaka, Appl. Phys. Len. 44, 600 (1984). 141. T. Hamasaki, M. Ueda, A. Chayahara, M. Hirose, and Y. Osaka, Appl. Phys. Lett. 44, 1049 (1984). 142. P. Roca i Cabarrocas, J. B. Chevrier, J. Huc, A. Lloret, J. Y. Parey, and J. E M. Schmitt, J. Vac. Sci. Technol. A 9, 2331 (1991). 143. M. Taniguchi, M. Hiorse, T. Hamasaki, and Y. Osaka, Appl. Phys. Lett. 37,787 (1980). 144. M. Ohnishi, H. Nishiwaki, K. Uchihashi, K. Yoshida, M. Tanaka, K. Ninomiya, M. Nishikuni, N. Nakanura, S. Tsuda, S. Nakano, T. Yazaki, and Y. Kuwano, Japan. J. Appl. Phys. 27, 40 (1988). 145. E N. Boulitrop, N. Proust, J. Magarino, E. Criton, J. E Peray, and M. Dupre, J. Appl. Phys. 58, 3494 (1985). 146. H. Chatham and E K. Bhat, Mater Res. Soc. Symp. Proc. 149,447 (1989). 147. H. Chatham, E Bhat, A. Benson, and C. Matovich, J. Non-cryst. Solids 115,201 (1989). 148. P.M. Meijer, J. D. E Passchier, W. J. Goedheer, J. Bezemer, and W. G. J. H. M. van Sark, Appl. Phys. Lett. 64, 1780 (1994). 149. W.J. Goedheer, E M. Meijer, J. Bezemer, J. D. E Passchier, and W. G. J. H. M. van Sark, IEEE Trans. Plasma Sci. PS-23,644 (1995). 150. W . G . J . H . M . van Sark, H. Meiling, J. Bezemer, M. B. vonder Linden, R. E. I. Schropp, and W. F. van der Weg, Sol. Energy Mater Sol. Cells 45, 57 (1997).

METHODS

OF DEPOSITION

OF HYDROGENATED

151. H. Meiling, W. G. J. H. M. van Sark, J. Bezemer, R. E. I. Schropp, and W. van der Weg, "Proceedings of the 25th IEEE Photovoltaic Specialists Conference, Washington, D.C., 1996," p. 1153. IEEE, New York, 1996. 152. J.P.M. Schmitt, J. Meot, P. Roubeau, and P. Parrens, "Proceedings of the Eighth E.C. Photovoltaic Solar Energy Conference, Florence, Italy, 1988" (I. Solomon, B. Equer, and P. Helm, Eds.), p. 964. Kluwer Academic, Dordrecht, 1989. 153. S. Tsuda, S. Sakai, and S. Nakano, Appl. Surf. Sci. 113/114, 734 (1997). 154. J. Yang, A. Banerjee, S. Sugiyama, and S. Guha, Appl. Phys. Lett. 70, 2975 (1997). 155. R. E. I. Schropp, C. H. M. van der Werf, M. Zeman, M. C. M. van de Sanden, C. I. M. A. Spee, E. Middelman, L. V. de Jonge-Meschaninova, A. A. M. van der Zijden, M. M. Besselink, R. J. Severens, J. Winkeler, and G. J. Jongerden, Mater. Res. Soc. Symp. Proc. 557, 713 (1999). 156. S. Fujikake, K. Tabuchi, T. Yoshida, Y. Ichikawa, and H. Sakai, Mater Res. Soc. Symp. Proc. 377, 609 (1995). 157. T. Yoshida, S. Fujikake, S. Kato, M. Tanda, K. Tabuchi, A. Takano, Y. Ichikawa, and H. Sakai, Sol. Energy Mater. SoL Cells 48, 383 (1997). 158. E. Middelman, E. van Andel, P. M. G. M. Peters, L. V. de JongeMeschaninova, R. J. Severens, G. J. Jongerden, R. E. I. Schropp, H. Meiling, M. Zeman, M. C. M. van de Sanden, A. Kuipers, and C. I. M. A. Spee, "Proceedings of the 2nd World Conference on Photovoltaic Energy Conversion, Vienna, Austria" (J. Schmid, H. A. Ossenbrink, P. Helm, H. Ehmann, and E. D. Dunlop, Eds.), p. 816. European Commision Joint Research Centre, Ispra, Italy, 1998. 159. A. Madan, P. Rava, R. E. I. Schropp, and B. von Roedern, Appl. Surf. Sci. 70/71,716 (1993). 160. W. G. J. H. M. van Sark, J. Bezemer, M. Kars, M. Kuiper, E. A. G. Hamers, and W. E van der Weg, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy Conference, Amsterdam, the Netherlands, 1994" (R. Hill, W. Palz, and P. Helm, Eds.), p. 350. H. S. Stephens & Associates, Bedford, U.K., 1994. 161. E. A. G. Hamers, W. G. J. H. M. van Sark, J. Bezemer, W. J. Goedheer, and W. E van der Weg, Int. J. Mass Spectrom. Ion Processes 173, 91 (1998). 162. W. G. J. H. M. van Sark, J. Bezemer, and W. J. Goedheer, unpublished results. 163. E.A.G. Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1998. 164. H. Shirai, D. Das, J. Hanna, and I. Shimizu, Appl. Phys. Lett. 59, 1096 (1991). 165. W.G.J.H.M. van Sark, J. Bezemer, P. G. van de Vliet, M. Kars, and W. E van der Weg, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy Conference, Amsterdam, the Netherlands, 1994" (R. Hill, W. Palz, and P. Helm, Eds.), p. 335. H.S. Stephens & Associates, Bedford, U.K., 1994. 166. H. Kausche, M. Mrller, and R. Pl~ittner, "Proceedings of the Fifth E.C. Photovoltaic Solar Energy Conference, Athens, Greece, 1983." Reidel, Dordrecht, 1983. 167. A. Morimoto, M. Matsumoto, M. Kumeda, and T. Shimizu, Japan. J. Appl. Phys. 29, L1747 (1990). 168. A. Ricard, "Reactive Plasmas." Socirt6 Fran~aise du Vide, Paris, 1996. 169. H.S. Butler and G. S. Kino, Phys. Fluids 6, 1346 (1963). 170. K. Krhler, J. W. Coburn, D. E. Home, E. Kay, and J. H. Keller, J. Appl. Phys. 57, 59 (1985). 171. M. A. Liebermann and S. E. Savas, J. Vac. Sci. Technol. A 16, 1632 (1990). 172. M.V. Alves, M. A. Liebermann, V. Vahedi, and C. K. Birdsall, J. Appl. Phys. 69, 3823 (1991). 173. J. Perrin, in "Plasma Deposition of Amorphous Silicon-Based Materials" (G. Bruno, P. Capezzuto, and A. Madan, Eds.), Chap. 4, p. 177. Academic Press, Boston, 1995. 174. P. M. Meijer and W. J. Goedheer, IEEE Trans. Plasma Sci. PS-19, 170 (1991). 175. P.M. Meijer, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1991. 176. K. Krhler, D. E. Home, andJ. W. Coburn, J. Appl. Phys. 58, 3350 (1985). 177. A.D. Kuypers and H. J. Hopman, J. Appl. Phys. 63, 1894 (1988). 178. W.J. Goedheer, private communication. 179. J.D.P. Passchier, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1994.

180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215.

216. 217. 218. 219. 220. 221. 222. 223. 224. 225.

AMORPHOUS

SILICON

95

S. Rauf and M. J. Kushner, J. Appl. Phys. 83, 5087 (1998). V.A. Godyak and R. B. Piejak, J. Vac. Sci. Technol. A 8, 3833 (1990). C.M. Horwitz, J. Vac. Sci. Technol. A 1, 1795 (1983). E Finger, U. Kroll, V. Viret, A. Shah, W. Beyer, X.-M. Tang, J. Weber, A. A. Howling, and C. Hollenstein, J. Appl. Phys. 71, 5665 (1992). C. Brhm and J. Perrin, J. Phys. D 24, 865 (1991). K.M.H. Maessen, Ph.D. Thesis, Universiteit Utrecht, Utrecht 1988. M.J.M. Pruppers, Ph.D. Thesis, Universiteit Utrecht, Utrecht 1988. S. Ishihara, K. Masatoshi, H. Takashi, W. Kiyotaka, T. Arita, and K. Moil, J. Appl. Phys. 62, 485 (1987). V.A. Godyak and R. B. Piejak, Phys. Rev. Lett. 65,996 (1990). G.J. Nienhuis, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1998. M.J. Kushner, J. Appl. Phys. 63, 2532 (1988). G.J. Nienhuis, W. J. Goedheer, E. A. G. Hamers, W. G. J. H. M. van Sark, and J. Bezemer, J. Appl. Phys. 82, 2060 (1997). J. Perrin, O. Leroy, and M. C. Bordage, Contrib. Plasma Phys. 36, 3 (1996). A.V. Phelps, J. Phys. Chem. Ref Data 19, 653 (1990). H. Tawara, Y. Itikawa, H. Nishimura, and M. Yoshino, J. Phys. Chem. Ref Data 19, 617 (1990). L. Layeillon, E Duverneuil, J. E Couderc, and B. Despax, Plasma Sources Sci. Technol. 3, 61 (1994). L. Layeillon, P. Duverneuil, J. E Couderc, and B. Despax, Plasma Sources Sci. Technol. 3, 72 (1994). J. R. Doyle, D. A. Doughty, and A. Gallagher, J. Appl. Phys. 68, 4375 (1990). E Kae-Nune, J. Perrin, J. Guillon, and J. Jolly, Japan. J. Appl. Phys. 33, 4303 (1994). E.R. Austin and E W. Lampe, J. Phys. Chem. 81, 1134 (1977). T.L. Pollock, H. S. Sandhu, A. Jodhan, and O. E Strausz, J. Am. Chem. Soc. 95, 1017 (1973). J. Perrin, J. E M. Schmitt, G. De Rosny, B. Drrvillon, J. Huc, and A. Lloret, Chem. Phys. 73,383 (1982). G.C.A. Perkins, E. R. Austin, and E W. Lampe, J. Am. Chem. Soc. 101, 1109 (1979). M. Hertl, N. Dorval, O. Leroy, J. Jolly, and M. Pralet, Plasma Sources Sci. Technol. 7, 130 (1998). J. R. Doyle, D. A. Doughty, and A. Gallagher, J. Appl. Phys. 71, 4771 (1992). A.G. Engelhardt and A. V. Phelps, Phys. Rev. 131, 2115 (1963). E. Krishnakumar and S. K. Srivastava, Contrib. Plasma Phys. 35, 395 (1995). H. Tawara and T. Kato, At. Data Nucl. Data Tables 36, 167 (1987). P. Haaland, J. Chem. Phys. 93, 4066 (1990). J.M. Wadehra and J. N. Bardsley, Phys. Rev. Lett. 41, 1795 (1978). E. Krishnakumar, S. K. Srivastava, and I. Iga, Int. J. Mass Spectrom. Ion Processes 103, 107 (1991). J. Perrin, J. Phys. D26, 1662(1993). W. Kurachi and Y. Nakamura, J. Phys. D 22, 107 (1989). H. Ehrhardt, L. Langhans, E Linder, and H. Taylor, Phys. Rev. 173, 222 (1968). A. E Hickman, J. Chem. Phys. 70, 4872 (1979). N. Itabashi, K. Kato, N. Nishiwaki, T. Goto, C. Yamada, and E. Hirota, Japan. J. Appl. Phys. 28, L325 (1989). J.M.S. Henis, G. W. Steward, M. K. Tripodi, and E E Gaspar, J. Chem. Phys. 57, 389 (1972). P. Kae-Nune, J. Perrin, J. Jolly, and J. Guillon, Surf. Sci. 360, L495 (1996). T. Fuyuki, B. Allain, and J. Perrin, J. Appl. Phys. 68, 3322 (1990). E.W. McDaniel and E. A. Mason, "The Mobility and Diffusion of Ions in Gases." Wiley, New York, 1973. J.D. E Passchier and W. J. Goedheer, J. Appl. Phys. 74, 3744 (1993). J. E Boeuf and L. C. Pitchford, Phys. Rev. E 51, 1376 (1995). C.K. Birdsall, IEEE Trans. Plasma Sci. 19, 65 (1991). J. E Boeuf and P. Belenguer, J. Appl. Phys. 71, 4751 (1992). M. Yan and W. J. Goedheer, Plasma Sources Sci. Technol. 8, 349 (1999). N. Sato and H. Tagashira, IEEE Trans. Plasma. Sci. PS-19, 10102 (1991).

96

VAN SARK

226. N.V. Mantzaris, A. Boudouvis, and E. Gogolides, J. Appl. Phys. 77, 6169 (1995). 227. M.J. Kushner, Solid State Technol. 6, 135 (1996). 228. G.G. Lister, Vacuum 45,525 (1994). 229. E. Gogolides and H. H. Sawin, J. Appl. Phys. 72, 3971 (1992). 230. P.M. Meijer, W. J. Goedheer, and J. D. P. Passchier, Phys. Rev. A 45, 1098 (1992). 231. I.P. Shkarofsky, T. W. Johnston, and M. P. Bachynski, 'q'he Particle Kinetics of Plasmas." Addison-Wesley, Reading, MA 1966. 232. G.J. Nienhuis and W. J. Goedheer, Plasma Sources Sci. Technol. 8, 295 (1999). 233. A.D. Richards, B. E. Thompson, and H. H. Sawin, Appl. Phys. Len. 50, 492 (1987). 234. D.P. Lymberopoulos and D. J. Economou, J. Phys. D 28, 727 (1995). 235. E.A.G. Hamers, W. G. J. H. M. van Sark, J. Bezemer, W. E van der Weg, and W. J. Goedheer, Mater. Res. Soc. Symp. Proc. 420, 461 (1996). 236. M. Heintze and R. Zedlitz, J. Non-cryst. Solids 198-200, 1038 (1996). 237. E. W. McDaniel, "Collision Phenomena in Ionized Gases." Wiley, New York, 1964. 238. P.J. Chantry, J. Appl. Phys. 62, 1141 (1987). 239. M.S. Barnes, T. J. Cotler, and M. E. Elta, J. Comput. Phys. 77, 53 (1988). 240. W.L. Morgan, Plasma Chem. Plasma Process. 12, 477 (1992). 241. D.L. Sharfetter and H. K. Gummel, IEEE Trans. Electron Devices ED16, 64 (1969). 242. W. Hackbusch, "Multigrid Methods and Applications." Springer-Verlag, Berlin, 1985. 243. J.D.P. Passchier, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1994. 244. A.A. Fridman, L. Boufendi, T. Hbid, B. V. Potapkin, and A. Bouchoule, J. Appl. Phys. 79, 1303 (1996). 245. J. Perrin, P. Roca i Cabarrocas, B. Allain, and J.-M. Friedt, Japan. J. Appl. Phys. 27, 2041 (1988). 246. J.L. Andtijar, E. Bertran, A. Canillas, C. Roch, and J. L. Morenza, J. Vac. Sci. Technol. A 9, 2216 (1991). 247. W . G . J . H . M . van Sark, J. Bezemer, E. M. B. Heller, M. Kars, and W. E van der Weg, Mater. Res. Soc. Symp. Proc. 377, 3 (1995). 248. G. Oversluizen and W. H. M. Lodders, J. Appl. Phys. 83, 8002 (1998). 249. M. Heintze and R. Zedlitz, Prog. Photovolt. Res. Appl. 1,213 (1993). 250. A. A. Howling, J.-L. Doffer, C. Hollenstein, U. Kroll, and E Finger, J. Vac. Sci. Technol. A 10, 1080 (1992). 251. W . G . J . H . M . van Sark, J. Bezemer, and W. E van der Weg, Surf. Coat. Technol. 74-75, 63 (1995). 252. L. Sansonnens, A. A. Howling, and C. Hollenstein, Plasma Sources Sci. Technol. 7, 114 (1998). 253. M. Capitelli, C. Gorse, R. Winkler, and J. Wilhelm, Plasma Chem. Plasma Process. 8, 399 (1988). 254. H. Curtins, N. Wyrsch, N. Favre, and A. V. Shah, Plasma Chem. Plasma Process. 7, 267 (1987). 255. L. A. Pinnaduwga, W. Ding, and D. L. McCorkle, Appl. Phys. Lett. 71, 3634 (1997). 256. L.A. Pinnaduwga and P. G. Datskos, J. Appl. Phys. 81, 7715 (1997). 257. O. Leroy, G. Gousset, L. L. Alves, J. Perrin, and J. Jolly, Plasma Sources Sci. Technol. 7, 348 (1998). 258. J.P.M. Schmitt, Thin Solid Films 174, 193 (1989). 259. L. Sansonnens, D. Franz, C. Hollenstein, A. A. Howling, J. Schmitt, E. Turlot, T. Emeraud, U. Kroll, J. Meier, and A. Shah, "Proceedings of the 13th European Photovoltaic Solar Energy Conference, Nice, France, 1995" (W. Freiesleben, W. Palz, H. A. Ossenbrink, and P. Helm, Eds.), p. 276. H.S. Stephens & Associates, Bedford, U.K., 1995. 260. D. Vender and R. W. Boswell, IEEE Trans. Plasma Sci. 18, 725 (1990). 261. C.K. Birdsall, IEEE Trans. Plasma. Sci. 19, 65 (1991). 262. C.K. Birdsall and A. B. Langdon, "Plasma Physics via Computer Simulation." Adam Hilger, Bristol, 1991. 263. V. Vahedi, "XPDP1 Manual." University of California, Berkeley, CA, 1994. 264. J. D. P. Passchier, Technical Report No. GF95.08, Utrecht University, Utrecht, 1995.

265. W . G . J . H . M . van Sark and J. Bezemer, Technical Report, Utrecht University, Utrecht, 1995. 266. Y. Ohmori, M. Shimozuma, and H. Tagashira, J. Phys. D 19, 1029 (1986). 267. E. A. Mason and E. W. McDaniel, '"I'ransport Properties of Ions in Gases." Wiley, New York, 1988. 268. D.B. Graves, J. Appl. Phys. 62, 88 (1987). 269. J.-P. Boeuf, Phys. Rev. A 36, 2782 (1987). 270. E. Gogolides and H. H. Sawin, J. Appl. Phys. 72, 3971 (1992). 271. A. Manenschijn and W. J. Goedheer, J. Appl. Phys. 69, 2923 (1991). 272. V. Vahedi, C. K. Birdsall, M. A. Lieberman, G. Dipeso, and T. D. Rognlien, Phys. Fluids B 5, 2719 (1993). 273. K. Nanbu and Y. Kitatani, Vacuum 47, 1023 (1996). 274. A.K. Jain and D. G. Thompson, J. Phys. B 20, L389 (1987). 275. H. Tawara, Y. Itikawa, H. Nishimura, and M. Yoshino, J. Phys. Chem. Ref Data 19, 621 (1990). 276. M.R. Wertheimer and M. Moisan, J. Vac. Sci. Technol. A 3, 2643 (1985). 277. H. Curtins, N. Wyrsch, M. Favre, and A. V. Shah, Plasma Chem. Plasma Process. 7, 267 (1987). 278. V.A. Godyak, Sov. Phys. Tech. Phys. 16, 1073 (1973). 279. M. Heintze and R. Zedlitz, J. Phys. D 26, 1781 (1993). 280. M. Heintze and R. Zedlitz, J. Non-cryst. Solids 164-166, 55 (1993). 281. J. Dutta, W. Bacsa, and C. Hollenstein, J. Appl. Phys. 72, 3220 (1992). 282. P. Mfrel, M. Chaker, M. Moisan, A. Ricard, and M. Tabbal, J. Appl. Phys. 72, 3220 (1992). 283. S. Vep~ek and M. G. J. Vep~ek-Heijman, Appl. Phys. Lett. 56, 1766 (1990). 284. J. Dutta, U. Kroll, P. Chabloz, A. Shah, A. A. Howling, J.-L. Doffer, and C. Hollenstein, J. Appl. Phys. 72, 3220 (1992). 285. T. Takagi, J. Vac. Sci. Technol. A 2, 282 (1983). 286. G. Turban, B. Drfvillon, D. S. Mataras, and D. E. Rapakoulias, in "Plasma Deposition of Amorphous Silicon-Based Materials" (G. Bruno, P. Capezzuto, and A. Madan, Eds.), Chap. 2, p. 63. Academic Press, Boston, 1995. 287. A. Matsuda and N. Hata, in "Glow-Discharge Hydrogenated Amorphous Silicon" (K. Tanaka, Ed.), Chap. 2, p. 9. KTK Scientific Publishers, Tokyo, 1989. 288. A. Matsuda, T. Kaga, H. Tanaka, L. Malhotra, and K. Tanaka, Japan. J. Appl. Phys. 22, L115 (1983). 289. D. Mataras, S. Cavadias, and D. Rapakoulias, J. Appl. Phys. 66, 119 (1989). 290. D. Mataras, S. Cavadias, and D. Rapakoulias, J. Vac. Sci. Technol. A 11, 664 (1993). 291. N. Itabashi, K. Kato, N. Nishiwaki, T. Goto, C. Yamada, and E. Hirota, Japan. J. Appl. Phys. 27, L1565 (1988). 292. N. Itabashi, N. Nishiwaki, M. Magane, S. Naito, T. Goto, A. Matsuda, C. Yamada, and E. Hirota, Jpn. J. Appl. Phys. 29, L505 (1990). 293. N. Hershkowitz, M. H. Cho, C. H. Nam, and T. Intrator, Plasma Chem. Plasma Process. 8, 35 (1988). 294. P. Awakowicz, Mater. Sci. Forum 287-288, 3 (1998). 295. R. van der Heijden, Master's Thesis, Utrecht University, Utrecht, 1996. 296. E. R. Mosburg, R. C. Kerns, and J. R. Abelson, J. Appl. Phys. 54, 4916 (1983). 297. G. Bruno, P. Capezzuto, G. Cicala, P. Manodoro, and V. Tassielli, IEEE Trans. Plasma Sci. PS- 18, 934 (1990). 298. S. Vep~ek and M. Heintze, Plasma Chem. Plasma Process. 10, 3 (1990). 299. J. C&abe, J. J. Gandfa, and M. T. Gutifrrez, J. Appl. Phys. 73, 4618 (1993). 300. N. Spiliopoulos, D. Mataras, and D. E. Rapakoulias, J. Electrochem. Soc. 144, 634 (1997). 301. E . A . G . Hamers, W. G. J. H. M. van Sark, J. Bezemer, H. Meiling, and W. E van der Weg, J. Non-cryst. Solids 226, 205 (1998). 302. G. Nolet, J. Electrochem. Soc. 122, 1030 (1975). 303. G. Turban, Y. Catherine, and B. Grolleau, Thin Solid Films 60, 147 (1979). 304. J.J. Wagner and S. Vep~ek, Plasma Chem. Plasma Process. 2, 95 (1982). 305. G. Turban, Y. Catherine, and B. Grolleau, Plasma Chem. Plasma Process. 2, 61 (1982).

METHODS OF DEPOSITION OF HYDROGENATED 306. E A. Longeway, H. A. Weakliem, and R. D. Estes, J. Appl. Phys. 57, 5499 (1985). 307. R. Robertson, D. Hils, H. Chatham, and A. Gallagher, Appl. Phys. Lett. 43, 544 (1983). 308. M. Heintze and S. Vep~ek, Appl. Phys. Lett. 54, 1320 (1989). 309. G. Turban, Y. Catherine, and B. Grolleau, Thin Solid Films 77, 287 (1981). 310. G. Turban, Pure AppL Chem. 56, 215 (1984). 311. P. Kae-Nune, J. Perrin, J. Guillon, and J. Jolly, Plasma Sources Sci. Technol. 4, 250 (1995). 312. R. Robertson and A. Gallagher, J. Appl. Phys. 59, 3402 (1986). 313. F. A. Baiocchi, R. C. Wetzel, and R. S. Freund, Phys. Rev. Lett. 53, 771 (1984). 314. R. S. Freund, R. C. Wetzel, R. J. Shul, and T. R. Hayes, Phys. Rev. A 41, 3575 (1990). 315. Hiden Analytical Ltd., 240 Europa Boulevard, Gemini Business Park, Warrington WA5 5UN, England. 316. P. Ho, W. G. Breiland, and R. J. Buss, J. Chem. Phys. 91, 2627 (1989). 317. J. Perrin, M. Shiratani, P. Kae-Nune, H. Videlot, J. Jolly, and J. Guillon, J. Vac. Sci. Technol. A 16, 278 (1998). 318. J. Perrin, C. B6hm, R. Eternadi, and A. Lloret, Plasma Sources Sci. Technol. 3, 252 (1994). 319. G. Turban, Y. Catherine, and B. Grolleau, Thin Solid Films 67, 309 (1980). 320. H. Chatham, D. Hils, R. Robertson, and A. Gallagher, J. Chem. Phys. 81, 1770 (1984). 321. A.A. Howling, L. Sansonnens, J.-L. Dorier, and C. Hollenstein, J. Appl. Phys. 75, 1340 (1994). 322. L. Boufendi and T. Bouchoule, A. Hbid, J. Vac. Sci. Technol. A 14, 572 (1996). 323. B.E. Thompson, K. D. Allen, A. D. Richards, and H. H. Sawin, J. Appl. Phys. 59, 1890 (1986). 324. J. Liu, G. L. Huppert, and H. H. Sawin, J. Appl. Phys. 68, 3916 (1990). 325. C. Wild and P. Koidl, J. Appl. Phys. 69, 2909 (1991). 326. R. J. M. M. Snijkers, M. J. M. Sambeek, G. M. W. Kroesen, and E J. de Hoog, Appl. Phys. Lett. 63, 308 (1993). 327. J. K. Olthoff, R. J. van Brunt, S. B. Radovanov, J. A. Rees, and R. Surowiec, J. Appl. Phys. 75, 115 (1994). 328. M. Fivaz, S. Brunner, W. Swarzenbach, A. A. Howling, and C. Hollenstein, Plasma Sources Sci. Technol. 4, 373 (1995). 329. D.A. Dahl, J. E. Delmore, and A. D. Appelhans, Rev. Sci. Instrum. 61, 607 (1990). 330. M. L. Mandich, W. D. Reents, and K. D. Kolenbrander, J. Chem. Phys. 92, 437 (1990). 331. W.D. Reents and M. L. Mandich, J. Chem. Phys. 96, 4429 (1992). 332. E.A.G. Hamers, J. Bezemer, H. Meiling, W. G. J. H. M. van Sark, and W. E van der Weg, Mater. Res. Soc. Symp. Proc. 467, 603 (1997). 333. R. J. M. M. Snijkers, Ph.D. Thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 1993. 334. E.R. Fisher and P. B. Armentrout, J. Chem. Phys. 93, 4858 (1990). 335. W.N. Allen, T. M. H. Cheng, and E W. Lampe, J. Chem. Phys. 66, 3371 (1977). 336. R.M.A. Azzam and N. M. Bashara, "Ellipsometry and Polarized Light." North Holland, Amsterdam, 1977. 337. B. Dr6villon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, Rev. Sci. Instrum. 53, 969 (1982). 338. N. Blayo and B. Dr6villon, Appl. Phys. Lett. 59, 950 (1991). 339. R.W. Collins, Rev. Sci. Instrum. 61, 2029 (1990). 340. H. Fujiwara, Y. Toyoshima, M. Kondo, and A. Matsuda, Phys. Rev. B 60, 13598 (1999). 341. R. Brenot, B. Dr6villon, P. Bulkin, P. Roca i Cabarrocas, and R. Vanderhaghen, Appl. Surf. Sci. 154-155, 283 (2000). 342. R.W. Collins, J. Koh, A. S. Ferlauto, P. I. Rovira, Y. Lee, R. J. Koval, and C. R. Wronski, Thin Solid Films 364, 129 (2000). 343. B. Dr6villon, Prog. Cryst. Growth Charact. Mater. 27, 1 (1993). 344. R. Ossikovski and B. Dr6villon, Phys. Rev. B 54, 10530 (1996).

AMORPHOUS

SILICON

97

345. H. Fujiwara, J. Koh, E I. Rovira, and R. W. Collins, Phys. Rev. B 61, 10832 (2000). 346. D.E. Aspnes, J. B. Theeten, and E Hottier, Phys. Rev. B 20, 3292 (1979). 347. A. Canillas, E. Bertran, J. L. Andtijar, and B. Dr6villon, J. Appl. Phys. 68, 2752 (1990). 348. Y. Lu, S. Kim, M. Gunes, Y. Lee, C. R. Wronski, and R. W. Collins, Mater. Res. Soc. Symp. Proc. 336, 595 (1994). 349. D.V. Tsu, B. S. Chao, S. R. Ovshinsky, S. Guha, and J. Yang, Appl. Phys. Lett. 71, 1317 (1997). 350. J. Koh, Y. Lee, H. Fujiwara, C. R. Wronski, and R. W. Collins, Appl. Phys. Lett. 73, 1526 (1998). 351. S. Guha, J. Yang, D. L. Williamson, Y. Lubianiker, J. D. Cohen, and A. H. Mahan, Appl. Phys. Lett. 74, 1860 (1999). 352. A.H. Mahan, J. Yang, S. Guha, and D. L. Williamson, Phys. Rev. B 61, 1677 (2000). 353. H. Fujiwara, J. Koh, C. R. Wronski, and R. W. Collins, Appl. Phys. Lett. 70, 2150 (1997). 354. H. Fujiwara, J. Koh, C. R. Wronski, and R. W. Collins, Appl. Phys. Lett. 72, 2993 (1998). 355. H. Fujiwara, J. Koh, C. R. Wronski, and R. W. Collins, Appl. Phys. Lett. 74, 3687 (1999). 356. N. Blayo and B. Dr6villon, J. Non-cryst. Solids 137 & 138, 771 (1991). 357. A. Matsuda, J. Vac. Sci. Technol. A 16, 365 (1998). 358. B. Dr6villon, J. Perrin, J. M. Siefert, J. Huc, A. Lloret, G. de Rosny, and J. E M. Schmitt, Appl. Phys. Lett. 42, 801 (1983). 359. R.A. Street, J. C. Knights, and D. K. Biegelsen, Phys. Rev. B 19, 3027 (1978). 360. J.C. Knights and R. A. Lujan, AppL Phys. Lett. 35, 244 (1979). 361. S. Nishikawa, H. Kakinuma, T. Watanabe, and K. Nihei, Japan. J. Appl. Phys. 24, 639 (1985). 362. G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, and Y. Goldstein, Phys. Rev. Lett. 47, 1480 (1981). 363. K.M.H. Maessen, M. J. M. Pruppers, J. Bezemer, E H. P. M. Habraken, and W. E van der Weg, Mater. Res. Soc. Symp. Proc. 95, 201 (1987). 364. K. Tanaka, K. Nakagawa, A. Matsuda, M. Matsumura, H. Yamamoto, S. Yamasaki, H. Okushi, and S. Izima, Japan. J. Appl. Phys. 20, 267 (1981). 365. P. Sichanugrist, M. Konagai, and K. Takahashi, Japan. J. Appl. Phys. 25, 44O (1986). 366. M. Hirose, J. Phys. (Paris), Colloq. 42, C4 (1981). 367. P. Chaudhuri, S. Ray, and A. K. Barua, Thin Solid Films 113, 261 (1984). 368. J. Shirafuji, S. Nagata, and M. Kuwagaki, J. Appl. Phys. 58, 3661 (1985). 369. S. Okamoto, Y. Hishikawa, and S. Tsuda, Japan. J. AppL Phys. 35, 26 (1996). 370. H. Meiling, R. E. I. Schropp, W. G. J. H. M. van Sark, J. Bezemer, and W. E van der Weg, "Proceedings of the Tenth E.C. Photovoltaic Solar Energy Conference, Lisbon, Portugal, 1991" (A. Luque, G. Sala, W. Palz, G. Dos Santos, and E Helm, Eds.), p. 339. Kluwer Academic, Dordrecht, 1991. 371. J.P.M. Schmitt, J. Non-cryst. Solids 59 & 60, 649 (1983). 372. C.C. Tsai, G. B. Anderson, and R. Thompson, J. Non-cryst. Solids 137138, 637 (1991). 373. E Roca i Cabarrocas, S. Hamma, S. N. Sharma, G. Viera, E. Bertran, and J. Costa, J. Non-cryst. Solids 227-230, 871 (1998). 374. C. Longeaud, J. P. Kleider, E Roca i Cabarrocas, S. Hamma, R. Meaudre, and M. Meaudre, J. Non-cryst. Solids 227-230, 96 (1998). 375. J.C. Knights, Japan. J. Appl. Phys. 18, 101 (1979). 376. R. B. Wehrspohn, S. C. Deane, I. D. French, I. Gale, J. Hewett, M. J. Powell, and J. Robertson, J. Appl. Phys. 87, 144 (2000). 377. A. A. Howling, J.-L. Doffer, and C. Hollenstein, Appl. Phys. Lett. 62, 1341 (1993). 378. A. Bouchoule, Ed., "Dusty Plasmas: Physics, Chemistry, and Technological Impact in Plasma Processing." Wiley, New York, 1999. 379. E Roca i Cabarrocas, J. Non-cryst. Solids 266-269, 31 (2000). 380. M. Otobe, T. Kanai, T. Ifuku, H. Yajima, and S. Oda, J. Non-cryst. Solids 198-200, 875 (1996).

98

VAN SARK

381. D.M. Tanenbaum, A. L. Laracuente, and A. Gallagher, Appl. Phys. Lett. 68, 705 (1996). 382. P. Roca i Cabarrocas, Mater. Res. Soc. Symp. Proc. 507, 855 (1998). 383. E. Stoffels, W. W. Stoffels, G. M. W. Kroesen, and E J. de Hoog, Electron Technol. 31,255 (1998). 384. C. Courteille, J.-L. Doffer, J. Dutta, C. Hollenstein, A. A. Howling, and T. Stoto, J. Appl. Phys. 78, 61 (1995). 385. S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, Phys. Rev. B 35, 8113(1987). 386. A.J. Read, R. J. Needs, K. J. Nash, L. T. Canham, P. D. J. Calcott, and A. Qteish, Phys. Rev. Lett. 69, 1232 (1992). 387. P. Roca i Cabarrocas, P. Gay, and A. Hadjadj, J. Vac. Sci. Technol. A 14, 655 (1996). 388. A. Fontcuberta i Morral, R. Brenot, E. A. G. Hamers, R. Vanderhaghen, and P. Roca i Cabarrocas, J. Non-cryst. Solids 266-269, 48 (2000). 389. R. Butt6, S. Vignoli, M. Meaudre, R. Meaudre, O. Marty, L. Saviot, and P. Roca i Cabarrocas, J. Non-cryst. Solids 266-269, 263 (2000). 390. Coming 7059 Material Information, Coming Glass Works, NY. 391. J. Wallinga, D. Knoesen, E. A. G. Hamers, W. G. J. H. M. van Sark, W. E van der Weg, and R. E. I. Schropp, Mater Res. Soc. Symp. Proc. 420, 57 (1996). 392. M.B. Schubert and G. H. Bauer, "Proceedings of the Twenty-First IEEE Photovoltaic Specialists Conference, Kissimee, U.S.A., 1990," p. 1595. IEEE, New York, 1990. 393. Y. Hishikawa, M. Ohnishi, and Y. Kuwano, Mater Res. Soc. Symp. Proc. 192, 3 (1990). 394. A. Shin and S. Lee, J. Non-cryst. Solids 260, 245 (1999). 395. N. Maley and J. S. Lannin, Phys. Rev. B 31, 5577 (1985). 396. A. J. M. Berntsen, W. G. J. H. M. van Sark, and W. E van der Weg, J. Appl. Phys. 78, 1964 (1995). 397. R.W. Collins and J. M. Cavese, J. Appl. Phys. 61, 1869 (1987). 398. Y. Toyoshima, K. Arai, A. Matsuda, and K. Tanaka, Appl. Phys. Lett. 56, 1540 (1990). 399. G. Ganguly and A. Matsuda, J. Non-cryst. Solids 164-166, 31 (1993). 400. S. Vep~ek, F.-A. Sarrott, S. Rambert, and E. Taglauer, J. Vac. Sci. Technol. A 7, 2614 (1989). 401. B.J. Garrison, M. T. Miller, and D. W. Bremmen, Chem. Phys. Lett. 146, 513 (1988). 402. M. Kitabatake, P. Fons, and J. E. Greene, J. Vac. Sci. Technol. A 8, 3726 (1990). 403. P. Roca i Cabarrocas, Mater. Res. Soc. Syrup. Proc. 149, 33 (1989). 404. G. Ganguly, T. Ikeda, I. Sakata, and A. Matsuda, Mat. Res. Soc. Proc. Syrup. 420, 347 (1996). 405. A. I. Kosarev, A. S. Smirnov, A. S. Abramov, A. J. Vinogradov, A. Y. Ustavschikov, and M. V. Shutov, J. Vac. Sci. Technol. A 15,298 (1997). 406. A. S. Abramov, A. Y. Vinogradov, A. I. Kosarev, M. V. Shutov, A. S. Smirnov, and K. E. Orlov, Tech. Phys. 43, 180 (1998). 407. J. P. Harbison, A. J. Williams, and D. V. Lang, J. Appl. Phys. 55, 946 (1984). 408. K.H. Miiller, J. Appl. Phys. 62, 1796 (1987). 409. J. Robertson, J. Non-cryst. Solids 164-166, 1115 (1993). 410. J. R. Abelson, Appl. Phys. A 56, 493 (1993). 411. R. Biswas, J. Appl. Phys. 73, 3295 (1993). 412. W. M611er, Appl. Phys. A 56, 527 (1993). 413. M. Hoedemaker, J. van der Kuur, E. J. Melker, and B. J. Thijsse, Nucl. lnstrum. Methods Phys. Res. B 127/128, 888 (1997). 414. J.F. Ziegler, J. P. Biersack, and U. Littmarck, "The Stopping and Range of Ions in Solids." Pergamon, New York, 1985. 415. B. Dr6villon, J. Huc, and N. Boussarssar, J. Non-cryst. Solids 59/60, 735 (1983). 416. B. Dr6villon and M. Toutlemonde, Appl. Phys. Lett. 59, 950 (1985). 417. J. Perrin, Y. Takeda, N. Hirano, H. Matsuura, and A. Matsuda, Japan. J. Appl. Phys. 28, 5 (1989). 418. P. Roca i Cabarrocas, P. Morin, V. Chu, J. P. Conde, J. Z. Liu, H. R. Park, and S. Wagner, J. Appl. Phys. 69, 2942 (1991). 419. E. A. G. Hamers, J. Bezemer, and W. F. van der Weg, Appl. Phys. Lett. 75,609 (1999).

420. D. A. Doughty, J. R. Doyle, G. H. Lin, and A. Gallagher, J. Appl. Phys. 67, 6220 (1990). 421. J. K. Hirvonen, in "Materials and Processes for Surface and Interface Engineering" (Y. Pauleau, Ed.), Chap. 9, p. 307. Kluwer Academic, Dordrecht, 1995. 422. J.E. Potts, E. M. Peterson, and J. A. McMillan, J. Appl. Phys. 52, 6665 (1981). 423. H. Meiling, J. Bezemer, R. E. I. Schropp, and W. E van der Weg, Mater. Res. Soc. Proc. Symp. 467, 459 (1997). 424. S. Habermehl and G. Lucovsky, J. Vac. Sci. Technol. A 14, 3024 (1996). 425. S.R. Kasi, H. Kang, C. S. Sass, and J. W. Rabalais, Surf. Sci. Rep. 10, 1 (1989). 426. L. Hanley, H. Lira, D. G. Schultz, S. B. Wainhaus, E de Sainte Claire, and W. L. Hase, Nucl. Instrum. Methods Phys. Res. B 125,218 (1997). 427. H. Sugai, Y. Mitsuoka, and H. Toyoda, J. Vac. Sci. Technol. A 16, 290 (1998). 428. K.H. Miiller, Phys. Rev. B 35, 7906 (1987). 429. J. W. Rabalais, A. H. AI-Bayati, K. J. Boyd, D. Marton, J. Kulik, Z. Zhang, and W. K. Chu, Phys. Rev. B 53, 10781 (1996). 430. K.H. Miiller, J. Appl. Phys. 59, 2803 (1986). 431. J.E. Yehoda, B. Yang, K. Vedam, and R. Messier, J. Vac. Sci. Technol. A 6, 1631 (1988). 432. R. J. Severens, M. C. M. van de Sanden, H. J. M. Verhoeven, J. Bastiaansen, and D. C. Schram, Mater. Res. Soc. Symp. Proc. 420, 341 (1996). 433. M . C . M . van de Sanden, R. J. Severens, W. M. M. Kessels, E van de Pas, L. van Ijzendoorn, and D. C. Schram, Mater. Res. Soc. Proc. Symp. 467, 621 (1997). 434. E . H . C . Ullersma, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1998. 435. R. Robertson and A. Gallagher, J. Chem. Phys. 85, 3623 (1986). 436. A. Gallagher, J. Appl. Phys. 63, 2406 (1988). 437. J.L. Guizot, K. Nomoto, and A. Matsuda, Surf. Sci. 244, 22 (1991). 438. A. J. Flewitt, J. Robertson, and W. I. Milne, J. Appl. Phys. 85, 8032 (1999). 439. J. Robertson, J. Appl. Phys. 87, 2608 (2000). 440. G. Ganguly and A. Matsuda, Phys. Rev. B 47, 3661 (1993). 441. K. Winer, Phys. Rev. B 41, 7952 (1990). 442. R.A. Street, Phys. Rev. B 43, 2454 (1991). 443. R. A. Street, Phys. Rev. B 44, 10610 (1991). 444. R.A. Street and K. Winer, Phys. Rev. B 40, 6236 (1989). 445. M.J. Powell and S. C. Deane, Phys. Rev. B 48, 10815 (1993). 446. M.J. Powell and S. C. Deane, Phys. Rev. B 53, 10121 (1996). 447. K. Gleason, K. S. Wang, M. K. Chen, and J. A. Reimer, J. Appl. Phys. 61, 2866 (1987). 448. M.J. McCaughy and M. J. Kushner, J. Appl. Phys. 65, 186 (1989). 449. S. Shirafuji, S. Nakajima, Y. E Wang, T. Genji, and K. Tachibana, Japan. J. Appl. Phys. 32, 1546 (1993). 450. J. Robertson, Mater. Res. Soc. Proc. Symp. 609, A1.4.1 (2000). 451. C. C. Tsai, J. C. Knights, G. Chang, and B. Wacker, J. Appl. Phys. 59, 2998 (1986). 452. A.J. Flewitt, J. Robertson, and W. I. Milne, J. Non-cryst. Solids 266-269, 74 (2000). 453. A. von Keudell and J. R. Abelson, Japan. J. Appl. Phys. 38, 4002 (1999). 454. S. Ramalingam, D. Maroudas, and E. S. Aydill, J. Appl. Phys. 86, 2872 (1999). 455. S. Yamasaki, T. Umeda, J. Isoya, and K. Tanaka, Appl. Phys. Lett. 70, 1137 (1997). 456. D.A. Porter and K. E. Easterling, "Phase Transformations in Metals and Alloys." Chapman & Hall, London, 1992. 457. E Roca i Cabarrocas, Y. Bouizem, and M. L. Theye, Philos. Mag. B 65, 1025 (1992). 458. C.M. Greenlief, S. M. Gates, and P. A. Holbert, J. Vac. Sci. Technol. A 7, 1845 (1989). 459. W.B. Jackson, J. Non-cryst. Solids 164-166, 263 (1993). 460. W. Beyer, J. Non-Cryst. Solids 198-200, 40 (1996). 461. W. Beyer and U. Zastrow, Mater. Res. Soc. Symp. Proc. 420, 497 (1996). 462. C.G. Van de Walle, Phys. Rev. B 49, 4579 (1994).

METHODS

OF DEPOSITION OF HYDROGENATED

463. J. Robertson, C. W. Chen, M. J. Powell, and S. C. Deane, J. Non-cryst. Solids 227-230, 138 (1998). 464. K.J. Chang and J. D. Chadi, Phys. Rev. Lett. 62, 937 (1989). 465. K.J. Chang and J. D. Chadi, Phys. Rev. B 40, 11644 (1990). 466. Y. Miyoshi, Y. Yoshida, S. Miyazaki, and M. Hirose, J. Non-cryst. Solids 198-200, 1029 (1996). 467. J. Robertson and M. J. Powell, Thin Solid Films 337, 32 (1999). 468. W. M. M. Kessels, R. J. Severens, M. C. M. van de Sanden, and D. C. Schram, J. Non-cryst. Solids 227-230, 133 (1998). 469. G.H. Lin, J. R. Doyle, M. Z. He, and A. Gallagher, J. Appl. Phys. 64, 341 (1988). 470. E Roca i Cabarrocas, Appl. Phys. Lett. 65, 1674 (1995). 471. H. Shirai, J. Hanna, and I. Shimizu, Japan. J. Appl. Phys. 30, L679 (1991). 472. M. C. M. van de Sanden, W. M. M. Kessels, R. J. Severens, and D. C. Schram, Plasma Phys. Controlled Fusion 41, A365 (1999). 473. M.C.M. van de Sanden, W. M. M. Kessels, A. H. Smets, B. A. Korevaar, R. J. Severens, and D. C. Schram, Mater. Res. Soc. Symp. Proc. 557, 13 (1999). 474. M. Stutzmann, Philos. Mag. B 60, 531 (1989). 475. A. Shah, J. Dutta, N. Wyrsch, K. Prasad, H. Curtins, E Finger, A. Howling, and C. Hollenstein, Mater. Res. Soc. Symp. Proc. 258, 15 (1992). 476. C.M. Ferreira and J. Loureiro, J. Phys. D 17, 1175 (1984). 477. J. Kuske, U. Stephan, O. Steinke, and S. R6hlecke, Mater. Res. Soc. Symp. Proc. 377, 27 (1995). 478. U. Kroll, J. Meier, M. Goetz, A. Howling, J.-L. Doffer, J. Dutta, A. Shah, and C. Hollenstein, J. Non-cryst. Solids 164-166, 59 (1993). 479. H. Meiling, J. E M. Westendorp, J. Hautala, Z. Saleh, and C. T. Malone, Mater. Res. Soc. Symp. Proc. 345, 65 (1995). 480. S. RShlecke, R. Tews, A. Kottwitz, and K. Schade, Surf. Coat. Technol. 74-75, 259 (1995). 481. C. Beneking, J. Appl. Phys. 68, 4461 (1990). 482. C. Beneking, J. Appl. Phys. 68, 5435 (1990). 483. C. Beneking, E Finger, and H. Wagner, "Proceedings of the Eleventh E.C. Photovoltaic Solar Energy Conference, Montreux, Switzerland 1992" (L. Guimar~es, W. Palz, C. de Reyff, H. Kiess, and E Helm, Eds.), p. 586. Harwood, Chur, Switzerland, 1993. 484. M. J. Colgan, M. Meyyappan, and D. E. Murnick, Plasma Sources Sci. Technol. 3, 181 (1994). 485. U. Kroll, Y. Ziegler, J. Meier, H. Keppner, and A. Shah, Mater. Res. Soc. Symp. Proc. 336, 115 (1994). 486. E.A.G. Hamers, W. G. J. H. M. van Sark, J. Bezemer, W. E van der Weg, G. J. Nienhuis, and W. J. Goedheer, "Proceedings of the Thirteenth European Sectional Conference on the Atomic and Molecular Physics of Ionized Gases," ESCAMPIG 96, Poprad, Slovakia, Europhys. Conf. Abs. 20E, 27 (1996). 487. W. G. J. H. M. van Sark, H. Meiling, E. A. G. Hamers, J. Bezemer, and W. E van der Weg, J. Vac. Sci. Technol. A 15, 654 (1997). 488. H. Meiling, W. G. J. H. M. van Sark, J. Bezemer, and W. van der Weg, J. Appl. Phys. 80, 3546 (1996). 489. G.E.N. Landweer and J. Bezemer, in "Amorphous Silicon and Related Materials, Advances in Disordered Semiconductors 1" (H. Fritzsche, Ed.). World Scientific, Singapore, 1989. 490. M. Zhu, M. B. vonder Linden, J. Bezemer, R. E. I. Schropp, and W. E van der Weg, J. Non-cryst. Solids 137-138, 355 (1991). 491. M. Zhu, M. B. vonder Linden, and W. E van der Weg, Mater. Res. Soc. Symp. Proc. 336, 449 (1994). 492. M.B. von der Linden, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1994. 493. W. G. J. H. M. van Sark, J. Bezemer, and W. E van der Weg, J. Mater. Res. 13, 45 (1998). 494. R. E. I. Schropp, H. Meiling, W. G. J. H. M. van Sark, J. Stammeijer, J. Bezemer, and W. E van der Weg, "Proceedings of the Tenth E.C. Photovoltaic Solar Energy Conference, Lisbon, Portugal, 1991" (A. Luque, G. Sala, W. Palz, G. Dos Santos, and E Helm, Eds.), p. 1087. Kluwer Academic, Dordrecht, 1991. 495. S.J. Jones, D. L. Williamson, T. Liu, X. Deng, and M. Izu, Mater. Res. Soc. Proc. Symp. 609, A7.4.1 (2000).

AMORPHOUS

SILICON

99

496. C.C. Tsai, R. Thompson, C. Doland, F. A. Ponce, G. B. Anderson, and B. Wacker, Mater. Res. Soc. Symp. Proc. 118, 49 (1988). 497. Y. S. Tsuo, R. Weil, S. Asher, A. Nelson, Y. Xu, and R. Tsu, "Proceedings of the 19th IEEE Photovoltaic Specialists Conference, New Orleans, 1987," p. 705. IEEE, New York, 1987. 498. H. Shirai, D. Das, J. Hanna, and I. Shimizu, Appl. Phys. Lett. 59, 1096 (1991). 499. A. Asano, T. Ichimura, and H. Sakai, J. Appl. Phys. 65, 2439 (1989). 500. A. Asano, Appl. Phys. Lett. 56, 533 (1990). 501. G. Parsons, IEEE Electron Device Lett. 13, 80 (1992). 502. N. Layadi, P. Roca i Cabarrocas, B. Dr6villon, and I. Solomon, Phys. Rev. B 52, 5136 (1995). 503. P. Roca i Cabarrocas, N. Layadi, B. Dr6villon, and I. Solomon, J. Noncryst. Solids 198-200, 871 (1996). 504. P. Roca i Cabarrocas, S. Hamma, A. Hadjadi, J. Bertomeu, and J. Andreu, Appl. Phys. Lett. 69, 529 (1996). 505. N. Shibata, K. Fukada, H. Ohtoshi, J. Hanna, S. Oda, and I. Shimizu, Mater Res. Soc. Symp. Proc. 95,225 (1987). 506. Y. H. Yang, M. Katiyar, G. F. Feng, N. Maley, and J. R. Abelson, Appl. Phys. Lett. 65, 1769 (1994). 507. S. Hamma and P. Roca i Cabarrocas, J. Appl. Phys. 81, 7282 (1997). 508. P. Roca i Cabarrocas, R. Brenot, P. Bulkin, R. Vanderhaghen, B. Dr6vilIon, and I. French, J. Appl. Phys. 86, 7079 (1999). 509. K. Saito, M. Kondo, M. Fukawa, T. Nishimiya, A. Matsuda, W. Futako, and I. Shimizu, Appl. Phys. Lett. 71, 3403 (1997). 510. C. Anandan, C. Mukherjee, T. Seth, P. N. Dixit, and R. Bhattacharyya, Appl. Phys. Lett. 66, 85 (1995). 511. C. Mukherjee, C. Anandan, T. Seth, P. N. Dixit, and R. Bhattacharyya, Appl. Phys. Lett. 68, 194 (1996). 512. A.C.W. Biebericher, J. Bezemer, W. F. van der Weg, and W. J. Goedheer, Appl. Phys. Lett. 76, 2002 (2000). 513. H. Kirimura, H. Maeda, H. Murakami, T. Nakahigashi, S. Ohtani, T. Tabata, T. Hayashi, M. Kobayashi, Y. Mitsuda, N. Nakamura, H. Kuwahara, and A. Doi, Japan. J. Appl. Phys. 33, 4389 (1994). 514. S. Morrison, J. Xi, and A. Madan, Mater. Res. Soc. Symp. Proc. 507, 559 (1998). 515. A. Madan, S. Morrison, and H. Kuwahara, Sol. Energy Mater. Sol. Cells 59, 51 (1999). 516. G. Scarsbrook, I. P. Llewellyn, S. M. Ojha, and R. A. Heinecke, Vacuum 38, 627 (1988). 517. L.J. Overzet and J. T. Verdeyen, Appl. Phys. Lett. 48, 695 (1986). 518. J.P. Booth, G. Cunge, N. Sadeghi, and R. W. Boswell, J. Appl. Phys. 82, 552 (1997). 519. A.C.W. Biebericher, J. Bezemer, W. F. van der Weg, and W. J. Goedheer, Mater. Res. Soc. Proc. Symp. 609, A4.1.1 (2000). 520. A.C.W. Biebericher, J. Bezemer, W. F. van der Weg, and W. J. Goedheer, unpublished results. 521. H. Wiesmann, A. K. Ghosh, T. McMahon, and M. Strongin, J. Appl. Phys. 50, 3752 (1979). 522. H. Matsumura, Japan. J. Appl. Phys. 25, L949 (1986). 523. H. Matsumura, Appl. Phys. Lett. 51,804 (1987). 524. H. Matsumura, J. Appl. Phys. 65, 4396 (1989). 525. J.R. Doyle, R. Robertson, G. H. Lin, M. Z. He, and A. Gallagher, J. Appl. Phys. 64, 3215 (1988). 526. F. Jansen, I. Chen, and M. A. Machonkin, J. Appl. Phys. 66, 5749 (1989). 527. A.H. Mahan and M. Van66ek, "Amorphous Silicon Materials and Solar Cells," AlP Conference Proceedings, Vol. 234 (B. Stafford, Ed.), p. 195. American Institute of Physics, New York, 1991. 528. E.C. Molenbroek, A. H. Mahan, E. Johnson, and A. C. Gallagher, J. Appl. Phys. 79, 7278 (1996). 529. M. Heintze, R. Zedlitz, H. N. Wanka, and M. B. Schubert, J. Appl. Phys. 79, 2699 (1996). 530. E.C. Molenbroek, A. H. Mahan, and A. C. Gallagher, J. Appl. Phys. 82, 1909 (1997). 531. K.F. Feenstra, R. E. I. Schropp, and W. F. van der Weg, J. Appl. Phys. 85, 6843 (1999).

100

VAN SARK

532. P. Papadopoulos, A. Scholz, S. Bauer, B. Schr6der, and H. Ochsner, J. Non-cryst. Solids 164-166, 87 (1993). 533. B. E Nelson, E. Iwaniczko, R. E. I. Schropp, H. Mahan, E. C. Molenbroek, S. Salamon, and R. S. Crandall, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy Conference, Amsterdam, the Netherlands, 1994" (R. Hill, W. Palz, and E Helm, Eds.), p. 679. H. S. Stephens & Associates, Bedford, U.K., 1994. 534. A.H. Mahan, E. Iwaniczko, B. E Nelson, R. C. Reedy, Jr., R. S. Crandall, S. Guha, and J. Yang, "proceedings of the 25th IEEE Photovoltaic Specialists Conference, Washington DC, 1996," p. 1065. IEEE, New York, 1996. 535. R.E.I. Schropp, K. E Feenstra, E. C. Molenbroek, H. Meiling, and J. K. Rath, Philos. Mag. B 76, 309 (1997). 536. R. S. Crandall, A. H. Mahan, B. Nelson, M. Van~ek, and I. Balberg, "AIP Conference Proceedings" (R. Noufi, Ed.), Vol. 268, p. 81. American Institute of Physics, Denver, 1992. 537. Q. Wang, E. Iwaniczko, Y. Xu, W. Gao, B. E Nelson, A. H. Mahan, R. S. Crandall, and H. M. Branz, Mater Res. Soc. Proc. Symp. 609, A4.3.1 (2000). 538. H. Meiling and R. E. I. Schropp, Appl. Phys. Lett. 70, 2681 (1997). 539. V. Chu, J. Jarego, H. Silva, T. Silva, M. Reissner, P. Brogueira, and J. E Conde, AppL Phys. Len. 70, 2714 (1997). 540. H. Meiling, A. M. Brockhoff, J. K. Rath, and R. E. I. Schropp, J. Noncryst. Solids 227-230, 1202 (1998). 541. J. Cifre, J. Bertomeu, J. Puigdollers, M. C. Polo, J. Andreu, and A. Lloret, Appl. Phys. A 59, 645 (1994). 542. A.R. Middya, S. Hazra, S. Ray, C. Longeaud, and J. E Kleider, "Proceedings of the Thirteenth European Photovoltaic Solar Energy Conference, Nice, France, 1995" (W. Freiesleben, W. Palz, H. A. Ossenbrink, and P. Helm, Eds.), p. 679. H. S. Stephens & Associates, Bedford, U.K., 1995. 543. E Brogueira, J. E Conde, S. Arekat, and V. Chu, J. AppL Phys. 79, 8748 (1996). 544. J.K. Rath, H. Meiling, and R. E. I. Schropp, Sol. Energy Mater Sol. Cells 48, 269 (1997). 545. H.N. Wanka, R. Zedlitz, M. Heintze, and M. B. Schubert, "Proceedings of the Thirteenth European Photovoltaic Solar Energy Conference, Nice, France, 1995" (W. Freiesleben, W. Palz, H. A. Ossenbrink, and E Helm, Eds.), p. 1753. H.S. Stephens & Associates, Bedford, U.K., 1995. 546. V. Brogueira, E Chu, A. C. Ferro, and J. E Conde, J. Vac. Sci. Technol. A 15, 2968 (1997). 547. E Alpuim, V. Chu, and J. P. Conde, Mater Res. Soc. Proc. Symp. 609, A22.6.1 (2000). 548. K. E Feenstra, Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1998. 549. C. Horbach, W. Beyer, and H. Wagner, J. Non-cryst. Solids 137 & 138, 661 (1991). 550. S. Bauer, B. Schr6der, and H. Oechsner, J. Non-cryst. Solids 227-230, 34 (1998). 551. A. H. Mahan, Y. Chen, D. L. Williamson, and G. D. Mooney, J. Noncryst. Solids 137-138, 65 (1991). 552. Y. Wu, J. T. Stephen, D. X. Han, J. M. Rutland, R. S. Crandall, and A. H. Mahan, Phys. Rev. Lett. 77, 2049 (1996). 553. R.P. Muller, J. K. Holt, D. G. Goodwin, and W. A. Goddard, III, Mater Res. Soc. Proc. Symp. 609, A6.1.1 (2000). 554. J. K. Holt, M. Swiatek, D. G. Goodwin, and H. A. Atwater, Mater Res. Soc. Proc. Symp. 609, A6.2.1 (2000). 555. B. Schrtider and S. Bauer, J. Non-cryst. Solids 266-269, 1115 (2000). 556. A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, and D. C. Schram, Meas. Sci. Technol. 1, 1326 (1990). 557. J. W. A. M. Gielen, P. R. M. Kleuskens, M. C. M. van de Sanden, L. J. van IJzendoorn, D. C. Schram, E. H. A. Dekempeneer, and J. Meneve, J. Appl. Phys. 80, 5986 (1996). 558. J. J. Beulens, A. J. M. Buuron, and D. C. Schram, Surf. Coat. Technol. 47, 401 (1991). 559. M.J. de Graaf, R. J. Severens, R. P. Dahiya, M. C. M. van de Sanden, and D. C. Schram, Phys. Rev. E 48, 2098 (1993). 560. R. E G. Meulenbroeks, M. E M. Steenbakkers, Z. Qing, M. C. M. van de Sanden, and D. C. Schram, Phys. Rev. E 49, 2272 (1994).

561. W.M.M. Kessels, A. H. M. Smets, B. A. Korevaar, G. J. Adriaenssens, M. C. M. van de Sanden, and D. C. Schram, Mater Res. Soc. Symp. Proc. 557, 25 (1999). 562. B.A. Korevaar, G. J. Adriaenssens, A. H. M. Smets, W. M. M. Kessels, H.-Z. Song, M. C. M. van de Sanden, and D. C. Schram, J. Non-cryst. Solids 266-269, 380 (2000). 563. M. C. M. van de Sanden, R. J. Severens, W. M. M. Kessels, R. E G. Meulenbroeks, and D. C. Schram, J. Appl. Phys. 84, 2426 (1998). 564. M. C. M. van de Sanden, R. J. Severens, W. M. M. Kessels, R. E G. Meulenbroeks, and D. C. Schram, J. Appl. Phys. 85, 1243 (1999). 565. J. J. Beulens, M. J. de Graaf, and D. C. Schram, Plasma Sources Sci. Technol. 2, 180 (1993). 566. M. C. M. van de Sanden, J. M. de Regt, and D. C. Schram, Plasma Sources Sci. Technol. 3, 501 (1994). 567. W. M. M. Kessels, C. M. Leewis, M. C. M. van de Sanden, and D. C. Schram, J. Appl. Phys. 86, 4029 (1999). 568. R. E G. Meulenbroeks, R. A. H. Engeln, M. N. A. Beurskens, R. M. J. Paffen, M. C. M. van de Sanden, J. A. M. van der Mullen, and D. C. Schram, Plasma Sources Sci. Technol. 4, 74 (1995). 569. W. M. M. Kessels, M. C. M. van de Sanden, and D. C. Schram, J. Vac. Sci. TechnoL A 18, 2153 (2000). 570. W. M. M. Kessels, M. C. M. van de Sanden, R. J. Severens, L. J. van Ijzendoorn, and D. C. Schram, Mater Res. Soc. Symp. Proc. 507, 529 (1998). 571. W. M. M. Kessels, Ph.D. Thesis, Technische Universiteit Eindhoven, Eindhoven, the Netherlands, 2000. 572. W.M.M. Kessels, R. J. Severens, A. H. M. Smets, B. A. Korevaar, G. J. Adriaenssens, D. C. Schram, and M. C. M. van de Sanden, J. Appl. Phys. 89, 2404 (2001). 573. W. M. M. Kessels, J. P. M. Hoefnagels, M. G. H. Boogderts, D. C. Schram, and M. C. M. van de Sanden, J. Appl. Phys. 89, 2065 (2001). 574. H.S. Nalwa, Ed., "Handbook of Advanced Electronic and Photonic Materials and Devices." Academic Press, Boston, 2000. 575. M. A. Green, "Solar Cells, Operating Principles, Technology and System Applications." University of New South Wales, Kensington, NSW, Australia, 1992. 576. M. Hack and M. Shur, J. Appl. Phys. 58, 997 (1985). 577. A. Catalano, in "Amorphous and Microcrystalline Semiconductor Devices---Optoelectronic Devices" (J. Kanicki, Ed.), Chap. 2, p. 9. Artech House, Norwood, MA, 1991. 578. A. Polman, W. G. J. H. M. van Sark, W. C. Sinke, and E W. Saris, Sol. Cells 17, 241 (1986). 579. H. Hartnagel, A. Dawar, A. Jain, and C. Jagadish, "Semiconducting Transparent Thin Films." Institute of Physics Publishing, Bristol, 1995. 580. E. Yablonovitch and G. D. Cody, IEEE Trans. Electron. Dev. ED-29, 300 (1982). 581. H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, Appl. Phys. Lett. 42, 968 (1983). 582. J. Daey Ouwens, R. E. I. Schropp, J. Wallinga, W. E van der Weg, M. Ritala, M. Leskel~i, andM. Hyrv~irinen, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy Conference, Amsterdam, the Netherlands, 1994" (R. Hill, W. Palz, and E Helm, Eds.), p. 1296. H.S. Stephens & Associates, Bedford, U.K., 1994. 583. M. Kubon, E. B/Shmer, E Siebke, B. Rech, C. Beneking, and H. Wagner, Sol. Energy Mater Sol. Cells 41/42, 485 (1996). 584. Y. Tawada, H. Okamoto, and Y. Hamakawa, Appl. Phys. Lett. 39, 237 (1981). 585. K. Miyachi, N. Ishiguro, T. Miyashita, N. Yanagawa, H. Tanaka, M. Koyama, Y. Ashida, and N. Fukuda, "Proceedings of the Eleventh E.C. Photovoltaic Solar Energy Conference, Montreux, Switzerland, 1992" (L. Guimar~es, W. Palz, C. de Reyff, H. Kiess, and P. Helm, Eds.), p. 88. Harwood, Chur, Switzerland, 1993. 586. R. R. Arya, A. Catalano, and R. S. Oswald, Appl. Phys. Lett. 49, 1089 (1986). 587. C. Beneking, B. Rech, T. Eickhoff, Y. G. Michael, N. Schultz, and H. Wagner, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy

METHODS OF DEPOSITION OF HYDROGENATED

588.

589. 590.

591. 592. 593.

594. 595.

596. 597. 598. 599. 600. 601. 602. 603.

604. 605. 606. 607.

608. 609. 610. 611. 612. 613.

614. 615.

616. 617. 618.

Conference, Amsterdam, the Netherlands, 1994," p. 683. Kluwer Academic, Dordrecht, 1994. G.E.N. Landweer, B. S. Girwar, C. H. M. van der Weft, J. W. Metselaar, and R. E. I. Schropp, "Proceedings of the Twelfth E.C. Photovoltaic Solar Energy Conference, Amsterdam, the Netherlands, 1994"' p. 1300. Kluwer Academic, Dordrecht, 1994. A. Banerjee and S. Guha, J. Appl. Phys. 69, 1030 (1991). Y. Kuwano, M. Ohnishi, H. Nishiwaki, S. Tsuda, T. Fukatsu, K. Enomoto, Y. Nakashima, and H. Tarui, "Proceedings of the 16th IEEE Photovoltaic Specialists Conference, San Diego, 1982," p. 1338. IEEE, New York, 1982. S. Guha, J. Yang, A. Pawlikiewicz, T. Glatfelter, R. Ross, and S. R. Ovshinsky, Appl. Phys. Lett. 54, 2330 (1989). J. Zimmer, H. Stiebig, and H. Wagner, J. Appl. Phys. 84, 611 (1998). R. E. Rochelau, M. Tun, and S. S. Hegedus, "proceedings of the 26th IEEE Photovoltaic Specialists Conference, Anaheim, 1996," p. 703. IEEE, New York, 1997. J.K. Rath, R. E. I. Schropp, and W. Beyer, J. Non-cryst. Solids 227-230, 1282 (1998). J. Bruns, M. Choudhury, and H. G. Wagemann, "proceedings of the Thirteenth European Photovoltaic Solar Energy Conference, Nice, France, 1995" (W. Freiesleben, W. Palz, H. A. Ossenbrink, and P. Helm, Eds.), p. 230. H.S. Stephens & Associates, Bedford, U.K., 1995. M. Zeman, J. A. Willemen, S. Solntsev, and G. W. Metselaar, Sol. Energy Mater Sol. Cells 34, 557 (1994). M. Zeman, R. A. C. M. M. van Swaaij, E. Schroten, L. L. A. Vosteen, and J. W. Metselaar, Mater Res. Soc. Syrup. Proc. 507, 409 (1998). M. Zeman, J. A. Willemen, L. L. A. Vosteen, G. Tao, and G. W. Metselaar, Sol. Energy Mater Sol. Cells 46, 81 (1997). X. Xu, J. Yang, and S. Guha, Appl. Phys. Lett. 62, 1399 (1993). Y. Lee, L. Jiao, Z. Lu, R. W. Collins, and C. R. Wronski, Sol. Energy Mater SoL Cells 49, 149 (1997). B.W. Faughnan and R. Crandall, Appl. Phys. Lett. 44, 537 (1984). Z.E. Smith, S. Wagner, and B. W. Faughnan, Appl. Phys. Lett. 46, 1078 (1985). A. Catalano, R. Bennett, R. Arya, K. Rajan, and J. Newton, "proceedings of the 18th IEEE Photovoltaic Specialists Conference, Las Vegas, 1985," p. 1378. IEEE, New York, 1985. M. Stutzmann, W. B. Jackson, and C. C. Tsai, Phys. Rev. B 34, 63 (1986). R.E.I. Schropp, A. Sluiter, M. B. vonder Linden, and J. Daey Ouwens, J. Non-cryst. Solids 164-166, 709 (1993). D. E. Carlson, K. Rajan, R. R. Arya, F. Willing, and L. Yang, J. Mater Res. 13, 2754 (1998). Y. Hamakawa, W. Ma, and H. Okamoto, in "Plasma Deposition of Amorphous Silicon-Based Materials" (G. Bruno, P. Capezzuto, and A. Madan, Eds.), Chap. 6, p. 283. Academic Press, Boston, 1995. L.L. Kazmerski, Renew. Sustain. Energy Rev. 1, 71 (1997). A.V. Shah, R. Platz, and H. Keppner, Sol. Energy Mater Sol. Cells 38, 501 (1995). T. Strand, L. Mrig, R. Hansen, and K. Emery, Sol. Energy Mater Sol. Cells 41/42, 617 (1996). R. Ruther andJ. Livingstone, Sol. Energy Mater Sol. Cells 36, 29 (1996). J. Merten and J. Andreu, Sol. Energy Mater Sol. Cells 52, 11 (1998). J. Yang, A. Banerjee, T. Glatfelter, K. Hoffman, X. Xu, and S. Guha, Proceedings of the 24th IEEE Photovoltaic Specialists Conference, Waikoloa HI, 1994," p. 380. IEEE, New York, 1995. S. Guha, J. Yang, A. Banerjee, T. Glatfelter, and S. Sugiyama, Sol. Energy Mater Sol. Cells 48, 365 (1997). S. Kiyama, S. Nakano, Y. Domoto, H. Hirano, H. Tarui, K. Wakisaka, M. Tanaka, S. Tsuda, and S. Nakano, Sol. Energy Mater Sol. Cells 48, 373 (1997). Y. Hamakawa, Appl. Surf. Sci. 142, 215 (1999). S. M. Sze, "Semiconductor Devices, Physics and Technology." Wiley, New York, 1985. M.J. Powell, IEEE Trans. Elec. Dev. ED-36, 2753 (1989).

AMORPHOUS

SILICON

101

619. K. Suzuki, in "Amorphous and Microcrystalline Semiconductor Devices---Optoelectronic Devices" (J. Kanicki, Ed.), Chap. 3, p. 77. Artech House, Norwood, MA, 1991. 620. A. Iqbal, W. B. Jackson, C. C. Tsai, J. W. Allen, and C. W. Bates, J. Appl. Phys. 61, 2947 (1987). 621. C. van Berkel, in "Amorphous and Microcrystalline Semiconductor Devices--Materials and Device Physics" (J. Kanicki, Ed.), Chap. 8, p. 397. Artech House, Norwood, MA, 1992. 622. W. B. Jackson and M. Moyer, Mater Res. Soc. Symp. Proc. 118, 231 (1988). 623. J. Kakalios, R. A. Street, and W. B. Jackson, Phys. Rev. B 59, 1037 (1987). 624. W.B. Jackson, J. M. Marshall, and M. D. Moyer, Phys. Rev. B 39, 1164 (1989). 625. A.M. Brockhoff, E. H. C. Ullersma, H. Meiling, E H. P. M. Habraken, and W. E van der Weg, Appl. Phys. Lett. 73, 3244 (1998). 626. C. van Berkel and M. J. Powell, J. Appl. Phys. 60, 1521 (1986). 627. M. Katayama, Thin Solid Films 341,140 (1999). 628. H.C. Tuan, J. Non-cryst. Solids 115, 132 (1989). 629. H. Matsumura, H. Hayama, Y. Nara, and K. Ishibashi, Japan. J. Appl. Phys. 20, 311 (1980). 630. R.L. Weisfield, IEEE Trans. Electron. Dev. ED-36, 2935 (1989). 631. I. Shimizu, S. Shirai, and E. Inoue, J. Appl. Phys. 52, 2776 (1981). 632. I. Shimizu, in "Semiconductors and Semimetals" (J. I. Pankove, Ed.), Vol. 21D, p. 55. Academic Press, Orlando, FL, 1984. 633. R. Schaffert, "Electrophotography." Focal, London, 1975. 634. J. Kodama, S. Araki, M. Kimura, and T. Inagaki, Japan. J. Appl. Phys. 29, L867 (1990). 635. R.A.C.M.M. van Swaaij, W. P. M. Willems, J. Bezemer, H. J. P. Lokker, and W. E van der Weg, Mater Res. Soc. Symp. Proc. 297, 559 (1993). 636. R. A. C. M. M. van Swaaij, S. J. Elmer, W. E M. Willems, J. Bezemer, J. M. Marshall, and A. R. Hepburn, J. Non-cryst. Solids 164-166, 533 (1993). 637. T. Takeda and S. Sano, Mater Res. Soc. Symp. Proc. 118, 399 (1988). 638. E. Fortunato, M. Vieira, I. Ferreira, C. N. Carvalho, G. Lavareda, and R. Martins, Mater Res. Soc. Syrup. Proc. 297, 981 (1993). 639. E.M.C. Fortunato, D. Brida, I. M. M. Ferreira, H. M. B. [~guas, P. Nunes, A. Cabrita, E Guiliani, Y. Nunes, M. J. E Maneira, and R. Martins, Mater Res. Soc. Proc. Symp. 609, A12.7.1 (2000). 640. H. Stiebig and N. Bohm, J. Non-cryst. Solids 164-166, 789 (1993). 641. R. Brtiggemann, T. Neidlinger, and M. B. Schubert, J. Appl. Phys. 81, 7666 (1997). 642. G. de Cesare, E Irrera, E Lemmi, and E Palma, Appl. Phys. Lett. 66, 1178 (1995). 643. M. Topi6, E Smole, J. Furlan, and W. Kusian, J. Non-cryst. Solids 227230, 1326 (1998). 644. J. Kr~, M. Topi~, E Smole, D. Knipp, and H. Stiebig, Mater Res. Soc. Proc. Symp. 609, A12.5.1 (2000). 645. D. Caputo and G. de Cesare, Sensors and Actuators A 78, 108 (1999). 646. D. Caputo, G. de Cesare, A. Nascetti, E Palma, and M. Petri, Appl. Phys. Lett. 72, 1229 (1998). 647. R.A. Street, X. D. Wu, R. Weisfield, S. Ready, R. Apte, M. Nguyen, and P. Nylen, Nucl. Instt~tm. Methods Phys. Res. A 380, 450 (1996). 648. R.A. Street, R. B. Apte, T. Granberg, M. P., S. E. Ready, K. S. Shah, and R. L. Weisfield, J. Non-cryst. Solids 227-230, 1306 (1998). 649. J.-P. Moy, NucL Instrum. Methods Phys. Res. A 442, 26 (2000). 650. J. C. Chou, Y.-E Wang, and J. S. Lin, Sensors and Actuators B 62, 92 (2000). 651. J. C. Chou, H. M. Tsai, C. N. Shiao, and J. S. Lin, Sensors and Actuators B 62, 97 (2000). 652. S. Jamash, S. D. Collins, and R. L. Smith, IEEE Trans. Electron. Dev. ED-45, 1239 (1998). 653. P. E Ruths, S. Askok, S. J. Fonash, and J. M. Ruths, IEEE Trans. Electron. Dev. ED-28, 1003 (1981). 654. E. Fortunato, A. Malik, A. S&:o, I. Ferreira, and R. Martins, J. Non-cryst. Solids 227-230, 1349 (1998). 655. E V. Hunt, "Electroacoustics, the Analysis of Transduction and Its Historical Background." American Institute of Physics, New York, 1982.

102

VAN SARK

656. M. Smits, private communication. 657. R . E . I . Schropp, M. Smits, H. Meiling, W. G. J. H. M. van Sark, M. M. Boone, and W. E van der Weg, Mater Res. Soc. Symp. Proc. 219, 519 (1991). 658. P.J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, Electron. Lett. 23, 1026 (1987). 659. E. Desurvire, R. J. Simpson, and P. C. Becker, Opt. Lett. 12, 888 (1987). 660. G.N. van den Hoven, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, Appl. Phys. Lett. 68, 1886 (1996). 661. A. Polman, J. Appl. Phys. 82, 1 (1997). 662. F. Priolo, G. Franzb, S. Coffa, and A. Camera, Mat. Chem. Phys. 54, 273 (1998). 663. F. Priolo, G. Franzb, S. Coffa, and A. Camera, Phys. Rev. B 57, 4443 (1998). 664. G. N. van den Hoven, J. H. Shin, A. Polman, S. Lombardo, and S. U. Campisano, J. Appl. Phys. 78, 2642 (1995). 665. J.H. Shin, R. Serna, G. N. van den Hoven, A. Polman, W. G. J. H. M. van Sark, and A. M. Vredenberg, Appl. Phys. Lett. 68, 697 (1996). 666. A. Polman, J. H. Shin, R. Serna, G. N. van den Hoven, W. G. J. H. M. van Sark, A. M. Vredenberg, S. Lombardo, and S. U. Campisano, Mater. Res. Soc. Symp. Proc. 422, 239 (1996). 667. S. Coffa, G. Franzb, A. Polman, and R. Serna, Phys. Rev. B 49, 16313 (1994). 668. P.G. Kik, M. J. A. de Dood, K. Kikoin, and A. Polman, Appl. Phys. Lett. 70, 1721 (1997). 669. E Priolo, G. Franzb, S. Coffa, A. Polman, S. Libertino, R. Barklie, and D. Carey, J. Appl. Phys. 78, 3874 (1995). 670. G. Franzb, F. Priolo, S. Coffa, A. Polman, and A. Camera, Appl. Phys. Lett. 64, 2235 (1994). 671. B. Zheng, J. Michel, E Y. G. Ren, L. C. Kimerling, D. C. Jacobson, and J. M. Poate, Appl. Phys. Lett. 64, 2842 (1994). 672. J. Palm, E Gan, B. Zheng, J. Michel, and L. C. Kimerling, Phys. Rev. B 54, 17603 (1996). 673. S. Lombardo, S. U. Campisano, G. N. van den Hoven, and A. Polman, J. Appl. Phys. 77, 6504 (1995).

674. L.H. Slooff, Master's thesis, FOMmInstitute for Atomic and Molecular Physics, Amsterdam, 1996. 675. J. Stimmer, A. Reittinger, J. E NiJtzel, G. Abstreiter, H. Holzbrecher, and C. Buchal, Appl. Phys. Lett. 68, 3290 (1996). 676. W. Fuhs, I. Ulber, G. Weiser, M. S. Bresler, O. B. Gusev, A. N. Kuznetsov, V. K. Kudoyarova, E. I. Terukov, and I. N. Yassiervich, Phys. Rev. B 56, 9545 (1997). 677. E. I. Terukov, O. I. Kon'kov, V. K. Kudoyarova, O. B. Gusev, and G. Weiser, Semiconductors 24, 884 (1998). 678. E. I. Terukov, M. M. Kazanin, O. I. Kon'kov, V. K. Kudoyarova, K. V. Kougiya, Y. A. Nikulin, and Kazanskii, Semiconductors 34, 829 (2000). 679. V. B. Voronkov, V. G. Golubev, A. V. Medvedev, A. B. Pevtsov, N. A. Feoktistov, N. I. Gorshkov, and D. N. Suglobov, Phys. Solid State 40, 1301 (1998). 680. J.H. Shin and M. Kim, J. Vac. Sci. Technol. A 17, 3230 (1999). 681. A. Masuda, J. Sakai, H. Akiyama, O. Eryu, K. Nakashima, and H. Matsumura, J. Non-cryst. Solids 226-229, 136 (2000). 682. T. F6rster, Discuss. Faraday Soc. 27, 7 (1959). 683. H. Kiihne, G. Weiser, E. I. Terukov, A. N. Kuznetsov, and V. K. Kudoyarova, J. Appl. Phys. 86, 1896 (1999). 684. M.B. Schubert, A. Hierzenberger, H. J. Lehner, and J. H. Werner, Sensors Actuators A 74, 193 (1999). 685. E. Betzig and J. K. Trautmann, Science 257, 189 (1992). 686. E. Betzig, P. L. Finn, and J. S. Weiner, Appl. Phys. Lett. 60, 2484 (1992). 687. S. Madsen, M. Mullenborn, K. Birkelund, and E Grey, Appl. Phys. Lett. 69, 544 (1996). 688. S. Madsen, S. I. Bozhevolnyi, K. Birkelund, M. Mullenborn, J. M. Hvam, and E Grey, J. Appl. Phys. 82, 49 (1997). 689. M. K. Herndon, R. T. Collins, R. E. Hollingsworth, P. R. Larson, and M. B. Johnson, Appl. Phys. Lett. 74, 141 (1999). 690. W. Gao, S. H. Lee, J. Bullock, Y. Xu, D. K. Benson, S. Morrison, and H. M. Branz, Sol. Energy Mater. Sol. Cells 59, 243 (1999).

Chapter 2 ATOMIC LAYER DEPOSITION Mikko Ritala, Markku Leskel~i Department of Chemistry, University of Helsinki, FIN-O0014 Helsinki, Finland

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Alternative Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Basic Features of ALD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. ALD Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Benefits of ALD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Limitations of ALD . . . . . . . . . . . . . . . . . . ......................... 4. ALD Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Flow-Type ALD Reactors with Inert Gas Valving . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Flow-Type ALDReactors with Moving Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . 5. ALD Precursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Requirements for ALD Precursors 9 5.2. Choice of Precursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Overview of Precursors and Their Combinations Used in ALD . . . . . . . . . . . . . . . . . . . 6. Film Materials and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Electroluminescent Display Phosphors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Transparent Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Passivating and Protecting Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Transition Metal Nitride Diffusion Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Solar Cell Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8. Optical Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Characterization of ALD Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Film Growth Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Reaction Mechanism Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103 104 104 104 106 108 108 108 109 112 113 . . . . 113 121 121 125 126 128 133 134 135 137 138 138 138 139 144 152

153

a d v a n t a g e o u s features, such as e x c e l l e n t c o n f o r m a l i t y a n d uni-

1. I N T R O D U C T I O N

formity, a n d s i m p l e a n d a c c u r a t e film t h i c k n e s s control. A t o m i c l a y e r d e p o s i t i o n ( A L D ) is a c h e m i c a l gas p h a s e thin film d e p o s i t i o n m e t h o d b a s e d o n a l t e r n a t e s a t u r a t i v e s u r f a c e re-

ALD was developed and world widely introduced with a n a m e o f a t o m i c l a y e r e p i t a x y ( A L E ) (for o t h e r n a m e s , see Sec-

actions. As d i s t i n c t f r o m the o t h e r c h e m i c a l v a p o r d e p o s i t i o n

tion 2) in the late 1970s b y S u n t o l a a n d c o - w o r k e r s in F i n l a n d

t e c h n i q u e s , in A L D the s o u r c e v a p o r s are p u l s e d into the reac-

[ 1-4]. T h e m o t i v a t i o n b e h i n d d e v e l o p i n g A L D w a s the desire

tor alternately, o n e at a time, s e p a r a t e d b y p u r g i n g o r e v a c u a tion p e r i o d s . E a c h p r e c u r s o r e x p o s u r e step saturates the s u r f a c e

to m a k e thin film e l e c t r o l u m i n e s c e n t ( T F E L ) flat p a n e l d i s p l a y s

w i t h a m o n o m o l e c u l a r l a y e r o f that precursor. T h i s results in a u n i q u e s e l f - l i m i t i n g film g r o w t h m e c h a n i s m w i t h a n u m b e r o f

[2, 5 - 9 ] . T h i s is a d e m a n d i n g a p p l i c a t i o n since electric fields in the r a n g e o f m e g a v o l t s p e r c e n t i m e t e r are a p p l i e d a c r o s s

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00 103

104

RITALA AND LESKELA,

polycrystalline or amorphous luminescent and insulator films (Sections 6.1. and 6.2). Nevertheless, ALD was successful in meeting the requirements of high dielectric strength, low pinhole density, and uniformity over the large-area substrates, and it has been employed in TFEL production since the carly 1980s [7-11]. Soon after the successful introduction of ALD, its applicability to epitaxial compound semiconductors was demonstrated by several groups [12-15], and since that semiconductors, especially the III-V compounds, have been the most extensively examined materials [16-25]. However, though many outstanding results have been achieved, the overall success in that field has remained limited with no reported commercial applications. Meanwhile, new nonepitaxial applications were taken into research more slowly but steadily. Solar cells, microelectronics, optics, protective applications, and gas sensors have been among the areas examined. Since the mid 1990s, rapidly increasing interest toward ALD has arisen from the silicon-based microelectronics. This increase is a direct consequence of the ever-decreasing device dimensions and the increasing aspect ratios in the integrated circuits (IC). The thin film deposition techniques used for a long time in the IC industry are foreseen to meet major conformality problems during the next few years, and ALD is currently considered as one of the most potential substitutes for them. At the same time, the films are shrinking so thin that the major concern of ALD, the low deposition rate, is becoming less important. In addition to thin films on planar substrates, ALD has also been examined in surface processing of porous materials. A great deal of this work has concentrated on chemical modification of high surface area silica and alumina powders for heterogeneous catalysts [26-33] but also nanoporous silicon layers [34, 35] and alumina membranes [36, 37] have been processed. As the current interest in ALD is largely centered on nonepitaxial films, this review chapter mainly focuses on these materials and the related chemistry. The growth of epitaxial semiconductors has been thoroughly reviewed elsewhere [16-25] and is touched here only from the chemistry point of view. In addition, the ALD processing of high surface area powders has been summarized in a number of articles [30--33] and is considered here only as a valuable source of information on the growth mechanisms (Section 7.2.2). In addition to these and other, more general review articles [5-9, 38-42], the proceedings of the biannually held topical international symposia [43-46] give a good overview of the development of the ALD method. We start with a few notes on the alternative names of ALD, followed by an introduction of the basic features, benefits, and limitations of the method. After examining ALD reactors, precursors will be discussed. This is followed by a summary of ALD made film materials. Finally, the various ways of optimizing and characterizing ALD processes are surveyed.

2. ALTERNATIVE NAMES At the time of its introduction, the method was given a name atomic layer epitaxy (ALE) [1, 2] where the term "epitaxy," coming from the Greek and meaning "on-arrangement," was used to emphasize the sequentially controlled surface reactions upon the previously deposited layer [7, 38]. However, as "epitaxy" is more commonly used in describing a growth of a single crystalline film on a single crystalline substrate with a well-defined structural relationship between the two, unfortunate confusions have arisen when applying the name ALE in the case of amorphous or polycrystalline films. For this and other reasons, many synonyms, all basically referring to the same method, have been suggested for ALE during the years (Table I). Among these, ALD appears to have become the most widely used one and is to be understood as a general name of this method coveting all kinds of films, whereas ALE should now be reserved for epitaxial films only. Though the words "atomic" and "layer" have also been questioned (Table I), their continuous use is strongly motivated by the desire to keep the terminology consistent, thereby assisting the follow-up of the literature. 3. BASIC FEATURES OF ALD

3.1. ALD Cycle In ALD, the film growth takes place in a cyclic manner. In the simplest case, one cycle consists of four steps: (i) exposure of the first precursor, (ii) purge or evacuation of the reaction chamber, (iii) exposure of the second precursor, and (iv) purge or evacuation. This cycle is repeated as many times as necessary Table I. Name Atomic layer deposition

Atomic layer epitaxy Atomic layer growth Atomic layer chemical vapor deposition Molecular layer epitaxy Digital layer epitaxy

AlternativeNames to the ALD Method Acronym

Comments

ALD

General, covers all kinds of films In a close connection with the original name ALE The original name, but should be reserved for epitaxial films only Like ALD but less used ALG ALCVD Emphasizes the relation to CVD MLE DLE

Molecular layering ML Successive layerwise chemisorption Sequential surface chemical reaction growth Pulsed beam chemical vapor deposition

Emphasizes molecular compounds as precursors Emphasizes the digital thickness control Dates back to old Russian literature

ATOMIC LAYER DEPOSITION

105

Fig. 1. An ALD film deposition cycle shown schematicallywith the TiC14-H20 process as an example. To illustrate the importance of surface species possibly remaining after the water pulse, or more generally, after the nonmetal precursor pulse, two hypothetical reaction routes have been sketched: (a) hydroxyl group terminated and (b) dehydroxylatedsurface after the water pulse. to obtain the desired film thickness. Depending on the process, one cycle deposits 0.1- to 3-,~ film thickness. The actual reactions taking place under each exposure step depend largely on the presence or the absence of reactive functional groups on the surface of the growing film. In the case of oxides, for example, surface hydroxyls often terminate the surface after exposure to water. Here, the ALD process is schematically illustrated by an example of the growth of TiO2 from TIC14 and H20 (Fig. 1). To emphasize the importance of the hydroxyl groups, two alternative reaction routes have been sketched out, one with a hydroxyl group terminated surface (Fig. l a) and the other with a completely dehydroxylated surface (Fig. lb). In reality, the hydroxyl coverage is temperature dependent, and thus the two routes may be mixed. When dosed onto the surface terminated with functional (here hydroxyl) groups, the precursor molecules react with these groups (Fig. l a) releasing some of their ligands. If there are no functional groups on the surface, the incoming molecule can only chemisorb, either intact or dissociatively (Fig. lb). As a consequence of a finite number of the reaction or chemisorption sites on the surface, in maximum only a monomolecular layer of the precursor becomes firmly bound to the surface. The following purge (or evacuation) period removes all the excess precursor molecules and volatile byproducts leaving only the monolayer on the surface. For simplicity, from here on, this monolayer will be called a chemisorption layer regardless of whether it is formed via exchange reactions (Fig. 1a) or true chemisorption (Fig. lb). Subsequently, the other precursor is dosed in and reacts with the chemisorption layer liberating the ligands and producing the desired solid. At the same time, the surface is converted back to its original state, i.e., in our example either hydroxyl terminated (Fig. 1a) or bare oxide sur-

face (Fig. l b). The second purge period completes the deposition cycle which is then repeated. Ideally, each exposure and purge step is complete. The precursor molecules chemisorb or react with the surface groups saturatively so that after the formation of the chemisorption monolayer no further adsorption takes place, and the purge periods remove all the excess precursor and volatile byproduct molecules. Under these conditions, the film growth is selflimiting: the amount of the film material deposited during each cycle is the same and is determined only by the density of the chemisorption or reaction sites at the surface. The self-limiting growth mechanism gives ALD a number of advantageous features (Table II) which are discussed in more detail in the next section. Most of the ALD processes are based on the above described exchange reactions between molecular precursors. Another possible reaction type is additive with elemental precursors but because only a few metals are volatile enough, the applicability of these reactions is limited. The third reaction type, quite rare as well, involves a self-limiting adsorption of a precursor followed by its decomposition by an appropriate energy pulse (Section 5.3.4). In a majority of the ALD processes reported, the reactions are activated only thermally under isothermal conditions. However, additional activation methods have also been examined. These include light irradiation with lasers [ 15, 17, 19, 47-51 ] or lamps [52-57] for promoting photolytic or photothermal reactions, and upstream generation of reactive radicals by thermal cracking [58-69] or with plasma discharges [70-75]. The alternate pulsing is definitely the most characteristic feature of ALD but almost as distinctive is the self-limiting growth mechanism. However, some deviations from the absolutely self-

106

RITALA AND LESKEL,~ Table II.

Characteristic feature of ALD Self-limiting growthprocess

Characteristic Features of ALD with the ConsequentAdvantages Inherent implication on film deposition Film thickness is dependent only on the number of deposition cycles No need of reactant flux homogeneity

Atomic level control of material composition

Separate dosing of reactants

No gas phase reactions

Processing temperature windows are often wide

Sufficient time is providedto complete each reaction step Processing conditions of different materials are readily matched

limited growth conditions may be accepted with certain precautions. The reactions may be somewhat incomplete leaving the chemisorption layer short from saturation, or there may be some precursor decomposition in addition to the chemisorption. As long as the reactions causing these nonidealities proceed in a surface controlled rather than a mass transport controlled manner, the coverage of the chemisorption layer and thereby the deposition rate remain everywhere the same, thus maintaining the advantageous characteristics of ALD. Alternatives to accepting these nonidealities would be to increase the exposure time to complete the reactions, or to lower the deposition temperature to avoid the decomposition, but these would be accompanied by negative effects of increased process time and reduced film quality. A common misconception is that ALD growth always proceeds in a layer-by-layer manner but this is often not the case as only a fraction of a monolayer may be deposited in each cycle. Reasons for the less than a monolayer per cycle growth are the limited number of reactive surface sites [33, 42] and the steric hindrances between bulky ligands in the chemisorption layer [8, 76]. As a consequence, even if saturatively formed, the chemisorption layer contains too few metal atoms for forming a full monolayer of the film material. On the other hand, also surface reconstructions may cause a decrease in the growth rate [77, 78], though in the apparently exceptional case of the 2 ML cycle-1 growth of AlAs they appear to have the opposite effect [19, 79-81]. Yet another misconception is that ALD would produce atomically smooth films. This indeed may often be the case with epitaxial or amorphous films, but the nucleation and the grain growth involved in the formation of polycrystalline films

Practical advantage Accurate and simple thickness control Large-area capability Large-batch capability Excellent conformality No problems with inconstant vaporization rates of solid precursors Good reproducibility Straightforward scale-up Capability to produce sharp interfaces and superlattices Possibility to interface modification Favors precursors highly reactive toward each other, thus enabling effective material utilization High quality materials are obtained at low processing temperatures Capability to prepare multilayer structures in a continuous process

usually lead to a measurable surface roughness which increases along with film thickness (Section 7.2.1) [39, 82-87].

3.2. Benefits of ALD Table II summarizes the relationships between the characteristic features of the ALD process and the resulting benefits. The benefits are now discussed with selected examples. It is worth emphasizing already here that the achievement of these benefits requires appropriate chemistry fulfilling the special requirements set for ALD processes (Section 5). As the film growth proceeds in a self-limiting manner, each cycle deposits exactly the same amount of material, and thus the film thickness may be accurately controlled simply by the number of deposition cycles. However, it must be recognized that during the very first cycles when the surface is converted from the substrate to the film material, the surface density of the chemisorption or reactive sites and, accordingly, the growth rate may change. The self-limiting growth mechanism also ensures that the precursor fluxes do not need to be uniform over the substrate. What is only needed is a flux which is large enough so that the chemisorption layer becomes saturated, all the excess will be subsequently purged away. As a result, ALD provides perfect conformality and trench-fill capability (Fig. 2) [88] as well as good large-area uniformity [88, 89] and large-batch capability. Batches as large as 82 substrates of a size 15.5 x 26.5 cm 2 [41 ] or 42 times 40 x 50 cm 2 substrates [90] may be processed in the existing ALD reactors, and this is certainly not the upper limit. The self-limiting growth mechanism also ensures good reproducibility and relatively straightforward scale-up.

ATOMIC LAYER DEPOSITION

Fig. 2. Cross-sectional SEM images of a 300-nm A1203 film deposited onto a patterned silicon substrate showing (a) perfect conformality and (b) trenchfill capability [88]. Note that on the top surface of the silicon wafer there is a thermal silicon oxide layer below the A1203 film. Reprinted with permission from M. Ritala et al., Perfectly conformal TiN and A1203 films deposited by atomic layer deposition, Chem. VaporDeposition 5, 7 (1999), 9 1999, WileyVCH Verlag GmbH.

Precursor flux homogeneity is not required in timescale either. Therefore, solid sources which often have inconstant sublimation rates are more easily adopted in ALD than in chemical vapor deposition (CVD). The separate dosing of the precursors, in turn, naturally eliminates all possible detrimental gas phase reactions. As the film is deposited in a layerwise manner, either a full monolayer or a fraction of a monolayer at a time, the material composition may be controlled down to a nanometer level, and in the most ideal cases even to an atomic level. This offers a simple way to create superlattices (Fig. 3a) [7, 18, 91, 92] and other multilayer structures with accurately controlled layer thicknesses, such as optical multilayers tailored for soft X-ray or visible range (Section 6.8), or nanolaminate insula-

107

Fig. 3. (a) (110) cross-sectional transmission electron microscopy (TEM) micrograph of a 1-ML InAs - 5-ML GaAs superlattice. (b) Cross-sectional scanning electron microscopy (SEM) micrograph of an Inl_xGaxP/GaAs single quantum well structure on a (011) sidewall of a GaAs substrate [18]. Reprinted with permission from A. Usui, Atomic layer epitaxy of III-V compounds: Chemistry and applications, Proc. IEEE 80, 1641 (1992), 9 1992, IEEE.

tors (Section 6.2). An outstanding demonstration of the accurate film thickness control and perfect conformality is shown in Figure 3b where a single quantum well structure has been grown into a trench. Note also the selective growth between the GaAs and SiO2 surfaces. Practice has shown that ALD made films often, though of course not always, possess superior quality as compared with films made by other methods at the corresponding temperatures. This can be related to the fact that in ALD each monomolecular layer reaction step is given enough time to reach completion while in other methods the continuous growth may prevent this by covering the unreacted species with new deposits. Many ALD processes may be performed over a relatively wide temperature range. Therefore, a common growth temperature is often found for different materials, thereby making it possible to deposit multilayer structures in a continuous manner. This is utilized, for example, in manufacturing of the TFEL displays where the insulator-luminescent material-

108

RITALA AND LESKEL,~

insulator three-layer structure (Section 6.1) is grown in one continuous process. 3.3. Limitations of ALD The major limitation of ALD is evidently its slowness since at best a monolayer of the film is deposited during one cycle. Typically, deposition rates of 100-300 nm h - 1 are obtained and 1 /zmh -1 appears to be the upper limit for most processes, though a record rate of 2 / z m h -1 was achieved for epitaxial GaAs in a specially designed reactor (Section 4.3) [93]. However, the low growth rate does not necessarily mean low productivity when the latter is considered in terms of film volume (= thickness x area) produced per time unit. By making use of the good large-batch and large-area processing capabilities of ALD, the low growth rate may be effectively compensated for. On the other hand, there are certain application areas, in particular integrated circuits, where single substrate processing is increasingly preferred because of the cost risks related to losing a batch of valuable substrates. Luckily, at the same time, the film thicknesses have shrunk down to a level where the low growth rate of ALD is losing its significance when weighted against the potential benefits. One limitation to a widespread use of ALD has been the lack of good and cost-effective processes for some important materials. Among these are, for example, metals, Si, SiO2, Si3N4, and several ternary and multicomponent materials. Many of these materials have been made by ALD (Table V in Section 6) but the processes are still far from ideal in a sense that long cycle times are required. 4. ALD REACTORS 4.1. Overview Just like CVD, ALD processes may also be performed in many kinds of reactors over a wide pressure range from atmospheric to ultrahigh vacuum (UHV). ALD reactors can be divided into two groups: inert gas flow reactors operating under viscous or transition flow conditions at pressures higher than about 1 Torr, and high- or ultrahigh-vacuum reactors with molecular flow conditions. The former resemble CVD reactors while the latter are like molecular beam epitaxy (MBE) reactors. In any case, when the special features and the needs of ALD are taken into consideration in the reactor design, some significant differences emerge as discussed in this section. The main parts of an ALD reactor are: 1. transport gas supply (if any), 2. sources of one or several of the following types: gas, liquid, and solid sources, 3. flow and sequencing control of the sources, 4. reaction chamber, 5. temperature control of the heated sources and the reaction chamber (and the substrate, if heated separately), 6. vacuum pump and related exhaust equipment.

Provisional items include: 7. in situ surface and gas phase analysis equipments, such as an ellipsometer and mass spectrometer, for process characterization and control (Section 7.2), 8. load-locks for changing substrates or sources, 9. separate preheating chamber for the substrates.

The last one is especially effective in maximizing throughput in large-batch processing. Besides equipping with a load-lock, often it may be desirable to make the ALD reactor a part of a larger cluster tool for an inert transfer of the substrates from one process step to another. As already noted, in ALD no strict precursor flux homogeneity is required. This gives freedom in the reactor design and assists in constructing large-batch reactors. On the other hand, cost-effectiveness of the process requires that both exposure and purge sequences are rapidly completed. For this reason, flow-type reactors are preferred especially in production scale use: purging of a properly designed reactor under viscous flow conditions is much more rapid than evacuation of a high-vacuum chamber. Another crucial aspect related to purging or evacuation is that the chamber and the lines which are to be purged or evacuated should have small volume and uniformly heated walls. Otherwise, long purge periods may be required to desorb precursor molecules adsorbed on "cold spots" on the walls. This is especially important in the growth of oxides where water is often used as an oxygen source. The desire for high precursor utilization efficiency is also an important aspect for the reactor design. In high-vacuum reactors, the precursor molecules make at best only a few collisions with the substrate surface before being pumped out and thus have a limited probability to react. On the other hand, in the flow-type reactors, and in the traveling-wave reactors (Section 4.2.4) in particular, a precursor molecule makes multiple hits while being transported through the reactor. As a consequence, reaction probability and thereby precursor utilization efficiency are increased, and the saturation of the chemisorption layer is accelerated which makes the process faster. MBE types of reactors are basically easy to operate in the ALD mode since they are usually equipped with shutters by means of which precursor fluxes from the Knudsen effusion cells can be chopped. When volatile reactants are used, their pulsing is realized with valves. What is still needed to make an ALD process is a proper choice of substrate temperature and evacuation periods between the alternate precursor pulses to ensure the self-limiting growth conditions. The major benefit of the MBE type of reactors is the rich variety of in situ analytical techniques which may be implemented for detailed reaction mechanism studies. Large chambers also make it easy to employ various sources of extra energy for activating the reactions (Fig. 4). On the other hand, the need of long exposure and evacuation times limits the throughput. CVD reactors with liquid and gas sources only are also relatively easy to operate in the ALD mode. For pulsing the precursors, simple solenoid or pneumatic valves may be used. However, if the valves are far from the reaction chamber and there

ATOMIC LAYER DEPOSITION

109

TODIFFUSIONPUMP

h f r',

SCREEN SUBSTRA~~,, PH3~

~

E~

[-~ ' HEATEI

"~ SHROUD

I__.JELECTRON GUN

CRACKINGr)

Fig. 4. An example of a high-vacuum ALD reactor incorporating RHEED (electron gun and screen) and a quadrupole mass analyzer (QMA) for in situ characterization, and a laser and a thermal cracking cell for activating the reactions [49]. Reprinted with permission from M. Yoshimoto, A. Kajimoto, and H. Matsunami, Laser-assisted atomic layer epitaxy of GaP in chemical beam epitaxy, Thin Solid Films 225, 70 (1993), 9 1993, Elsevier Science.

are long tubings in between, their effective purging calls for special attention. Even more problematic is the pulsing of solid sources which need to be heated far above room temperature where no mechanical valves can be used. In the flow-type ALD reactors described in the next two sections, these issues have been specially addressed.

4.2. Flow-Type ALD Reactors with Inert Gas Valving The ALD reactors commercially available [90] and those in industrial use in TFEL manufacturing are all of a flow type with inert gas valving [3, 4, 38]. These reactors are carefully designed to minimize the pulse and purge times and to maximize the precursor utilization efficiency. They are available in both small size for research and large size for production [90] (Fig. 5). The main points of these reactor designs are now examined. The discussion is limited mainly to those features which are special to ALD whereas more common issues, like mass flow controllers, pumps, heaters, and their controllers etc., are not dealt with. For a detailed model of mass transport in the flow-type ALD reactors, see Ref. [94].

4.2.1. Transport Gas Inert gas, most often nitrogen, is used for transporting the precursor vapors and purging the reaction chamber. A continuous flow of the inert gas is regulated with mass flow controllers.The flow rate is optimized together with the total pressure and the reactor geometry to give the best combination of speed, transportation and utilization efficiency of the reactants, inert gas valving (Section 4.2.3), and the consumption of the inert gas itself. In small research reactors, the flow rate is about 0.5 slm whereas the largest production reactors require 20-50 slm. The operating pressures are typically in the range of 1-10 Torr.

Fig. 5. A photograph of an ASM Microchemistry F-950 ALD reactor for production of fiat panel displays and solar cells. (Courtesy ASM Microchemistry, Espoo, Finland.)

A crucial aspect of the transport gas is purity because it is the main source of impurities in an ALD process. In the minimum, 99.999% purity should be used. In Section 4.2.4, a calculation of the effects of the impurities is presented. 4.2.2. Sources The source chemicals may be divided into two groups depending on if their vapor pressures at room temperature, or close to it, are higher or lower than the total pressure inside the reactor (1-10 Torr). The high vapor pressure sources; i.e., gases and highly volatile liquids, are led into the reactor from their external cylinders or vessels by pulsing with fast valves. No bubblers or transport gases are necessary since the source vapors enter the reactor as a consequence of the pressure difference. Once entered into the reactor, the vapor is transported further by the carrier gas flow inside the reactor. However, as large scale manufacturing requires large doses, carrier gas transportation already from the source vessel may become necessary. For low vapor pressure source chemicals, two options exist. The first one is to have them in external vessels which, together with the source lines and the required valving systems, are properly heated to ensure effective transportation. The second option is to place the source chemicals inside the reactor where they are heated to temperatures where appropriate vapor pressures are obtained. In research reactors, for instance, a vapor pressure around 0.1 Torr has been found to be a good starting point for a new precursor. To realize pulsing of solid sources inside the reactor, a clever inert gas valving system (next section) was developed [3, 4].

4.2.3. Inert Gas Valving An exact mathematical description of the inert gas valving sys. tern has been given elsewhere [3, 4, 38], so here only the basic principle is introduced. The inert gas valving is based on a

110

RITALA AND LESKELA,

Fig. 6. A schematic of the inert gas valving system where the direct connection to the exhaust is (a) between the source and the reaction chamber, or (b) behind (upstream of) the source. The shading shows the area where the flow barrier is formed when set on.

Fig. 7. Schematics of a small research ALD reactor with two inert gas valved source lines and a traveling-wave reaction chamber inserted to a main vacuum tube (not to scale). The intermediate space contains inert gas at a pressure slightly higher than that inside the tubings and the reaction chamber.

4.2.4. Reaction Chamber design where each source tube is connected both to a reaction chamber and directly to an exhaust so that the exhaust connection is either between the source and the chamber (Fig. 6a) or behind the source (Fig. 6b). Each tube is also equipped with two inert gas flows: one is the transport gas and the other is the valving gas. The valving gas enters the source tube between the source and the reaction chamber. A practical way to realize the two flows is to employ coaxial tubes [3, 4]. When the source is in its off state, the valving gas flow is on and the transport gas flow is off. The valving gas flow divides into two parts, one purging the reaction chamber and the other one setting up a laminar flow barrier (shaded areas in Fig. 6). The flow rate of the valving gas in the flow barrier is adjusted to counterbalance the diffusion rate of the precursor toward the chamber so that the precursor vapor pressure in the chamber does not exceed a predetermined level, for example, one part per million (ppm) of its pressure in the source. In other words, the velocity of the valving gas in the barrier is set equal to or greater than the velocity by means of which the specified precursor isobar diffuses. When the source is turned on, the valving gas is turned off and the transport gas is turned on, thereby breaking the flow barrier. All this can be done rapidly with valves located at room temperature, no matter how hot the source itself is. The source vapors are led into the reaction chamber through separate lines which all, i.e., also those through which vapors from the external gas or liquid sources are led in, are equipped with the inert gas valving system. Usually, the valving points are close to the chamber and the separate lines merge just in front of it so that the volume to be purged is minimized and well heated and there is hardly any film growth before the chamber. The operation of the inert gas valving system is easily tested by pulsing only one precursor into the chamber while keeping the other one behind the flow barrier. No film deposition is observed when the barrier holds.

The reactors may be equipped with two kinds of reaction chambers: a compact, cassette-like, traveling-wave reactor chamber, and a more open tubular chamber. They both may be combined easily with the inert gas valving system. The open chambers have the benefit that they can incorporate any arbitrarily shaped substrate. However, they are not as fast and as cost-effective as the traveling-wave reactors which therefore are preferred with planar substrates in both research and large scale production. In the traveling-wave reactor geometry, the substrates are located face to face close to each other. The distance between two substrates is typically only a few millimeters leaving a narrow flow channel in between. As an example, Figure 7 shows schematics of a small reactor where there is only one substrate pair. A connection to two inert gas valved source lines is shown as well. In practice, there are usually more source lines to facilitate deposition of multicomponent films or multilayer structures. Favorably, the substrates are located close to the point where the source lines merge since this minimizes the chamber wall area subjected to the film growth. The whole assembly of the source lines and reaction chamber is inserted into a vacuum tube outside which heaters are located. The temperature increases stepwise from the gas inlets toward the reaction chamber so that each solid source may be set independently to an appropriate temperature. In large-batch reactors, there may be tens of substrates arranged in pairs so that the gases flow over the front but not on the backsides of the substrates (Fig. 8). Instead of the one flow channel in the small reactor, in the large reactor there are several of them parallel with each other. Connections to the sources are basically similar to the small reactor. Together with the selflimiting film growth mechanism, these similarities between the research and large scale reactors assist in scale-up of ALD processes. When pulsed into the reaction chamber, the precursor molecules are transported by the carrier gas along the flow

ATOMIC LAYER DEPOSITION

Fig. 8. Reaction chamber of a large scale ALD reactor incorporating several substrates in pairs so that narrow flow channels are left between each pair.

channel between the substrates. The flow velocity and pressure are adjusted to maintain essentially pluglike flow conditions which keep the adjacent precursor pulses separated--like waves--and ensure effective and rapid purging of the small volume left between the substrates. In the small research reactors with two 5 • 5 cm 2 substrates (Fig. 7), purge times as short as 0.1 s are enough for separating the precursor pulses. If the pulses were not well separated, films with nonuniform thickness would be obtained, and in the worst case particles might form in gas phase reactions. While traveling along the narrow flow channel, the precursor molecules undergo multiple collisions with the substrates. As a result of these multiple hit conditions, the precursor molecules have a high probability to find an open chemisorption or reaction site and thus become effectively utilized. At the same time, the surface becomes rapidly saturated: often 0.2 s is enough for the saturation in the previously described research reactor. A low operation pressure favors high hitting frequency but reduces the precursor transport capability of the carrier gas. The optimal pressure is thus a compromise of the two factors. The special conditions in the traveling-wave reactors have a number of interesting consequences. In the beginning of the precursor pulse, its vapor pressure in the flow channel is very much location and time dependent [95]. At first, only the leading edge of the substrate; i.e., the edge closest to the inlet, receives precursor molecules. Because of their high hitting frequency, and preferably also high reactivity, the precursor molecules become rapidly exhausted from the pulse front to the open surface sites. Thus, the latter parts of the substrate do not receive any precursor molecules before the leading parts

111

Fig. 9. Propagation of a TIC14 pulse along a flow channel over substrate surfaces which the preceding water pulse has left hydroxyl group terminated. The multiple hit conditions ensure that the hydroxyl groups become effectively consumed in exchange reactions at the TIC14 pulse front. HC1 molecules formed as reaction byproducts travel in front of the TIC14 pulse and thus may readsorb and block reaction sites from TIC14.

have become covered. In other words, the precursor pulse front rolls like a wave over the substrate saturating the surface on its way (Fig. 9). Experimentally, this can easily be seen and verified by underdosing one precursor and by observing two distinct regions on the substrate: one covered with a uniform film and another one covered with no film. The higher the precursor reactivity, the sharper the border between the two areas. In research reactors, borders as sharp as a few millimeters are observable. In principle, the steepness of the border could be used in studying the reactivities of the precursors. Quantitative evaluation would, however, require constant doses throughout the experiment which, especially with solid sources, may often be difficult to realize. The sharp border between the growth and nongrowth areas points out the possibility of maximizing the precursor utilization. The closer the border is set to the substrate, the less precursor is wasted to the growth on the downstream side chamber walls or to the exhaust. However, at the same time the risks related to variations in precursor doses are increased. In the traveling-wave reactor geometry, the surface hitting densities estimated from the partial pressures with the basic equations of the kinetic gas theory lose their meaning quite a lot. This is illustrated by considering the effects of impurities in the carrier gas. Taking again the research reactor (Fig. 7) as an example, we have, approximately, a total pressure of 5 Torr and 200 stdcm 3 min -1 carrier gas flow rate to the flow channel limited by the two 5 x 5 cm 2 substrates. A typical moisture content of 1 ppm in the carrier gas means a partial pressure of 5 x 10 -6 Torr which at room temperature implies a hit-

112

RITALA AND LESKEL/~

ting density of 2.4 • 1015 water molecules cm -2 s -1 . For water, a high reactivity toward a surface covered with metal precursors may be assumed and therefore the sticking coefficient should approach unity. Then, the amount of oxygen corresponding to a typical ALD oxide film growth rate (3.0 x 1014 oxygen atoms cm -2 cycle- 1) would become adsorbed in about 0.1 s already from the residues in the carrier gas. However, from the flow rate of the carrier gas, one can calculate that in the same time (0.1 s), only 9 x 1012 H20 molecules enter the flow channel. When averaged over the 50-cm 2 substrate area, this gives only 1.8 • 10 ] 1 oxygen atoms cm -2 which is more than 3 orders of magnitude less than that estimated from the hitting density. Clearly, the ordinary hitting density calculations cannot be applied. What actually happens is that the moisture impurities become adsorbed at the upstream edge of the substrate, i.e., right after the point where the precursor flow lines merge and film growth starts (cf. Fig. 7). Assuming a coverage of 1 • 1014 molecules cm -2 and a cycle time of 1.0 s, this means that 0.9-cm 2 area adsorbs the incoming moisture impurities. In practice, a somewhat larger area, typically 5 cm 2, may be disturbed close to the leading edge but besides the impurities other factors also contribute to this area. In any case, the upstream edge of the substrate serves as an effective internal getter for the impurities. By moving the substrates a bit further away from the merging point of the separate precursor lines, the getter region would be eliminated from the substrate but then films would grow more extensively on the chamber walls. Therefore, in research it is more convenient to accept the leading edge area and to consider only the area outside that as representative for the true ALD growth. A less favorable consequence of the multiple hit conditions is that also the reaction byproducts, like HC1, have a high prob-

AsH 3 + H 2

H 2

TMG

ability to adsorb. As they are formed in the reactions at the front edge of the precursor pulse, the byproducts travel in front of this pulse (Fig. 9) and thereby they have a possibility to decrease the growth rate by blocking reaction sites from the precursor molecules [96, 97]. This effect may explain the differences which are sometimes observed in the growth rates obtained with the traveling-wave and other kinds of reactors. In addition to the limitations on substrate shape, the traveling-wave reactors are also restricted in respect to the utilization of extra energy sources like plasma, hot filaments, or light. Because of the compact construction of the reaction chamber, there hardly is any room for the implementation of the extra energy sources, especially in the large-batch reactors. The multiple wall collision conditions, in turn, make it difficult to transport reactive radicals from their remote sources over the entire substrates. Therefore, these reactors are quite limited to thermally activated reactions only.

4.3. Flow-Type ALD Reactors with Moving Substrates The alternate precursor dosing as required in ALD may be realized not only by chopping precursor fluxes to the stationary substrates as above, but also by moving substrates between separate precursor fluxes which are either constantly on or accordingly pulsed. While a high-vacuum version of such a reactor was used in the very first ALD experiments in 1974 [1, 5, 7], also with this approach flow-type systems have subsequently become dominating. In these reactors, inert gases are used for transporting the precursors and for setting up shrouds between the zones with the different precursors. The most popular type of moving substrate reactors is based on the rotating susceptor design [3, 4, 13, 20, 63, 93, 98-100], an example of which is shown in Figure 10. A fixed part with

+ H 2

I I

Windows

AsH a +H_ 9 Fixed

~ .ooo..

S

9.

~..... ...." ..

TMG+H2

F--w.~176

iil

,o,

substrate

Rotating~11 part R

Substrate Quartz ~" tube

rRotating g

H.... . . "

. . . . h

'

~

~

Rotating part

Fixed part

-7 ~

feedthrou

Exhaust Fig. 10. Schematics of a rotating susceptor ALD reactor [98]. The susceptor consists of fixed and rotating parts. The precursor streams are directed into windows in the fixed part below which the substrate rotates and cuts through the streams. A wedge and a large H2 flow from the center tube prevent mixing of the two precursors. Reprinted with permission from M. A. Tischler and S. M. Bedair, Self-limiting mechanism in the atomic layer epitaxy of GaAs, Appl. Phys. Lett. 48, 1681 (1986), 9 1986, American Institute of Physics.

ATOMIC LAYER DEPOSITION two openings covers the rotating susceptor. The source gases are continuously directed to the openings and flow unimpeded through the fixed part except when the substrate cuts through the streams. The exposure times are controlled by the rotational speed and, if needed, they may be elongated by pausing the substrate. A carrier gas flown with a high rate at the center and guided by the wedge on the fixed part prevents mixing of the source gases. The fixed part also shears off a part of the boundary layer above the substrate. With a small clearance between the fixed and moving parts, the rotation speed could have been increased up to 120 rpm which corresponds to 85 ms exposure times and gives a high, self-limited (1 ML cycle- 1) growth rate of 2 # m h -1 for GaAs [20, 93]. On the other hand, the rotating susceptor reactors have limitations in that they are difficult to adopt into processes which require complex sequencing of several sources, like a growth of multilayer structures or compositionally varied multicomponent films.

Table III.

113 Requirements for ALD Precursors Comments

Requirement Volatility

For efficient transportation, a rough limit of 0.1 Torr at the applicable maximum source temperature Preferably liquids or gases

No self-decomposition

Would destroy the self-limiting film growth

Aggressive and complete

Ensure fast completion of the surface

mechanism reactions

reactions and thereby short cycle times Lead to high film purity No problems of gas phase reactions

No etching of the film or substrate material No dissolution into the film or substrate Unreactive volatile byproducts

No competing reaction pathways Would prevent the film growth Would destroy the self-limiting film growth mechanism To avoid corrosion Byproduct readsorption may decrease the

5. ALD PRECURSORS Sufficient purity

Chemistry, especially the choice of proper precursors, is certainly the key issue in a successful design of an ALD process. In this section, we first examine the properties required for the ALD precursors. Next, some practical aspects of choosing the precursors are discussed. Finally, a comprehensive survey of the precursors used in ALD is carried out.

growth rate To meet the requirements specific to each process

Inexpensive Easy to synthesize and handle Nontoxic and environmentally friendly

5.1. Requirements for ALD Precursors Requirements for ALD precursors are summarized in Table III. The precursor chemistry of ALD is convenient to compare with CVD. There are many similarities but because of the certain characteristics of ALD, differences exist as well. However, the unique features of ALD are not reflected that much in the individual compounds which are usually the same as those used in CVD (see Table IV). Rather, it is how they are combined together which makes the difference. For ALD, the most aggressively reacting precursor combinations are looked for while in CVD too aggressive reactions must be avoided.

5.1.1. Volatility The volatility requirement is of course common to ALD and CVD but as the self-limiting growth mechanism makes ALD less susceptible to small variations in precursor fluxes, solid precursors are more easily adopted to ALD than to CVD. Solids do possess some disadvantages, however. First, because solids are often loaded inside the ALD reactor in a limited source volume, the sources must be reloaded frequently, possibly after each run, which is laborious especially in industry. Second, if the particle size is too small, the particles may be transported by the carrier gas, even if operated under reduced pressure, to the substrates where they cause detrimental defects. For these reasons, liquid or gaseous precursors should be preferred, if available.

The required precursor vapor pressure is reactor specific and depends on many factors, like source geometry, substrate area, and flow rates. In research scale flow-type reactors, for example, a vapor pressure of 0.1 Torr is usually appropriate and ensures effective transportation (cf. Section 4.2.2). In large scale production, higher doses and accordingly higher precursor vapor pressures are often desired. The minimum requirements to the precursor volatility are thus set by these vapor pressures and the highest applicable source temperatures (e.g., 500~ Precursor vapor pressure data are not always available, and especially with low volatility solids such measurements may be quite troublesome. In these cases, thermogravimetric (TG) measurements can be used for examining the volatility [ 101 ] and for estimating the required source temperatures [ 102]. One option is to use the conventional constant heating rate measurements. From the weight loss curves of compounds which have already been used in ALD, one can identify certain temperatures, such as those corresponding to 10 or 50% weight losses, and one can plot these as a function of the source temperatures used in a given type of an ALD reactor (Fig. 11). On basis of this data set and a similar TG measurement, a source temperature may be estimated for any new compound to be used in a similar reactor. Another possibility is to perform isothermal weight loss measurements over a range of temperatures. After calibration with a compound with a known vapor pressure, vapor pressures of the compounds of an interest may be estimated [ 102].

114

RITALA AND LESKEL,~ Table IV.

Metal precursor

A Summary of the Precursor Combinations Used and Examined in ALD Thin Film Processes a

Nonmetal and other precursors

Reference

Film material

Elements

Zn

Cd

S Se Se(C2 H5)2, prepyrolyzed Te S Se Te

ZnS ZnSe ZnSe ZnTe CdS CdSe CdTe

[1, 2, 116] [116-120]

A1203 A1203 A1203 A1203 :P A1N AlAs GaN GaP

[2-4, 107, 128-136]

[1211 [118, 1221 [1231 [1161 [122, 124-127]

Halides

A1C13

H20 02 ROH H20/ROH + P205/(CH30)3PO NH3 AsH 3

GaC1

GaC13

GaBr GaI InC1

InC13

SIC14

Si2C16

GeC14 SnC14 SbC15 TiCI4

NH3 PH3 P4 + As4 AsH3 NH3 AsH3 CuC1 + H2S AsH3 AsH3 PH3 ((CHa)3C)PH2 AsH3

In203 In203 :Sn

N2H4 Atomic Hb

Si3N4 Ge

H20 H20 + SbCI5 H20 H2-plasma H20

SnO2 SnO2 :Sb

(CH3)2NNH2

ZrC14 ZrI4

CuGaS 2 GaAs GaAs InP InP InAs

H20/H202 H20/H202 + SnC14 H2S H20 NH3 H2S Si2H6 Atomic Hb

H202 NH3 (+ Zn)

TiI4

GaPl_xAsx GaAs GaN GaAs

H202 NH3 H20 H202

In2S3 SiO2 Si3N4 C1 dopant in SrS and CaS Si Si

Sb205 Ti TiO2 TiO2 TiN TiN TiO2 TiN ZrO2 ZrO2

[137, 138] [129, 139] [140, 141] [142] [143] [144] [1451 [146, 147] [14, 145, 148-153] [154] [143, 155, 1561 [1571 [158]

[1581 [1451 [129] [148, 153] [86, 115, 159] [86, 159, 1601 [1611 [162-167] [168] [169] [60, 170] [611 [1711 [62] [34, 35, 172-174] [1751 [1751 [74] [82, 96, 107, 176-1821 [183, 184] [88, 111,112, 185, 186] [114] [187-190] [186, 191] [83, 133, 192-195] [196]

ATOMIC LAYER DEPOSITION

Table IV. Metal precursor

HfCh NbCI5 TaCI:

Tal: MoC15

WOxFy WF6 MnC12 MnI2 CuC1

ZnC12

CdCI2

Nonmetal and other precursors H20 NH3 (+ Zn) (CH3)2NNH2 H2-plasma H20 NH3 + H20 NH3 NH3 + Zn (CH3)ENNH2 H202 Zn NH3 (+ Zn) (CH3)2NNH2 H20 Si2H6 NH3 H2S H2S H2 Zn GaC13 + H2S H2S H2Se H2S + Se HF H2S

115

(Continued)

Film material HfO2 NbN NbN Ta Ta205 TaOxNy Ta3N5 TaN Ta3N5 Ta205 Mo MoN, Mo2N MoN, Mo2N WO3 W W2N Dopant in ZnS Dopant in ZnS Cu Cu CuGaS2 ZnS ZnSe

Reference [84, 131,195, 197, 198] [103, 112, 185] [114] [74] [3,4, 104-106, 130, 131,135, 195, 199-202] [113] [113, 185] [113] [114] [2031

[2041 [114, 1851 [114] [2051 [206] [207] [3,4,8]

[208] [209, 210] [ll0] [157] [2-4, 85, 211-213] [214]

ZnS 1-x Sex ZnF2 CdS

[lO8]

A1203 A1203 A1203 A1203 A1203 A1N AlP AlAs

[36, 37, 88, 89, 133, 134, 162, 194, 216-224] [ 184, 225-229] [228] [217]

[215] [123,213]

Alkyl compounds AI(CH3)3

AI(CH3)2C1 AI(CH3)2H Al(C2H5)3

AI(CH2CH2 (CH3)2)3 Ga(CH3)3

Ga(CH3)2(C2H5)

H20 H202 N20 NO2 O2-plasma NH3 PH3 AsH3 H20 NH3 PH3 AsH3 H20 NH3 AsH3 AsH3 NH3 N2-H2-plasma PH3 AsH3 ((CH3)3C)AsH2 AsH3

A1203 A1N AlP AlAs A1203 A1N AlAs AlAs GaN GaN GaP GaAs GaAs GaAs

[75] [230--233] [234] [13, 17, 47, 58, 79, 80, 235, 236] [237] [238] [239] [79, 240] [241] [242,243] [17,47]

[244] [245-249] [71] [234, 239, 250, 251] [12, 13, 15, 17, 48, 70, 78, 79, 93, 98, 99, 235, 236, 252-256] [99, 257, 258] [252]

116

RITALA AND LESKELA Table IV.

Metal precursor Ga(C2H5)3

Ga(C2Hs)2C1 Ga(CH2CH2(CH3)2)3 Ga(CH2C(CH3)3)3 In(CH3)3

((CH3)2(C2H5)N)In(CH3)3 In(CH3)2C1 In(CH3)2(C2H5) In(C2Hs)3 Sn(CH3)4 Sn(C2H5)4 Zn(CH3)2

Zn(C2H5)2

Cd(CH3)2

Hg(CH3)2

Alkoxides Al(OC2H5)3 AI(OCH2CH2CH3)3 Ti(OC2Hs)4 Ti(OCH(CH3)2)4 Zr(OC(CH3)3)4

(Continued)

Nonmetal and other precursors NH3 NH3, thermally cracked PH3 AsH3 ((CH3)3C)AsH2 ((CH3)2N)3As AsH3 AsH3 ((CH3)3C)AsH2 H20 PH3 ((CH3)3C)PH2 AsH3 ((CH3)3C)AsH2 AsH3 AsH3 NH3 PH3 AsH3 NO2 NO2 H20 H20 + AI(CH3)3 H2S + H20 H2S H2S + H2Se H2Se (C2H5)2Te (CH3)(CH2CHCH2)Te H20 H20 + B2H6 H20 + AI(CH3)3 H20 + Ga(CH3)3 H2S + H20 H2S (C2H5)2S2 (CzH5)2Se2 H2S H2Se (CzH5)2Te (CH3)(CH2CHCH2)Te ((CH3)2CH)2Te + temperature modulation CH3 (allyl)Te H20/ROH H20/ROH H20/ROH -}-P205 H20 H20 Bi(C6Hs)3 + H20 H20

Film material GaN GaN GaP GaAs GaAs GaAs GaAs GaAs GaAs In203 InP InP InAs InAs InAs InAs InN InP InAs SnO2 SnO2 ZnO ZnO: A1

Reference [243, 259, 260] [63] [49] [17, 19, 47, 50, 252] [258, 261] [262] [263] [191 [258] [264] [78, 265, 266] [267, 268] [48, 269] [270] [257] [92] [246-248] [250, 251]

ZnOl_xSx ZnS ZnS ZnSe CdS CdSe CdTe CdTe CdTe HgTe

[911 [271] [271] [272] [272] [273] [274-276] [276-278] [276, 279-282] [2831 [283] [52, 89, 272, 284-293] [289-292, 294] [272] [293] [288] [288, 295,296] [297] [297] [298-302] [279] [283] [283, 303] [53] [303]

A1203 A1203 A1203 :P TiO2 TiO2 BixTiyOz ZrO2

[129] [129] [141] [304, 305] [306-308] [3091 [310]

ZnOl_xSx ZnS ZnS 1 -x Sex ZnSe ZnTe ZnTe ZnO ZnO:B ZnO: A1 ZnO :Ga

ATOMIC LAYER DEPOSITION Table IV.

117

(Continued)

Metal precursor

Nonmetal and other precursors

Nb(OC2H5)5 Ta(OC2H5)5

H20 H20 NH3 H2S H2S

Nb205 Ta205 TaOxNy PbS PbS

[136, 192, 202, 311 ] [133, 136, 192, 197, 202, 312, 313] [314] [315] [315]

H202 03 H2S HF

MgO MgO CaS

Pb(OC(CH3)3)2 Pb40(OC(CH3)3)6

Film material

Reference

~-diketonato complexes Mg(thd)2c

Sr(thd)2

03 03 + Ti(OCH(CH3)2)4 + H20 H2S H2S + Se HF

Ba(thd)2 Ga(acac)2d

H2S O3/H20 H2S H2S 03, 02 H2S H2S 03 Co(thd)2 + 03 Ni(thd)2 + 03 Mn(thd)3 + 03 03 H2S H2S H2S H2S H2S 03 H2S 03 03 03 H2 H2S

Co304 NiO NiO Cu Dopants in CaS, SrS and ZnS

[316] [317] [87, 169, 318-321] [215] [322] [322] [169, 296, 318, 323-325] [109] [2151 [318, 326] [35, 327] [288] [3151 [328, 329] [330] [331] [332, 333] [332] [333] [334] [335] [169, 296, 326, 336-338] [339] [339] [340] [340] [334] [295, 296] [332] [341,342] [333] [186, 210, 343, 344] [296, 319, 336, 345-352]

H20 Ti(OCH(CH3 )2)4 + H20 H2S H2S Ti(OCH(CH3)2)4 + H20 H2S Ti(OCH(CH3)2)4 + H20 H2S H2S 03 H2S

MgO SrTiO3 SrS SrS BaTiO3 BaS BaTiO3 Dopant in ZnS Dopant in ZnS ZrO2 Dopant in SrS

[241,353-355] [356-358] [359] [359] [356, 357] [359] [357] [295] [295] [322] [360]

Ca(thd)2

In(acac)3 Pb(thd)2 Y(thd)3 La(thd)3

Ce(thd)4 Ce(thd)3 (phen)e Ce(tpm)3 f Ce(tpm)4 Ce(tfa)4g Mn(thd)3 Co(thd)2 Ni(acac)2 Ni(thd)2 Cu(thd)2 Ln(thd)3 h

CaF2 SrO (SrCO3) SrTiO3 SrS SrSl_xSex SrF2 BaS Ga203 In2S3 PbS Y203 Y202 S La2S3, La202S La203 LaCoO3 LaNiO3 LaMnO3 CeO2 Dopant in CaS, SrS and BaS Dopant in SrS Dopant in SrS Dopant in SrS Dopant in SrS MnOx Dopant in ZnS

Cyclopentadienyl compounds Mg(C5H5)2 Sr(C5 i pr 3H2)2i Sr(C5Me5)2j Ba(C5Me5)2 Ba(C5tBu3H2)2k Mn(C5H5)2 Mn(C5MeH4)(CO)3 Zr(C5H5)2C12 Ce(CsMe4H)3

118

RITALA AND LESKELA Table IV.

Metal precursor

(Continued) Reference

Nonmetal and other precursors

Film material

H2S H20

ZnS ZnO

[212, 361,362] [361,363]

NH 3 + temperature modulation AsH 3 ((CH3)2N)3As NH 3 AsH 3 Temperature modulation

A1N AlAs AlAs A1N AlAs Si Si Si Si SiC

[365] [366] [262] [367-369] [81,370-372] [54,55] [373, 374] [60, 64-66, 1701 [375] [376, 377] [72, 73] [591 [51, 57, 378] [67]

Carboxylates Zn(CH3COO)2 /

Hydrides ((CH3)3N)A1H3

((CH3)2(C2H5)N)AIH3

Stl-h SiC12H2

Si2H6

H2 Atomic Hb UV light C2H2 NH 3-plasma NH 3, thermally cracked Temperature modulation Thermal precracking and temperature modulation

Si SiC SiC Si Si Ge Ge Ge

[60] [379, 380]

NH3 NH 3 + Sill4 NH3 H2S

TiN

Dopant in SrS

[384, 385] [384, 385] [386] [387]

H20 N(C2H5)3 H202 H2S 03 03

SiO2 SiO2 SiO2 PbS NiO NiO

[3881 [389] [390, 391] [315,392] [341] [341]

AI(OC2H5)3 AI(OCH(CH3)2)3 Ti(OC2H5)4 Ti(OCH(CH3 )2 )4 AI(OCH(CH3 )2)3 Ti(OCH(CH3 )2 )4 CrO2C12 Al(OC2Hs)3 Ti(OCH(CH3 )2)4

A1203 A1203

[393] [393] [3931 [3931 [393] [3931 [394] [3931 [393]

Si2C16 C2H2

C2H4 Si3H8 Si(C2H5)2H2 GeH4 Ge(CH3)zH2 Ge(CzH5)2H2

Si3N4 Si3N4 Si Si

Temperature modulation Temperature modulation Temperature modulation Atomic Hb Temperature modulation

[lOO] [65, 381 ] [3821 [55, 56] [68, 69] [383]

Alkyl- and silylamides Ti(N(CH3 )2 )4 Ti(N(C2H5)(CH3))4 Ce(N (Si(CH 3)3 )2)3

TixSiyNz TiN

Others Si(NCO)4 CH30Si(NCO)3 Pb((C2H5)2NCS2)2 Ni(apo)2 m Ni(dmg)2 n

Two metal compounds A1C13

AI(CH3)3

ZrCh

AlxTiyOz AlxTiyOz A1203

AlxTiyOz AlxCryOz AlxZryOz TixZryOz

ATOMIC LAYER DEPOSITION Table IV. Metal precursor

TaCI5

(Continued) Film material

Nonmetal and other precursors

HfC14

119

Reference

Si(OC2H 5)4

ZrxSiyOz

[393]

Si(OC4H 9)4

ZrxSiyO z

[393]

AI(OC2H 5)3

AlxHfyOz

[393]

Ti(OCH(CH3 )2 )4

TixHfyOz

[393]

Ta(OC2Hs)5

Ta205

[393, 395]

aClassification goes according to the type of the metal precursor. Processes with two metal precursors with no separate nonmetal source are listed separately in the end of the table. bObtained by thermal dissociation of H2. Cthd is 2,2,6,6,-tetramethyl-3,5-heptanedione. Alkaline earth and yttrium thd-complexes used may also contain a neutral adduct molecule or they may have been slightly oligomerized. d acac is acetyl acetonate. ephen is 1,10-phenanthroline. f tpm is 1,1,1-trifluoro-5,5-dimethyl-2,4-hexanedione. g tfa is 1,1,1-trifluoro-2,4-pentanedione. hLn is Ce, Pr, Nd, Sm, Eu, Gd, Tb, Tm. i i Pr is - C H ( C H 3)2. JMe is - C H 3. k t Bu is - C ( C H 3)3. /Converts to Zn40(CH3COO) 6 when annealed [364]. m apo is 2-amino-pent-2-en-4-onato. n dmg is dimethylglyoximato.

600

ZnCI2

500

lnCl3

o

400 ZrC!4 300-

TaCIs

[.-, 0

200

rIO0

o

'5'0

I

"

100

I

150

'

I

200

"

I

250

"

I

300

'

I

350

'

I

400

Source temperature in ALD / *C Fig. 11. Correlation between temperatures corresponding to 10 and 50% mass losses in TG measurements and source temperatures used in research scale ALD reactors [102]. The TG measurements were carded out in 1-atm nitrogen atmosphere with a heating rate of 10~ min -1 .

TG measurements also reveal if the volatilization takes place in one step, or if there are decomposition reactions involved [ 101 ].

5.1.2. Stability Against Self-Decomposition The self-limiting film growth via the surface exchange reactions is obviously achievable only under conditions where the precursors do not decompose on their own. A simple way to test if a precursor is thermally decomposing is to pulse only that compound in the reactor and to see if any film grows. As the decom-

position reactions may often be catalyzed by the film material, it is advised to carry out the decomposition experiments not only on bare substrates but also on previously deposited films and to see if their thicknesses increase. Because the decomposition is a thermally activated reaction, its rate increases exponentially with temperature. On the other hand, the longer the exposure time, the more pronounced the decomposition in comparison to the desired exchange reaction (Section 7.1.1). This explains why in processing of porous materials and in many surface chemistry studies, both with long exposure times of minutes, decomposition is observed at significantly lower temperatures than in film growth experiments with fast pulsing. Clearly, it is a material-, process-, and application-dependent choice where to set the uppermost limit for the acceptable decomposition rate. In fortuitous cases, the product of the decomposition reaction is the same as that of the exchange reactions, like, for example, in the growth of oxides from metal alkoxides and water where also the thermal decomposition of the alkoxide deposits the same oxide. In such a case, quite a substantial contribution of the decomposition may be accepted, provided of course that the decomposition proceeds in a surface reaction rate limited manner, thereby maintaining the good uniformity and conformality (Section 7.1.2). On the other hand, if the decomposition reaction causes incorporation of contaminants into the film, it must be minimized to a level where the resulting contamination can be tolerated.

120

RITALA AND LESKELA

5.1.3. Aggressive and Complete Reactions The alternate pulsing means that there are no risks of gas phase reactions in ALD. Therefore, precursors which react aggressively with each other can be used. In fact, such combinations should be preferred to ensure rapid completion of the reactions and thereby short cycle times as well as effective precursor utilization. This is in marked contrast with CVD where too reactive precursor combinations must be avoided. Thermodynamically, this means that the reactions used in ALD should have as negative a Gibbs free energy change AG as possible [39], while in CVD AG should still be negative but close to zero. The reactions also need to be completed so that no impurities are left in the films. The aggressiveness of the reaction does not necessarily guarantee the completion. Especially at low temperatures, kinetic reasons may prevent the completion and thus some unreacted ligands from the metal precursors may be incorporated into the films. Likewise, nonmetal precursors such as H20 or NH3, for example, may leave - O H or - N H x residues if the reactions are incomplete. The amount of these residues in the films decreases as the temperature is increased but if that is increased too much, the precursor decomposition may start to produce new kinds of contaminants.

5.1.4. No Etching Reactions A negative consequence of the alternate supply of the precursors is that there are no competing reaction pathways for possible etching reactions where the film itself, substrate, or an underlying film is etched by one of the precursors. Such etching reactions have, for example, prevented the growth of Nb205 from NbC15 and H20 and have been interpreted to involve a formation of volatile oxochlorides [103]:

are in the next step partially replaced by elemental selenium, thereby avoiding the need to use the highly toxic H2Se [108, 109] (cf. Section 5.3.2). 5.1.5. No Dissolution to the Film or the Substrate

The precursors should chemisorb on the surface upon which they are dosed but they are not allowed to dissolve into that material. Examples of precursor dissolution are rare but one is the attempt to deposit metallic copper from CuC1 and elemental zinc, the latter being used as a reducing agent [110]. Metallic copper with only about 3 at.% zinc was indeed obtained but the film growth was evidently not self-limiting and growth rates were high, above 5 ,~ cycle -1 . The results were explained with the following mechanism in which the copper film is formed as desired by the reductive exchange reaction: CuCl(ads) + 0.5Zn(g) --~ Cu(s) + 0.5ZnC12(g) However, once copper has been formed on the surface, the dissolution of zinc into copper starts to complicate the process. When dosed onto a copper surface with a CuC1 chemisorption layer, Zn first reduces CuC1 as before but then, rather than just adsorbing on the surface, zinc also dissolves into the copper, Cu(s) + Zn(g) -+ Cu(Zn)(s) The resulting Cu(Zn) alloy is not stable and during the following purge period Zn outdiffuses and evaporates Cu(Zn)(s) --~ Cu(s) + Zn(g) The outdiffusion is slow, however, and also continues during the next CuC1 pulse. This leads to a CVD-type of growth and thereby to a loss of the self-limiting growth mechanism: CuCl(g) + 0.5Zn(g) -+ Cu(s) + 0.5ZnC12(g)

Nb2Os(s) + 3NbC15(g) ~ 5NbOC13(g) Similar etching is also observed in the analogous TaC15-H20 process but only above a certain threshold temperature of about 300~ and even then the etching is slow enough not to totally prevent the film growth but just to cause a decrease of the deposition rate with longer TaC15 pulse times [ 104-106]. A simple test to verify an existence of etching reactions is to expose a film to one precursor only and to observe a disappearance of the film or part of it. A somewhat less detrimental type of gas-solid reaction is the one which involves an exchange of the film constituents, like a replacement of a metal cation in an oxide with another metal having a higher affinity toward oxygen [ 107]:

The precursor may dissolve not only into the film material but also into the substrate. Processes where this can possibly take place are the growths of transition metal nitride films onto silicon substrates from the metal halides and ammonia with elemental zinc as an additional reducing agent (Section 5.3.6) [103, 111-114]. If dissolved into silicon, zinc forms detrimental electrically active defects. In fact, this has been regarded as such a major concern that the zinc-based processes have not been taken into a more detailed study even if they produce the highest quality nitrides (Section 6.5) and the occurrence of zinc dissolution into silicon still remains to be verified. 5.1.6. Unreactive Byproducts

4A1C13(g) + 3TiO2(s) --+ 2A1203(s) + 3TiCl4(g) Such reactions are often self-terminated once the surface becomes covered by the exchange reaction product (A1203 in the preceding example), and therefore they may be tolerated unless very sharp interfaces are required. On the other hand, the same kind of replacement reactions may also be utilized in making, for example, metal sulfoselenides where sulfur atoms deposited through reactions between metal precursors and H2S

Preferably, the precursors should produce unreactive byproducts which would be easily purged out of the reactor. Reactive byproducts may cause corrosion problems in the reactor or in the exhaust. In addition, they may readsorb on the film surface and block adsorption sites from the precursor molecules, thereby decreasing the growth rate (Section 4.2.4). In the worst case, the byproducts may etch the film. Nonetheless, in many successfully implemented ALD processes (e.g., ZnC12-H2S,

ATOMIC LAYER DEPOSITION

121

A1C13-H20, TiC14-H20) hydrogen chloride is formed as a byproduct and routinely handled in properly designed reactors. Thus, the unreactivity of the byproducts may be considered only as a secondary, though still an important requirement while planning an ALD process.

and catalogues and data sheets of commercial suppliers. Any comments on moisture or air sensitivity give hope for fast reactions, especially in the growth of oxides but also in more general terms, though at the same time they imply that special care must be devoted to the precursor handling.

5.1.7. Other Requirements

5.2.2. Thermodynamic Consideration

Precursor purity requirements are specific to each process and application, and also depend on the nature of the impurities. Naturally, semiconductors are more sensitive to impurities than, for example, protective coatings. If nonvolatile and unreactive with the precursor, the impurities are of less concern because they remain in the source. The other requirements, such as low cost, easy synthesis and handling, nontoxicity and environmental friendliness, are all common to the CVD precursor requirements. However, all these and the above requirements may not always be fulfilled simultaneously, and often only these last ones can be sacrificed while developing a new ALD process. If toxic or otherwise dangerous compounds cannot be avoided, special care must of course be given to their handling before and after the process, and appropriate safety systems must be installed. While considering the cost issue, it must be kept in mind that a price of any chemical is largely determined by its demand. Therefore, no compound should be rejected from research just because of its current price. Rather, one should have a look at its synthesis procedure and try to estimate how much the price might be lowered if the precursor would be taken into a large scale use. Furthermore, in many cases the contribution of the precursor chemicals to the final price of a thin film device is rather small.

Thermodynamics refers to equilibrium conditions while ALD is certainly a nonequilibrium process: the precursors are dosed into the reactor alternately and the byproducts are constantly pumped out. In addition, thermodynamics tells nothing about reaction rates. In any case, thermodynamic calculations provide valuable information about the compounds under consideration for ALD, provided of course that relevant thermodynamic data are available. Today, these calculations are easily made with relatively inexpensive commercial PC programs with integrated databases, but while evaluating the results the previously mentioned limitations of thermodynamics must carefully be kept in mind. The simplest calculation is the vapor pressure of the compound. Additionally, the stable form, e.g., monomer vs dimer, in the gas phase at each temperature of an interest is easily checked. To estimate a reactivity of a pair of precursors, A G for a suggested net reaction is calculated and is compared with other alternatives, all balanced to deposit an equal amount of the film. If otherwise possible and reasonable, the reaction with the most negative AG should be chosen. However, in some cases, like in the growth of In203 from InC13 and H20 [115], reactions with even slightly positive A G have been used and have been explained to be possible because of the continuous feed of one precursor and the pump out of the byproducts. On the other hand, it also must be emphasized that in ALD the two precursors can meet each other only if there is a certain mechanism by means of which at least one of them can adsorb on the surface. Thermodynamic estimations of such mechanisms are of course impossible because of a lack of thermodynamic data for the intermediate surface species. The occurrence of possible side reactions, like etching (Section 5.1.4), may also be estimated by thermodynamic calculations. One may either calculate AG for the suggested side reaction or perform equilibrium composition calculations for a system where the film or the substrate material is exposed to one precursor vapor.

5.2. Choice of Precursors After examining the desired properties of the ALD precursors, we now present some basic ideas about how to proceed in selecting precursors for a new process. The necessary background information can be looked for from basically two sources: literature and thermodynamic calculations.

5.2.1. Literature Survey For planning a new ALD process and choosing precursors for it, looking at the literature makes a good start. While searching the literature, all the alternative names of the method (Table I) should be taken into account. If no ALD process for the particular film material has been reported, processes of any material containing the constituent elements should be looked for to see which kind of precursors have been used. To assist the literature survey, ALD processes reported so far have been summarized in Table IV in Section 5.3. In addition to ALD literature, CVD publications also contain valuable information, such as volatility data and reaction and decomposition temperatures. For example, notations of precursor combinations too reactive for CVD are often especially promising. Other potential sources of volatility data are publications on synthesis or thermal analysis of the compounds

5.3. Overview of Precursors and Their Combinations Used in ALD Table IV summarizes the precursors and their combinations used in ALD as comprehensively as the authors know (compiled in June 2000). For the materials of the greatest interest in nonepitaxial applications (oxides, nitrides, sulfides, fluorides, metals) rather extensive referencing has been attempted, whereas for the widely examined epitaxial semiconductors, especially for the III-V compounds, only a few examples have been given for each precursor combination and review articles

122

RITALA AND LESKELA,

[7, 16-25, 38] are recommended for broader coverage including also the semiconductor dopant precursors which are not dealt with here. Basically, all the processes which have resulted in film growth are included in Table IV, even if some of them are slow requiring unpractically long exposure times. The evolution of ALD precursor chemistry has been reviewed [396] so only a rather concise summary is presented. Other recommended review articles can be found in Refs. [7, 8, 18, 19, 39], for example. 5.3.1. Metal Precursors

Elemental zinc and sulfur were used in the first ALD experiments for growing ZnS [ 1, 2]. Subsequently, zinc and cadmium have been used in reactions with sulfur, selenium, and tellurium (Table IV), but except for these and mercury the use of metal elements is limited because of their low vapor pressures. Soon after the first demonstrations of ALD, metal chlorides were taken under study. Among the first processes examined were also two of the most successful ALD processes, namely, ZnC12-H2S for ZnS and A1C13-H20 for A1203 [2-4]. Though both these processes are based on solid chlorides and are therefore somewhat laborious in production, they have been used in industry from the very beginning of the ALD manufacturing of the TFEL displays. For doping of the ZnS :Mn phosphor, MnC12 is used, even if it has quite a low vapor pressure. Among the first chloride precursors examined were also the liquids TIC14 and SnC14, the former of which has also been adopted to the TFEL production for making AlxTiyOz insulators (Section 6.2.1). Subsequently, basically all possible volatile chlorides have been examined (Table IV). By contrast, of the other halides only TiI4, ZrI4, TaI5, WF6, and MnI2 have been examined so far. Especially the iodides should be examined in more detail because the low metal-iodine bond energies suggest that iodide residues could be removed from the films more completely than chlorides. As the interest toward ALE (here the name ALE is used to emphasize the epitaxial deposits) of the III-V materials arose, a natural starting point was to choose metal alkyls, like Ga(CH3)3, as precursors because at that time they were already well known and were broadly used in metal organic vapor phase epitaxy (MOVPE). However, this choice is not completely in line with the previously discussed requirements to ALD precursors because the reactions with the group V hydrides usually require such high temperatures that pyrolysis of the organometallic compounds occurs and complicates the control of the self-limiting growth conditions [ 18, 19, 22, 48,255,397]. Indeed, a mechanism which would explain the different resuits obtained under different GaAs growth conditions has been speculated about for a long time. The current opinion is that the two key requirements for the self-limiting growth are an avoidance of complete gas phase decomposition of Ga(CH3)3 in the boundary layer above the substrate and a high enough methyl radical flux to compensate for the methyl radicals which desorb from the surface [22]. On the other hand, with the aid of laser assistance the growth temperature may be lowered so

that the thermal decomposition is significantly decreased, and at the same time the width of the temperature range for the selflimiting film growth is increased [ 15, 17, 48, 49]. Another consequence of the metal alkyl pyrolysis is carbon residual incorporation causing relatively high p-type carrier concentrations [ 18, 19]. However, with careful control of the growth conditions, in particular by reducing the flow rate and the exposure time of the metal alkyl and by increasing the corresponding parameters for the group V hydride, low carrier concentrations and even n-type conductivity could have been achieved [19, 93,253,254]. In any event, because of these reasons, chloridebased processes emerged as another main route to ALE of IIIV compounds [18]. Here the precursors have been either binary chlorides, often formed in situ, or alkyl chlorides which pyrolyze in the reactor into the binary chlorides. With the chloride-based processes, the heavy carbon contamination is avoided and the n-type materials are easily obtained. The early work on the III-V compounds in the late 1980s was focused on compounds of Ga, A1, In, As, and E Somewhat later, in the early 1990s, ALE of gallium and aluminum nitrides from the trialkyls was examined [242, 243,259, 260], and later InN was also grown [246-248]. In addition to the III-V compounds, metal alkyl precursors have successfully been used also in the ALD of epitaxial or nonepitaxial II-VI compounds and polycrystalline or amorphous oxides. Here ZnS, CdS, A1203, and ZnO have been the most thoroughly examined materials (Table IV). Reactions with H2S and H20 are facile and thus proceed at low temperatures, occasionally even at room temperature [274, 298-302], where the pyrolysis of the metal alkyls is much weaker than at the temperatures typically used in the III-V processes. Metal alkoxides offer chlorine-free alternatives to the growth of oxide thin films. The first ALD experiments were made on aluminum alkoxides using water or alcohols as oxygen sources [ 129], and subsequently titanium, tantalum, and niobium alkoxides (mainly ethoxides) have successfully been used in reactions with water (Table IV). For tantalum and especially for niobium, alkoxides are important precursors because of the etching problems in the chloride processes (Section 5.1.4). Alkoxides decompose thermally at elevated temperatures and therefore the ALD processes are limited to temperatures below 400~ On the other hand, the decomposition product often is a rather pure oxide and therefore the decomposition may be accepted to a certain extent. All the previously mentioned alkoxide processes produce good quality films, but zirconium tetra-tert-butoxide [310] resulted in ZrO2 films which were clearly of a lower quality than those obtained from ZrC14. This is unfortunate because the liquid alkoxide was hoped to solve a problem encountered in the ZrC14-H20 process where very fine particles from the solid ZrC14 source are often transported by the cartier gas and are incorporated into the films. After the success of the ZnS :Mn TFEL phosphor, the strive toward full color displays turned the ALD research on other TFEL phosphors, most of which have alkaline earth metal sulfides as the host materials and rare-earth metals as the dopants (Section 6.1). These electropositive metals have few volatile

ATOMIC LAYER DEPOSITION compounds,/~-diketonates being the well known and the most thoroughly examined exception. Though the/3-diketonates, especially those of the alkaline earth metals, suffer somewhat from instability, they have served as reasonably good precursors for the TFEL phosphors (Table IV). For example, the Sr(thd)2Ce(thd)4-H2S process has been used in a pilot scale growth of SrS:Ce [338]. On the other hand, while reactive with H2S, most of the/3-diketonates do not react with water at temperatures where they would not decompose already on their own. Here, Ga(acac)3 has been an exception and reacted with water but the Ga203 films obtained were heavily carbon contaminated [327]. Mg(thd)2, in turn, has been used together with H202 to grow MgO films but the deposition rate was low, only 0.1-0.2 ~ cycle -1 [316]. Thus, oxides are best grown from the /3-diketonates with ozone as the oxygen source (Table IV). In reactions with ozone, the large/3-diketonato ligands are probably burned into smaller molecules and thus these reactions essentially differ from most of the other ALD processes where the ligands are removed more or less intact, either after protonation by the hydrogen containing nonmetal precursor or as a consequence of radical desorption. Cyclopentadienyl compounds (metallocenes) have been examined as alternatives to alkaline earth and rare-earth metal /~-diketonates with a number of promising results (Table IV). The use of cyclopentadienyls in ALD was first demonstrated in the growth of MgO from Mg(CsHs)2 and H20 [241,353, 354], and subsequently Mn(CsHs)2 and Mn(CsMeH4)(CO)3 were examined as dopant sources for ZnS :Mn [295] and Ce(CsMe4H)3 for SrS :Ce [360]. In any event, so far the greatest progress with the cyclopentadienyls has been made in the growth of SrTiO3 and BaTiO3 [356-358] (Section 6.2.2), because these can be deposited from the/~-diketonates only with ozone and then the resulting film is amorphous which requires high temperature annealing to get crystallized [322]. Using Sr(Csipr3H2)2 together with Ti(Oipr)4 and H20, crystalline SrTiO3 was obtained already at 250~ [356-358]. Despite some decomposition of Sr(Csipr3H2)2, a good control of film stoichiometry was achieved by varying the pulsing ratio of the two metal compounds. BaTiO3 films were obtained with an analogous process with Ba(CsMes)2 [356, 357] or Ba(Cs/Bu3H2)2 [357] as the barium precursor. These Sr and Ba compounds also react with hydrogen sulfide forming the corresponding sulfides at remarkably low temperatures: wellcrystallized SrS was obtained already at 120~ [359]. Overall, cyclopentadienyl compounds form a large family of potential precursors since these are known for many metals and the ligands can be varied by substitutions in the carbon 5-ring, largening the ring system (indene, fluorene) and by linking two tings together by a bridge. Cyclopentadienyls have often been considered too air sensitive but the foregoing experiences demonstrate that with a reasonably careful handling they can be used without difficulty. The first experiments on these compounds have been promising but the full potential still remains to be explored and may provide interesting findings in the near future.

123

5.3.2. Nonmetal Precursors

For the nonmetals, the simple hydrides have mostly been used: H20, H202, H2S, H2Se, H2Te, NH3, N2H4, PH3, ASH3, SbH3, and HE These are all sufficiently reactive but some of them are very poisonous and therefore their alkyl derivatives have been examined as substitutes. Hydrogen peroxide is oxidizing by its nature while most of the others, hydrazine in particular, are reducing. The oxidizing power of H202 is seldom made use of, however. By contrast, the reducing action is highly needed in the growth of transition metal nitrides where the metals have higher oxidation states in their precursors than in the nitrides. Ammonia is powerful enough to reduce most of the transition metal chlorides to the desired metallic nitrides, though films with better conductivity are usually obtained when elemental zinc is used as an additional reducing agent (Section 5.3.6). However, TaC15 is not reduced by ammonia and insulating Ta3N5 is obtained [113]. A hydrazine derivative (CH3)2NNH2 does not reduce tantalum either [ 114], and TaN is obtained only with zinc as a reducing agent [ 113]. Molecular oxygen, 02, is usually too inert to react with the typical metal compounds under reasonable growth temperatures. Instead, ozone 03 has been used to grow oxides from many/~-diketonate compounds (Table IV) which do not react with the most common oxygen sources water and hydrogen peroxide. Other less used oxygen sources include N20 and alcohols. A new approach applicable to many oxides is to use metal alkoxides as both metal and oxygen sources (Section 5.3.5). Similarly to oxygen, also molecular nitrogen, N2, and hydrogen, H2, are quite inert toward the common metal sources at low temperatures. They are indeed often used as carrier gases, but while nitrogen is in most cases truly inert, hydrogen sometimes participates the surface reactions and removes surface terminating ligands (Section 7.2.1) [18]. Hydrogen has also been used as a reducing agent in ALD but this requires either catalytically active surfaces or high temperatures (Section 5.3.6). On the other hand, when dissociated by thermal cracking or plasma discharge, reactive atomic species are produced from hydrogen and nitrogen [60-62, 64-66, 68-71, 74]. Also oxygen may be dissociated in a plasma discharge but until now atomic-oxygenbased ALD processes have only briefly been demonstrated [75]. For the chalcogens (S, Se, Te), elements can be used as precursors, though usually only when the metal source also is an element (Table IV). It has also been demonstrated that elemental Se replaces sulfur atoms on the surface of the growing ZnS and SrS films. With this replacement reaction, the corresponding sulfoselenides with as much as 90 anion-% Se were deposited from ZnC12 or Sr(thd)2, H2S, and Se [108, 109], thereby avoiding the use of the highly toxic H2Se. Finally, elemental As4 and P4 have been employed in the growth of GaAs and GaP from GaC1 with hydrogen as a carrier gas [ 146, 147]. 5.3.3. In situ Synthesized Precursors

A majority of the precursors used in ALD are synthesized beforehand but in some cases precursors generated in situ have

124

RITALA AND LESKEL)k

been used as well. In situ synthesis makes it possible to use compounds which are otherwise difficult to handle because of their high reactivity or which easily age when stored for long times. The most common way for the in situ synthesis is to employ gas-solid reactions. As in CVD, also in ALD this has most often been used with chlorides, especially with gallium and indium chlorides, but also strontium and barium/3-diketonates and tungsten oxyfluorides have been synthesized in situ. Gallium and indium chlorides were synthesized from metallic gallium and indium and hydrogen chloride at around 750~ [ 18]. For in situ synthesis of [Sr(thd)2]n, reactions between solid Sr, SrO, Sr(OH)2, or SrCO3 and Hthd vapor were examined and the best results were obtained with Sr and SrO [325]. [Ba(thd)2]n was synthesized from Ba(OH)2 and Hthd [326], and WOxFy from WO3 and ~r 6 [205]. A risk related to the in situ precursor synthesis by the gas-solid reactions is the possibility that part of the gaseous reactant passes the source to the reaction chamber and etches the film. Therefore, the souce must be properly designed to ensure complete reactions. The in situ generation of HF differs from the preceding solid-gas reactions in that HF was obtained by decomposing NH4F thermally [215]. The ammonia liberated in the decomposition apparently had no effect in that study since the fluoride films deposited (ZnF2, CaF2, SrF2) are inert toward ammonia. In addition, gas-gas reactions have been employed for in situ generation of desired precursor compounds too. Chlorides of gallium and indium were formed by mixing Ga(C2Hs)3 and In(CH3)3 vapors with HC1 in a reaction zone heated around 100~ thereby avoiding problems related to the low vapor pressures of the binary chlorides and alkyl chlorides [18].

5.3.4. Single Source Precursors

In general, ALD processes employ two or more precursors which each contain one of the film constituent elements (see Section 5.3.5, however). Single source precursors which contain all the film constituents are actively examined in CVD, but in ALD they are not directly applicable because the selflimiting growth mechanism by its nature requires exchange reactions between different precursors and stability against selfdecomposition. On the other hand, single source ALD processes can be realized by ramping the temperature repeatedly so that the adsorption takes place at a low temperature and the decomposition takes place at a higher temperature. Simple thermal heating and cooling of the substrate is inevitably too slow to be practical except for very thin films, but heating with laser or lamp or photodissociation with high energy photons makes the process faster. However, so far such processes have not been examined for compound films for which the single source CVD precursors are usually aimed, but only for deposition of elemental silicon [51, 54, 55, 57, 65, 67,378, 381 ] and germanium [55, 56, 383]. For example, to deposit germanium, Ge(C2Hs)2H2 was adsorbed at 220~ with a release of hydrogen and a formation of a monolayer of Ge(C2Hs)2, and then the ethyl groups

were desorbed by heating above 400~ [383]. Similarly, silicon was deposited in a self-limiting manner at 180-400~ by first adsorbing Si2H6 and then by heating the substrate with a UV laser to desorb the surface terminating hydrogen atoms [51, 378]. The combination of using only one precursor and short heating (or dissociating) light pulses also offers an interesting possibility to have the precursor continuously present in the reactor and omit the purging. Within the duration of short light pulses, adsorption of new molecules in place of the decomposed chemisorption monolayer is negligible, and thus self-limiting film growth is achieved. This approach has been used for ALD of silicon and germanium from Sill4 and GeH4 by heating with a Xe flash lamp [54-56]. In fact, with these particular precursors the continuous presence is vital because the surface density of the chemisorbed species is determined by the balance between adsorption and desorption; i.e., the chemisorbed species have a high desorption probability and might thus be lost during a purge period. 5.3.5. Combinations o f Two Metal Compounds

Quite recently a novel approach to the ALD of oxides was introduced [393]. In this process, two metal compounds, at least one of which is an alkoxide and thus contains a metal-oxygen bond, were used (Table IV). The metal alkoxide serves as both the metal and the oxygen source while the other metal compound, typically a metal chloride, acts as the other metal source: bM(OR)a + aMtXb --+ MbMtaOab + a b R X Depending on whether M and M t are similar or different, binary or mixed oxides are obtained. The major benefit of not using separate oxygen sources like water or hydrogen peroxide is the less susceptible oxidation of the substrate surface. This is especially important when thin high permittivity dielectric layers are to be deposited directly on silicon without creating an interfacial silicon oxide layer (Section 6.2.2).

5.3.6. Reducing Agents and Other Additional Reagents Under this heading, reagents which take part in the film formation reactions but do not leave any constituents to the film are considered. The most obvious of these are the reducing agents in the growth of elemental films. For this purpose, both molecular and atomic hydrogen as well as elemental zinc and disilane have been examined. Atomic hydrogen which may be produced by either plasma discharge or thermal cracking is very reactive and facilitates even the deposition of metallic titanium and tantalum from their chlorides [74]. Also SiC12H2 [60, 6466, 170], Si2C16 [61], GeC14 [62], and Ge(CH3)2H2 [68, 69] have been reduced with atomic hydrogen. Molecular hydrogen, by contrast, is quite inert and reduces CuC1 [209, 210] and Cu(thd)2 [210, 343, 344] only on appropriate metal surfaces (Section 6.6). For instance, the Cu(thd)2-H2 process resuited in a film growth only when the surface was seeded with a predeposited platinum-palladium layer [210, 343, 344], and

ATOMIC LAYER DEPOSITION even then the copper deposition could not be repeated in a different reactor where high partial pressures of hydrogen could not be used and where the residence time of the precursors was much shorter [186]. The ALD studies on Ni(acac)2, Cu(acac)2, and Pt(acac)2 reduction by H2 also indicated the low reactivity of molecular hydrogen; metallic deposits seemed to be obtained only through interactions with substrates or as a consequence of thermal decomposition of the metal precursors [342]. Finally, high temperatures of 815-825~ were required to obtain monomolecular layer growth when SiC12H2 was reduced by H2 [373,374]. Elemental zinc is a powerful reducing agent and has been employed in the ALD of copper [110] and molybdenum [204] but it suffers from its tendency to dissolve into the metallic films. Though the films contain only a few atomic percentages of zinc, the dissolution and subsequent outdiffusion during the process destroy the self-limiting growth mechanism (Section 5.1.5). In the growth of transition metal nitrides, the dissolution of zinc into the films is not a problem [ 112] and intermediate zinc pulses have been employed in improving the properties of the films deposited from metal chlorides and ammonia (Section 6.5). In addition to acting as a reducing agent, zinc may also assist in removing chlorides from the surface by forming ZnC12. In the TaC15-NH3 process, the use of zinc is vital because otherwise semiconducting Ta3N5 is obtained instead of the desired TaN [ 113], but in the other cases the positive effect of zinc is not necessarily just simply due to a reducing action but also other chemical and structural factors appear to be involved [112]. However, as zinc forms electrically active states in silicon, the concern that zinc could dissolve into a silicon substrate has limited further interest toward these zinc-based ALD nitride processes. The most recently examined reducing agent is disilane Si2H6 which was successfully used in the ALD of metallic tungsten from ~VF 6 [206] (Sections 6.6 and 7.2.2). No silicon or fluorine could be detected in the films by X-ray photoelectron spectroscopy. Moving to other additional reagents, pyridine [ 165, 166] and ammonia [ 167] have been used in catalyzing reactions between the alternately pulsed SIC14 and H20. In this way, the deposition temperature of SiO2 was decreased remarkably from above 300~ to room temperature and at the same time the reactant exposure required to complete the surface reactions was decreased from 109 to 104-105 L (1 L = 10 -6 Toffs). Unfortunately, also these catalyzed reactions required tens of seconds to get completed and thus the main problem of SiO2-ALD, i.e., the long cycle times causing low deposition rates per time unit, still remains. The mechanism proposed for explaining the catalytic effect of pyridine and ammonia involves hydrogen bonding of the nitrogen atom in the catalyst molecule to surface hydroxyl groups (during the SIC14 pulse) or water molecules (during the H20 pulse) with a concomitant weakening of the O--H bond and an increase of the nucleophilicity of the oxygen atom. The catalytic effect decreased as the temperature was increased above room temperature which may be related to decreased surface coverages of SIC14 and, perhaps more importantly, of catalyst molecules. As good film properties were achieved with

125

these catalyzed processes, they are clearly an interesting approach to very low temperature ALD and they deserve further studies to clarify their applicability to other materials. Additional reagents may also be used for assisting the completion of the reactions. Occasionally, the complete ligand removal from the metal precursors is hard and may thus lead to impurity incorporation. This has been a severe problem in the epitaxial growth of the III-V semiconductors where low impurity levels are required; especially aluminum containing compounds are prone to carbon incorporation. In the growth of AlAs from AI(CH3)2H and ASH3, dimethylamine ((CH3)2NH) supplied intermediately after AI(CH3)2H was used to remove methyl groups from the surface [240]. A mechanism which involves reactions between the methyl groups and amine and hydrogen radicals was suggested to explain the observed decrease of the carbon content from 6 x 1020 to 8 x 1019 cm -3 as determined by secondary ion mass spectrometry (SIMS). Nitrogen contents were not reported, however. Anyhow, the idea of using separate reagents for assisting surface ligand removal is evidently worth further consideration.

6. FILM MATERIALS AND APPLICATIONS Table V summarizes the film materials deposited by ALD thus far. As in Table IV, all the reported materials have been included regardless of how effective the processes actually are. For references, see Table IV. In this section, the most important nonepiTable V.

Thin Film Materials Deposited by ALD a

II-VI compounds

ZnS, ZnSe, ZnTe, ZnS 1-x Sex, CaS, SrS, BaS, SrSl_xSex, CdS, CdTe, MnTe, HgTe, Hg 1-x Cdx Te,

II-VI-based TFEL phosphors

Cd 1-x Mnx Te ZnS:M (M = Mn, Tb, Tm), CaS:M (M = Eu, Ce, Tb, Pb), SrS :M (M = Ce, Cu, Tb, Pb)

III-V compounds

GaAs, AlAs, AlP, InP, GaP, InAs, AlxGal_xAs, Gaxlnl_xAs, Gaxlnl_xP

Nitrides semiconductors/dielectric

A1N, GaN, InN, SiNx, Ta3N5

metallic

TiN, Ti-Si-N, TaN, NbN, MoN, W2N

Oxides dielectric

A1203, TiO2, ZrO 2, HfO 2, Ta205, Nb205 , Y203, MgO, CeO 2, SiO 2, La203 , SrTiO3, BaTiO 3, BixTiyOz

Transparent conductors/ semiconductors

In203, In203 9Sn, SnO2, SnO2 "Sb, ZnO, ZnO" A1, ZnO" B, ZnO 9Ga, Ga203, WO 3, NiO, Co 304, MnOx

Ternary oxides Fluorides

LaCoO 3 , LaNiO 3, LaMnO3 CaF2, SrF2, ZnF 2

Elements

Si, Ge, Cu, Mo, Ta, W

Others

La2S 3, PbS, In2S 3, CuGaS2, SiC

aFor references, see Table IV.

126

RITALA AND LESKEL,~

taxial thin film materials, grouped according to their applications, are discussed. As the epitaxial semiconductors were limited outside the main scope of this presentation, they are not dealt with here but rather review articles [19-23] are suggested for the III-V compounds, and [24, 25] for the II-VI compounds. In contrast to the compound semiconductors, little has been published thus far on the material properties of the ALD made Si and Ge films, the focus in these studies has been on the film growth and the related chemistry. Also deposits other than thin films are skipped here; the use of ALD in processing of porous materials [30-33] and in nanotechnology [398] have been reviewed in the references cited.

6.1. Electroluminescent Display Phosphors As already noted, ALD was originally developed by Suntola and co-workers for making thin film electroluminescent (TFEL) displays [2, 5-9]. In this application, ALD has been very successful and has been used for nearly 20 years in manufacturing [7-11 ]. In addition, research on using ALD in making thin films for the TFEL displays has been active all the time and has formed a solid basis for the more recent ALD research, particularly that on insulators (Section 6.2). Therefore, it is instructive to first have a closer look at the TFEL display itself. A schematic of a conventional TFEL display is shown in Figure 12. A more recently developed, so-called inverted structure is otherwise similar but the places of the transparent and metal electrodes have been exchanged. In the conventional structure, glass is used as a substrate because viewing is through the substrate. Also in the inverted structure glass is often used but also opaque ceramics may be applied as substrates because the viewing is on the opposite side. The benefit of glass is its low price whereas ceramics make it possible to use high annealing temperatures for improving the phosphor crystallinity. If soda lime glass is used, it is passivated by an ALD made A1203 to prevent sodium outdiffusion (Section 6.4). The ac-

Fig. 12. Schematics of a TFEL display with a conventional structure. In the inverted structure the metal and transparent electrodes have changed places and the viewing is from the film stack side of the substrate.

tual TFEL device structure consists of an electrode-insulatorsemiconducting phosphor-insulator-electrode film stack where the electrodes are patterned into stripes perpendicular to each other while the other films are continuous. The electrode on the viewing side must of course be transparent and thus indiumtin oxide (ITO) is usually used. The other electrode is metal; in the conventional structure it is aluminum but in the inverted structure molybdenum or tungsten with better thermal properties must be used. A passivating layer is finally deposited on the top of the structure. At present, ALD is used in industrial scale for all the other films except the electrodes which are sputtered. ZnS :Mn, A1203 and A1203/TiO2(ATO) are the dominant ALD made materials used by the industry. The thickness of the phosphor layer is in the range of 500-1000 nm while the insulators are about 200-nm thick, and the three layers are deposited in one continuous ALD process. In the TFEL displays, each crossing point of the bottom and top electrodes defines a picture element (pixel). A pixel is lit by applying an ac (typically 60 Hz) voltage to the two electrodes. At low voltages, the insulator-phosphor-insulator structure acts like three capacitors in series, but when the electric field in the phosphor layer exceeds a certain threshold value, electrons begin to flow through the phosphor from one insulator-phosphor interface to the other. When arriving at the interface, the electrons are trapped in the interface states from which they are emitted when the polarity of the electric field reverses. For an effective operation of the typically used phosphor materials, the threshold field must be in the range of 1 to 2 MV cm -1, so that once released, the electrons are rapidly accelerated to energies high enough to impact excite the luminescent centers which then emit light while returning to the ground state. The phosphor layer must withstand these high fields without destructive breakdown. Likewise, the insulators must possess high breakdown strength and low leakage currents at the operation voltages. Pinhole-freeness over the large-area substrate is a key aspect in meeting these requirements. In the late 1970s, few techniques existed for making high quality insulator-phosphorinsulator structures, and that was the main motivation for developing ALD. Unlike the other flat panel displays, the TFEL displays have complete solid-state structures which gives them many advantages like wide operating temperature, ruggedness, exceptionally broad viewing angle, and fast response. On the other hand, operation voltages around 200 V are typically needed which means that the driving electronics and thus the whole display is rather expensive as compared to its main competitors, especially liquid crystal displays. Therefore, TFEL displays are not found in laptops but rather they are found in applications like medical, instrumentation, and transportation where their special characteristics are valued. Quite recently a new kind of TFEL display, active matrix EL (AMEL) display has been developed [399]. Here, the insulatorphosphor-insulator-transparent top electrode film stack is deposited directly on single crystal silicon-on-insulator (SO1) wafers to which all the required driving circuitry has been integrated. This makes it possible to make small high resolution

ATOMIC LAYER DEPOSITION displays for head mounted applications, for example. On the other hand, the deposition on top of the driving circuitry sets strict demands on the film conformality, thus favoring the use of ALD (Fig. 13).

Fig. 13. Cross-sectional image of an AMEL display. Only the films of the TFEL structure are shown, the driving circuitry below is not shown. The ZnS : Mn and AlxTiyOz films are made by ALD. (Courtesy B. Aitchison, Planar Systems Inc.)

Table VI.

127

Comprehensive review articles on TFEL phosphor materials can be found in Refs. [ 11,400, 401 ], so here they are discussed chiefly from the ALD point of view. A summary of the ALD made TFEL phosphors is presented in Table VI. The most important of the TFEL phosphors is the yellow-orange emitting ZnS : Mn which is made by ALD primarily from ZnC12, MnCI2, and H2S [3, 4, 8, 402], though alternatives have been used for both zinc (Zn(C2Hs)2) and manganese (Mn(thd)3, Mn(CsHs)2, Mn(CsMeH4)(CO)3) [295,296, 402]. The concentration of Mn is typically 0.5-2 mol%. In ALD, the doping is realized most simply by replacing a certain number of the zinc precursor pulses with manganese precursor pulses. Though this seems to lead to delta doping depth profiles, concentration quenching has not been found to be a major problem. Apparently, surface roughness and diffusion smooth the doping profile. On the other hand, due to the forbidden transitions in the Mn luminescence the Mn-Mn energy transfer is not very probable. The other option for doping is to supply the dopant simultaneously with the matrix cation but in that approach differences in reactivities may cause nonuniformity over the substrate. ZnS :Mn is the most efficient TFEL phosphor ever found (3-8 lmW-1). No major differences in the performance can be found between the ALD films [402, 403] and those made

Luminescent Thin Films Made by ALD for TFEL Devices

Phosphor

Emission

Luminance

material

color

cd m -2 at 60 Hza

CIE coordinates x

y

Reference

ZnS :Mn 2+ (chloride-process)

Yellow

440

0.52

0.48

[402]

ZnS :Mn 2+ (organometallic precursors)

Yellow

430

0.54

0.46

[402, 403]

0.28

0.64

[351]

0.68

0.31

ZnS :Tb 3+

Green

35

ZnS : Tb 3+ (O, C1)

Green

75

ZnS :Tm 3+

Blue

< 1 (300 Hz)

CaS : Eu 2+

Red

CaS : Tb 3+

Green

CaS :Pb 2+

Blue

2--6

[350] [345]

20 2.5 (300 Hz)

[404, 405] [319]

0.17

0.13

[406]

0.144).15

0.07-0.15

[407]

130

0.30

0.54

[408]

8

0.08

0.20

[408] [360]

80 SrS : Ce 3+

Bluish-green

SrS :Ce 3+ (filtered)

Blue

SrS :Ce 3+, y3+

Bluish-green

100

0.3

0.5

SrS :Ce 3+, y3+ (filtered)

Blue

20

0.21

0.39

SrS :Pr 3+

White

30 (300 Hz)

SrS :Tb 3+

Green

5.5

SrS : Mn 2+

Green

3.5 (300 Hz)

0.37-0.44

0.55-0.61

[409]

SrS :Mn 2+, Pb 2+

White

7 (300 Hz)

0.28

0.39

[409]

SrS : Cu +

Blue (green)

25

0.17

0.30

[410]

SrS :Pb 2+

Bluish-green

17 (300 Hz)

0.26

0.33

[406]

[360] [345] [347]

SrS :Pb 2+ (filtered)

Blue

1.8 (300 Hz)

0.14

0.09

[406]

CaF2 :Eu 2+

Blue (450 nm)

2 (1 kHz)

0.2

0.1

[215]

ZnS : Mn2+/SrS :Ce 3+

White

0.49

0.48

[338, 402, 408]

480 b

a Note that the voltages in the luminance measurements vary in different references from 25 to 50 V above the threshold. bValue for one pixel; in patterned full devices values of 21 and 70 cd m -2 with 60 and 350 Hz, respectively, have been achieved for areal luminance [411,412].

128

RITALA AND LESKELA

by other methods, like thermal and electron beam evaporation or sputtering. A clear advantage of ALD is, however, a larger grain size at the beginning of the film growth which ensures that in the ALD made films the dead layers, i.e., layers with no emission due to poor crystallinity, are thinner than in the films made by the other techniques [413, 414]. The emission band of ZnS :Mn is so broad that with proper filters it may also be used as a red or a green phosphor for multi- and full color displays. To avoid parallax, the filters need to be placed close to the film stack and because this is not possible in the conventional structure (Fig. 12) where the substrate would be left in between, the inverted structure was developed by replacing the positions of the metal and the transparent electrodes [10]. ZnS :Tb is the other zinc sulfide-based material which has shown EL properties good enough for applications. In the deposition, Tb(thd)3 has been used as a precursor and good results have been obtained when several subsequent Tb(thd)3/H2S cycles have been used instead of one. Thus, the actual structure has been of a TbSx/ZnS sandwich type [350, 351]. The rareearth ions (Ln 3+) are large as compared to the zinc ion and therefore in practical rare-earth concentrations (few percent) the rare-earth ions when homogeneously distributed cannot locate at the zinc site in ZnS but rather a Ln202S center is formed [415]. Due to the excellent performance of ZnS :Mn in the long wavelength part of the visible spectrum, quite a lot of the more recent phosphor research has been devoted to the blue phosphors which are needed to complement ZnS :Mn in making a full color display. Here, the most intensively studied material has been bluish-green emitting SrS : Ce for which the basic process uses Sr(thd)2, Ce(thd)4, and H2S as the precursors [337, 338], but also different fluorinated fl-diketonate Ce complexes have been studied as source materials for the Ce dopant [339, 340]. The use of cyclopentadienyl compounds as precursors began with Ce compounds [360] but also the host material SrS has been made from metalorganic precursors, from Sr(C5ipr3H2)2 for instance [359, 416]. Despite all the efforts, the performance of SrS:Ce after blue filtering (10-20 cd m -2 depending on the filter) is still somewhat lacking the level required (2030 cd m -2) for commercializing the full color displays. The total EL brightness of SrS : Ce is good (> 100 cd m -2) but unfortunately the majority of the emission falls in the green region (Table VI). Quite recently, SrS :Cu and CaS :Pb have been taken under study as new potential blue phosphors. Especially for CaS :Pb, deposited from Ca(thd)2, Pb(C2Hs)4, and H2S, very promising results have been reported: deep blue emission, CIE (Comission Internationale de l'Eclairage) color coordinates ranging from (0.14, 0.07) to (0.15, 0.15), and luminance of 80 cd m -2 with low driving voltage but the efficiency is still an issue [407]. In addition to the previously mentioned, many other potential phosphors have been deposited by ALD in the search of materials for full color TFEL displays (Table VI). The materials studied are rare-earth doped zinc and alkaline earth sulfides. The rare-earth ions, besides cerium and terbium, include europium (red), samarium (red), praseodymium (white), and

thulium (blue). Most of the materials have been examined already in the 1980s and the EL performance levels reached by ALD are also here quite similar to those obtained by the other film deposition methods. Unfortunately, the EL properties of these materials are far below the level needed in TFEL devices. 6.2. Insulators

6.2.1. Insulators for TFEL Displays

In the TFEL displays (Section 6.1, Fig. 12), the insulator films limit current transport across the TFEL device. Since high electric fields of about 2 MV cm -1 are typically used, high dielectric field strength (high breakdown field, EBD) and pinholefreeness over the whole display area is required. Therefore, the insulators seem to be perhaps the most critical part in the preparation of reliable TFEL displays. A detailed discussion on the role of the insulators and their requirements has been presented in Refs. [11,400, 401], so here we just summarize the most important properties of the insulator films: (i) (ii) (iii) (iv) (v)

high electric field strength, high relative permittivity, er, pinhole-free structure, self-healing breakdown mode, convenient and stable interface-state distribution from which electrons are emitted into the phosphor at proper electric fields, (vi) good thickness uniformity and conformality, (vii) good adhesion and stability with the adjacent electrode and phosphor layers, (ix) stress-free. The insulator films should preferably be amorphous because polycrystalline films lead to rough interfaces and they contain grain boundaries through which electrons can flow and ions can migrate. The requirements of high field strength and high permittivity are contradictory since, in general, insulators with high permittivity suffer from low breakdown fields. In addition, their breakdown mechanism is usually propagating rather than self-healing. Therefore, insulators with moderate permittivity but high EBD have usually been preferred. A convenient figure of merit for the insulators is the charge storage factor, eOerEBD, which shows the maximum charge density that can be stored in a capacitor made of a given insulator. Here, it must be noted, however, that while er is usually well defined, EBD is a statistical quantity and depends on the measurement method and the definition of breakdown; i.e., whether the breakdown field is that causing a destructive breakdown or a certain leakage current density, like 1 #A cm -2. Table VII summarizes dielectric properties of ALD made insulators potential for TFEL displays. In addition to those listed in Table VII, several other potential insulator films have also been grown by ALD (Y203, MgO, CeO2, A1N, see Tables IV and V) but their dielectric properties have not been reported in enough detail. On the other hand, some of the high permittivity insulators (TiO2, Nb2Os, SrTiO3, BaTiO3) are considered too leaky to be applied in the TFEL

ATOMIC LAYER DEPOSITION Table VII.

129

Dielectric Properties of ALD Made Insulators Potential for TFEL Displaysa EBD (MV cm-1 )

eoer EBD (nC mm -2)

Material

er

A1203

7-9 8

3-8 5

16-50 42

[129, 133, 135, 136, 216, 220, 225, 227, 237] [136]

NbxAlyOz

Reference

A12O3/TIO2

9-18

5-7

40-80

[ 107, 417]

A1203/Ta205

10-20

2-6.6

20-55

[130, 131,133, 135]

HfO2

13-16

1-5

Ta205/HfO 2

19-23

2.5-5

40--66

[ 131,197]

ZrO2

20

1

20

[ 133 ]

Ta205

23-25

0.5-1.5

Ta205/ZrO2

25-28

2-2.5

40-60

[ 133]

TaxTiyOz

27-28

1

33

[418]

8

5-10

[131,197]

[131,133, 197]

Nbx TayOz

25-35

0.5-1

25

[202]

Nbx Tay Oz/ZrO2

31-33

3

83

[ 192]

Ta2Os/Nb205

38

0.5

17

[202]

aTypically the best results or a range of the best values are given for each material. The notation of AB/CD refers to a stacked insulator (nanolaminate) with a variable number of layers. Note that the EBD values depend on its definition, and consequently also eOerEBD depend on the definition of EBD. Most of the results are based on EBD corresponding to a leakage current density of 1 ~A cm -2.

displays as such, without a combination with higher resistivity materials, and are therefore not included in Table VII. In the commercial TFEL displays, the ALD made insulators are A1203/TiO2 (ATO) or just A1203 which are made from the corresponding chlorides and water. For aluminum, AI(CH3)3 may also be used. The A1203/TiO2 insulator [107, 399,402, 417, 419] is a good representative of composite structures where advantageous characteristics of two or more materials are combined in realizing insulators which are at the same time reliable (high EBD) and efficient (high 6r). In other words, the eOer EBD value of the composite exceeds those of its binary constituents (Table VII). Later, Ta205 based composite insulators have been examined in great detail (Table VII). Ta205 has a relatively high permittivity of 25 but in the as-deposited state it is usually quite leaky due to oxygen deficiency. To improve this shortcoming, a concept of nanolaminate was introduced. Nanolaminates consist of alternating layers of two or more insulator materials so that each separate layer has a thickness in a range of 1-20 nm (Fig. 14a) [197]. Due to the sequential film deposition in ALD, the preparation of nanolaminates with accurately varying composition depth profiles is straightforward. The ALD made nanolaminates studied so far have consisted of stacked layers of Ta2Os, ZrO2, HfO2, A1203, Nb2Os, and their solid solutions deposited from Ta(OC2Hs)5, TaC15, ZrC14, Zr(OC(CH3)3)4, HfC14, A1C13, Nb(OC2Hs)5, and H20 at 325~ and below. Figure 14 compares the dielectric properties of HfO2-Ta205 nanolaminates to their binary constituents. The labels describe the nanolaminate configuration as N • (dHfo2 + dTa2Os) where N is the number of the HfO2-Ta205 bilayers, and dHf02 and dTa205 are the thicknesses of the corresponding single layers in nanometers. A number of conclusions can be drawn:

(i) the leakage current in the nanolaminates is lowered in relation to both constituents and is strongly dependent on the actual nanolaminate configuration (Fig. 14b), (ii) the permittivity is nearly, though not entirely a linear function of the relative thickness of the binary constituents (Fig. 14c), (iii) the charge storage factor has a maximum, about 10-fold of that of the binaries, at a certain relative thickness of the constituents (Fig. 14d). An interesting observation is that in the nanolaminates the leakage current density is lowered not only in relation to the more leaky component, Ta205, but also in relation to the higher resistivity HfO2 (Fig. 14b). In other words, the addition of layers of the high leakage current material Ta205 to HfO2 has a positive effect on the leakage current properties. This improvement, which at first sight seems somewhat surprising, is attributed to the elimination of grain boundaries extending through the whole insulator from one electrode to the other. Polycrystalline insulator films, like HfO2 here, usually exhibit extra conductivity along the grain boundaries. In the nanolaminate structure, the continuous grain growth of HfO2, and thus the continuous grain boundaries, are interrupted by the amorphous Ta205 layers. Another potential explanation for the improved leakage current properties of the nanolaminates is the trapping of electrons at an interface next to a weak point in one sublayer, thereby decreasing the injecting electric field in the vicinity of this point. Nevertheless, if these two mechanisms were the only ones responsible for the reduced leakage current, the layer thicknesses should not have such a significant effect as observed (Fig. 14b). Therefore, it appears that also some other, layer thickness-dependent factors are involved. Especially the crystal structures and crystallite sizes of the poly-

130

RITALA AND LESKEL,~ PERMITTIVlTY i

^l

i

!

!

^l

"razos i 9

I

imm

....

IlfOz

25

~

bilayer

[!!x112"S+L5)l

23 -

~/

i~. ~o.~o)u/,,/*

21 . . . .

i

TazOs i

i10X03.5'5)1

i

Hf02 m|

.

I

l~o~

17

ITO

I

N x (dHfo2"dra~R)6)

16

glass substr~te

[i00%

l

I

t

J

I

0

10

20

30

40

...

.

.

.

I

!

I

!

I

60

70

80

90

THICKNESS,

.

.

.

.

.

.

.

N X(dHio2*dTi206

oo

)

i

,o

4

"

/ 0o%

[~(s;~sL,.~.

eo

-6

4o -6

"'I i

~

ts

1

i

I

.

:.s

1

s

_l

s.s

l

4

4.s

~9 ,..~

~00~

\e

,.

tW~f

_

*' .jt~2o__._slJ ff~i-66zi0-Jl /

isx(lo-m)i __ _ ~ " ~ 18,(lr.5; 2_5I!"

2o

, o.s

-'*

/. 1 3 , ~ 2 . 5 2.5)t

1~o~3,,5;5)i

.....

o

%

Q VALUIE, nClmm 2

%

=,~

I

1100

(c)

LEAKAGE CURRENT DENSITY, log A. / c. m. . 2. .

"e Hm=t------~

50

HfO 2 RELATIVE

(a)

- .

"

__

,-- underlayer

AIzO~

- 2.

""

"

19

Ta,O

ITO

/

13~(z~-zs_~ ..~ .~e~.~)l /Ir,xao-s)i

ra~__~

[100% Hf-

D _c

0 0 ,I,.I ~

C9

1/) tO) ,4.,,o

19

o

0 O

~) E> C)

o

E

(-

(M 0 0

tO 0 0

E

....,

J...... 10

20

30

t I

[

40

50

_.

60

2 O (deg.)

70

L_

J

801717.217.417.617.81{1

.2

O(deg.)

Fig. 27. X-ray 0-20 scan of In20 3 films grown on (a) MgO and (c) YSZ substrates. The corresponding (004) In203 rocking curves are shown in (b) and (d). The obvious splitting of the higher intensity substrate peaks in (a) and (b) is due to saturation of the X-ray detector. (Reprinted with permission from E. J. Tarsa, J. H. English, and J. S. Speck, Appl. Phys. Lett. 62, 2332 (1993), 9 1993, American Institute of Physics.)

6.2. Electrical Properties of ITO Films

6.2.1. Effects of Oxygen Pressure on the Electrical Properties of the Films Deposited at Room Temperature The electrical properties of ITO films deposited at room temperature are considered next. As explained in Section 6, all the films deposited at room temperature were amorphous. Figure 28 shows plots of resistivities versus oxygen pressure for 0 wt%, 5 wt%, and 10 wt% Sn-doped In203 films [81-83]. The resistivities of the films were strongly dependent on the oxygen pressure and followed a similar tendency. High resistivity was achieved at low oxygen pressure of 1 • 10 -3 Torr for all the ITO films. With increasing oxygen pressure to between 1 • 10 -2 and 1.5 • 10 -2 Torr, the resistivities reduced to their minimal values of 1.8 • 10 -4, 4.8 • 10 -4, and 5.4 • 10 -4 f2 cm for 0 wt% (undoped In203), 5 wt%, and 10 wt% Sn-doped ITO films, respectively. From oxygen pressure greater than 1.5 • 10 -2 Torr, an abrupt increase in the resistivities of the films was noticed. The optimal oxygen pressure that yielded the lowest resistivity films

lies within a narrow range of (1-1.5) • 10 - 2 Yorr [79-92]. The poor resistivity obtained at low oxygen pressure (1 • 10 -3 Torr) and high oxygen pressure (> 1.5 • 10 -2 Tort) was ascribed to nonstoichiometry resulting from a deficit of oxygen vacancies. Composition wise, an increase in the resistivity of the films with increasing Sn doping content was witnessed at the optimum oxygen pressure of 1 • 10 -2 Torr. The increase in the resistivity of the films at this oxygen pressure with increasing Sn doping content was attributed to scattering caused by Sn atoms [73]. The results suggested that at room temperature, lower resistivity films could be obtained from an undoped In203 target compared to a Sn-doped In203 target by the PLD technique. Figure 29 shows (a) the carrier concentration and (b) the Hall mobility plotted against oxygen pressure, respectively [81-83]. At an oxygen pressure of 1 • 10 -3 Torr, the carrier concentration varied from 4.5 • 1018 to 3.5 • 1020 cm -3 and was minimum for 10 wt% Sn-doped In203 film. It increased to about 8 • 1020 cm -3 at an oxygen pressure of 5 • 10 -3 and then decreased slightly to around (5-6) • 1020 cm -3 at an oxygen pressure of 1 • 10 -2 Torr for all the films, irrespective of the change

LASERS IN THIN FILMS PROCESSING

10 4

10 2

E 0

- - 0 - - 0 wt% Sn-doped - - A - - 5 wt% Sn-doped --O-- 10 wt% Sn-doped

10 0

jO

V

CL 10 .2

10 -4

"

'

'

'I

'

'

'

'

'

'

10 -a

'

'I

'

'

'

'

'

'

10 .2

"-

10 -1

Oxygen pressure (Torr) Fig. 28. Plots of resistivities (p) versus oxygen pressure for 0 wt%, 5 wt%, and 10 wt% Sn-doped In203 films deposited at room temperature.

1021

(a)

C~ |

E v

o

E

--O-- 0 wt% Sn-doped

1019

-~OA~05::/o Sn-doped U --~-- 10 wt% Sn-doped.,~---~

/

10 TM . . . . . . . . . . . . . . . . . . . . . . 40-

A

o

>

30

E

20-

=L

10

(b)

oa

o

~--

o . . . .

i

.

10 -3

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

1 '0-2

10-1

O x y g e n pressure (Torr) Fig. 29. (a) and (b) show the cartier concentration (n) and the Hall mobility (/z) plotted against oxygen pressure for the ITO films deposited at room temperature.

in Sn doping content. In the region of optimal oxygen pressure of (1-1.5) • 10 -2 Torr, little change of the carrier concentration with changes in Sn doping content occurred. From oxygen pressure above 1.5 x 10 -2 Torr, the carrier concentrations of all the films decreased very sharply and this decrease corresponded to the poor resistivity observed (Fig. 28). The cartier concentration of the undoped and Sn-doped In203 films responded in a

185

similar way to the changes in oxygen pressure. As described in Section 2, for undoped In203 films free cartiers are generated by the creation of oxygen vacancies [46, 170], while in ITO films generation of free carriers occurs through the creation of oxygen vacancies and substitutional four-valence Sn atoms. The creation of an oxygen vacancy supplies a maximum of two electrons, while the substitution of an In atom with a Sn atom provides an electron to the conduction band as represented in Eqs. (3) and (4) in Section 2. Equation (3) applies mainly to In203, while Eqs. (3) and (4) are true for crystalline ITO films. However, in amorphous state (i.e., films deposited at room temperature), it has been reported that the increasing presence of Sn atoms in ITO films does not contribute free carriers to the conduction band, rather they act as scattering centers [73, 144]. In Figure 30 is illustrated the structures of amorphous and crystalline ITO material, portraying a distorted and an orderly structure, respectively. Therefore, the high carrier concentrations observed in the undoped and Sndoped In203 amorphous films at the optimal oxygen pressure were a consequence of the creations of oxygen vacancies. On the other hand, the low carrier concentrations achieved at low (< 1 x 10 -3 Torr) and high (> 1.5 • 10 -2 Torr) oxygen pressures could be due to a defect in oxygen vacancies leading to nonstoichiometric films [46]. In Figure 29b, low Hall mobility ( E o

~o~

-A--5 wt% S n 4 o p e d

40

.

.

.

.

.

.

i

.

.

.

.

.

.

.

.

i

.

!

.

.

.

.

.

.

.

.

(c)

30 20

::L 10 .

.

.

.

.

.

.

.

.

10 -a

.

.

.

.

.

.

.

.

10 .2

.

.

.

.

101

Oxygen pressure (Torr) Fig. 31. Resistivity (p), carrier concentration (n), and Hall mobility (lZ) plotted against oxygen pressure for 0, 5, and 10 wt% Sn doped In20 3 films deposited at 200~ (Adapted from F. O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, H. Matsui, and M. Motoyama, Appl. Phys. Lett. 74, 3059 (1999); E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, H. Matsui, and M. Motoyama, Japan. J. Appl. Phys. 1 38, 2710 (1999); F. O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, K. Yamada, H. Matsui, and M. Motoyama, Thin Solid Films 350, 79 (1999) from American Institute of Physics, Japan Society of Applied Physics, and Elsevier Science.)

Sn-doped In203 films. This observation was not unusual since the combined effect of energetic vapor and thermally induced crystallization was expected to aid surface migration of In and Sn cations with a consequential enhancement in the film resistivity [47, 171, 172]. The ITO conduction mechanism is partly controlled by the intrinsic doping by oxygen vacancies; hence at the optimum oxygen pressure, resistivity was lowered. Undoped In203 films showed a somewhat higher resistivity above 3.6 x 10 - 4 ~ cm at this region of oxygen pressure. The reason for the high resistivity in the undoped In203 films has been discussed in Section 5. From oxygen pressure above 1 x 10 -2 Torr, a rapid increase in the resistivities occurred in all the films, irrespective of the changes in the Sn doping content. The resistivity of the films deposited at 200~ was better than or comparable to the values reported for ITO films deposited by other techniques [6, 73, 85, 90, 171-173]. Several groups have observed that oxygen pressure in the region of (1-1.5) • 10 -2 Torr is optimal for achieving highly conducting ITO films deposited on heated substrates by the PLD process [90, 92, 171 ]. It is especially interesting to note that low resistivity films were achieved within a narrow oxygen pressure range of (1-1.5) • 10 -2 Torr. This is important for the optimization and standardization of the PLD growth conditions. Figure 3 l b shows a plot of the carrier concentration as a function of oxygen pressure for films grown at 200~ A high carrier concentration of around 1021 cm -3 was obtained for Sn-doped In203 films deposited at oxygen pressures over the range 1 • 10 -3 to 1 • 10 -2 Torr. As expected, the carrier concentration was maximal for the samples that yielded the lowest resistivities. Lower carrier concentrations of (2-4) x 1020 cm -3 were observed for the undoped In203 films as described in Section 5. At higher oxygen pressures (> 1 x 10 -2 Torr), the carrier concentrations of the films declined rapidly to around 8 x 1019 cm -3. This behavior is similar to that observed in

LASERS IN THIN FILMS PROCESSING the ITO films deposited at room temperature. Carl et al. [47] also observed a similar behavior for sputtered ITO films. The decrease in the cartier concentrations with increasing oxygen pressure has been associated with an increase in the absorption of free electrons [73]. Plots of the Hall mobilities versus oxygen pressure for films deposited at temperature of 200~ are shown in Figure 3 l c. A similarity in the behavior of the carrier mobility for the undoped and 10 wt% Sn-doped In203 films with changes in oxygen pressure is apparent. Moderately low mobilities were observed at low oxygen pressure over the range 1 • 10 -3 to 5 x 10 -3 Torr. This was followed by an increase in the mobility with increasing oxygen pressure to about 1 • 10 -2 Torr before decreasing with a further increase in oxygen pressure. In contrary, the Hall mobility of the 5 wt% Sn-doped In203 films tended to stabilize at about 33 cm 2 V -1 s -1 cm for oxygen pressures between 1 • 10 -3 and 1.5 • 10 -2 Torr before decreasing with further increase in oxygen pressure. The best Hall mobilities of 43-47 cm 2 V -1 s -1 were observed for the films deposited under oxygen pressure of (1-1.5) x 10 -2 Torr, particularly for the undoped and 10 wt% Sn-doped In203 films. At low and high oxygen pressures, the low mobilities exhibited by the films could be related to the poor crystallinity, as discussed in Section 6. On the other hand, the high carrier concentration (-'~1021 cm -3) observed in the films deposited at low oxygen pressures suggested that scattering by impurity centers due to excess cations (Sn and In) was responsible for the low Hall mobility [48, 55, 73, 174]. In general, the sharp drop in the resistivity at higher oxygen pressures was caused by the drastic reduction of the carrier concentration and the Hall mobility.

--13-- undoped In203 --O-- 5 wt% Sn-doped --A--10wt% Sn-doped ~

12

E O

10

/D

~13 (a)

8 0

~, O r-

X

6

4

V

2

5'0 '

100 ' 1~i0 ' 200 ' 2~i0 ' 300 ' 3~i0

Temperature (~ 12 10 i

E O

O

O

x v

8 6D

4 - - D - - undoped In20 a

t-

~

--O-- 5 wt% Sn-doped - - ~ - I D ~ D - - A - - 10 wt% Sn-doped 0 0

6.2.3. Effects of Substrate Temperature on the Electrical Properties of the Films The influence of the substrate temperature on the electrical properties of the films is considered next. Figure 32a-c shows the dependence of resistivity, carder concentration, and Hall mobility on the substrate temperature for undoped In203 and 5 wt% and 10 wt% Sn-doped In203 films deposited at an oxygen pressure of 1 • 10 -2 Torr, respectively [80]. The error (experimental and instrumental) in the data presented here was less than 5%. At low substrate temperature (< 100~ the least resistivity of ~ 2 x 10 -4 f2 cm was obtained for undoped In203 film. The creation of oxygen vacancies contributed to the high carrier concentrations shown in Figure 32b. Moderate Hall mobility (40 mJ cm -2 per pulse) for both excimer lasers and not the pulsed frequency. Evidence of improvements in the crystalline structure and optoelectronic properties was observed in the laser-annealed films. We have carried out studies on excimer laser irradiation of ITO films during growth by PLD [79, 211,212]. Remarkable improvements on the overall properties of the films were observed even at room temperature. The experimental procedure as well as the results of the ITO films will be considered in subsequent sections.

7.3. Film P r e p a r a t i o n by Laser Irradiation

Depositions were carried out using the same KrF (248 nm) laser system described earlier in Section 4.5. The only addition to

the arrangement was the laser irradiation assembly consisting of a beam splitter, reflecting mirrors, and focusing lens to direct part of the laser beam at the substrate surface. A schematic diagram of the experimental setup is shown in Figure 43 [79]. The laser system was operated at a total energy of 290-310 mJ and a pulsed frequency of 20 Hz. The laser beam from the system was split into two equal parts using a beam splitter. Half of the energy was focused on the target using a spherical lens with a focal length of 25 cm, thereby yielding an energy density of approximately 3 J cm -2. The other half of the energy was directed at the substrate surface via an independent quartz glass window using a single convex lens with a focal length of 70 cm. The energy density of the laser beam incident on the substrate was roughly 70 mJ cm -2. During depositions, undoped In203 (0 wt% Sn-doped) and Sn-doped In203 (3 wt%, 5 wt%, 8 wt%, and 10 wt%) sintered ceramic targets were used. The objective was to determine the effect of target composition on the properties of the laser-irradiated films. Films were deposited at different oxygen pressures, from 1 • 10 -3 to 4.5 • 10 -2 Torr, and substrate temperatures ranging from room temperature (20~ to 400~ The substrates were clamped onto the holder using stainless steel strips, thus producing a well-defined step in the nonirradiated part of the film close to the focused laser beam on the substrate in order to enable the film thickness to be properly determined. Films with reasonable uniformity were deposited on SiO2 fused-quartz glass with substrate areas of 6.25 cm 2. The middle part of the substrate that was irradiated with the laser energy pulses was oval in shape with a total area of about 1 cm 2. The above conditions produced deposition rates of approximately 15 nm/min. The thickness of the films was around 80 + 20 nm. The thickness of the films was measured from the welldefined edge by the stainless strip in the nonirradiated part (close to the laser-irradiated portion) using a stylus profilometer. Because the energy density of the irradiation beam was lower than the threshold of 120 mJ cm -2 necessary to cause reablation of the deposited film, no major change in the film thickness was expected [205]. Therefore, the measured thickness on the nonirradiated parts of the films was considered to be similar to the laser-irradiated parts, in view of the reasonable uniformity attained over the substrate during deposition. The films were characterized for electrical, optical, and structural properties using the techniques already described in Section 4.7. Both the laser-irradiated and the nonirradiated parts of the films were analyzed in order to compare their properties directly. 7.4. Effect of S n - D o p i n g on the Electrical Properties of Laser-Irradiated ITO Films

This part consists of the electrical properties of the laserirradiated ITO films deposited by PLD. The films were deposited from ITO targets of different Sn doping content. The properties of the laser-irradiated and nonirradiated parts of the films are compared. From XRD analysis it was found that the

LASERS IN THIN FILMS PROCESSING

197

Fig. 43. An illustration of a PLD system with a laser irradiation wing. (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Murai, Japan. J. AppL Phys. Lett. 2 39, L377 (2000), 9 2000, Japan Society of Applied Physics.)

laser-irradiated films deposited at room temperature and those deposited at 200~ were crystalline with strong (111) preferred orientation, while the nonirradiated portions of the films deposited at room temperature were amorphous [79]. The experimental results of the microstructural properties of the laserirradiated films are discussed in Sections 7.5 and 7.6. Figure 44 shows the resistivity of ITO films with Sn doping over the range 0 to 10 wt% deposited at room temperature and 200~ for the laser-irradiated and nonirradiated parts. At room temperature, the nonirradiated parts of the films showed reasonably low resistivity which increased slightly from 2.2 x 10 -4 to 2.6 x 10 -4 f2 cm with increasing Sn doping content from 0 to 10 wt%. This small increase in the resistivity at high Sn doping content was attributed to the electrical inactivity of Sn at high doping levels [104, 110]. This observation is consistent with observations made for amorphous films, as discussed in Section 6.2. In contrast, the laser-irradiated (crystalline) parts of the undoped In203 (0 wt% Sn-doped) films deposited at room temperature and 200~ exhibited higher resistivity values of (4-6.5) x 10 - 4 ~ cm. The high resistivity observed in the In203 films was due to a deficit of oxygen vacancies leading to nonstoichiometric compositions, as discussed in Section 5 [88, 144]. Within Sn doping content over the range 3 to 10 wt%, the resistivity reduced to between 8.9 x 10 -5 and 1.3 x 10 - 4 ~ cm for the laser-irradiated parts of the films deposited at room temperature and 200~ The minimum resistivity of 8.9 x 10 -5 f2 cm

/k

E

P O 2 - 1xl 0 .2 Torr - - r l - - RT (laser-irradiated) - - O - - RT (nonirradiated)

6

/k-- 200~ (laser-irradiated)

0

--~7-- 200~ (nonirradiated) v

4

~

0,&,,,--

XQ.

2 .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

6'

.

.

.

.

.

0_____--0

0------0

.

.

{' Sn content

.

.

.

.

.

'1'0

(wt%)

Fig. 44. Resistivity (p) against Sn doping content for the laser irradiated and the nonirradiated parts of ITO films deposited at room temperature and 200~ respectively. (Reprinted with permission from F. O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, J. Appl. Phys. 88, 4175 (2000), 9 2000, American Institute of Physics.)

was observed for the laser-irradiated part of an ITO film deposited from a 5 wt% Sn-doped In203 target at 200~ With a

198

ADURODIJA 14-

(a)~

12

|

E

.O

10

v

8

(:3

o

x E

0 ~ 0 _ ~ _ ~ _ _ 0 ~ 0

PO2 - l x l 0.2 TOrT --E]-- RT (laser-irradiated) --O-- RT (nonirradiated)

6, /fl"

4,

J

- - A - - 200~ (laser-irradiated)

2 70

0

- - 0 - - 200~ (nonirradiated) i

i

i

i

i

i

60, S" t/)

50-

T.-

40

E

30

0

~

0

~

0

~

0

~

0

O v

:=L

2010 0

Sn content (wt%) Fig. 45. Plots of (a) carrier concentration (n) and (b) Hall mobility (#) against Sn doping content for the laser irradiated and the nonirradiated parts of ITO films deposited at RT and 200~ respectively. (Reprinted with permission from F. O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, J. Appl. Phys. 88, 4175 (2000), 9 2000, American Institute of Physics.)

further increase in the Sn doping content from 5 to 10 wt%, the resistivity increased slightly and the cause was associated with the increasing presence of impurity scattering centers [73, 144,

]]0]. Figure 45 shows (a) the carrier concentration and (b) the Hall mobility measured from the laser-irradiated and the nonirradiated parts of ITO films deposited at room temperature and 200~ respectively. The nonirradiated parts of the films deposited at room temperature yielded steady carrier concentrations of (7.4-8.8) x 102~ cm -3 for Sn doping content over the range 0 to 10 wt%. This feature suggested that Sn doping had little effect on the creation of free carriers in the amorphous ITO films [ 143]. For the laser-irradiated parts of the films deposited at room temperature and 200~ (crystalline films), the cartier concentrations indicated a strong dependence on Sn doping content, as shown in Figure 45a. In the case of the undoped In203 films, low carrier concentrations of (1.5-2.5) x 10e~ cm -3 were observed at both substrate temperatures. The carrier concentrations increased sharply to about (1.1-1.3) x 1021 cm-3 with increasing Sn doping content to 5 wt%. A further increase in the Sn doping content from 5 to 10 wt% resulted in a shallow increase from 1.1 x 1021 to 1.2 x 1021 cm -3 for the films deposited at room temperature. However, for the films deposited at 200~ the carrier concentrations saturated at 1.3 x 1021 cm -3 for 5 wt% doping content, before decreasing slightly to about 1.2 x 1021 cm -3 with further increase in Sn doping content to

10 wt%. The carrier concentrations of the laser-irradiated parts of the ITO films deposited at room temperature and the nonirradiated parts of the films deposited at 200~ showed close resemblance. From the experimental data reported above, the marked increase in the carrier concentration was attributed to the diffusion of Sn atoms from interstitial sites or grain boundaries into the In cation sites due to improvement in the crystalline structure caused by photochemical and/or thermal crystallization effects [213]. This is expected since a Sn atom has a valence of four electrons compared to In with a valence of three electrons. However, the slight reduction in the carrier concentration of the ITO films with increasing Sn doping content within 5 and 10 wt% implied an increase in the electrical inactivity of Sn atoms at higher doping levels. Yamada et al. [ 110] and Krstlin et al. [104] have shown in their respective studies on the doping mechanism of Sn in In203 powder and ITO films deposited by spray pyrolysis that the doping efficiency decreases with increasing Sn content, above 5 wt%. They reported that for Sn doping content above 5 wt%, complexes that do not donate free electrons but only existed as impurity scattering centers in the ITO material are formed. They have shown that the impurity scattering centers reduce the doping efficiency and the mobility of free carriers [ 104, 110]. The results on the relationship between Sn doping and carrier concentration for the laserirradiated films closely agreed with those reported by Krstlin et al. and Yamada et al. A similar observation has also been made by Kim et al. on laser deposited ITO films at 250~ [88]. Apparently, the Hall mobility of the nonirradiated parts of the films deposited at room temperature remained unaffected (~32 cm 2 V -1 s -1) by the change in Sn doping content from 0 wt% to 10 wt%, as shown in Figure 45b. This behavior is consistent with the stable resistivity and cartier concentration shown in Figures 44 and 45a. For the laser-irradiated parts of the films deposited at room temperature, high Hall mobilities of 39-63.3 cm 2 V -1 s -1 were observed for Sn doping over the range 0 to 10 wt%. At room temperature, the laserirradiated part of an undoped In203 produced a maximum mobility of 63.3 cm 2 V -1 s -1, which gradually decreased to 39 cm 2 V -1 s -1 with increasing Sn doping content to 10 wt%. The Hall mobilities of the laser-irradiated parts of the films deposited at room temperature are comparable to those of the nonirradiated parts deposited at 200~ In contrast, the laser-irradiated parts of the films deposited at 200~ showed a remarkable increase in the Hall mobility, irrespective of the changes in Sn doping content. A similar relationship between the Hall mobility and Sn doping has been reported for ITO films deposited by electron-beam evaporation and PLD [88, 144]. The observed steady decrease in the mobility has been attributed to the presence of complexes that act as scattering centers. In general, laser irradiation of the growing ITO films on unheated and heated glass substrates by PLD was found to enhance the electrical properties. The increase in the Hall mobility of the laser-irradiated films even at 200~ is associated with the improvement in the crystallinity of the films. The moderately low mobility measured at high Sn doping con-

LASERS IN THIN FILMS PROCESSING 100 ie"

..~.-=-..

~..'"

-3

:I::

80

!S

".. ",

"',,

-... %.,",, "'-,.,

::, ",,,

~,

laser-irradiated '"~::ix~'. ""'"'-. 9"8 X 102~ -2 "'".\~\ "'"',, 02 pressure - 1x10-2 Tor;'~'~\. ""'-,.... o -,"-,",. I T:-RT(18~ .... "'"~:~?!i~'~,3, | ~ (0 wt% Sn) .......:~i7%>. I --'-_-_-_-: (3 wt% Sn) ........~.~: [

"~

40

20- |

(5 wt% Sn) (8 wt% Sn)

.............

t

S)z

n

560

,

(10 wt%

(1-2) X lO2' )

' 10'00 ' 15'00 " 20'00 " 25'00 "

Wavelength (nm) 100

80"" -

9

n(em -3 )

60-

"-

40

[

20

j ........ ...........

T,- RT( 18~ )

1l . . . . .

]

.........

(3 wt% Sn) (5 wt% Sn) (8 wt% Sn) (10 wt% Sn)

the filling up of the lower energy levels in the conduction band by electrons released from the Sn atoms. A similar feature has been reported for ITO films deposited by electron-beam evaporation and PLD [5, 88] as well as fluorine doped tin oxide (SnO2:F) films [5].

7.4.1. Electronic Transport Properties Carder mobilities of ITO films are reported to be greatly affected by disorder due to the structure of In203 as well as modification of the network resulting from Sn doping [73, 144]. It is well established that with increasing Sn doping content, complexes that do not contribute free electrons, but only exist as scattering centers that reduce the mobilities of free electrons, are formed in the ITO films [73, 104, 110, 144, 214]. Electron scattering sources such as grain boundaries, acoustical phonons, and neutral and ionized impurity centers have been found to affect the electrical and optical properties of ITO films [73]. However, in most of the cases that have been studied, grain boundaries and acoustical phonons played secondary roles, since the mean-free path of the electron is smaller than the average crystallite sizes and also shows little dependence on growth temperatures over the range 100 to 500~ [73,215]. The experimental data on the laser-irradiated and nonirradiated parts of the films were studied further in order to clarify the dominant scattering process. Therefore, the mean-free path (l) was calculated using a sufficiently degenerate gas model, given by [73, 144, 216] Vf --(37r2)1/3(h/m*)n

0 500

1000

1500

2000

2500

Wavelength (nm) Fig. 46. Transmittance curves as a function of wavelength for (a) laserirradiated and (b) nonirradiated parts of ITO films containing different Sn doping contents. (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, J. Appl. Phys. 88, 4175 (2000), 9 2000, American Institute of Physics.)

tent is explained on the basis of the interaction of scattering centers and formation of neutral scattering defect [73, 144, 214]. Figure 46a and b shows the respective optical transmittance measured at wavelengths over the range 190 to 2500 nm for the laser-irradiated and nonirradiated parts of the 0-10 wt% Sn-doped films deposited at room temperature. The films showed high optical transmittance greater than 85% in the visible range of the solar spectrum. From Figure 46a and b, the Sn doping could be correlated to the optical properties of the laserirradiated and nonirradiated parts of the films. For the laserirradiated parts of the films, the changes in the NIR and absorption edge could be related directly to the cartier concentration shown in Figure 45b. It is seen that the Sn doping content (carrier concentration) increased with increasing NIR, while the optical absorption edge shifted (Burstein-Moss shift) toward the shorter wavelength, thus implying bandgap widening. The shift in the absorption edge could also be related to the increase in

199

l

1/3

-- V f r -- (37r2)1/3 (h/e2)p_ln_2/3

(21) (22)

where Vf, m*, and n represent the electron velocity at the Fermi surface, electron effective mass, and carder concentration, respectively. The relaxation time and the resistivity are denoted by r and p. Within the limits of experimental error ( 1.5 x 10 -2 Torr), the crystalline quality deteriorated in a similar way earlier described in Section 6 for films deposited by the conventional PLD method. Figure 50a shows typical surface AFM micrographs of a nonirradiated part of a film deposited at 1 x 10 -2 Torr, and Figure 50b-d represents the laser-irradiated parts of ITO films deposited at oxygen pressure of 1 x 10 -2, 1 x 10 -3, and 2.5 x 10 -2 Torr, respectively. The nonirradiated part of the films exhibited smooth surface features, indicating an amorphous phase. In the case of the laser-irradiated parts, contrasting morphologies were displayed with changes in oxygen pressure. At low oxygen pressures of 1 x 10 -3 Torr, the films appeared

The dependences of the resistivity on the oxygen pressure for the laser-irradiated and the nonirradiated parts of ITO films deposited at room temperature are shown in Figure 51. In both cases, a strong influence of oxygen pressure on the resistivity, particularly at oxygen pressures above 1.5 x 10 -2 Tom is apparent. At low oxygen pressure (1 x 10 -3 Torr), the laser-irradiated part of the ITO film yielded a resistivity of 3.1 x 10 -4 f2 cm compared to 4.7 x 10 -3 f2 cm for the nonirradiated part. With increasing oxygen pressure to the optimal region of (1-1.5) x 10 -2 Torr, the resistivity of the laser-irradiated and the nonirradiated parts of the films decreased to minimal values of 1.2 x 10 -4 and 2.3 x 10 -4 ~2 cm, respectively. However, a further increase in oxygen pressure (> 1.5 x 10 -2 Torr) resuited in a sharp rise in the resistivities of both parts of the films. The lower resistivity observed in the laser-irradiated parts of the films was associated with the improvement in the crystallinity of the films due to the photocrystallization effect. Table II shows the electrical properties of ITO films deposited by a multitude of techniques. It is seen that at low-temperature PLD ITO films displayed lower resistivities, higher carrier concentrations, and higher mobilities compared to the other techniques. The carrier concentration and the Hall mobility plotted against the oxygen pressure for the laser-irradiated and the nonirradiated parts of ITO films deposited at room temperature are shown in Figure 52. At low oxygen pressures of 1 x 10 -3 Torr, cartier concentrations of 7.7 x 1020 and 4.7 x 1020 cm -3 were measured for the laser-irradiated and the nonirradiated parts of the films, respectively. With increasing oxygen pressure to 1.5 x 10 -2 Torr, the carrier concentrations increased to optimal values of 1.3 x 1021 and 8.8 x 1020 cm -3 for the laserirradiated and the nonirradiated parts of the films, respectively. This oxygen pressure region also produced the lowest resistivity, as shown in Figure 51. Further increases in oxygen pressure (> 1.5 x 10 -2 Torr) led to a rapid decrease in the carrier concentration. This behavior is similar to what was reported for ITO films deposited by conventional PLD [82]. The carrier concentrations of the laser-irradiated and the nonirradiated parts of the films were lower, particularly at oxygen pressures below 1.5 x 10 -2 Torr. At all oxygen pressures, the carrier concentrations of the laser-irradiated parts were much higher than those of the nonirradiated parts of the films. The improvement in the

202

ADURODIJA

Fig. 50. Typical surface AFM pictures of (a) a nonirradiated part of the films deposited at oxygen pressure of 1 x 10 - 2 Torr. (b) to (d) show the laser-irradiated part of ITO films deposited at oxygen pressures of 1 x 10 - 2 , 1 x 10 - 3 , and 2.5 x 10 - 2 Torr, respectively. All films were deposited at room temperature.

carrier concentration was a consequence of the activation of Sn atoms into Sn 4+ within the host In203 crystal lattice during the photocrystallization process. The migration of Sn atoms was enhanced by the laser irradiation; hence more Sn atoms could substitute for In atoms in the lattice, leaving one electron each more than the requirement for bonding. The dependence of Hall mobility on oxygen pressure for the laser-irradiated and the nonirradiated parts of the ITO films are shown in Figure 52b. The effects of oxygen pressure on the Hall mobility in both parts of the films followed similar tendencies. At low oxygen pressures of 1 x 10 -3 Torr, the laser-irradiated part of a film exhibited a moderately low Hall mobility of 26.2 cm 2 V-1 s-1 that rose to 40.4--45.2 cm 2 V -1 s-1 with increasing oxygen pressure to between 5 x 10 -3 and 2 x 10 -2 Torr.

Further increases in oxygen pressure to 4.5 x 10 -2 Torr resulted in a sharp decrease in the carrier mobility to 2.2 cm 2 V -1 s -1. In the case of the nonirradiated parts of the films, a very low Hall mobility of 4.5 cm 2 V -1 s -1 was observed at a low oxygen pressure of 1 x 10 .3 Torr followed by a rapid increase to 30.4 cm 2 V -1 s -1 with increasing oxygen pressure to 1 x 10 .2 Torr. Between oxygen pressures of 1 x 10 .2 and 2 x 10 .2 Tort, no appreciable change in Hall mobility of the nonirradiated part of the films occurred. However, at an oxygen pressure of 4.5 x 10 .2 Torr, the mobility and the carrier concentration of the nonirradiated part of the films could not be determined due to the very high resistivity. The best Hall mobility was obtained for the laser-irradiated and the nonirradiated parts of the ITO films deposited at the optimal oxy-

LASERS IN THIN FILMS PROCESSING Table II.

Film

Deposition

material

technique

203

Compilation of the Electrical Properties of In203 and ITO Films Deposited by a Multitude of Techniques Deposition temperature (~

Cartier

Resistivity

concentration

Hall mobility

( x l 0 - 4 f2cm)

( x l 0 2 0 cm - 3 )

(cm 2 V - 1 s - 1 )

Comment

References

In203

PLD

RT

3.6

5

35

-

[83]

In203

PLD

RT

2.5

6

30

-

[80]

In203

PLD

100

1.8

9

47

-

[80]

In203

PLD

200

5

4

28

-

[80]

In20 3

PLD

350

11.5

2

25

-

[83]

In203

TE

400

4

4

72

-

[222]

In 2 0 3

TE

320-350

2

4.7

70

-

[23 ]

In 2 0 3

TE

150

8-16

0.5-1.1

60-95

-

[ 16]

In2 0 3

RE

200--400

20-30

0.35

25-60

-

[ 126] [92]

ITO

PLD

RT

2.8

-

-

-

ITO

PLD

RT

4.5

5

30

-

[82]

ITO

PLD

RT

4

-

-

-

[89]

ITO

PLD

RT

4

6

12

-

[91 ]

ITO

PLD

200

1.7

9

33

-

[82]

ITO

PLD

310

2

-

-

-

[85]

ITO

PLD

350

1.3

~ 10

-~48

-

[80]

ITO

PLD

RT

1.2

10

40

PLI

[79]

ITO

PLD

200

0.89

~- 12

55

PLI

[212]

ITO

PLD

300

0.84

--~12

57

PLI

[212 ]

ITO

DCMS

RT

5.5

7.1

16

-

[38]

ITO

RFMS

370

0.64).8

36

27

-

[41 ]

ITO

RFMS

Unheated

~4

-

-

-

[ 155]

ITO

RFMS

130

~4

10

~10

-

[49]

ITO

RFMS

200

1.59

10

--~40

-

[224]

ITO

RFMS

300

2.47-1.4

11.5-12.4

22-36

-

[225]

ITO

RFMS

Unheated

2.55

15.9

15.4

Annealed 400 ~ C

[55]

ITO

EBE

300

0.44

13.8

103

-

[27, 28] [226]

ITO

ARE

200

1.64

> 10

30

-

ITO

ARE

370

0.7

~10

~30

-

[15]

ITO

HDPE

280

1.23

10.7

47.5

-

[227]

-

-

[ 147]

ITO

HDPE

180

1.7

-

ITO

CVD

260

28.3

-

ITO

CVD

450

"~4.5

10

-

[64]

5-22

-

[228]

ITO

Spray

480

1.5

11

43

-

[229]

ITO

Spray

350-450

1.6-1.8

8.8

43

-

[230]

ITO

Sol-gel

-

30-50

-

-

Annealed 5 5 0 ~

[231 ]

evaporation, REmreactive evaporation, PLI--pulsed laser irradiation, D C M S - - - d c magnetron sputtering, R F M S ~ r f magnetron sputtering, E B E ~ electron beam evaporation, ARE~activated reactive evaporation, HDPE~high density plasma-enhanced evaporation, CVD---chemical vapor deposition. TEmthermal

gen pressure. The higher Hall mobility observed for the laserirradiated part was associated with the improvement in the crystallinity of the films. The relationship between the Hall mobility and oxygen pressure is consistent with those earlier reported for ITO films deposited at room temperature and (200~ by PLD, as discussed earlier in Section 6.2 [81]. In general, the poor electrical properties obtained in the films deposited at low oxygen pressure (1 x 10 -3 Torr) and high oxygen pressures

(> 1.5 x 10 - 2 Torr) was due to the poor crystalline quality, as shown in Figures 49b and 50.

7.5.3. Optical Properties of the Films The optical properties of the films ( ~ 100 nm) were determined by measuring the transmittance at wavelengths over the range 190 to 2500 nm. Figure 53a and b shows the transmittance spectra versus the wavelength for the laser-irradiated and the nonir-

204

ADURODIJA

100

D

ITO (5 wt% Sn-doped) -D-laser-irradiated --O-- nonirradiated /

10 .2 O

/

80

E O

0"-9,

C

o O E:

v

v

O

10 .3

60

t/

.........

t~

X EL

E U) 10-4 '

'

' ' I

'

'

'

'

'

'

10-3

'

'i

,

,

,

,

,

,

10-2

40

I .........

i .............

6

~"

2.5x10 .2

0 ' s60 ' 10'00

sbo 20'00 2s'oo

Wavelength (nm) r,,

~i

~

",, '.',,

i

o

4

",,

".,.~

"-, "...... "-.

"-....

rro (5 ~0/0 Sn-dop~) b

2

[]~D

- O - nonirradiated . . . .

!

.

.

.

.

.

.

.

.

!

.

.

.

.

.

.

.

"~

.

40

~ .........

(b)

4030

20

--o

E o,~ 2 0 : : L10

~

o

o~

0

o O

ITO (5 wt% Sn-doped) laser-irradiated

r ~ ~ E I - ~ D

--I-I--laser-irradiated

~>

~

4.5x10 2

10 -1

80

o

2x10 -2

"

,,

100

8

l x l 0 -2

...........

20

Fig. 51. The dependence of the resistivity (p) on the oxygen pressure for the laser-irradiated and the nonirradiated parts of the ITO films deposited at room temperature.

'?'E

~'.,,'.,.: "'.,..,\"\

iiii 1.5x10 -2

Oxygen pressure (Torr)

12

l x l 0 -3

[ ..........

E t~ t._

E-

POE (Torr) at aT(18~ ~ ~ i " . , , , , " ' , ,

,

,

,,!

10-3

,

,

,

. . . .

i

.

.

.

.

.

10-2

.

.

i[ . . . . . . . . .

1.5x10 -2 ITO (5 wt% S n - d o p e d )

2x102

/i .............

25x102

"

s60

n~

4"5x10"2

0'00 15'00 20'00 2so0

Wavelength (nm)

[] ,

. . . .

/I...........

/1 0

l x l 0 -2

.

10-~

Oxygen pressure (Torr) Fig. 52. (a) The carrier concentration(n) and (b) the Hall mobility (/1,)as a

Fig. 53. Optical transmittance spectra versus the wavelength for the laserirradiated (a) and the nonirradiated (b) parts of the ITO films deposited under oxygen pressure over the range 1 x 10 - 3 to 4.5 x 10 - 2 Torr at room temperature.

function of oxygen pressure for the laser-irradiated and the nonirradiated parts of the ITO films deposited at room temperature.

radiated parts of I T O films deposited at o x y g e n pressures over the range 1 x 10 -3 to 4.5 x 10 - 2 Torr. The films deposited at low o x y g e n pressure ( = 1 x 10 -3 Torr) were visually b r o w n i s h in color and less transparent ( < 8 5 % ) to the visible light ( 4 0 0 -

800 nm). The transmittance (visible) of both the laser-irradiated and the nonirradiated parts of I T O films increased with increasing o x y g e n pressure to 4.5 x 10 - 2 Torr. At the optimal o x y g e n pressure region, ( 1 - 1 . 5 ) x 10 - 2 Torr, transmittance above 90% was m e a s u r e d for the laser-irradiated films, while that of the nonirradiated films was slightly less than 90%.

LASERS IN THIN FILMS PROCESSING

205

I

The NIR was also affected by the laser irradiation and the change in oxygen pressure during growth of the ITO films. With increasing oxygen pressure, the NIR of the nonirradiated part of films decreased accordingly, while that of the laser-irradiated parts remained reasonably high. In addition, the absorption edge was found to change with changes in oxygen pressure.

I

- (a)

'

I

'

I

'

laser-irradiated part of 5 wt% Sn-doped ITO, different temp. and _ 0 2 pressure - l x l 0 -2 Torr

"-"

6"

6"

7.6. Effect of Substrate Temperature on the Properties of Laser-Irradiated ITO Films So far it has been shown that at room temperature crystalline ITO films with improved optoelectrical properties can be achieved by laser irradiation of the substrate during PLD process. In this section the effect of the substrate temperature on the material properties of the laser-irradiated films is discussed. The discussion covers the properties of the laser-irradiated and nonirradiated parts of the films.

oo~

c

1000C

iii - -I

20

7.6.1. Structural and Morphological Properties The XRD spectra of the laser-irradiated and the nonirradiated portions of the ITO films deposited at substrate temperatures ranging from 18~ to 400~ under oxygen pressure of 1 x 10 -2 Torr are shown in Figure 54 [223]. Crystalline films with a strong (111) preferred orientation were observed for the laser-irradiated films deposited at all temperatures. In contrast, the nonirradiated parts of the ITO films deposited at substrate temperatures lower than 150~ were amorphous, while above 150~ the films were crystalline exhibiting strong (111) preferred orientation as expected. Details on the structural properties of ITO films deposited without laser irradiation have been described in Section 6. With increasing substrate temperature, a slight shift in the diffraction peak positions to lower 20 angles were observed and the cause was associated with induced strain in the films during growth. In addition, the (222) diffraction peak intensities of the laser-irradiated films were much stronger than those of the nonirradiated parts of the films. The surface morphology of the films deposited at various temperatures was also analyzed using the AFM. Figure 55 shows the surface AFM micrographs of the laser-irradiated and nonirradiated parts of ITO films deposited at 100~ [223]. Figure 56 shows the surface AFM micrographs of the laserirradiated and nonirradiated parts of ITO films deposited at 300~ [223]. These samples represented the low and high deposition temperature regimes where amorphous and crystalline films are achieved without laser irradiation. At 100~ the nonirradiated films were amorphous as confirmed from XRD analysis Figure 54a. At 300~ the nonirradiated and the laserirradiated part of the films were crystalline. The crystallinity of the ITO films was highly improved with increasing substrate temperature as shown from both the XRD and AFM analyses. These data indicated that laser irradiation of the substrate during growth even at higher temperature is effective in enhancing the structural properties of ITO films. Below a substrate temperature of 100~ crystallization of the films was supposed

,

I

i

30

I

,

40

I

,

50

I

,

60

70

20 ( d e g ) - (b)

nonirradiated part of 5 wt% Sn-doped ITO,

different temp. and 02 pressure - l x l 0-" Torr t"

~,

-

~

300~ ....... _ ? s

-

1000

'-

:

~---

I

20

30

40

-_:

....

I

,

50

-_.!_.,

I

_.~_-.-_"

--

I

60

-

i

70

20 ( d e g ) Fig. 54. XRD spectra of the (a) laser-irradiated and (b) nonirradiated parts of ITO films deposited at oxygen pressure of 1 x 10 -2 Torr, as a function of substrate temperature. (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Murai, Appl. Surf Sci. 177, 114 (2001 ), 9 2001, Elsevier Science.)

to proceed through a photochemical mechanism (photocrystallization). On the other hand, above a substrate temperature of 150~ film crystallization occurred through the combined effects of photo and thermal mechanisms (photothermal crystallization) [133,213].

206

ADURODIJA

Fig. 55. SurfaceAFM micrographs of the (a) laser-irradiated and (b) nonirradiated parts of an IT9 film deposited at a temperature of 100~ (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Murai, Appl. Surf. Sci. 177, 114 (2001), 9 2001, Elsevier Science.)

7.6.2. Electrical Properfies The dependences of the resistivity on the substrate temperature for the laser-irradiated and the nonirradiated parts of the IT 9 films are shown in Figure 57 [223]. All films were deposited at the optimum oxygen pressure of 1 x 10 -2 Torr. At room temperature, the lowest resistivity of 1.2 x 10 -4 f2 cm was achieved for the laser-irradiated part of the film compared to 2.3 x 10 -4 f2 cm for the nonirradiated part as already explained in Sections 7.4 and 7.5. With increasing substrate temperature the resistivities of both parts of the films decreased linearly, while the differences between the resistivity values narrowed and coincided at 300~ The measured resistivity at 300~ was 8.4 x 10 -5 f2 cm. When the substrate temperature was raised to 400~ the resistivities of the laser-irradiated and the nonirradiated parts of the

Fig. 56. SurfaceAFM micrographs of the (a) laser-irradiated and (b) nonirradiated parts of an IT9 film deposited at temperature of 300~C. (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Murai, Appl. Surf. Sci. 177, 114 (2001), 9 2001, Elsevier Science.) films increased to 1.1 x 10 - 4 and 1.2 x 10 - 4 ~ cm, respectively. The increase in the resistivity was associated with film contamination originating from the components of the substrate holder. The carrier concentration and the Hall mobility as a function of the substrate temperature for the laser-irradiated and the nonirradiated parts of the IT 9 films are shown in Figure 58a and b [223]. With increasing substrate temperature from room temperature to 200~ the carrier concentration of the nonirradiated part of the films increased from 8.8 x 1020 to 1.2 x 1021 cm -3 and saturated with further increase in temperature to 400~ The initial increase in the carrier concentration at temperature between room temperature and 200~ (amorphous-crystalline) was a consequence of the thermal excitation of the Sn atoms into Sn 4+ cations [73]. In the case of the laser-irradiated parts

LASERS IN THIN FILMS PROCESSING

~- 20-1 ~ /

O

1

ITO(5wt%Sn-doped) P~-lxlO2T~ --r'l--laser-irradiated --O--nonirradiate~d

~0

~

1.5

1.0

rn~

0

100

200

300

400

Temperature (~ Fig. 57. Dependence of the resistivity (p) on substrate temperature for the laser-irradiated and the nonirradiated parts of ITO films. (Reprinted with permission from F. O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Mural, Appl. Surf. Sci. 177, 114 (2001), 9 2001, Elsevier Science.)

14

13i

(a)

E 12

/

o

0

0 ,-X

r-

~o:~.~~8~______~c )

j / O/

ITO (5 wt% Sn-doped) Po2- lxl 0-2Torr --El--laser-irradiated --O-- nonirradiated

10

9 Ot 8

60

'

I

'

I

"

I

"

I

55

207

of the ITO films, no appreciable change in the carrier concentration was observed at substrate temperatures over the range 18 to 400~ The high carrier concentration obtained in the laser-irradiated parts of the films even at low substrate temperature was attributed to photothermal crystallization effect [213]. However, a slight increase in the carrier concentration with increasing substrate temperature from room temperature to 400~ was observed and could be due to further improvement in the crystallinity of the films. From 200~ the carrier concentrations of the laser-irradiated and nonirradiated parts of the ITO films were ~ 1.2 • 1021 cm -3. These results further ascertain the effectiveness of Sn atoms as carrier contributors in crystalline ITO films [73]. The carrier concentration of the ITO films was strongly enhanced at low substrate temperature by the laser irradiation effect. The relationships between the Hall mobility and the substrate temperature for the laser-irradiated and the nonirradiated parts the ITO films are shown in Figure 58b. The Hall mobilities of the laser-irradiated and nonirradiated parts of the films increased appreciably from 40 and 30 cm 2 V -1 s -1 at room temperature to 57 and 56 cm 2 V -1 s -1 at 300~ respectively. A further increase in the substrate temperature to 400~ resuited in a decrease in the Hall mobility to 47 cm 2 V -1 s -1 for the laser-irradiated and 45 cm 2 V -1 s -1 for the nonirradiated parts of the films. At temperature of 400~ the observed increase in the resistivity was primarily a consequence of the reduced Hall mobility. The high Hall mobilities of 57 and 56 cm 2 V -1 s -1 measured for the laser-irradiated and the nonirradiated parts of the ITO film deposited at 300~ also contributed to the lowering of the resistivities of the films. The relationship between the Hall mobility andthe substrate temperature (from 18 to 300~ is consistent with those previously reported for sputtered ITO and In203 films [48, 55]. The thermal effects on the Hall mobility were noticed from the narrowing of the narrowing of the difference between the values of mobilities of the laser-irradiated and the nonirradiated parts of the films with increasing temperature. The higher Hall mobility values observed in the laser-irradiated parts of the films compared to the nonirradiated parts were chiefly due to the enhancement of the crystallinity.

!

~

)

50

45 E o

40

=.

35

7.6.3. Optical Properties

30

25

o

16o'26o'36o'46o Temperature (~

Fig. 58. (a) The carrier concentration (n) and (b) the Hall mobility (/z) as a function of temperature for the laser-irradiated and the nonirradiated parts of ITO films, respectively. (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Mural, Appl. Surf. Sci. 177, 114 (2001), 9 2001, Elsevier Science.)

The effects of the substrate temperature on the optical properties of the laser-irradiated and the nonirradiated parts of the films were also manifested. Figure 59a and b shows the optical transmittance curves as a function of wavelength for the laser-irradiated and nonirradiated parts of ITO films deposited at substrate temperatures over the range 18 to 300~ [223]. In comparison, no significant change in transmittance (~90% in the visible region) occurred in the laser-irradiated parts of the films, while the nonirradiated parts showed an increase from 85 to about 90% with increasing substrate temperature. In addition, higher NIR that changed slightly with changes in the substrate temperature was noticed for the laser-irradiated parts

208

ADURODIJA

100

"t

) 80

V

ll) 0r

60 o

m m m

E

40

r

..........

200~

...........

300~

8. OTHER TCO M A T E R I A L S - - Z I N C OXIDE (ZnO) THIN FILMS

t.__

20 ITO (5 wt% Sn-doped) laser-irradiated

0

I

s6o

0

0'00 5'00 20'oo 2 '00" Wavelength (nm)

100

(b) 80 v

(1) 0r

60

ii J~i!

",

~:

,,

ii

i

'i

40

it

.........

"-.

,,:,,

150~

"":72

I

t-t_

F-

o

I!'

1111~

E

200~ 300~

20 ITO (5 wt% Sn-doped) nonirradiated ,

0

plying a widening of the optical bandgap with increasing substrate temperature, as shown in Figure 59b. This feature is similar to what was observed in ITO films deposited by conventional PLD (i.e., without laser irradiation), sputtering, and evaporation methods [80-92, 171]. In the case of the laser-irradiated parts of the films, no apparent change in the absorption edge occurred for substrate temperature over the range 18 to 300~ as shown in Figure 59a. These results suggested that the optical properties of ITO films could be enhanced by laser irradiation of the substrates even on heated substrate by laser irradiation during growth by PLD.

560 ' 0'00 15'00 20'0o' 2doo Wavelength (nm)

Fig. 59. Optical transmittance curves as a function of the wavelength for (a) the laser-irradiated and (b) the nonirradiated parts of ITO films deposited at temperature over the range room temperature to 300~ (Reprinted with permission from E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Murai, Appl. Surf.. Sci. 177, 114 (2001), 9 2001, Elsevier Science.)

of the films, while the nonirradiated parts indicated lower NIR that increases with increasing substrate temperature. Furthermore, the absorption edge of the nonirradiated parts of the ITO films shifted (B-M shift) to shorter wavelength, im-

This section focuses on other TCO thin films that have been prepared by PLD with particular emphasis on ZnO films. ZnO is well known for its high conductivity, piezoelectricity, and high optical transparency; hence it is ideally suited for applications such as transparent electrodes, piezoelectric transducers, tribology, and surface acoustic devices [232-243]. Like ITO, ZnO has been the subject of numerous studies and several techniques, including PLD, have been used to grow ZnO thin films on a variety of substrates [6, 207-209, 234, 244-258]. ZnO has a hexagonal crystal structure of the wurtzite group [244, 259264]. Basically, the microstructure, crystal orientation, and defect density control the properties of ZnO films. The presence of dopants can also affect the properties of ZnO films [264]. Generally ZnO exhibits n-type conduction resulting from oxygen deficiencies and interstitial Zn ions which act as donors in the ZnO crystal lattice. High quality ZnO thin films have been deposited by the PLD technique since 1983 [207-209, 248-258]. More recently, PLD has been used to grow epitaxial ZnO films on sapphire substrate in order to study the nonlinear optical and piezoelectric properties and their use as a buffer layer for epitaxial GaN growth [249, 250, 265-267]. Like ITO films, the relatively low deposition temperature of high quality ZnO films has been the argument in favor of PLD technique. For example Narasimhan et al. have demonstrated that strong c-axis-oriented ZnO films can be deposited at room temperature [251 ]. Different kinds of lasers such as Nd:YAG (~. = 1064 nm) [249], Cu-vapor (k = 510 and 578 nm) [250], and excimers (KrF and ArF) [208, 209, 248, 249] have been used to deposit ZnO films. The pulsed excimer lasers appeared to be a popular choice because of their high excitation energy of the ionized or ejected species in the plume. Apart from the conventional PLD, UV-assisted irradiation during deposition has been investigated [207]. Therefore, in this section we intended to provide an overview on the electrical, optical, and structural properties of ZnO films deposited by PLD as drawn from the works of Suzuki et al. [253, 254] and Hayamizu et al. [252]. ZnO is usually doped with impurity atoms in order to enhance the electrical properties. Aluminum is the most used element to doped ZnO to form Al-doped or ZnO:A1. Gallium (Ga) has

LASERS IN THIN FILMS PROCESSING

10~

[-

:_

la ( i n Vacuum)

"m

1o-

~"

==

:

== == Q.

209

10 2=

i...

. ! 10 =

IE

.

10"

101

I0' N

10 0

0

-

~~

i

_

(at) U,,l

~.,"

10-

-'11

.

.

.

......

A I, O,(0. 75wt~)

~

A IzO,(2w't~i)

.

AI2Oz(7wt%)

133 "

-: I0,,__ I0-1 r

i

-

10 0

100

_

-

I

200

L

....

300

5

r

9

~ .

k,F

_.J

:3:;

-1018..---10-2

SUBSTRATE TEMPERATURE ( ~ Fig. 60. Dependenceof the electrical properties of Al-doped ZnO films deposited in vacuum on glass substrates. (Reprinted with permission from A. Suzuki, T. Matsushita, N. Wada, Y. Sakamoto, and M. Okuda, Japan. J. Appl. Phys. 2 35, L56 (1996), 9 1996,Japan Society of Applied Physics.)

also been found as an efficient dopant in ZnO films, thus forming Ga-doped ZnO or ZnO:Ga. The effects of the A1 and Ga dopant elements in ZnO films will be discussed in detail in subsequent paragraphs. Prior to this, the effect of oxygen pressure on the properties of undoped ZnO films deposited at substrate temperature over the range 25-300~ has been reported by Narasimhan et al. [251]. They observed that optimal oxygen pressure of around 1 x 10 -2 Torr yielded the lowest resistivity of (2-3) x 10 -3 f2cm for the ZnO films. This oxygen pressure agreed with that used to produce high quality ITO films as discussed in previous sections of this chapter. The dependence of the resistivity, carder concentration, and Hall mobility on the substrate temperature for ZnO films containing different A1 doping contents is shown in Figure 60 [254]. These films were deposited on glass substrates using an ArF (193 nm) excimer laser with a fluence of 1 J cm -2 and a pulse rate of 10 Hz in a vacuum of 1 x 10 -8 Torr. The optimum doping efficiency was achieved at 2 wt%, similar to other deposition techniques like sputtering [254]. The lowest resistivities obtained at room temperature and 300~ were 5.6 x 10 -4 and 1.4 x 10 -4 ~ cm, respectively. Apparently, the low resistivity resulted from the higher carrier concentration and mobility compared to 0.75 and 7 wt% A1 doping content. Figure 61

shows the optical transmittance of ZnO:A1 films deposited at 300~ indicating high transmittance to the visible light [254]. The 2 wt% Al-doped ZnO film displayed strikingly high near infrared reflectance, thus confirming the improvement in the electrical properties compared with the 0.75 and 7 wt% A1 doping content. Analyzing the microstructure of the films using XRD, Suzuki et al. noticed that crystalline film could be produced at substrate temperatures over the range 25 to 300~ Another salient feature was that the surface of the films deposited at 300~ was very flat. The same group (Suzuki et al.) also reported interesting resuits on the doping effect of Ga on the properties of ZnO films. The dependence of the resistivity, carrier concentration, and Hall mobility on the substrate temperature for ZnO films containing different Ga doping content is shown in Figure 62 [253]. All the films were deposited on glass substrates. The deposition conditions are similar to those used for growing ZnO:A1 films as described above. The best resistivities of 2.1 x 10 -4 and 2.9 x 10 -4 f2 cm were obtained for the 7 wt% Ga doped ZnO films at 200 and 300~ respectively. The low resistivity was also due to the high carrier concentration and Hall mobility. Table III shows a compilation of the electrical properties 6f ZnO films deposited by various techniques at different de-

210

ADURODIJA 100

T ~un=300*C (in Vacuum)

o~ v

80

m 0 Z < Fk-

%

"'~"~"~.

60

.•.L

l=03(7wt~) (d, lT3na)

% % %.,=

"",,

40

. f , A I ~ O s (0.75wX % ) ~

(d-18Tnm)

CO

z .p-. t-'-4

r

~j

Fig. 65. Schematic structure of an 9 with an IT9 anode deposited by PLD. IT9 film, deposited at room temperature in oxygen pressure of 1 x 10-2 Torr, is used in the device. (Reprinted with permission from H. Kim, C. M. Gilmore, A. Piqur, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, J. Appl. Phys. 86, 6451 (1999), 9 1996, American Institute of Physics.)

FWHM=I.9'

Z LLI

I'--" Z 1."-4

12

14

1'6.... (8 2"0~ 0 (deg)

2"2-

:)4

Fig. 64. (a) XRD spectra of ZnO films grown on glass substrates. (b) X-ray rocking curveof the (002) peak. (Reprinted with permissionfrom S. Hayamizu, H. Tabata, H. Tanaka, and T. Kawai, J. Appl. Phys. 80 (1996), 9 1996, American Institute of Physics.)

plane. The rocking curve at FWHM was found to be 1.9 ~ and the fluctuation of the c-axis of the ZnO film was very little. The effects of UV irradiation on the electrical, structural, and optical properties of ZnO films during deposition by sputtering and PLD have been studied [207-209]. Ithas been found that UV irradiation during sputter deposition of ZnO films in the presence of extra Zn atoms produced some improvements in the optoelectronic properties via improvement in the crystallinity of the films. On the other hand, Craciun et al. [207] have obtained highly textured ZnO films on Si (100) and sapphire substrates by in situ UV-assisted PLD. Using this method, they were able to grow highly textured ZnO films on Si substrates at low temperature of 100~ On the sapphire substrates epitaxial films with [001 ]ZnOII[001 ]sap and [ 100]ZnO I1[110]sap were obtained at 400~ The FWHM of the rocking curve of the (002) diffraction peak was found to be 0.168 ~. These experimental data have shown that PLD is an effective deposition tool for producing high quality ZnO films.

9. APPLICATIONS OF PLD ITO FILMS As enumerated in Section 1.1, a number of applications require TCO (IT9 film in the form of a transparent conducting electrodes. Some of the these devices, including solar cells, liquid

crystal flat panel displays, and organic light emitting diodes (9 are very sensitive to high-temperature (> 200~ treatment. Hence, low-temperature deposition techniques of high quality films are desirable. In solar cells the commonly used technique for depositing IT9 films include sputtering and spray pyrolysis. IT9 films deposited by PLD have been used to fabricate ITO/InP solar cells by Jia et al. [85]. The IT9 films were deposited at room temperature and 310~ The results of their studies have shown that ITO/InP cells fabricated from IT9 films deposited at room temperature and 310~ yielded open circuit voltages of 660 and 610 mV and short circuit currents of "~23.5 and ~23 mA, respectively. The improvement in the device affected mainly the open circuit voltage, implying a preservation of the junction properties via low-temperature deposition. Higher spectra response and acceptable dark current characteristics were also confirmed from the device fabricated from IT9 deposited at room temperature [85]. IT9 films deposited by PLD have also been used to fabricate 9 devices [88, 89]. IT9 film is usually chosen as an anode to these devices, because of the high efficiency for hole injection into the organic materials. An illustration of an 9 structure is shown in Figure 65 [88, 89]. The device consisted of a hole transport layer (~50 nm thick) of N , N tdyphenyl-N,N-bis(3-methyl)-l,lt-diphenyl-4J-diamine and an electron transport layer (ETL/EML, 70 nm thick) of tris(4methyl-8-hydroxyquinolinolato)aliminum (III) (Almq3). An alloy of Mg:Ag (ratio = 12 : 1 and thickness of 100 nm) was used as the cathode contact on the ETL layer. The device had an active area of ~ 4 m m 2. The current-voltage-luminance characteristic of the device measured in nitrogen atmosphere is shown in Figure 66 [88, 89]. The current-voltage and luminance-

L A S E R S IN T H I N F I L M S P R O C E S S I N G 1800 - ,

,

' !

-',

".

1600

[] cu, nt

14oo

O

i 9

,

9 ,

,

,,

.~ 8000

10. CONCLUSION

El

(a)

7000

O Luminance

[3 O

6000

1,2o(i 5000 ~'-"

xooo v

..., e-

Q

800

8 c:

o,m,

E

ro 4(10

..J - 1ooo

2OO

-~

-20

- i..... "

-f

-15

-10

9

-i"=-"

-,

-5

"

"

0

,

-

w

5

9

,

10

9

15

20

Voltage (V) 7000

1 ./

(b)

6000

./

/ O"

v

lID 3O00 r O

~00

_J 1000

O

o'

O

,/ I

0

.

I

the films. ITO films d e p o s i t e d at substrate t e m p e r a t u r e s b e l o w 100~ even t h o u g h they w e r e a m o r p h o u s indicated low resistivity. Crystalline films w e r e only p r o d u c e d at substrate temperatures a b o v e 100~ and the films exhibited h i g h e r conductivity. F u r t h e r m o r e , irradiating the surfaces of the g r o w i n g I T O

at t e m p e r a t u r e s as low as 2 0 0 ~ T h e e n h a n c e m e n t in the electrical properties was primarily due to p h o t o c h e m i c a l and phot o t h e r m a l i n d u c e d crystallization during the laser irradiation of the g r o w i n g films. A p p l i c a t i o n s of the laser d e p o s i t e d ITO films at r o o m t e m p e r a t u r e to solar cells and O L E D device fabrications have s h o w n s o m e e n c o u r a g i n g p e r f o r m a n c e s .

.../

0

"~

In conclusion, experimental investigations of PLD for TCO films depositions have shown that high quality films can be produced even at room temperature. A direct relation between the quality of the In203, ITO, and ZnO films and experimental conditions (laser energy density, substrate distance, background oxygen pressure, substrate temperature, and growth rates) was established. The experimental studies also showed a good qualitative agreement with the theoretical evaluations. Compared to other deposition techniques it is observed that low resistivity and highly transparent ITO and ZnO films could be prepared at low substrate temperature by PLD. The qualities of the films were highly susceptible to the changes in the oxygen pressure and the substrate temperature. In particular, oxygen pressure is found to exert significant influence on the overall properties of

films by laser e n e r g y pulses during the P L D p r o c e s s the microstructural and electro-optical properties of the films w e r e i mproved. Electrical resistivity b e l o w 10 - 4 f2 c m was attained

ff

c Ig

213

Acknowledgments

.

I

9

I

9

I

9

i

9

i

i

I

9

l

.

200 400 600 800 1000 1200 1400 1600 1800

Current (A/m~) Fig. 66. (a) Current-voltage-luminance (1-V-L) and (b) luminance--current (L--l) characteristics of a heterostructure device with PLD ITO film as the hole injecting layer to TPD layer. ITO film, grown at room temperature in oxygen pressure of 1 • 10-2 Torr, was used in the device. (Reprinted with permission from H. Kim, C. M. Gilmore, A. Piqur, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, J. Appl. Phys. 86, 6451 (1999), 9 1999, American Institute of Physics.)

voltage curves showed a typical diode characteristic with the power output observed only in the forward bias. In addition, the current and luminance data superimpose reasonably well, in agreement with what has been achieved with commercial ITO films. The external quantum efficiency for such a heterostructure device was reported as rlext - - 1 . 5 % at 100 A m -2 compared to 1.5-2.5% for commercial ITO films [287-289]. The results indicated that I T O films d e p o s i t e d at r o o m t e m p e r a t u r e by P L D are of g o o d quality and also p r e s e n t the potential for i m p r o v e m e n t of the p e r f o r m a n c e s of these devices.

The author acknowledges the immense contributions of Drs. M. Motoyama, T. Ishihara, H. Izumi, H. Yoshioka, and K. Murai to this work. The results of some of the works reported in this chapter were partly supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan.

REFERENCES 1. K. B~ideker,Ann. Phys. Leizpzig 22, 749 (1907). 2. C.C. Wu, C. I. Wu, J. C. Sturm, and A. Kahn, Appl. Phys. Lett. 70, 1348 (1997). 3. ELi, H. Tang, and J. Shinar, Appl. Phys. Lett. 70, 2741 (1997). 4. S.A. Van Slyke, C. H. Chen, and C. W Tang, Appl. Phys. Lett. 69, 2160 (1996). 5. K.L. Chopra, S. Major, and D. K. Pandya, Thin Solid Films 102, 1 (1983). 6. I. Hamberg and C. G. Granqvist, J. Appl. Phys. 60, R123 (1986). 7. E. Ritter, "Progress in Electro-Optics" (E. Camatini, Ed.). Plenum, New York, 1975. 8. J.L. Vossen, Phys. Thin Films 9, 1 (1977). 9. J.C. Manifacier, Thin Solid Films 90, 297 (1982). 10. Z.M. Jarzebski, Phys. Status Solidi A 71, 13 (1982). 11. G. Haacke, Annu. Rev. Mater Sci. 7, 73 (1977). 12. G. Rupprecht, Z. Phys. 139, 504 (1954). 13. N. Rucher and K. J. Becker, Thin Solid Films 53, 163 (1978). 14. P. Nath and R. E Bunshah, Thin Solid Films 69, 63 (1980).

214

ADURODIJA

15. P. Nath, R. E Bunshah, B. M. Basol, and O. M. Staffsud, Thin Solid Films 72, 463 (1980). 16. Z. Ovadyahu, B. Ovryn, and H. W. Kraner, J. Electrochem. Soc. 130, 917 (1983). 17. P. Manivannan and A Subrahmanyam, J. Phys. D 26, 1510 (1993). 18. J.L. Yao, S. Hao, and J. Wilkinson, Thin Solid Films 189, 227 (1990). 19. K. Korobov, M. Leibovitch, and Y. Shapira, Appl. Phys. Lett. 65, 2290 (1994). 20. M. Abbas, I. A. Qazi, A. Samina, M. Masaood, A. Majeed, and A. ul Haq, J. Vac. Sci. Technol. A 13, 152 (1995). 21. P. Thilakan and J. Kumar, Thin Solid Films 292, 50 (1997). 22. S.-W. Jan and S.-C. Lee, J. Electrochem. Soc. 134, 2061 (1987). 23. C.A. Pan and T. P. Ma, Appl. Phys. Lett. 37, 163 (1980). 24. Z. Ovadyahu and H. Wiesmann, J. Appl. Phys. 52 (1981). 25. I. Hamberg, A. Hjortsberg, and C. G. Granvist, Appl. Phys. Lett. 40, 362 (1982). 26. M. Penza, S. Cozzi, M. A. Tagliente, L. Mirenghi, C. Matucci, and A. Quirini, Thin Solid Films 349, 71 (1999). 27. I.A. Rauf, J. Mater Sci. Lett. 12, 1902 (1993). 28. I.A. Rauf, J. Appl. Phys. 79, 4057 (1995). 29. I.A. Rauf, Mater Len. 23, 73 (1995). 30. H. Haitjema and J. J. Ph. Elich, Thin Solid Films 205, 93 (1991). 31. C. Goebbert, R. Nonniger, M. A. Aegerter, and H. Schmidt, Thin Solid Films 351, 79 (1999). 32. H. Bisht, H.-T. Eun, A. Mehrtens, and M. A. Aegerter, Thin Solid Films 351,109 (1999). 33. Ph. Parent, H. Dexpert, G. Tourillon, and J.-M. Grimal, J. Electrochem. Soc. 139, 282 (1992). 34. I. Baia, M. Quintela, L. Mendes, E Nunes, and R. Martins, Thin Solid Films 337, 171 (1999). 35. L.J. Meng, A. Maqrarico, and R. Martins, Vacuum 46, 673 (1995). 36. T. Karasawa and Y. Miyata, Thin Solid Films 223, 135 (1993). 37. L. Davis, Thin Solid Films 236, 1 (1993). 38. S. Ishibashi, Y. Higuchi, Y. Ota, and K. Nakamura, J. Vac. Sci. Technol. A 8, 1399 (1990). 39. M. Higuchi, S. Uekusa, R. Nakano, and K. Yokogawa, J. Appl. Phys. 74, 6710 (1993). 40. B.S. Chiou and S. T. Hsieh, Thin Solid Films 229, 146 (1993). 41. S. Ray, R. Benerjee, N. Basu, A. K. Batabyal, and A. K. Barua, J. Appl. Phys. 54, 3497 (1983). 42. S.B. Lee, J. C. Pincenti, A. Cocco, and D. L. Naylor, J. Vac. Sci. Technol. A 11, 2742 (1993). 43. S. Kulkarni and M. Bayard, J. Vac. Sci. Technol. A 9, 1193 (1991). 44. E K. Song, Y. Shigesato, I. Yasui, C. W. Ow-Yang, and D. C. Paine, Japan. J. Appl. Phys. 37, 1870 (1998). 45. Y. Shigesato and D. C. Paine, Thin Solid Films 238, 44 (1994). 46. E K. Song, H. Akao, M. Kamei, Y. Shigesato, and I. Yasui, Japan. J. Appl. Phys. 38, 5224 (1999). 47. K. Carl, H. Schmitt, and I. Friedrich, Thin Solid Films 295, 151 (1997). 48. J. C. C. Fan, E J. Bachner, and G. H. Foley, Appl. Phys. Lett. 31,773 (1977). 49. M. Buchanan, J. B. Webb, and D. E Williams, Thin Solid Films 80, 373 (1981). 50. K. Ishibashi, K. Watanabe, T. Sakarai, O. Okada, and N. Hosokawa, J. Non-Cryst. Solids 218, 354 (1997). 51. R.W. Moss, D. H. Lee, K. D. Voung, R. A. Condrate, Sr., X. W. Wang, M. DeMarco, and J. Stuckey, J. Non-Cryst. Solids 218, 105 (1997). 52. J.C.C. Fan and E J. Bachner, J. Electrochem. Soc. 122, 1719 (1975). 53. L.-J. Meng and M. P. dos Santos, Thin Solid Films 289, 65 (1996). 54. H.M. Zahirul Alam, P. K. Saha, T. Hata, and K. Sasaki, Thin Solid Films 352, 133 (1999). 55. H. Nanto, T. Minami, S. Orito, and S. Takata, J. Appl. Phys. 63, 2711 (1988). 56. R. Aitchison, Austral. J. Appl. Sci. 5, 10 (1954). 57. J.A. Thornton and V. L. Hedgcoth, J. Vac. Sci. Technol. 13, 117 (1976). 58. S. Yoshida, Appl. Opt. 17, 145 (1978). 59. R.R. Mehta and S. E Vogel, J. Electrochem. Soc. 119, 752 (1972).

60. Y. Suzuki, E Niino, and K. Katoh, J. Non-Cryst. Solids 218, 30 (1997). 61. Y. Murayama, J. Vac. Sci. Technol. 12, 818 (1975). 62. R. E Howson, J. N. Avaritsiotis, M. I. Ridge, and C. A. Bishop, Thin Solid Films 58, 379 (1978). 63. T. Ishida, H. Kobayashi, and Y. Nakato, J. Appl. Phys. 73, 4344 (1993). 64. T. Maruyama and Kitamura, Japan. J. Appl. Phys. 2 28, L1096 (1989). 65. M. Privman, J. Berger, and D. S. Tannhauser, Thin Solid Films 102, 117 (1983). 66. J.-W. Bae, S.-W. Lee, K.-H. Song, J.-I. Park, K.-J. Park, Y.-W. Ko, and G.-Y. Yeom, Japan. J. Appl. Phys. 1 38, 2917 (1999). 67. T. Maruyama and K. Fukui, J. Appl. Phys. 70, 3848 (1991). 68. T. Maruyama and K. Fukui, Thin Solid Films 203, 297 (1991). 69. R.G. Gordon, Mater Res. Syrup. Proc. 426, 419 (1996). 70. Y. Djaoued, V. H. Phong, S. Badilescu, E V. Ashrit, E E. Girouard, and V.-V. Truong, Thin Solid Films 293, 108 (1997). 71. A. Gurlo, M. Ivanovskaya, A. Pfau, U. Weimar, and W. G6pel, Thin Solid Films 307, 288 (1997). 72. Y. Takahashi, S. Okada, R. B. H. Tahar, K. Nakano, T. Ban, and Y. Ohya, J. Non-Cryst. Solids 218, 129 (1997). 73. R.B.H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, J. Appl. Phys. 83,2631 (1998). 74. G. Yi and M. Sayer, Ceram. Bull. 70, 1173 (1991). 75. H. Dislich, J. Non-Cryst. Solids 57, 371 (1988). 76. D.M. Mattox, Thin Solid Films 204, 25 (1991). 77. W. Quin, R. E Howson, M. A. Akizuki, J. Matsuo, G. H. Takaoka, and I. Yamada, "Extended Abstracts of the 44th Spring Meeting of the Japan Society of Appl. Phys., Vol. 2," 1997, p. 466. 78. R. E Howson, J. Matsuo, and I. Yamada, "Extended Abstracts of the 44th Spring Meeting of the Japan Society of Appl. Phys.," 1997, p. 463. 79. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, Japan. J. Appl. Phys. Lett. 2 39, L377 (2000). 80. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, M. Motoyama, and K. Murai, J. Vac. Sci. Technol. A 18, 814 (2000). 81. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, K. Yamada, H. Matsui, and M. Motoyama, Thin Solid Films 350, 79 (1999). 82. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, H. Matsui, and M. Motoyama, Japan. J. Appl. Phys. 1 38, 2710 (1999). 83. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, H. Matsui, and M. Motoyama, Appl. Phys. Lett. 74, 3059 (1999). 84. E. J. Tarsa, J. H. English, and J. S. Speck, Appl. Phys. Lett. 62, 2332 (1993). 85. Q.X. Jia, J. E Zheng, H. S. Kwok, and W. A. Anderson, Thin Solid Films 258, 260 (1995). 86. X. W. Sun, H. C. Huang, and H. S. Kwok, Appl. Phys. Lett. 68, 2663 (1996). 87. H.S. Kwok, X. W. Sun, and D. H. Kim, Thin Sold Films 335, 229 (1998). 88. H. Kim, C. M. Gilmore, A. Piqu6, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, J. Appl. Phys. 86, 6451 (1999). 89. H. Kim, A. Piqu6, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, Appl. Phys. Lett. 74, 3444 (1999). 90. E Hanus, A. Jadin, and L. D. Laude, Appl. Surf. Sci. 96-98, 807 (1996). 91. Y. Wu, C. H. M. Maree, R. E Haglund, Jr., J. D. Hamilton, M. A. Morales Paliza, M. B. Huang, L. C. Feldman, and R. A. Weller, J. Appl. Phys. 86, 991 (1999). 92. J. E Zheng and H. S. Kwok, Thin Solid Films 232, 99 (1993). 93. A.L. Dawar and J. C. Joshi, J. Mater Sci. 19, 1 (1984). 94. H. Kawazoe and K. Ueda, J. Amer Ceram. Soc. 82, 3330 (1999). 95. J.C.C. Fan and J. B. Goodenough, J. Appl. Phys. 48, 3524 (1977). 96. V.M. Vainshtein and V. I. Fistul, Soy. Phys. Semicond. l, 104 (1967). 97. H.K. Mtiller, Phys. Status Solidi 27, 723 (1968). 98. S.J. Wen, G. Campet, J. Portier, G. Couturier, and B. Goodenough, Mater Sci. Eng. B 14, 115 (1992). 99. T. Maruyama and T. Tago, Appl. Phys. Lett. 64, 1395 (1994). 100. S.J. Wen, G. Couturier, G. Campet, J. Portier, and J. Claverie, Phys. Status Solidi A 130, 407 (1992). 101. S. Takaki, K. Matsumoto, and K. Suzuki, Appl. Surf. Sci. 33/34, 919 (1988).

LASERS IN THIN FILMS PROCESSING 102. J. C. Manifacier, L. Szepessy, J. E Bresse, M. Perotin, and R. Stuck, Mater Res. Bull. 14, 163 (1979). 103. V.A. Johnson and K. Lark-Horovitz, Phys. Rev. 71,374 (1947). 104. H. K6stlin, R. Jost, and W. Rems, Phys. Status Solidi A 29, 87 (1975). 105. G. Frank and H. Ktistlin, Appl. Phys. A 27, 197 (1982). 106. E T. J. Smith and S. L. Lyu, J. Electrochem. Soc. 128, 2388 (1981). 107. J.H. de Wit, J. Solid State Chem. 20, 143 (1977). 108. E.C. Subbarao, E H. Sutter, and J. Hirizo, J. Amer. Ceram. Soc. 48, 443 (1965). 109. N. Nadaud, N. Lequeux, M. Nanot, J. Jove, and T. Roisnel, J. Solid State Chem. 135, 140 (1998). 110. N. Yamada, I. Yasui, Y. Shigesato, H. Li, Y. Ujihira, and K. Nomura, Japan. J. Appl. Phys. 1 38, 2856 (1999). 111. D.B. Chrisey and G. K. Hubler, Eds., "Pulsed Laser Deposition of Thin Films." Wiley, New York, 1994. 112. S. M. Green, A. Piqu6, K. S. Harshavardhan, and J. S. Bernstein, in "Pulsed Laser Deposition of Thin Films" (D. B. Chrisey and G. K. Hubler, Eds.), p. 24. Wiley, New York, 1994. 113. A. Yariv, "Introduction to Optical Electronics," 2nd ed. Holt, Riehart & Winston, New York, 1976. 114. M. Stehle, J. Non-Cryst. Solids 218, 218 (1997). 115. H. Hosono, M. Kurita, and H. Kawazoe, Thin Solid Films 351, 137 (1999). 116. J.T. Cheung, in "Pulsed Laser Deposition of Thin Films" (D. B. Chrisey and G. K. Hubler, Eds.), p. 4. Wiley, New York, 1994. 117. R. E van Ingen, R. H. J. Fastenau, and E. J. Mittemeijer, J. Appl. Phys. 76, 1871 (1994). 118. H.U. Kreds, S. Fahler, and O. Bremert, Appl. Su~ Sci. 86, 86 (1995). 119. E Antoni, E. Fogarassy, C. Fuchs, J. J. Grob, B. Prevot, and J. E Stoquert, Appl. Phys. Lett. 67, 2072 (1995). 120. E. Sobol, "Phase Transformations and Ablation in Laser Treated Solids." Wiley, New York, 1995. 121. E. van der Riet, J. C. S. Kools, and J. Dieleman, J. Appl. Phys. 73, 8290 (1993). 122. D. B. Chrisey, J. S. Horowitz, and K. S. Grabowski, Mater Res. Soc. Symp. Proc. 191, 25 (1990). 123. T. Yano, T. Oosie, M. Yoneda, and M. Katsumura, J. Mater Sci. Lett. 15, 1994 (1993). 124. D. C. Paine, T. Whitson, D. Janiac, R. Beresford, C. Ow-Yang, and B. Lewis, J. Appl. Phys. 85, 8445 (1999). 125. T.J. Vink, W. Walrave, J. L. C. Daams, P. C. Baarslag, and J. E. A. van der Meerakker, Thin Solid Films 266, 145 (1995). 126. C.H. Yi, Y. Shigesato, I. Yasui, and S Takaki, Japan. J. Appl. Phys. 2 34, L244 (1995). 127. H.P. Klug and L. E. Alexander, "X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials," 2nd ed. Wiley, New York, 1974. 128. S. Muranaka, Japan. J. Appl. Phys. 2 30, L2062 (1991). 129. S. Muranaka, Y. Bando, and T. Takada, Thin Solid Films 25, 355 (1987). 130. S.R. Foltyn, in "Pulsed Laser Deposition of Thin Films" (D. B. Chrisey and G. K. Hubler, Eds.), p. 89. Wiley, New York, 1994. 131. L.-C. Chen, in "Pulsed Laser Deposition of Thin Films" (D. B. Chrisey and G. K. Hubler, Eds.), p. 167. Wiley, New York, 1994. 132. D.B. Geohegan, Mater Res. Soc. Symp. Proc. 201,557 (1991). 133. A. Gupta, in "Pulsed Laser Deposition of Thin Films," p. 265. Wiley, New York, 1994. 134. H. S. Kim and H. S. Kwok, Appl. Phys. Lett. 61, 2234 (1992). 135. R. E Wood, K. R. Chen, J. N. Leboeuf, A. A. Puretsky, and D. B. Geohegan, Phys. Rev. Lett. 79, 1571 (1997). 136. J.A. Venebles, G. D. T. Spiller, and M. Hanbucken, Rep. Prog. Phys. 47, 399 (1984). 137. B. Lewis and J. C. Anderson, "Nucleation and Growth of Thin Films." Academic Press, New York, 1978. 138. L. Mao, R. E. Benoit, and J. Proscia, Mater Res. Soc. Symp. Proc. 317, 191 (1994). 139. Q.Y. Ying, H. S. Kim, D. T. Shaw, and H. S. Kwok, Paal. Phys. Lett. 55, 1041 (1989). 140. H.S. Kwok and Q. Y. Ying, Physica C 177, 122 (1991).

215

141. K. Saxena, S. E Singh, R. Thangaraj, and O. E Agnihotri, Thin Solid Films 117, 95 (1984). 142. H. Hoffman, J. Pickl, M. Schmidt, and D. Krause, Appl. Phys. 16, 239 (1978). 143. K. Ellmer, K. Diesner, R. Wendt, and S. Fiechter, in "Polycrystalline Semiconductors IV--Physics, Chemistry and Technology" (S. Pissini, H. E Strunk, and J. H. Werner, Eds.), p. 541. Trans Tech, Zug, Switzerland. 144. Y. Shigesato and D. C. Paine, Appl. Phys. Lett. 62, 1268 (1993). 145. E. Burstein, Phys. Rev. 93, 632 (1952). 146. J.A. Thornton and W. D. Hoffman, Thin Solid Films 171 (1989). 147. T. Oyama. N. Hashimoto, J. Shimizu, Y. Akao, H. Kojima, K. Aikawa, and K. Suzuki, J. Vac. Sci. Technol. A 10, 1682 (1992). 148. M. Kamei, Y. Shigesato, I. Yasui, N. Taga, and S. Takaki, J. Non-Cryst. Solids 218, 267 (1997). 149. H. Izumi, K. Ohata, T. Sawada, T. Morishita, and S. Tanaka, Japan. J. Appl. Phys. 30, 1956 (1991). 150. E. Terzini, G. Nobile, S. Loreti, C. Minarini, T. Ploichetti, and E Thilakan, Japan. J. Appl. Phys. 38, 3448 (1999). 151. P.K. Song, Y. Shigesato, M. Kamei, and I. Yasui, Japan. J. Appl. Phys. 38, 2921 (1999). 152. R.W.G. Wyckoff, in "Crystal Structures," 2nd ed., Vol. 2, p. 41 Krieger, Malabar, FL, 1986. 153. JCPDS Card No. 06-0416. 154. W.-E Wu, B.-S. Chiou, and S.-T. Hsieh, Semicond. Sci. Technol. 9, 1242 (1994). 155. W.-E Wu and B.-S. Chiou, Thin Solid Films 293, 244 (1997). 156. J.A. Thornton, in "Annual Review of Materials Science" (R. A. Huggins, R. H. Bube, and R. W. Roberts, Eds.), p. 239. Annual Rev. Inc., Palo Alto, CA, 1977. 157. J. Michler, M. Mermoux, Y. von Kaenel, A. Haouni, G. Lucazeau, and E. Blank, Thin Solid Films 357, 189 (1999). 158. T. C. Huang, Adv. X-rayAnal. 33, 91 (1990). 159. V. Craciun, I. W. Boyd, E Andreazza, and C. Boulmer-Leborgne, J. Appl. Phys. 83, 1770 (1997). 160. E. Hasegawa, A. Ishtani, K. Akimoto, M. Tsukiji, and N. Ohta, J. Electrochem. Soc. 142, 273 (1995). 161. R. Feidenhans'l, Surf. Sci. Rep. 10, 105 (1989). 162. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, J. Mater. Sci.: Mater Electronics 12, 57 (2001). 163. C.V.R. Vasant Kumar and A. Mansingh, J. Appl. Phys. 65, 1270 (1989). 164. G. Yi, Z. Wu, and M. Sayer, J. Appl. Phys. 64, 2717 (1989). 165. K. Sreenivas, M. Sayer, T. Laursen, J. L. Whitton, R. Pascual, D. J. Johnson, D. T. Amm, G. I. Sproule, D. E Mitchell, M. J. Graham, S. C. Gujrathi, and K. Oxorn, Mater Res. Syrup. Proc. 200, 255 (1990). 166. R. Ramesh, A. Inam, W. K. Chan, E Tillerot, B. Wilkens, C. C. Chang, T. Sands, J. M. Tarascon, and V. G. Keramidas, Appl. Phys. Lett. 59, 3542 (1991). 167. Y. A. Boikov, S. K. Esayan, Z. G. Ivanov, G. Brorsson, T. Cleaeson, J. Lee, and S. Safari, Appl. Phys. Lett. 61,528 (1992). 168. M. Kamei, T. Yagami, S. Takaki, and Y. Shigesato, Appl. Phys. Lett. 64, 2712 (1994). 169. M. Kamei, Y. Shigesato, S. Takaki, Y. Hayashi, M. Sasaki, and T. E. Haynes, Appl. Phys. Lett. 65, 546 (1994). 170. J. R. Bellingham, W. A. Phillips, and C. J. Adkins, J. Phys. Condens. Matter 2, 6207 (1990). 171. J. E Zheng and H. S. Kwok, Appl. Phys. Lett. 63, 1 (1993). 172. R. Latz, K. Michael, and M. Scherer, Japan. J. Appl. Phys. 30, L149 (1991). 173. K. L Narasimhan, S. P Pai, V. R. Palkar, and R. Pinto, Thin Solid Films 295, 104 (1997). 174. S. Noguchi and H. Sakata, J. Phys. 13, 1129 (1980). 175. H. Daves, Proc. IEE 101,209 (1954). 176. S.A. Agnihotry, J. Phys. D 18, 2087 (1985). 177. R.A. Smith, "Wave Mechanics of Crystalline Solids." Chapman and Hall, London, 1961. 178. T.S. Moss, Proc. Phys. Soc. London Sect. B 67, 775 (1954). 179. C.H.L. Weijtens, J. Electrochem. Soc. 138, 3432 (1991).

216 180. 181. 182. 183.

ADURODIJA

M.D. Stoev, J. Touskova, and J. Tousek, Thin Solid Films 299, 67 (1997). T.L. Barr and Y. L. Liu, J. Phys. Chem. Solids 50, 657 (1989). Y. Shigesato, S. Takaki, and T. Haranoh, J. Appl. Phys. 71, 1 (1992). H. Yoshioka, E O. Adurodija, H. Izumi, T. Ishihara, and M. Motoyama, Electrochem. Solid State Lett. 3, 540 (2000). 184. C.D. Wagner, W. M. Riggs, L. E. Davis, J. E Moulder, and G. E. Mullenberg, "Handbook of X-ray Photoelectron Spectroscopy." Perkin-Elmer, Eden Prairie, MN, 1979. 185. S. Doniach and M. Sunjic, J. Phys. C 3, 285 (1970). 186. I. Yamada, Mater Sci. Forum 264, 239 (1997). 187. G. Riesse and S. Weissmentel, Thin Solid Films 355-356, 105 (1999). 188. A. Luches, in "Physical Processes in Laser-Materials Interactions" (M. Bertolotti, Ed.), p. 443. Plenum, New York, 1981. 189. K. Kanaya and S. Okayama, J. Phys. D 5, 43 (1972). 190. L. Katz and A. S. Penfold, Rev. Mod. Phys. 24, 28 (1952). 191. P.G. Merli, Optik 56, 205 (1980). 192. R.N. Brickell, N. C. Giles, and J. E Schetzina, AppL Phys. Lett. 49, 1095 (1986). 193. R.L. Abber, in "Handbook of Thin-Film Deposition Processes and Technique" (K. K. Schuegraf, Ed.), p. 270. Noyes, Park Ridge, NJ, 1988. 194. S.A. Hussein, N. H. Karam, S. M. Bedair, A. A. Fahmy, and N. A. E1Masry, Mater. Res. Soc. Symp. Proc. 129, 165 (1988). 195. S. Otsubo, T. Minamikawa, Y. Yonezawa, T. Maeda, A. Morimoto, and T. Shimizu, Japan. J. Appl. Phys. 28, 2211 (1989). 196. T. Minamikawa, Y. Yonezawa, S. Otsubo, Y. Yonewawa, A. Morimoto, and T. Shimizu, in "Advances in Supercoductivity II" (T. Ishiguro and K. Kajimura, Eds.), p. 857. Springer-Verlag, Tokyo, 1990. 197. M. Kanai, K. Horiuchi, T. Kawai, and S. Kawai, Appl. Phys. Lett. 57, 2716 (1990). 198. R. C. Estler, N. S. Nogar, R. E. Muenchausen, R. C. Dye, C. Flamme, J. A. Martin, A. Garcia, and S. Fotlyn, Mater Len. 9, 342 (1990). 199. A. Morimoto, S. Otsubo, T. Shimizu, T. Minamikawa, and Y. Yonezawa, Mater Res. Soc. Symp. Proc. 275, 371 (1990). 200. H. Tabata, T. Kawai, and S. KawaJ, Appl. Phys. Lett. 58, 1443 (1991). 201. H. Tabata, T. Kawai, S. Kawai, O. Murata, J. Fujioka, and S. Minakata, Appl. Phys. Lett. 59, 2354 (1991). 202. H. Tabata, O. Murata, T. Kawai, S. Kawai, and M. Okuyama, Japan. J. Appl. Phys. 31, 2968 (1992). 203. A. Ito, A. Machida, and M. Obara, Japan. J. Appl. Phys. 2 36, L805 (1997). 204. P.E. Dyer, A. Issa, P. H. Key, and P. Monk, Supercond. Sci. Technol. 3, 472 (1990). 205. K.H. Wu, C. L. Lee, J. Y. Juang, T. M. Uen, and Y. S. Gou, Appl. Phys. Len. 58, 1089 (1991). 206. T. Sz6r6nyi, Z. K~intor, and L. D. Laude, Appl. Surf. Sci. 86, 219 (1995). 207. V. Craciun, R. K. Singh, J. Perriere, J. Spear, and D. Craciun, J. Electrochem. Soc. 147, 1077 (2000). 208. V. Craciun, J. Elders, J. G. E. Gardeniers, and I. W. Boyd, Appl. Phys. Len. 65, 2963 (1994). 209. V. Craciun, J. Elders, J. G. E. Gardeniers, J. Geretovsky, and I. W. Boyd, Thin Solid Films 259 (1995). 210. H. Hosono, M. Kurita, and H. Kawazoe, Japan. J. Appl. Phys. 2 37, L1119 (1998). 211. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, Mater. Sci. Len. 19, 1719 (2000). 212. E O. Adurodija, H. Izumi, T. Ishihara, H. Yoshioka, and M. Motoyama, J. Appl. Phys. 88, 4175 (2000). 213. H. Tabata, O. Murata, T. Kawai, S. Kawai, and M. Okuyama, Japan. J. Appl. Phys. 31, L2968 (1998). 214. E. Gerlach and Rautenberg, Phys. Status Solidi B 86, 479 (1978). 215. R.B.H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, J. Appl. Phys. 82, 865 (1997). 216. C. Kittel, "Introduction to Solid State Physics," 5th ed., Chap. 6. Maruzen, Tokyo, 1985. 217. C. Erginsoy, Phys. Rev. 79, 1013 (1950). 218. E. Conwell and V. E Weiskopf, Phys. Rev. 77, 388 (1950). 219. R.B. Dingle, Philos. Mag. 46, 831 (1955).

220. R. Clanget, Appl. Phys. 2, 247 (1973). 221. Fujisawa, T. Nishino, and Y. Hamakawa, Japan. J. Appl. Phys. 27, 552 (1988). 222. M. Mizuhashi, Thin Solid Films 70, 91 (1980). 223. E O. Adurodija, H. Izumi, T. Ishihara, H. Voshioka, M. Motoyama, and K. Murai, Appl. Surf. Sci. 177, 114 (2001). 224. K. Utsumi, O. Matsunaga, and T. Takahata, Thin Solid Films 334, 30 (1998). 225. X.W. Sun, L. D. Wang, and H. S. Kwok, Thin Solid Films 360, 75 (2000). 226. K. Aikawa, Y. Asai, and T. Hosaka, Proc. ISSP 195-198 (1993). 227. Y. Shigesato, S. Takai, and T. Haranoh, J. Appl. Phys. 71, 3356 (1992). 228. E. Kawamata and K. Ohshima, Japan. J. Appl. Phys. 18, 205 (1979). 229. G. Blandenet, M. Court, and Y. Lagarde, Thin Solid Films 77, 81 (1982). 230. L. A. Ryabova, V. S. Salun, and I. A. Serbinor, Thin Solid Films 92, 327 (1982). 231. T. Maruyama and A. Kojima, Japan. J. Appl. Phys. 2 27, L 1829 (1993). 232. S. V. Prasad, S. D. Walck, and J. S. Zabinski, Thin Solid Films 360, 107 (2000). 233. J. Exarhos and S. K. Sharma, Thin Solid Films 270, 27 (1995). 234. I. Petrov, V. Orlonov, and A. Misiuk, Thin Solid Films 120, 55 (1984). 235. L.I. Maissel and R. Glang, "Handbook of Thin Film Technology," p. 124. McGraw-Hill, New York, 1970. 236. D.L. Raimondi and E. Kay, J. Vac. Sci. Technol. 7, 96 (1970). 237. E S. Hickernell, J. Appl. Phys. 44, 1061 (1973). 238. K. Machida, M. Shibutani, Y. Maruyama, and T. R. Matsumoto, IECE 62, 358 (1979). 239. T. Shiosaki, S. Ohnishi, and A. Kawabata, J. Appl. Phys. 50, 3113 (1979). 240. J. S. Zabinski, J. Corneille, S. V. Prasad, N. T. McDevitt, and J. B. Bultman, J. Mater. Sci. 32, 5313 (1997). 241. S.V. Prasad and J. S. Zabinski, Wear 203-204, 498 (1997). 242. H. Nanto, T. Minami, S. Shooji, and S. Tanaka, J. Appl. Phys. 55, 1029 (1984). 243. R.M. White and E W. Voltmer, Appl. Phys. Lett. 7, 314 (1965). 244. T. Yamamoto, T. Shiosaki, and A. Kawabata, J. Appl. Phys. 51, 3113 (1980). 245. K. Matsubara, I. Yamada, N. Nagao, K. Tominaga, and T. Takagi, Surf. Sci. 86, 290 (1979). 246. M. Kadota, T. Kasanami, and M. Minakata, Japan. J. Appl. Phys. 31, 3013 (1992). 247. W.T. Seeber, M. O. Abou-Helal, S. Barth, D. Beil, T. H6che, H. H. Afify, and S. E. Demain, Mater. Sci. Semicond. Proc. 2, 45 (1999). 248. Z.Y. Ning, S. H. Cheng, S. B. Ge, Y. Chao, Z. G. Gang, Y. X. Zhang, and X. G. Liu, Thin Solid Films 307, 50 (1997). 249. X.W. Sun and H. S. Kwok, J. Appl. Phys. 86, 408 (1999). 250. L.N. Dinh, M. A. Schildbach, M. Balooch, and W. McLean II, J. Appl. Phys. 86, 1149 (1999). 251. K.L. Narasimhan, S. E Pai, V. R. Palkar, and R. Pinto, Thin Solid Films 295, 104 (1997). 252. S. Hayamizu, H. Tabata, H. Tanaka, and T. Kawai, J. Appl. Phys. 80, (1996). 253. A. Suzuki, T. Matsushita, Y. Sakamoto, N. Wada, T. Fukuda, H. Fujiwara, and M. Okuda, Japan. J. Appl. Phys. 35, 5457 (1996). 254. A. Suzuki, T. Matsushita, N. Wada, Y. Sakamoto, and M. Okuda, Japan. J. Appl. Phys. 2 35, L56 (1996). 255. H. Sankur and J. T. Cheng, J. Vac. Sci. Technol. A 1, 1806 (1983). 256. T. Nakayama, Surf. Sci. 133, 101 (1983). 257. N.J. Ianno, L. McConville, N. Shaikh, S. Pittal, and E G. Snyder, Thin Solid Films 220, 92 (1992). 258. M. Joseph, H. Tabata, and T. Kawai, Appl. Phys. Lett. 74, 2534 (1999). 259. Y.J. Kim and H. J. Kim, Mater. Lett. 21,351 (1994). 260. S. Takada, J. Appl. Phys. 73, 4739 (1993). 261. T. Hata, E. Noda, O. Morimoto, and T. Hada, Appl. Phys. Lett. 37, 633 (1980). 262. N. Fujimura, T. Nishihara, S. Goto, J. Xu, and T. Ito, J. Cryst. Growth 130, 269 (1993). 263. W. Gopel and U. Lampe, Phys. Rev. B 22, 6447 (1980).

LASERS IN THIN FILMS PROCESSING 264. Y. Morinaga, K. Sakuragi, N. Fujimura, and T. Ito, J. Cryst. Growth 174, 691 (1997). 265. J.-M. Liu and C. K. Ong, Appl. Phys. A 67, 493 (1998). 266. H. Cao, J. Y. Wu, H. C. Ong, J. Y. Day, and R. E H. Chang, Appi. Phys. Lett. 73, 572 (1998). 267. J. Narayan, K. Dovidenko, A. K. Sharma, and S. Oktyabrsky, J. Appl. Phys. 84, 2597 (1998). 268. G.A. Hiram, J. McKittick, J. Siqueiros, O. A. Lopez, T. Cheeks, O. Contreras, and J. Y. Yi, J. Vac. Sci. Technol. A 14, 791 (1996). 269. T. Minami, H. Nanto, and S. Takata, Appl. Phys. Lett. 41,958 (1982). 270. R.E.I. Schropp and A. Madan, J. Appl. Phys. 66, 2027 (1984). 271. M. Brett, R. Mcmahon, J. Affinito, and R. Parsons, J. Vac. Sci. Technol. A 1,162 (1984). 272. R. Menner, R. SchLffler, B. Sprecher, and B. Dimmler, "Proc. 2nd World Conf. Exhib. Photovoltaic Solar Energy Conv.," Vienna, 1998, p. 660. 273. S. J~iger, B. Szyszka, J. Szczyrbowski, and G. Br~iuer, Surf. Coat. Technol. 98, 1304 (1998). 274. J. Aranovich, A. Ortiz, and R. H. Bube, J. Vac. Sci. Technol. 16, 994 (1979). 275. J. Song, I.-J. Park, and K.-H. Yoon, J. Korean Phys. Soc. 29, 219 (1996). 276. S. Major, A. Banerjee, and K. L. Chopra, Thin Solid Films 108, 333 (1983).

217

277. S. Fujihara, J. Kusakado, and T. Kimura, J. Mater. Sci. Lett. 17, 781 (1998). 278. T. Tominaga, N. Umezu, I. Moil, T. Ushiro, T. Moilga, and I. Nakabayashi, Thin Solid Films 334, 35 (1998). 279. R. Cebulla, R. Wendt, and K. Ellmer, J. Appl. Phys. 83, 1087 (1998). 280. T. Minami, H. Nanto, and S. Takata, Japan. J. Appl. Phys. 23, L280 (1984). 281. T. Minami, H. Sato, H. Nanto, and S. Takata, Japan. J. Appl. Phys. 24, L781 (1985). 282. J. Hu and R. G. Gordon, J. Appl. Phys. 71,880 (1992). 283. T. Minami, H. Sato, H. Sonohara, S. Takata, T. Miyata, and I. Fukuda, Thin Solid Films 253, 14 (1994). 284. B. Sang, A. Yamada, and M. Konagai, Japan. J. Appl. Phys. 37, L1125 (1998). 285. W. Tang and D. C. Cameron, Thin Solid Films 238, 83 (1994). 286. D. Raviendra and J. K. Sharma, J. Appl. Phys. 58, 838 (1985). 287. J. Kido and Y. Iizumi, Chem. Lett. 10, 963 (1997). 288. J. Kido and Y. Iizumi, Appl. Phys. Lett. 73, 2721 (1998). 289. H. Murata, C. D. Merritt, H. Mattoussi, and Z. H. Kafifi, Proc. SPIE 3476, 88 (1998).

Chapter 4 COLD PLASMA PROCESSES IN SURFACE SCIENCE AND TECHNOLOGY Pierangelo Gr6ning Department o f Physics, University o f Fribourg, Fribourg, CH-1 700 Switzerland

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Plasmathe Fourth State of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. ColdPlasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. PlasmaChemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. CarbonThin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. PlasmaPolymerization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. SurfaceTreatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. SurfaceTermination by H2 Plasma Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. I N T R O D U C T I O N

219 219 221 224 226 226 236 240 253 257 257 257

describes the amount of ionization to be expected in a gas in thermal equilibrium:

1.1. Plasma the Fourth State of Matter

T3/2 ni ~ 2.4 • 10 15 e-Ui/kT m nn ni

Plasmas are ubiquitous, comprising more than 99% of the known matter in the universe. Taking into consideration the energy of the particles constituting the plasma, plasma is energetically the fourth and highest state of the matter, apart from the solid, liquid, and gaseous states. Irving Langmuir and his collaborators at General Electric were the first to study phenomena in plasma in the early 1920s while working on the development of vacuum tubes for high currents. It was Langmuir [1] who in 1929 used the term "plasma" for the first time to describe ionized gases. In our everyday life encounters with plasmas are limited to a few examples: the aurora borealis (Fig. 1) at the polar regions, the flash of a lightning bolt, the conducting gas inside a fluorescent neon tube, and the small amount of ionization in the flame of a welding torch. The reason plasmas are so rare in our everyday life can be seen from the Saha equation, which

Saha equation

Here ni and nn are, respectively, the density of ions and neutral atoms, T is the temperature, k is the Boltzmann constant, and Ui is the ionization energy of the gas. For dry air at room temperature the fractional ionization ni/nn "~ 10 -122 predicted by the Saha equation is negligibly low. As the temperature increases and Ui is only a few times k T the degree of ionization rises abruptly, and the gas goes into the plasma state. Not any ionized gas can be called a plasma. Of course, there is always some small degree of ionization in any gas [ 1, 2]. A useful and common definition for the plasma state is as follows:

The plasma is a quasineutral gas of charged and neutral particles which exhibits collective behavior. "Quasineutral" means that the plasma is neutral enough so that the electromagnetic forces do not vanish. Then one can take the

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00 219

220

GRONING

Fig. 3. Low pressure (p = 10 -2 mbar) microwave plasma excited at the ECR condition. Left 02 and right Ne plasma.

Fig. 1.

Aurora borealis (from the website http://gedds.pfrr.alaska.edu).

where Te is the electron temperature, the quantity to characterize the kinetic energy of the electrons. The electron temperature Te is used in the formula of L o because the electrons, being more mobile than the ions, generally do the shielding by moving so as to create a surplus or deficit of negative charge. Finally, a criterion for an ionized gas to be a plasma is that it is dense enough that ~o is much smaller than the dimensions of the system. The plasma contains a multitude of different neutral and charged particles, as well as ultraviolet (UV) and vacuum ultraviolet (VUV) radiation. It is broadly characterized by the following basic parameters: 9 the gas pressure (p) or the density of the neutral particles, nn (Fig. 3), 9 the ion and electron density, ni and ne, which are equal in the quasineutral state of the plasma (ni ~- ne =: n, n is called the plasma density), 9 the energy distributions of the neutral particles, fn (E), the ions, fi (E), and the electrons, f e ( E ) .

Fig. 2. Classification of plasmas as a function of electron density and temperature (1 eV --~ 11,600 K). The Debye length ~.D characterizes the interaction distance between charges.

One of the physical parameters defining the state of a neutral gas in thermodynamic equilibrium is its temperature T, representing the mean kinetic energy of the particles: 1 3 -m(v) 2 kT 2 =2

ion and electron densities equal ni ~- ne =: n, where n is a common density called the plasma density. In a plasma the motion of the particles can cause local concentrations of positive and negative electric charges which create long-range Coulombic fields that affect the motion of the charged particles far away from the charge concentrations. Thus elements of the plasma affect each other, even at large separations, giving the plasma its characteristic "collective behavior." The local charge concentrations in a plasma are confined to small volumes of size ~.O, called the Debye length (Fig. 2). The Debye length describes quantitatively the ability of the plasma to shield out electric potentials that are applied to it. The formula for the Debye length ~.D can be deduced from the Poisson equation and it is

~.D= (eOkTe) 1/2 rte e2

Debye length

The plasma is a mixture of particles with different electric charges and masses. The electrons and the heavy particles (neutrals and ions) in the plasma can be approximately considered, thermally, as two or better three subsystems, each in its own thermal equilibrium. Therefore, in analogy to the temperature of a neutral gas, the plasma can be characterized by the three temperatures, the electron, Te, the ion, Ti, and the gas temperature (neutral), Tg. Thermodynamic equilibrium in the plasma will only exist if all temperatures of the different subsystems are equal. The essential mechanisms in the plasma are excitation and relaxation, dissociation, ionization, and recombination. To maintain a steady state in the plasma density, the recombination's must be balanced by an ionization process; i.e., an external energy source is required. Usually an electric field is used as

COLD PLASMA PROCESSES energy source, acting directly on the charged particles only. The energy transfer W from the electric field E to a simple charged particle with mass m is given by W = eff~. 7 = (eEt)2 2m where ~ is the distance travelled in time t. The expression for the energy transfer W from the electric field E to a charged particle shows clearly that the field primarily gives energy to the electrons since the mass of the ions m i is much larger than those of the electrons me (mi >> me). From the electrons the energy is transferred to atoms and ions by collisions. Therefore, at low pressures, the electron temperature Te is much higher than those of the ions Ti and neutrals (gas) Tg, respectively. The three temperatures converge to similar values at a pressure around 100 mbar and the plasma becomes arclike. Atmospheric pressure plasmas have temperatures of a few thousand Kelvin. Such plasmas, where local thermodynamic equilibrium (Te = Ti = Tg) is achieved, in volumes of the order of the mean free path length for collision, are called local thermodynamic equilibrium (LTE) plasma or thermal plasma. In low pressure plasmas, where the collision rate and therefore the energy transfer from electrons to neutrals is reduced, the electron temperature is much higher than the temperature of the ions and the gas (Te >> T/ ~ Tg). In such plasmas the LTE conditions are not achieved and therefore are called non-LTE plasmas or cold plasmas, because the ion and gas temperatures are at about

221

room temperature (Ti ~ Tg ~- RT), whereas the electron can reach temperatures of 104-105 K (1-10 eV).

1.2. Cold Plasma Cold plasma processes are nowadays used in various technological applications. Cold plasmas are used for coating, polymerisation, activation and cleaning of workpieces, for etching of microelectronic and micromechanical devices, and for finishing of textiles. In the microelectronic industry plasma surface cleaning is established as the cleaning technique for the nanometer scale. In comparison to wet chemical processes plasma processes are much environmental friendly, cheaper and a higher cleaning degree can be achieved. This makes plasma processes very attractive for the industry and is the driving force that the field of applications increases permanently. There are many excellent books reviewing the physics and chemistry [4, 5], the diagnostic [6], and the applications [7, 8] of cold plasmas. Here we will only introduce briefly the principles and a few important parameters of cold plasmas, without pretension on completeness (Fig. 4). 1.2.1. Electron Temperature Te In cold plasmas the electrons and the heavy particles are not in thermodynamic equilibrium, even at local scale in the order of the Debye length ~.D. Such plasmas can be excited and

Fig. 4. Surfaceanalytical system at the University of Fribourg (Switzerland) to investigate cold plasma processes. The system is equipped with an ESCA system (1) for photoelectron spectroscopy (XPS, UPS) and photoelectron diffraction (XPD), with an ECR microwave plasma (2) and a room temperature AFM/STM(3). The whole systemis operating at a base pressure of 5 x 10-11 mbar.

GRONING

222

sustained by direct current (DC), radio frequency (RF), or microwave (MW) electric fields applied to the gas. From the electric field the energy is transferred to the available free electrons by accelerating them, as mentioned before9 Concomitantly the electrons lose energy in collisions with the gas. As long as the energy of the electrons is too low to excite or ionise the gas, the collisions will necessarily be elastic and therefore heat the gas. Since the energy transfer from the electron to the gas is extremely small in the elastic collision the electron gains energy from the electric field until it is sufficiently high to cause ionization or excitation through inelastic collisions. The electrons produced in the ionization process are in turn accelerated by the electric field and produce further ionization up to the plasma state. In thermodynamic equilibrium the velocity distribution and consequently the energy distribution of the particles in the gas is Maxwellian. In cold plasma the electrons are in a nonequilibrium state (Te >> Tg ~- RT). The slower electrons make elastic collisions only, whereas electrons with higher energies are liable to lose a much larger fraction of their energy by inelastic collisions. Therefore the energy distribution of the electrons in cold plasmas is shifted to higher energy compared to the Maxwell-Boltzmann distribution (Fig. 5). Instead of using the Maxwell-Boltzmann distribution fMa (E) it is better to approximate the electron energy distribution in cold plasma by the Druvestyn distribution fo (E): fD(E)-I.O4.(E)-3/2E1/2

e x p ( -0"55 ) ( E )E2 2 Druvestyn distribution

.I 0.7

-'-

0.6

MaxwelI-Boltzmann Druvestyn

Average energy = 1 eV

A

iil ~.

0.5

c o

im

.12

0.4

The Druvestyn distribution considers the motion of electrons in a weak electric field, such as exist in cold plasmas9 Characteristic for both energy distribution functions is the high-energy tail. For reactions in the plasma requiring relevant electrons energies between 3 and 10 eV the Druvestyn distribution predicts a higher reaction rate than the Maxwell-Boltzmann distribution. 1.2.2. Plasma Potential Vp

A very important parameter in cold plasma processing is the plasma potential Vp which defines the kinetic energy of the ions impinging on the surface of a solid in contact with the plasma. The plasma potential is a consequence of the enormous difference in the temperature, i.e., speed (v), between the electrons and the ions in the cold plasma. A sample inserted on an electrically insulated sample holder into the plasma will be struck by electrons and ions with currents densities predicted from Avogadro's law to be je -ji--

[e(Vpds ~, 1.0 9

I...

0.2

IJ,l

Average energy = 5 eV 0.1

0.0.- I 0

_ .

2

4

6

8

10

4

k Te

Vfl)] 3/4 plasma sheath

The plasma sheath is for the electrons a potential barrier in front of the substrate. Only electrons with enough kinetic energy can overcome this barrier. However, the ions are accelerated by the plasma sheath toward the substrate. According to the voltage drop (Vp - Vfl) in this space charge region, the kinetic energy Ekin of the ions impinging on the substrate is given by

O') tl) C

4

e . ni 9 (vi )

Since (re) >> (vi) the electron current density is much larger than the ion one ([jel >> [ji I). Hence the sample will be immediately negatively charged, until the electron current is reduced by electrostatic repulsion just enough to balance the ion current. The negative potential, which balances the electron and ion current, is called the floating potential Vfl. The same charging effect occurs also with the plasma container walls, so that the plasma is positively charged with respect to the container. This potential is called the plasma potential Vp. The plasma potential is in fact the electric potential of the plasma due to the ion excess caused by the higher recombination rate of the electrons at the plasma container walls compared to the ions. The Debye shielding effect causes a positive space charge region, called the plasma sheath, in front of all surfaces (Vfl) in contact with the plasma (Vp). Therefore the plasma potential Vp is always the highest positive potential in a plasma system. At low pressures where the collision mean free path is much larger than the plasma sheath ds, the latter is approximately given by

I,..

i~ 0.3

- e . ne . (Oe)

12

14

E l e c t r o n E n e r g y E (eV)

Fig. 5. Electron energy distribution according to Maxwell-Boltzmann and Druvestyn.

El,in = e ( Vp - Vfl)

As suggested above the plasma potential is a consequence of the finite volume of the plasma device, i.e., determined by the recombination rates in the plasma and at the plasma container walls9 With increasing gas pressure, the electron-ion re-

COLD PLASMA PROCESSES

223

combination probability in the gas increases relative to that of the electrons at the container walls. This means thatthe plasma potential is pressure dependent and decreases with increasing gas pressure. Typical values for the plasma potential Vp are between 5 and 30 V. Accordingly the kinetic energies of the ions impinging the substrate are several electronvolts, which is about thousand times higher than the ion temperature T/ and high enough to induce significant physical and chemical effects on the substrate surface.

1.2.3. Self-Bias The physical etching effect of the ions during plasma treatment can be increased by negatively biasing the sample to increase the kinetic energy of the ions hitting the surface. Whereas for metallic samples a simple DC supply can be used to charge it negatively, an RF source has to be applied for insulating samples to use the self-biasing effect [9] of the plasma (Fig. 6). The enormous difference in speed between the electrons and the ions in the cold plasma causes, by applying an RF potential, initially (t = 0) an excess electron current on the substrate (Fig. 7a). Therefore the substrate begins to charge negatively until (few cycles) the DC-offset voltage (fbias) on the RF potential balances the electron and ion current on the substrate (Fig. 7b). By self-biasing, negative DC potentials (Ubias) up tO a few hundreds of volts can be obtained, depending on the RF power ( P ~ ) and the gas pressure (p): Ubias

~X( PRF

Fig. 7. Self-biasing of a substrate (a) initial potential (t = 0), (b) steady state (in practice the asymmetry between electron and ion current is much larger than indicated).

In the steady state the substrate potential is positive only during a very short fraction of each cycle. Therefore the substrate will be almost continuously bombarded with ions of an average kinetic energy (Ekin ~- e 9Ubias) defined by the bias potential Ubias. Self-biasing can be used for ion etching and sputter deposition of insulators. 1.2.4. Plasma Excitation

To excite and sustain cold plasmas an electric field has to be applied to the gas. This can be done by DC, RF, or MW power, whereby the electric energy is transferred via the electrons to the plasma. In the situation without collisions the electron energy W in an electric field (E(t)) is given by the equation of motion and me ~2

W =

2

--

(EAet) 2

2meco 2

(E(t) = E'cos(cot))

sin2(cot)

The formula suggests that besides a high electric field strength (EA), a low frequency (co) is required to reach a maximal electron energy (W). This is in opposition to the practice where the MW discharge is more efficient than the RF discharge, and the RF discharge is more efficient than the DC discharge in promoting ionization and sustaining the discharge. MacDonald and Tetenbaum [10] explained this behavior by the model in which the electron making an elastic collision at an atom, reversing its motion at the time the electric field changes the direction, will continue to gain velocity and energy. In this way, electrons could reach ionization energies for quite weak electric fields. Taking into account the elastic electron atom collisions at a frequency v the mean power (P) absorbed by an electron from the electric field is according to Venugopalan [ 11 ] given by (P) -Fig. 6. itor).

Schematic configuration for self-biasing a sample (C: blocking capac-

(E'e) 2

v

2me 1)2 -k-co2

The formula shows that the power absorption reaches a maximum when the collision frequency 1) equals the electric field

224

GRONING Table I.

Characteristics of the Various Cold Plasmas

DC

RF

MW

ECR

Coupling of the electric power

Internal and conductive electrodes

Internal as well as external electrodes, conductive or nonconductive

No electrodes

No electrodes

Pressure (mbar) Ionization degree Ion density (cm-3) Kinetic energy of ions hitting the substrate (eV)

0.5-10 0.45), the film growth is bulk diffusion controlled, giving rise to an equiaxed recrystallized grain structure. A similar zone schema was introduced by Thornton [ 17, 18] but with four zones, an additional transition zone T between zone 1 and zone 2. In 1978, Lardon et al. [19] extended the structure zone schema by the bias potential ( U b i a s ) parameter by taking into account the influence of energetic particle bombardment on the morphology of the condensate. As mentioned above energetic particle bombardment leads to dis-

placement of coating atoms and generation of lattice defects, which increases the mobility of the adatoms, resulting a denser and more homogenous structure of the coating as shown by the images (a2) and (b2) in Fig. 8. The bombardment of the surface with energetic ions can be interpreted as a local heating, which increases the mobility of the atom in the impact zone. Therefore energetic particle bombardment influences the morphology of a coating in the sense that the boundaries in the zone structure model are shifted to lower T/Tm values. An excellent review, on the interaction of low energy ions with surfaces, has been given by Carter and Armour [20].

2. APPLICATIONS 2.1. Carbon Thin Films The versatility of cold plasma in thin film technology can impressively be demonstrated by the deposition of carbon thin films. The electronic structure of the carbon atom is ls22s2p 2. Due to its three possible hybridization states (sp, sp 2, sp3), carbon can exist in various stable allotropic forms (Fig. 9). The thermodynamically stable form of carbon at normal pressure and temperature is graphite. The free-energy difference between the different allotropic phases is relatively small, for instance, 0.03 eV/atom between diamond and graphite, which is slightly higher than kT at room temperature (0.025 eV). However, there is always a large energy barrier between the different

COLD PLASMA PROCESSES

227

Fig. 9. Allotropicstable forms of carbon: (a) graphite, (b) diamond, (c) lonsdaelite, (d) fullerene C60, (e) single-walled nanotube (SWNT),(f) onion C540.

allotropic phases, which makes them all very stable at normal conditions. For instance, 15 GPa static pressure and a temperature of 1800 K is needed to transform graphite into diamond. With plasmas all stable allotropic as well as amorphous carbon phases can be synthesized or deposited as thin films, depending on the plasma and substrate conditions.

2.1.1. Amorphous Carbon Films Amorphous carbon films can be produced by sputter deposition, a PVD process, and by chemical vapor deposition (CVD) with hydrocarbon-containing gases. Amorphous carbon thin films may be broadly classified as: (i) amorphous carbon films, usually deposited by PVD processes, (ii) hydrogenated carbon films, a-C :H, usually deposited by plasma-assisted CVD (PACVD). Both types of films contain different amounts of s p 2 and s p 3 bonded carbon. The amount of s p 2 bonded carbon can be measured directly using nuclear magnetic resonance spectroscopy. The classification of amorphous carbon according to carbon bond type and hydrogen content can be represented in a triangular phase diagram [21] (Fig. 10). The comers at the base of the triangle correspond to diamond (100% s p 3 carbon) and graphite (100% s p 2 carbon). The upper limit for formation of solid films is defined by the tie line between the compositions of polyethylene - ( C H 2 ) n - and polyethyne - ( C H ) n - .

Fig. 10. Classificationdiagram for amorphous carbon films. Reprinted with permission from [21], 9 1996, John Wiley & Sons.

Hard forms of amorphous hydrogenated carbon (a-C:H), also known as "diamondlike carbon" (DLC), were first produced by Aisenberg and Chabot [22] in 1971. The expression diamondlike refers to the properties of the coating like high hardness (up to 6000 HV), high thermalconductivity, high chemical inertness, low wear, and low friction [23, 24]. Due to their outstanding properties DLC coatings are industrially used for a variety of applications, i.e., protective coatings on magnetic hard discs, sliding bearings, medical implants, forming tools, as well as many special applications. Figure 11 shows an

228

GRONING L uoias[V] .. Zhard.~ ,.

Uhigh-

glOw

coating thickness z [nm]

I

~. --IP

Fig. 11. Aluminium yarn storage disk coated with 3 ktm DLC for applications in spinning machines. (Photo: Berna/Bernex AG, CH-4600 Olten, Switzerland.)

45ca

=- 4 0 (.-3 w = q) c

35-

r'--

30--

'o 0

Ik,.,

o 25=E =,==,

20I'""'

0

'

':

'

:

i

. . . .

I

. . . .

-200

'

. . . .

I

. . . .

-400

'

. . . .

I

-600

Substrate bias [V]

P01ymer-like

! DLC film

film Fig. 12. Typical microhardness of DLC films as a function of the negative substrate bias (deposition: MW CH4 plasma, p = 20 mbar).

aluminium yarn storage disk from a spinning machine coated with 3 I.tm DLC. DLC consists of an amorphous network of s p 3 and s p 2 hybridized carbon and can be synthesized at room temperature by PACVD [25-27] or other ion-assisted processes. Any hydrocarbon with sufficient vapor pressure can in principle be used as precursor for PACVD of DLC films. Commonly used process gases are acetylene (C2H2) and methane (CH4). The DLC deposition is a nonequilibrium process characterized by the interaction of energetic ions with the surface of the growing film. The deposition of DLC by PACVD has to be done on negatively biased substrates to actuate reactions like thermal and pressure spikes at the growth surface by energetic ions. Tsai and Bogy [28] calculated for 100 eV ions thermal spikes of 3300 K and pressures of 1.3 x 101~Pa for a period of 10 -1~ s. The lifetime of these spikes is much longer than the vibrational period (~10 -14 s) for diamond and thus well beyond what is required to allow bonding. The DLC process forms a metastable amorphous material whose structure is conserved due to extremely high quenching rates of the thermal spikes. The hardness of the DLC films can be varied by adjusting the substrate bias, as shown in Figure 12.

I

2~

"-

"*'-(or deposition time t [s])

Zint

q l - ~

Fig. 13. Bias voltage curve for DLC multilayer structure. ~. is the repeat unit of the multilayer structure. Reprinted with permission from [ 133], 9 1987, Elsevier Science.

The characteristic process of DLC deposition is the interaction of the impinging energetic ions with the hydrocarbons physisorbed on the surface of the growing film. This causes an increased deposition rate with increasing ion flux and decreasing substrate temperature. Further the properties of the DLC films are independent of the chemical precursor used if the negative bias is high enough (Us < - 1 0 0 V), as found by Koidl et al. [29]. For lower bias voltages the impact energy is to small for efficient hydrocarbon dissociation and the film becomes soft and polymerlike, as indicated in Figure 12. In recent years many research groups have reported new types of coating, consisting of multiphase materials with structures in the nanometer range, that exhibit outstanding mechanical properties [30-32]. The fact that the hardness of DLC films depends only on the applied negative substrate bias allows one to deposit DLC as nanoscaled multilayer coatings consisting of alternative hard and soft a-C:H layers [33]. The thickness of the multilayer repeat unit and the interface width between these layers can be controlled in the nanometer range by the substrate bias. A typical bias voltage function for a DLC multilayer structure is shown in Figure 13. Hauert et al. [33] have deposited DLC multilayer coatings with different repeat unit thicknesses k and interface widths Zint. They found that the wear resistance of the different multilayer coatings depends strongly on the repeat unit thickness )~ and especially on the interface width Zint as shown in Figure 14. The friction coefficient of all samples was between 0.07 and 0.18. Though the main cause of the DLC multilayer structure on the tribological behavior is not fully understood, the experiments demonstrate the enormous potential that DLC multilayer structures can have in tribology. PACVD in combination with magnetron sputtering allows the deposition of DLC with different dopands. The electrical conductivity of metal-containing hydrogenated amorphous carbon (M-a-C : H) films, for example, can be varied over many orders of magnitude [34]. Also, depending on the type of metal and the amount used, the M-a-C :H film may exhibit different hardness, friction, and wear [35]. The excellent friction behavior combined with the chemical inertness makes DLC coatings interesting for biomedical implants. Moreover, the release of

COLD PLASMA PROCESSES

229

Fig. 14. Wear rate of 300 nm thick DLC multilayer coatings as a function of the repeat unit thickness ~ and interface with Zint. Reprinted with permission from [33].

metal ions or wear particles from metallic orthopedic implants into the surrounding tissue, which is believed to lead to bone resorption and consequently to failure and loss of the implant, can be minimized or prevented by using DLC as a protective coating [36]. Francz et al. [37] have shown that by additional incorporation of different metals into the a-C:H matrix, thin film coatings with new biological properties can be generated. They found that by adding Ti to the carbon matrix, cellular reactions such as tendential differentiation of osteoblasts together with a reduced osteoclast activity could be obtained. 2.1.2. Diamond Films

In 1971 Deryagin and Fedoseev reported successful continuos growth of diamond at low pressures by methods which they later described [38]. The outstanding properties of diamond, including its hardness, chemical inertness, good optical transparency, and highest thermal conductivity, triggered enormous research activity in diamond thin film deposition. The book "Low-Pressure Synthetic Diamond" edited by Dischler and Wild [39] gives a nice overview on the manufacturing and applications of diamond thin films. Today, diamond thin films can be deposited by various low pressure techniques [40] such as hot-filament, MW plasma, DC discharge, or plasma jet techniques. Plasma is among the most widely used techniques (PECVD) for gas activation, permitting the deposition of diamond thin films. The low pressure diamond deposition process is fundamentally different from those of a-C:H. Characteristic for the a-C :H deposition process is the physical effect of the impinging energetic ions with the hydrocarbons physisorbed on the surface of the growing film. In opposition to that the diamond deposition process is the result of various chemical reactions on the surface of the growing film. The difference in the two deposition processes clearly finds expression by the precursor gas needed. While for diamond deposition the hydrocar-

Fig. 15. Bachmann diagram for CVD diamond film growth. Reprinted with permission from [41], 9 1991, Elsevier Science.

bon precursor must be strongly diluted with hydrogen (typically CH4/H2 = 1/99), the a-C : H deposition process does not need the hydrogen. Further differences of the two deposition processes are the pressure, which is a few ten of millibars for diamond and below 1 millibar for a-C :H, and the needed substrate temperature, 600 to 1100~ for diamond and room temperature for a-C : H. The hydrogen chemistry is essential for the diamond growth at low pressures. The triangular CHO diagram of Bachmann et al. [41] shows with which gas compositions CVD diamond can be grown (see Fig. 15). The growth surface of diamond can be represented schematically by a layer of carbon atoms terminated with atomic hydrogen. Individual hydrogen atoms are removed and provide a chemically active site for addition of carbon. Hydrogen abstraction has been estimated to occur every 70 ~ts on average, with each such site being refilled after 15 its [42, 43]. Growth occurs when a hydrocarbon radical is attached at an active site of the lattice and loses its hydrogen atoms through hydrogen abstraction. Among the different radicals (methane, methyl, acetylene, acetyl), methyl radicals are usually accepted as the main growth species, especially for the (100) surface [44]. First, a surface hydrogen atom recombines with atomic hydrogen of the plasma to H2 molecules, producing a radical site on the surface (Fig. 16b). This site can react with a hydrogen atom (Fig. 16a) or a methyl radical (Fig. 16c). The next step is the abstraction by atomic hydrogen of the plasma of a hydrogen atom of the methyl group or of another surface atom (Fig. 16d). Finally, another hydrogen atom is abstracted to leave two adjacent radical carbon atoms. They react to form a carbon-carbon bond (Fig. 16e) forming an adamantane molecule. In parallel, a methyl group can add to the CH2 radical site to form an ethyl group (C2H5), diversifying the growth mechanisms [45]. Fren-

230

GRONING

klach et al. [46, 47] proposed a growth mechanism based on the addition of acetyl to a radical site. Characteristic of CVD diamond deposition is the need for nucleation centers. On commercial silicon wafer without any treatment the CVD diamond process leads to the deposition of individual nanocrystallites with a density lower than 105 nuclei per cm 2. The main reason for this extremely low nucleation density is the high surface energy of diamond relative to that of the substrate material. Surface nucleation enhancement is necessary in order to get a continuous polycrystalline film. Three main mechanisms are known for diamond nucleation: (a) nucleation on dislocation ledges, kinks, or intentional scratches, (b) diffusion barrier enhanced nucleation, (c) nucleation on a molecular precursor. The corresponding techniques are: (a) scratching the substrate with diamond, nitrides or other ceramic powders, to create defects which act as nucleation centers [48]; the nucleation density is

Fig. 16. Methylbased diamond growth model according to Harris [45].

between 105 to 101~ cm -2. No oriented diamond film has been observed yet on such prepared substrates, (b) enhanced nucleation on a precursor such as thin metal films, graphite fibers, C60, or others [48, 49]; the nucleation density is between 106 and 10 l~ cm -2 depending on the precursor. A further technique is the bias enhanced nucleation by applying a DC or RF voltage during the first minutes of the deposition [48, 50, 51]. The nucleation density obtained with this technique is between 108 and 1011 cm-2. At present it is the only nucleation technique involving the oriented growth of the diamond film relative to the silicon substrate as shown in Figure 17. The mechanisms of oriented bias enhanced nucleation are still not well understood and one crucial question is the structure of the interlayer between the silicon substrate and the diamond film formed during the growth and especially during the bias enhanced nucleation process. The nature of this interlayer has been investigated by a number of analytical techniques including X-ray photoelectron spectroscopy (XPS) [53], transmission electron microscopy (TEM) [54], and IR spectroscopy [55]. No clear picture can be drawn whether oriented diamond nucleates on the/3-SIC interlayer that is formed during the nucleation process or directly on silicon. TEM investigations show nucleation on all materials [56, 57]. Gerber et al. [58, 59] have proposed a subplantation model for the oriented nucleation. They claimed that ion bombardment of the a-C :H layer formed on top of the SiC layer leads to subplantation effects in the a-C : H layer which cause a high compressive stress. Locally this stress transforms the s p 2 to an s p 3 structure, giving rise to a diamond nucleation center. We investigated the silicon surface during the first minutes of bias enhanced nucleation by using X-ray photoelectron diffraction (XPD) [60, 61]. XPD is a natural extension to regular XPS [62]. A spectral feature is selected out of a XPS spectrum from a single-crystalline sample. The intensity modulation of this particular signal is measured as a function of the electron emission angle. Based on the forward focusing effect (Fig. 18)

Fig. 17. SEM pictures of (100)-oriented polycrystalline diamond film grown by PECVD on silicon (100): (a) top view, (b) side view. Reprinted with permission from [52].

COLD PLASMA PROCESSES of the electrons by atoms the measured intensity modulation gives information on the surface atomic structure. Figure 19 shows the deconvoluted Cls XPS spectrum together with XPD pattern of the C - S i and C - C components. The diffractograms show for both components the typical structure of a (100) surface. The C - S i diffractogram proves the oriented growth of a/5-SIC layer with respect to the silicon (100) substrate ( S i - S i diffractogram not shown). The formation of oriented/5-SIC is not surprising because the structure can be formed by substitution of Si atoms with carbon atoms from the plasma. The formation of oriented/3-SIC is independent of the

Fig. 18. Schematic illustration of the forward focusing effect associated with photoelectron diffraction.

231

bias and appears also without bias [61]. This proves that the presence of oriented/3-SIC is not a sufficient condition for oriented diamond growth! The diffractogram of the C - C component is identical to that of the C - S i component, indicating the presence of small carbon clusters in the/5-SIC matrix. The clusters are oriented with respect to the silicon (100) substrate and act as nucleation centers for the oriented diamond growth. The small diamond crystallites which are formed during the bias-enhanced nucleation (Fig. 20) do not significantly contribute to the analysis because their coverage is below 1% and therefore below the XPS detection limit. In opposition to the fl-SiC layer, oriented carbon clusters are only formed at sufficiently high negative bias voltage (Ubias < -- 100 V). Unfortunately, the initially euphoric expectations in diamond thin films as the universal solution for all kind of problems in wear, tribology, electronics, etc., have not yet come true. Nevertheless diamond thin films are nowadays used in many applications such as surface acoustic wave filters (Sumitomo Electric), thermal heat sinks in electronic devices, inert electrodes in electrochemical disinfection of fresh water and purification of waste water [63], conductive atomic force microscope tips (Fig. 21), etc. Also very promising is the field electron emission behavior of diamond films. Since the first observations and investigations of the low field electron emission properties of natural and chemical vapor deposited diamond in the early 1990s [65, 66], the interest in this field has steadily increased until the present day. Over 150 patents issued on diamond field emitters prove the big economic interest for that application [67]. The estimated annual turnover of 20 billion dollar for fiat panel displays in the year 2002 may be the strong driving force to de-

Fig. 19. Fitted Cls XPS signal together with XPD patterns of the C--Si and C - C components of the silicon (100) surface after 8 min of biasenhanced nucleation and 10 min deposition. Reprinted with permission from [60], 9 1997, American Physical Society.

232

GRONING

velop micrometer sized electron emission structures for which carbon thin films are good candidates. Field emission is usually due to the tunnelling of electrons through the narrow surface potential barrier created by an intense electric field. In the case of a typical metal having a work

Fig. 20. HRSEM picture of the silicon surface after the bias-enhanced nucleation. The white spots are diamond crystallites. Reprinted with permission from [60], 9 1997, American Physical Society.

function of 5 eV, fields in the range of 2500 V ~m -1 are required to get detectable field emission currents (> 1 nA). For technological applications such high fields are very difficult to generate on fiat surfaces. In order to create sufficiently high fields for electron field emission one usually has to rely on the field enhancing effect of tiplike structures. The local electric_. field F at the apex of a_.tip exposed to an electric field F0 can be expressed by F = F0 9 13, where 13 is the field enhancement factor. It depends on the tip geometry and on the tip orientation in the field. In the case of a needle shaped tip, with radius r and height h, parallel to the field F0, the field enhancement factor 13 is equal, in first approximation, to the aspect ratio h / r . Many research groups have shown that the electron field emission behavior of CVD diamond films depends dominantly on the surface morphology. Films exhibiting bad crystalline quality show the best electron emission properties, especially the lowest threshold field. Usually these are films with nanocrystalline structures which are characterized by a Raman spectrum showing a very weak or even absent 1332 cm -1 diamond line and by a strong feature of s p 2 bonded carbon (Fig. 22).

Fig. 21. CVD pyramidal diamond tip on silicon cantilever. The diamond tip has been modified by focused ion beam etching [64] (from CSEM "Scientific and Technical Report 1999" [57]).

Fig. 22. SEM images and Raman spectra of: (a) weakly emitting CVD diamond grown at 850~ and 1% CH4 in H2, (b) good emitting CVD diamond grown at 950~ and 5% CH4 in H2. Reprinted with permission from [68]. Reprinted with permission from [69], 9 1999, American Vacuum Society.

COLD PLASMA PROCESSES These films can be grown at relatively high substrate temperature Ts > 950~ and high carbon precursor concentration (e.g., > 3% CH4). The electron field emission phenomenon was first reported by Wood in 1897. In 1928 Fowler and Nordheim delivered the first generally accepted explanation of electron field emission in terms of the newly developed theory of quantum mechanics [70]. They treated the conduction electrons in the metal as a gas of free particles obeying the Fermi-Dirac statistic. The electrons are confined in a metal by the surface potential barrier, the shape of which is considered to be determined by the potential inside the metal (work function 40, the image charge potential, and the applied external potential as schematically illustrated in Figure 23. The result of this quantum mechanic calculation is the wellknown Fowler-Nordheim relation for the emission current den-

233

sity je, e3

je -- 4(2zr)2]h~

F2 exp ( - 4 2~-~eq~ ) 3 h e F1"5 Fowler-Nordheim relation

where je is in A m -2 and F is the field in V m -1. The Fowler-Nordheim relation shows that the emission current density depends only on the work function ~b and the local electric field F present at the emission site. Because usually neither ~ nor F is known it is impossible to determine these emission characterizing values from a simple I - V measurement. To get the second necessary equation to determine ~b and F we measured the field emitted electron energy distribution (FEED). Figure 24 shows the electron energy distribution expected for the classical Fowler-Nordheim field emission. The energy distribution shows a peak centered at the Fermi energy EF of the emitter. At 0 K temperature the peak would show a sharp cutoff toward the high energy side, showing the position of the emitter's Fermi level E F. With increasing temperature this cutoff broadens due to the thermal excitation of electrons at the Fermi level into states of higher energy. The low energy side shows the exponentially decreasing tunneling probability with decreasing energy due to the increasing width of the tunneling barrier. The transmission probability D(E) for an electron with energy E to tunnel through a potential barrier is given in the WKB (Wentzel-Kramers-Brillouin) approximation by [71 ]

{av

DWKB(E) = exp ----~- + [ C v ( E Fig. 23. Schematic illustration of the surface potential barrier V (x) under the action of an external electric field.

Fig. 24.

]

EF)]

transmission probability

Classical Fowler-Nordheim electron emission model and the resulting energy distribution of the emitted electrons.

234

GRONING

Fig. 25. Schematicillustration of (a) single-wall carbonnanotube, (b) multi-wall carbon nanotube. with

[2me q~l/2 Cv-2~/ -~ From the Fowler-Nordheim relation je (I-V curve) and the tunneling transmission probability D(E) (fit of the low energy 4 2 ~ q ~ 3/2

av=3V h2 F

side of the FEED) it is now possible to determine the work function q~, the local electric field F, and the field enhancement factor 13 at the emission site. With this approach we proved that the electron field emission of diamond and DLC films is classical Fowler-Nordheim tunnelling [68, 69, 72]. We demonstrated that the excellent field electron emission behavior of CVD diamond films is due to very high field enhancement at the film asperities. This explains why diamond films with nanocrystalline structures (Fig. 22b) show the best field electron emission behavior. For nanocrystalline diamond films we found typically a work function of 5 eV, characteristic for carbon allotropes, and field enhancement factors up to 800. The corresponding local electric field at the emission site is typically 2500 V ~m -1 , which is equal to the required field for electron emission of flat metal surfaces. Since the excellent electron field emission behavior of CVD diamond is only based on a geometrical effect, it is evident that carbon nanotubes (see next section) with their needle shaped structure are optimal electron field emitters [73-75]. 2.1.3. Carbon Nanotubes Carbon nanotubes (CNT) are ultrathin carbon fibers with nanometer-size diameter and micrometer-size length and were discovered by Iijima in 1991 [76] in the carbon cathode used for arc-discharge processing of fullerenes (C60). The structure of CNT may be viewed as enrolled cylindrical graphene sheets and closed by fullerenoid end caps. There are single-wall carbon CNT (SWCNT) and multiwall CNT (MWCNT), consisting of several nested coaxial single wall tubules. Typical dimensions of MWCNT are outer diameter: 2-20 nm, inner diameter: 1-3 nm, and length: 1-100 l.tm. The intertubular distance is 0.340 nm, which is slightly larger than the interplanar distance in graphite. Excellent reviews on the synthesis and the physical properties can be found in [77-79] (see Fig. 25). CNTs can be prepared by arc evaporation [80], laser ablation [81 ], pyrolysis [82], electrochemical methods [83, 84], and

also PECVD [75]. The CNT formation by PECVD and pyrolysis as well is a catalytic process using metallic catalysts. In the arc method metallic catalysts improve the production yield and control the diameter of the CNTs. The catalytic methods for making CNTs have their origin in the corresponding work on carbon fibers [85]. Baker and Harris [86] proposed a model for the catalytic filament growth where hydrocarbon is decomposed on the surface of the metal particle, producing hydrogen and carbon, which then dissolves in the metal. The dissolved carbon then diffuses through the particle, to be deposited on the trailing face, forming the filament. This model seems also to be applicable for general CNT growth (Fig. 26). However the growth mechanisms responsible for the structure type of the growing CNT (SWCNT or MWCNT) are still unknown. For the PECVD technique we found that CNTs grow exactly at the same process conditions as used for diamond films. In the PECVD the substrate pretreatment is the only step which defines the structure of the carbon deposit (diamond or CNT). In the case of CNT a metallic catalyst has to be deposited. We performed sputter-coating (Ni, Fe) or spin-coating (Fe(NO3)3) for the catalyst deposition. Figure 27 shows scanning electron microscope (SEM) pictures of CNT brush grown perpendicular to the substrate. The backscattered electron image (Fig. 27b) reveals small metal clusters (white spots) on top of the CNT bundle. This image supports emphatically that the growth model for carbon fibers proposed by Baker and Harris is also valid for CNTs. Figure 28b shows a TEM picture of a nanotube end with the encapsulated metal catalyst.

Fig. 26. Proposedmodelfor catalytic growthof CNTsaccordingto the model of Baker and Harris [86] proposedfor carbon filaments.

COLD PLASMA PROCESSES

Fig. 27. SEM pictures of a CNT brush: (a) secondary electron image and (b) backscattered electron image. Catalyst: 0.0025 mol Fe(NO3)3 in ethanol, T = 700~ 2% CH4 in H2, p = 50 mbar (from [87]).

Fig. 28. (a) SEM image of nanotubes inside the CNT brush in Figure 27 (from [87]). (b) TEM image from the end of a CNT with the encapsulated metal catalyst (from Anke Weidenkaff, Universit~it Augsburg, Germany).

235

236

GRONING

Fig. 29. SEM image of patterned CNT film grown on a silicon wafer. The Fe(NO3) 3 catalyst was deposited by microcontact printing. From a 0.01 mol Fe(NO3)3 ethanol solution (from [87]).

The oriented growth of the CNT inside the brush is forced by the tube density. Above a critical density the direction of the growing nanotube is confined by the surrounding growing tubes. A zoom with the SEM into the CNT brush (Fig. 28a) shows straight as well as twisted nanotubes forming a kind of tissue. The straight tubes may have the lowest growth rate and may limit the growth rate of the whole brush by anchoring the "head" of the brush to substrate. This "head" (Fig. 27) is composed by clusters of the metal catalyst and probably by amorphous carbon. Fast growing nanotubes cannot get through this "head" and are forced to twist. This explains the constant height of the nanotubes in the brush. Since the CVD process needs a catalyst for the CNT growth it is relatively easy to prepare patterned CNT films. It has been shown recently that patterned CNT can be prepared by standard lithographic techniques [88, 89]. We used microcontact printing to pattern the catalyst onto the substrate [90]. For this a polydimethylsiloxane stamp was first hydrophilized to considerably increase the affinity between the stamp and the metal catalystethanol solution. The stamp was subsequently inked and after drying the catalyst was printed on a silicon wafer. Figure 29 shows a SEM image of patterned CNT film produced by the described microcontact printing technique.

2.2. Plasma Polymerization 2.2.1. Generals The development of plasma polymerization processes began in the 1950s [91, 92] and since the 1960s plasma polymerization processes have been studied intensively [93-95]. Plasma polymerization is essentially a PECVD process. It refers the deposition of polymer films through reactions of the plasma with an organic monomer gas. Plasma polymerization is a specific type of plasma chemistry and involves homogeneous (Table I)

Fig. 30. Reactiondiagram of the plasmapolymerizationprocess accordingto Poll et al. [96].

and heterogeneous (Table III) reactions; the former are reactions between plasma species and the latter are reactions between plasma and surface species and the surface species itself. The two types of reactions are often called "plasma-state polymerization" and "plasma-induced polymerization" [96]. Several kinetic models of plasma polymerization have been proposed. The most popular are the models of Yasuda [8], Poll et al. [96], and Lam et al. [97]. These models involve ablation and polymerization mechanisms in a competitive process (see Fig. 30). The expression "plasma polymerization" is strictly spoken not correct because the process results in the preparation of a new type of material and is not a kind of polymerization in the classical sense. In contrast to conventional polymerization, based on molecular processing, the plasma polymerization is an atomic process with rearrangements of the atoms within the monomer. Consequently the materials formed by plasma polymerization are very different from conventional polymers. Its structures are more like highly crosslinked oligomers. This special structure makes plasma polymers generally chemically and physically different from conventional polymers. Plasma polymers are generally: (1) chemically inert, (2) very adherent to a variety of substrates including polymer, glass, and metal surfaces, (3) pinhole-free, (4) easily formed with thicknesses from microns down to nanometers, and as multilayer films (Section 2.1.1) or films with grading of chemical or/and physical properties. Plasma polymers find applications as adhesion promoters for all kind of substrates, membranes for gas separation or vapor barriers, UV protection coatings, antireflection coatings, photoresist, antiadhesive film, etc. Plasma polymerization is a field somewhere between physics and chemistry. The choice, excitation, and characteriza-

COLD PLASMA PROCESSES

237

Fig. 31. Schematicillustration of the different film structures of plasma polymers: (a) grafted monomers, (b) low crosslinked (polymerlike), (c) highly crosslinked, compact (hard coating).

tion of suitable plasmas presume a well-founded knowledge of plasma physics, but their applications to relevant technical problems require the experience and intuition of chemistry. Systematic investigations on a large scale of plasma polymerization began in the 1970s on three classes of monomer, hydrocarbons, fluorocarbons, and siloxanes. As mentioned in Section 2.1.1 the plasma polymerization process allows formation of films with a variety of physical and chemical properties, starting from the same monomer, only by changing the plasma parameters. In general the energy flux into the growing plasma polymer film is decisive for the structure and the properties of the film. With increasing energy flux the film usually becomes harder, more disordered, and crosslinked with reduced hydrogen content. In opposition a low energy flux causes a plasma polymer that retains more the molecular structure of the monomer. The approach to create soft plasma polymers instead of hard coatings in the PECVD process is the minimization of the plasma-precursor and plasma-film interactions. Summarized, the following plasma conditions may aspire to achieve enhanced control of the plasma polymerization chemistry [98]: (1) minimization of the W~ F M parameter, called the Yasuda parameter [8] (W: power coupled into the plasma; F: flow rate; M: monomer molecular weight), (2) use of monomers with polymerisable double bonds, (3) use of a Faraday cage around the substrate, (4) sample position downstream from the plasma zone, (5) use of cold substrate, (6) pulsed plasma excitation to reduce the plasma on time (periodicity T ~ 10 .3 s). It is obvious that precautions (3)-(6) reduce the demanded plasma-precursor and plasma-film interactions. The W / F M parameter is a value associated with the molecular weight of the polymer forming radical. It contains the dissociation probability, represented by the plasma power P, the dwell-time of the monomer in the plasma zone, represented by the flow rate F, and the molecular weight of the precursor M. The smaller the W / F M parameter, the more the plasma polymer retains the chemical structure of the precursor. Figure 31 shows schematically the different film structures which can be created by plasma polymerization. Plasma polymerization conditions with very weak plasma interactions lead to the formation of an ultrathin film of grafted monomers (Fig. 31 a). Such films are of great interest in biosensor surface engineering. Adsorption is an ubiquitous phe-

Fig. 32. Polyethersulphonemembrane with a 0.4 lxm thick plasma polymer coating for permeability selective gas separation. Reprinted with permission from [99].

nomenon that occurs when molecules and materials meet at surfaces. In biosensors applications, the nonspecific adsorption of biomolecules may lead to reduced sensitivity or to a loss of sensitivity with time. Grafted monomer films can be used as spacer layers for specific immobilization of biomolecules. Crosslinked plasma polymers show excellent gas barrier properties, which make them interesting as membranes for permeability selective gas separation (Fig. 32). This application of plasma polymers was discussed in great detail by Nomura et al. [ 100] who have described the gas separation behavior of a variety of plasma polymers. They found that the separation of H2/N2 and H2/CO2 is molecular sieve type, i.e., based on difference in molecular size, and for O2/N2, CO2/CH4 solution-diffusion type separation, whereby sieve type separations were more effective. The permeability ratio for the above mentioned gas mixtures is between 3 and 50 [ 100-102]. In highly crosslinked plasma polymers (Fig. 31 c) the chemical structure of the precursor is no longer retained. The chemical and physical properties of these films differ completely from those of conventional polymers. The films are generally chemically inert, compact, pinhole-free, and hard. Well known examples of such films are diamondlike carbon synthesized from hydrocarbons discharges, SiO2 and Si3N4 synthesized from silane, and siloxane plasmas. Such films are used to impart abrasion resistance to softer, especially optical, substrates. An excellent review on plasma polymerization of organosilicones has been given by Wr6bel and Wertheimer [8]. A promising application of plasma polymers is as solid lubricant or antiadhesive film in surface micromachining. Surface micromachining, defined as the fabrication of micromechanical structures from deposited thin films, is one of the core technologies underlying microelectromechanical systems (Fig. 33), which promises to extend the benefits of microelectronic fabrication technology to sensing and actuating functions. Such microstructures typically range from 0.1 to several ~tm in thickness, with lateral dimensions of 3-300 ~tm, and lateral and vertical gaps to other structures or to the substrate of around 1 ~m. The large surface area and the small offset from adjacent surfaces makes microstructures especially vulnerable to adhesion upon contact.

238

GRONING

The adhesion of microstructures to adjacent surfaces can occur either during the final steps of the micromachining process (release-related adhesion) or after packaging of the device, due to overranging of input signals or electromechanical instability (in-use adhesion). The causes of strong adhesion can be traced to the interfacial forces existing at the dimensions of microstructures. These include capillary, electrostatic, van der Waals, and chemical forces. An effective treatment of microstructures to reduce stiction must provide a hydrophobic, conductive surface with a low surface energy in order to avoid electrostatic forces and the formation of water layers on the surface, thereby eliminating van der Waals and capillary forces altogether. Plasma polymers in the form of grafted monomers or ultrathin polymerlike films [103] are effective to reduce stiction. The Centre Suisse d'Electronique et de Microtechnique (CSEM) used such a film to prevent stiction in an electrostatic microshutter array for high-speed light switching (Fig. 34). Each microshutter consists of a shutter blade, a suspension beam, and several electrodes and stoppers. The microshutter is

a typical bistable microelectromechanical device where the active position of the movable shutter is confined by mechanical stoppers. These stoppers are exposed to very large mechanical loads by adsorbing the momentum and the kinetic energy of the shutter. It was observed that after millions of cycles shutters could become immobilized against the stoppers. A solution for this in-use stiction problem is a hydrophobic antistiction coating of the shutter and stopper walls.

2.2.2. Plasma Polymerized Fluorinated Monomer Coatings As already mentioned, the plasma polymerization involves deposition and ablation mechanisms in a competitive process. This behavior can be observed particularly well in fluorocarbon sustained discharges. Pioneering work on fluorocarbon sustained discharges was done by Coburn and Winters [ 104] in the late 1970s. They found that fluorocarbon sustained discharges can be operated in overall polymerization or etching conditions depending on the F/C ratio of the precursor (Fig. 35). Typically, a high F/C ratio of the precursor, e.g., CF4, leads to efficient etching, whereas a low F/C ratio, e.g., C2F4, favors easy polymerization. The ability to tune the fluorocarbon sustained discharge for polymerization or etching demands the presence of three competitive active species in the discharge, namely CFx radicals as reactive fragments for the polymer deposits, the F atoms to trigger the etching by forming volatile fluorides and charged particles. The excess of one of these species defines the polymerizing or etching behavior of the discharge. If we consider the CF2 radicals as the main polymerizing species then the characteristic of the fluorocarbon discharge can be simply determined by the corresponding chemical equation: CF4

Fig. 33. SEM imagefroma microelectromechanical system(fromSandiaNational Lab Server (http://www.sandia.gov)).

plasma>

CF2 + 2F

C2F6 plasma> 2CF2 + 2F plasma> C4F10 4CF2 + 2F

etching condition boundary condition polymerizing condition

Fig. 34. Electrostaticmicroshutter array in polysilicon. (a) Close-up picture of the shutter array. (b) Layout of the shutter design (length 100 ~m) (from CSEM"Scientific and Technical Report 1999" [64]).

COLD PLASMA PROCESSES

Fig. 35. Boundary between polymerization and etching conditions as a function of the fluorine to carbon (F/C) ratio and the negative substrate bias. Additional oxygen displaces the boundary to lower F/C ratio, hydrogen to higher F/C ratio (according to Coburn and Winters [104]).

Therefore, a better criterion for characterizing the plasma behavior is the ratio of the active species [F]/[CFx] rather than the F/C ratio of the precursor. The active species in excess defines the etching or polymerizing behavior of the plasma. The relative ratio of the active species can be varied by changing precursor gas or by varying the type and the amounts of additive gases. Oxygen as additive gas increases the etching behavior of the fluorocarbon discharge, while the addition of hydrogen increases the polymerization behavior. In fact, hydrogen reacts with F atoms, leading to unreactive HF resulting in a reduced etching activity. Obviously similar behavior can be obtained with a precursor containing hydrogen, such as CHF3. On the other hand, active carbon sites can be saturated by O atoms and converted to inactive CO, CO2, and COF2. F atoms are no longer recombined and their content therefore increases, resulting in a higher etching activity. Positively charged particles are the third active species influencing the characteristic of the fluorocarbon discharge. These particles are accelerated to the substrate and affect etching and heterogeneous polymerization processes. With increasing particle energy (substrate bias) the etching process is enhanced, as indicated by the bias dependence of the polymerization/etching boundary in Figure 35. We take advantage of the behavior illustrated in Figure 35 to develop a "self-thickness-limited" plasma polymerization process to create an ultrathin antiadhesive film [103]. With the process we were able to produce films with an extremely low surface energy of 4 mJ m -2 and 5 nm thickness, autocontrolled by the plasma. The developed deposition process takes place in two steps, a growth and a treatment step. With the CF4/H2 gas mixture used, we tuned the plasma conditions such that the polymerization starts close to the polymerization/etching boundary (Fig. 36, point I). Due to the mobile electrons in the plasma the growing insulating polymer film becomes negatively charged until it reaches the polymerization/etching boundary (Fig. 36, point E). At this point, the etching process balances the polymerization process and the deposition changes from the growth to the treatment step. During the growth step (t < 2 min) the film is characterized by small CF2

239

Fig. 36. Schematic illustration of the a "self-thickness-limited" plasma polymerization process. Reprinted with permission from [ 103], 9 1996, American Vacuum Society.

[Cls I

CF2 ~-.~.~,~.,.~...~d~ C~/~ CHx i m

c C m

'

'

I

295

.

.

.

.

I

290

.

.

.

.

I

285

.

.

.

Binding Energy [eV]

.

I

'

'

280

Fig. 37. Cls XPS spectra for different deposition times. (a) Ni substrate, (b) 2 min, (c) 6 min, (d) 10 min. Reprinted with permission from [103], 9 1996, American Vacuum Society.

and high CHx content (Fig. 37b). In this phase of the deposition process the antiadhesive property of the film is not extraordinary but the adhesion to the Ni substrate is excellent. During the treatment step the CHx groups at the film surface are transformed to CF2 groups (Fig. 37c and d). At the end of the deposition process the plasma polymer film contains 85% CF2 groups (Fig. 38) and shows the extremely low surface energy of 4 mJ m -2, which is 4 times lower than that of Teflon | The

240

GRONING

excellent hydrophobic behavior of this film is demonstrated in Figure 39 by a water droplet on a Swiss coin covered with such a plasma polymer film. The film was tested as an antiadhesive coating for the replication of micro-optical structures, using a Ni shim with a very fine surface relief grating (400 nm periodicity) to hot emboss (T = 180~ polycarbonate. The tests demonstrate the excellent antiadhesive property of the film against the polycarbonate and reveal a good adhesion of film with the Ni shim [ 105, 106].

Fig. 38. DeconvolutedCls XPS spectrum of the PPFM film. Reprinted with permission from [103], 9 1996, AmericanVacuum Society.

2.3. Surface Treatments The most widespread industrial application of cold plasmas is in cleaning and treatment of surfaces, particularly of polymer surfaces. Plasma treatment of polymer surfaces to increase their adhesive properties regarding painting, printing, or metallization is nowadays a well established and successful processes in the automobile, food packaging, capacitor (Fig. 40), and electronic industries. The images in Figure 41 show two applications of metallized polymer foils where cold plasma treatment of the polymer is used to improve the adhesion to the metal film. One example is A1/Zn metallized (d = 15 nm) polypropylene (PP) for high energy density capacitors [108]. Such capacitors are used in high power electronics. On the new Swiss high power locomotive of the "type 465," 3000 kg or 4000 km of this segmented metallized polymer foils (d = 15 ~tm, b = 15 cm) are installed as capacitors. Compared to the conventional high power capacitor technology where metal and paper sheets are wound to a capacitor, the new technology with the segmented

Fig. 39. Waterdroplet on a Swiss coin covered with a 5 nm thick antiadhesive plasma polymerfilm. Reprinted with permission from [103], 9 1996, American Vacuum Society.

Fig. 40. Schematicdrawingof the high energydensity capacitor manufacturedby Montena SA, CH-1728 Rossens, Switzerland. Reprinted with permission from [107].

COLD PLASMA PROCESSES

Fig. 41. On the left: mosaic structure of A1/Zn metallized PP used as high energy density capacitors. The picture illustrates the self-healing effect of the mosaic structure after an electrical breakdown in a segment. Reprinted with permission from [107]. On the right: laser microstructured test device of Cu metallized PI for the application as a flexible electronic circuit board.

electrode metallized on PP allows one to increase the energy density by a factor of more than two. The segmentation of the electrode is important for the self-healing effect in the case of a breakdown through the dielectric (PP), which makes the capacitor defect-tolerable and safe. In case of such a breakdown in one of the segments the small current gates interconnecting the segments serve as fuses; they isolate the segment and therefore the breakdown from the rest of the electrode [ 109]. The other example is Cu metallized polyimide (PI) which will be used as microstructured flexible electronic circuit boards. The patterning is made by laser delamination irradiating the metallized PI with UV light through a mask. In the domain of surface cleaning the cold plasma has been established as the cleaning technique for the nanometer scale. In comparison to wet chemical processes cold plasmas are environmentally friendly and cheaper, and a higher cleaning degree of the surface can be achieved.

2.3.1. Plasma Treatment to Improve Adhesive Properties The notion of adhesion can be misleading, because it refers to several meanings depending on the context [110, 111]. In physics or chemistry, the adhesion is directly connected to the intermolecular forces acting across an interface. From a technological point of view, the adhesion corresponds to the mechanical force or energy that is required to separate two bodies in intimate contact. The two different meanings of "adhesion" are illustrated in Figure 42. When two bodies are brought into intimate contact (path: "bond formation" in Fig. 42) a new interface is formed at the expense of two free surfaces. The nature of the interaction at the interface determines the adhesion energy (Ea). Thermodynamically, this energy is defined as the difference between the energy of the initial state (Ei), when the two bodies are separated, and the final state ( E f ) , when they are in intimate contact. The adhesion energy (Ea) is then, according to Duprr,

Ea := Ei - E f = (YA + ?'B) -- YAB

Dupr6 equation

241

Fig. 42. Illustrationof the two different notions of the "adhesion."

Here, VA, FB are the surface energies of the bodies A and B, and YAB is the interface energy of the two bodies in contact. From the Dupr6 equation it is clear that the adhesion energy Ea is in the order of the surface energies of the bodies, also mJ m -2. In this thermodynamic sense the adhesion is a pure interface phenomenon determined by a few monolayers of atoms at the interface. Apart from the formation of a mechanical bond we may examine the process to break this bond (path: "adhesion test"). While the adhesion energy from the Dupr6 equation is on the order of mJ m -2 the energy Wa measured in an adhesion test amounts to several hundreds of J m -2. The reason for this huge difference in the adhesion energy is the deformation energy Wd, which has to be brought up in all adhesion tests. This indicates that the measurement of the practical adhesion is actually a superposition of adhesive and elasticity properties at the interface. The following factors or theories contribute to mechanism of adhesion: 9 9 9 9

mechanical interlocking, diffusion theory, electronic theory, adsorption theory.

2.3.1.1. Mechanical Interlocking This theory associates adhesion to mechanical interlocking around the irregularities at the substrate surface. However, the effects of topography on adhesion are much more complex. The potential bonding area of a rough surface is clearly greater than for a smooth surface. However, the surface topography has to be appropriate. For example, if the viscosity of an adhesive is high, the irregularities on the surface have not to be deep and narrow, because then the wetting may be far from complete. The Washburn equation, which describes the time t for a liquid to move a distance z in a capillary of radius r, gives an indication of the wetting rate for irregularities by the adhesive: t -

2r/

z2

F cos0 r

Washburn equation

242

GRONING

Here r/and y are the viscosity and surface tension of the adhesive, respectively. 0 is the wetting angle of the adhesive on the substrate. The wetting rate may therefore be much lower for small capillaries and for low energy surfaces such as for nonpolar polymers.

2.3.1.2. Diffusion Theory The intrinsic adhesion between polymers can be affected by the mutual diffusion of polymer molecules across the interface. But this requires that the macromolecules or chain segments of the polymers possess sufficient mobility and are mutually soluble. The latter requirement may be restated by the condition that they possess similar values of solubility parameters. The condition of similar solubility parameters is only valid if the polymers are amorphous. If the polymer possesses a significant degree of crystallinity then the free energy of crystallization makes it more resistant to form a solution and the diffusion process can be neglected for the adhesion.

2.3.1.3. Electronic Theory If the two bodies (A and B) in contact have different electronic band structures it is likely to have some electron transfer on contact to balance the Fermi levels: This will result in the formation of a double layer of electrical charges at the interface. Deryaguin's theory essentially treats the interface between two bodies as a capacitor where the electrostatic pressure Pc of this double layer capacitor corresponds to the adhesion force: S0 (~bA -- ~ B ) 2

Pc=--d-2 4~A -- 4~B

e

e =" Vc

4~A,~B

electrostatic pressure contact voltage work functions elementary charge charge separation

For a contact potential of 1 V and a charge separation of 0.5 nm the electrostatic pressure Pc is 20 MPa, which is only a fifth of the pressure created by van der Waals forces under the same conditions. The effect of charge transfer at the interface on the adhesion is secondary at best.

Nowadays it has become generally accepted that while the adsorption theory has the widest applicability, each of the other theories may be appropriate under certain circumstances and often make a contribution to the intrinsic adhesion forces which are acting across the interface. Therefore, the following well known basic requirements have to be considered for good adhesion: 9 absence of weak boundary layers, 9 good contact between the bodies, 9 avoidance of stress concentration at the interface which could lead to disbonding.

2.3.2. Surface Cleaning Maybe the most important requirement for good adhesion is that the weak boundary layer can be removed. In some cases one has to prevent the formation of a weak boundary layer. In practice, it cannot be considered that the bulk structure of the solid is preserved at the surface. Technical solids show in general a surface structure with a reaction layer and a contamination layer on top, as sketched in Figure 43. These layers can act as a weak boundary layer and prevent adequate adhesion. For this reason it is very important to proceed to a surface cleaning process to remove the contamination from these layers, and if necessary also the oxide layer, to obtain optimal adhesion. The crucial effect that the contamination layer may have on adhesion and tribology will be shown here using the example of the thermosonic wire bonding process. 2.3.2.1. Thermosonic Wire Bonding Thermosonic wire bonding is the most widely used assembly technique in semiconductors to connect the internal semiconductor die to the external leads (Fig. 44). To prevent high cost and unreliable microelectronic devices wire bonding failures must be eliminated. The microelectronic industry accepts a failure rate of 1 ppm for the wire bonding process. Approximately 27% of failures in microelectronic devices are caused by wire bonding failure [112]. Therefore the wire bonding process is the most expensive step in microelectronic packaging. The continuous increase in microelectronic packing density demands a permanent

2.3.1.4. Adsorption Theory The adsorption theory of adhesion is the most widely applicable theory. It proposes that, if sufficiently intimate molecular contact is achieved at the interface, the materials will adhere because of the interatomic forces, which are established between the atoms at the interface of the bodies in contact. The strength of these bonds and their range can be estimated using classic approaches of electrostatics and electrodynamics if the spatial structure and distribution of molecules and atoms are known. The adsorption theory allows the definition of the thermodynamic work of adhesion Ea (Dupr6 equation) required to create two surfaces by breaking a solid.

Fig. 43. Schematicillustration of the surface structure of a technical surface.

COLD PLASMA PROCESSES

243

Fig. 45. Thermocouple in the bondability analyzer (diameter of Au and Ni wire 25 ~tm)(from [107], reprinted with permission).

Fig. 44. (a) Capillary with the bond wire and the microelectronic device. (b) Wire bond on 80 Ixm large contact (from ESEC SA, CH-6330 Cham, Switzerland).

progress in wire bonding, which is only possible by a detailed understanding of the physics of the bonding process. The thermosonic wire bonding process begins with a gold ball at the end of the wire, centered within the inside chamfer of the bonding capillary. During the bonding process the gold ball is vibrated at the ultrasonic frequency over the bond pad. The heat generated by this friction process causes microwelding at the interface [113], yielding to a stable mechanical and electrical bond. Since the bonding process is a kind of welding process it is crucial to dissipate maximal friction heat Q at contact surface. This demands a maximal friction coefficient/z. Several investigations have shown that the wire bond quality of Au and Ag contacts is determined decisively by the organic contamination layer on the bond pad [ 114-116]. One origin of the organic contamination is the die bonding process, where the die is hot glued on the substrate. During this process organic material can be evaporated and deposited on the contacts. From XPS and pull force measurements, we found that good bond contact quality is only achieved if the organic contamination layer on the bond pad is thinner than 4 nm. To study the influence of the contamination on the tribosystem of the thermosonic wire bonding process we developed an apparatus which allows one to characterize the bonding behavior of the bond pad and to study bonding process in detail and in real time [117]. The principle of the developed bondability analyzer is the measurement of the temperature at the bond ball during the thermosonic wire bonding process by using a thermocouple instead of the bond wire (Fig. 45). The temperature at the bond ball is directly correlated to the dissipated heat during the bonding process. With the bondability analyzer we found that the thin contamination layer acts as a very efficient lubricant. Removing the contamination layer by plasma cleaning increases the friction coefficient/z and consequently the dissipated heat by a factor of four, as indicated by the thermosignals in Figure 46. This result absolutely conforms to measurements of the static friction coefficient/Zs of Cu(111) sliding on Cu(111) (Fig. 47), both surfaces covered

Fig. 46. Thermosignals of the bondability analyzer performed on an Ag plated Cu lead frame before and after mr/H 2 plasma cleaning (friction time 20 ms). Reprinted with permission from [107].

6.~ *-.5 C '

4

or

."

9

I

&

c0 3

t~

a

limiting value PS =0.38+ 0.07

'~

i

"~I.~...~.

..

t --{-)

-

0.01

r

'""

~

"

" '~'" "I

0.1

' '

"

"

"r

" "~ I

1

""

Trifluoroethanol coverage

~"

~'"

~''"

' ' ;i:

10

~'

( ML )

Fig. 47. The static friction coefficient/Zs as a function of triflouroethanol coverage on Cu(111). Reprinted with permission from [ 118], 9 1995, American Chemical Society.

244

GRONING

with trifluoroethanol (CF3CH2OH) [118]. The measurements show that below monolayer coverage the molecular adsorbates have no influence on the static friction coefficient tZs, while a sharp drop in tZs occurs at monolayer coverage over a thickness of 10 monolayers. Systematic investigations have shown that plasma cleaning (Ar/H2 plasma) of bond pads improves the pull force and reproducibility of thermosonic wire bonds significantly. The cleaning process of Ag contacts by Ar/H2 plasma is described in Section 2.3.4. Plasma cleaning of bond pads of different materials (Cu, Ag, Au) to improve the quality and the reproducibility of wire bond contacts is nowadays a successful and well established process in IC packaging.

2.3.3. Plasma Treatment of Polymers Owing to the low intrinsic adhesive properties of polymers, many applications of these materials require a surface pretreatment. Therefore, surface pretreatments of polymers in order to enhance their adhesive properties are of great technological importance. Plasma treatment of polymers is one of the more recent methods to achieve improved adhesion in systems such as polymer-adhesive [ 119, 120] of polymer-metal interfaces [ 121 ]. The merits of plasma surface treatment to improve the macroscopic adhesion strengths are generally accepted. Different effects of the plasma treatment on polymers are known. They include cleaning by ablation of low-molecular-weight material, activation of the surface, dehydrogenation, change in surface polarity and wetting characteristics, crosslinking and chain scission, and structural modification. These effects depend very much on the considered polymer and plasma used.

2.3.3.1. Chemical and Structural Modifications of Surfaces Plasma treatment is a very efficient process to increase the surface energy y, i.e., wettability of polymers, dramatically. After plasma treatment polymer surfaces can easily show water contact angles 0 smaller than 15 ~ as illustrated in Figure 48. The increase of the surface energy y of polymers by plasma treatment is related to the surface cleaning and the formation of polar bonds at the surface. For example, O2 plasma is very effective to increase the surface energy of polyolefines as PP or polyethylene (PE) by forming oxygen functionalities (Fig. 49). The oxidation of PP ( - C H C H 3 - C H 2 - ) in the O2 plasma occurs via dissociation of the methyl group ( - C H 3 - ) [122], as indicated by the relative intensity decrease of the associated peak in the valence band (Fig. 50). As discussed at the beginning of this section the practical adhesion Wa is related to the thermodynamic work of adhesion Ea defined by the Dupr6 equation. Under the assumption of an ideal surface treatment (bulk properties not affected), the practical adhesion is completely determined by thermodynamic work of adhesion Ea, i.e., the surface energies YA, ~ of the two bodies and the interface energy YAB of the bodies in intimate contact. Therefore it makes sense to maximize the surface energy y of the bodies to get optimal practical adhesion. In reality the plasma treatment of polymers is not limited to the topmost surface atoms and is therefore not an ideal surface treatment. For this reason plasma treatment on polymers has to be carried out very carefully. Plasma "overtreatment" is probably the most frequent cause for adhesive failures of metal films on polymers.

Fig. 48. Schematicillustration of the surface energy y of a plasma treated polymer as a function of the plasma exposure time.

COLD PLASMA PROCESSES

245

Fig. 51. Illustration of the side-chain scission in PMMA due to low energy ions. Reprinted with permission from [124], 9 1995, Elsevier Science.

Fig. 49. Cls XPS spectraofPP (a) as received, (b) 02 plasmatreated (t = 5 s, p = 1 • 10-2 mbar). Reprinted with permission from [123].

Fig. 52. Cls XPS spectra of PMMA, untreated and after 02 plasma treated with to different ion fluxes. Reprinted with permission from [124], 9 1995, Elsevier Science.

Fig. 50. XPS valenceband spectra of PP (a) as received, (b) 02 plasma treated (t = 5 s, p = 1 • 10-2 mbar). Reprinted with permission from [123].

The susceptibility of a polymer on structural changes induced by plasma treatment depends strongly on its chemical structure. For example, polymethylmethacrylate (PMMA) is very susceptible for structural changes during plasma treatment especially in plasma with high ionization degree [124]. Positive ions from the plasma react and neutralize at the partially negatively charged carbonyl oxygen (Fig. 51). After that, the created electron hole in the carbonyl group becomes filled by an electron transfer from the neighboring nonpolar C - C bond, cleaving side chains from the polymer backbone. In noble gas plasmas, where no incorporation of chemical active species is possible, all side chains within a thickness of 10 nm are removed after few seconds of plasma treatment. The ion induced degradation process is in competition to the aspired formation of polar bonds and must be suppressed. The C l s XPS spectra in Figure 52 illustrate the effect of the ion flux during 02 ECR plasma treatment on the chemical composition of the PMMA surface. The ion flux was varied by changing the position of the sample relative to the plasma zone.

246

GRONING

Fig. 53. Deconvoluted Cls XPS spectra of PMMA (left) and PET (right): (a) as received, (b) 02 plasma treated, and (c) Ar plasma treated. Reprinted with permission from [126], 9 1999, American Institute of Physics.

In this way the influence of the UV/VUV radiation is the same for both treatments and differences in surface modifications are correlated to the ion flux. Polymers with delocalized electrons (phenyl ring) in their chemical structure are generally less susceptible to ion induced damage [ 125-127]. This is because electron transfer from the delocalized electrons system to electron hole, created by the ion neutralization, can occur without breaking a bond. This is the reason plasma treatment on polyethyleneterephtalate (PET) is in general very successful, while it is very difficult on PMMA. The Cls XPS spectra in Figure 53 illustrate the type of chemical modifications on the PMMA and PET surface undergoing 02 and Ar ECR plasma treatment. The spectra reveal as already mentioned the etching of polar oxygen groups indicated by the lower intensity of the corresponding peaks (peaks located above E8 = 285 eV). The etching of oxygen functionalities is much stronger on the PMMA surface than on the PET surface, indicating that the plasma reaction on the polymer surface depends on the whole chemical structure of the monomer.

The stability of a polymer in the plasma is primarily determined by the response of the polymer on the plasma induced damage and less on the primary damage itself. Generally, surface modifications of polymers by plasma are always accompanied with degradation reactions of the polymer in the near surface layer. The thickness of the modified surface layer is typically 10 nm. This plasma modified surface layer is initially in a highly excited state and likes to relax. In the presence of a reactive metal film (adhesive layer, e.g., Cr) the functional groups introduced by the plasma tend to segregate to the metal, forming a covalent bond [ 123]. This process becomes equal to a phase separation process between the plasma modified surface layer and the bulk polymer, resulting in the formation of a weak boundary a few nanometers underneath the surface. Plasma pretreated metallized polymer foils show therefore usually cohesive fractures in peel strength measurements. Gong et al. [ 128] studied the effect of sticker groups ( - C O O H ) on the fracture energy of AI-cPBD-A1 interfaces (cPBD: carboxylated polybutadiene (PBD)) and found that a small amount of sticker groups improves the fracture energy considerably. They found a crit-

COLD PLASMA PROCESSES

247

Fig. 54. XPS spectra from the fracture surfaces from peel test fragments of Cu metallized polyimide (UPILEX) with a Cr adhesive layer peel strength of 12 N cm -1 . Reprinted with permission from [123].

ical concentration around 3 mol% to give a maximum bond strength. They showed that the sticker groups tend to segregate to the metal surface, resulting in a large concentration gradient of the sticker groups in the lattice layer close to the metal substrate. This investigation suggests that plasma modified polymers are very susceptible to reorganization processes, which may limit the cohesion in a few nanometers thick surfaces of the polymer, as seen above. These processes may be important for the aging behavior of the plasma modified polymer/metal interface. Because the plasma induced phase separation process occurs a few nanometers underneath the polymer/metal interface, surface sensitive techniques must be used to detect this effect, as shown in Figure 54 for Cu metallized PI. The small Cr signals (adhesive layer) in the XPS spectrum of the "Cu/Cr-side" peel test fragment indicate the cohesive failure in the polymer. The identical C 1s spectra of the "PI-side" fragment and the untreated PI and its difference to the spectra of the "Cu/Cr-side" fragment reveals that the cohesive fracture occurs along the interface of the plasma modified surface layer and the bulk polymer. To avoid phase separation processes between the plasma modified polymers and the bulk polymers degradation reactions must be minimized in the plasma treatment. As discussed, plasma surface modifications on polymers are mainly due to the formation of functional groups and degradation reactions. Radicals in the plasma remove hydrogen atoms on the polymer surface to form carbon radicals. Successively, these radicals combine with other radicals in the plasma to form new functional groups. On the other hand electrons and ions bombard the polymer surface making chain scission to form carbon radicals at the end of the polymer fragments. This may result in degradation reactions of the polymer chain to yield degradation products with low molecular weight. These low

Table IV.

Reaction Constants of the Dominant Recombination Processes in an O2 plasma [129]

Reaction

Rate constant k

e + O + ~ O* + O

0) and a large bandgap semiconductor showing "true" negative electron affinity(NEA: X < 0). Reprinted with permission from [163], 9 1996, Elsevier Science.

Ktittel et al. [162] have shown that the diamond (100) as well as the diamond (111) surface can be polished and hydrogen terminated in H2 plasma at 870~ and 40 mbar. The initial surface roughness of 7 nm (RMS) can be reduced to 1 nm by this plasma treatment (Fig. 66). This smooth and hydrogen terminated C(100) - (2x 1) : H surface shows a sharp (2x 1) LEED pattern and a strong NEA peak in the UPS spectrum upon annealing to 300~ [163]. At higher temperatures the hydrogen desorbs and the diamond (100) surface shows PES behavior. Few research groups have shown that 02 plasma produces moderately high erratic rates of reactive ion etching of diamond although accompanied by an increase of the surface roughness [165-168]. The addition of Ar results in a greater uniformity and better reproducibility than pure 02 plasma [166, 168]. In contrast, the etching of diamond in SF6 [167] and CF4 [169] plasmas produces round asperities on the diamond surface but without a decrease in overall roughness. The plasma etching of CVD diamond is attributed to ion-enhanced chemical etching. Steinbruchel et al. [ 170] have shown that reactive ion etching of

Fig. 66. AFM images of the diamond C(100) and C( l l l ) surfacesbefore and after H2 plasmatreatment. T =870~ p = 40 mbar. Reprinted with permission from [163], 9 1996, Elsevier Science.

=6h,

COLD PLASMA PROCESSES a wide range of materials occurs by a process of either physical sputtering or ion-enhanced chemical etching. In both processes, the etch yield Y(E) can be described by the following expression: Y(E) = a ( ~ i

- v/Eth)

Ei is the kinetic energy of the ion, Eth is the threshold energy for ion etching, and A is a constant, which is for ion-enhanced chemical etching significantly higher than for physical sputtering [171]. 2.4.2. H2 Plasma Treatment o f Graphite

The interaction of hydrogen atoms with graphitic surfaces is of outstanding interest for material science and combustion, as well as fundamental research. It is, e.g., a hot topic in astrophysics where the understanding of adsorption and diffusion processes of hydrogen on interstellar dust grain is believed to be a key issue for the explanation of H2 formation. Further, defects control many physical properties of solids and dominate the electronic behavior of nanoscale metallic and semiconducting systems, particularly at low dimensions. Graphite was one of the first materials for which long range order electronic effects caused by surface defects have been predicted and experimentally observed using scanning tunneling microscopy [ 172, 173]. Graphite is a semimetal composed of stacked hexagonal planes of sp 2 hybrid bonded carbon atoms. The ABAB stacking of these planes in a three-dimensional crystal creates two inequivalent sites with different properties with regard to the electronic structure: ot site atoms are exactly located above atoms of the underlying plane, whereas fl site atoms are located above the center of the hexagonal rings of the underlying plane. The weak Van der Waals interaction between adjacent planes leads to a suppression of the charge density at the Fermi level E F at ct sites [ 174].

255

The study of changes in the electronic structure of graphite due to adsorbates is relevant for other carbon materials (such as nanotubes, fullerenes, etc.) having the six membered ring as a structural unit. Recent theoretical work showed the existence of a chemisorbed state and a partial tetrahedrization (sp 3 hybridization) of the carbon atom in the graphite basal plane [175]. Different models used for the simulation of hydrogen adsorption on graphite yield qualitatively the same results but quantitative discrepancies regarding activation energies and chemisorption energies are current debated. Chen et al. [ 176] found the chemisorption of hydrogen on the basal plane of graphite to be endothermic. A metastable state exits in all examined configurations, the most stable one being the on-top site. The on-top configuration also shows the lowest activation barrier of ~ 1.8 eV. This high energy barrier makes it impossible to populate this state with atomic hydrogen formed in a thermal source [ 177], where the energy of the atoms is only k T. We showed that in cold H2 plasma the energy of the ions hitting the substrate (typically ~ 10 eV) is large enough to populate the hydrogen chemisorption state on graphite [178]. By performing a combined mode of scanning tunneling and atomic force microscopy we found long range electronic effects caused by hydrogen-carbon interaction at the graphite surface. Two types of surface modifications could be distinguished by this method: chemisorption of hydrogen on the basal plane and atomic vacancy formation. 2.4.2.1. Chemisorbed Hydrogen

Scanning the cold plasma treated graphite surface in the AFM contact mode with simultaneous acquisition of the current signal reveals clear superlattice-type modifications of the electronic properties over a distance of 25 lattice constants (Fig. 67). However, no modifications were detected in the topography im-

Fig. 67. (a) Current image of a H2 plasma treated graphite surface recorded in AFM contact mode (94/~ x 94/~). The inset shows the center of the fast Fourier transform of the image. (b) The same data as (a) after applying a two-dimensional band pass filter to isolate the superlattice component. Reprinted with permission from [175], 9 1999, Elsevier Science.

256

GRONING

age. The inset of Figure 67a shows the center of the Fourier transform of the current image. The six inner spots correspond to the (~,/3 • ~/-3)R30 ~ superstructure. The six outer spots with the same orientation are due to the second harmonic of the superlattice, whereas the six outer spots rotated by 30 ~ originate from the regular graphite lattice. The threefold symmetry of the scattering pattern is clearly seen in Figure 67b, which shows the same data as (a) but after applying a two-dimensional band pass filter to isolate the superlattice contribution. Kelly et al. [179] discussed the dependence of the orientation of the threefold scattering pattern on the type of atom (ct or/3 site atom), which is affected by an atomic vacancy. Scattering patterns originating from ct site defects are rotated by 60 ~ relative to the ones from/3 site atoms, reflecting the symmetry of the dangling bonds of the nearest neighbors. These bonds are also affected if the hybridization of a carbon atom is changed by forming an additional bond to a chemisorbed hydrogen atom. Only one type of carbon atom seems to be affected. If c~ and/3 sites were involved, one would expect a sixfold symmetric scattering pattern. A more detailed analysis of the bandpass filtered current image shows that the

measured scattering pattern results from two interfering scattering patterns with the same orientation, but with an origin shift of 2.46 ,~, i.e., the distance between two carbon atoms of the same type. 2.4.2.2. Atomic Vacancies

Typical images of the simultaneously recorded current and topography images of a local defect are shown in Figure 68. The topographic structure of this defect consists of three local depressions with a corrugation of 0.3 ,~. This strong enhancement of the corrugation, as compared to the 10 times weaker corrugation of the defect free zones, is due to atomic vacancies in the first carbon monolayer, which were formed upon the H2 plasma treatment. The vacancy formation probability is found to be five times smaller than hydrogen chemisorption. The depressions in Figure 68b are separated by 4.1 ,~. The direction and the distance between the topographic minima show that carbon atoms of the same type (or or/3 site atoms) are affected (distance between second nearest neighbors of the same type is x/~. 2.46 ,~ - 4.26 ,~). The current image shows the lo-

Fig. 68. Simultaneouslyrecorded current and topography image of a H2 plasma treated graphite surface in AFM contact mode (58 A • 78 A). (a) Current image with fast Fourier transform (inset). Current range: 2 nA (black)-40 nA (white). (b) Topography image with line profile from A to B. (c) Calculated LDOS in the vicinity of a single atomic vacancy using a tight binding model. Reprinted with permission from [175], 9 1999, Elsevier Science.

COLD P L A S M A PROCESSES cal density of states (LDOS) in the vicinity of the defect and again the (~/3 • ~/3)R30 ~ superlattice, which is visible over 25 lattice constants. The calculated LDOS for a single atomic vacancy [ 172] (Fig. 68c) shows in all details the same features as the experiment. The threshold energies for sputtering off carbon atoms have been calculated by Bohdansky and Roth [ 14] (see Section 1.3). For the interaction of hydrogen ions (proton) with graphite an energy threshold of Eth ~" 36 eV is estimated. The maximum ion energy in ECR plasma treatment is given by the plasma potential. The maxium ion energies in the plasma chamber used for this experiment range from ~,22 eV (p = 10 -4 mbar) to about 9 eV (p = 10 -1 mbar) [180], which is below the estimated energy threshold for vacancy formation by sputtering. A possible channel for vacancy formation is the neutralization process of the ions. The charge transfer from the surface to the approaching ion leads to a weakening and a finite destruction cross section of the s p 2 bonds [ 181 ].

3. O U T L O O K In the past 15 years many cold plasma processes have been established in various technological applications. Many innovative new products have only become possible by using cold plasma processes. Many industries, e.g., optical, microelectronic, food packaging, and mechanical engineering industries, use cold plasma processes in various areas of applications (Fig. 69). On an industrial scale plasma processes are relatively cheap s o that even for low cost products (e.g., food packaging) plasma processes are widely used. Compared to wet chemical processes the consumption of chemicals is much lower for plasma processes, which make them much more ecologically safe. The ecological pressure makes plasma processes very attractive for the industry and is a strong driving force that the field of applications increases permanently.

Fig. 69. Areasof application for cold plasma processes.

257

With the present contribution we touched briefly on a few cold plasma processes important in surface science and technology. The selection of examples is by no means complete. Important and well established industrial applications, for example, reactive ion etching of semiconductors especially silicon or plasma polymerization of organosilicones and organometallics, are not discussed in this chapter. Nevertheless we hope that the present contribution gives an illustrative introduction of cold plasma processes in surface science and technology. For the future, efforts in plasma diagnostics (not discussed in this chapter) have to be done for a better understanding of the particular plasma processes. This will allow design of new and better plasma sources with characteristics optimized for intended processes, which guarantee that the areas of applications increase permanently.

Acknowledgments I thank M. Collaud Coen, A. Schneuwly, R Ruffieux, R Schwaller, O. Nilsson, M. Bielmann, and O. Grrning for a lot of excellent work done on the investigations presented here. Generous financial support was received from the Swiss National Science Foundation (Programs NFP 36 and NFP 47 and PPM) and the Commission of Technology and Innovation (CTI) of Switzerland.

REFERENCES 1. I. Langmuir, Phys. Rev. 33, 954 (1929). 2. E E Chen, "Introduction to Plasma Physics." Plenum Press, New York, 1974. 3. S. Ichimaru, "Basic Principles of Plasma Physics." Benjamin-Cummings, Redwood City, CA, 1973. 4. B. Chapman, "Glow Discharge Processes." Wiley, New York, 1980. 5. A. Grill, "Cold Plasma in Materials Fabrication." IEEE Press, New York, 1994. 6. A. Auciello and D. L. Flamm, "Plasma Diagnostic," Vol. 1. Academic Press, San Diego, 1990. 7. R. d'Agostino, "Plasma Deposition, Treatment, and Etching of Polymers." Academic Press, San Diego, 1990. 8. H. Yasuda, "Plasma Polymerization." Academic Press, Orlando, 1985. 9. H.S. Butler and G. S. Kino, Phys. Fluid 6, 1346 (1963). 10. A. D. MacDonald and S. J. Tetenbaum, "Gaseous Electronics" Vol. 1. Academic Press, New York, 1978. 11. M. Venugopalan, "Reactions under Plasma Conditions," Vol. 1. WileyInterscience, New York, 1971. 12. J. Asmussen, J. Vac. Sci. Technol. A 7, 883 (1989). 13. R. Behrisch, G. Maderlechner, B. M. U. Scherzer, and M. T. Robinson, Appl. Phys. 18, 391 (1979). 14. J. Bohdansky, J. Roth, and H. L. Bay, J. Appl. Phys. 51, 2861 (1980). 15. S. Schiller, Chr. Metzner, and O. Zywitzki, Surf. Coat. Technol. 125, 240 (2000). 16. B. A. Movchan and A. V. Demchshin, Phys. Met. Metallogr. 28, 83 (1969). 1Z J.A. Thornton, J. Vac. Sci. Technol. 11,666 (1974). 18. J. A. Thornton, Annu. Rev. Mater. Sci. 7, 239 (1977). 19. M. Lardon, R. Buhl, H. Singer, H. K. Pukler, and E. Moll, Thin Solid Films 54, 317 (1978).

258

GRONING

20. G. Carter and D. G. Armour, Thin Solid Films 80, 13 (1981). 21. P. K. Bachmann, in "Ullman's Encyclopaedia of Industrial Chemistry," Vol. A 26, p. 720, 1996. 22. S. Aisenberg and R. Chabot, J. Appl. Phys. 42, 2953 (1971). 23. K. Enke, H. Dimigen, and H. Htibsch, Appl. Phys. Lett. 36, 291 (1980). 24. C. Donnet, T. LeMogne, L. Ponsonnet, M. Belin, A. Grill, V. Patel, and C. Jahnes, Tribol. Lett. 4, 259 (1998). 25. J. A. Thornton, in "Deposition Technologies for Films and Coatings" (R. E Bunshah et al., Eds.). Noyes, Park Ridge, NJ, 1982. 26. J. Robertson, Progr. Solid State Chem. 21, 199 (1991). 27. S.R.P. Silva, J. Robertson, and G. A. J. Amaratunga, "Amorphous Carbon: State of the Art." World Scientific, Singapore, 1997. 28. H. Tsai and D. B. Bogy, J. Vac. Sci. Technol. A 5, 3287 (1987). 29. P. Koidl, C. Wild, R. Locher, and R. E. Sah, in "Diamond and Diamondlike Films and Coatings" (R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl, Eds.), NATO-ASI Series B: Physics, Vol. 266, p. 243. Plenum, New York, 1991. 30. W.D. Sproul, Science 273, 889 (1996). 31. U. Helmersson, S. Todorova, L. Market, S. A. Barnett, J.-E. Sundren, and J. E. Greene, J. Appl. Phys. 62, 481 (1987). 32. W.D. Sproul, P. J. Rudnik, M. E. Grahan, and S. L. Rhode, Surf. Coat. Technol. 43/44, 270 (1990). 33. R. Hauert, J. Patscheider, L. Knoblauch, and M. Diserens, Adv. Mater 11, 175 (1999). 34. B. Meyerson and F. W. Smith, Solid State Comm. 34, 531 (1980). 35. H. Dimigen, H. Htibsch, and R. Memming, Appl. Phys. Lett. 50, 1056 (1987). 36. T.L. Jacobs, J. H. Spence, S. S.Wagal, and H. J. Often, "Applications of Diamond Films and Related Materials: Third International Conference," 1995, p. 753. 37. G. Francz, A. Schroeder, and R. Hauert, Surf. Interface Anal. 28, 3 (1999). 38. B.V. Deryagin and D. V. Fedoseev, Science 233, 102 (1975). 39. B. Dischler and C. Wild, "Low-Pressure Synthetic Diamond." SpringerVerlag, Berlin/Heidelberg, 1998. 40. P. K. Bachmann, in "Properties and Growth of Diamond" (G. Davies, Ed.), EMIS Datareviews Series, p. 349. Short Run, Exeter, 1994. 41. P. K. Bachmann, D. Leers, and H. Lydt, Diamond Relat. Mater. 1, 1 (1991). 42. J. E. Butler and R. L. Woodlin, Philos. Trans. Roy. Soc. London Ser. A 342, 209 (1993). 43. L. S. Piano, in "Diamond: Electronic Properties and Applications" (L. S. Pan and D. R. Kania, Eds.), p. 65, 1995. 44. R. Gat and J. C. Angus, in "Properties and Growth of Diamond" (G. Davies, Ed.), EMIS Datareviews Series, p. 325. Short Run, Exeter, 1994. 45. S.J. Harris, Appl. Phys. Lett. 56, 2298 (1990). 46. S. Skotov, B. Weimer, and M. Frenklach, J. Phys. Chem. 99, 5616 (1995). 47. M. Frenklach and K. E. Spear, J. Mater Res. 3, 133 (1998). 48. H. Liu and D. S. Dandy, Diamond Relat. Mater. 4, 535 (1995). 49. M. Ece, B. Oral, J. Patscheider, and K.-H. Ernst, Diamond Relat. Mater. 4, 720 (1995). 50. B.R. Stoner, G. H. M. Ma, S. D. Wolter, and J. T. Glass, Phys. Rev. B 45, 11067 (1992). 51. C. Wild, P. Koidl, W. Miiller-Sebert, H. Walcher, R. Kohl, N. Herres, R. Locher, and R. Brenn, Diamond Relat. Mater. 2, 158 (1993). 52. E. Maillard-Schaller, Study of the Interface between Highly Oriented Diamond and Silicon, Ph.D. Thesis No. 1145, Physics Department, University of Fribourg, Switzerland, 1996. 53. S.D. Wolter, B. R. Stoner, J. T. Glass, P. J. Jenkins, D. S. Buhaenko, C. E. Jenkins, and P. Southworth, Appl. Phys. Lett. 62, 1215 (1993). 54. N. Jiang, B. W. Sun, Z. Zhang, and Z. Lin, J. Mater. Res. 9,2695 (1994). 55. W. Kulisch, B. Sobisch, M. Kuhr, and R. Beckmann, Diamond Relat. Mater. 4, 401 (1994). 56. S.D. Wolter, T. H. Boert, A. Vescan, and E. Kohn, Appl. Phys. Lett. 68, 3558 (1996).

57. C.L. Jia, K. Urban, and X. Jiang, Phys. Rev. B 52, 5164 (1995). 58. J. Gerber, M. Weiler, O. Sohr, K. Jung, and H. Ehrhardt, Diamond Relat. Mater 3, 506 (1994). 59. S. Sattel, N. Weiler, J. Greber, H. Roth, M. Scheib, K. Jung, H. Ehrhard, and J. Robertson, Diamond Relat. Mater 4, 333 (1995). 60. E. Maillard-Schaller, O. M. Kiittel, P. Grrning, O. Grrning, R. G. Agostino, P. Aebi, L. Schlapbach, P. Wurzinger, and P. Pongartz, Phys. Rev. B 55, 15895 (1997). 61. E. Maillard-Schaller, O. M. Ktittel, P. Grrning, and L. Schlapbach, Diamond Relat. Mater 6, 282 (1997). 62. C.S. Fadley, in "Synchrotron Radiation Research" (R. Z. Bachrach, Ed.). Plenum, New York, 1989. 63. A. Olbrich, B. Ebersberger, C. Boit, Ph. Nierdermann, W. H~ani, J. Vancea, and H. Hoffmann, J. Vac. Sci. Technol. B 17, 1570 (1999). 64. Centre Suisse d'Electronique et de Microtechnique SA (CSEM), CH-2007 Neuch~tel, Switzerland. 65. M. W. Geis, N. M. Elfremov, J. D. Woodhouse, M. D. McAleese, M. Marywka, D. G. Socker, and J. E Hochedez, IEEE Trans. Electron. Device Lett. 12, 456 (1991). 66. C. Wang, A. Garcia, D. Ingram, M. Lake, and M. E. Kordesch, Electron. Lett. 27, 1459 (1991). 67. IBM Patent Server, www.patents.ibm.com. 68. O. Grinning, Field Emission Properties of Carbon Thin Films and Carbon Nanotubes, Ph.D. Thesis No. 1258, Physics Department, University of Fribourg, Switzerland, 1999. 69. 0. Grrning, O. M. Ktittel, P. Grrning, and L. Schlapbach, J. Vac. Sci. Technol. B 17, 1970 (1999). 70. R. H. Fowler and L. W. Nordheim, Proc. Roy. Soc. London Ser. A 119, 173 (1928). 71. The WKB method was published in 1926 independently by the following three authors: G. Wentzel, Z. Phys. 38, 518 (1926); H. A. Kramers, Z. Phys. 39, 828 (1926); L. Brillouin, C. R. Acad. Sci. Paris 183, 24 (1926). 72. O. Grrning, O. M. Ktittel, P. Grrning, and L. Schlapbach, J. Vac. Sci. Technol. B 17, 1064 (1999). 73. W.A. de Heer, A. Ch~telain, and D. Ugarte, Science 270, 1179 (1995). 74. O. M. Ktittel, O. Grrning, Ch. Emmenegger, and L. Schlapbach, Appl. Phys. Lett. 73, 2113 (1998). 75. 0. Grrning, O. M. Ktittel, Ch. Emmenegger, P. Grrning, and L. Schlapbach, J. Vac. Sci. Technol. B 18, 665 (2000). 76. S. Iijima, Nature 354, 56 (1991). 77. P.J. E Harris, "Carbon Nanotubes and Related Structures, New Materials for the Twenty-First Century." Cambridge Univ. Press, Cambridge, UK, 1999. 78. K. Tanaka, T. Yamabe, and K. Fukui, "The Science and Technology of Carbon Nanotubes." Elsevier, New York, 1999. 79. D. Tomanek and R. J. Enbody, "Science and Application of Nanotubes," Proccedings of Nanotube 99. Kluwer Academic/Plenum, New York, 2000. 80. T. W. Ebbesen, Annu. Rev. Mater. Sci. 24, 235 (1994). 81. T. Guo, P. Nikolaev, A. Thess, D. T. Colbert, and R. E. Smalley, J. Phys. Chem. 55, 10694 (1995). 82. M. Endo, K. Takeuchi, S. Igarashi, K. Kobori, M. Shiraishi, and H. W. Kroto, J. Phys. Chem. Solids 54, 1841 (1993). 83. W. K. Hsu, J. P. Hare, M. Terrones, H. W. Kroto, D. R. M. Walton, and P. J. E Harris, Nature 377, 687 (1995). 84. W. K. Hsu, M. Terrones, J. P. Hare, H. Terrones, H. W. Kroto, and D. R. M. Walton, Chem. Phys. Lett. 262, 161 (1996). 85. M.S. Dresselhaus, G. Dresselhaus, I. L. Spain, and H. A. Goldberg, Eds., in "Graphite Fibers and Filaments." Springer Verlag, New York, 1988. 86. R.T.K. Baker and P. S. Harris, Chem. Phys. Carbon 14, 83 (1978). 87. P. Grrning et al., Physics Department, University of Fribourg, Prrolles, CH- 1700 Fribourg, Switzerland. 88. J. Kong, H. T. Soh, A. M. Cassell, C. F. Quate, and H. Dai, Nature 395, 878 (1998).

COLD PLASMA PROCESSES 89. S. Fan, M. G. Chapline, N. R. Franklin, T. W. Tombler, A. M. Cassell, and H. Dai, Science 283, 512 (1999). 90. H. Kind, J.-M. Bonard, Ch. Emmenegger, L.-O. Nilsson, K. Hernadi, E. Maillard-Schaller, L. Schlapbach, L. Forro, and K. Kern, Adv. Mater. 11, 1285 (1999). 91. H. Krnig and G. Helwig, Z. Phys. 129, 491 (1951). 92. H. SchmeUenmeier, Exp. Techn. Phys. 1, 49 (1953). 93. J. Goodmann, J. Polym. Sci. 44, 551 (1960). 94. A.P. Bradley and J. P. Hammes, J. Electrochem. Soc. 110, 15 (1963). 95. T. Williams and M. W. Hayes, Nature 209, 769 (1966). 96. H. U. Poll, M. Artz, and K. H. Wickleder, European Polym. J. 12, 505 (1976). 97. D. K. Lam, R. E Baddour, and A. E Stancell, in "Plasma Chemistry of Polymers" (M. Shen, Ed.). New York, 1976. 98. B.D. Ratner, Polymer 34, 643 (1993). 99. Ch. Oehr and H. Brunner, Vakuum Forsch. Praxis 1, 35 (2000). 100. H. Nomura, P. W. Kramer, and H. Yasuda, Thin Solid Films 118, 187 (1984). 101. J. Sakata, M. Yammamoto, and M. Hirai, J. Appl. Polym. Sci. 31, 1999 (1986). 102. A. E Stancell and A. T. Spencer, J. Appl. Polym. Sci. 16, 1505 (1972). 103. P. GrSning, A. Schneuwly, L. Schlapbach, and M. T. Gale, J. Vac. Sci. Technol. A 14, 3043 (1996). 104. J.W. Coburn and H. E Winters, J. Vac. Sci. Technol. 16, 391 (1979). 105. R. Jaszewsld, H. Schift, P. Grrning, and G. Margaritondo, Micro. NanoEng. 35, 381 (1997). 106. R.W. Jaszewski, H. Schift, B. Schnyder, A. Schneuwly, and P. Grrning, Appl. Surf. Sci. 143, 301 (1999). 107. A. Schneuwly, Engineering Relevant Surfaces: Treatment, Characterisation and Study of Their Properties, Ph.D. Thesis No. 1225, Physics Department, University of Fribourg, Switzerland, 1998. 108. A. Schneuwly, P. Grrning, L. Schlapbach, C. Irrgang, and J. Vogt, IEEE Trans. Dielectrics Electrical Insulation 5, 862 (1998). 109. A. Schneuwly, P. Grrning, and L. Schlapbach, Mater Sci. Eng. B 55,210 (1998). 110. A.J. Kinloch, "Adhesion and Adhesives." Chapman and Hall/Cambridge Univ. Press, London, 1990. 111. L.-H. Lee, "Fundamentals of Adhesion." Plenum, New York, 1991. 112. S. Trigwell, Solid State Technol. 45 (1993). 113. A. Carrass and V. P. J~icklin, Dtsch. Verb. Schweisstech. 173, 135 (1995). 114. A. Schneuwly, P. Grrning, L. Schlapbach, and V. J~icklin, IEEE J. Electron. Mater. 27, 990 (1998). 115. N. Onda, A. Dommann, H. Zimmermann, C. Liichinger, V. J~icklin, D. Zanetti, E. Beck, and J. Ramm, "Semicon Singapore Proc." 1996. 116. E. Wandtke, Transfer 40, 34 (1996). 117. A. Schneuwly, P. Grrning, L. Schlapbach, and G. Miiller, IEEE J. Electron. Mater. 27, 1254 (1998). 118. C. E McFadden and A. E Gellmann, Langmuir 11,273 (1995). 119. E.M. Liston, J. Adhes. 30, 199 (1989). 120. E. Occhiello, M. Morra, G. Morini, E Garbassi, and D. Johnson, J. Appl. Polym. Sci. 42, 2045 (1991). 121. L.J. Gerenser, J. Vac. Sci. Technol. A 8, 3682 (1990). 122. U.W. Gedde, K. Pellfolk, M. Braun, and C. Rodehed, J. Appl. Polym. Sci. 39, 477 (1990). 123. P. Grrning, S. Berger, M. Collaud Coen, O. Grrning, and B. Hasse, "5th European Adhesion Conference EURADH'2000," Lyon, 2000, p. 299. 124. P. Grrning, O. M. Kiittel, M. Collaud Coen, G. Dietler, and L. Schlapbach, Appl. Surf. Sci. 89, 83 (1995). 125. G. Marietta, S. M. Catalano, and S. Pignataro, Surf. Interface Anal. 16, 407 (1990). 126. P. Grrning, M. Collaud, G. Dietler, and L. Schlapbach, J. Appl. Phys. 76, 887 (1994). 127. P. GrSning, M. Collaud Coen, O. M. Ktittel, and L. Schlapbach, Appl. Surf. Sci. 103, 79 (1996). 128. L. Gong, A. D. Friend, and R. P. Wool, Macromolecules 31, 3706 (1998). 129. A.T. Bell, Techniques and Applications of Plasma Chemistry (J. R. Hollahan and A. T. Bell, Eds.), p. 1. Wiley, New York, 1974.

259

130. Y. Yamada, T. Yamada, S. Tasaka, and N. Inagaki, Macromolecules 29, 4331 (1996). 131. N. Inagaki, S. Tasaka, and T. Umehara, J. Appl. Polym. Sci. 71, 2191 (1999). 132. N. Inagaki, S. Tasaka, and K. Mochizuld, Macromolecules 32, 8566 (1996). 133. R. Michael and D. Stulik, Nucl. lnstrum. Methods B 28, 259 (1987). 134. H. Niino, M. Nakano, S. Nakano, A. Yabe, H. Moriya, and T. Mild, Japan. J. Appl. Phys. 28, L2225 (1989). 135. R. M. Overney, R. LiJthi, H. Haefke, J. Frommer, E. Meyer, H.-J. Giintherodt, S. Hild, and J. Fuhrmann, Appl. Surf. Sci. 64, 197 (1993). 136. R. M. Ovemey, H.-J. Giintherodt, and S. Hild, J. Appl. Phys. 75, 1401 (1994). 137. K. Harth and S. Hibst, Surf. Coat. Technol. 59, 363 (1994). 138. Y. Khairallah, E Arefi, J. Amouroux, D. Leonard, and P. Bertrand, J. Adhes. Sci. Technol. 8, 363 (1994). 139. N. Inagald, S. Tasaka, and K. Hibi, J. Adhes. Sci. Technol. 8, 395 (1994). 140. H. Yasuda, J. Macromol. Sci. Chem. A 10, 383 (1976). 141. S.N. Magonov, K. Qvarnstrrm, V. Elings, and H.-J. Cantow, Polym. Bull. 25,689 (1991). 142. A. Wawkuschewski, H.-J. Cantow, and S. N. Magonov, Adv. Mater. 6, 476 (1994). 143. M. Collaud Coen, G. Dietler, S. Kasas, and P. Grrning, Appl. Surf. Sci. 103, 27 (1996). 144. M. Collaud Coen, P. Grrning, and R. Lehmann, submitted for publication. 145. H. Niino and A. Yabe, J. Photochem. Photobiol. A 65,303 (1992). 146. M. Collaud Coen, P. Grrning, G. Dietler, and L. Schlapbach, J. Appl. Phys. 77, 5595 (1995). 147. B. Berghaus, German Patent DPR 668.639, 1932. 148. B. Berghaus, German Patent DPR 851.560, 1939. 149. K.R. Thampi and M. Gratzel, J. Mol. CataL 60, 31 (1990). 150. A.A. Said, J. Mater. Sci. Lett. 11, 1903 (1992). 151. "Ullman's Encyclopedia of Industrial Chemistry," 5th ed., Vol. A 11, p. 619, 1988. 152. A. Nagy and G. Mestl, Appl. Catal. 188, 337 (1999). 153. X. Bao and J. Deng, J. Catal. 99, 391 (1986). 154. X. Bao, M. Muhler, Th. Schedel-Niedrig, and R. Schlrgl, Phys. Rev. B 54, 2249 (1996). 155. X. Bao, B. Pettinger, G. Ertl, and R. Schlrgel, Ber. Bunsenges. Phys. Chem. 97, 97 (1993). 156. M. Bielmannm, P. Ruffieux, P. Schwaller, L. Schlapbach, and P. Grrning, submitted for publication. 157. R. Paniago, R. Matzdorf, G. Meister, and A. Goldmann, Surf. Sci. 336, 113 (1995). 158. Plasma cleaner LFC 150, Balzers Instruments, PO 1000, FL-9496 Balzers, Lichtenstein. 159. E J. Himpsel, J. A. Knapp, J. A. VanVechten, and D. E. Eastmann, Phys. Rev. B 20, 624 (1979). 160. J. van der Weide, Z. Zhang, P. K. Baumann, M. G. Wensell, J. Bernholc, and R. J. Nemanich, Phys. Rev. B 50, 5803 (1994). 161. R. L. Bell, "Negative Electron Affinity Devices." Clarendon, Oxford, 1973. 162. O. M. Ktittel, L. Diederich, E. Schaller, O. Carnal, and L. Schlapbach, Surf. Sci. Lett. 337, L812 (1995). 163. L. Diederich, O. M. Kiittel, E. Schaller, and L. Schlapbach, Surf. Sci. 349, 176 (1996). 164. L. Diederich, Negative Electron Affinity of Hydrogen-Terminated Diamond Surfaces Studies by Photoelectron Spectroscopy, Ph.D. Thesis No. 1210, Physics Department, University of Fribourg, Switzerland, 1998. 165. G.B. Sandhu and W. K. Chu, Appl. Phys. Lett. 55,437 (1989). 166. A. Vescan, W. Ebert, T. H. Borst, and E. Kohn, Diamond Relat. Mater 5, 774 (1996). 167. C. Vivensang, L. Ferlazzo-Manin, M. V. Ravet, G. Turban, E Rosseaux, and A. Gicquel, Diamond Relat. Mater 5, 840 (1996). 168. S. A. Grot, R. A. Ditzio, G. Sh. Gildenblat, A. R. Badzian, and S. J. Fonash, Appl. Phys. Lett. 61, 2326 (1992).

260

GRONING

169. K. Kobayashi, N. Mutsukura, and Y. Machi, Thin Solid Films 200, 139 (1991). 170. Ch. Steinbruchel, H. W. Lehmann, and K. Frick, J. Electrochem. Soc. 132, 180 (1985). 171. Ch. Steinbruchel, Appl. Phys. Lett. 55, 1960 (1989). 172. H.A. Mizes and J. S. Foster, Science 244, 559 (1989). 173. J. Xhie, K. Sattler, U. Muller, N. Venkateswaran, and G. Raina, Phys. Rev. B 43, 8917 (1991). 174. D. Tomanek, S. G. Louie, H. J. Mamin, D. W. Abraham, R. E. Thomson, E. Ganz, and J. Clarke, Phys. Rev. B 35, 7790 (1987). 175. L. Jeloaica and V. Sidis, Chem. Phys. Lett. 300, 157 (1999).

176. J.P. Chen and R. T. Yang, Surf. Sci. 216, 418 (1989). 177. U. Bischler and E. Bertel, J. Vac. Sci. Technol. A 11,458 (1993). 178. P. Ruffieux, O. Grrning, P. Schwaller, L. Schlapbach, and E Grrning, Phys. Rev. Lett. 84, 4910 (2000). 179. K. E Kelly and N. J. Halas, Surf. Sci. 416, L1085 (1998). 180. S. Nowak, P. Grrning, O. M. Ktittel, M. Collaud, and G. Dietler, J. Vac. Sci. Technol. A 10, 3419 (1992). 181. V.V. Khvostov, M. B. Guseva, V. G. Babaev, and E. A. Osherovich, Surf. Sci. 320, L123 (1994).

Chapter 5

ELECTROCHEMICAL FORMATION OF THIN FILMS OF BINARY III-V COMPOUNDS L. Peraldo Bicelli Dipartimento di Chimica Fisica Applicata del Politecnico, Centro di Studio sui Processi Elettrodici del CNR, 20131 Milan, Italy

V. M. Kozlov Department of Physics, National Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine

Contents 1. 2. 3. 4.

5.

6. 7. 8.

9.

10.

11.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G r o u p III-V Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrodeposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Codeposition: Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Thermodynamic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Kinetic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Codeposition from Aqueous Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Pourbaix's Equilibrium Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Parasitic Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Classification of Cathodic Codeposition Processes . . . . . . . . . . . . . . . . . . . . . . . . . Codeposition from Molten Salts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sequential Electrodeposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrodeposition of Group III-V Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. A l u m i n u m Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Gallium Phosphide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3. Indium Phosphide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4. Gallium Arsenide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. Indium Arsenide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. Gallium Antimonide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7. Indium Antimonide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8. I n d i u m - B i s m u t h Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diffusion Process and Formation of Group III-V Compounds . . . . . . . . . . . . . . . . . . . . . . 9.1. The I n d i u m - B i s m u t h System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. The I n d i u m - A n t i m o n y System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

262 263 266 266 266 270 271 271 273 274 275 276 277 278 279 280 283 293 297 299 303 304 304 308

Influence of the Substrate Structure and Morphology on the Diffusion Process 10.1. The I n d i u m - A n t i m o n y System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. The G a l l i u m - A n t i m o n y System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. Amorphous Antimony Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

310 310 312 313 313 315 315

.............

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

261

262

PERALDO BICELLI AND KOZLOV

1. INTRODUCTION Currently, electronic and optoelectronic industries provide some of the largest markets and challenges for thin-film semiconductors. Current techniques for the growth of these materials include physical methods (e.g., molecular beam epitaxy (MBE), liquid-phase epitaxy (LPE), liquid encapsulated Czochralski (LEC), sputtering), and chemical methods (e.g., chemical vapor deposition (CVD), metalorganic chemical vapor deposition (MOCVD), metalorganic vapor phase epitaxy (MOVPE), electrodeposition). Physical methods are expensive but give relatively more reliable and reproducible results. Most of the chemical methods are more economical, but their full potential for obtaining device-quality films has not been completely explored in many cases. Moreover, several authors (e.g., [ 1]) projected in recent time a future in which solid-state synthesis will be conducted in so-called round-bottom flasks, the strategies being more similar to those of organic chemistry than to those of the high-temperature methods currently employed. Emerging syntheses of technologically important semiconductors, including those of group III-V family, have been outlined [2]. They are based on solution-chemical processes performed in mild reaction conditions, making it possible to turn down the heat on semiconductor growth and to control crystallite size and morphology. Among these processes, electrodeposition has also been considered (this mainly refers to II-VI chalcogenides). Electrochemical synthesis is one of the oldest methods for the formation of thin films and may offer a simple and viable alternative to the very complicated and highly expensive high-temperature and/or high-vacuum processes. It offers especially attractive features, such as simplicity, low cost, high output, and scalability compared with the competing methods of deposition, such as MBE and CVD. Moreover, it is generally performed near room temperature, and it is thus appealing as a low-temperature and isothermal technique that avoids the deleterious effects of interdiffusion, contamination, and dopant redistribution, which are typical of high-temperature processes. The main advantages of electrodeposition include the following: 1. It affords precise process control by means of current or voltage modulation and thus the control of film thickness, morphology, stoichiometry, doping, etc. This is due to its electrical nature, as electrical parameters are inherently easier to control than thermal parameters. 2. It makes possible the growth of uniform films on different substrates and over large and/or irregular areas, from cm 2 to m 2. 3. It occurs closer to equilibrium conditions than many high-temperature vacuum deposition methods, but, on the other hand, it allows the electrodeposition of compositionally nonequilibrium materials or modulated structures.

4. It is particularly suited to the fabrication of heterojunctions simply through a change in the deposition electrolyte. 5. It allows an efficient use of chemical precursors, because deposition occurs on the working electrode only and not on other reactor surfaces. 6. It is less polluting, as it does not involve the use of toxic or gaseous precursors, such as, e.g., ASH3, AsC13, or metalorganic chemicals. 7. It provides the possibility of a technological transfer from the established plating industry and, thus, a wide range of industrial experience. The electrochemical deposition technique is particularly suited to the preparation of polycrystalline and amorphous thinfilm semiconductors for applications in which the use of highperformance materials is not necessary and cost effectiveness is the most important aspect. For example, advanced optoelectronic devices for mid-infrared detection imply the use of both sources and detectors of low band-gap semiconductors, which, in principle, do not need to be monocrystalline but may be polycrystalline, 1-2-/zm-thick films. Polycrystalline materials are also used for solar energy conversion, and in several cases good quality materials have been achieved that were appropriate for efficient devices. For example, high efficiencies (10.6% under 100 mW cm -2 illumination) were obtained with an allelectroplated CdS/p-MCT (mercury cadmium telluride) heterojunction solar cell, in which p-MCT was a ~ 1.2-/~m thin film of polycrystalline Cd-rich mercury cadmium telluride [3]. A remarkable achievement of the electrochemical method is the preparation of polycrystalline thin films of materials with considerable molecular complexity, such as ternary chalcogenides. Further exciting developments have been anticipated for superlattices and other nanostructured semiconductors, as well as in microdiode arrays and quantum dots. In addition, a variety of electrodeposition techniques, either single or in combination with others (i.e., direct current, pulsed current, direct plus pulsed current, electroless deposition, etc.), have been reported to produce better quality materials, but they have mainly been applied to the electrodeposition of metals and alloys. Notwithstanding the numerous attractive features of the electrodeposition technique in the preparation of thin-film semiconductors, there are also several drawbacks, as described elsewhere in this chapter. Here, we only recall that the target materials often suffer from contamination with impurity phases, have a poor morphology, and are nonhomogeneous in their thickness, and their stoichiometry is far from the expected one. Although the processes involved in compound semiconductor electrodeposition are quite complex because of the need to maintain stoichiometry, electrodeposition has successfully been applied to several II-VI compounds, notably binary and ternary Cd and Zn chalcogenides. In contrast, the electrodeposition of III-V compound semiconductors has not received as much attention, despite the increasing interest in them for a series of

BINARY III-V COMPOUNDS applications. Indeed, III-V compounds are found in several important areas of application of modem microelectronic techniques because of their use, e.g., in the production of advanced optoelectronic devices, infrared detectors and optical communication systems, photovoltaic and photoelectrochemical solar cells, semiconductor laser and light-emittting diodes (LEDs), very high-speed integrated circuits, high-speed computers, and magnetoresistive sensors. Purpose of this review chapter is to chart the progress of the science of the formation by electrochemical deposition of III-V compound thin films. The challenging problems presented by the physicochemical characterization of these electrosynthesized compounds is also addressed, along with the valuable information gained on the thermodynamic and kinetic aspects of their formation and growth. Strategies for improving the compositional purity and morphological quality of these materials are considered, too. It is also pertinent to underline again the relatively advanced level of the existing knowledge base for II-VI compounds, whereas the synthesis of III-V compounds has been much less successful. The use of less conventional electrolytes (e.g., low-temperature organic melts) and more sophisticated techniques (e.g., electrochemical atomic layer epitaxy), however, may offer an attractive way out of these difficulties.

263

Fig. 1. Atomicarrangement in (a) zinc-blende (B-3 structural type), (b) cesium chloride (B-2), and (c) lithium hydroxide (B-10). Four unit cells are depicted in the last case to show the layered structure [4]. Reprinted from [89] with the kind permissionof Elsevier Science.

2. GROUP III-V COMPOUNDS

The typical III-V family consists of the nine 1 : 1 binary semiconductor compounds formed by the elements of group IliA, A1, Ga, and In, and those of group VA, P, As, and Sb, that is, AlP, AlAs, and A1Sb; GaP, GaAs, and GaSb; InP, InAs, and InSb. They crystallize with the zinc-blende (cubic) structure, and their atoms are tetrahedrally coordinated, forming approximately covalent sp 3 bonds, as shown in Figure 1a [4]. The zinc-blende structure belonging to the B-3 structural type may be related to the diamond lattice belonging to the A-4 type. In this latter structural type, two fcc lattices are shifted with respect to each other by 1/4 along the space diagonal. In the zinc-blende structure (e.g., ZnS), the sites of the first of the two fcc lattices are occupied by the atoms of one element (e.g., Zn), and those of the second of the two fcc lattices, by the atoms of the other element (e.g., S). The space group is F43m, and there are four molecules per unit cell. As for the other two IliA and VA elements, T1 and Bi, respectively, the situation is completely different. Indeed, no compounds are formed between T1 and P or As, as well as between Bi and A1 or Ga. The phase diagram [5] shows the existence of the two compounds T17Sb2 [6] and T1Bi2 (with a homogeneity range between 34 and 46 at.% T1 [6]) both with a very low melting point, 226~ (but with a question mark [5]) and 213~ [5], respectively, as well as the existence of three In-Bi compounds, InBi, InsBi3, and InBi2, with even lower melting points (110~ for the former and around 90~ for the latter two). Notwithstanding its 1 : 1 composition, InBi does not belong to the typical III-V family, owing to its completely different structure, i.e.,

a tetragonal unit cell with the atoms arranged in layers (Fig. lc). Moreover, it has metallic bonds with fourfold coordination. We will now describe the properties of typical III-V compounds in more detail. First of all, it is interesting to examine their phase diagrams, which are very simple. The main results may be summarized as follows. All nine binary phase diagrams show the presence of a 1 : 1 binary compound that melts congruently. It does not form solid solutions with the two pure elements and has, with one exception (InSb), a higher melting point than both of them. Note, however, that the phase diagrams of A1-P and A1-As systems are speculative, owing to the few data available. They were assumed to be topologically similar to those of other III-V systems, such as, for example, GaAs. Moreover, the phase diagram of A1-Sb has been assessed from the data of several authors. Finally, the Ga-P diagram is incomplete, only ranging to a 50 at.% P content. In some cases, there are one or, exceptionally, two eutectics between the compound and the pure elements: A1-Sb, two eutectics at 657 4- 2.5~ and 0.4 at.% Sb and 627 + 2.5~ and 98.5 at.% Sb Ga-Sb, one eutectic at 588.5~ and 88.4 at.% Sb In-Sb, one eutectic at 494~ and 68.2 at.% Sb In-As, one eutectic at 731 ~ and 87.5 at.% As These eutectics appear in all antimonides and, in the case of the In compounds, in arsenide, mainly at the side of the group V element.

264

PERALDO BICELLI AND KOZLOV Table I.

Percentage of the Ionic Character of III-V Bonds P

Table III.

As

Sb

Energy Gap (eV) of III-V Compounds P

As

Sb

A1

9

6.5

4

AI

--

2.15 (ID)

1.6 (ID)

Ga

6.5

4

2.5

Ga

2.3 (ID)

1.43 (D)

0.68 (D)

In

4

2.5

1

In

1.34 (D)

0.36 (D)

0.17 (D)

Data are from [7]. Table II.

D and ID, direct and indirect gap transition, respectively. Data are from [ 10].

Standard Gibbs Free Energy (kJ mol-1 ) of Formation of III-V Compounds

Table IV.

Melting Point (~

of III-V Compounds and of Their Elements

P (white, 44.14) P

As

A1 (660.452) AI

>-166.5

Ga

>-88

In

-77.0

As (~815)

Sb (630.755)

1760

1058 4- 10

Sb

>-116.3 -67.8

-38.9

-53.6

-25.5

-~2500

Ga (29.774)

1467 4- 3

In (156.634)

1071

1238 943

709.6 525

Melting points of elements are in parentheses. Data are from [5]. Data are from [8].

The chemical bond in the III-V compounds is not completely covalent, because group V elements are slightly more electronegative than those of group III elements, and this imparts a weak ionic character to the prevailing covalent bond. The percentage of ionic character of the bond in each compound, determined from the difference in the electronegativities of V and III elements, is collected in Table I [7]. In this and in the following tables of this type, each compound is virtually presented at the intersection point of the horizontal line, corresponding to its group III element, with the vertical line corresponding to its group V element. At this same point, the value of the considered quantity is reported, in the present case of the percentage of ionic character. The ionic character of the bonds decreases from left to right and from top to bottom, so that AlP is the most heteropolar and InSb the least heteropolar compound. In this same direction moves the stability of the compounds toward their bond rupture, as expressed, e.g., by their Gibbs free energy of formation from the elements in standard conditions [8], which is reported in Table II. Unfortunately, not all experimental data are available, as for AlP, AlAs, and GaP the enthalpy of formation only is known, as often occurs. However, the entropy contribution is expected to decrease during the formation in solid-state conditions of the compound from the elements, thus implying that the Gibbs free energy of the process is higher (less negative) than the related enthalpy, as indicated in Table II. The correlation between the values connected to the difference in electronegativity and the thermodynamic values is easy to understand. InSb has the weakest bond among the typical III-V compounds but InBi has an even weaker bond; its Gibbs free energy is only - 3 . 7 2 kJ mo1-1 [9]. So, InBi is considered to be an intermetallic compound, and all typical compounds of the III-V family are semiconductors, but the values of their band gap energy decrease from left to right and from top to bottom,

just like the ionic character of their bonds. This is shown in Table III [10]. GaP has the highest value (2.3 eV), and InSb, the smallest one (0.17 eV). Owing to its very low band gap, InSb, too, is often considered as an intermetallic compound [ 11 ]. The gap transition is mainly a direct one (D in Table III); those of the A1 compounds and GaP, however, are indirect ones (ID in Table III). Although the structure is the same, the melting points of the nine compounds are different and reflect the strength of the bonds, as evident is from a comparison of the values reported in Table IV to those of Table I. The melting points of the single elements are also shown in the table. They are listed in parentheses close to the chemical symbol of the pure element, to clearly show the differences in the values of the compounds and their elements. Indeed, the melting points of both elements and III-V compounds are important, because several of them are prepared in molten salt electrolytes at high temperatures or are deposited at room temperature and then submitted to thermal annealing to complete the process of formation through diffusion and reaction (mainly in the solid state) and/or to improve the crystallinity and morphology of the samples. Moreover, In and, more especially, Ga have low melting points, and this may create several problems during the electrochemical process of compound formation and the subsequent heat treatment. Furthermore, about half of the value of the activation energy of the diffusion process is due to the energy of formation of the vacancies [ 12], which is strictly related to the melting temperature of the phases where diffusion occurs, namely that of the elements and of the compound. The comparison of the melting temperature of the III group element with that of the V group element forming a compound through diffusion and reaction may indicate which of them is prevailingly diffuse. So, for example, Ga and In are expected and observed to be the diffusing species, respectively, in the case of GaSb and InSb formation. Finally, it is also interesting to compare the lattice constants of the nine III-V compounds that have the same cubic struc-

BINARY III-V COMPOUNDS Table V.

Lattice Constants (/~) of the Cubic Zinc-Blende Structure of III-V Compounds

A1 (1.26) Ga (1.26) In (1.44)

P (1.10)

As (1.18)

Sb (1.36)

5.451 5.4506 5.869

5.662 5.6538 6.058

6.1347 6.095 6.4782

Atomic radii for tetrahedral coordination of the elements are in parentheses. Data are from [6, 13]. Table VI.

PossibleModulation Ranges of the Energy Gap and of the Lattice Constant of III-V Compounds

Ternary compounds

Binary compounds

Energy gap (eV)

Lattice constant (~)

Ga-As-Sb Ga-In-Sb In-As-P In-As-Sb

GaAs-GaSb GaSb-InSb InAs-InP InAs-InSb

1.43-0.68 0.68-0.17 0.36--1 . 3 4 0.36--0.17

5.6538-6.095 6.095-6.4782 6.058-5.869 6.058-6.4782

Data are from [10] and [6].

ture [6]. In this case, there are at least two factors influencing such parameters, the steric and chemical interactions. The former is expressed by the dimension of the elements as given by their atomic radii for tetrahedral coordination [ 13], the latter by the bond strength. They influence the lattice constant in opposite ways, but the former is expected to be the prevailing factor, as experimentally observed. Indeed, as shown in Table V, the lattice constants increase from left to fight and from top to bottom. To more clearly demonstrate this correlation, the values of the atomic radii have also been listed in the table, close to the symbol of each element. Because A1 and Ga have the same atomic radius, the lattice constants of the compounds in the first two lines have practically the same value, which increases from left to fight. The mass densities (g cm -3) follow the same trend as that of the lattice constants. Interesting correlations among binary III-V semiconductor compounds regarding some of their physical properties and parameters (e.g., lattice dynamics, piezoelectric and optical properties, electron affinity, effective mass, and variation with pressure of the band gap energy) are reported in a review by Adachi [ 14]. An attractive opportunity provided by the electrochemical approach is the ease with which substitutional alloys may be generated, not only in the case of metal alloys but alloy compounds. Some examples of group III-V combinations that have been electrosynthesized are those resulting from the GaAsGaSb, GaSb-InSb, InAs-InP, and InAs-InSb systems, which will be examined in the following. They are interesting because both the band gap and the lattice constant can in principle be modulated over a wide range, as shown in Table VI. However, according to Rajeshwar [ 15], the greater number of active

265

species in the case of the electrosynthesis of semiconductor alloys with respect to that of metal alloys renders the composition modulation a little more difficult. Adachi [ 14] suggested an interpolation scheme as a useful tool for estimating some physical parameters of ternary alloy compounds from those of the corresponding binary compounds (e.g., AlxGal-xAs from AlAs and GaAs), whereas Tomashik [ 16] proposed a composite tetrahedral heptahedron enabling graphic representation of all possible systems formed by 16 III-V compounds consisting of four cationic and four anionic species. As a matter of fact, multicomponent systems of compound semiconductors are of great interest in the search for new semiconducting materials with superior properties. However, the investigation of such systems is a very complex and labor-consuming task, and such a graphic representation may be particularly useful when the number of constituent components increases. In addition to alloys, superstructures (e.g., superlattices) may be considered, too. They differ from the former because their composition is modulated along one direction, whereas the plane perpendicular to it is compositionally homogeneous. The current interest in nanomodulated superstructures lies in their unique optoelectronic properties and interesting quantization effects [17]. A typical example is the CdSe-ZnSe supeflattice, with alternating layers of CdSe and ZnSe along the z reference axis. This temary system may be prepared by potential or current pulsing between the limits characteristic of CdSe and ZnSe formation [ 15, 18, 19]. The next challenge lies in securing truly nanomodulated thin films. The recent electrochemical technique called ECALE (electrochemical atomic layer epitaxy) makes it possible to achieve nanometer-thick epitaxial films of compound semiconductors from aqueous solutions through layer-by-layer deposition under ultrahigh purity conditions [20, 21]. It is based on a thin-layer methodology and on underpotential deposition to alternately lay down atop a suitable substrate a monolayer of each species of a binary compound, e.g., Ga-As or In-As, as discussed below. Such a technique is also potentially applicable to the electrosynthesis of superstructures and has recently been applied in the case of the CdS-ZnS system [22]. Another possible new technique is the electrochemical fabrication of microdiode arrays, which consists of the electrochemical synthesis within the pores of special membranes of an array containing, e.g., more than 109 CdSe or graded CdSe/CdTe cylinders with a diameter of 200 nm. After removal of the membrane (e.g., by dissolution in aqueous NaOH), an array of wires freely standing on a metal substrate is obtained. Currentvoltage data show that the Ni-CdSe array is rectifying, with a rectification ratio of 1000 at q-2 V [23]. The unique size-dependent, optical, photocatalytic, and nonlinear optical properties of colloidal nanocrystalline semiconductor particles, called quantum dots, continue to attract considerable interest. In contrast to the preparation of high-quality quantum dots of II-VI semiconductors, that of III-V semiconductors has proved to be problematic. However, the synthesis and properties of well-crystallized GaP and InP quantum dots have recently been reported; the diameter of the former ranges

266

PERALDO B ICELLI AND KOZLOV

from 20 to 65 A, and that of the latter is about 25 ~ [24]. They were obtained by heating a solution containing the precursor species (GaP and InP) with a mixture of trioctylphosphine oxide and trioctylphosphine as a colloidal stabilizer. Instead, the Argonne National Laboratory [25] used an electrochemical technique to produce quasi-periodic quantum dot arrays, with excellent control over dot size and interdot spacing to be used in microelectronic applications. The manufacturing costs are expected to be orders of magnitude lower than those of conventional nanofabrication.

electrodeposition of the metal on an inert substrate followed by a thermal treatment in the presence of the other component (P or PH3) in the gaseous phase. Several other methods are applied, mainly to prepare II-VI group semiconductors, which have been studied more extensively, and reference is made to [27]. More details on semiconductor electrodeposition, including deposit characterization techniques, are reported in a recent handbook [ 10].

4. CODEPOSITION: BASIC CONSIDERATIONS

3. ELECTRODEPOSITION Fundamental thermodynamic and kinetic considerations related to the electrodeposition of alloy and compound semiconductors are presented, with emphasis on the processes of interest in the case of binary III-V semiconducting compounds. Although the main aspects of metal electrodeposition may be applied to semiconductor electrodeposition, semiconductors present some typical properties that cannot be ignored: 1. Inside a semiconductor, at its interface with the electrolyte, a typical space-charge layer is formed that is practically nonexistent at the metal-electrolyte junction. 2. Semiconductors have a much higher resistivity than metals, and the interfacial potential and charge distribution may change dramatically during electrodeposition, once some semiconducting layers have been deposited. 3. Semiconductors are sensitive to several defects that influence their resistivity, so that, in extreme cases, they may even become a degenerate solid, losing their characteristic properties. 4. Owing to other properties, electrochemical behavior, particularly the current density-potential characteristics of semiconductors, is more complex than that of metals, as shown by Gerischer (e.g., [26]). Characteristic aspects of compound semiconductor electrodeposition are (i) the very negative Gibbs free energy of compound formation from the elements, which may be beneficial for simultaneous electrodeposition, and (ii) the great difference in the standard reduction potentials of the different components, owing to which several difficulties are encountered, particularly in the case of III-V compounds formed from a typical metallic (A1, Ga, In) and nonmetallic (P, As, Sb) element. Indeed, for simultaneous deposition the reduction potentials have to be equal. The most common methods used to prepare thin films of III-V group compounds are simultaneous cathodic electrodeposition (codeposition), a pure electrochemical method, and sequential (consecutive) electrodeposition of precursor multilayers with subsequent annealing treatment, a mixed electrochemical and thermal method. Another mixed method, typically applied to phosphides (such as InP), is the preliminary

Cathodic codeposition makes it possible to directly obtain an alloy or a compound in a single electrochemical step and, when the control of the material resistivity is possible, to prepare even high-thickness films. This method has a wide application for the preparation of several members of the III-V semiconductor family, from both aqueous and molten salt solutions, as well as of many binary and ternary chalcogenides. The codeposition of alloy and compound semiconductors is quite difficult, as the conditions favorable for deposition of one component normally differ from those necessary for the other one. Moreover, electrodeposition is complicated if a desired stoichiometry is requested, which is the rule for semiconductors. The factors governing codeposition at a given current density and temperature are (e.g., [28-31]) (i) the deposition potential of the individual ions in the electrolyte, (ii) the cathodic polarization caused by the difference in deposition potentials, (iii) the relative ion concentration in the bath, (iv) the dissolving tendency of the deposited compound, and (v) the hydrogen overpotential on the deposit surface at the cathode. The role of these parameters has been discussed by Brenner [28], mainly for alloy electrodeposition.

4.1. Thermodynamic Aspects Krrger [29] analyzed the influence of both the characteristic thermodynamic parameters of the codeposition method and the experimental variables on the deposit composition. He based his analysis on a model that was applied to the case of the cathodic deposition of alloys or of binary compounds with a welldefined stoichiometry and metallic or semiconducting properties. This theory was then shown to also be applicable to the case of the cathodic deposition of the ternary semiconducting compound CuInSe2 [32]. In the following discussion, the formation of binary compounds only will be examined. Following Krrger's theory [29], let us consider the simultaneous electrodeposition of the two species M and N to prepare the MrNs compound, where N is the more noble of the two elements, i.e., that forming first. This means that its potential in standard conditions, E~, is greater (more positive) than that of the other one. According to the well-known Nernst equation, the equilibrium potentials of M and N in a solution of their ions, EM and EN, respectively, depend on the activities of the same ions in

BINARY III-V COMPOUNDS the electrolyte, a (M m+) and a (N n+), and on the activities of M and N in the deposit, a (M) and a (N):

EM = E~ + ( R T / m F ) ln[a(Mm+)/a(M)] EN = E~q + (RT/nF) ln[a(Nn+)/a(N)] The latter activities are equal to 1 if the deposit is a pure, perfect element and are smaller than 1 if the deposit is a compound. R and F are the gas and Faraday constants, respectively, and T is the temperature. As true reversible potentials are rarely met in practice, Krt~ger [29] introduced the concept of quasi-rest potentials to help explain zero current conditions that otherwise only approximate true thermodynamic reversibility. The electrode potentials at which codeposition is possible are equal to the quasi-rest potentials of the compound plus a polarization increasing with the current density. Because polarization is established with a relaxation time not higher than 10 -8 s, the quasi-rest potential can be determined by opening the electrolysis circuit, so that overpotentials and ohmic drops are absent, and measuring the electrode potential within about 10 -3 s after interruption of the deposition current density. Quasi-rest potentials are important for characterization of the bulk of the deposit. They originate in four factors: (i) the equilibrium potentials of the components, which may differ widely; (ii) the changes in the activities of the components in the deposit when the compound is formed; (iii) the interfacial activities of the ionic species during electrodeposition, which may significantly differ from their bulk activities; and (iv) the relative magnitudes of the exchange current densities of the components in the deposit. Krrger assumed that the quasi-rest potential is an equilibrium potential of the deposit relative to the electrolyte with activities of the potential-determining species, as they are at the solid-electrolyte interface during electrodeposition. With this assumption, the first three factors can be taken into account by expressing previous potentials, EM and EN, in terms of the activities of the ionic species at the deposit-electrolyte interface during electrodeposition and of the activities of the components in the deposit. The former activities can often be approximated by the concentrations as they are at the interface, whereas this is usually not possible for the latter activities. EM and EN are now the quasi-rest potentials. Electrodeposition of M and N usually occurs at potentials more negative than the quasi-rest potentials, the difference being the overpotential, /TM and ON. The latter is related to the kinetic factors influencing the different steps of the deposition process, such as charge transfer, crystallization, mass transport, and so on, and increases at increasing current density. The conditions necessary to obtain the simultaneous deposition of the two kinds of ions at the cathode can be written as EM + riM

"

-

EN + r/N

This equation may be fulfilled in different ways, but two common cases may be considered. If the deposition potentials are not far apart, they may be brought together by decreasing

267

the ionic activity of the more noble species, N, with respect to that of the less noble one, M. However, there is a limit to the application of this method related to the logarithmic dependence of EN on the activity of N n+ ions, also because extremely diluted electrolytes in an ionic species would soon be depleted. Instead, if EN is markedly different from EM. Three kinds of approach are possible. (i) A chemical approach, e.g., by introducing a complexant into the bath, decreasing the activity of the discharging N n+ ions through the formation of a complex. (ii) An electrochemical approach, e.g., by increasing the cathodic overpotential of N by adding some particular agents. (iii) An instrumental approach, e.g., by performing a potentiostatic electrolysis in conditions of the limiting current density of N, so that EN may be decreased as desired. A practical rule is that codeposition requires that the deposition potentials differ by less than 200 mV. Another way to solve this problem is to take advantage of the favorable Gibbs free energy of formation of the compound from the elements, A G. The activities a (M) and a (N) of M and N appearing in the Nernst equations change their values during electrodeposition as a consequence of a change not only in the concentration of M and N in the deposit, but also in their physicochemical state, e.g., whether they are part of a compound or not. So, the activities in the deposit also reflect the environment of its constituents. They are related through the solid-state reaction

rM + sN = MrNs + A G where AG (G in Krrger's paper [29]) is the connected Gibbs free energy and r = s = 1 in the case of III-V compounds. Assuming that such a reaction occurs in equilibrium conditions, it results in

a(MrNs)/[a(M) r x a(N) s] -- e x p ( - A G / R T ) where a (Mr N s) ~ 1 for all practical purposes. Hence, [a(M) r • a(N) s] - exp(AG/RT) so a high value of a (M) gives rise to a small value of a (N), and vice versa, whereas the activities of M and N in the compound are determined by their concentrations and by the thermodynamic stability of the deposit [ 11 ]. The limiting values of a (M) and a (N) are determined by the activities of the coexisting phases in the phase diagram. Assuming that MrNs is the only compound in the system, as in the case of the considered III-V compounds, almost pure M and N are in coexistence with the compound at the MrNs-M and N-MrNs phase boundaries, respectively, and the limiting values are a(M) -- 1,

a(N) = exp(AG/sRT)

a(N) = 1,

a(M) = exp(AG/rRT)

and

respectively. The variations of a(M) and a(N) over the existence range of the compound produces a related variation in the quasi-rest

268

PERALDO BICELLI AND KOZLOV

potential of M and N; the total variations are AEM --

-AG/mrF

and

AEN =

-AG/nsF

respectively. Owing to the negative value of the Gibbs free energy of formarion of the compound, A G, the quasi-rest potentials of both components shift in the anodic direction when their activity in the deposit decreases, that is, the formation of the compound produces a positive shift of the individual potentials. To proceed further, it is important to consider whether the deposition rate constants appearing in the exchange current densities of the two individual components, M and N, are of the same order of magnitude or differ considerably. In the former case, the two species have equal weights in determining the potential. The species with the larger value of the product of the discharge rate constant and the activity in the electrolyte at the deposit-electrolyte interface is believed to be dominant in determining the potential. In the latter case, the component with the highest rate constant may be determing the potential under all conditions and is favored over the other one. The treatment of this last case requires the exact knowledge of the kinetics of the charge transfer process and cannot be generalized. Therefore, the first case only, the most interesting for compound electrodeposition, will be discussed, as is usually done (e.g., [10, 27]). Because a deposit of one composition can have only one quasi-rest potential, the necessary condition for codeposition to form the compound is E (Mr Ns) = EM = EN Taking this equality of the quasi-rest potentials into account, a relation is obtained among the activities, both of the ionic species in solution at the electrolyte-deposit interface and of the components in the solid, and the standard potentials,

This means that at the MrNs-M phase boundary, a(M m+) >> a(Nn+), and M is the potential-determining species for all possible compositions of the compound. It is worth noting that the activities of the ionic species in the electrolyte are those close to those at the deposit surface; the bulk are not. At the N-MrNs phase boundary [Eq. (2)], two cases arise, depending on whether ( E ~ - E~) is greater or smaller than (-AG/mrF), namely, whether the difference in the reversible deposition potentials of the individual components N and M is larger (class I) or smaller (class II) than the shift in deposition potential of the less noble component M, as a result of compound formation.

4.1.1. Class I: (E~ - E~) > (-AG/mrF); a(M m+) >> a(N n+) Although the ratio between the two activities is not as large as at the M boundary, M remains the potential-determining species over the entire deposition range. The condition for codeposition can be realized by maintaining a low N n+ ion concentration in the electrolysis solution. This means that the rate of the electrodeposition process is controlled by the diffusion of the more noble species of the two. An increase in the mass transport in the solution (e.g., by stirring the bath) increases the surface activity of the N n+ ions, thus increasing the molar fraction of N in the deposit. In these systems, the codeposition potential shifts monotonically with composition and varies between a minimum value equal to E~ + (RT/mF)ln[a(Mm+)], where the deposit, rich in M, is formed by the compound and an excess of M, and a maximum value differing fromthe minimum one by (-AG/mrF), where the deposit is rich in N and contains an excess of N over the compound composition. This is shown in Figure 2.

(RT/F) l n [ a ( M m+) 1/m/a(Nn+)1/n] = (E~

-

! N--~.-

i

I

E~i) + (RT/F)ln[a(M)l/m/a(N)l/n]

I I I I i

or, at the Mr N s-M phase boundary, where a (M) = 1, /

(RT/F) ln[a (M m+) 1/m/a(Nn+)1/n] = ( E ~ - E ~ ) - AG/nsF

,

~i, I

/ _-

I

(1)

~

"

. . . . . .

~

Eqlqe p

I

-

9 I N,o-

MrNi--

'

and at the N-MrNs phase boundary, where a (N) = 1,

-

I

~ '

.M -

-

4-k~rNo~"

'

I

~ I

-

- -

!

: 1

(RT/F) ln[a (M m+) 1/m/a(Nn+)1/n] = ( E ~ - E~) + A G / m r f

! i

~

(2)

The last term in both equations has been obtained by introducing the activities of the components in the deposits expressed as a function of A G, which was previously considered. Equations (1) and (2) determine the ratio in which the various species contribute to the exchange current density, that is, which of them is the main potential-determining species. Because it has been assumed that N is more noble than M, (E~ - E~i) is positive, and the thermodynamic quantity is negative. Hence, the second member of Eq. (1) is always positive.

A

I

I

F------. G/.~F ----4

- ~

G/.~F ~

---

1

Fig. 2. (A) Equilibrium potentials E of M and N as a function of the activities and (B) corresponding current density vs. cathode potential curve for deposition of class I compounds. Reproduced from [29] with the kind permission of the Electrochemical Society, Inc.

BINARY III-V COMPOUNDS Figure 2A depicts the variation in the M and N potentials, with the activities of M and N in the deposit for constant values of a (M m+) and a (N n+) equal to one. This figure does not represent the situation in the electrolyte at the deposit-electrolyte interface during electrodeposition, but it indicates how differences in the nobility of the two components are affected by their interaction in the deposits. It shows which species must be expected to be potential determining and helps in selecting an electrolyte composition that allows codeposition. For example, codeposition of the noble N and the less noble M is only possible if a(M m+) >> a(Nn+), so that the curve due to N in Figure 2A is shifted toward more cathodic potentials to intersect that due to M. For electrolytes with ion activities differing from those of the figure, the curves have to be shifted accordingly. Figure 2B depicts the corresponding current density-cathode potential curve for MrNs deposition from an electrolyte with a (M m+) ~ 1 and a (N n+) 0.16. The average crystallite sizes determined by X-ray diffraction, of the electrochemically prepared GaSb and InSb were 60 and 35 nm, respectively; those of

the Ga-rich and of the In-rich phase ranged from 28 to 88 and from 20 to 49 nm, respectively. In 1996, McChesney et al. [52] carried out InSb electrodeposition from the bath (0.3 M citric acid, 0.033 M InC13, and 0.047 M SbCI3 ) used by Ortega and Herrero [45]. They worked at room temperature and without electrolyte stirring, to limit the preferential Sb deposition, because Sb discharge at the cathode was diffusion-limited, as discussed above. The substrate was a Ti sheet, and the applied potential ranged from - 0 . 4 to - 1 . 4 V vs. SSC (Ag-AgC1, 0.197 vs. SHE). As already observed by Ortega and Herrero, the deposit stoichiometry depended on the potential. At increasing negative values, the deposits consisted of Sb, Sb + InSb, Sb + In + InSb, and In + InSb mixtures, as was shown by X-ray diffraction [52]. The films obtained between -0.750 and -0.950 V vs. SSC were amorphous; all of the other ones were polycrystalline. The amorphous films were crystallized by heating at 250~ for 15 min in nitrogen, producing an In + InSb deposit. The results duplicated those by Ortega and Herrero [45], with one substantial exception: stoichiometric InSb could not be obtained. Substrates of Cu and ITO were also investigated, and it was noted that the type of substrate greatly affected the deposit composition. For example, on both substrates, mixtures of In and InSb were deposited under most conditions, as no correlation was observed between applied potential and deposit stoichiometry, contrary to what occurred in the case of the Ti substrate. This result was attributed to the different cathodic overpotentials associated with the various materials. Because thin films for electronic devices often require a particular substrate (e.g., ITO in the case of photodetectors), this point could be a limitation for the electrochemical method. In any case, it could not be neglected. In an attempt to deposit pure InSb, McChesney et al. [52] also tried solutions with different In-to-Sb ratios as well as different deposition conditions (higher temperatures and bath stirring), but they mostly obtained Sb or In plus InSb thin films. According to the authors, these results indicate the existence of kinetic barriers to the formation of the compound, barriers that might be surmounted by operating at high temperatures, that is, in nonaqueous baths. Carpenter and Verbrugge [116] recently prepared InSb by electrochemical codeposition of In and Sb from a novel molten salt electrolyte at 45~ This electrolyte consisted of an organic chloroindate obtained from a mixture of InC13 and 1-methyl3-ethylimidazolium (ImC1) in the appropriate ratio, which was heated with stirring at 50-65~ The resulting melt was left for several hours at 45~ to equilibrate before use. For the codeposition measurements, SbC13 was added with stirring immediately before deposition. The organic molten salt was formed by the reaction of the two solids as follows: ImC1 + InC13 - Im + + InC14 in analogy to the behavior of the previously reported lowmelting chloroaluminates [148, 203] and chlorogallates [109, 152] involving A1C13 or GaC13, respectively, instead of InC13.

BINARY III-V COMPOUNDS This was the first report of a low-temperature organic chloroindate melt, besides the high-temperature molten salt system, InC13-KC1, where the presence of InC14 was recognized by Raman spectroscopy in 1969 [204]. Either acidic or basic melts of InC13-ImC1 were expected to be formed, depending on whether the InC13-to-ImC1 molar ratio was greater or smaller than 1, respectively, because of the presence of excess metal chloride (a Lewis acid) or the presence of chloride ions from the dissociation of excess ImC1. However, only the basic melts formed a clear liquid without solid particle suspension at 65~ so the basic 45 to 55 chloroindate melt was utilized in all experiments, in analogy to a similar basic clorogallate melt from which Ga was successfully electrodeposited [ 109]. The availability of a series of group III metal (A1, Ga, In) chloride-ImC1 melts provided an interesting opportunity to perform comparative chemical and electrochemical research. Moreover, Carpenter and Verbrugge observed that SbC13-ImC1 melts, too, could be prepared at 65~ (possibly because of the formation of SbC14). This was the first time that the existence of a melt similar to previous ones but involving a group V metal was reported. However, in the considered paper, the InC13-ImC1 melt only was investigated in several electrochemical experiments (such as voltammetric, cyclic voltammetric, and depositioncorrosion) to determine the electrochemical reactions accessible in the melt, particularly In electrodeposition. Although the exact mechanism of the process was not clear, it appeared that both In(I) and In(Ill) species were involved in the electrochemistry of the melt. Moreover, current oscillation phenomena were observed at the more negative potentials ( - 1 . 3 to - 1 . 5 V vs. In) during experiments performed at the lower scan rates (e.g., at 50 instead of 100 mV s-l). Similar oscillation phenomena have been observed for a number of electrochemical systems, and, in general, they are representative of complex chemical processes. Despite of their interest, the authors did not discuss them further. The codeposition experiments were carried out on a Pt microcylinder electrode in the 45 to 55 bath containing 0.1 M SbC13, where the Sb(III) concentration was much lower than that of In(III). The counterelectrode and reference electrode consisted of In and were made by dip-coating a Pt wire in molten In. Cyclic voltammetry showed that for scanning of the potential to large negative values, from 1.00 to - 1 . 0 0 V vs. In, the voltammogram for the codeposition process was similar to that for In deposition. In contrast, when the minimum value was - 0 . 5 0 V vs. In only, Sb(III) deposited before In(III), indicating that codeposition of In and Sb was possible. A preliminary characterization was carded out on deposits obtained by codeposition on Pt and glassy carbon disks at potentials ranging from - 0 . 3 to - 1 . 2 V vs. In. The deposits were often not homogeneous and were poorly adherent. One of the most homogeneous deposits was yielded with the use of a square-pulse potential source to control the potential of the working electrode with respect to the reference electrode between 0 and - 1 . 2 V vs. In with a half-cycle period of 100 ms.

303

The atomic ratios of In to Sb in the deposits were determined by EDX analysis. They ranged from 14 to 0.7, and those most rich in In were obtained from Sb-poor electrolytes. The deposition potential influenced the composition ratio in a complex way, and, according to the authors' opinion, further studies were required to fully explain this behavior. Interesting results were obtained by XPS investigation, which clearly showed the presence of InSb and made it possible to determine the oxidation states of Sb and In. Those of Sb, corresponding to Sb 3d electrons, were obtained by a peak-fitting analysis of the spectra from samples deposited with the use of a pulsed potential. The largest peak was assigned to InSb, but smaller peaks due to Sb metal [Sb(0)] and Sb oxides (Sb203 and Sb205) were also observed. A semiquantitative analysis of the data showed that about 67% of Sb in the examined layer (about 20 A thick) was due to InSb, and the remaining 33% was due to Sb metal and its oxides. The authors assumed it likely that process optimization and deposit annealing at relatively low temperatures (350~ would increase this percentage and improve the deposit quality. They concluded that the series of group III metal chloride-organic cloride melts could, in principle, be used as electrolytes for the deposition of almost any III-V compound, both binary and ternary (A1GaAs, GalnSb, etc.); ternary compounds are of great interest for electronic and/or optoelectronic applications. In a patent [205] preceding the paper discussed above [116], the same authors described the method of preparation thin films by codeposition from an organic chloroindate melt containing a salt of at least one metal selected from the group consisting of P, As, and Sb, and an InC13-dialkylimidazolium chloride wherein each alkyl group contained no more than four C atoms, and the molar ratio of the InC13 to the organic chloride ranged from about 45-55 to 2-3. Substitution of small amounts of InC13 with a trichloride salt of another group III metal could be employed to obtain deposits containing other group III metals. For molar ratios of the metal salt to InC13 other than 45-55, the melt was heated to 45~ or greater.

8.8. Indium-Bismuth Compounds Research on codeposition of In and Bi to obtain InBi thin films is scarce [206]. Sadana and Wang [207] showed that In-Bi alloys can be obtained from aqueous baths containing diethylenetriamine pentaacetate complexes of the two metals. Alloys containing up to 90 wt.% In were deposited by varying the current density and bath composition. The authors observed that increasing the current density, and In content of the bath decreased the percentage of Bi in the deposit. Moreover, the current efficiency decreased with increasing current density, but it was not significantly affected by a change in the In content of the bath. Deposits containing 63-89 wt.% In were of good visual quality and were promising decorative finishes. Later, Sadana and Wang examined the effect of pH, temperature, and stirring on the composition and properties of the deposits [208]. X-ray analysis of the original and annealed (at 50~ for 200 h) deposits showed the existence of two intermediate phases. The

304

PERALDO B ICELLI AND KOZLOV

first was InBi, and the second had a much lower Bi content than that required for In2Bi (the phase expected, according to the phase diagram, in addition to InBi and InsBi3 [5]) and was assumed to be In3Bi. However, the structure and lattice parameters were the same as those reported for In2Bi [6]. Note that the authors did not consider InsBi3, which, on the other hand, is difficult to recognize in the presence of the other two In-Bi intermetallic compounds [85], as discussed below. In 1993, a bath based on Trilon B (dinatrii-ethylendiaminetetraacetate) containing indium nitrate, bismuth nitrate (total concentration 0.25 M), and ammonium nitrate was developed for the deposition of In-Bi alloys having good weldability and high corrosion resistance [209]. The electrodeposition conditions were investigated, as were the structure and some properties of the deposits, such as their microhardness, internal stress, and corrosion resistance. Polarization measurements showed that the deposition of In in the alloy began at a potential more positive than the equilibrium potential of pure In in the same electrolyte. The alloys containing 10-15 at.% In showed a sharp decrease in the corrosion rate, and this behavior was explained by the presence in their structure of an excess of the intermetallic phase and the smoothed profile of the deposit surface. Some decrease in the corrosion resistance of alloys obtained at low cathodic polarization was apparently due to the deterioration of the quality of the deposits and their inclusion of indium hydroxide.

9. DIFFUSION PROCESS AND FORMATION OF G R O U P I I I - V COMPOUNDS Because of their different aims, another group of research papers on III-V compounds will be considered separately. They examine the electrochemical preparation of some of these compounds by electrodeposition of a group III element either on a bulk substrate of a group V element (In on Bi, In on Sb) or on a previously electrodeposited thin film of a group V element, followed by an annealing treatment (In on Sb, Ga on Sb). In these papers, the process of diffusion (mainly in the solid state) and chemical reaction at different temperatures to form the III-V compound was more closely examined, as was the influence of the substrate structure and morphology on the same process (In or Ga on crystalline and amorphous Sb thin films).

9.1. The Indium-Bismuth System Already in 1969 [210], it was shown that the plating of In on Bi cathodes at room temperature leads to the formation of intermetallic compounds (In2Bi and InBi), because In diffusion inside the Bi substrate is fast not only at high [211] but also at low [210] temperature. The availability of more accurate techniques and instrumentation made it possible to identify a third intermetallic compound (InsBi3) in addition to In2Bi and InBi [85] and to outline the In diffusion process [86], as shown in the following. Such a compound never emerged on the electrode surface and, therefore, could not be observed during the electrochemical measurements.

3O

It

E 20 [ 10 m-t

o

0

iii .........ii .........

-10

2 4 6 8 4 Charge Density, l 0 Cm -- "2

10

30

2.0

fi__L

10 o

;~

; ....

0 -10 0

0.2

0.4

0.6

0.8

1

Time, h Fig. 23. (a) Open-circuit potential vs. In of the Bi cathode as a function of the charge circulated during In deposition at 4.8 A m -2. (b) Time dependence of the cathode potential vs. In after In deposition at 7.2 A m - 2 for 2 h (curve A) and 2.7 h (curve B). Reprinted from [86] with the kind permission of Elsevier Science.

Indium exhibits an electrochemical behavior that is practically reversible on both the cathodic and anodic sides. At higher current densities, anomalies may be observed on the cathodic side, particularly in indium sulfate baths. They are always associated with a strong increase in the overvoltage and a decrease in the current efficiency due to hydrogen evolution [64, 65]. Therefore, experimental conditions (electrolyte composition, pH, current density, etc.) were selected in which the parasitic process did not occur. Indium was electrodeposited at 25~ in galvanostatic conditions from an aqueous solution of InC13 (0.67 N, pH 1.3) on a bulk Bi electrode. The anode was made of In, and an In wire inserted in a Luggin glass capillary was used as the reference electrode. The potential of the Bi electrode vs. In was measured during and after electrodeposition at current densities from 2.4 to 21.4 A m -2. The deposition time was varied from 1.2 to 8.3 h to obtain 2.8-12.6-#m-thick deposits. Figure 23a depicts the open-circuit potential vs. In of the Bi cathode as a function of the circulated charge. It was obtained by periodically opening the circuit for about 30 s during galvanostatic electrodeposition. Thermodynamic and X-ray diffraction results showed that the three plateaus observed around 15, 5, and 0 mV vs. In on the open-circuit curve were due to the formation of InBi, In2Bi, and In, respectively. The cathode potential was monitored even after In electrodeposition to obtain information on the changes occurring in the composition of the electrode surface. As shown in Figure 23b, a double transition took place in most cases, because In and In2Bi as well were not stable on the electrode surface. Thus, curve B presents an extended plateau whose value corresponds to In2Bi followed

BINARY III-V COMPOUNDS M

,,

,

:

::

,,

.

~.~ ~f t ~

.

.t"

~ 1 7 6 1 7""6

0

.

J

E- ~' InBi

I;.'0"-

.

,

"~-o

-

uaui...

,'--100

,

. "''r .... 200

.

.

.--300

Time, h Fig. 24. Cumulative thickness of the deposit (o) and thickness of the In2Bi (M), InsBi 3 (0), and InBi (A) layers as a function of time after In deposition at 21.4 A m -2 for 3 h. The standard deviation from the average value is also indicated. Reprinted from [85] with the kind permission of Elsevier Science.

by a potential increase up to the typical value of InBi, whereas curve A (due to a thinner deposit obtained at the same current density as curve B) had a faster evolution showing the plateau of InBi only. This time evolution was due to In diffusion into and reaction with Bi, as shown by SEM and EDX analyses of the sample surface and cross section. Indeed, in all of the cases where the final electrode potential vs. In was equal to zero, isolated In microcrystals were observed on the sample surface immediately after electrodeposition. These microcrystals emptied out and collapsed on the sample surface, just as though In diffused into the bulk of the electrode. The smaller the deposited In quantity, the faster was the time evolution. Simultaneously with the SEM observations, the In surface concentration of the 12.6-/zm-thick deposits was analyzed by EDX as a function of time. Because the emission depth of the backscattered electrons was smaller than 1/zm, only the deposit surface was investigated. Because of the time needed to perform the analysis, the In surface concentration was initially not higher than 90 wt.% and then regularly decreased to 35.6 wt.%, very close to that of InBi (35.46 wt.%). Interesting details on changes in the morphology and composition of the deposits were obtained by analyzing their inner structure as a function of time. To obtain the cross section, the samples were cut after immersion in liquid nitrogen for a few seconds. The results showed that the deposit had a multilayered structure, that inside each layer one of the three intermetallic compounds was present, and that their sequence from the surface to the bulk was In2Bi/InsBi3/InBi. By SEM-EDX analysis, the thickness of each layer was also determined, as was the cumulative thickness of the deposit as a function of time. Figure 24 shows the trend of these thicknesses and, therefore, that of the diffusion and reaction process, for a film deposited at 21.4 A m -2 for 3 h. It clearly indicates that InsBi3 never emerged on the electrode surface. After a certain time (around 100 h in the example) the previous sequence of the intermetallic compounds (In2Bi/InsBi3/InBi) changed to In2Bi/InBi, the latter being the unique compound at the end of the analyzed time scale (1500 h). So, InsBi3 exclusively appeared as a separation phase.

305

To emphasize the difficulty of observing InsBi3 when the other In-Bi intermetallic compounds are present, it is worth noting that InsBi3 was recognized in 1967, in addition to In2Bi and InBi [212, 213], in a revised In-Bi equilibrium phase diagram [214]. A more recent In-Bi phase diagram is reported in Massalski's handbook [5], and the presence of InsBi3 has also been confirmed by thermodynamic calculations [9]. To give further support to the SEM-EDX results, the deposits were submitted to X-ray diffraction analysis. The results mimicked those already discussed: In entirely disappeared from the surface, the two transient compounds In2Bi and InsBi3 evolved, the latter disappearing before the former, and the InBi layer continuously increased. To evaluate the In diffusion coefficient in the three In-Bi compounds, the mechanism of the process was investigated, with the intention of creating an interpretative model [86]. First, assuming that InBi only was formed, two subsequent steps were envisaged during electrodeposition: (i) the In 3+ charge transfer process and (ii) In diffusion into the InBi layer toward the InBi-Bi interface to further form InBi. The kinetics of the first step was determined by the current density, i, which was constant in the electrochemical experiments. The moles of In deposited on the unit surface area, mdep, increased linearly with time, t, according to Faraday's law, mdep -

it/zF

where z is the number of charges transferred during the electrochemical process (z -- 3) and F is Faraday's constant, as usual. Schmalzried [215, pp. 53, 95] had already analyzed the case where two metals M (In) and N (Bi) react to form the intermetallic compound MrNs (InBi), separated from the reactants by two phase boundaries, so that the reaction proceeds by diffusion of the participating components through the reaction product. The overall driving force for the reaction is the difference in Gibbs free energy between the reactants and the reaction product. For a very low solubility of the reactants in the reaction product, the particle fluxes are locally constant. As long as the local thermodynamic equilibrium is maintained within the reaction layer and at the phase boundaries, a parabolic growth rate law results. Consequently, the number of moles of In that could be removed from the unit surface area to form the intermetallic compound, mrem, also shows a parabolic time dependence: mrem-

(D't) 1/2

where D* is proportional to the In diffusion coefficient, D, and to the difference between the In chemical potential at the two phase boundaries of the reaction product, that is, to the standard Gibbs free energy of formation of InBi from the elements. Generally, D will depend to a greater or lower extent upon the component activities. However, as a first approximation, its average value over the reaction layer can be used, especially when the activities of M and N within the region of homogeneity of phase MrNs do not vary by more than a power of 10. For intermetallic compounds with very small values of the standard Gibbs free energy of formation from the elements (e.g., for

306

PERALDO B ICELLI AND KOZLOV

t

t

turn

t

~

Time

Fig. 25. Comparisonof the time dependence of the number of In moles deposited on the unit surface at several current densities, mdep (straight lines), and the number of In moles removed from the unit surface, mrem (parabolic curve). In case b, the arrowindicates the time at whichm r e m " - m d e p . Reprinted from [86] with the kind permission of Elsevier Science.

NiA1, it is lower than - 100 kJ m o l - 1), this simplification is not valid. However, this is not the case for the In-Bi intermetallic compounds, whose values are higher than - 15 kJ mo1-1 [9], as shown below. Indium only was assumed to diffuse, because of a mobility higher than that of Bi, as shown by its lower melting point (156.634~ in comparison with that of Bi (271.442~ Figure 25 indicates the typical time dependence of both mdep and mrem at room temperature, mdep depends on the electrodeposition rate, and, therefore, different straight lines are obtained at the different (constant) current densities. In contrast, just one curve depicts the removed In quantity, which depends, at constant temperature and pressure, on the material properties only (particularly on the In diffusion coefficient). Three different situations may occur: 1. mrem > mdep. All of the electrodeposited In diffuses into the cathode, forming an InBi layer, the growth rate of which is determined by the current density. 2. mrem < mdep. In accumulates on the electrode surface because the diffusion and reaction process is not able to remove all of the electrodeposited material. 3. mrem = mdep. The maximum possible growth rate of the layer is observed without In surface accumulation. The intersection point of the mrem(t) curve with each of the mdep(t) straight lines gives the limiting time, t*, above which In surface accumulation takes place at each current density. The experimental curves (e.g., Fig. 23a) made it possible to determine this time, because just at this same time, the opencircuit potential vs. In decreased from the typical value for InBi toward zero, indicating a progressive surface enrichment with In. So, by equating mrem to mdep, and introducing the experimental t* values for several runs, it was possible to determine

Fig. 26. Scheme of the cathode composition and of In diffusion into the In-Bi compounds at the end of the electrodeposition process (upper part), and In wt.% as a function of the deposit thickness (lower part). Reprinted from [86] with the kind permission of Elsevier Science.

the average D* value and from this the average In diffusion coefficient in InBi, at 25~ D ~ 1 x 10 -15 m 2 s -1. For this calculation, the value of Chevalier [9] for the InBi standard Gibbs free energy of formation at 25~ was utilized. Chevalier determined the free energies for InBi, InsBi3, and In2Bi by averaging the experimental data of different authors [216-218]. They were found to be small: - 3 . 7 2 , - 1 4 . 2 , and - 5 . 5 4 kJ m o l - 1, respectively. It is worth examining the very high value of D(InBi) at room temperature. Much lower values, usually between 10 -20 and 10 -50 m 2 s -1, were obtained for common metals and for Ge and Si. Values comparable with that for In in InBi were only observed during the diffusion of very small atoms (e.g., around 10-15 m 2 s- 1 for Li in Ge and Si, and 10-17 m 2 s- 1 for C in body-centered cubic (bcc) Fe at 70~ or at high temperatures (e.g., around 10 -15 m 2 s -1 for Zn in Cu at 734~ and 10 -17 m 2 s -1 for Fe in Fe at 727~ [12]. In the most general case, when the diffusion process was not able to remove all of the deposited In to form InBi, the deposit was composed of In, In2Bi, InsBi3, and InBi at the end of the electrodeposition process, as schematically shown in Figure 26, and the deposit composition evolved with time. The behavior of such multiphase product layers with respect to In diffusion and reaction was evaluated by applying previous treatments to each of the individual phases as their range of homogeneity was sufficiently narrow, and it was assumed that local equilibrium was maintained [215, p. 95]. This resulted in a parabolic growth rate for each reaction product and, therefore, for the total thickness of the multiphase layer. However, the difference between the In chemical potential at the InrBis interfaces, A/z(InrBis), was no longer proportional to the standard free energy of formation of InrBis from the elements, as was the case when only one intermetallic compound (InBi) was formed. This difference was calculated by the method suggested by Schmalzried [215, p. 124], taking into account that, as shown in Figure 26, each intermetallic compound was produced at its respective righthand interface by reaction of the diffusing species (In) with the

BINARY III-V COMPOUNDS intermetallic compound that had a lower In content, while it was consumed at its left-hand interface by reaction with In to form the compound that had a higher In content. By applying the equilibrium conditions at the two interfaces of each reaction product layer, the difference A/tin between the In chemical potentials at the left- and right-hand boundaries was evaluated from thermodynamic data. This difference at either side of the In2Bi and InBi layers had a positive sign, whereas for InsBi3 it was negative. Therefore, In diffusion through In2Bi and InBi was favorable, whereas it was not through InsBi3; this explains why the latter compound was never observed on the electrode surface and no additional plateau could be found in the In electrodeposition curve. As long as metallic In was present on the sample surface, the ratios of the thicknesses, Ax, of the different intermetallic compounds were independent of time and are given by [Ax(InrBis)/Ax(InBi)]

= {[D(InrBis) • Alz(InrBis)]/[D(InBi)

• A/z(InBi)]} 1/2

where InrBis refers to In2Bi or InsBi3. The thicknesses of the layers of the different In-Bi intermetallic compounds were experimentally determined as a function of time, as were their ratios to that of InBi. Time was measured starting from the end of the electrodeposition process. With the introduction of the average experimental values in the previous equation, together with the estimated values of D(InBi) and A/z(InrBis), the average In diffusion coefficients in the In2Bi and InsBi3 layers (at 25~ were finally obtained: D(In2Bi) ~ 1 • 10 -16 m 2 s -1 D(InsBi3) ~ 3 x 10 -16 m 2 s -1 The average In diffusion coefficient also turned out to be very high in IneBi and InsBi3 compared with the values of other metals at room temperature. The presence of a multiphase product layer between In and Bi made it possible to explain the observed potentiometric behavior. After electrodeposition, In diffusion with reaction occurred, utilizing metallic In on the deposit surface. As soon as In was no longer available at the sample surface, In2Bi and InsBi5 decomposed. As previously observed, the chemical potential of In at the In2Bi-InsBi3 interface increased within InsBi3, whereas that at the InsBi3-InBi interface decreased within InBi. Therefore, InsBi3 would be expected to be more readily decomposed than IneBi, as was observed experimentally (Fig. 24). Following a similar argument, it may be expected that even during In electrodeposition, InsBi3 did not appear on the electrode surface, because, otherwise, the In chemical potential would strongly increase within the outermost deposit layer (of InsBi3), and this is an unfavorable condition for In diffusion. Hence, the surface would immediately be covered by In or InzBi. So, the assignment of the quasi-plateau at 5 mV vs. In to IneBi and not to InsBi3 seems to be reasonable. To summarize the results, during In electrodeposition on Bi cathodes, In diffused and reacted with Bi, forming over-

307

layers of In-Bi intermetallic compounds ordered according to their relative composition. The solid-state process continued after electrodeposition until a layer of InBi only formed. The exceptionally high mobility at room temperature of In in In-Bi intermetallic compounds could explain this singular behavior. The influence of temperature on the process of In-Bi intermetallic compound formation, in particular of InBi, was also investigated [87]. Indium was electrodeposited on Bi electrodes for 1.5-4.5 h at current densities from 5.0 to 14.3 A m -2 and at temperatures from 30~ to 70~ to observe the time evolution of the deposit composition. The coulometric thickness of the deposited In films ranged from 2.8 to 6.1 /zm. For the SEM-EDX analysis, thicker deposits (12.6/zm) were prepared, at 25~ and 70~ by electrodeposition at 21.4 A m -2 for 3 h. At the higher electrodeposition temperatures, the plateau in the electrochemical curves due to InBi formation was more extended and was observed at slightly higher potentials. Moreover, no intermediate quasi-plateaus were noted, the In diffusion rate being so high that the two In-Bi compounds less stable than InBi could not be formed. This different behavior was clearly indicated by SEM and EDX analyses of the surface and cross section of the thicker deposits during time evolution after electrodeposition at 25~ and at 70~ Moreover, X-ray diffraction confirmed the results. By considering the charge transfer and mass transfer phenomena, the authors also estimated the coefficient of In diffusion into InBi. The InBi Gibbs free energy of formation from the elements at different temperatures, AG(T), was evaluated at 273 K from literature data [216-219], according to the Gibbs-Helmholtz equation. However, because of the spread in the values of the different authors, the equation AG(T) = - 1 4 6 4 . 4 - 7.58128 x T

(in Jmo1-1)

given by Chevalier [9] was preferred. Chevalier optimized the experimental data of other authors during his thermodynamic evaluation of the In-Bi phase diagram. The results showed a relatively small difference in the Gibbs free energies at the different temperatures, which implied a very small difference in the plateau voltages of InBi, within the range of the experimental error. The values obtained for the diffusion coefficient at 30-70~ ranged from 0.79 • 10 -15 to 3.77 x 10 -15 m 2 s -1 . Again, these values were unusually high. Applying an Arrhenius-type relation, In D(InBi) as a function of 1/ T, the values of 32.8 kJ mo1-1 and 3.7 • 10 -1~ m 2 s -1 were estimated for the activation energy and the frequency factor of the process, respectively. The very small value of the activation energy (usually about 100-400 kJ mol-1 for many materials of interest [12]) was certainly a factor contributing to the high diffusion coefficient observed for In in InBi, notwithstanding the exceptionally small frequency factor. The theoretically predicted and experimentally observed values are often between 10 -5 and 10 -7 m 2 s- 1 [ 12].

308

PERALDO BICELLI AND KOZLOV

9.2. The Indium-Antimony System The investigation of the In-Bi system was extended to the InSb system [89]. The Sb cathode was prepared by melting highpurity Sb. The other experimental conditions, counterelectrode, reference electrode, and electrolyte, were the same as those of the In-Bi system. The electrodes (In anode and Sb cathode) were polarized for 10 min at a constant current density of 2 A m -2 to deposit In. After a very small potential transient, which was related to the nucleation process on a foreign substrate, the cathode potential attained a nearly constant value. The current was then switched off and the electrode potential vs. In immediately decreased to zero, indicating the presence of In on the electrode surface. A similar experiment was carried out by periodically opening the circuit for about 60 s during electrodeposition to monitor the changes occurring in the surface composition. The open-circuit potentials did not reach constant values, as found in the similar case of In deposition on Bi. As a matter of fact, at the beginning of the experiment, their values were positive and close to that of bare Sb, whereas the following showed a progressively decreasing value until they reached 0 V vs. In. Hence, the cathode behaved like a mixed electrode, and no plateau due to the formation of InSb was observed. After the current was switched off, the electrode potential was still monitored. After about 15 min, the electrode potential showed a typical inflection, an extremely short quasi-plateau, which, on the basis of thermodynamic data, was attributed to InSb emerging on the electrode surface. Then, the electrode potential increased again, because InSb immediately dissolved into the electrolyte, and the potential returned toward the initial open-circuit value because of the bare Sb substrate. To verify the above InSb and In dissolution, a special experiment was performed. Two In electrodeposits on Sb were prepared under the same conditions (10 A m -2, 300 s). At the end of the process, one of the samples was immediately taken from the bath, while the other was left in rest conditions. After 66 h, the former sample showed a very small X-ray diffraction peak due to InSb in addition to the peaks of the unreacted In, whereas the latter sample showed neither InSb nor In peaks, in agreement with electrochemical results [220]. As In disappeared not only because of the solid-state diffusion and formation of InSb, but prevailingly because of its dissolution into the electrolyte, it was impossible to obtain reliable values of the In diffusion coefficient from electrochemical resuits. Therefore, another method was followed based on X-ray data, which also made it possible to estimate the D values at high temperatures [89]. For this purpose, thin (0.8/zm) and thick (18/zm) In deposits were prepared for observation of the formation of the intermetallic compound. At the end of the deposition process, the electrodes were immediately removed from the electrolyte to avoid In dissolution into the bath, rinsed in water, and dried. To study the influence of temperature, they were annealed at 70~ 110~ and 135~ for increasing times (up to several hundred hours).

I x

I

q

__L

|..

20

40

30

,

9

..

,

50

20 Fig. 27. Comparison of the schematic ASTM lines of In, Sb, and InSb [6] with the X-ray diffraction pattern of a 0.8-/xm-thick deposit heated at 135~ for 51.5 h. Reprinted from [89] with the kind permission of Elsevier Science.

Thin In deposits obtained at room temperature consisted of isolated microcrystals with an average size of 5/zm and showing quite regular crystal planes. EDX investigation indicated that these crystals were due to In, whereas on the remaining regions of the surface Sb only was found. When the deposits were heated, the surface of the microcrystals became rounded, especially at the highest temperature (135~ not far from the In melting point. Thick deposits were rough and imperfect with typical holes, but the In dot map analysis of their cross section showed their practical continuity. The SEM-EDX analysis was performed at several points of this section from the surface toward the bulk of the specimen 2 years after electrodeposition. It showed the continuous decrease in the In atomic percentage, which reached a value close to 50% at the deposit-substrate interface, indicating the formation of InSb. These results indicated the much slower In diffusion and reaction process for the Sb substrate than for the Bi substrate. At higher temperatures, the deposits were continuous and InSb was more easily observed, for example, after the samples were heated for 334 h at 110~ From scans of their cross section, they showed the three-layer structure In-InSb-Sb from the surface to the bulk. The X-ray diffraction pattern of a thin deposit heated at 135~ for 51.5 h is compared in Figure 27 with the schematic ASTM peaks of In, Sb, and InSb [6]. Although some lines are superimposed on the ASTM spectra, it was possible to select for each phase at least one typical reflection peak not influenced by the nearby peaks. This peak was at 20 = 28.6 ~ for Sb (because ofthe {012} planes), at 33.0 ~ for In ({ 101 }), and at 46.6 ~ for InSb ({ 311 }). The comparison of the sample peaks with the ASTM identification peaks showed that the deposit contained In and InSb.

BINARY III-V COMPOUNDS Both EDX and X-ray diffraction analyses indicated the increasing formation of the InSb phase with heating time and temperature. However, because of the very low rate of the process, InSb could be detected either after a very long aging of the deposits at room temperature or after a severe annealing. The In diffusion coefficient was estimated at different temperatures from the decrease with time of the most intense X-ray diffraction peak of In ({ 101 }). Because the same sample area was always examined, it was assumed that the intensity of this line was proportional to the In quantity in the deposit. So, from the In moles deposited on and removed by diffusion from the unit surface area, mrem = mdep(1 --

11/10)

where I0 and 11 are the intensities of the In line immediately after deposition and after deposit heating, respectively. As previously shown, mdep and mrem could be determined from the deposition and the diffusion time (in this case the heating time), respectively. The Schmalzried theory, discussed in detail for the similar case of InBi formation [86], could also be applied in this case, because of the relatively high standard Gibbs free energy of formation of InSb from the elements, equal to - 2 5 . 5 kJ mo1-1 [8]. Again, In only was assumed to diffuse, because of its higher mobility, as shown from the much lower melting point: 156.634~ and 630.755~ for In and Sb, respectively. The average D values and their standard deviation, estimated from the experimental 11/I0 ratio, ranged from (0.10 40.04) • 10 -19 m2s -1 at 25~ to (2.59 + 0 . 3 3 ) • 10 -19 m2s -1 at 135~ From the linear dependence of In D on I/T, the activation energy (30 + 2 kJmo1-1) and the frequency factor [(1.8 4- 0.5) x 10 -15 m 2 s -1 ] of the diffusion process were determined. The obtained D values were discussed in connection with the results of other authors. As stated in Section 8.7, Mengoli et al. [84] determined the time dependence of the percent conversion of the In-Sb samples to InSb at high temperatures. As the initial quantities of In and Sb were known, it was possible to evaluate the InSb moles formed on the unit surface area as a function of time. From the observed square root dependence, the diffusion coefficient was estimated. The values turned out to be around 3 • 10 -18 and 7 • 10 -18 m 2 s -1, at 175~ and 185~ respectively, in reasonable agreement with the previous values, considering that at these temperatures In was in the molten state. In contrast, no agreement was found with the D values obtained by Hobson and Leidheiser [88]. Performing a chemical analysis of the deposits, these authors determined the InSb quantity formed both after In electrodeposition at 45~ on bulk Sb and during a subsequent heat treatment in boiling water. The D values were around 1.5 • 10 -16 and lower than 1.7 • 10 -18 m 2 s -1, respectively. The authors maintained that the data available when the paper was written were insufficient to explain such a great difference in the diffusion coefficients. So far, their highest value remains unexplainable and perhaps not convincing, also because when the Schmalzried relation-

309

ship [215] was applied to their data, an even higher diffusion coefficient was found (10 -12 instead of 10 -16 m 2 s -1) [89]. Eisen and Birchenall [221] investigated the In and Sb selfdiffusion in InSb at 478-521~ with a tracer technique, determining the activation energy and frequency factor. The data yielded slightly different diffusion coefficients for group III and V atoms, 8.3 • 10 -19 and 5.9 • 10 -19 m 2 s -1, respectively, at 478~ The values are on the order of those of the substitutional elements in Ge, thus tendingto support a vacancy mechanism in InSb, too, which has a similar strong tetrahedral coordination. A reasonable mechanism for self-diffusion accounting for the above data seemed to be the vacancy diffusion in each of the two fcc sublattices formed by the two constituents of InSb. On the basis of bond strength considerations, the authors could also assume that the diffusing entities in InSb were neutral atoms and could explain the higher diffusion coefficient of In with respect to Sb. Contrary to what was observed in the case of In electrodeposition on Bi cathodes, the In diffusion coefficient in InSb is very low, about five orders of magnitude lower than that in InBi [87]. This different behavior was related to the different crystalline structures of the two compounds. As already discussed, the majority of the 1 : 1 compounds formed by elements of group IliA and VA of the periodic table, to which In, Sb, and Bi belong, crystallize with the zinc-blende (cubic) structure with tetrahedrically coordinated atoms (Fig. l a). Exceptions in this series are the compounds involving the more metallic elements, particularly InBi, which has a tetragonal unit cell and metallic bonds with fourfold coordination. Its B-10 structural type (Fig. l c) consists of layers of like atoms normal to the c axis, with adjacent In layers separated by two Bi layers (In-Bil-Bi2-In stacking). Each In layer is bonded to the Bi layer to either side of it, and the closest In-Bi interatomic distance (3.13/~) is appreciably greater than the value expected for a covalent bond (2.92/~) or for an ionic structure (2.86 ~) and much greater than the size of the closest approach of In and Sb in InSb (2.80 ~). Moreover, the size of the closest approach of Bi atoms in neighboring Bi layers (3.68 ~) is somewhat larger than the interatomic separation of Bi atoms in adjacent layers of metallic Bi (3.47 ~). This arrangement gives rise to a marked cleavage plane normal to the c axis [222]. A structure of this type can also be described as a distorted cesium chloride (cubic) arrangement (Fig. lb) when the axial ratio c/a approaches the value of ~/~/2 and the atoms in the layers Bil and Bi2 lie in the same plane (In-Bi-In stacking). However, in this case, the distortion is so great that a fourfold coordination results and only a formalresemblance exists between InBi and a distorted cesium chloride arrangement. The typically layered structure of InBi is expected to be highly favorable to diffusion, particularly in the case of metals, such as In, that have a low melting point and, therefore, a high mobility. Instead, a compound such as InSb with strong bonds and a more compact atomic arrangement is found to be more "impervious." It is now worth recalling that the In diffusion process is accompanied by a chemical reaction to form the intermetallic

310

PERALDO BICELLI AND KOZLOV

compound. The In quantity removed from the unit surface area of the deposit in the time unit depends not only on the diffusion coefficient but also on the Gibbs free energy of formation from the elements of the intermetallic compound. The absolute value of this thermodynamic quantity is much higher in InSb than in InBi but not high enough to compensate for the difference in the diffusion coefficients. So, the structural factor prevailed over the physicochemical one, and it was not possible to observe the deposited In microcrystals collapsing on and disappearing from the sample surface, as occurred in the case of In deposits on Bi cathodes [85].

10. INFLUENCE OF THE SUBSTRATE STRUCTURE AND MORPHOLOGY ON THE DIFFUSION PROCESS I0.I. The Indium-Antimony System In general, diffusion and reaction processes in the solid state are scarcely reproducible phenomena, because of the consistent influence of the crystal geometry (surface coverage, material morphology) and structure (mono- or polycrystalline, with preferred orientation, amorphous, with grain and dislocation boundaries and other structural defects), so that only the order of magnitude of the average diffusion coefficient is significant. Because the geometry and structure of the In deposit and the Sb substrate depend on the way they were prepared, the values obtained for the In diffusion coefficient typically refer to In electrodeposits on a bulk Sb substrate [89]. To deepen the understanding of these aspects, which to the authors' knowledge have never been examined before, the influence of the substrate geometry and structural properties on the diffusion coefficient was investigated [90]. For this purpose, crystalline and amorphous Sb deposits were prepared by electrochemical deposition under different experimental conditions. Indium was then electrodeposited on the two different substrates, and the formation of InSb was examined at several temperatures. Sb was electrodeposited on an Fe disk from an aqueous solution of 0.3 M SbC13, 1.6 M H2SO4, and 1.7 M HC1. Two optimized conditions were found to produce either crystalline or amorphous Sb deposits. Crystalline deposits were obtained by electrodeposition at 440 A m -2 and 50~ and the amorphous ones were obtained at 40 A m -2 and 22~ The deposition time was 20 min in both cases. The average thickness of the deposits was 33 and 3/zm, respectively. Moreover, two different types of crystalline deposits were prepared: those obtained from the electrolyte either not containing any special addition agent or containing the organic compound Trilon B at a concentration of 40 g liter -1. Before being utilized, the structures of the Sb deposits were checked by X-ray diffraction. Whereas the crystalline deposits presented the typical diffraction peaks of rhombohedral Sb, the amorphous ones showed a characteristic broad band in the range 20 - 24-36 ~ and minor bands at higher values, but no peaks due to the crystalline phase. As for the deposit morphology, Figure 28 compares the SEM micrograph and the rough-

ness profile of the crystalline Sb deposit obtained from the electrolyte not containing Trilon B (c-Sb) with those of amorphous Sb (a-Sb). The crystalline deposits presented regularly shaped rosette-like crystals with a mean size of 15-20 # m (Fig. 28a), whereas the morphology of the amorphous deposits was completely different (Fig. 28c). Typical spheroidal particles were observed to have an average size of about 2 # m and were arranged along the etching lines of the Fe disk. This is due to the fact that the thinner amorphous deposits were still influenced by the surface inhomogeneities of the same Fe disk. The corresponding roughness profiles along 200/zm of a central line are shown in Figure 28b and d, together with the average value of the maximum individual roughness depth, Rmax. Both curves as well as the numerical values dramatically indicate the great difference in the surface profiles, as also expected on the basis of the morphological aspects of the deposits. Crystalline deposits obtained in the presence of Trilon B (ct-Sb) were similar to c-Sb deposits. However, EDX results showed a high quantity of carbon on their surface because of the adsorption of the organic salt. Indium was deposited from the usual chloride bath at 35~ at a current density of 177 A m -2 for 1.5 min on the Sb substrates with the different structures. The deposits completely covered the substrate surface and their thickness (about 0.9/zm) did not hinder the X-ray observation of the growing InSb intermetallic compound. Those on c-Sb presented a much smoother profile than the original substrate, whereas those on a-Sb did not show any practical difference. After In deposition on Sb, the samples were heated at 40~ 70~ 110~ and 140~ in vacuum for increasing times. Of course, the deposits on the amorphous substrate were heated only up to the time at which the Sb transition from the amorphous to the crystalline phase did not occur. Although according to Hashimoto and Nohara [223], very thin (nm-sized) amorphous Sb layers inherently in an unstable supercooled state may easily be crystallized at room temperature by some trivial perturbation; micrometer-sized layers are much more stable. So, a specific investigation was made of the crystallization process of a-Sb, whose main lines will be discussed later. The In diffusion coefficient was estimated from X-ray resuits according to the Schmalzried theory [215]. The values obtained for the different substrates and temperatures are collected in Table XI, and the dependence of In D on 1/ T is depicted in Figure 29. The observed linear behavior made it possible to determine the activation energy and the frequency factor of the In diffusion process in crystalline InSb on the c-Sb substrate: 63 + 4 kJmo1-1 and (8.20 • 2.50) • 10 -1~ m 2 s -1, respectively; on the ct-Sb substrate: 65 4- 4 kJmo1-1 and (2.64 41.50) x 10 - l ~ m 2 s -1, respectively; and on the a-Sb substrate: 534-4 kJmo1-1 and (2.064-0.80) • 10 - l ~ m 2 s - l , respectively. As shown in Table XI and Figure 29, the In diffusion coefficient strongly depended on the substrate and increased according to the sequence D(ct-Sb) < D(c-Sb) < D(a-Sb). Moreover, from previous results [89] for bulk Sb substrates, b-Sb, D(b-Sb) was practically equal to or, at the two highest temperatures, even lower than D(ct-Sb).

BINARY III-V COMPOUNDS

311

Fig. 28. SEM micrograph and roughness profile (a and b, respectively) of the c-Sb substrate and (c and d, respectively) of the a-Sb substrate. Reprinted from [90] with the kind permission of Elsevier Science. Table XI.

Indium Diffusion Coefficient as a Function of Temperature for the Different Sb Substrates 9. 3 7

Substrate

40 ~C

Crystalline Sb without Trylon B D x 1019 0.204 + 0.150 (m 2 s - 1) Crystalline Sb with Trylon B D x 1019 (m2s -1) Amorphous Sb without Trylon B D • 1019 (m 2 s - 1 )

70 ~C

110 ~C

2.14 4- 1.05

23.1 -t- 8.5

69.2 + 21.0

0.352 + 0.245

2.91 4- 1.15

17.6 + 6.5

17.1 4- 6.5

112 4- 30

Reprinted from [90] with the kind permission of Elsevier Science.

,

,

140 ~C

-4$

-47 0.0024

3.44 + 1.25

9

0.0026

)28

0.003

0.0032

492 4- 90 Fig. 29. Dependence of the logarithm of the In diffusion coefficient on the reverse of the absolute temperature (Arrhenius plot) for In electrodeposits on a-Sb (curve 1), c-Sb (curve 2), and ct-Sb (curve 3). Reprinted from [90] with the kind permission of Elsevier Science.

312

PERALDO BICELLI AND KOZLOV

The diffusion coefficient is well known to be influenced by at least two main factors, geometrical and structural, as mentioned above. The former depends on the surface morphology of the Sb substrate, because in comparison with a smooth surface profile, a rough one presents a higher effective area for diffusion. However, the D(ct-Sb) and D(c-Sb) values were smaller than the value of D(a-Sb), notwithstanding the higher surface roughness of the crystalline substrates with respect to the amorphous one. So, the structural factor was prevailing. To give direct evidence of this hypothesis, an a-Sb sample was heated for 3 h at 110~ to induce complete crystallization. The so obtained crystalline phase (ca-Sb) showed a very smooth morphology similar to that of the original amorphous material. On this substrate, In was deposited, as usual, and the sample was heated at 110~ for 1 h, 30 min to determine the In diffusion coefficient. The value of D(ca-Sb) was found to be practically equal to that for the c-Sb substrate; that is, it was smaller than for the a-Sb substrate. This confirmed that the differences observed between D(a-Sb) and D(c-Sb) or D(ca-Sb) were due entirely to the structural and not to the geometrical factor. The two different crystalline substrates had practically the same morphology, but that obtained in the presence of the addition agent was shown to have foreign particles selectively adsorbed on its surface, possibly mainly localized at the grain boundaries. This certainly hindered the In intergranular diffusion, thus explaining why D(ct-Sb) was smaller than D(c-Sb), as also confirmed by the difference in the pre-exponential factor and not in the activation energy for diffusion into the two substrates. Finally, the small D values of the bulk Sb substrate were tentatively ascribed to its high defectiveness. To explain the results, the path of In was considered during its diffusion from the In-InSb to the InSb-Sb interface inside the growing InSb layer. Because the latter was always polycrystalline, this part of the overall process could not be a cause of the observed differences in the D(c-Sb) and D(a-Sb) values. Instead, a chemical reaction between In and Sb occurred at the InSb-Sb interface, where In further diffused into the either crystalline or amorphous Sb substrate. So, after nucleation and growth of the new InSb phase, the InSb-Sb interface was shifted more and more into the bulk of the Sb deposit. Hence, this last step, strictly depending on the Sb structure, was at the heart of the observed behavior. As for the substrate structure, in crystalline (rhombohedral) Sb the atoms are incorporated into two-dimensional networks of puckered sixfold tings forming typical layers. The threefold coordinated atoms in the same layer are at a distance of 2.87 .~, and the nearest atoms in adjacent layers are at 3.37/k [4]. The structure of amorphous Sb was investigated by several authors, and the experimental interatomic distances were found to be generally larger (e.g., [224]) and the density lower (e.g., [225]) than those in rhombohedral Sb. Moreover, the interlayer correlation existing in the crystalline form was minimized in the amorphous structure, a feature probably accounting for the semiconducting properties and low density of a-Sb [226]. The electrodeposited a-Sb samples were submitted to structural characterization by X-ray diffraction, and the radial distil-

bution function was determined [227]. The results of the analysis could be interpreted on the basis of the model reported in the literature for rhombohedral Sb. The prevailing structural disorder in the amorphous sample was due to the average distance between neighboring double layers, which was higher by 27% than in crystalline Sb deposits. So, even electrodeposited Sb followed the rule that some interatomic distance strongly increased from the crystalline to the amorphous phase. These resuits, indicating the more open structure of a-Sb than of c-Sb, might explain the more favorable conditions for In diffusion in the former material. These more favorable conditions were due entirely to the lower activation energy for the a-Sb substrate, as the pre-exponential factor was higher for the c-Sb phase. Because the latter represents the frequency of successful attempts to overcome the energy barrier, the higher value found for the crystalline material was related to its more regular structure. The authors concluded that the amorphous substrate was more suitable than the crystalline one for the preparation of InSb by solid-state diffusion and reaction, because the process was moderately fast, even at low temperatures. Indeed, in contrast to the In diffusion coefficient for c-Sb, that for a-Sb lies slightly beyond the upper limit of the often mentioned range normally considered for common metals and semiconductors [ 12].

10.2. The Gallium-Antimony System The influence of the amorphous and the crystalline structure of Sb on Ga diffusion into the same Sb substrate has also been studied, and interesting results are already available [91 ]. The Ga diffusion coefficient was determined at 50~ 75~ and 100~ and the formation of the GaSb semiconductor compound was observed. The D values were on the order of 10 -18 to 10-16 m 2 s- 1. At these temperatures, Ga was at least partially in the molten state, and the geometrical factor prevailed over the structural one, because, owing to its larger surface area, the c-Sb substrate was more suitable than the a-Sb substrate for promoting the Ga diffusion and reaction process: D(c-Sb) > D(a-Sb). However, in the case of a crystalline substrate with the same morphology as amorphous Sb obtained by a-Sb crystallization, the reverse occurred: D(ca-Sb) < D(a-Sb). The primary role played by the surface morphology when Ga was in the molten state was explained by high Ga fluidity. Indeed, Ga in the liquid phase is expected to be able to easily reach surface regions where the diffusion process is less difficult, as also shown by the very high value of the frequency factor for both c-Sb and a-Sb substrates (about 10 -5 and 10 -6 m 2 s - i , respectively). The diffusion coefficients were also determined at 20~ a temperature at which Ga is in the solid state. Values around three orders of magnitude lower were achieved, and the structural factor prevailed over the geometrical one, that is, D(c-Sb) < D(a-Sb), despite the larger surface area for diffusion of the c-Sb substrate. This behavior was similar to what was previously observed for In diffusion into a-Sb and c-Sb [90] and was attributed, in this case too, to the high structural disor-

BINARY III-V COMPOUNDS der in a-Sb, which also presented higher interatomic distances than c-Sb.

10.3. Amorphous Antimony Crystallization As already stated, to select the annealing treatment that best avoided crystallization during the diffusion measurements, specific research was carried out on a-Sb crystallization [227]. Several authors studied amorphous Sb films of several thicknesses prepared in different ways and at various temperatures, indicating the strong dependence of their stability against crystallization on the preparation conditions [223, 228-234]. The results indicated the important role of the thickness in the crystallization of amorphous Sb films and, therefore, the difficulties in obtaining amorphous samples some micrometers in thickness. In particular, they showed that it was not possible to avoid crystallization during vacuum deposition at room temperature. On the contrary, this was possible by electrodeposition of Sb on Fe substrates and adequately selection of the electrolyte composition and the current density, as shown above [90]. To investigate the influence of temperature on a-Sb crystallization and the mechanism of the process, the deposits were heated at 70~ and 110~ for increasing times, and the changes in the intensity of the main X-ray diffraction peak of c-Sb were analyzed. As pointed out by several authors [235], the complex process of amorphous material crystallization usually occurs in several more or less distinguishable steps. They can consist of nucleation and crystal growth controlled either by short-range diffusion or by interfacial chemical reactions, and the slowest step is rate-determining. So, the experimental results were discussed on the basis of the classical JMAYK (Johnson-MehlAvrami-Yerofeev-Kolmogorov) nucleation-growth equation, and the kinetic parameters were determined. They were interpreted according to Sest~ik's treatment [235], and it was found that the a-Sb crystallization process occurred through instantaneous bulk nucleation and subsequent three-dimensional growth controlled by diffusion. The three-dimensional growth of the nuclei was directly verified by SEM observation and indirectly by X-ray determination of the crystallite size. The activation energy for Sb diffusion in a-Sb during crystallization was about 25.1 kJ mo1-1. It is worth noting that this value is smaller, but not far from that determined in the same temperature range for In diffusion in a-Sb with formation of crystalline InSb: 53 kJ mo1-1 [90]. The mechanism of the process is in agreement with current ideas that in so-called amorphous materials small clusters of the crystalline phase are often dispersed that are not detectable by usual X-ray analysis and may act as nucleation centers. 11. CONCLUSIONS In this review chapter, we examined the general advantages and disadvantages of the electrochemical deposition process used to obtain the different III-V semiconductors, focusing on principles, methods, and results. We examined in detail the particular electrodeposition conditions, discussing the goal already

313

reached, what remains open, and the future expectations of the researchers in the field. Another point that was stressed concerns the diffusion and reaction process mainly occurring in the solid state during the formation of III-V compounds. The mechanism of the process was investigated, as was the influence of the structure and morphology of the substrate on this same process. The short introduction (Section 1) lists the main aspects of the electrochemical methodology used to prepare III-V compounds, comparing them with those relevant to the physical and chemical processes more frequently used. Section 2 analyzes the typical properties of III-V semiconductors that make them so unique and of interest for practical applications. They include, for example, the ionic character of their bonds, the Gibbs free energy of formation from the elements, the band gap, the melting point, and the lattice constant. The formation of multinary compounds, truly nanomodulated thin films, microdiode arrays, and quantum dots (of increasing interest) is also briefly stressed. Generally speaking, the electrodeposition of III-V semiconducting thin films involves three consecutive stages, which have to be carefully controlled. The first stage involves the formation of stable precursor ions in solution(s) or melt to be submitted to the desired redox reactions. The second concerns the simultaneous or consecutive discharge of the compound components at the cathode. The last stage is the generation of a homogeneous thin film with the desired stoichiometry, structure, morphology and with a low defectivity, which may eventually be obtained by a final thermal treatment. Although the deposition parameters may "easily" be optimized in the case of a single element deposition, the situation becomes more complicated when two or more chemical species have to be codeposited. Krrger [29] developed the theoretical basis for simultaneous deposition, the standard deposition methodology, and his theory is presented in Section 4. A deposition potential is usually chosen that optimizes the stoichiometry of the deposit. In general, it is such that one of the elements (the more noble one) is deposited at a rate controlled by mass transfer toward the cathode surface, while the other element (which is present in excess) reacts with it to form the compound. Another essential aspect of codeposition is the thermodynamic stability of the compound to be electrodeposited in the electrolyte. This stability was discussed in the case of aqueous electrolytes by several authors with the aid of the classical potential-pH plots due to Pourbaix [49]. These equilibrium diagrams also make it possible to determine the parasitic reactions that may join the main processs, typically hydrogen evolution and/or arsine or stibine formation (Section 5). An argument that deserved a separate analysis is codeposition from molten salts, particularly the high-temperature ones, because the operative conditions needed to achieve deposits of some quality are severe. So, an important aspect is the stability against arbitrary perturbations of the growing depositelectrolyte interface, which was investigated by Huggins and Elwell [79], as reported in Section 6.

314

PERALDO BICELLI AND KOZLOV

Research on the sequential electrodeposition method of III-V compound semiconductors started in the earlier 1990s. Although less straightforward than codeposition, it presents several advantages, because it does not require a compromise between diverging requirements, because each element may be deposited under appropriate conditions. So, for example, it is insensitive to large differences in the deposition potentials of the two elements; on the other hand, the choice of the deposition sequence is often problematic. Moreover, this method requires a final thermal treatment to favor interdiffusion and chemical reaction (Section 7). Section 8 surveys the electrochemical formation of thin films of the different III-V compounds, giving problems and strategies and critically analyzing the state of the art of the subject. Research on GaP dates back to the work by Cuomo and Gambino [ 110] and by De Mattei et al. [ 111 ], in 1968 and 1978, respectively. Epitaxial layers were electrodeposited at about 800-1000~ from a highly corrosive metaphosphate melt containing Ga203 on single-crystal cathodes. InP, too, was codeposited from a bath containing P as a metaphosphate, but more difficulties were encountered, and no epitaxial growth could be observed [ 112]. Codeposition from an aqueous electrolyte containing InC13 and NH4PF6 was tried by Sahu [47, 48], but with unsatisfactory results. A method that seems to work better is the heat treatment of electrodeposited In films with gaseous P [45] or PH3 vapors [134]. The pioneering research by Ortega and Herrero [45] has recently been deepened by Cattarin et al. [134], who prepared both p- and n-type polycrystalline InP films. However, these films presented cathodic and anodic dark currents, respectively, attributed to processes that occurred on metallic areas, presumably of the bare Ti substrate, owing to the irregular surface and poor morphology of the InP film. This morphology was a consequence of the formation of In globules during the phosphorization treatment performed at a temperature (between 400~ and 600~ much higher than the In melting temperature. Because of the considerable interest in GaAs films with controlled properties, several authors studied their electrodeposition from molten salts as well as from aqueous solutions. Ten-micrometer-thick epitaxial films were obtained by De Mattei et al. in 1978 [113] on GaAs single-crystal electrodes by electrodeposition at 720-760~ from molten NaF and B203, a highly reactive bath also containing Ga203 and NaAsO2. Of growing importance in more recent times is a series of lowtemperature melts (40~ or even 20~ formed by an organic chloride salt and either A1C13 or GaC13, from which Wicelinsky and Gale in 1986 [114] and Carpenter and Verbrugge in 1990 [109], respectively, codeposited GaAs. Although the resuits were encouraging, the stoichiometry and morphology of the deposits were still unsatisfactory. However, the potential of these melts must not be underestimated. A systematic investigation of GaAs codeposition from aqueous baths was first reported by Chandra and Khare [51 ] in 1987, but the films obtained were multiphase. Moreover, these resuits could not be duplicated by Yang et al. [70]. On the basis of his thermodynamic calculations, Perrault [53] found a large

potential-pH compatibility domain existing between GaAs and Ga(III) and As(Ill) ionic species in aqueous solutions. Nevertheless, GaAs was not obtained from acid or alkaline and neutral solutions. Yang et al. [70] again reported the problems encountered in codepositing GaAs films of practical interest from aqueous baths. Indeed, the deposits obtained from alkaline solutions were thick, powdery, and scarcely adherent to the substrate, whereas those from acid solutions were thinner, more compact, but not uniform in composition. Both types of deposits were microcrystalline and yielded crystalline GaAs, with some loss of As content, after annealing. Thin GaAs films approximating the stoichiometric composition were codeposited by Gao et al. [175] from acid solutions. The photoelectrochemical response of the electrodeposited films in contact with a redox electrolyte was poor because of their nonuniform composition and porosity as well as the presence of impurities and defects. Not much better results were obtained by preparing GaAs following the consecutive deposition method, and additional difficulties had to be faced in determining the deposition sequence, which presented minor drawbacks. In 1995, Andreoli et al. [179], following this method, deposited As on Ga predeposited on a Ti substrate, which practically did not alloy with Ga. After the two-layer samples were annealed, GaAs films were obtained that more homogeneously covered the substrate than did those prepared by Yang et al. [70], although they presented Ga-rich and As-rich areas. The reverse sequence (i.e., As first and Ga second) was not practicable, because As was reduced to AsH3 during Ga electrodeposition [ 168]. In 1990, Sticking and co-workers [20] developed a typical sequential method, called electrochemical atomic layer epitaxy, and, in 1992 [21, 100], prepared nanometer-thick GaAs films of high purity as well as high structural and morphological perfection. They were obtained by alternately depositing layers of As and Ga on single-crystal Au electrodes, while strictly controlling the electrolyte composition and electrodeposition conditions. The same technique was followed by previous authors [ 101 ] and by Foresti et al. [ 104] to prepare InAs. In the latter case, single-crystal Ag substrates were used for their lower cost, although they are more reactive than the Au ones. In 1989, Ortega and Herrero [45] first achieved InAs thin films by codeposition from citric acid solutions containing the chlorides of both In and As. The as-electrodeposited samples were amorphous and presented low crystallinity, even after annealing. They showed a p-type conductivity. InAs was later (1992) also obtained by Mengoli et al. [168] by In plating of electrodeposited As and submitting the samples to a subsequent thermal treatment. No overall composition changes occurred; the X-ray diffraction spectra practically matched the standard spectrum of polycrystalline InAs with respect to peak positions and related intensities. The average grain size was in the range of 40050 nm. So, none of the expected difficulties were encountered with As, because of its low electrical conductivity and volatility.

BINARY III-V COMPOUNDS Mengoli and co-workers [83] also succeeded in preparing GaSb by electrodepositing Ga on Sb at not too negative potentials to avoid Sb degradation to SbH3. However, it was not easy to control the thickness of the Ga layer because of the simultaneous hydrogen evolution. After a mild heat treatment, the deposits were chemically homogeneous on their surface and perpendicular to it. More recently (1996), McChesney et al. [52] attempted to grow GaSb following the codeposition method, but the control of stoichiometry was limited by the concurrent evolution of H2 and SbH3. Much research was carried out on InSb formation. In 1985, Sadana and Singh [44] systematically studied the achievement of In-Sb alloys from acid citrate baths of several compositions and recognized the InSb phase in the electrodeposits both before and after annealing. Subsequently, Ortega and Herrero [45] investigated In and Sb codeposition from citric acid solutions, mainly examining InSb formation as a function of the deposition potential and determining the conditions needed to obtain deposits free from the In and Sb phases. This research was practically duplicated by McChesney et al. [52], but the formation of stoichiometric InSb could not be repeated. In 1991, InSb was prepared according to the sequential method of depositing Sb as the first element. The efficiency of conversion of the two-layer film to InSb was investigated as a function of the annealing conditions [84]. The binary compound was obtained when annealing was carried out at temperatures slightly higher than the In melting point, whereas pure InSb was achieved when the heat treatment was performed at 185~ for 5 h. In 1994, a novel low-temperature molten salt electrolyte was reported by Carpenter and Verbrugge [ 116] that consisted of InC13 and an organic chloride from which codeposition of In and Sb was possible at 45~ after the addition of SbC13. Electrochemical experiments showed that the chemical process leading to InSb deposit formation from this chloroindate melt is quite complex. In the authors' opinion, it is likely that improved-quality deposits containing a large fraction of InSb are attainable through an optimized electrochemical control and after low-temperature (350~ annealing. Moreover, in a patent [205], the same authors also referred to the existence of organochloroindate melts comprising a salt of at least one group V element (P, As, Sb), which, in principle, could be used as electrolytes for the electrodeposition of almost any III-V compound after the replacement of a small amount of InC13 with a trichloride salt of another group III metal. The above sections show the importance of the diffusion and reaction process in obtaining III-V compounds, and in the last two sections of the chapter, these arguments are discussed in more detail. So, the diffusion and reaction process of In into Bi [85-87] was compared with that of In into Sb [89] (Section 9). A diffusion coefficient five orders of magnitude higher was observed in the former case, and it was related to the different structural types of the two binary compounds: InBi has a typically layered structure favorable to diffusion, and InSb has a zinc-blende structure with tetrahedrically coordinated atoms and practically covalent bonds.

315

In Section 10, a more subtle difference is considered in comparing the In diffusion and reaction process into either crystalline or amorphous Sb [90]. In this case, too, the main role was played by the structure. Indeed, diffusion was easier into amorphous Sb with a more open structure and larger interatomic distances than crystalline Sb, although this latter presented a higher surface area (i.e., an area more favorable to diffusion). So, the structural factor prevailed over the geometrical one. In conclusion, the systematic part of this chapter details the practical difficulties encountered in preparing high-quality thin films of III-V semiconductors following the electrochemical methodology. As a matter of fact, electrodeposition of compound semiconductors is complicated because of the need to maintain stoichiometry. Investigation is still at the level of fundamental research, and even the most recent work often lacks of a comprehensive film characterization that could be achieved with the use of the most advanced techniques, which could be used to systematically control the material quality. Clearly, electrodeposition is a fascinating and promising method for preparing III-V semiconductors as thin films, but considerable development is required before it can be established whether such a technique has a place in future technology, as in the case of II-VI compounds. Perhaps the immense potential of electrosynthesis science and technology for the production of advanced semiconducting materials and structures has scarcely been explored, and the numerous application possibilities uniquely suitable for electrosynthesized thin films have not yet been fully examined. As for the near future, the results of this survey leave us under the impression that the electrodeposition of III-V thin films can hardly compete with its vacuum counterpart, but that it can play a role in yielding advanced products with highly specific properties, such as superlattices, well-ordered atomic layer epitaxial films, and microdiode arrays.

Acknowledgments V. M. Kozlov gratefully acknowledges the Cariplo Foundation, "A. Volta" Center for Scientific Culture, for financial support. L. Peraldo Bicelli thanks Prof. M. L. Foresti (University of Florence, Italy) for fruitful discussions regarding electrochemical atomic layer epitaxy.

REFERENCES 1. A. Stein, S. W. Keller, and T. E. Mallouk, Science 259, 1558 (1993). 2. W. E. Buhro, K. M. Hickman, and T. J. Trentler, Adv. Mater 8, 685 (1996). 3. B.M. Basol and E. S. Tseng, Appl. Phys. Lett. 48, 946 (1986). 4. T. Ernst, in "Landolt-Boernstein. Zahlenwerte und Funktionen" (K. H. Hellwege, Ed.), Vol. 6, Band I, Teil 4, pp. 19 (A-7 type), 24 (B-2 type and B-3 type), 27 (B-10 type). Springer-Vedag, Berlin, 1955. 5. T.B. Massalski, "Binary Alloy Phase Diagrams," Vol. l, pp. 88 (A1-As), 95 (Al-Bi), 145 (A1-P), 161 (Al-Sb), 200 (Ga-As), 206 (In-As), 231 (T1-As), 501 (Ga-Bi), 509 (In-Bi), 547 (T1-Bi); Vol. 2, pp. 1149 (GAP), 1157 (Ga-Sb), 1386 (In-P), 1391 (In-Sb), 1831 (TIP), 2023 (T1-Sb). American Society for Metals, Metals Park, OH, 1986-1987.

316

PERALDO BICELLI AND KOZLOV

6. JCPDS, Powder diffraction file, No. 12-470, 1972 (ALP); 17-915, 1974 (AlAs); 6-0233, 1967 (A1Sb); 32-397, 1990 (GAP); 32-389, 1990 (GaAs); 7-215, 1967 (GaSb); 32-452, 1990 (InP); 15-869, 1972 (InAs); 6-0208, 1967 (InSb); 32-113, 1990 (InBi); 23-850, 1983 (InsBi3); 11-566, 1972 (In2Bi); 31-106, 1990 (TI7Sb2); 14-5, 1972 (T1Bi2); 5-0642, 1974 (In); 35-732, 1990 (Sb); 5-0519, 1974 (Bi). 7. C. A. Coulson, "Valence," 2nd ed., p. 139. Oxford Univ. Press, Oxford, 1961. 8. D. D. Wagman, V. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, and R. L. Nuttall, J. Phys. Chem. Ref Data 11, 2-130 (ALP,AlAs), 2-132 (GAP, GaAs, GaSb), 2-134 (InP, InAs, InSb) (1982). 9. P.Y. Chevalier, Calphad 12, 383 (1988). 10. R.K. Pandey, S. N. Sahu, and S. Chandra, "Handbook of Semiconductor Electrodeposition," Vol. 5, p. 261. Dekker, New York, 1996. 11. C.D. Lockhande and S. H. Pawar, Phys. Status Solidi A 111, 17 (1989). 12. C.A. Wert and R. M. Thomson, "Physics of Solid" p. 54. McGraw-Hill, New York, 1970. 13. S. Koritnig, in "Landolt-Boernstein. Zahlenwerte und Funktionen" (K. H. Hellwege, Ed.), Vol. 6, Band I, Teil 4, p. 527. Springer-Verlag, Berlin, 1955. 14. S. Adachi, J. Appl. Phys. 58, R1 (1985). 15. K. Rajeshwar, Adv. Mater. 4, 23 (1992). 16. V. N. Tomashik, Neorg. Mater. 32, 1178 (1996) [Inorg. Mater. (USSR) 32, 1030(1996)]. 17. S.D. Lester and H. G. Strectman, Superlattices Microstruct. 2, 33 (1986). 18. J. Yahalom and O. Zadok, J. Mater. Sci. 22, 499 (1987). 19. V. Krishnan, D. Ham, K. K. Mishra, and K. Rajeshwar, J. Electrochem. Soc. 139, 23 (1992). 20. B.W. Gregory, M. L. Norton, and J. L. Stickney, J. Electroanal. Chem. 293, 85 (1990). 21. I. Villegas and J. L. Stickney, J. Electrochem. Soc. 139, 686 (1992). 22. E Loglio, M. Tugnoli, E Fomi, and M. L. Foresti, in "Giornate dell'Electrochimica Italiana," p. 10. Divisione di Elettrochimica, Societ~ Chimica Italiana, Como, Italy, 1999. 23. J.D. Klein, R. D. Herrick II, D. Palmer, M. J. Sailor, C. J. Brumlik, and C. R. Martin, Chem. Mater. 5, 902 (1993). 24. O. I. Micic, J. R. Sprague, C. J. Curtis, K. M. Jones, J. L. Machol, A. J. Nozik, H. Giessen, B. Fluegel, G. Mobs, and N. Peyghambarian, J. Phys. Chem. 99, 7754 (1995). 25. S. Bandyopadhyay, A. E. Miller, D. E Yue, G. Banerjee, and R. E. Ricker, J. Electrochem. Soc. 142, 3609 (1995). 26. H. Gerischer, in "Physical Chemistry" (H. Eyring, D. Henderson, and W. Jost, Eds.), Vol. 9A, Chap. 5. Academic Press, New York, 1970. 27. G. Mengoli, M. M. Musiani, and E Paolucci, Chim. Ind. 73,477 (1991). 28. A. Brenner, "Electrodeposition of Alloys: Principles and Practice." Academic Press, New York, 1963. 29. F.A. Krt~ger, J. Electrochem. Soc. 125, 2028 (1978). 30. R. Weil, Plating Surf. Finish. 12, 46 (1982). 31. G.F. Fulop and R. M. Taylor, Annu. Rev. Mater. Sci. 15, 197 (1985). 32. D. Pottier and G. Maurin, J. Appl. Electrochem. 19, 361 (1989). 33. I.G. Dioum, J. Vedel, and B. Tremillon, J. Electroanal. Chem. 139, 329 (1982). 34. J.W. Cuthbertson, N. Parkinson, and H. P. Rooksby, J. Electrochem. Soc. 100, 107 (1953). 35. G. Tammann and A. Koch, Z. Anorg. Chem. 133, 179 (1924). 36. E Ducelliz, Bull. Soc. Chim. 7, 606 (1910). 37. R.D. Engelken, J. Electrochem. Soc. 135, 834 (1988). 38. R. D. Engelken and T. P. Van Doren, J. Electrochem. Soc. 132, 2904 (1985). 39. M. Takahashi, K. Uosaki, and H. Kita, J. Electrochem. Soc. 131, 2305 (1984). 40. M. W. Verbrugge and C. W. Tobias, J. Electrochem. Soc. 132, 1298 (1985). 41. R. D. Engelken and T. P. Van Doren, J. Electrochem. Soc. 132, 2910 (1985). 42. R.D. Engelken, J. Electrochem. Soc. 134, 832 (1987).

43. M. Fracastoro-Decker and L. Peraldo Bicelli, Mater. Chem. Phys. 37, 149 (1993). 44. Y.N. Sadana and J. P. Singh, Plating Surf. Finish. 12, 64 (1985). 45. J. Ortega and J. Herrero, J. Electrochem. Soc. 136, 3388 (1989). 46. S. Cattarin, M. M. Musiani, U. Casellato, P. Guerriero, and R. Bertoncello, J. Electroanal. Chem. 380, 209 (1995). 47. S.N. Sahu, J. Mater. Sci. Lett. 8, 533 (1989). 48. S.N. Sahu, Sol. Energy Mater. 20, 349 (1990). 49. M. Pourbaix, "Atlas of Electrochemical Equilibria in Aqueous Solutions," 2nd ed., pp. 504 (P), 516 (As), 524 (Sb), 168 (A1), 428 (Ga), 436 (In), 533 (Bi). NACE, Houston, TX, and CEBELCOR, Brussels, 1974. 50. R.P. Singh, S. L. Singh, and S. Chandra, J. Phys. D: Appl. Phys. 19, 1299 (1986). 51. S. Chandra and N. Khare, Semicond. Sci. Technol. 2, 214 (1987). 52. J.-J. McChesney, J. Haigh, I. M. Dharmadasa, and D. J. Mowthorpe, Opt. Mater. 6, 63 (1996). 53. G.G. Perrault, J. Electrochem. Soc. 136, 2845 (1989). 54. J. O'M. Bockris and K. Uosaki, J. Electrochem. Soc. 124, 1348 (1977). 55. S.-M. Park and M. E. Barber, J. Electroanal. Chem. 99, 67 (1979). 56. H. Gerischer, J. Electroanal. Chem. 82, 133 (1977). 57. A.J. Bard and M. S. Wrighton, J. Electrochem. Soc. 124, 1706 (1977). 58. R.L. Meek and N. E. Schumber, J. Electrochem. Soc. 119, 1148 (1972). 59. A. Yamamoto and S. Yano, J. Electrochem. Soc. 122, 260 (1975). 60. M. Tomkiewicz and J. M. Woodall, Science 196, 990 (1977). 61. A.B. Ellis, S. W. Kaiser, J. M. Bolts, and M. S. Wrighton, J. Am. Chem. Soc. 99, 2839 (1977). 62. D. Cahen and Y. Mirovsky, J. Phys. Chem. 89, 2818 (1985). 63. L. Peraldo Bicelli, J. Phys. Chem. 96, 9995 (1992). 64. R. Piontelli and G. Serravalle, Electrochim. Metal. 1,149 (1966). 65. A.N. Campbell, Can. J. Chem. 55, 1710 (1977). 66. I.A. Menzies and L. W. Owen, Electrochim. Acta 11,251 (1966). 67. J. Scarminio, S. N. Sahu, and F. Decker, J. Phys. E: Sci. Instrum. 22, 755 (1989). 68. S. Chandra and S. N. Sahu, J. Phys. D: Appl. Phys. 17, 2115 (1984). 69. M.P.R. Panicker, M. Knaster, and E A. Krrger, J. Electrochem. Soc. 125, 566 (1978). 70. M.-C. Yang, U. Landau, and J. C. Angus, J. Electrochem. Soc. 139, 3480 (1992). 71. D. Elwell, J. Cryst. Growth 52, 741 (1981). 72. G.P. Ivantsov, Dokl. Akad. Nauk SSSR 81, 179 (1951). 73. J.W. Rutter and B. Chalmers, Can. J. Phys. 31, 15 (1953). 74. C. Wagner, J. Electrochem. Soc. 101,225 (1954). 75. W.W. Mullins and R. E Sekerka, J. Appl. Phys. 35,444 (1964). 76. W.A. Tiller, J. Cryst. Growth 2, 69 (1968). 77. H.J. Scheel and D. Elwell, J. Electrochem. Soc. 120, 818 (1973). 78. A.A. Chernov, J. Cryst. Growth 24-25, 11 (1974). 79. R.A. Huggins and D. Elwell, J. Cryst. Growth 37, 159 (1977). 80. R.A. Huggins, J. Electrochem. Soc. 122, 90C (1975). 81. A.R. Despic and K. I. Popov, J. Appl. Electrochem. 1,275 (1971). 82. U. Cohen and R. A. Huggins, J. Electrochem. Soc. 122, 245C (1975). 83. E Paolucci, G. Mengoli, and M. M. Musiani, J. Appl. Electrochem. 20, 868 (1990). 84. G. Mengoli, M. M. Musiani, E Paolucci, and M. Gazzano, J. Appl. Electrochem. 21,863 (1991). 85. S. Canegallo, V. Demeneopoulos, L. Peraldo Bicelli, and G. Serravalle, J. Alloys Comp. 216, 149 (1994). 86. S. Canegallo, V. Demeneopoulos, L. Peraldo Bicelli, and G. Serravalle, J. Alloys Comp. 228, 23 (1995). 87. S. Canegallo, V. Agrigento, C. Moraitou, A. Toussimi, L. Peraldo Bicelli, and G. Serravalle, J. Alloys Comp. 234, 211 (1996). 88. M. C. Hobson, Jr., and H. Leidheiser, Jr., Trans. Metal. Soc. AIME 233, 482 (1965). 89. V. M. Kozlov, V. Agrigento, D. Bontempi, S. Canegallo, C. Moraitou, A. Toussimi, L. Peraldo Bicelli, and G. Serravalle, J. Alloys Comp. 259, 234 (1997). 90. V.M. Kozlov, V. Agrigento, G. Mussati, and L. Peraldo Bicelli, J. Alloys Comp. 288, 255 (1999).

BINARY III-V COMPOUNDS 91. V.M. Kozlov and L. Peraldo Bicelli, J. Alloys Comp. 313, 161 (2000). 92. B.W. Gregory, D. W. Suggs, and J. L. Stickney, J. Electrochem. Soc. 138, 1279 (1991). 93. B.W. Gregory and J. L. Stickney, J. Electroanal. Chem. 300, 543 (1991). 94. S. Bedair, in "Atomic Layer Epitaxy" (S. Bedair, Ed.), p 304. Elsevier, Amsterdam, 1993. 95. A.A. Gewirth and B. K. Niece, Chem. Rev. 97, 1129 (1997). 96. D. M. Kolb, in "Advances in Electrochemistry and Electrochemical Engineering" (H. Gerischer and C. W. Tobias, Eds.), Vol. 11. Wiley, New York, 1978. 97. K. Juttner and W. J. Lorenz, Z. Phys. Chem. N. E 122, 163 (1980). 98. J.L. Stickney, S. D. Rosasco, B. C. Schardt, and A. T. Hubbard, J. Phys. Chem. 88, 251 (1984). 99. C. K. Rhee, B. M. Huang, E. M. Wilmer, S. Thomas, and J. L. Stickney, Mater. Manuf Processes 10, 283 (1995). 100. I. Villegas and J. L. Stickney, J. Vac. Sci. Technol. A 10, 3032 (1992). 101. T.L. Wade, L. C. Ward, C. B. Maddox, U. Happek, and J. L. Stickney, Electrochem. Solid-State Lett. 2, 616 (1999). 102. M. L. Foresti, G. Pezzatini, M. Cavallini, G. Aloisi, M. Innocenti, and R. Guidelli, J. Phys. Chem. B 102, 7413 (1998). 103. G. Pezzatini, S. Caporali, M. Innocenti, and M. L. Foresti, J. Electroanal. Chem. 475, 164 (1999). 104. M. Innocenti, E Forni, E. Bruno, G. Pezzatini, and M. L. Foresti, in "Giornate dell'Elettrochimica Italiana," p. 8. Divisione di Elettrochimica, Socie~ Chimica Italiana, Como, Italy, 1999. 105. M.L. Foresti, private communication. 106. T.G. Carver and H. Leidheiser, Jr., J. Electrochem. Soc. 109, 68 (1962). 107. W.R. Buck III and H. Leidheiser, Jr.,Nature (London) 204, 177 (1964). 108. A.D. Styrkas, V. V. Ostroumov, and G. V. Anan'eva, Zh. Prikl. Khim. 37, 2431 (1964). 109. M. K. Carpenter and M. W. Verbrugge, J. Electrochem. Soc. 137, 123 (1990). 110. J.J. Cuomo and R. J. Gambino, J. Electrochem. Soc. 115, 755 (1968). 111. R.C. De Mattei, D. Elwell, and R. S. Feigelson, J. Cryst. Growth 44, 545 (1978). 112. D. Elwell, R. S. Feigelson, and M. M. Simkins, J. Cryst. Growth 51, 171 (1981). 113. R.C. De Mattei, D. Elwell, and R. S. Feigelson, J. Cryst. Growth 43, 643 (1978). 114. S.P. Wicelinski and R. J. Gale, Proc. Electrochem. Soc. 86-1, 144 (1986). 115. M.W. Verbrugge and M. K. Carpenter, AIChE J. 36, 1097 (1990). 116. M.K. Carpenter and M. W. Verbrugge, J. Mater. Res. 9, 2584 (1994). 117. C. E Smart, German Patent DE 929,103, 1955. 118. C. E Smart, U.S. Patent US 2,755,537, 1956. 119. M. Kumagai, T. Takagahara, and E. Hanamura, Phys. Rev. B: Condens. Matter 37, 898 (1988). 120. M. Nagano, Japan. J. Appl. Phys. 38, 3705 (1999). 121. D.Z.-Y. Ting, Microelectron. J. 30, 985 (1999). 122. C. A. Hoffman, J. R. Meyer, E J. Bartoli, J. R. Waterman, B. V. Shanabrook, B. R. Bennet, and R. J. Wagner, Proc. SPIE 2554, 124 (1995). 123. M.J. Shaw, Phys. Rev. B: Condens. Matter 58, 7834 (1998). 124. S. Chandra, N. Khare, and H. M. Upadhyaya, Bull. Mater Sci. 10, 323 (1988). 125. W. Rudorff and E. J. Kohlmeyer, Z. Metallkl. 45, 608 (1954). 126. A. P. Tomilov and N. E. Chomutov, "Encyclopedia of the Electrochemistry of the Elements," Vol. 3. Dekker, New York, 1975. 127. P.N. Yocom, The preparation of transition-metal phosphides by fused salt electrodes, Ph.D. thesis, Univ. of Michigan, 1958. 128. K.W. B6er, Phys. Status Solidi A 40, 355 (1977). 129. G. A. Bukhalova and I. V. Mardirosova, Russ. J. lnorg. Chem. 11,497 (1966). 130. K.J. Bachmann, E. Buehler, J. L. Shay, and S. Wagner, Appl. Phys. Lett. 29, 121 (1976). 131. S.N. Sahu, J. Mater Sci. Electron. 3, 102 (1992). 132. J. Bielinski and A. Bielinska, Surf. Technol. 24, 219 (1985). 133. X. Rajnarayan and M. N. Mungole, Surf. Technol. 24, 233 (1985).

317

134. S. Cattarin, M. Musiani, U. Casellato, G. Rossetto, G. Razzini, E Decker, and B. Scrosati, J. Electrochem. Soc. 142, 1267 (1995). 135. S.N. Sahu and A. Bourdillon, Phys. Status Solidi A 111, K 179 (1989). 136. R.B. Gore, R. K. Pandey, and S. Kulkarni, J. Appl. Phys. 65, 2693 (1989). 137. J. Herrero and J. Ortega, Sol. Energy Mater 17, 357 (1988). 138. R. Piercy and N. A. Hampson, J. Appl. Electrochem. 5, 1 (1975). 139. P. Zanella, G. Rossetto, N. Brianese, E Ossola, M. Porchia, and J. O. Williams, Chem. Mater. 3, 225 (1991). 140. G. Harbeke, O. Madelung, and U. R6ssler, in "Landolt-Boernstein. Numerical Data and Functional Relationships in Science and Technology" (O. Madelung, Ed.), Vol. 17a, p. 281. Springer-Verlag, Berlin, 1982. 141. S. Chandra, "Photoelectrochemical Solar Cells," Vol. 5, p. 175. Gordon and Breach, New York, 1985. 142. O. Khaselev and J. A. Turner, Science 280, 425 (1998). 143. I. V. Zubeck, R. S. Feigelson, R. A. Huggins, and P. A. Petit, J. Cryst. Growth 34, 85 (1976). 144. I.G. Dioum, J. Vedel, and B. Tremillon, J. Electroanal. Chem. 137, 219 (1982). 145. H.L. Chum, V. R. Koch, L. L. Miller, and R. A. Osteryoung, J. Am. Chem. Soc. 97, 3264 (1975). 146. R.A. Carpio, L. A. King, R. E. Lindstrom, J. C. Nardi, and C. L. Hussey, J. Electrochem. Soc. 126, 1644 (1979). 147. C. L. Hussey, L. A. King, and J. S. Wilkes, J. Electroanal. Chem. 102, 321 (1979). 148. J. S. Wilkes, J. A. Levisky, C. L. Hussey, and M. L. Druelinger, Proc. Electrochem. Soc. 81-9, 245 (1981). 149. S. E Wicelinski and R. J. Gale, Proc. Electrochem. Soc. 87-7, 591 (1987). 150. M. Lipsztajn and R. A. Osteryoung, J. Electrochem. Soc. 130, 1968 (1983). 151. J.S. Wilkes, J. A. Levisky, R. A. Wilson, and C. L. Hussey, Inorg. Chem. 21, 1263 (1982). 152. S.P. Wicelinski, R. J. Gale, and J. S. Wilkes, J. Electrochem. Soc. 134, 262 (1987). 153. S.P. Wicelinski, R. J. Gale, and J. S. Wilkes, Thermochim. Acta 126, 255 (1988). 154. S.P. Wicelinski, R. J. Gale, K. M. Pamidimukkala, and R. A. Laine, AnaL Chem. 60, 2228 (1988). 155. S. E Wicelinski, R. J. Gale, S. D. Williams, and G. Mamantov, Spectrochim. Acta, Part A 45,759 (1989). 156. C. L. Hussey, Adv. Molten Salt Chem. 5, 185 (1983). 157. E K. Lay and M. Skyllas-Kazacos, J. Electroanal. Chem. 248, 431 (1988). 158. M.W. Verbrugge and M. K. Carpenter, U.S. Patent US 4,883,567, 1989. 159. K. R. Murali, V. Subramanian, N. Rangarajan, A. S. Lakshmanan, and S. K. Rangarajan, J. Mater Sci. Mater Electron. 2, 149(1991). 160. M.M. Musiani, E Paolucci, and P. Guerriero, J. Electroanal. Chem. 332, 113 (1992). 161. A. P. Tomilov and N. E. Chomutov, "Encyclopedia of the Electrochemistry of the Elements," Vol. 2, p. 21. Dekker, New York, 1975. 162. G. Wranglen, J. Electrochem. Soc. 108, 1069 (1961). 163. R. Piontelli and G. Poli, J. Electrochem. Soc. 109, 551 (1962). 164. T. E. Dinan, W. E Jon, and H. Y. Cheh, J. Electrochem. Soc. 136, 3284 (1989). 165. L. Astier, R. Michelis-Quiriconi, and M.-L. Astier, French Patent F 2,529,713, 1984. 166. K.R. Murali, M. Jayachandran, and N. Rangarajan, Bull. Electrochem. 3, 261 (1987). 167. S. Chandra and N. Khare, Semicond. Sci. Technol. 2, 220 (1987). 168. G. Mengoli, M. M. Musiani, and E Paolucci, J. Electroanal. Chem. 332, 199 (1992). 169. N. Ibl, Surf. Technol. 10, 81 (1980). 170. T.L. Lam, A. Kaike, I. Ohno, and S. Naruyama, J. Metal. Finish Soc. Jpn. 24, 425 (1983). 171. J. Houlston, Product. Finish. 42, 20 (1989). 172. G. Holmbom and B. E. Jacobson, J. Electrochem. Soc. 135, 2720 (1989). 173. G. Devaraj, K. I. Vasu, and S. K. Seshadri, Bull. Electrochem. 5, 333 (1989).

318

PERALDO BICELLI AND KOZLOV

174. G. Devaraj, G. N. K. Ramesh Bapu, J. Ayyapparaju, and S. Guruviah, Bull. Electrochem. 5,448 (1989). 175. Y. Gao, A. Han, Y. Lin, Y. Zhao, and J. Zhang, J. Appl. Phys. 75, 549 (1994). 176. P. Cowache, D. Lincot, and J. Vedel, J. Electrochem. Soc. 136, 1646 (1989). 177. Y. Gao, A. Han, Y. Lin, Y. Zhao, and J. Zhang, Thin Solid Films 232, 278 (1993). 178. R. Dorin and E. J. Frazer, J. Appl. Electrochem. 18, 134 (1988). 179. P. Andreoli, S. Cattarin, M. Musiani, and E Paolucci, J. Electroanal. Chem. 385, 265 (1995). 180. K. Onabe, Japan. J. Appl. Phys. 21,964 (1982). 181. J. O'M. Bockris and B. E. Conway, Trans. Faraday Soc. 45,989 (1949). 182. J. Herrero and J. Ortega, Sol. Energy Mater. 16, 477 (1987). 183. E. Dalchiele, S. Cattarin, M. Musiani, U. Casellato, P. Guerriero, and G. Rossetto, J. Electroanal. Chem. 418, 83 (1996). 184. J.L. Valdes, G. Cadet, and J. W. Mitchell, J. Electrochem. Soc. 138, 1654 (1991). 185. O. Alvarez-Fregoso, J. G. Mendoza-Alvarez, and O. Zelaya-Angle, J. Appl. Phys. 82, 708 (1997). 186. L. Levy, D. Ingert, N. Fekin, and M. P. Pileni, J. Cryst. Growth 184-185, 377 (1998). 187. T. van Buuren, L. N. Dinh, L. L. Chase, W. J. Siekhaus, and L. J. Terminello, Phys. Rev. Left. 80, 3803 (1998). 188. Sh. Z. Khamundldaanova, G. E Rubinchik, and A. M. Murtazaev, Dokl. Akad. Nauk Uzb. SSR 30, 47 (1973). 189. A.L. Pitman, M. Pourbaix, and N. Zoubov, J. Electrochem. Soc. 104, 594 (1957). 190. R. K. Iyer and S. G. Deshpande, J. AppL Electrochem. 17, 936 (1987). 191. T.B. Belitskaya, V. M. Kochegarov, and Yu. I. Chernov, Elektrokhimiya 6, 215 (1970). 192. E C. Walsh and D. R. Gabe, Surf. Technol. 13, 305 (1981). 193. R. Walker and S. J. Duncan, Metal Finish. 9, 21 (1982), Part 1; 10, 77 (1982), Part 2; 11, 59 (1982), Part 3. 194. V.M. Mogilev and A. I. Falicheva, Zashchita Metallov 10, 192 (1974). 195. L. Domnikov, Metal Finish. 71, 50 (1973). 196. Y.N. Sadana, J. P. Singh, and R. Kumar, Surf. Technol. 24, 319 (1985). 197. T. Okubo and M. Landau, Proc. Electrochem. Soc. 88-2, 547 (1988). 198. V.V. Losev and A. P. Pchelnikov, Electrochim. Acta 18, 589 (1973). 199. G. Gunawardena, D. Pletcher, and A. Razaq, J. Electroanal. Chem. 164, 363 (1984). 200. I.A. Ammar and A. Saad, J. Electroanal. Chem. 34, 159 (1972). 201. L. L. Wikstrom, N. T. Thomas, and K. Nobe, J. Electrochem. Soc. 122, 1201 (1975). 202. M.E. Straumanis and L. Hu, J. Electrochem. Soc. 119, 818 (1972). 203. T. A. Zawodzinski, Jr., and R. A. Osteryoung, Inorg. Chem. 28, 1710 (1989). 204. J.H.R. Clarke and R. E. Hester, J. Chem. Phys. 50, 3106 (1969).

205. M. K. Carpenter and M. W. Verbrugge, U.S. Patent US 5,264,111, 1993. 206. V. M. Kochegarov and V. D. Samuilenkova, Elektrokhimiya 1, 1470 (t965). 207. Y.N. Sadana and Z. Z. Wang, Surf. Technol. 25, 17 (1985). 208. Y.N. Sadana and Z. Z. Wang, Metal Finish. 83, 23 (1985). 209. V.V. Povetldn and T. G. Shibleva, Zashchita Metallov 29, 518 (1993). 210. L. Peraldo Bicelli, C. Romagnani, and G. SerravaUe, Electrochim. Metal. 4, 233 (1969). 211. C. Sunseri and G. Serravalle, Metall. Ital. 7-8, 373 (1976). 212. O. H. Henry and E. L. Badwick, Trans. Metall. Soc. AIME 171, 389 (1947). 213. E.A. Peretti and S. C. Carapella, Trans. Am. Soc. Metall. 41,947 (1949). 214. B.C. Giessen, A. Morris, and N. J. Grant, Trans. MetaIL Soc. AIME 239, 883 (1967). 215. H. Schmalzried, "Solid State Reactions," pp. 53, 95, 124. Academic Press, New York, 1974. 216. R. Boom, P. C. M. Vendel, and F. R. De Boer, Acta Metall. 21,807 (1973). 217. H.P. Singh, M. H. Rao, and S. Misra, Scr. Metall. 6, 621 (1972). 218. H.P. Singh, Scr. Metall. 6, 519 (1972). 219. P. M. Robinson and M. B. Bever, Trans. Metall. Soc. AIME 233, 1908 (1965). 220. V. M. Kozlov, V. Agrigento, D. Bontempi, S. Canegallo, C. Moraitou, A. Toussimi, L. Peraldo Bicelli, and G. Serravalle, unpublished observations. 221. F.H. Eisen and C. Birchenall, Acta Metall. 5,265 (1957). 222. P. Binnie, Acta Crystallogr. 9, 686 (1956). 223. M. Hashimoto and T. Nohara, Thin Solid Films 199, 71 (1991). 224. L. A. Zhukova and O. Yu. Sidorov, Fiz.-Khim. Issled. Metall. Protsessov 13, 53 (1985). 225. H. Krebs, E Schultze-Gebhardt, and R. Thees, Z. Anorg. Chem. 282, 177 (1955). 226. N. E Mott and E. A. Davis, "Electronic Processes in Non-Crystalline Solids" 2nd ed., p. 439. Clarendon, Oxford, 1979. 227. V.M. Kozlov, B. Bozzini, V. Licitra, M. A. Lovera, and L. Peraldo Bicelli, Int. J. Nonequilibrium Processing, in press. 228. J.J. Hauser, Phys. Rev. B: Condens. Matter 9, 2623 (1974). 229. N. Kaiser, H. Mtiller, and Ch. Gloede, Thin Solid Films 85, 293 (1981). 230. M. Hashimoto, H. Sugibuchi, and K. Kambe, Thin Solid Films 98, 197 (1982). 231. N. Kaiser, Thin Solid Films 115, 309 (1984). 232. M. Hashimoto and M. Matui, Appl. Surf. Sci. 33-34, 826 (1988). 233. M. Hashimoto, K. Umezawa, and R. Murayama, Thin Solid Films 188, 95 (1990). 234. P. Jensen, E Melinon, M. Treilleux, A. Hoareau, J. X. Hu, and B. Cabaud, Appl. Phys. Lett. 59, 1421 (1991). 235. J. ~est(tk, in "Kinetic Phase Diagrams Nonequilibrium Phase Transitions" (Z. Chvoj, J. ~est~, and A. T~ska, Eds.), Vol. 10, p. 219. Elsevier, Amsterdam, 1991.

Chapter 6

FUNDAMENTALS FOR THE FORMATION AND STRUCTURE CONTROL OF THIN FILMS: NUCLEATION, GROWTH, SOLID-STATE TRANSFORMATIONS Hideya Kumomi Canon Research Center, 5-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0193, Japan

Frank G. Shi Department of Chemical and Biochemical Engineering and Materials Science, University of California, lrvine, California, USA

Contents 1.

2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Structures and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Structures and Formation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Nucleation, Growth, and Solid-State Transformations . . . . . . . . . . . . . . . . . . . . . . . . 1.4. Scope of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory of Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Thermodynamics of Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Kinetics of Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Observables in Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement of Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Characteristic Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Energy Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control of Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Grain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Size Distribution of Grains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Grain Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

319 319 320 320 320 321 321 323 333 338 338 342 345 347 347 352 352 361 362 369 370

between them. Unless the thin film is freestanding, it touches the other adjacent layer(s) like a substrate, and at least one surface becomes an interface. In addition to these basic components, thin films may include the finer structures. Atoms composing the film and the chemical bonds among them provide the (atomic) nanostructure. The defects in the atomic structure are also the issues. They are vacancies, interstitial atoms, impurities, broken bonds,

1. INTRODUCTION 1.1. Structures and Properties Thin films can be treated as being three-dimensional condensed matter with the dimension in one direction much smaller than the dimensions in the other perpendicular directions. The basic structure consists of the two surfaces and the intermediate bulk

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

319

320

KUMOMI AND SHI

deformed bonds, atomic surface roughness, etc. The chain or group of these defects makes the microstructures. They are voids, stacking faults, spatial fluctuation of the atomic composition, segregation of the impurities, dislocations and twin boundaries in crystalline films, surface undulation, spatial variation of the film thickness, and so on. In the case of polycrystalline thin films, the granular structures should also be considered. They are the variation of crystallographic orientation among the grains, the variation of the grain size, and the grain boundaries where the adjacent grains meet. These structures could be connected closely with the mechanical, chemical, electrical, and optical properties or functions of the thin films, and their spatial uniformity. In other words, the properties or their uniformity of thin films would be limited by their structures. For instance, the point defects and the dislocations in the epitaxial thin films always limit their performance. The surface roughness of polycrystalline Si (poly-Si) thin films used as the gate electrodes of metal oxide silicon transistors inhibits one from decreasing the film thickness down to be comparable to the surface roughness, and hence from reducing the device dimensions. When the poly-Si thin films serve as the active layers of thin film transistors, the electric potential barrier localized at the grain boundaries hinders the carrier transport and reduces the performance of the devices. For piezoelectric polycrystalline thin films, the fluctuation of the normal orientation among the grains attenuates the overall piezoelectric efficiency of the films. Thus it is often necessary to control the structures of thin films for improving their properties, functions, or uniformity. The control of the thin films structures has long been one of the central problems in modern materials science and technology.

1.2. Structures and Formation Process Thin films could be prepared through one or more steps of the processes. Except certain kinds of organic membranes or soap bubbles, thin films need to be formed over the substrates. The preparation and the treatment of the substrates must be the initial step. The subsequent step involves the deposition of materials on the substrates from vapor, liquid, or solution. There are many possibilities that these formation processes provide the origins of the thin films structures. For example, if there is imperfect smoothness at the substrate surface, it directly causes the interfacial roughness or becomes the origin of the defects which could propagate in the deposited film. If the deposition over substrates without any epitaxial relation to the deposited films evolves by island growth of crystallites like Volmer-Weber or Stranski-Krastanov modes, the grain boundaries must be formed where the adjacent islands meet. The as-deposited thin films may be further treated with the postdeposition processes which not only improve the asdeposited structures but also introduce some new structures. For instance, the surface roughness of the as-deposited thin films can be reduced by etching or polishing techniques, while these processes bring some defects into the thin films. Amorphous thin films deposited onto a single crystalline substrate can be

crystallized, layer by layer in solid phase, with energies applied to the films. If there are some impurities like oxides at the interface to the substrate, the dislocations or the stacking faults propagate from the impurities through the crystallized layer. If the substrate is also amorphous, the crystallization evolves with random nucleation of crystallites and their growth in the deposited films. The grain boundaries are formed at the meeting points of the adjacent crystallites. Polycrystalline thin films deposited on an insulating amorphous substrate can be melted and recrystallized by sweeping a stripe heater over the thin films, which is known as zone melting technique. The length of the achieved single crystalline regions along the sweeping direction is limited by thermal stress and undesirable random nucleation of the crystallites. Hence most of the thin films microstructures originate in the formation processes. For the purpose of controlling the structures, it is only one approach, or at least one of the best approaches, to control the formation processes. Motivated by this fact, a number of scientific investigations have been devoted to elucidate the mechanisms in the formation processes of the thin films, and many engineering efforts have been spent to introduce novel techniques to the formation processes.

1.3. Nucleation, Growth, and Solid-State Transformations The elementary process responsible for the thin film formation is the phase transformation of matters. The deposition process starts with the phase transformation of deposited species from vapor or liquid phase in the free space over the substrate to adherent states at the substrate surface. The postdeposition process also involves the phase transformation such as amorphouscrystalline or liquid-crystalline phase transition. The phase transformation is generally initiated by nucleation and growth of clusters of new phases. For example, the dislocations in crystals are formed by the nucleation and growth of the embryo dislocations. Without continuous supply of atomic steps containing kinks, the deposition of epitaxial thin films proceeds layer by layer with the nucleation of two-dimensional clusters and their lateral growth. The deposition of polycrystalline thin films and the crystallization of amorphous thin films on amorphous substrates are just the processes of crystallite nucleation and growth. It is important to understand the nucleation, the growth, and the resultant solid-state transformations for investigating the formation of the thin films.

1.4. Scope of This Chapter In view of the above discussion, this chapter aims at providing the fundamentals for the formation and the structure control of thin films focusing on nucleation and growth processes. The formation of polycrystalline thin films and their granular structures is mainly dealt with as a typical example. Section 2 describes the state-of-the-art theories for nucleation and growth, basic parameters of nucleation and growth, and the theoretical basis for the observables in the nucleation and growth. Section 3 describes the experimental methods for

FUNDAMENTALS OF THIN FILMS

321

measuring the nucleation and growth and their theoretical bases with some examples shown. Section 4 describes the strategies and the methods for controlling the grain size, the size distribution of grains, the location of grains in the formation of polycrystalline thin films by the control of the nucleation and growth by showing some examples. At the end of this introductory section, some of the important or recent reviews on thin films formation [ 1-16] are cited, which might be helpful to those who are interested in the general issues beyond the scope of this chapter.

2. THEORY OF NUCLEATION AND GROWTH Theories of the nucleation and growth consist of both thermodynamic and kinetic parts. The thermodynamic part relates to the potential for the formation of a new phase: it describes the formation free energy of the clusters in the new phase and the size distribution of the cluster population in the equilibrium state. The kinetic part presents the formation rate of a new phase: it describes the growth and shrinkage of clusters, the dynamic evolution of size distribution of the clusters, and the rates of nucleation, growth, and the volume fraction transformed into the new phase. In the followings, the theories of nucleation and growth are reviewed and the theoretical bases for the observables in the nucleation and growth are summarized. It is noticed in this chapter that the terms "particle," "domain," "grain," "cluster," and "crystallite" are used synonymously but in different ways according to the situations.

2.1. Thermodynamics of Nucleation and Growth The thermodynamics study of nucleation and growth dates back to the 19th century [17, 18]. The pioneering efforts in the early 20th century [ 19-24] laid down the firm foundation for our current thermodynamic understanding of nucleation and growth.

Fig. 1. Dependenceof the free energy of a cluster, W(g), on the cluster size, g, and the equilibrium distribution of the cluster size, ne (g).

are often called subcritical or embryo and supercritical clusters, respectively. The value of the maximum, W (g,) -= W,, is called the free-energy barrier to nucleation. Up to the size of go, W(g) is positive and the formation of the cluster is unfavorable. Particularly in the region of g < g,, the derivative, 0 W(g)/Og, is positive, and the subcritical clusters prefer to shrink and dissolve back into the matrix of the mother phase. In the region of g > g,, 0 W(g)/Og is negative, and the supercritical clusters tend to grow thereafter. There is a special region around g,, called the critical region, the nucleation barrier layer, or the nucleation boundary layer, in which the cluster is hardly influenced by the drift field made by the gradient of W(g) and readily diffuses in the size space by a small fluctuation less than one quantum unit. The left and right boundaries of the critical region are derived as the two solutions of

W, - W(g) < kT

2.1.1. Free Energy of Nucleus Nucleation starts with formation of small clusters of the new phase in a matrix of the mother phase. The thermodynamical stability of the cluster is evaluated by the free energy of the cluster, W, which is defined as the difference in the free energy between the cluster and the equivalent in the matrix. Generally, W is a function of the cluster size, g, and has a peak in the size space. As illustrated in Figure 1, W(g) increases from 0 with g, shows a maximum at g = g,, and then decreases monotonically to become negative after g -- go. The size of g, is called the critical size, which can be derived as a solution of

for g, where k denotes Boltzmann constant and T is the absolute temperature. Instead of the exact form of W(g) in Eq. (2.2) for calculating the boundaries, its approximation by the quadratic expansion around g = g,,

1[ 02W(g) ] W(g) "~ W, + -~ Og2 g = g , (g _ g,)2

g=g,

for g,. The g,-sized cluster is called a critical cluster or simply a nucleus. The clusters in the regions of g < g, and g > g,

(2.3)

is frequently used for solving Eq. (2.2). Substituting Eq. (2.3) for W(g) in Eq. (2.2), the boundary sizes are approximated as 1

g = g, 4-6

Og

(2.2)

with 6 =

2kT

02W(g)] -1/2 Og2 g_g,

1 -- ~/-~g

(2.4) where 26 corresponds to the width of the critical region, and Z is called the Zeldovich factor. With 8, Eq. (2.3) can be rewritten

322

KUMOMI AND SHI

as

W(g) "~ W, - kT

( )2

the half width of the critical region is =/2dkT

g - g*

V

Nucleation is the process in which the cluster grows beyond the critical size, g,, crossing the free-energy barrier to nucleation, W,. If g, is as small as 1 or W, _< kT, the nucleation occurs without any other conditions. It is frequent, however, that g, >> 1 and W, >> kT. In such conditions, if there is initially no cluster in the vicinity of the critical region, it seems that the nucleation scarcely occurs within the thermodynamic aspect of nucleation. Practically, there is another driving force to nucleation other than the drift field of W(g), which makes the cluster nucleate in any condition. This issue will be explained in detail later in Section 2.2.1.

g* = J 2 k T d l - d ( d v Alz

1)d(~rx)dA/z -(d+l)

and the size at which W(g) changes its sign is O'K

go = The model expressed by Eq. (2.5) is valid when the nucleating cluster has a single interface to the matrix, such as homogeneous nucleation of isotropic clusters. If the nucleation is heterogeneous, e.g., formation of clusters on a substrate, the clusters have the other interface to the substrate in addition to that to the matrix. For such cases where the cluster has multiple interfaces, Eq. (2.5) should be slightly modified into N

W(g) = - g A l z + Z

2.1.2. Classical Model for the Nucleation Free Energy

criKigl-1/d

(2.7)

i=1

The early developed model for the nucleation free energy is based upon the capillary approximation to clusters, which is today called the classical model. Provided a cluster is formed in a matrix, the cluster consists of the surface (or interface) to the matrix and the body wrapped by the surface. The Gibbs free-energy change by the existence of this cluster, W, can be a sum of contributions from the volume energy and the surface energy as (2.5)

W(g) = - g A g + o K g 1-1/d

where g is the number of monomers such as atoms or molecules in the cluster and represents the size of the cluster, A/z (> 0) is the chemical potential standing for the difference of the free energy per monomer between the phases of the cluster and the matrix, tr denotes the interfacial energy density (i.e., per unit areas) at the interface between the cluster and the matrix, x is the geometrical factor with which Kg 1-1/d becomes the area of the interface between the cluster and the matrix, and d stands for the effective geometrical dimension of the cluster. If the cluster has a compact spherical shape, d = 3 and x = (36zr V?) 1/3 where V1 is the volume that a monomer occupies in the cluster. The plot of W(g) in Figure 1 is drawn based on Eq. (2.5). In the case of the classical model, the g-dependence of W(g) is due to the competition between the volume energy term, - g A / z , and the surface energy term, crKg1-1/d. For W(g) of Eq. (2.5), the critical size is calculated from Eq. (2.1) as d-1 g* =

d

~g AN

d

0 W(g) ~-1 = g Og A N

the gradient of the free energy can be expressed as

8g

=

-- lj

]

the free-energy barrier to nucleation is A/x (~)d(d W,= d-1 g*=

-- 1)d-1 A/z

(2.6)

where N is the number of the kinds of the interfaces, and ~ri and xi are the interfacial energy density and the geometrical factor of the ith interface, respectively. It is noted that the basic features in the size dependence of Eq. (2.7) do not differ from those of Eq. (2.5). 2.1.3. Nonclassical Models for the Nucleation Free Energy

The classical model for the free energy to nucleation has long been used for explaining and investigating phenomena related to nucleation. In fact, the theoretical predictions of the classical model can successfully describe some kinds of nucleation in undercooled liquids and glasses. However, a few discrepancies have been also found between the classical model and experimental results. The classical model have been criticized as well from theoretical points of view, mainly on the applicability of the model to the small clusters. Since the number of monomers composing the surface of the cluster gets close to the total number of monomers in the cluster as the cluster size decreases, the linear decomposition of the free energy into the volume energy term and the surface energy term becomes questionable. In the theoretical prediction using the classical model, the values measured for the bulk materials are often used for the thermodynamic parameters (i.e., A/x and or) in Eqs. (2.5) and (2.7), since it is difficult to measure the values for the small clusters. These values for the small clusters would change from those for the bulk materials. For example, because of the large curvature, the surface bond structures of small spherical clusters must be deformed from those of the fiat surface, and thus the surface or interfacial energy density could be different between the bulk and the small clusters. To improve or transcend the classical model, a number of attempts have been devoted to establishing nonclassical or modem models. One of the typical attempts is to compensate the interfacial energy for the small clusters considering its dependence on the curvature. The other typical attempt is the fieldtheoretical approach to the free-energy barrier to nucleation.

FUNDAMENTALS OF THIN FILMS Other than these, many new models have been still proposed. Since it is out of the scope of this chapter to review all of the modem models, they are not mentioned in any more detail here. The readers are referred to the brilliant reviews [25-35] for more details. It should be noted, however, that many models have not been sufficiently tested by experimental studies, as will be discussed in detail later in Section 3.5.1.

2.1.4. Equilibrium Size Distribution of Clusters If the system is in the equilibrium state, the size distribution of clusters is determined only by the size dependence of the free energy, according to the statistical consideration [36, 37]. Suppose that the monomers in the system are distributed into the clusters with various size. The total number of the monomers, N, is the sum of the monomers composing the clusters, N

N -- Z gn(g)

2.2. Kinetics of Nucleation and Growth

where n(g) is the number of g-sized clusters. Considering all the possible combinations for distributing the monomers into the clusters, the partition function can be written as

Z : A Z I - I I INexp( Eg)]n(g) n(g) g n(g)! --~

(2.9)

where A is a constant and Eg represents the potential energy of g-sized clusters. Since the most probable distribution is the largest term in the sum of Eq. (2.9), this can be derived by seeking the maximum at OZ/On(g) = 0, which is -~-~

(2.10)

where C is a constant. Considering the number of monomers (g = 1) in Eq. (2.10), one obtains

C= n(1) N

the available monomers. For the case of heterogeneous nucleation where something other than monomers provides the nucleation sites, the number of the sites, ns, could be smaller or larger than that of monomers, n (1). Even if ns > n(1), the maximum number of clusters, nmax, which is achieved when all the clusters are monomers, does not exceed n (1), and hence, Eq. (2.12) is valid. If ns < n(1), nmax is equal to ns, and thus, n(1) in Eq. (2.12) should be replaced by ns. The g-dependence of Eq. (2.12) is plotted together in Figure 1 using the classical model for W(g) of Eq. (2.5). As shown in the figure, ne(g) exhibits a minimum at g = g, and diverges infinitely after that, which is never observed experimentally. The equilibrium size distribution of Eq. (2.12) is physically meaningless in the size range far larger than the critical region. However, this is useful in deriving the actual size distribution of clusters around the critical region, as will be described in Section 2.2.

(2.8)

g=l

n(g) = CgN exp

323

exp( e~T)

When the system is in the initial stage of nucleation and growth, the number of clusters, n(g), is much smaller than N, and N n (1). Thus the equilibrium distribution, ne (g), is approximated by

ne(g)--n(1)exp(gE1-Eg) kT

(2.11)

Noting that W(g) is defined as the free energy of g-sized clusters with that of untransformed monomers being set to zero, and if the potential energy of monomers, el, can be approximated by that of the untransformed monomers, Eq. (2.11) can be written as

ne(g)-'n(1)exp[ -W(g) ]kT

(2.12)

The above result is derived for homogeneous nucleation in which all the monomers can play the role of a nucleation site. The nucleation sites, however, are not necessarily equivalent to

The kinetics study of nucleation and growth was initiated also in the early 20th century. Since then, a number of studies have been devoted to establishing and improving the kinetic theory. In the first half of the 20th century, the master difference equation describing the kinetic process was reduced to a continuous partial differential equation by approximating the free energy of clusters in the critical region with some analytical functions [20, 24, 38-41], based upon the Szilard model [42]. The reduced equation is today called the "FarkasBecker-Drring-Zeldovich-Frenkel equation" or simply the "Zeldovich-Frenkel equation." This is a kind of Fokker-Planck equation describing general diffusion processes and was expected to be solved. It had not been easy, however, to obtain a complete form of the analytical solution, and the solution techniques have been investigated for over half a century introducing the further approximations. The first asymptotic form of the analytical solution was given by Zeldovich [24] with a quadratic approximation of the free energy. Similar approaches are adopted by Wakeshima [43], Lifshitz and Slyozov [44], and Feder et al. [45] and lead to simple approximated solutions. Probstein [46], Kantrowitz [47], and Chakraverty [48] got a start on a technique of expanding the solution into a series and reducing the equation into an eigenvalue problem. Collins [49] and Kashchiev [50-53] developed this methodology and obtained a series solution by approximating the critical region with a square potential well. Until recently, Kashchiev's solution had been the most accurate and the most utilized for analyzing experimental data [54-57]. Kelton et al. [58] compared all of the analytical solutions which had been obtained by 1983 and concluded that Kashchiev's result best coincided with their numerical solution of the master equation. On the other hand, Binder and Stauffer [25] indicated that mathematical and physical errors in Kashchiev's approach happened to be canceled out in the final result and thus lead to the conclusion of Kelton et al. Shizgal and Barrett [59] enumerated every problem in Kashchiev's

324

KUMOMI AND SHI

treatment. Shneidman [60] pointed out that the time lag for nucleation Kashchiev obtained counted only the relaxation time for clusters to diffuse across the critical region. Wu [61-63] reported that the coincidence Kelton et al. found between Kashchiev's solution and the numerical results could be observed only within the investigated range of temperature. For the purpose of obtaining more accurate and problem-free solutions, Shneidman [60, 64-67] and Shi et al. [68-73] proposed new methods using a singular perturbation approach based on boundary-layer theory. Demo and Ko~f~ek [74] further introduced a method which is based upon the boundary-layer theory combined with the Green function technique. These methods provide the analytical solutions with the fewest approximations and hypotheses at present. About that time when Farkas-Becker-Drring-ZeldovichFrenkel equation was established, the "Kramers-Moyal expansion" [75, 76] was introduced to another approximation of the master equation. A set of equations obtained by this expansion without relying on the Szilard model is called the "Kramers-Moyal equation" which is equivalent to the master equation except for continuity. Matkowsky et al. [77] derived an asymptotic solution of this equation considering dynamical aspects of Markov process. Shizgal and Barrett [59] reduced the Kramers-Moyal equation to a kind of Fokker-Planck equation and further to an equivalent Schrrdinger equation to which one could apply various methods developed in quantum physics for obtaining an approximated solution. Gitterman et al. [78-82] approximated the free energy in the critical region with the quadratic potential well of a harmonic oscillator and solved the corresponding Schrrdinger eigen value problem. Demeio and Shizgal [83] applied the Wentzel-KramersBrillouin (WKB) approximation to the Schrrdinger equation. Trinkaus and Yoo [84] did not adopt the Schrrdinger equation but directly solved the Fokker-Planck equation using the Green function method. However, these solutions provide very complicated expressions and have not been tested sufficiently by experiments. Recently, Shi proposed a new approximation of the master equation [85] by replacing the Kramers-Moyal expansion with a mesoscopic description of inhomogeneous and nonequilibrium Markov process [86, 87]. The obtained equation is valid for all cluster sizes much greater than 1, while Farkas-BeckerDrring-Zeldovich-Frenkel equation is valid only within the critical region. The equation can be analytically solved by the singular perturbation method based on the boundary-layer theory, yielding an analytical expression for the size distribution of clusters for both in the critical regions and beyond [88, 89]. In the following, the fundamental concept of the kinetic approach, the master equation, the approximated equation, and the solution will be described in detail. 2.2.1. Basic Concept: Diffusion Field in the Size

Space

The essence of the kinetic approach to nucleation and growth is to consider the rate of transition between the different cluster sizes and the size distribution of clusters. The transition rate is

Fig. 2.

Illustration for showing the transition among the clusters at the sizes

of g l, g2, and g3.

defined as F(gi ] g j) which is the probability of changing the cluster size from gj to gi per unit time. The size distribution of clusters is described by the number concentration of clusters as a function of their size, f ( g ) , namely, the number of g-sized clusters per unit volume. Suppose that there are clusters at three different sizes, g l < g2 < g3, and they grow or shrink to one of these sizes as illustrated in Figure 2. The change of the concentration of gz-sized clusters, f (g2), during a unit time should be a sum of four kinds of contributions, 0f(g2) = r(g2 I g l ) f ( g l ) - r(g~ I g2)f(g2) Ot - F(g3 I g2)f(g2) + F(g2 I g3)f(g3)

(2.13)

As will be explicitly described later, the size dependence of the transition rate is determined by the driving force from the drift field. In the subcritical region of nucleation, 1-'(gj ] gi) < I'(gi [ g j) for gi < g j, while the sign of the first inequality reverses in the supercritical region. Let us consider here that the clusters at the three sizes are all in the subcritical region; i.e., gl < g2 < g3 < g. - 3. If the size distribution of the clusters, f (g), is uniform or monotonically increasing so that f ( g l ) < f(g2) < f(g3), the sign of Eq. (2.13) must be negative. Furthermore, if this is realized for any possible combinations of the three cluster sizes in a successive domain of the subcritical region, the clusters cannot grow on average over the domain. On the other hand, if the size distribution is monotonically decreasing, the sign of Eq. (2.13) could be positive even if the net rate of the transition is backward. Moreover, if the size distribution keeps decreasing throughout a size space with satisfying the condition that Eq. (2.13) is positive for any combination of the three cluster sizes, the size distribution evolves toward the fight and above, as shown in Figure 3b. Therefore, the net growth of the clusters is possible also in the subcritical region. Thus the nucleation and growth of clusters can be considered as a process of diffusion accompanied by drift of clusters in the size space. The diffusion is driven by the diffusion field made by the gradient of the size distribution, while the drift is due to the free-energy barrier to nucleation. As illustrated in Figure 3a, the clusters in the subcritical region diffuse to grow resisting the backward force of the drift, then pass diffusing across the critical region without the drift, and after that, stably grow by both the diffusion and the drift in the supercritical region. The diffusion and drift process is theoretically derived in the following, by the kinetic description of the nucleation and growth.

FUNDAMENTALS OF THIN FILMS

325

K (g, t) is the inflow rate of g-sized clusters introduced into the system from the outside at t, and L(g, t) is the outflow rate of gsized clusters discharged from the system at t. Equation (2.14) is the master equation that describes all of the processes related to nucleation, growth, and coarsening of clusters with any possible transitions between the cluster sizes. Mathematically, the master equation is equivalent to Pauli's equation in quantum statistics [90] or to the description of Markov process for random walk. If the clusters are hardly introduced from or discharged to the outside of the system, K ( g , t) ~ L(g, t) "~ 0 for g > 1. Furthermore, if the system is completely closed, K ( g , t) -L(g, t) -- 0 for all g. In such cases, the gth equation of Eq. (2.14) can be rewritten as a recurrence formula, a f (g, t) = J ( g - 1, t) - J(g, t) at

(2.15)

where N(t)

J(g, t) =_ Z

g

~-~[F(i l j, t ) f ( j , t) - F ( j ]i, t ) f ( i , t)]

i=g+l j:l

Fig. 3. Size dependence of (a) the free energy of a cluster, W(g), and (b) the size distribution of the clusters, f (g).

2.2.2. Master Equation Considering the balance between inflow and outflow of monomers and clusters into and from g-sized clusters like Eq. (2.13), the dynamic evolution of the cluster concentration should be described by N(t)

a f ( 1 , t) = Z[F(1 at

[ g', t ) f ( g ' , t) - F(g' I l, t ) f ( 1 , t)]

g~=l

+K(1, t)-L(1,

t)

N(t)

a f (2, t) at = ~[F(2

] g', t ) f ( g ' , t) - r'(g' I 2, t ) f ( 2 , t)]

g~=l

+ K (2, t) - L(2, t) (2.14)

N(t)

a f (g, t) at

Z[F(g

[g', t ) f ( g ' , t) - l-'(g' I g, t ) f ( g , t)]

g1=l

+ K (g, t) - L(g, t)

af(N,t) at

N(t)

= ~--~ [l-'(N I g', t ) f ( g ' , t) - l-'(g' [ N, t ) f < N , t)] g~=l

+ K (N, t) - L ( N , t)

where f ( g , t) is the number concentration of g-sized clusters at a time of t, N -- N ( t ) is the total number of the monomers distributed to 1- through N-sized clusters at t, F(g I g', t) is the rate of transition from gt-sized clusters to g-sized clusters at t,

(2.16) is the rate for clusters to pass the size of g at t and is called the "flux" of clusters in the size space. As mentioned in Section 2.2.1, clusters are made to drift by the gradient of the free energy in the size space. Since the forward transition (addition) rate should be different from the backward (dissociation) one, variables in the transition rate are not commutative; i.e., F(i [ j) -r F ( j I i). It has been a custom in reaction rate theory to distinguish them as F(i I j)

I

ot(i I i) a~ I, J ,

for i < j for/ > j

(2.17)

Since Eq. (2.14) is a set of difference equations, it cannot be analytically solved. Instead, the numerical solutions have been often attempted to obtain using numerical calculation of computers [9, 25, 58, 59, 82, 91-107]. These numerical results are used for evaluating analytical solutions of continuous equations approximated from the master equation and for directly estimating experimental results. It should be noted, however, the numerical results are also limited by the finite space and time for the computation and are never exactly valid. Moreover, it is impossible with the numerical solutions to quantitatively estimate any parameter of the nucleation and growth from experimental data. The proper analytical solutions are indispensable to the comprehensive study of nucleation and growth, and the proper approximation of the master equation is necessary for obtaining an analytically solvable equation.

2.2.3. Kinetic Description of lnhomogeneous Nonequilibrium Process For proper approximation of the master equation, it is useful to start with general kinetic description of inhomogeneous and nonequilibrium processes. Provided that the variable g can be treated as continuous in the size space, the system is closed, and the transition rate does not explicitly depend on time, Eq. (2.14)

326

KUMOMI AND SHI

is equivalent to the master equation of the Markov process [108-110],

Op(x,t) = f[r(x Ot

I x')p(x',t)- r(x'lx)p(x t)]dx'

[F(x Ix + r)p(x + r, t)

[2 d--(X)

- F(x + r I x)p(x, t)] dr

(2.18)

where x denotes a continuous state variable, p(x, t) is the state probability to be found at x and a time of t, F(x I x ' ) d x ' is the rate of transition from one state x' to the other state x, and r - x ~ - x is the transition length. When the transition rates of a process depend on its state variable, x, whether linearly or nonlinearly, the Markov process must be inhomogeneous, or else it is homogeneous. The process of nucleation and growth is essentially inhomogeneous because the transition rate depends on the cluster size except in its critical region. For reducing Eq. (2.18) into solvable forms, it is necessary to approximate the right hand side, and hence to obtain F (x I x') and 1-"(x ~ I x) for all x'. In the actual process, however, one can only know a small transition,

for the observable transition rate, F(x, dx), where all possible transitions of the elementary processes with any transition length, r, are allowable. The time evolution of p(x, t) at x resuits from all the possible contributions of - ~ < r < c~. It is possible with Eq. (2.20) to describe the kinetics of an inhomogeneous nonequilibrium process whose transition lengths are comparable to or even larger than the inhomogeneity of the system. Considering further the limit of x t ~ x + r with small transition lengths as Ir/xl 1

(2.40a)

f(1, t) = fe(1, t)

for all t

(2.40b)

for g./g --+ 0

(2.40c)

In the following, the solutions are obtained in the critical region first. The solutions beyond the critical region will be shown later in Sections 2.2.7 and 2.2.8. Let us first introduce the scaled concentration of clusters,

(2.38) except for a subtle difference between the terms of 13(g, 1) and fl(g + 1 I g). Equation (2.38) was originally obtained by a simple quadratic approximation of Eq. (2.15) with Eqs. (2.30) and (2.31) and had been most frequently used for investigating nucleation and growth. Fortunately, in most previous studies, the incorrecmess of involving fl(g + 1 I g) used to be compensated by mistaking fl(g, 1) for fl(g + 1 I g) without awareness of their subtle but significant difference. This fact also con-

f(g, 0) = 0

f(g, t) --+ 0 fe(g,t)

(2.37)

Equation (2.36) is quite similar to Farkas-Becker-DrringZeldovich-Frenkel equation,

Ot

1/dgl - - v / d

y(g, t) =-

f(g, t) fer(g,t)

(2.41)

where fer(g, t) ~ fe[g, t - tg(1, g)] -- fl (g, t) exp [ -- W(g)] kT

(2.42)

is the equilibrium number concentration of g-sized clusters at a retroactive time when the cluster whose size is g at t was a

FUNDAMENTALS OF THIN FILMS monomer. Here, 0) f f l ] 'gt - t)g (]1 , ,

fl(g,t)=

for t _< tg(1, g) f o r t > t g ( l g)

(2.43)

is the retroactive concentration of monomers or nucleation sites (hence, fer(X, O) = re(x, 0)), where tg(1, g) -- fl g dg ,, t

(2.44)

is the time for clusters to grow from monomer to g. The deterministic growth rate of the cluster, ~ _= dg/dt, will be defined later by Eq. (2.92). In addition to the transformation by Eq. (2.41), the transformations by scaled variables and parameters, r--

S2

g x------g.

2fl(g., t)

and

e=

8

(2.45)

g.

lead the nucleation limit of the kinetic description given by Eq. (2.36) into

~xx + 3(1 - x

7x

(2.46)

under a condition of Or~at > fer(X,t) at

(2.47)

Eq. (2.46) is reduced to

r

ay(x, t)

x2/3

at

E2 a2y(x, t)

2

ax 2

4- ~x 4- 3(1 - x-l/3

Suppose that the left and right outer solutions, yout(X, s), can be asymptotically expanded to a perturbation series with respect to the power of E, (x)

Yout(X, s) ~ ~

)]

ay(x, t) ax

f0

y(x, t) e x p ( - s t ) dt

y e ( 1 / g . , s ) - 1 yen(1/g., s) = 0 forn > 1 yr (cxz, s) = 0

4, I 22~~

4. 6(1 - x-l~3 ]

X2/3

[y(x, s)s - y(x, 0)] = 0

(2.49)

y(x, s) = 0 for x 2>> 1

(2.53b)

Oyo(x, s) ax ayl (x, s) ax

sr

x -2/3

3 1 - x - 1 / 3 yo(x, s) -- 0 sr x -2/3 3 1-x-l/3yl(x's)=0

(2.54) 2 aYn-2(x, s) ayn (x, s) 4 . 6 ( 1 - x-l/3) ~ aX 2 3x ax ax - 2srx-Z/3yn(x, s) = 0 for n >_ 2

It is found in the detailed analysis by Hoyt and Sunder [ 117] that the perturbation terms of n > 2 are negligible for the solutions of Eq. (2.54) under the boundary conditions of Eq. (2.53). It is apparent that the first order solutions vanish (yl (x, s) = 0) for both the left and the fight outer regions. Therefore, only the leading order solution (n = 0) remains in Eq. (2.52), and we obtain the left and fight outer solutions:

e (x,s)=-1(1--xl/3) Yout

s

sr

1--g,1/3

x exp[sr(x 1/3 -- g,1/3)]

(2.55a) (2.55b)

For convenience to obtain the inner solution, we introduce a variable transformation of Yin(X, s) ~ Fin(X, s) with an inner variable, X _-- (x - 1)e ~ (~ > 0), and transform Eq. (2.48) into E2(1-()(1 -Jr-E~X) 02Fin(X, s)

-ff-s (2.50)

and the boundary conditions described by Eqs. (2.40b) and (2.40c) into

y(1/g., s) = 1Is

(2.53a)

By substituting Eq. (2.52) into Eq. (2.48) and equating the coefficients for the same power of e, one obtains a set of equations:

2 r

for n > 0

r (x, s) = 0 Yout

leads Eq. (2.48) into an ordinary differential equation about x,

2a2y(x's)ax2

(2.52)

The boundary conditions for each coefficient are

(2.48) Then, the Laplace transform of the scaled concentration,

y(x, s) --

Enyn(X, S) as ~ ~ 0 +

n---0

a2yn_2(x, s)

r [ ay(x, t) 7T~.- t) afer(X' t) ] x 2/3 at 4" aert.~,, / at e2 a2y(x, t) [ e2 -1/3)] ay(x' t) = T ---------y-ax +

329

(2.51)

Since the principal term of Eq. (2.48), ay(x, s)/ax, changes its sign at x = 1 in the interval of [ l / g . , c~], there exists a "boundary layer" around x -- 1. Following the boundary layer theory, the size space can be divided into three successive intervals: the left outer region, the inner region, and the right outer region, which correspond to the subcritical, critical, and supercritical regions, respectively. Then Eq. (2.48) can be entirely solved by obtaining the solutions in these regions and by asymptotically matching them.

OX 2

4" 3E -r (1 4" e r X)[1 - (1 4" e r X) -1/3] O r i n ( X , s) ax E2-r a Fin(X, s)

3

ax

- r(1 4. e (X)-l/3sYin(X, s) = 0

(2.56)

and the boundary condition into Y i n ( ~ , s) = 0

(2.57)

Here if E ~ 0 with a variable X being fixed, )~ --+ 1. As well as the outer solutions, the asymptotic expansion of Yin(X, s) gives a perturbation series" oo Fin(X,

s) ~ ~ n=0

Enyn(X, s)

as E ~ 0 +

(2.58)

330

KUMOMI AND SHI

By substituting Eq. (2.58) into Eq. (2.56) and equating the coefficients for the same power of E, one obtains a set of equations:

02 yo(X, s) - 2st(1 + ~X)-I/3yo(X, s) -- 0 OX 2 02yn(X, s) 02yn_l (X, s) +X 8X 2 OX 2 -2sr(l+EX)-l/3yn(X,s)=0 forn>_l

(2.59)

Yin(X, s) -- 1 [A(s)i sr erfc(X) + B(s)i sr erfc(-X)] (2.60) where

is~erfc(X)- ~~,,

(t - X) sr (st)!

e

_t 2

x-+l-

lim

dt

e-t2dt

1[

E/31 /3 exp(1 - g.1/3 ) ]st 1-'(1 + s t )

l+v

-- g,(l+v)/dzF1 (1, 1 + v; 2 + v; g,1/d)] -'- x(l+v)/df~p(X 1/d, 1, 1 + V)

(2.61)

Yin(X , s) -

[g(l+v)/d2F 1(1 1 + v; 2 + v; x l/d)

1

#(g) =_

Yin(X, s)

X---~-cx~ lim

2f0z

y(g, t) -- f (g, t)/fer(g, t). Equations (2.64) are valid also for arbitrary values of d and v, for which Eqs. (2.64d) and (2.64f) are generalized as

lim

X---~+oo

~

is the complementary error function. Three kinds of time constants are considered here. The first is # (g)r which corresponds to the time lag for the concentration of subcritical clusters to approach its steady state. The second is Z r which is the relaxation time for the inner solution, and thus the relaxation time for the cluster concentration in the critical region to establish its steady state. The last is r which stands for the duration for clusters to pass diffusing across the critical region. It is noted in Eqs. (2.64) that the size distribution of clusters f(g, t) is dynamically scaled with fer(g,t) since

is the repeated error function. The coefficients A(s) and B(s) in Eq. (2.60) are determined by asymptotically matching Eq. (2.60) to the outer solutions of Eq. (2.55) as lim Yout(X, t s) -

is the unit step function and erfc(z)- 1

Here again, only the leading order solution can remain. Thus the inner solution satisfying the boundary condition [Eq. (2.57)] is obtained as

2 f?

where |

r

x--~1+ Yout(X,S)

_g,(l+v)/d~(g,1/d, 11, + v)

(2.64g)

which give

A(s) = s 1-g. B(s) = 0

~. -

where F(z) stands for the gamma function. By substituting Eq. (2.62) into Eq. (2.60) and restoring the variables, one obtains

'I

Yin(X, s) -- ~ss 3(1 -- g,1/3) exp(1 -- g,1/3 (2.63)

Finally, considering the initial condition of Eq. (2.40a), the inverse Laplace transform of Eqs. (2.55) and (2.63) gives the outer and inner solutions in real g space, Yoeut(g, t) -- |

- lz(g)r] - |

1

F

Yout(g, t) -- 0

1

f(g, t) -- ~fer(g, t)[~/(g, t, r) - r/(g, 0, r)]

(2.64c)

(2.65a)

with I-

r/(g,

r) - erfc] g - g*

t

'

(2.64b)

L

8

For future convenience, the size distribution without regarding the depletion of monomers and nucleation sites is defined here

as

with /z(g) - -

_

where 2 F1 (a, b; r z) denotes the hypergeometric function, and 9 (z, s, a) stands for the Lerch transcendent. Furthermore, even if the free energy of clusters is altered from its capillary approximation, the results obtained are the same as Eqs. (2.64), and only #(g) and Z change. Thus the dynamic scaling is essential to the dynamic evolution of the cluster-size distribution, independent of the actual form of the free energy. With Eq. (2.64h) we obtain the universal form of the size distribution in the critical region,

(2.64a)

Yin(g, t) = ~[r/(g, t, r) - r/(g, 0, r)]

g.1/d) _+_

-

(2.64h)

(2.62)

x 1-'(1 + s r ) i S r e r f c ( x - )1E

ln(1

tg(1, g ) - 1 / 3 1 / 3 = g, - x z

- In

[ 1 -xl/3 ] /3 (2.64d) 1 -- g.1

rl(g, t ' r) _ erfc[ g -8 g, + exp ( ) ~ r - t ) ]

(2.64e)

z"

X = g~g,lim-' # (g) -- g,1/3 - 1 + l n [ ! ( 1 -

1

fo(g, t) = ~ fer(g, O)[r/(g, t, ~0) - r/(g, O, ~o)]

(2.66)

where fer(g, O) -- fe(g, O) and

82 g,1/3)]

(2.64f)

r0 -- 2fl(g., 0)

(2.67)

FUNDAMENTALS OF THIN FILMS

2.2.7. Size Distribution of Clusters in the Supercritical Region Equation (2.64c), Yout(g, t) = 0, gives the fight outer solution of Eq. (2.28), which does not mean that f(g, t) is exactly zero but negligibly smaller than fer(g, t) in the supercritical region. This result does not provide, however, the exact form of f(g, t) and was obtained starting from the nucleation limit of the kinetic description by Eq. (2.46). For obtaining a solution of Eq. (2.28) in the supercritical region, it does not help to introduce y (g, t) - f (g, t)/fer (g, t) unlike the treatment in the critical region, since f(g, t)/fer(g, t) > g, + 8 as qg(g, t) = lim f ( g , t) =

t~

Jss(g,, t) fl(g, t)

(2.80)

Comparing Eq. (2.80) to the infinite time limit of Eq. (2.72), and using Eq. (2.76), the overall cluster concentration for g >> g. + & is finally obtained as

f(g,t) = r

t)

~p(g, t, r) - 7t(g, 0, r) 7t(g, cx~, r) - ~(g, 0, r)

(2.81a)

with qg(g, t) =

Jss (g,, t)

(2.81b)

fl(g, t)

~(g, t, r) z"

tg(g, + 8, g, r) =

g

fg

dgr

(2.81c) (2.81d)

It is noted that Eq. (2.81) is applicable to any forms of W(g) and fl(g, t). Of course, if employing Eq. (2.39) for fl(g, t), one finds that the steady-state distribution, qg(g, t), obeys a powerlaw size dependence, qg(g, t) cx g V/Ct-1

where t (r) is the time when /3 (g,, t) = 82/~', and hence, t(r0) = 0. Since tg(g, + 8, g, r) of Eq. (2.76) monotonously

~

which indicates that the flux of clusters is constant throughout the size region, g < gs. Then the constant flux can be represented by the steady-state flux at the critical size:

=erfc l+exp

dg r ,+8 fl [g~ t ( r ) ]

Provided here that the steady-state distribution has been established up to a certain size, gs >> g, +8, the following relation can be derived from Eqs. (2.28) and (2.29),

(2.75)

As will be shown by Eqs. (2.92) and (2.93) in Section 2.3.2, the rate of cluster growth, ~, can be nearly equal to/3 (g, t) for g >> g,, and hence, the time for clusters to grow, Eq. (2.72d), can be approximated as

(2.78)

J(g, t) = fl(g, t) f (g, t)

as was predicted in Eq. (2.74).

FUNDAMENTALS OF THIN FILMS Similarly to Eqs. (2.66) and (2.73), the size distribution without regarding the depletion of monomers and nucleation sites is defined here as

fo(g, t) = qg(g, 0)

~(g, t, to) - ~(g, O, to) 7t(g, oo, r0) - ~P(g, 0, r0)

(2.82)

2.2.9. Beyond the Early Stages of Nucleation and Growth The theoretical results presented in Sections 2.2.4-2.2.8 are valid under the condition of the one-step transition (Szilard model) expressed by Eq. (2.25). The multistep transition, in other words, coalescence or coagulation of clusters, is not negligible when the concentration of clusters is high and (1) if the clusters are spatially mobile so that the probability of their collision is large, or (2) when the clusters have grown and the average distance between the surfaces of adjacent clusters (i.e., growth front) becomes small so that they readily impinge upon the neighboring clusters by their own further growth. Even though the clusters are not mobile, the coalescence is inevitable in the late stages of phase transformations where the accumulated number concentration of clusters becomes high and the clusters having early nucleated have grown large. Thus the theoretical results are applicable only to the early precoalescence stages of phase transformations driven by nucleation and growth. There is another reason that the applicability is restricted to the early stage. The nucleation sites and/or the monomers should be consumed by nucleating and growing clusters and should be depleted with time unless they are continuously supplied faster than or at least as fast as their consumption. It is found in Eqs. (2.12), (2.64) or (2.65), (2.72) with (2.71), and (2.81) with (2.78) and (2.79) that the size distribution of clusters is proportional to the number concentration of nucleation sites or that of the monomers, fl (g, t). This result originates in deriving Eq. (2.46) under the condition of Or/Ot 0 fs(1, 0) fl (g, t) Of (g, t)

f(g,t)

Ot

(2.83)

Ofl(g, t) >> Ofl(g,t) Ot Ot

~

--

1 Ofl(g,t)] -1 fl(g,t) Ot

size distribution in the critical region as

f (g, t) _ fer(g, t) exp( )~r ) f X+exp(x)

e x p ( - z 2) dX+exp()~-t/r) (Z -- X) r/td dz (2.86) which is readily reduced to Eq. (2.65) for td >> r. For rare cases with td < r, Eq. (2.65) should be replaced by Eq. (2.86) which influences the size distribution in the supercritical region through the boundary condition at g = g. + 6 [corresponding to Eq. (2.70a)]. Consequently, the solutions of the kinetic equations shown in this chapter are applicable to the early stage of nucleation and growth before the complete depletion of nucleation sites or monomers and the occurrence of coalescence become considerable. Except the earliest stage where f (1, t)/f (1, 0) ~ 1, it is necessary to take the depletion of nucleation sites or monomers into account. The dependence of fl (g, t) on g and t is given by

w/~

-~d

fl(g,t) = { 1 - X [ t - t g ( g ) ] } f ( 1 , O)

(2.87)

where X (g, t) is the transformed or clustered volume fraction when g-sized clusters at t were monomers and is generally defined as

X (t) = -~1

gf (g' t) dg

(2.88)

If Eqs. (2.87) and (2.88) are explicitly included into the kinetic equations, Eqs. (2.46) and (2.68) become differential-integral equations of f(g, t) which, unfortunately, have not been completely solved. It is possible, however, to draw a qualitative picture of the cluster-size distributions in the late stages, if the coalescence is still negligible. Since X(t) increases with time approaching 1 and tg(g) increase with g, fl (g, t) of Eq. (2.87) must monotonously increase with g. On the other hand, the scaled size distribution [Eqs. (2.64) and (2.72)] always decreases with g. Therefore, the resultant size distribution could have a plateau or a peak so as to be a lognormal-like distribution in the supercritical region. For the purpose of analyzing the experimental data with the theoretical results for the size distribution, fl (g, t) could be treated as a predetermined quantity, because X (t) can be measured independently.

(2.84)

respectively. The first condition [Eq. (2.83)] is obviously satisfied before complete depletion of monomers, i.e., fs (1, t) = 0. The second condition [Eq. (2.84)] requires that the depletion of nucleation sites or monomers is sufficiently slow and the nucleation is still in the transient period where the steady-state distribution has not been established and hence Of(g, t)/Ot > 0 in the critical region. After the transient period, the effects of the nucleation site and/or monomer depletion have to be considered. Letting the time scale for the depletion be td

333

(2.85)

and if td varies slowly with time, Eq. (2.48) can be solved under the initial and boundary conditions of Eq. (2.40) to obtain the

2.3. Observables in Nucleation and Growth

Although the theoretical expressions for the size distribution of clusters are obtained, they cannot always be applied to experimental observations directly. Experimentally observable quantities are shown in the following with their theoretical basis.

2.3.1. Size Distribution of Clusters The kinetic theory of nucleation and growth provides the size distribution of clusters both in the critical and supercritical regions. Since the size of observable large clusters can be precisely measured, the result far beyond the critical region [Eq. (2.81)] is applicable directly to the data measured. It is usually impossible, however, to compare the result for the critical

334

KUMOMI AND SHI

region with the experimental results. Even with the up-to-date techniques for experimental investigations, the clusters around the critical size are generally too small to observe quantitatively. Furthermore, since clusters which have not exceeded the critical region are not stable, they could be surely detected only by in situ observations, which makes the experimental approach more difficult. Instead of directly using Eq. (2.65), the nucleation rate which is one of the typical observables can be derived from it as described in Section 2.3.3. There is a point which one should pay attention to in the expression of the size distribution. The kinetic theory originally provides the size distribution expressed in the number of monomers composing the clusters, g. When the observed cluster sizes are described by g, one can directly apply f ( g , t) to them. On the other hand, the cluster size is usually measured in a unit of length and is described by a characteristic length, r, such as the radius of spherical clusters and the side length of cubic clusters. The thermodynamic theory of nucleation and growth had been originally described with r. When the size distribution measured in the length unit needs to be treated as is, it is necessary to transform f (g, t) into f (r, t). However, even if r = r(g) is a function of g and the inverse function g = g(r) exists, f ( g ( r ) , t) is not simply equivalent to f(r, t). Instead, the transformation is derived from the conservation of clusters. First, the accumulated number concentration of clusters should be the same whichever expression is adopted,

N(gs, t) --

f (g, t) dg =

f (r, t) dr

dg vg(g, t) = ~ -- dt -- fl(g' t) - ~(g, t) = fl(g,t)

1-exp

0g kT

(2.92)

Equation (2.92) is called the deterministic growth rate which is equivalent to the result of the reaction rate theory [118]. The growth rate, vg(g, t), changes its sign from negative to positive at the critical size. Since ~(g, t)/fl(g, t) ~ 0 as g ~ cx~,

vg(g, t) .~ fl(g, t)

(2.93)

forg >> g, + 3 . The addition rate of monomers into clusters is generally given by Eq. (2.39) in which the jumping frequency of monomers into clusters, w, usually exhibits a temperature dependence of thermal activation processes; i.e., w -- m0 exp -~--~

(2.94)

where w0 is the jumping frequency at Eg = 0 or T --~ e~, and Eg is the activation energy for the growth of clusters. Thus the addition rate of monomers and hence the growth rate are also thermally activated as

vg(g, t) -- fl(g, t) o(. exp - ~ - ~

(2.95)

(2.89) 2.3.3. Nucleation Rate

s

where rs = r(gs). Equation (2.89) is satisfied if

fg+Ag/2 f(g,t)dg dg-Ag/2

is expressed using Eq. (2.34) as

=

fr+Ar/2

dr-Ar/2

f(r,t)dr

(2.90)

is valid for arbitrary g, Ag, r = r(g), and Ar = r(g + Ag/2) r(g - Ag/2). If f (g, t) and f (r, t) are continuous throughout the size range, the limit of Ag, Ar ---> 0 leads Eq. (2.90) to f (g, t) Ag -- f (r, t) Ar. Thus the transformation is

f (r, t) -- f (g(r) t) dg(r) ' dr

(2.91)

It should be noted in Eq. (2.91) that dimensionality of f (r, t) differs from that of f ( g , t). Since g is a dimensionless number and r has a dimension of length [L], the dimension of f (r, t) is smaller than f (g, t) by 1 with respect to [L]. If the size distribution is observed in a space with a Euclidean dimension of De, the dimension is [L -De ] for f ( g , t), and [L -De-1 ] for f(r, t), respectively.

2.3.2. Growth Rate

The growth rate or the growth velocity defined as the change of the size of a cluster per unit time is one of the important parameters that control the nucleation and growth. The net growth rate should be the difference between the forward transition (addition) rate and the backward transition (dissolution) rate, which

The nucleation rate is also one of the essential parameters for nucleation and growth, which is the number of clusters nucleating per unit volume and unit time. If the nucleation is defined as the passage of clusters across the nucleus size, gn, the nucleation rate is just the flux of clusters at g = gn. Thus the definition of the nucleation rate depends on that of the nucleus.

2.3.3.1. Nucleation Rate of Nuclei in the Critical Region Clusters having passed through the critical region are often regarded as the stable clusters. The flux of clusters in the critical region, given by Eq. (2.96), can be rewritten as

0 f(g,t) J (g, t) -- - f l ( g , t) fer(g, t) Og fer(g, t) f (g, t) Ofl (g, t) ] + -fl-~i t) Og .j

(2.96)

Since in the critical region, O In ~ f ( g ' t ) >> 8 In fl (g, t) Og fer(g, t)

Og

for the early stage before the complete depletion of monomers or nucleation sites, the second term of Eq. (2.96) is negligible, and hence

0 f(g,t) J (g, t) = -fl(g, t) fer(g, t) m ~

0g fer(g, t)

(2.97)

FUNDAMENTALS OF THIN FILMS Substituting Eq. (2.65) for J (g, t) in Eq. (2.97), the flux of clusters in the critical region is given by 1

J(g, t) -- ~/~fl(g, t)fer(g, t)[((g, t, r) - ((g, O, r)] (2.98a) with ((g,t r)=,

e x p [ - { g-6 g* + e x p ( ~ r r - t ) }

2]

(2.98b)

which is often called the transient nucleation rate. Equation (2.98) increases from 0 with time and asymptotically approaches 1

Jss(g, t) = ~ f l ( g ,

t) fer(g, t)

335

usually far beyond the critical region. As shown by Eqs. (2.92) and (2.93), fl(g, t)/~(g, t) g, + 3, and hence

A(g, t) = fl(g, t) - or(g, t) ~ fl(g, t)

1

1

O(g, t) -- ~[fl(g, t) + c~(g, t)] ~ 2fl(g, t) Thus from Eq. (2.29), the flux of clusters in the supercritical region is

J(g, t) -- fl(g, t) [ f (g, t)

Of(g, 2l t______~) Og 1

where f (g, t) is given by Eq. (2.72) or (2.81), which, as well as the flux of clusters in the critical region, approaches the steadystate value with time. If Ofl (g, t)/Og .~ O, the steady-state flux for g > g. + 6 is derived from Eq. (2.72) as Jss(g, t) = fl(g, t) fea(g, t)

x {exp[--( g -a g * ) 2] - ((g, 0, r)/]

(2.99) x [{erfc(1) - erfc(1 + e~) } {q~(g)

which is called the steady-state nucleation rate. The flux without regarding the depletion of monomers and nucleation sites, as well as Eqs. (2.66), (2.73), and (2.82), can be also defined as

Jo(g, t) = ~ f l ( g ,

x [((g, t, to) - ((g, 0, to)] Js0(g) = Jss(g, O)

(2.100) (2.101)

While, strictly in terms of thermodynamics, the smallest stable cluster should be the cluster at the right boundary of the critical region, the nucleation rate has been often calculated at the critical size conventionally. With Eqs. (2.98) and (2.99), the nucleation rate at the critical size and its steady-state value are given by

Jss(g., t) - ~r

exp[-e2Z]}

(2.102) t)fer(g., t){1 - exp[-e2Z]} (2.103)

When g. is sufficiently larger than 3, exp[-exp(2)v)] rtr

(2.114)

where rtr is the transient period and usually is taken to be proportional to r. With this approximation, Eq. (2.112) for t > Z'tr can be reduced to

x

L t{fm(t')} l-1/dfl

(g,, t') dt' (2.119)

for t >> ~.r when the monomers and the nucleation sites have been almost depleted. If the depletion of monomers and/or nucleation sites is negligible (i.e., J(g,, t) ~ Jo(g,, t)) in the early stage, Eq. (2.118) can be reduced to

N(g.,t) = Jss(g*' O)r {El[exp(2)~r r- t ) ] -

XJMA(gs, t ) . = 1 - e x p [ - V1Jss(g,, O)

L •

flo(1 + v/d)

flo v (t -- rtr) gs/d + --d-

_ exp(_e2Z ) _2tr} _

(2.120)

gl+V/d]] (2.115)

where E1 (z) =-- f ~ e zt / t dt is the exponential integral. Furthermore, if the depletion of monomers and/or nucleation sites has

FUNDAMENTALS OF THIN FILMS been negligible until t > )~r, N(g., t) of Eq. (2.120) asymptotically approaches a linear dependence on time with a slope of

dN(g,,t) = Jss(g,, 0)[1 - exp(-e2Z)] dt (2.121)

Jss (g,, O)

Otherwise, N(g.,t) approaches the constant [Eq. (2.119)] without showing the asymptotic behavior to the linear dependence on time. Generally, for gs :/: g., N(gs, t) does not possess any simple expression like Eq. (2.120). It is possible, however, to draw a picture of the basic feature for sufficiently large gs. If the steady-state flux has been established at the size of gs (>> g. +3) since a time of rtr(gs), and if the depletion of monomers and/or nucleation sites is still negligible at t (> rtr(gs)), the accumulated number concentration of clusters larger than gs can be approximated to

N(gs, t) .~

Jss(gs, O) dt I + (gs)

Jo(gs, t') dt' d0

= Jss(g,, 0)[t - rtr(gs)] + C

(2.122)

where OC/Ot = 0. Thus N(gs >> g, + 3, t) also approaches the linear dependence on time with the same slope as N(g,, t).

2.3.5.2. Up to the Late Stage If the Johnson-Mehl-Avrami formalism is employed to consider the depletion of monomers and nucleation sites and/or the effect of coalescence, one can obtain an approximated expression for the accumulated number concentration of the cluster, NJMA(g, t) --

fot[1 -- XJMA(g, t')]Jo(g, t')dt'

(2.123)

which is approximately valid up to the late stage where the effect of the coalescence becomes significant. When Eqs. (2.114) and (2.116) are good approximations to Jo(g, t') and tl), the fight hand side of Eq. (2.123) can be analytically integrated into

XJMA(g,

1

tion in their industrial applications, because the grain size often dominates their performance as the materials. The grain size in question is generally the final grain size that is achieved after complete transformation and never changes any more. The transformation is completed when the nucleation and growth stops. In the case of thin films deposited as polycrystalline from vapor or liquid sources, the nucleation of new clusters is terminated only by stopping the supply of species for the clusters, while the clusters cease growing when they impinge upon the adjacent clusters. In the case of thin films formed by the transformation of the starting thin films, the nucleation and growth come to the end when the nucleation sites and the monomers surrounding the clusters are completely depleted, respectively. If the clusters are formed by precipitation of the monomers dispersed in the matrix and are separately located in the completely transformed thin films, the nucleation stops when either of the monomers surrounding the clusters or the nucleation sites is completely depleted, while the growth can last as long as the monomers surrounding the clusters exist. If the thin film is formed by filling up its untranformed region with the clusters, the nucleation ceases at the complete depletion of the nucleation sites, and the growth of each cluster is terminated by their impingement upon the adjacent clusters, but the growth of the last cluster continues until the untransformed region disappears. For any case, the mean of the final grain size, g~, is just the number of monomers available to compose the clusters per the number of the clusters, which is given by dividing the initial concentration of monomers by the finally accumulated number concentration of clusters. Although Eq. (2.118) predicts that the accumulated number concentration becomes constant as t --+ e~, this equation cannot be applied to the present situation where the coalescence of clusters would play a crucial role in controlling the final grain size. Instead, the JohnsonMehl-Avrami formalism shown in Section 2.3.4 can be utilized for estimating the final concentration of clusters [123]. If one adopts the same situation and approximation as those for Eq. (2.124), the mean of the final grain size can be estimated from Eq. (2.124) as gf--

[ 1 0 8 ( J s s ) d ] 1/(l+d)

NJMA(t) = 1 +---d -~1

337

fm(O) limt ~ ~ NjMA(t)

-~0 =

1

fm(O)

( Vl ) 1/(l+d) F(2

I

[ f l O ] d/(l+d)

(1 v1 ,ss,,, o, o ,t ,tr,l+')l -1" l+d' 10--8 (2.124) for t > rtr, where F(a, z) -- f z ta-le-t dt is the incomplete gamma function. NJMA(t) of Eq. (2.124) increases from t = rtr and converges to a constant.

x

Jss(g,,0)

The grain size of granular structures like polycrystalline thin films has been one of the parameters that attract the most atten-

-1

(2.125a)

Here, flo - WXvd{fm (0) } l- 1/d vanishes in

t~o Jss(g., O)

. _ . . .

t~o flogl. -1/d fe(g., 0)/~/-~8 ~/2rr dk T

f(1, o)Aul/d[~d - 1)w,] 2.3.6. Final Grain Size

+d

1~d-l~2 e x p ( W, (2.125b)

Hence, ~ is independent of the growth rate and its components such as the activation energy of growth, Eg. It is remarkable that

338

KUMOMI AND SHI

g~ is determined only by the initial concentration of monomers available to compose the clusters, fm (0), the initial concentration of nucleation sites, f (1, 0), the effective dimension, d, the chemical potential, A/z, the temperature, T, and the free-energy barrier to nucleation, W,.

3. MEASUREMENT OF NUCLEATION AND GROWTH For understanding the formation of thin films or for controlling the microstructures of thin films, it is indispensable to precisely measure the characteristics of the thin films and the physical quantities or the parameters that control the nucleation and growth in the formation of thin films. Among the various parameters, the energy barriers to nucleation and growth are most essential and should be the final destination in the measurement. However, it is necessary and useful to measure preliminary quantities such as sizes and concentrations, not only for attaining the energy barriers, but also for evaluating the thin films. This section provides the fundamentals for measuring these quantities and parameters in the experiments.

3.1. Dimensions

3.1.1. Size and Shape of Clusters The kinetic theory describes the dynamic evolution of nucleation and growth in the size space. The size of clusters must be measured for analyzing experimental data with the theoretical results for the size distribution of clusters. Even when one attempts to measure the nucleation rate, it is of importance to strictly regulate the size of the smallest sampled clusters, since the flux of clusters depends on the cluster size. We cannot avoid paying attention to the cluster size in any cases. As shown in Section 2.2, the size of clusters is originally defined as the number of monomers composing the clusters, g, in the kinetic theory of nucleation and growth. Although high resolution microscopy enables one to directly observe the atomic images of the clusters, it is impossible to precisely count all the monomers included in a cluster unless the clusters are two-dimensional islands with uniformly layered thickness of monomers. Furthermore, it is in practice difficult to count more than hundreds or thousands of monomers in a cluster. Instead, the size of clusters is usually measured in a unit of length and then transformed into the number of monomers. Otherwise, the theoretical results are transformed into those expressed by the cluster size in a unit of length, if possible. For both approaches, the transformation should be given by gV1 = V

(3.1)

where V is the volume of a g-sized cluster measured in the unit of length. Thus we have to measure the volume of clusters for measuring their sizes. For clusters having a single compact shape such as a sphere, a cube, and a crystallographic habit, it is satisfactory to measure a characteristic length of clusters, r, like the diameter or the side length. The volume of the cluster can be calculated by

V = Kr 3 for three-dimensional clusters or V = Kr2/~ for twodimensional ones, where tc denotes the geometrical factor and stands for the film thickness. Otherwise, we have to record all the information about the shape of each cluster besides the characteristic length. This is possible for two-dimensional clusters, while it is not always possible for three-dimensional ones. It is often necessary to regard their variational three-dimensional shapes as an approximate compact one. The sizes and shapes of clusters can be measured by various experimental methods. The Raman spectroscopy can be applied to estimate the averaged size of crystalline clusters in the thin films [ 124, 125], which also involves the other structural information such as strain or stress. This method by itself could not always provide the absolute dimensions of the clusters without relying on the empirical conversion from the Raman spectra to the average size of clusters. X-ray diffraction has been also used for estimating the average size of crystallites at each crystallographic orientation [ 126-130], neglecting the influence from the random stress. This also relies upon the empirical Sherrer's formula [131] which relates the half-width of the crystalline spectra to the average size. Furthermore, since these spectroscopy or diffraction methods consider the crystalline region having perfectly single crystallinity to be a single cluster, the clusters involving imperfectness of crystallinity such as stacking faults and twin boundaries could not be correctly measured. On the other hand, one can measure the absolute dimensions of clusters from the real images of thin films in which the shapes of the clusters are clearly recognizable. The images of thin films can be captured by using various microscopy techniques. For three-dimensional clusters dispersed over the substrates, optical microscopy is available for capturing their plan-view images if they are larger than several micron meters. However, with the optical microscope, we can measure only the outlines of clusters projected onto the image planes, because of its shallow focus depth of field. It is thus necessary to make some approximation to the threedimensional shapes of the clusters by regarding them as hemispheres and so on. For the smaller clusters, scanning electron microscopy (SEM) is suitable for capturing their plan-view and slanted-view images [132-135]. With SEM, the shapes of the clusters can be observed in detail due to the sufficient focus depth of field. It is not easy, however, to quantitatively measure the complete three-dimensional shapes unless their twodimensional images are captured from various directions. For two-dimensional clusters which epitaxially grow over the substrates under high vacuum conditions and have the thickness of atomic steps, the reflection electron microscopy is effective in determining their size and shapes [136]. For two-dimensional clusters which are formed by partial transformation of the starting thin films and thus are embedded in the untransformed matrices at the same thickness, optical microscopy is also available for observing the plan views [57, 137], if the optical indices are sufficiently different between the clusters and the matrices, and if the clusters are larger than several micron meters. Surface tracing microscopy such as scanning tunneling microscopy [138] and atomic force microscopy [139, 140] can

FUNDAMENTALS OF THIN FILMS

339

area of the crystallites with a specific crystallographic orientation from the others and to measure their sizes [123, 145-148, 158], although it is not easy to measure all the crystallites with various orientations. Unless the clusters are periodically placed and uniform in size, the location of the grain boundaries must be random, and their shapes widely varies. Thus it is indispensable to record the shape of each cluster for measuring their sizes. Fig. 6. Plan-view bright-field TEM image of a two-dimensional crystalline Si cluster embedded in amorphous Si thin films with the thickness of 0.1 #m, and the results of the image processing and analysis. The volume of this crystallite is determined to be V = 0.5966 # m 3, and the number of monomers (i.e., S i atoms) is estimated to be g = 2.953 x 1010.

capture the images of the embedded clusters, when the structural or electrical properties of the film surfaces are different between the cluster and the matrices. If the matrices can be removed by etching techniques leaving only the clusters on the substrates, the optical microscope [ 137, 141 ], SEM [ 142, 143], and the above-mentioned surface tracing microscopy are able to capture the embossed shapes of the clusters. For the smaller two-dimensional clusters embedded in the films thinner than micron meters, transmission electron microscopy (TEM) is suitable for measuring their size from the plan-view images [123, 126, 127, 144-163]. With the plan-view images of these two-dimensional clusters, their volume can be precisely determined, regardless of their shapes, by measuring the areas of the clusters and multiplying them by the film thickness. Figure 6 shows the example of measuring the size of a crystalline two-dimensional Si cluster embedded in amorphous Si thin films from its plan-view bright-field TEM image. The planview TEM is also applicable to three-dimensional clusters embedded within thin films, if their diameters are not much smaller than the film thickness. In this case, one can only measure the outlines of the clusters projected onto the film plane, and one needs some assumption to their three-dimensional shapes. For the smaller three-dimensional clusters embedded in thin films, only the cross-sectional-view TEM works. However, in this case, the observable cross-section of the clusters is not always equal to their maximum cross-section, and their sizes would be less estimated than they are. It is generally more difficult to measure the size of clusters which are densely packed and impinge upon the adjacent clusters. When the thin film has a columnar structure composed by the two-dimensional clusters, and the surface of the film is not fiat so that the grain boundaries are seen where the two surfaces of the adjacent clusters meet at a certain contained angle, SEM is able to capture the images of the grain boundaries and hence the shapes of cluster. When the surface of the columnar thin films is flat, but ditches are engraved along the grain boundaries, SEM or surface tracing microscopy are available for capturing the images of the clusters. Otherwise, TEM works if the scattering of the incident electron beam inside the cluster is uniform and different from that at the grain boundaries. If the film is polycrystalline and composed by the randomly oriented crystallites, the dark-field TEM images are able to distinguish the

3.1.2. Effective Dimension of Clusters The kinetic theory of nucleation and growth provides the expressions of the number concentration or the flux of clusters and the other observables derived from them. All of these theoretical expressions include the effective geometrical dimension of clusters, d, through the addition rate of monomers,/3(g, t), if fl(g, t) is given by the general form of Eq. (2.39). Moreover, if the free energy of clusters, W(g), includes a term or a factor relating to the geometry of the clusters like the capillary model described by Eq. (2.5), the theoretical expressions for the observables further include d through W(g). The effective geometrical dimension, or simply the effective dimension d, can be integer and equivalent to the Euclidean dimension of clusters, if the clusters keep a compact shape at any size. Otherwise, d is a noninteger. Furthermore, if the geometry of the cluster is fractal, d should be irrational [164, 165]. Generally in the case of noninteger effective dimensions, the value of d is not a priori given and has to be experimentally determined. If the fractal objects have a self-similar shape, their effective dimension can be and has been often determined using the boxcounting method [ 166, 167]. In this method, the dimension is measured from the slope on the log-log plot of number of boxes needed to cover the entire surface of the object as a function of the size of the boxes. For the precision of the determination, the range of the box size should be as wide as possible. In other words, the image of the object should have much great detail at the boundary. Such an image is obtained only by constructing that of the whole object with a number of the partial images captured at high magnification, since the spatial resolution in imaging systems increases with the magnification in general. This method is thus effective in investigating a small number of similar objects, but it is not always appropriate when the size of the objects is widely distributed and it is unknown whether the same d governs them all. One would often be faced with such a situation when treating the clusters in thin films formed by nucleation and growth. An alternative method [ 168] is proposed for experimentally determining arbitrary d, which is suitable for many clusters with a variety of sizes as shown in the following. 3.1.2.1. Fractal Dimension of the Self-Similar Surface of

Objects Let us first consider the surface area of a g-sized cluster, which is expressed by

S(g) - x g 1-1/a

(3.2)

340

KUMOMI AND SHI

where tc is the geometrical factor. Equation (3.2) suggests that one can determine d from the g-dependence of S(g). Provided here that the surface of the clusters has a self-similar fractal structure, the observed surface area of the clusters, s (r), should be scaling with the cluster size expressed in a unit of length, r, as

s(r) = qr D

(3.3)

where q denotes the undetermined coefficient and D stands for the fractal dimension with respect to the surface area of the cluster. It is noted that s(r) differs from S(g) because s(r) is the surface area observed with a certain finite resolution while S(g) is the actual one. On the other hand, the observed surface area of the self-similar fractal cluster can be scaled also with the resolution of the measurement. Thus the undetermined coefficient q, and hence s(r), also should be a function of the resolution expressed by the characteristic length scale of the measurement, R , as

s(r,R) =q(R)r o

(3.4)

Thus the surface area of a cluster at a size which is equal to the resolution of the measurement (i.e., r = R) becomes lim s(r, R) - s(R, R) = q ( R ) R D

r---~R

(3.5)

Taking the minimum curvature of the observable curved surface to be the resolution, R, the observed surface area of the R-sized cluster should be the actual surface area of the perfect sphere with a radius of R,

s ( R , R ) -- zr(2R) D~-I

(3.6)

where De is the Euclidean dimension of the space the cluster belongs to. Equations (3.5) and (3.6) lead to the coefficient, q, as

q(R) - rr2 De-1R De-D-1

(3.7)

What the above formulation means can be understood by the example of the Koch snowflake shown in Figure 7. Since De = 2 for the Koch snowflake, the surface corresponds to the perimeter. Let us consider first that an r-sized (Fig. 7c) and an r x p-sized (Fig. 7a) Koch snowflakes are observed at the same resolution of R. The observed surface areas of both are related by Eqs. (3.4) and (3.7) as

s(pr, R) = 2zr R 1-o (pr) o = pO2rc R l - O r o = pOs(r, R)

(3.8) If one observes the r-sized Koch snowflake at the higher resolution of R / p (Fig. 7d), the observed surface area is calculated using Eq. (3.8) as

s(r, R / p ) -- 2 z r ( R / p ) l - O r o = lpD(2:rrRl-OrD) P 1

= --s(pr, R) (3.9) P Therefore, the homothetic magnification by p makes the Koch snowflake of Figure 7d fit in that of Figure 7a.

Fig. 7. Relation among the surface area, the size, and the resolution in the measurement of the surface area (i.e., the perimeter) of the self-similar Koch snowflakes. The identical structure (b) is reproduced after the magnification of increase in the size the original (a) by enhancing the resolution to R x by p from (c) to (a) results in the same surface area as that resulting from the identical magnification of (d) which is as large as (c) but observed with the finer resolution of R x 1/p.

1/p. The

Equations (3.4) and (3.7) indicate that, for the self-similar fractals, the increase in size and the enhancement of the resolution are in the one-to-one correspondence, and the observed surface area is scaled with the same fractal dimension, D, to both the size and the resolution. This observation suggests that one can determine the fractal dimension not only by changing the resolution (e.g., the size of boxes in the box-counting method) but also by investigating the size dependence of the surface area.

3.1.2.2. Effective Dimension of the Self-Similar Surface of Clusters The effective dimension, d, in Eq. (3.2) is then derived by relating the observed surface area, s(r, R), to the actual one, S(g). Considering a case of De -" 3 for simplicity, the observed surface area is given by Eqs. (3.4) and (3.7) as

s(r, R) -- s3(r, R) = 4rcrDR 2-D

(3.10)

If the resolution could be made infinitely small, Eq. (3.10) would diverge to infinity, which indicates that s3 (r, R) is never the actual surface area. Reminded that clusters are the condensed matters of monomers, one may take the radius of the monomer to be the resolution limit for a proper estimate of the actual surface area from the observed one. Then let us define the effective radius of g-sized cluster as the radius of a perfect sphere whose volume is equal to that of the cluster by

(3gV1) 1/3 r(g) --

4zr

(3.11)

If the limit of Eq. (3.10) by R --~ r(1) is regarded as the actual surface area, this is given by

S(g) =- S3(r(g)) --

lim sa(r, R)

R--~r(1)

--47rFD(3V1) (2-D)/3 __ = (36zr V 2) 1/3gD/3

(3.12)

FUNDAMENTALS OF THIN FILMS Comparing Eq. (3.12) to Eq. (3.2), we obtain the relation between the effective dimension and the fractal dimension, and the geometrical factor: 3 d = 3- D

x -- x3 -- (36~r V2) 1/3

Similarly to Eq. (3.12), the actual surface area of the flank is given by

S(g) =- S2(r(g)) =

(3.13)

In conclusion, for determining the effective dimension, we only need to measure the surface area of clusters at a fixed resolution as a function of their size and then evaluate d from the index of the power-law dependence using Eqs. (3.10) and (3.13).

341

lim sz(r, R)

R---~r(1)

el -D/2 __ 27rerD-l(_~)

-- 2(yrev1)l/2 g(O-1)/2 Thus the geometrical factor becomes tr ~- K2 = 2 ( T r e V 1 ) 1/2

3.1.2.3. Effective Dimension of Pseudo Two-Dimensional Clusters However, it is not easy to measure the surface area of complicated three-dimensional objects. In reality, the three-dimensional clusters are observed by their two-dimensional images. For instance, the three-dimensional clusters deposited over substrates are usually captured by the plan-view or slanted-view images, and the clusters embedded in matrices are also observed by their cross-section. In the case of crystallization of thin films, the crystalline clusters are essentially restricted within the pseudo two-dimensional space of the starting thin films. Thus, practically, the method for measuring the effective dimension of clusters should treat the pseudo two-dimensional clusters. Let us suppose that the pseudo two-dimensional cluster has a disklike shape with a thickness of ~ and the planar dimensions of r (>> ~), as shown in Figure 8a. One may regard this cluster as a thin foil sliced from the three-dimensional cluster to which the cluster could originally grow without any restriction. If it is possible to measure the surface area of the flank of the cluster, the observed surface area of the flank can be approximately related to that of the imaginary three-dimensional cluster as

s2(r, R) ,~ s3(r, R) • m 2r

(3.14)

Here, r is the effective radius of this disklike cluster when observed from the normal direction to the disk, which is expressed by r(g) --

(gV1) 1/2 -~-

(3.15)

Fig. 8. Illustration of a pseudo two-dimensional cluster having a disklike shape. (a) Slanted view. (b) Plan view from the normal direction.

(3.16)

(3.17)

Even with Eq. (3.16), it is still difficult to measure the surface area of the flank. Instead, it is possible to measure the perimeter of the plan view as shown by Figure 8b. Since the fractal dimension of the perimeter should be D - 1 according to the dimension analysis, the observed perimeter is given by

p(r, R) -- 21rr D-1R 2-D = pog(D-1)/2 = pog 1-3/(2d)

(3.18a)

p o = 2 y r R 2 - D ( V~-~ 1 ) (D-1)/2

(3.18b)

where

The effective dimension can be thus determined from the power-law correlation observed between the perimeter of the pseudo two-dimensional clusters and their size.

3.1.2.4. Example of Determining the Effective Dimension Figures 9 and 10 show an example of determining the effective dimension by measuring the perimeter of pseudo twodimensional clusters. The clusters are Si crystallites formed by the solid-phase crystallization of amorphous Si (a-Si) thin films over SiO2 substrates [ 169]. The a-Si thin films are deposited on the substrates by low-pressure chemical-vapor deposition using Sill4 gas at a temperature of 823 K, under a pressure of 40 Pa, and at a rate of 2.8 x 10 -5/xm S- 1 . The substrates are Crystalline Si wafers coated by amorphous SiO2 films which are formed by thermal oxidation of the wafers. The thickness of the a-Si films is ~ = 0.1/zm. Then, Si + ions accelerated to 70 keV are implanted into the a-Si films at room temperature and at a dose of 1 x 1013 mm -2. The a-Si thin films are crystallized in solid phase by the isothermal annealing at a temperature of 873 K in nitrogen atmosphere for 1.08 x 105 s [ 171 ]. The crystallization is initiated by the continuous nucleation of crystalline clusters at random locations of the thin films, and it is advanced by their epitaxial growth at the interfaces between the crystallites and the amorphous matrix. When the crystallites are smaller than the film thickness (e =0.1/zm, in this example) they may grow three-dimensionally. After their growth front reaches the top surface of the thin film or the bottom interface to the SiO2 substrate, their growth is restricted in the direction of the film plane. Consequently, the crystallites larger than "~0.1 # m become the pseudo two-dimensional clusters, as shown by the schematic slanted view of the partially crystallized film in Figure 9a. In this type of crystallization, the crystallites grow involving the

342

KUMOMI AND SHI twin boundaries which provide the preferential growth points at their surface [172, 173]. The multiple twinning thus makes the shape of the planar crystallites look like dendrites. As shown in the plan-view TEM images of Figure 9b, the dendritic crystallites are formed at random locations with a wide spread of size from submicron to a few micron meters. Figure 10 plots the correlation between the size and the perimeter, which consists of 1095 dendritic crystallites sampled from several tens of the images like that shown in Figure 9b. Each small dot corresponds to a sampled crystallite. The perimeter is measured by the image analysis as shown in Figure 6, but at the resolution of 0.02 • 0.02 # m 2 per pixel. In Figure 10, the plots for the dendritic crystallites exhibit an apparent power-law correlation and definitely differ from the ideal correlation for compact circular objects which is expressed by pc(g) = 2:rr = 2~/7r Vlg/s and plotted by a dotted line together. This fact confirms that the dendritic Si crystallites have a fractal surface. By the fitting of a power-law function to all of the 1095 plots, the perimeter is estimated as p(g) = 1.60 x 10-5g 1-3/(2• Thus the effective dimension is determined to be d = 3.45. With this coefficient and Eq. (3.18b), the actual resolution is estimated to be R ,~ 0.05 #m, which is comparable to but larger than the pixel size of 0.02/zm, and hence consistent. It is additionally noted that the fitted solid line for the dendrites, p(g), and the dotted line for the compact circular objects, pc(g), cross at g ~ 4.35 x 107, because p(g) is measured at the limited resolution of R 0.05 #m, while Pc(g) is the actual perimeter with R = r(1).

Fig. 9. Planar Si crystallites formed by the solid-phase crystallization of a 0.1 /zm thick a-Si thin film over the SiO2 substrate. The schematic slantedview (a) and a plan-view bright-field TEM image of the partially crystallized a-Si thin film, in which dendritic crystallites are embedded at random locations of the amorphous matrix.

Fig. 10. Correlationbetween the size of planar Si crystallites and their perimeter, which is measuredfrom the plan-view TEM images as shown by Figure 9b. The crystallites are formed at 873 K by the solid-phase crystallization of a 0.1 #m thick a-Si thin film over the SiO2 substrate. The correlation consisting of 1095 crystallites exhibits a power-law dependency which apparently differs from that of the compact circular objects represented by the dotted line with Pc(g) = 27rr = 2@rrVlg/e.

3.2. Ratios

3.2.1. Transformed Fraction The transformed fraction has been measured for investigating the formation processes of thin films for a long time. In thin films engineering, the transformed fraction is used for detecting the completion of the transformation of the starting thin films, or the complete coverage of the substrate surface by the deposited thin films. Also, in thin films science, the transformed fraction could be utilized for investigating the thermodynamics and kinetics of the nucleation and growth. There are various experimental methods available for mea' suring or estimating the transformed fraction. If taking examples in polycrystalline thin films formed by solid-phase crystallization of amorphous thin films, a calorimetric technique such as differential scanning calorimetry [ 174, 175] may be applied to detect the complete transformation. The transformed fraction can be otherwise monitored by the X-ray diffraction [ 176, 177], optical reflectivity or transmission [ 178-181 ], electrical resistivity or conductivity [182-187, 189, 190], and, for some cases, luminescence, electron spin resonance, photocurrent measurements, and so on. Although the measured quantities by these methods reflect the transformed fraction, they do not directly provide the actual values of the transformed fraction. In addition to the average size of clusters, Raman spectroscopy is able to estimate the transformed fraction [125, 188, 191,192]. It is also necessary, however, to employ the empirical conversion from the Raman spectra to the transformed fraction. Thus the

FUNDAMENTALS OF THIN FILMS .5

i

,

i

,

i

,

343

5

t-

0.4

.orE

g

0.3

O~

~ E

0.2

E ze2

/

//

4

t-

Q

3

9

'5 ~, 1 E~3

0.1

t

0

0.0

. 0

.

. 5

. 10

0


__ge

(3.23)

if g. < ge, where C -- f l ( g , t ) e x p ( - W . / k t ) / ~ / ~ and the ,, 1-1/d /8)

co >.,

9|

I

'

I

'

I

'

I

'

t

~ 2.17

1.04

X.. X... t~

1.03

co 2.16 >.,

~ 1.o2 e-

2.18

1.06

~* 1.05 . n x_

351

x.,.

t-

1.01

,~ 2.15

I1) (1) i.Ii

m 1.oo

IJ.

1

400

,

,

410

I

420

Annealing Temperature

,

r

430

,

9

440

T (K)

Fig. 18. Temperaturedependence of the free-energybarrier to nucleation, W,, observed in the solid-phase crystallization of 100 nm thick amorphous CoSi2 thin films. The plots of W, are recalculated by the direct method using the absolute values for Vg and Jss (g,) reported in Table I of [228]. The solid line indicates the linear dependence based on the enthalpic and entropic barriers determined by Eq. (3.36).

be H, = 0.240 eV and - TS, = 1.899 • 10 -3 T eV, respectively. The positive value obtained for H, is a manifestation of the small size of the critical clusters. Since the enthalpic barrier is the difference in the enthalpy between the critical cluster and the monomer, it should be described as H, -- hcn (g,) - g, ha, where hcn(g,) represents the enthalpy of g,-sized crystalline critical cluster, and ha is the enthalpy of a monomer in the bulk amorphous phase. It is noted that, under the same conditions of the crystallization, the enthalpy of a bulk crystalline phase, hc, should be less than that of a bulk amorphous phase, ha. Thus the positive H, indicates that there is another positive contribution to hcn (g,) which is most likely due to the interface creation associated with the nucleation. If the crystallization temperature is raised higher, the critical size, g,, increases in general. For such a sufficiently large critical crystallite, the positive contribution may become negligibly small compared to hc, resulting in a negative H,. It is more remarkable here that the entropic barrier, - T S, ~ 0.76--0.82 eV, is significantly larger than the enthalpic barrier, H, = 0.240 eV. In other words, the freeenergy barrier to nucleation comes mainly from the entropic barrier, which corresponds to the difference in the ordering between the crystalline and amorphous CoSi2. Conversely, the relatively small enthalpic barrier indicates that the difference in the bond strength between the two phases is not large. These observations suggest that the nucleation event is essentially a process of topological rearrangement of the disordered amorphous structure into the ordered crystalline one. Figure 19 shows another example of the temperature dependence of W, which is measured in the solid-phase crystallization of a-Si thin films by the direct method using the size distribution of clusters [199] as shown in the analysis of Figure 14. The enthalpic and entropic barriers are determined to be H, = 1.332 eV a n d - T S , = 9.458 x 10-4T eV, respectively. As for the positive value obtained for H,, the same discussion is valid here as that for the solid-phase crystallization of a-CoSi2. However, unlike the result for CoSi2, both

860

870

880

Annealing Temperature

890

900

T (K)

Fig. 19. Temperaturedependence of the free-energybarrier to nucleation, W,, observed in the solid-phase crystallization of a-Si thin films. The results are obtained by the direct method using the size distribution of clusters as shown in the analysis of Figure 14. The plot data of W, originate in the same source used in Figure 6 of [168]. The solid line indicates the linear dependency based on the determined enthalpic and entropic barriers by Eq. (3.36)

the enthalpic barrier (H, = 1.332 eV) and the entropic barrier ( - T S, "~ 0.81--0.85 eV) are significant parts of the freeenergy barrier to nucleation in the a-Si thin films. This observation suggests that the nucleation of crystallites in the a-Si thin films used for this experiment progresses not only by the topological rearrangement of a simply disordered amorphous structure like a continuous random network model, but also with some enthalpic changes accompanied by constructing new atomic bonds from dangling bonds or broken bonds.

3.5.3. Energy Barrier to Growth The energy barrier to growth, Eg, has been central to the study of the growth mechanisms of thin films and the control of the growth rate. Since Eg is just the enthalpic barrier associated with the atomic jump, displacement, or diffusion, its value can be determined simply as the activation energy of the growth rate, Vg, or the frequency of monomer addition per unit area, co', by their Arrhenius plots. Figure 20 shows the Arrhenius plot of the growth rate, Vg, of CoSi2 crystallites grown by the solid-phase crystallization of a-CoSi2 thin films. The data for Vg are collected from Table I of [228] and are the same as those used for calculating W, shown in Figure 18. With this Arrhenius slope, the energy barrier to growth is determined to be Eg = 1.134 eV. Figure 21 shows the Arrhenius plot of the frequency of the monomer addition per unit area, co', observed in the solid-phase crystallization of a-Si thin films. The data for co' are obtained by the analysis of the size distribution of clusters as shown in Figure 14, in which the values of co are determined as one of the optimized fitting parameters. With this Arrhenius slope, the energy barrier to growth is determined to be Eg =3.42 eV, which is close to the estimates by the Arrhenius plots of Vg, for the similar a-Si thin films, e.g., Eg =3.3 eV [123] and 3.14-0.6 eV [159].

352

KUMOMI AND SHI Corresponding Annealing Temperature T 440 25 20

~-

!

430 '

420 9

i

410 9

!

(K) 400

'

'

i

- -

~ 15 E '~ 10 7

~ ~

5 4

$

a

n--

2

e-

i

' 27.0

26.5

27.5

28.0

28.5

29.0

1/kT (eV-1)

Reciprocal Quantum Unit

Fig. 20. Arrhenius plot of the growth rate, Og, of CoSi2 crystallites grown by the solid-phase crystallization of a-CoSi2 thin films. The data for Vg are collected from Table I of [228] and are the same as those used for calculating W, shown in Figure 18. The upper horizontal axis represents the corresponding annealing temperature.

Corresponding Annealing Temperature T 900

890

880

870

(K) 860

t- _,, 8 ._o 7 6
5 x 10 TM cm -2) it is clear that conventional rapid thermal annealing at 11001200~ can activate the dopants but not remove the ion-induced structural damage [14, 15]. At higher annealing temperatures (> 1400~ it is difficult to provide a sufficiently high N2 pressure to prevent dissociation of the GaN surface. Three different approaches have been reported: the first is use of an NH3 ambi-

2. R A N G E S T A T I S T I C S Table I lists experimental and calculated range data for elements implanted into GaN. The first two columns give the element and implantation energy. The next three columns give the depth

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00 375

376 Table I.

PEARTON

nn~

Implantation Images for Dopants and Isolation Species in GaN Experiment

I

'

I

'

I

'

I

'

I

GaN

TRIM 10 6

Energy

Rm

Rp

A Rp

Rp

A Rp

(keV)

(lzm)

(/zm)

(/zm)

(/zm)

(#m)

H

40

0.428

0.428

0.172

0.383

0.089

H

50

0.571

0.517

0.157

0.570

0.137

Li

100

0.408

0.362

0.146

0.491

0.146

Be

100

0.360

0.332

0.130

0.357

0.112

C

260

0.538

0.460

0.185

0.543

0.130

F

100

0.137

0.189

0.110

0.170

0.067

Na

100

0.106

0.089

0.096

0.154

0.065

Mg

100

0.112

0.089

0.066

0.148

0.063

I

Si

150

0.173

0.159

0.173

0.190

0.075

700

Element

S

200

0.170

0.103

0.290

0.199

0.074

Zn

300

0.104

0.13

0.08

0.159

0.063

Ge

500

0.107

0.126

0.077

0.260

0.096

Se

500

0.112

0.125

0.067

0.235

0.085

[:3

105 --O-- Si+ --&-- Mg* --I'-- Unimplanted

Q.

104

,

I

i

O ~O

I

800

,

I

900

,

11O0

Anneal Temperature (~ Fig. 1. Sheet resistivity in Si, Mg, and Mg/P implanted GaN, as a function of annealing temperature. The implant dose was 1014 cm - 2 at an energy of 100 keV in each case. '

'''"1

,

,

, , ''"1

i

100% act of the peak (Rm), the projected range (Rp) or first moment, and the range straggle (ARp) or second moment of the depth distribution. The depth distributions were measured using secondary ion mass spectroscopy (SIMS) as described elsewhere [19, 20]. The values of Rm and ARp were determined by applying a Pearson IV computer fitting routine to the experimentally measured depth profile. The final two columns are the values of range and range straggle determined from TRIM92 calculations [21 ], using the value 6.0 gm/cm 3 for the density of GaN. The agreement between experiment and transport-of-ionsin-matter (TRIM) calculations appears to vary substantially with the mass of the implanted element. For the higher elements, Be and F, the agreement is good. For the lightest element, H, the experimental values are less than the calculated values, the discrepancy increasing with the mass and becoming as large as a factor of two for the range data. We have no explanation for this observation other than some unaccounted affect in the TRIM simulation for projectiles that have a much greater mass than the light N atoms in the GaN. The values of ARp show more random variations of a small magnitude. It has been observed that it is more difficult to sputter craters and measure the resulting crater depths in GaN than in the other III-V semiconductors, so a larger experimental error is suggested as well as the need for more SIMS measurements to confirm or improve these preliminary results.

3. DONOR IMPLANTS (Si, O, S, Se, AND Te) Most of the n-type doping in GaN by implantation has been performed with Si + implants. Figure 1 shows the sheet resistance of initially resistive GaN after Si + or Mg + implantation, as a function of annealing temperature. At temperatures above 1050~ the Si becomes electrically active, producing

I

1000

1016

~Si

i

| 11111

J

~Ar

C'q !

E

o ~,

10 14

d

100% activ

= O o O

=

1012

o o o *-, o o

10 10

/

1 1

r~

10 8

1013

]014

]015

]016

1017

dose (cm -2) Fig. 2. Sheet electron density vs implantation dose of each ion for Si- and M-implanted GaN annealed at 1100~ for 15 s. The top line represents 100% activation of the implanted dose assuming full ionization.

a sharp decrease in resistivity [22]. Variable temperature Hall measurements showed the ionization level to be ~30-60 meV. Subsequently ion channeling, nuclear reaction analysis, and particle-induced X-ray emission measurements showed that almost 100% of the Si goes onto the Ga site at 1100~ [23], creating the shallow donor state. Figure 2 shows the sheet electron concentration in Siimplanted GaN for 1100~ annealing, as a function of implant dose. For the two highest dose Si-implanted samples (5 and 10 x 1015 cm -2) 35% and 50%, respectively, of the implanted Si ions created ionized donors at room temperature. The possibility that implant damage alone was generating the free elec-

ION IMPLANT DOPING trons can be ruled out by comparing the Ar-implanted samples at the same dose with the Si-implanted samples at the same dose which had over a factor of 100 times more free electrons. If the implantation damage was responsible for the carrier generation or for enhanced conduction by a hopping mechanism then the Ar-implanted samples as a result of Ar's heavier mass would have demonstrated at least as high a concentration of free electrons as the Si-implanted sample. Since this is not the case, implant damage cannot be the cause of the enhanced conduction and the implanted Si must be activated as donors. The significant activation of the implanted Si in the high-dose samples and not the lower dose samples is explained by the need for the Si concentration to exceed the background carbon concentration (~ 5 x 1018 cm-3) that was thought to be compensating the lower dose Si samples. For samples implanted with Si at liquid nitrogen temperature to doses below about 3 • 1015 cm -2, the GaN was not amorphous after implantation and exhibited a small decrease in damage with increasing annealing temperature. This behavior is illustrated in Figure 3a, where Rutherford backscattering channeling (RBS-C) spectra are shown for 2 x 1015 cm -2 Siimplanted GaN at liquid nitrogen temperature and annealed at 400, 800, and 1100~ In this case, even at 1100~ RBS-C shows that the damage is not completely removed. For lower Si doses down to 5 x 1013 cm -2, damage removal is more extensive during annealing, but the damage removal is still not completely removed even at 1100~ On the other hand, for Si doses greater than about 5 • 1015 cm -2, annealing up to 1100~ does not result in any appreciable reduction in damage as observed in RBS-C spectra. Figure 3b, which shows the peak damage from such RBS-C spectra as a function of Si dose for as-implanted and 1100~ annealing, illustrates this behavior. Most of the data in Figure 3b refer to liquid nitrogen implants, but the limited data at room temperature, where the initial damage is usually lower, show similar trends. For doses greater than 1016 cm -2 shown in Figure 3b, the RBS-C spectra show that the disorder reaches the 100% level, which indicates the formation of an amorphous layer after implantation. It is interesting to examine the annealing behavior of such layers. Cross sectional transmission electron microscopy (XTEM) micrographs show the as-implanted disorder for a Si dose of 4 • 1016 cm -2 (liquid nitrogen implant) and revealed a thick amorphous layer with a dense, deeper band of extended defects (D) in crystalline GaN. Misfit dislocations (M) thread toward the surface from the underlying GaN. When this high dose sample is annealed at 1100~ the amorphous layer recrystallizes as polycrystalline GaN, with no detectable epitaxial growth. The underlying disorder is observed to coarsen but is otherwise unchanged. Thus the XTEM observations are consistent with the RBS-C data in Figure 3b, where the disorder is only marginally reduced at 1100~ Further comparison of RBS-C data and cross sectional transmission electron microscopy (XTEM) (not shown) indicates the crystallization occurs between 800 and 1100~ Oxygen implantation also creates n-type doping in GaN [24]. Figure 4 shows an Arrhenius plot of the sheet resistivity of

377 m

.,.-

1

1

150 9

i

i

i

(rim)

Depth

--

1 O0 i

i

I

50 '

r

' " I

~

0 '

' ' "

'~' I

20 x

x.X~ X

m

,A

-!

I

I'o

I

.

0

1.0

1.2

1.4

'

10 2

.

b)

' ' l "'"I

'

'

'

1.6

1.8

(MeV)

Energy I ' ' " I

"

'

"

'

I ' ' " I

'

'

'

'

I'

9 ~'0~/~///

r W

a

0U') 101 a

-

/

I

t

/

/ f .=.

A

. . . . . .

A'~ ,,w

'

1013

'

'

I 1 ' " [

10 ~4

I

'

.

I,,,,I

I

.

1015

.

|

i,,..I

10 ~6

|

9

L i a l "1

101"/

DOSE (cm -2) Fig. 3. (a) 2 MeV He + RBS-C spectra illustrating the annealing of 90 keV Si ion damage (2 x 1015 cm -2) in GaN at temperatures of 400~ 10 min (filled circles), 8000~ 10 min (stars), and l l00~ 30 s (filled triangles). The unimplanted (open circles), as-implanted (open triangles), and random (crosses) spectra are also shown. (b) Peak disorder from RBS-C spectra plotted as a function of dose for 90-100 keV Si ions; as-implanted, liquid nitrogen temperature (filled circles) and room temperature (filled triangles) implants; annealed 1100~ (30 s) for liquid nitrogen (open circles) and room temperature (open triangles) implants.

GaN before and after O + implantation and 1100~ annealing. The oxygen creates a shallow donor state with activation energy 29 meV, but there is relatively low efficiency, i.e., < 10% of the implanted oxygen becomes electrically active. Figure 5 shows an Arrhenius plot of S + activation in GaN. The sheet carrier concentration measured at 25~ shows an activation energy of 3.16 eV for the annealing temperature range between 1000 and 1200~ and basically saturates thereafter. The maximum sheet electron density, ~, 7 • 1013 cm -2, corresponds to a peak volume density of "-~5 • 1018 cm -3. This is well below that achieved with Si + implantation and anneal-

378

1013

9

'"

'

I

"

'

'

I

'"

'

'

I

''

"

"

'I

'

'

r

l

'

""

'

1012

Te + ~ GaN

E El

~"

ev C

PEARTON

O

= 335 me V

v

r-

101~

O :~

1 013

t_

v

,,I,=,1

t,-"

o.

1010

o t--o

r

t._

10 9

o~

o,=== t._ L_

a

It

r

10s

2

4

6

8 1000/T

10

12

14

t--. r

(K'~)

Fig. 4. Arrhenius plot of sheet resistivity of GaN before and after O +implantation.

1012

--

0.55

I

I

I

I

0.60

0.65

0.70

0.75

',-, 0.80

v 0.85

0.90

1000/T (K~)

1014

Fig. 6. Arrhenius plot of sheet electron density in Te+-implanted GaN versus annealing temperature.

e _ ~

E

v

O

S+ ~ GaN 5xlO' I cm2

tO

o=.=

L__

t--

o

t-' 0

1013

D

r

L_ t~ L_

ro t'O9

1012 0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

1000/T (K~) Fig. 5. Arrhenius plot of sheet electron density in S + -implanted GaN versus annealing temperature.

ing (> 102o cm -3) [25-28]. In the latter case, the carrier density showed an activation energy of 5.2 eV. The physical origin of this activation energy contains several components--basically it is the energy required to move an implanted ion onto a substitutional lattice site and for it to show electrical activity. This latter requirement means that compensating defects must also

be annealed out. Even though implanted Si + at the same dose showed evidence of site switching and self-compensation, it still produces a higher peak doping level than the nonamphoteric donor S, which is only slightly heavier (32S vs 28Si). From temperature-dependent Hall measurements, we find a S + donor ionization level of 48 4- 10 meV, so that the donors are fully ionized at room temperature. Similar data are shown in Figure 6 for Te + implantation. The activation starts around the same temperature as for S, but much lower sheet electron densities are obtained, the activation energy is significantly lower (1.5 eV), and the carrier concentration does not saturate, even at 1400~ It is likely that because of the much greater atomic weight of 128Te, even higher annealing temperatures would be required to remove all its associated lattice damage, and that the activation characteristics are still being dominated by this defect removal process. Residual lattice damage from the implantation is electrically active in all III-V semiconductors, producing either high resistance behavior (GaAs) or residual n-type conductivity (InP, GaN). The only data available on group VI doping in epitaxial material are from Se-doped MOCVD material, where maximum electron concentrations of 2 x 1018-6 x 1019 cm -3 were achieved [29, 30]. These are also below the values reported for Si doping and suggest that the group VI donors do not have any advantage over Si for creation of n-type layers in GaN. From limited temperaturedependent Hall data, we estimate the Te ionization level to be 50 4- 20 meV. Data for activation of Si + implants in GaN are shown in Figure 7. The activation energy of 5.2 eV is higher than that for the

ION IMPLANT DOPING 1016

379

1016

I

.

.

.

I

.

. . . .

I

'

'

'

I

t

I

,

'

I

. . . .

'

I

,

t

unimplanted lxl015 cm -2 5xl 0 ls c m -2

I

A

E

t,,} c O

' 101s

Ea =

,

.

1015

5.2 eV C,I !

i m

E

L...

c c O

1014

r~

1014 .-

1013

==

O

I,,= ==

t._ I==

r

=,

1013 -

1012 Si in G a N

-2

'

900

1 0 0 k e V 5 x l 0 ~s c m "2

x~

.

1012 0.5

I

0.6

,

,,

I

I,

]

I

1000

t

I

t

1100

1200

annealing temperature

10 s e c a n n e a l

=

,

I

,

0.7

I

0.8

.

,

,

13 00

(~

Fig. 8. Sheet electron concentration for unimplanted and Si-implanted (100 keV) A1GaN (15% A1N) at the doses shown versus annealing temperature.

,

0.9

1000/T ( I l K ) Fig. 7. Arrhenius plot of sheet electron density in S i + - i m p l a n t e d GaN versus annealing temperature.

group VI dopants discussed above, but overall Si is the best choice for creating n-type doping in GaN. A1GaN layers will be employed in heterostructure transistors to realize a two-dimensional electron gas and to increase the transistor breakdown voltage. As discussed in the introduction, implantation can be used to reduce the transistor access resistance of the A1GaN barrier. One would anticipate that the addition of A1 to the GaN matrix will increase the damage threshold as is the case for A1GaAs as compared to GaAs [31 ], but little work has been reported in this area. Recently the first implantation doping studies have been reported for A1GaN [32, 33]. For the work by Zolper et al. [34], the A1GaN layer used for the Si implantation was nominally 1.0/zm thick grown on a c-plane sapphire substrate. The A1 composition was estimated to be 15% based on X-ray and photoluminescence measurements. The as-grown minimum backscattering yield measured by channeling Rutherford backscattering was 2.0% and is comparable to a high quality GaN layer. The A1GaN samples were implanted with Si at room temperature at an energy of 100 keV at one of two doses, 1 or 5 • 1015 cm -2. The higher Si dose has previously been shown not to amorphize GaN and produce an as-implanted channeling yield of 34% in GaN. Samples were characterized by channeling Rutherford backscattering (C-RBS) with a 2 MeV beam with a spot size of 1 mm 2 at an incident angle of 155 ~ Aligned spectra are taken with the beam parallel to the c axis of the GaN film. Random spectra are the average of five off-axis, off-planar orientations.

Electrical characterization was performed using the Hall technique at room temperature. Figure 8 shows the sheet electron concentration versus the annealing temperature for the Si-implanted A1GaN sample. Data for an unimplanted sample is included as a control. First of all it is clear that the unimplanted samples have significant donors produced by the annealing process alone. This may be due to the activation of unintentional impurities, such as Si or O, in the film. O may be a particular suspect due to the tendency of O to incorporate in Al-containing material. At the highest temperature, the high dose Si-implanted sample has four times higher free electron concentration (1.7 • 1015 cm -2) than the unimplanted sample. This corresponds to 34% activation of the implanted Si. Figure 9 shows aligned C-RBS spectra for 15 % A1 in A1GaN either as-grown (unimplanted), after Si implantation at a dose of 1 or 5 x 1015 cm -2, and for the higher dose samples after annealing. As was the case for GaN, the 1 • 1015 cm -2 sample shows limited dechanneling while the higher dose sample shows a marked damage peak. The minimum channeling yield for the high dose sample was 26.67% which is lower than that seen for GaN which showed Xmin between 34% and 38% implanted under the same conditions. This means the addition of 15% aluminum to the GaN matrix increases its damage threshold as is the case for A1 additions to GaAs to form A1GaAs [31 ]. The spectrum for the annealed sample shows limited damage removal, again consistent with that seen for GaN at this temperature [35]. There is evidence, however, of improvement in the near surface as seen by the reduction in the first surface peak. This peak has been suggested to be due to preferential sputtering of nitrogen from the film surface [36]. The reduction of this peak via annealing suggests the surface stoichiometry

380

PEARTON

600

10 7

....

, ........... , . . . .

, ......

, ..

...

500 10 6

4OO

n-to-p

r~

o

300

to

10 s 200

,__

100

--t~ unimplanted ~~Ca: n-type C a + P : n-type

10 4

0 0

100

200

300

400

~

500

channel n u m b e r

10 3

In Figure 1 we had also shown activation data for Mg and Mg/P implanted GaN. The purpose of the co-implant scheme is to enhance occupation of Ga substitutional sites by the group II acceptor Mg. An n-to-p conversion was observed after 1050~ annealing, corresponding to movement of the Mg atom onto substitutional sites. Similar results were observed for Ca and Ca/P implanted GaN [13], as shown in Figure 10. The n-to-p conversion occurred at 1100~ and the p-type material showed an activation energy of ~ 169 meV for the Ca acceptor (Fig. 11). Ion channeling results found that 80% of the Ca was near Ga sites asimplanted, with a displacement of "~0.2/~ from the exact Ga site. Upon annealing at 1100~ the Ca moved onto the substitutional Ga lattice positions [37]. The effects of postimplant annealing temperature on the sheet carrier concentrations in Mg + and C + implanted GaN are shown in Figure 12. There are two important features of the data: first, we did not achieve p-type conductivity with carbon and, second, only ,~ 1% of the Mg produces a hole at 25~ Carbon has been predicted previously to have a strong self-compensation effect [38], and it has been found to produce

,

'

,

'

'

. . . . .~

-'--'"

IOO0

'

9

'

.1__,..

. .

11 O0

1050

I

|

,

,

1150

,

1200

annealing t e m p e r a t u r e (~ Fig. 10. Sheet resistivity in Ca or Ca/P implanted GaN, as a function of annealing temperature. The implant dose was 1014 cm -2 at an energy of 100 keV in each case.

1013

- i ' ' ' l

. . . .

'

!

'

'

'

'

1

'

'

'

"

1

'

'

'

'

1

'

'

'

'

1

'

'

'

'

1

-

'

'

'

"

A

E

0 r 0 ~

..l==,

.4,,,o

c

1012

-

8 4. A C C E P T O R IMPLANTS

|

95O

Fig. 9. Channeling Rutherford backscattering spectra for as-grown, unimplanted, Si-implanted (100 keV, 1 or 5 x 1015 cm -2) and implanted (100 keV, 5 x 1015 cm -2) annealed A1GaN.

is restored during the anneal. Further study is needed to better understand this effect. The redistribution of implanted Si, Mg, and C in Alo.123Gao.88N was studied by Polyakov and co-workers [33]. While Si and C demonstrated no measurable diffusion by SIMS after at 1140~ 1 h anneal, Mg did show appreciable profile broadening and indiffusion under these conditions. Activation of a modest Si dose (5 • 1014 cm -2) was also achieved by annealing at 1140~ with a resulting peak electron concentration of 1.2 x 1018 cm-3. More work is needed on the effect of A1 composition on the implantation properties of A1GaN.

|

Ca: p-type Ca+P: p-type

E

a

%"

=169meV

0

1011 2.8 2.9 . , ,

.

I

,,

,

,

I

3

:

t . ,

I

. . . .

I

.

,

,

,

I

. . . .

|.l

i . ,

I , ,

,_.

3.1 3.2 3.3 3.4 3.5 3.6 IO00/T (K "1)

Fig. 11. in GaN.

Arrhenius plot of activation energy of implanted Ca acceptors

p-type conductivity only in metal-organic molecular beam epitaxy where its incorporation on a N-site is favorable [39]. Based on an ionization level of ~ 170 meV, the hole density in Mgdoped GaN would be calculated to be ~ 10% of the Mg acceptor concentration when measured at 25~ In our case, we see an order of magnitude less holes than predicted. This should be related to the existing n-type carrier background in the material and perhaps to residual lattice damage which is also n-type in GaN. At the highest annealing temperature (1400~ the hole density falls, which could be due to Mg coming out of

ION I M P L A N T D O P I N G 8X1012

E o

6xl

012 /

\ \

E: o

\ \ \ \ \ \

L_

t,(I) o r..

Theoretical evidence suggests that Be may be an effective acceptor in GaN when co-incorporated with oxygen [44]. Be solubility in GaN is predicted to be low, due to the formation of Be3N2, but the co-incorporation might enhance the solubility. There have been some experimental indications of such a result [45], but these have not been verified. Table II summarizes the current level of understanding of m a x i m u m achievable doping levels, ionization energies, and diffusivities for implanted species in GaN.

r-1 /\ / \

/

4x10~2

O L_ ,,m. L_ L_

/

/

/

/

/

/

/

/

\ \ \ rq

(...

2X1012

.

900

a 1000

.

I

.

1100

o

Mg p-type

9

Mg n-type

9

C

I

,

1200

5. D A M A G E R E M O V A L

5 x l 014 c m 2

M g * , C * --+ G a N

i

n-type

I

1300

,

I

,

1400

1500

Annealing Temperature (~ Fig. 12. Sheetcarder densities in Mg+- or C+-implanted GaN as a function of annealing temperature. Table II.

Characteristics of Different Implanted Dopants in GaN Max achievable doping level (cm-3)

Donors Si S Se Te O Acceptors Mg Ca Be C

5x 5x 2x 1x 3x

1020 10TM 1018 10TM 10TM

Diffusivity (cm2 s- 1)

_980~ The sheet resistance for the InN drops steadily over the temperature range, which correlates to the problems of nonstoichiometry in InN. The large size differences between the N and In make the material less stable. The sheet resistance for InGaN and InA1N, on the other hand, increases with annealing. The InA1N sheet resistance increases by a factor of 102 from the value for the as-grown material when annealed at 800~ Its resistance then remains constant to 900~ and then decreases slightly at 1000~ For InGaN the sheet resistance remains constant up to 700~ and then increases rapidly with increasing temperature. This suggests that simple N vacancies are not the cause of the residual n-type conductivity in these samples since at the highest

O~

o 20 Ix: m 15 =E tic: -o 10 N

= E "O Z

InAIN InGaN

--B,

,

5 0 0

200

400

600

800

1000

1200

Anneal Temperature (~ Fig. 20. The rms data normalized to the as-grown roughness as a function of anneal temperature for A1N, GaN, and InN. The initial rms values were 4 nm (A1N), 8.9 nm (GaN), and 16.1 nm (InN).

temperatures we are losing N from the surface, as described below. However, these samples become less conducting, suggesting creation of compensating acceptors or annealing of the native donors is occurring. It is likely, in contrast to the binary nitrides, that the VN have several different energy levels in the temaries because of the differences in strength between In--N and Ga--N bonds. Some of these may be creating a deep acceptor which compensates the shallow donors, or a deep level electron trap, making the material more resistive. There could also be the presence of compensating VGa- or Vin-related defects, which might be easier to form in ternaries because of different sizes and bond strengths of the In and Ga. Finally, it is possible that at least some of the conductivity in the ternaries is due to carbon-related donors [34], and subsequent annealing might produce carbon self-compensation, as in other III-V's. At this point we cannot be more precise regarding the differences between the binaries and the ternaries and this is under close examination. The rms data normalized to the as-grown roughness as a function of anneal temperature are shown in Figure 20 (top)

ION IMPLANT DOPING for A1N, GaN, and InN. The A1N is still smooth at 900~ but becomes quite rough at 1000~ Further surface reconstruction continues at higher annealing temperatures. At 1150~ the sample becomes smooth again--in fact slightly smoother than the as-grown sample. GaN shows no roughening, becoming smoother with annealing due to defect annealing and surface reconstruction. InN, on the other hand, is a factor of 2 rougher than for as-grown samples at 650~ indicating the weaker bond strength of this material. In Figure 20 (bottom) the rms roughnesses for InA1N and InGaN are shown as a function of rapid thermal anneal temperature. We see that the InA1N remained smooth until 800~ and at 900~ has increased an order of magnitude in roughness. At 1000~ the rms roughness returns to a value close to that of the value for the as-grown material. We found this to be a result of In droplets forming on the surface above 800~ and then evaporating above 900~ The InGaN surface was unchanged at 700~ with the roughness increasing above that temperature. In all cases we found that the nitride surface was deficient in nitrogen after high temperature annealing. For uncapped annealing, the III-V nitrides were thermally stable to relatively high temperatures. A1N and GaN remain smooth and stoichiometric at 1000~ InN and InGaN up to 800~ and InN up to 600~ Above these temperatures capping is necessary to prevent the loss of N and, sometimes, In. Consistent with the predicted melting temperatures and thermal stabilities of the nitrides, we found A1N to be somewhat more stable than GaN, and much more stable than InN. InA1N was found to be more stable than InGaN, as expected from a consideration of the binary component N2 vapor pressures. A1N may prove to be a good capping material for the other nitrides, because of its high stability and the fact that it can be selectively removed by wet etching in KOH based solutions.

6.2. Susceptors ~ It would be convenient for GaN device processing if development of a similar process for rapid thermal processing of III nitrides occurred, in which an overpressure of N2 is supplied to a susceptor. In this section we compare use of powdered A1N or InN as materials for use in the susceptor reservoirs and compare the results with those obtained by simple proximity annealing. The GaN, A1N InN, InGaN, and InA1N samples were grown using metal-organic molecular beam epitaxy on semiinsulating, (100) GaAs substrates of A1203 c-plane substrates in an Intevac Gen II system as described previously. The group-III sources were triethylgallium, trimethylamine alane, and trimethylindium, respectively, and the atomic nitrogen was derived from an electron cyclotron resonance Wavemat source operating at 200 W forward power. The layers were single crystal with a high density (1011-1012 cm -a) of stacking faults and microtwins. The GaN and A1N were resistive as-grown, and the InN was highly autodoped n-type (> 102~ cm -3) due to presence of native defects. InA1N and InGaN were found to contain both hexagonal and cubic forms. The In0.75A10.asN and

8o

387

i

GaN InN

9

9 InAIN 9 AIN

=1 o t...

",22o 1,1 o

z

o 600

800

1000

1200

Anneal Temperature (OC) 80

InN powder ~60

40

GaN

9 9

AIN

9

/

2o

0 600

800

1000

1200

Anneal Temperature (~ Fig. 21. Root-mean-square surface roughness of nitrides normalized to the as-grown value, as a function of anneal temperature using either A1N powder (top) or InN powder (bottom) in the susceptor reservoirs.

In0.sGa0.sN were conducting n-type grown (~ 102~ cm -3) due to residual autodoping by native defects. The samples were annealed either (i) face down on samples of the same type, i.e., GaN when annealing GaN, InN for InN, etc., or (ii) within a SiC-coated graphite susceptor in which the reservoirs were filled with either powdered A1N or InN (average particle size ~ 10/zm). Annealing was performed for 10 s at peak temperatures between 650 and 1100~ in flowing Na gas. The sheet resistance was measured at room temperature on a van der Pauw Hall system with 1:1 InHg alloyed contacts (400~ 2 min) on the comers. An atomic force microscope (AFM), operated in tapping mode with Si tips, was used to measure the root-mean-square (rms) roughness of the samples. The surface morphology was examined with a SEM. Energy dispersive X-ray spectroscopy (EDAX) was used to analyze the surface composition of some samples. AES was used to investigate near-surface stoichiometry before and after anneal. A comparison of the annealing temperature dependence of nitride rms surface roughness for sample processed in the graphite susceptor with either A1N or InN powder in the reservoirs is shown in Figure 21. One would expect the InN powder to provide higher vapor pressure of Na at equivalent tem-

388

PEARTON

Fig. 22. Energy dispersive X-ray spectrum of GaN surface after annealing in susceptor containing InN powder in the reservoir.

peratures than A1N [70, 85, 86] and this appears to be evident in the rms data for InN, where the surface roughens dramatically above 600~ with A1N powder while the roughening is less obvious with InN powder. The data in Figure 21 need to be considered in the light of the results from the other materials. For example, the GaN and A1N rms values are consistently higher for the InN powder annealing. These results clearly indicate large-scale (~ 1 #m) roughness evident on the samples annealed with the InN powder. SEM examination of all the samples revealed the cause of this roughening. After 1100~ annealing with A1N powder there is no change in morphology from the control samples. By sharp contrast, metallic droplets are visible on samples annealed with InN powder even at 800~ Similar droplets were observed in all materials after annealing with InN powder at >750~ EDAX measurements identified these droplets as In in each case (Fig. 22). Therefore, it is clear that the InN powder initially provides good surface protection for annealing temperatures >750~ through incongruent evaporation of In from the powder leads to condensation of droplets on the samples contained within the reservoir. At temperatures approaching 1100~ these droplets evaporate from the surface of GaN or A1N, leading to an apparent surface smoothing when measured by AFM. Some other features of the annealing are salient with respect to implant activation processes. First, if we employed 90% N2" 10% H2 as the purge gas in the RTA system instead of pure N2, we noticed that the temperature at which surface dissociation was evident by either AFM or SEM was lowered by 100-200~ for each of the nitrides. A similar effect was observed if 02 was present in the annealing ambient, and thus, it is critical to avoid residual 02 or H2 in RTA systems during annealing of the nitrides. Second, under optimized ambient conditions (pure N2 purge gas, and use of either the proximity

geometry or powdered A1N in the susceptor reservoirs), AES was able to detect N2 loss from the surface of GaN even after 1000~ anneals, and from InA1N and InGaN after 800~ anneals [85]. However, N2 loss for A1N was detectable only after anneals at 1150~ emphasizing the extremely good thermal stability of this material. Indeed Zolper et al. [87] have recently reported use of sputtered A1N as an encapsulant for annealing GaN at temperatures up to 1100~ for Si + or Mg + ion implant activation. The A1N could be selectively removed with KOH solutions after the annealing process [88]. The loss of N2 from binary nitride surfaces during annealing produced thin ( 1000~ InA1N and InGaN to 800~ and InN up to 600~ Similar thermal stabilities were obtained for faceup annealing in graphite susceptors in which A1N powder provides a N2 overpressure. An attempt to increase this overpressure through use of InN powder was unsuccessful because of In droplet condensation on all samples at temperatures >750~ This could only be rectified if one could design a two-zone rapid thermal processing chamber in which a reservoir of InN powder was maintained at >750~ while the samples to be annealed were separately heated to their required temperatures.

6.3. AIN Encapsulant The existing commercial rapid thermal processing (RTP) equipment typically relies on a series of tungsten-halogen lamps as heat sources to rapidly heat up the semiconductor wafers [90]. However, this type of lamp-based RTP system suffers from many problems such as their point heat source nature, fluctuating lamp temperature during processing, and only modest temperature capacity (< 1100~ Recent interest in developing wide bandgap compound semiconductors has pushed the processing temperature requirements to much higher values (up to

ION IMPLANT DOPING 1600

,.

.

.

.

!

'

,..

,

,

...........................................!.............

1400 0

.

,

,

!

'

.....t

,

,

,

!

,

,

,

I

i

I

o.N,,oo

1200

o

1 0 0 0

m

800

am

io,, ~=

600

}..

400 200 i

i

__I

l

i

20

1600

'"

'

.

.

.

i

i

L.

40

.

.

! '

I

I

" '

!

1,oo ..........................................' 0

1200

l

l

I

I

80

'

'

'

I '

........I

!,

i 100

" '

I '

~

" 120

'

'

; oo ~

iiiiiiiiiiiiiiiiiiii

o

r

I

60

I ooo

I,.

8oo 600 ~"

400 2O0 0

..... 0

! ' -2 0

'

, ..I . . . . 4 0 6 0 Time,

Fig. 23.

I

,

I 80

i

,

,

, 100

~ , 120

sec

Time-temperature profiles for RTP annealing of GaN at 1500~

1500~ Presently, there are no specific RTP systems that can operate at such high temperatures. In the study of annealing of GaN up to 1400~ [91], a custom system (based on MOCVD system) that employed rf heating was built and utilized. There is an urgent need in GaN and SiC technology to develop new RTP systems which can provide uniform heating to very high temperatures (> 1500~ Most existing RTP equipment utilizes either an array of 10 or more tungsten-halogen lamps or a single arc lamp as heat sources [ 17]. This lamp-based RTP equipment can achieve only modest processing temperatures (< 1100~ primarily because of the pointlike nature of the sources and large thermal mass of the systems. To realize higher temperature capacity, new types of heat sources have to be employed. In the past few years, there has been development of novel molybdenum intermetallic composite heaters that may be used in air at temperatures up to 1900~ [91 ]. These heaters have high emissivity (up to 0.9) and allow heat up time of the order of seconds and heat fluxes up to 100 W / c m 2. This novel RTP unit is capable of achieving much higher temperatures than the lamp-based RTP equipment. Figure 23 shows some typical time-temperature fluctuation to rapidly heat up and cool down the wafer, the Zapper TM unit relies on wafer movement (in/out of furnace horizontally) to achieve rapid ramp-up and ramp-down rates similar to those of conventional RTP systems.

389

A variety of undoped GaN layers ~ 3 / z m thick were grown at ~ 1050~ by metal--organic chemical vapor deposition using trimethylgallium and ammonia. Growth was preceded by deposition of thin (~200 ~,) GaN or A1N buffers (growth temperature 530~ on the A1203 substrates. Capacitance-voltage measurements on the GaN showed typical n-type background carrier concentrations of < 3 • 1016 cm -3. Si + was implanted to a dose of 5 x 1015 cm -2, 100 keV, producing a maximum Si concentration of ~ 6 x 1020 cm -3 at a depth of ~800 ,~. Some of the samples were encapsulated with 1000-1500 A of A1N deposited in one of two ways. In the first, A1N was deposited by reactive sputtering of pure A1N targets in 300 mTorr of 20% N2 Ar. The deposition temperature was 400~ In the second method, A1N was grown by metal-organic molecular beam epitaxy (MOMBE) at 750~ using dimethylamine alane and plasma dissociated nitrogen. The samples were sealed in quartz ampoules under N2 gas. To ensure good purity of this ambient the quartz tube (with sample inside and one end predoped) was subjected to an evacuation/N2 purge cycle for three repetitions before the other end of the tube was closed, producing a final Ne pressure of ~ 15 psi. This negative pressure was necessary to prevent blowout of the ampoule at elevated annealing temperatures. The samples were then annealed at 1100-1500~ for a dwell time of ~ 10 seconds (Fig. 23). The time difference for reaching the annealing temperature was between 4 and 6 seconds. To compensate for this heating time lag inside the ampoule, the dwell time was purposely extended to ~ 15 seconds. Ramp rates were 80~ s -1 from 25-1000~ and 30~ s -1 from 1000-1500~ producing an average ramp-up rate over the entire cycle of ~50~ s -1 . The typical ramp-down rate was ,-~25~ s -1 . Thermocouple measurements of temperature uniformity over a typical wafer size (4 inch diameter) were +8~ at both 1400 and 1500~ After removal of the samples from the ampoules they were examined by SEM, AFM, and van der Pauw geometry Hall measurements obtained with alloyed Hgln eutectic contacts. SEM micrographs of unencapsulated GaN surfaces annealed at 1200, 1300, 1400, or 1500~ showed that the 1200~ annealing does not degrade the surface, and the samples retain the same appearance as the as-grown material. After 1300~ annealing, there is a high density (~ 108 cm -2) of small hexagonal pits which we believe is due to incongruent evaporation from the surface. The 1400~ annealing produces complete dissociation of the GaN, and only the underlying A1N buffer survives. Annealing at 1500~ also causes loss of this buffer layer, and a smooth exposed A1203 surface is evident. By sharp contrast to the results for GaN, both the sputtered and MOMBE A1N were found to survive annealing above 1300~ For the sputtered material we often observed localized failure of the film, perhaps due to residual gas agglomeration. For the MOMBE films this phenomenon was absent. Also in the sputtered material the rms surface roughness tended to go through a maximum, due to some initial localized bubbling, followed by the film densification.

390

PEARTON 101s ,

6O

t'q!

i

E r

t

v

o

4o ~ "

E

~>

v

o o

10+5

.J.=l

o

.P.,i

,.Q o

rj ep,4

20

rJ

~ 1014 ,

.

.

.

.

'

.

O e=-i

} unencapsulated

rD

0

. I

1000

} AIN capped

'

I

1200

'

1600

1400

Annealing Temperature (~ Fig. 24. Sheet carrier density and electron mobility in capped and uncapped Si-irnplanted GaN, as a function of annealing temperature. Fig. 26. TEM cross-sections of Si-implanted (5 • 1015 cm -2, 150 keV) GaN after high temperature annealing. GaN --!1-- AIN 10 =

101

100

,lOO

,

g-

, 'oo

,

, 'oo

' 1400

'

1500

'

1600

Annealing T e m p e r a t u r e (~ Fig. 25. Root-mean-square surface roughness of GaN and A1N after unencapsulated annealing at different temperatures.

The clear result from all this data is that the implanted GaN needs to be encapsulated with A1N in order to preserve the surface quality. We have previously shown that A1N is selectively removable from GaN using KOH-based solution. Figure 24 shows the sheet carrier concentration and electron mobility in the Si+-implanted GaN, for both unencapsulated and A1N-encapsulated material, as a function of annealing temperature. For unencapsulated annealing we see an initial increase in electron concentration, but above 1300~ the GaN layer disintegrates (Fig. 25). By contrast, for A1N-encapsulated samples the Si + implant activation percentage is higher ('~90%)

and peaks around 1400~ This corresponds to a peak cartier concentration of > 5 x 1020 cm -3. For 1500~ annealing both cartier concentration and mobility decrease, and this is consistent with Si-site switching as observed in Si+-implanted GaAs at much lower temperatures [92]. The results in Figure 24 are compelling evidence of the need for high annealing temperatures and the concurrent requirement for effective surface protection of the GaN. There is clear evidence from both ion channeling and TEM measurements that temperatures above 1300~ are required to completely remove implantation damage in GaN. Since the residual damage tends to produce n-type conductivity, it is even more imperative in acceptor-implanted material to completely remove its influence. However, a premium is placed on prevention of surface dissociation, because loss of nitrogen also leads to residual n-type conductivity in GaN. The combination of RTP annealing in the Zapper TM unit at 1400-1500~ and high quality A1N encapsulants produces metallic doping levels (~ 5 x 1020 cm -3) in Si+-implanted GaN. Figure 26 shows that annealing Si-implanted GaN at 1400~ removes all of the extended defects, whereas annealing at 1100~ leaves a large density of these defects. Since the activation anneal for GaN was initially done in the range of 1100~ the formation of a Pt/Au Schottky contact on n-type GaN was studied after such a high temperature anneal with and without a A1N encapsulation layer. Since A1N has a higher dissociation temperature it should act to suppress the dissociation of the GaN. One set of samples was n-type as-grown with a background donor concentration of 5-10 • 1016 cm -3 (samples A1, A2). The second set of

ION IMPLANT DOPING

391

10 "2 sample AI: no cap

10 ~ A


1400~ is sufficient to completely remove extended defects, whereas 1100~ annealing leaves a high degree of disorder. Figure 36 shows SIMS profiles before and after 1450~ annealing of implanted S in GaN. There is clearly no motion of the sulfur under these conditions, which suggests that, as expected, the structural quality of the GaN may have a strong influence on the apparent diffusivity of dopants. The samples in the present experiment are much thicker than those employed in the previous work, and the extended defect density will be correspondingly lower in the implanted region ( ~ 5 • 108 cm -2 compared to ~ 101~ cm -2 in the thin samples). The Si ionization level was measured as 48 + 10 meV from Hall data. The other group VI donors, Se and Te, have low diffusion coefficients in all compounds semiconductors (for example, Dse = 5 • 10 -15 cm2s -1 at 850~ in GaAs)[100, 101], and we find a similar result for these species implanted into GaN. Figure 37 shows the SIMS profiles before and after 1450~ annealing for Se, while Figure 38 shows similar data for Te.

,

10 TM

0.0

Depth (pm) Fig. 36. SIMSprofiles before and after annealing at 1450~ of implanted S (200 keV, 5 • 1014 cm-2) in GaN. The profiles are essentially coincident.

10~

Se I

,

0.2

I

,

0.4 Depth

I

,.,

I

0.6

100 1.0

.

0.8

(pm)

Fig. 37. SIMSprofiles before and after annealing at 1450~ of implanted Se (300 keV, 5 • 10TM cm-2) in GaN. The profiles are essentially coincident.

1021 -

1 0 20

,

10 7

: T e in GaN 600keV 3x 1014cm-2 As implanted and annealed at 1450~

10 8

O~ r O

10 5 0 :3

GaN--*

E o Io~

O, 10 4 ~"

O

E

10 3

lo' O

10 2 r

Te

1017

& 101

1016 0.0

0.1

I 0.2

0.3

0.4

[~ 0.5

I 0.6

10 0 0.7

Depth (pm) Fig. 38. SIMSprofiles before and after annealing at 1450~ of implanted Te (600 keV, 3 x 1014cm-2) in GaN.

396

PEARTON 0 2 0

.

.

.

.

I

'

,

r

,

,

I

'

'

'

'

I

'

'

10 21

' "'

~as-impl'anted

9

E ,2o ,"

,~, ..~

1 0 *9

0

o 1 O20

o

e,,

8c 8

29Si' positive SIMS, 0 2 beam Mg, negative SIMS, Cs beam

g 1018

0 =o

1019

g

oo

0 1017

........................ 0

0.5

1

1.5

2

depth (l~m) Fig. 39. in GaN.

o

SIMS profiles before and after annealing at 1125~ of implanted O

In both cases, the effective diffusivity at this temperature is < 2 x 10 -13 cm 2 s -1 . From limited temperature-dependent Hall data, we obtained an estimate of 50 4- 20 meV for the Te ionization level. Figure 39 shows SIMS profiles of implanted O before and after 1125~ annealing. There was also no detectable redistribution of the oxygen. Most of the common acceptor and donor species have been implanted into GaN at room temperature, and subsequently annealed up to 1450~ With the exception of Be, which shows an apparent damage-assisted redistribution at 900~ none of the species show detectable motion under these conditions. This bodes well for the fabrication of GaN-based power devices such as thyristors and insulated gate bipolar transistors which will require creation of doped well or source/drain regions by implantation. The low diffusivities of implanted dopants in GaN means that junction placement should be quite precise and there will be fewer problems with lateral diffusion of the source/drain regions toward the gate. Finally, the results show the effectiveness of the A1N cap in protecting the GaN surface from dissociation, since if any of the surface was degraded during annealing, the implant profiles would not longer overlap. 8. p - n JUNCTION FORMATION

In order to fabricate devices such as the enhancement lateral GaN MOSFET, there are several key process modules that must be developed, such as gate oxide deposition, p - n junction formation by implantation, ohmic contact improvement, and device passivation. There has already been significant progress in some of these areas, including the recent demonstration of the first GaN MOSFET using GdGaOx as the gate dielectric [ 104]. Moreover, the group of Murakami et al. [ 105] reported excellent p-ohmic specific contact resistivities of ~,10 -5 f2 cm 2 using Ta-based metallization. The formation of p - n junctions by ion implantation is one of the key process steps in the fabrication

1018=

,

0

,

,

2o00

, 9

4000

,

~.

6000

Depth (A) Fig. 40.

SIMS profiles of Si and Mg in an implanted GaN junction.

of the lateral MOSFET. Previous work has shown that low dose (< 5 x 1013 cm -2) Si + implants can be efficiently activated in GaN by annealing at > 1100~ Careful attention must be paid to avoiding loss of Ne from the GaN surface during annealing and various approaches such as A1N capping, Ne overpressures, or use of powdered GaN in the reservoirs of susceptors containing the samples to be annealed have been reported [106-111 ]. A key requirement for good activation appears to be that the starting GaN have high resistivity. Higher dose implants of Si + require higher annealing temperatures for optimum activation, in the range > 1400~ Less success has been obtained with p-type implantation because of the generally high n-type residual background cartier concentration in GaN and the large ionization level ('~ 170 meV) of Mg. In this section we report the fabrication of n + p junctions in GaN by implantation of e9si+, followed by A1N-capped rapid annealing at 1100~ Rectifying characteristics were obtained, but there was evidence of incomplete implant damage removal. A -v5000 A thick p-GaN layer was grown on c-plane A1203 by MOCVD at 1040~ Mg doping was derived from a CpeMg precursor. The total Mg concentration measured by SIMS was 1019 cm -3, corresponding to a hole concentration at 25~ of ,~1017 cm -3. 29Si+ ions were implanted in a nonchanneling direction to a dose of 2 • 1014 cm -2 at an energy of 120 keV. Part of each sample was masked with photoresist during the implant step. After removal of this resist, the sample was capped with sputtered A1N and annealing performed at 1100~ under a 1 atm Ne ambient. The n-type regions were metallized with Ti/A1, while the p-regions were metallized with Ni/Au. From past experiments, it is known that the diffusivity of implanted Si is < 10 -le cm -2 s -1 at l l00~ We also found that there was no detectable motion of the Mg during annealing as shown in the SIMS profiles of Figure 40. This suggests that

ION IMPLANT DOPING 10

397 9

I

'

I

'

I

'

I

'__

I

"

I

'

109 A

< GaN A L.

I-I

lOs

o.

10 7

N + Implant

f

O O

--El-- p-type --B--n-type

o

10 s

ir / 9

-10

I

5

-10

I

-5

i

I

0

I

5

I

10

Junction Voltage (V) Fig. 41. I - V characteristics from an implanted GaN junction (Si-implant into Mg-doped p-GaN).

the majority of the Mg is incorporated substitutionally, or we should have expected significant redistribution during annealing. Note that the junction depth will be difficult to determine from the SIMS data, because the background sensitivity for Si is relatively high. From a TRIM simulation we estimate the junction depth to be ~4000 A~based on the distance at which the Si concentration falls to ,~ 1017 cm -3 (the hole concentration due to the Mg acceptors). We assume that at 25~ essentially all of the Si donors are ionized (Ed ~ 28 meV) and we have activated >90% of the implanted donors. The current-voltage (l-V) characteristic from a typical implanted junction is shown in Figure 41. The reverse breakdown voltage is 13 V at a current density of 5.1 x 10 -4 A cm -2. From the slope of the forward section of the characteristics, the junction ideality factor is ~2. This is indicative of generationrecombination being the dominant current conduction mechanism in the junction. It is shown that heteroepitaxial GaN contains a high density of threading dislocations, and these are a source of possible generation-recombination centers. Plan view TEM was performed to examine the effectiveness of the damage removal by the annealing step. The micrographs showed that the GaN clearly contains a significant density of dislocations. These are not observed in unimplanted control samples, and thus we ascribe their origin to condensation of point defects created during the implant step. Separate measurements have shown that annealing temperatures > 1400~ are necessary to remove these dislocations. We expect that creation of n + p junctions will be simpler than p+n junctions, because of the lower activation efficiency of p-implants and the more stringent requirement for avoidance of N2 loss from the near-surface region. The I-V characteristics we obtained here can certainly be improved, both in terms of breakdown voltage and ideality factor. 9. ISOLATION Implant isolation has been widely used in compound semiconductor devices for interdevice isolation such as in transis-

8oo

400

I

500

,

I

600

9

l

700

,

I

800

,

I

900

,

1000

A n n e a l T e m p e r a t u r e (~ Fig. 42. Sheet resistance versus annealing temperature for N implanted initially n- and p-type GaN. The N was implanted at multiple energies to give an approximately uniform ion concentration of 4 x 1018 cm -3 across ~500 nm.

tor circuits or to produce current channeling such as in lasers [ 111-113]. The implantation process can compensate the semiconductor layer either by a damage or chemical mechanism. For damage compensation, the resistance typically goes through a maximum with increased postimplantation annealing temperature as the damage is annealed out and hopping conduction is reduced. At higher temperatures the defect density is further reduced below that required to compensate the material and the resistivity decreases. For chemical compensation, the postimplantation resistance again increases with annealing temperature with a reduction in hopping conduction but it then stabilizes at higher temperatures as a thermally stable compensating deep level is formed. Typically there is a minimum dose (dependent on the doping level of the sample) required for the chemically active isolation species to achieve thermally stable compensation [ 114]. Thermally stable implant isolation has been reported for n- and p-type A1GaAs where an A 1 - O complex is thought to form [ 114, 115] and for C-doped GaAs and A1GaAs where a C--N complex is postulated [116]. With this background, the implant isolation properties of the III-N materials are reviewed. As shown in Figure 42, N-implantation (at doses of 10121013 cm -3) effectively compensates both p- and n-type GaN. For both doping types the resistance first increases with annealing temperature then reaches a maximum before demonstrating a significant reduction in resistance after a 850~ anneal for n-type and a 950~ anneal for p-type GaN. This behavior is typical of implant-damage compensation. The defect levels estimated from Arrhenius plots of the resistance/temperature product are 0.83 eV for initially n-type and 0.90 eV for initially p-type GaN (Fig. 43). These levels are still not at midgap, but are sufficiently deep to realize a sheet resistance > 109 ft/square. The implantation has also been reported to effectively isolate n-type GaN, with the material remaining compensated to over 850~ Interestingly, H-implanted compensation of n-type GaN is reported to anneal out at ~400~ with

398

PEARTON 34

'

I

'

I

"

I

'

I

'

I

"

I

10 4

'

B

,, I

9

,

I

9

,,, !

9

i

,

I"

9

A

GaN

f

75~moplanted

32

/

/

10 3

Ino.75Alo.2sN O Implant

v

0

c:

10 2

.,..,

(%) n, z-

10~ 10 0

i

28

--e--medium dose --l--high dose

10-I

n p-type o Z ,

2.7

I

2.8

=

I

2.9

=

I

3.0 looorr

,

I

.

3.t

,

!

3.2

.

I

3.3

10-2

10-3

3.4

( K "1)

Fig. 43. Arrhenius plots of sheet resistance in N+-implanted n- and p-GaN annealed at 750 ~C.

an anomalous dependence on implant energy. The reason for this is presently not known. In light of this result, however, H-implantation in GaN will require further study, as H is often the ion of choice for photonic device isolation applications that require deep isolation schemes. Moreover, both the He and N isolation appear to rely solely on implantation damage without any chemical compensation effects analogous to those in the O/AI/GaAs case [ 111, 114, 115]. However, the implantationinduced defects in GaN are more thermally stable than other III-V semiconductor materials, such as GaAs or InP, where the damage levels begin to anneal out below 700~ [ 111 ]. This may be a result of the higher bandgap of GaN or the more polar nature of the lattice causing more stable defects. Further work is still required to understand the nature of the implantation damage in GaN. Figure 44 shows the annealing temperature dependence of sheet resistivity in O+-implanted AI0.eGao.8N. Very high sheet resistances (~1012 f2/square) can be obtained because of the large bandgap of this material, but once again the isolation is due to damage and not to chemical deep levels. Similar results were obtained with n + implantation. Deep level transient spectroscopy measurements showed states at Ec - 0.67, Ec - 0.60, and Ec - 0.27 eV in N+-implanted GaN [ 117]. It is not known what effect the annealing ambient has, since the presence of oxygen or hydrogen is known to enhance the decomposition of the GaN surface and lead to preferential N2 loss [118-122]. Figure 44 shows the evolution of normalized sheet resistance in O+-implanted In0.75A10.esN with subsequent annealing. The sheet resistance increases up to ~600~ and then is reduced to the original unimplanted values at ,~800~ This behavior is typically of that seen in other implanted III-V semiconductors and is caused by the introduction of deep acceptor states related to the implant damage that compensate the shallow native donors. This produces an increase in sheet resistance of the material, the magnitude of which is dose dependent. The usual situation is that all of the shallow levels are compensated, but

1

4O0

9

t

50O

.

,

t

6O0

9

I

.

i

7OO

I

BOO

,

1

9OO

AnnealTemperature(~ Fig. 44. Normalized sheet resistance (relative to the unimplanted values) versus anneal temperature for In0.75A1N implanted with various doses of O + at multiple energies.

some residual conductivity remains due to the presence of interdefect hopping of trapped carriers from one closely spaced trap site to another. In other words, there is an excess of deep states over that required for optimum compensation. Subsequent annealing removes these excess states, leading to an increase in sheet resistance of the material. Continued annealing above ~600~ for Ino.75Alo.25N reduces the deep acceptor concentration below that required to trap all of the original free electrons, and the conductivity increases back to the preimplanted value. In the present case, annealing above 800~ actually produces a sheet resistance lower than in the as-grown samples due either to loss of nitrogen from the uncapped material or the existence of additional shallow donor states created by the implantation. Similar results were obtained for N+-implanted In0.75A10.esN. The data show the same basic trends as for oxygen implantation and lead to the conclusion that neither oxygen nor nitrogen produces a significant concentration of chemical deep states in InA1N or the high resistance values would be maintained even at the maximum annealing temperatures. Oxygen and nitrogen are known to create chemical deep levels in A1GaAs. Note that even in this relatively conducting InA1N, implantation and optimized annealing is capable of producing increases in sheet resistance of 3-8 • 103 times (absolute values > 108 f2/square). This is well above the values required for electronic device isolation (> 106 f2/square). Temperature-dependent measurements of the sheet resistance of an In0.75A10.esN sample implanted with either a medium or high dose of O + ions and annealed at 600~ are shown in Figure 45. The activation energy obtained for the medium dose sample is ~0.29 eV, consistent with its lower sheet resistance relative to that of the higher dose material where the activation energy was 0.54 eV. Note that for optimum implant isolation it is desirable to create midgap states. In InA1N the states created are still relatively high in its band gap, similar to the behavior of InP and InGaAs.

ION IMPLANT DOPING

399 ....

38

I 10 4

9 medium dose m highdose

37

9

I

9

I

9

I

9

9

,.

JL ~lk

F

I'

m ~ E0=0.54 eV

In~176 N implant

9

Q. v r-

600 C anneal

~j/~/ml

9

n,

-

iu

32 2.7

9

, 2.8

9

Ea=0.19 eV 9

I 2.9

.

., 3.0

.

m .... 3.1

m 3.2

50%In

--O--

m 3.3

.

'

\

\

\

\

----.--.

0 Z

.

i-

"IO G) .N 10 0

33 ~ ( ~ 4 W

9

o,m

10 i

34

I

InGaN low O dose

8 ~o e"

.

9

Fig. 45. Arrhenius plots of sheet resistance of N+-implanted In0.75AI0.25N after annealing at 600~

Turning to InxGal_xN, Figure 46 shows the increase in sheet resistance of O+-implanted material of three different compositions as a function of annealing temperature. The maximum increases in sheet resistance are between 102 and 104 for both low and high dose conditions, with consistently higher values for the higher doses. Once again there is no evidence for a chemically active deep acceptor state for oxygen. Similar data were obtained for N + ion implantation in InGaN. The maximum increases in sheet resistance are less than a factor of 103, slightly lower than for the O + implant resuits. This is most likely a result of the slightly different growth conditions for this set of samples leading to higher initial conductivities. The same trends in sheet resistance with annealing temperature are evident as for O + implantation. In this highly conducting InxGal_xN the absolute sheet resistances achievable are borderline for electronic device isolation but are acceptable for applications such as current path delineation in photonic devices. The results for F + implantation in InGaN also showed there is basically no difference from the results for N + or O + implants, indicating that none of these elements produce chemical deep states in InxGa]_xN and that all of the changes in electrical properties are due to introduction of damage-related deep levels and their subsequent annealing. Examples of the measurement temperature dependence of sheet resistance, corrected for the temperature dependence of mobility, are shown in Figure 47 for In0.33Ga0.67N implanted with a high dose of N +, and annealed at either 500 or 800~ In the former case, an activation energy of 0.40 eV is obtained. This is relatively high in the bandgap of this material (,-,2.8 eV). As discussed earlier, implant isolation is most effective when the damage-related states are at midgap, as in the case in the AlxGal_xAs and InxGal-xP materials systems. The behavior of InA1N and InGaN is similar to that of InP and InGaAs, where the damage-related levels are relatively high in the gap. The result is that initially n-type material achieves only moderate resistivities upon implantation with nonchemically active ions. The other side of this situation

i

10 -i

m 3.4

1000/'i'(K)

-

9

10o

!

9

200

,

I

=

I

300

(a)

9

400

L

=

500

-

I

*

,I

6O0

,.

I

700

800

Anneal Temperature(~ lO4

A

r-1 10 3

era

~9

10 ~

"o

10o

InGaN high O dose

~N

--m-- 33% In --0-- 50% In --&-- 75% In

m ~ 10-1 o Z lO-Z 100

200

300

(b)

400

500

600

700

800

900

Anneal Temperature(~

Fig. 46. Normalized sheet resistance versus anneal temperature for InxGal_x N implanted with (a) low doses and (b) doses of O + at multiple energies.

''

34

'

I

"

r"

9

"

I

,--

......

i

33

32

ino.33Gao.67N N implant high dose

~" I-~-

31

m

=..

9

~ 800 ~ 500

30-

Ea=25 meV ...-~.~, 2.7

w. 2.8

, 2.9

,

i 3.0

, ,

, i. 3.1

,

, 3.2

1000/l'(K) Fig. 47. Arrhenius plots of sheet resistance of N + implanted In0.33Ga0.67N implanted with a high dose of N + and subsequently annealed at either 500 or 800~

PEARTON

400

108

9

~

'

I

~

"

~

I

'

'

"

I

'

'

'

I

~

[

10 ~o

'

10 7

I

i|

-4~0 -/-N --~F

10 9

10 6

10 8

r-q

.

105

F-q

10 4

10 7

v V

O.

10 3

o'j

10 6 ,I

105

- 0 - as-grown F-isolation N-isolation

10 2

i

101

i

10 4

100 0

20

40 60 percent In

80

100

10 3

I

I

t

,

,

,

. ,

..

200 400 600 800 1000 annealing temperature (~

Fig. 48. Maximum sheet resistance versus percent In for InGaN either asgrown or implanted with F or N and annealed at the temperature for maximum compensation for each composition (ion concentration ~ 5 x 1019 cm-3).

Fig. 49. Sheet resistance versus annealing temperature for O-, N-, or F-implanted In0.75AI0.25N (ion concentration ~ 5 x 1018 cm-3).

is that if one starts with initially p-type InP one can achieve very high resistivities because the Fermi level moves from near the valance band and through midgap on its way to the states in the upper part of the band and therefore an optimum choice of dose can place the Fermi level at midgap. To date no one has produced p-type InGaN or InA1N, but it will be interesting to see if this behavior is observed in these materials. Upon annealing at 800~ where it again becomes very conducting, the N+-implanted In0.33Ga0.67N displays an activation energy of only ~25 meV, consistent with the values obtained in as-grown samples. To summarize the results for the alloys, implant isolation of the In-containing nitrides (INN, InGaN, and InA1N) was first reported using F-implantation [123]. That work showed that InN did not demonstrate significant compensation while the ternaries increased in sheet resistance by roughly an order of magnitude after a 500~ anneal. Data from a more extensive study of InxGl-xN implant isolation for varying In composition using N- and F-implantation is summarized in Figure 48 [124]. The InGaN ternaries only realize a maximum of a 100-fold increase in sheet resistance independent of ion species after a 550~ anneal. Pure InN shows a higher increase of 3 orders of magnitude but still only achieves a maximum sheet resistance of 104 f2/square. This may be high enough for some photonic device current-guiding applications but is not sufficient for interdevice isolation in electronic circuits. The damage levels created by N-implantation are estimated from an Arrhenius plot of the resistance/temperature product to be a maximum of 390 meV below the conduction band [124]. The defect level is high in the energy gap, not near midgap, as is ideal for implant compensation. The position of the damage level is anal-

ogous to the defect position reported for implant compensated n-type InP and InGaAs [ 125] but different from the damageassociated, midgap states created in GaAs and A1GaAs. As shown in Figure 49, In0.75A1025N, in contrast to InGaN, can be highly compensated with N- or O-implantation with over a 3 order-of-magnitude increase in sheet resistance after a 600700~ anneal while F-implantation produces only a 1 orderof-magnitude increase in sheet resistance [ 123, 126]. The compensating level in InA1N is also high in the bandgap with the deepest level estimated from Arrhenius plots as being 580 meV below the conduction bandedge in high dose N-isolated material; however, it is sufficiently deep to achieve highly compensated material. The enhanced compensation for N- and O-implantation, as compared to F-implantation, in InA1N suggests some chemical component to the compensation process. For N-implantation a reduction in N-vacancies, which are thought to play a role in the as-grown n-type conduction, may explain the enhance compensation. For O-implantation, the enhanced compensation may be the result of the formation of an O - A 1 complex as is thought to occur in O-implanted A1GaAs. Figure 50 schematically summarizes the present knowledge of the position in the bandgap of the compensating implanted defect levels in III-N materials and compares these to those in GaAs and InP. Although the levels are not at midgap, as is ideal for optimum compensation as occurs in GaAs and p-type InP, with the exception of InGaN, the levels are sufficiently deep to produce high resistivity material. Very effective isolation of A1GaN/GaN heterostructure filed effect transistor structures has been achieved using a combined P+/He + implant process [127]. The groups of Asbeck and Lau at UCSD demonstrated that a dual energy (75/180 keV) P+ im-

ION IMPLANT DOPING

401 n,p GaN

n-lnGaN (47*/, InN)

n & p-GaAs

n-lnAIN (75% InN)

-i-n: 830 meV

n & p-lnP

EC

I --E2

l p: 900 meV

EV Eg =

1.42 eV

1.35 eV

-2.5 eV

~2.5 eV

3.39 eV

Fig. 50. Schematicrepresentation of the position in the energy gap of compensating defect levels from implant isolation in GaAs, InP, In0.47Ga0.53N, In0.75A10.25N,and GaN. plant (doses of 5 x 10 ]] and 2 x 10 ]2 cm -2, respectively), followed by a 75 keV He + implant (6 x 1013 cm-2), was able to produce sheet resistance of ~ 1012 f2/(9 in A1GaN/GaN structures with 1 /zm thick undoped GaN buffers. The temperature dependence of the resistivity showed an activation energy of 0.71 eV, consistent with past measurements of deep states induced in GaN by implant damage. In this section we report on the defect levels created on nand p-type GaN by Ti, O, Fe, or Cr implantation. The annealing temperature dependence of the sample resistance was measured up to 900~ The thermally stable, electrically active concentration of deep states produced by these species was found to be < 7 x 1017 cm -3 in both conductivity types of GaN, with the sample resistivity approaching its original, unimplanted value by "-900~ in all cases. The defect levels created in the implanted material are within 0.5 eV of either bandedge. 0.3/zm thick n (Si-doped) or p (Mg-doped) type GaN layers were grown on 1/zm thick undoped GaN on (0001) sapphire substrates by rf plasma activated molecular beam epitaxy. The carrier concentration in the doped layers was 7 x 10 ]7 cm -3 in each case. Ohmic contacts were formed in a transmission line pattem (gap spacings of 2, 4, 8, 16, and 32 /zm) by e-beam evaporation and lift-off of Ti/Au (n-type) or Ni/Au (p-type) annealed at 700~ under N2. The total metal thickness was 4000 A, so that these regions could act as implanted masks. A schematic of the resultant structure is shown in Figure 51 (top). The samples were then implanted at 25~ using multipleenergy Ti +, O, Fe, or Cr ions. An example of the calculated ion distribution for the Ti + implant scheme is shown at the bottom of Figure 51. The doses and energies were chosen to create an average ion concentration of ~ 1019 cm -3 throughout the 0.3/zm thick doped GaN layers. In the case where the implanted species is chemically active in the GaN it is the ion profiles that are the important feature, since it is the electrically active fraction of these implanted species that determines the isolation behavior. In the case where the isolation simply results from damage-related deep levels,

Ti/Au (Ni/Au for p-Gab0 --4000 A

0.3 ~tm n/p-GaN i

1 ~tm undoped GaN

A1203

substrate

1020

1019

~

O3

1018

1017

1016

1015 0

I 1000

f~ I 2000

I 3000

..... 4000

Depth (A)

Fig. 51. Schematicof GaN structure for measurementof sheet resistance after implantation (top) and ion profiles for Ti+ implant sequence (bottom). then it is the profile of ion damage that is important. Figure 52 shows both the calculated ion profiles (top) and damage profiles (bottom) for the multiple energy O + implant scheme, obtained

402

PEARTON 10 20

1 0 20

1019

1019

'E 10 TM

~

10 TM

0

101~

o

o

1017 0+--). Ga_N

~.

o

o

lx1014 cm2, 50 keV 0 0 2x10 TMcm"2, 100 keV 0 o 3x1014 cm-2, 200 keV 0

1016

1016

o

1015

I 1000

0

d ......

Depth

1015

I

2000

3000

0

4000

1000

2000

(A)

3000

4000

Depth (A)

1 0 23

10 23

E r

E

10 22

(3

0,.., ,..=

(n t- 1 022 (1) a

E' G)

C3

%

r- 1021

o

,

O

O

121 I:D H 121

O O

>

,

10 20

0

, 1000

qb

"

0

.=

8" t-

i = , = i

o >

' 2000

,%

I 3000

, I

H

o o o

1 021

'

H,

o

oo

I

.

%

o o

|

o

. 4000

Depth Ok) Fig. 52. Ion (top) and damage (bottom) profiles for multiple energy O + implant sequence into GaN.

from TRIM simulations. Note that the defect density is generally overstated in these calculations due to recombination of vacancies and interstitials. In any case, the doses are below the amphorphization threshold for GaN. Both Fe and Cr were implanted at 100 keV (1014 cm-2), 300 keV (2 x 1014 cm-2), and 500 keV (3 x 1014 cm-2). The ion and vacancy profiles for the Fe + implants are shown at the top and bottom, respectively, of Figure 53. The sheet resistance of the implanted regions was measured for annealing temperatures up to 900~ and for measurement temperatures up to ~250 ~C. Figure 54 shows the annealing temperature dependence of sheet resistance for Cr + (top) and Fe + (bottom) implanted nand p-type GaN. The trends in the sheet resistance are typical of those observed with damage-related isolation. The as-

1020

=

0

I

1000

I

I

2000

,

3000

4000

Depth Ok) Fig. 53. Ion (top) and damage (bottom) profiles for multiple energy Fe + implant sequence into GaN.

implanted resistance is 6-7 orders of magnitude higher than that of the unimplanted material due to creation of deep traps that remove carriers from the conduction and valence bands. Subsequent annealing tends to further increase the sheet resistance, by reducing the probability for hopping conduction as the average distance between trap sites is increased. Beyond particular annealing temperatures (500-600~ in this case) the trap density begins to fall below the carrier concentration and carriers are returned to the conduction or valence bands. This produces a decrease in sheet resistance toward the original, unimplanted values. If Cr or Fe produced energy levels in the bandgap with concentrations greater than the carrier density in the material, then the sheet resistance would remain high for annealing temperatures above 600~ For these two impurities it is clear that the electrically active concentration of deep states

ION IMPLANT DOPING

10TM

1012

1,.,

1012

m

101~ n-type ~

.=

-

Cr+-~ G a N

10lo lo ,

403

I

.

.

1012

0+-->GaN

10lo

1010

108

~

106

n,' 106 _ - t - -

108

8

p-type r

n,.~',,,106 p-type original m

10 4

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

_

i

102

I 400

I 600

,I 800

-

m

104

m

m

=,

=,

==

,=,

==

=,

-

--IF- n-type --II-- p-type p-type original

~

==

~ . ,

m

=,

=.

_

102 0

1012

104

i=,

I

I

I

I

200

400

600

800

102 1000

10TM

1012

10lo 108

~

106

=,

=,,

10lo

10lo

i,

m

~

~

m

~

m

=,

=,,

=,

'

= = . ,

=,,

=,

~

,=,

i=,

,=

~,~ 108

--[

ill

I 200

i

r

ri" 106

106

m

p-type original

104

104 n-type original

i

I 400

108

--IF- n-type --II-- p-type

n-type original

102 0

,m

Ti*~ GaN _

-- [

106

o

Fe+---> G a N

v

n,'

i,

Annealing Temperature (~

10lo D ~ j ~ 08

=D

n-type original

102 1000

m

m

~"

~

10 4

Annealing Temperature (~

1012

=,

|ill

I 200

0

104

-

p-type original =,

_

n-type original

i

106

m

m

_

p-type

I 600

i

_"-"

"t104

i

I 800

102 1000

Annealing Temperature (~

102

I

I

I

I

200

400

600

800

,

102 1000

A n n e a l i n g T e m p e r a t u r e (~

Fig. 54. Evolutionof sheet resistance of GaN with annealing temperature after either Cr+ (top) or Fe+ (bottom) implantation.

Fig. 55. Evolutionof sheet resistance of GaN with annealing temperatureafter either O+ (top) or Ti+ (bottom) implantation.

is < 7 x 1017 cm-3; otherwise all the carriers would remain trapped beyond an annealing temperature of 600~ Similar data are shown in Figure 55 for O + (top) and Ti + (bottom) implants in both n- and p-type GaN. Basically the same trends are observed as for Cr + and Fe + implants. The sheet resistances tend to be lower for the O + implants because of the lower vacancy and interstitial concentrations created. We do not believe this is a result of O-related shallow donor states because these are not activated until annealing temperatures above 1100~ Once again, the concentration of electrically active deep states related to the chemical nature of both Ti and O must be < 7 • 1017 cm -3 when they are introduced into GaN by ion implantation. Figure 56 shows Arrhenius plots of the sheet resistance of Cr + (top) or Fe + (bottom) implanted n- and p-type GaN annealed at either 450~ (n-type) or 600~ (p-type). These an-

nealing temperatures were chosen to be close to the point where the maxima in the sheet resistances occur for the two different conductivity types. The activation energies derived from these plots represent the Fermi level position for the material at the particular annealing temperatures employed. Note that the values are far from midgap (1.7 eV for hexagonal GaN) but are still large enough to create very high sheet resistances in the ion damaged material. Within the experimental error (+0.04 eV), the activation energies are the same for Cr + and Fe + implants for both conductivity types. This again suggests the defect states created are damage related and not chemical in nature. Similar data are shown in Figure 57 for O + (top) and Ti + (bottom) implants in both n- and p-type GaN annealed at either 300~ (O +, n-type), 450~ (Ti, n-type), or 600~ (O and

404

PEARTON

1011

1013

9 0

1012

1011

.

Cr*----, n-GaN Cr* ~ p-GaN .

.~ . ~

E

iv// ~

101o -

e

O* --~ n-GaN

2

O+ -+ p-GaN c ~ ~ ,

J

"-" ~

=~0~.49 eV E a = 0.45 eV

r-] 101o

109

r

rv'

r

1/)

109 -

108

eV

-

eV

108

o" 107

10~ 2.4

2.0

2.8

3.2

3.6

2.0

I

I

I

2.4

2.8

3.2

1000/T (K~) 101:'

1 ooo/r

0

Fe*--.~n - G a N ~ Fe* --->p-GaN ~ ' "

~

1012

1011 / 1 ~ ~ , , /

Ti + -~ n-GaN Ti+~p-GaN

,,

,,,, ,,,

///'i / ~ ~ .

/

0 eV

r-1 v

~

1010

n,'

10 9

10 9

V

.

2.0

l 0

i

1011

E a = 0.48 eV

101o

10s

(K4) i

9

3.6

2.4

.

2.8

=

.

eV

108 -

.

3.2

-

3.6

IO00/T (K-~) Fig. 56. Arrhenius plots of sheet resistance in Cr + (top) or Fe + (bottom) implanted n- and p-GaN, after annealing at either 450~ (n-type) or 600~ (p-type).

Ti, p-type). The activation energies are again similar to those obtained with Cr + or Fe + implants, except for the case of O + into n-GaN. This difference may be related to the lower damage density with O + implantation described earlier. The defect states in the gap are most likely due to point defect complexes of vacancies and/or interstitials and the exact microstructure of these complexes and their resultant energy levels are expected to be very dependent on damage density and creation rate. This might also explain the differences reported in the literature for the activation energies obtained with different implant species. Figure 58 shows a schematic of the energy level positions found in this work for Ti, Cr, Fe, and O implanted p- and n-type GaN annealed to produce the maximum sheet resistance. A1-

2.0

I

I

2.4

2.8

,

I

3.2

3.6

looorr (K Fig. 57. Arrhenius plots of sheet resistance in O + (top) or Ti + (bottom) implanted n- and p-type GaN, after annealing at either 300~ (O +, n-type). 450~ (Ti, n-type), or 600~ (O + and Ti +, p-type).

though the levels are not a midgap as is ideal for optimum compensation, they are sufficiently deep to produce high resistivity material. In GaN contaminated with transition metal impurities, no-phonon photoluminescence lines attributed to Fe 3+ at 1.3 eV and Ti 2+ at 1.9 eV have been reported, but to date there are no electrical measurements. The main points of this investigation may be summarized as follows: (i) Ti, O, Fe, and Cr do not produce electrically active deep energy levels in the GaN bandgap with concentrations approaching 7 x 1017 cm -3 when introduced by implantation.

ION IMPLANT DOPING

Fig. 58. Schematic representation of the position in the energy gap of defect levels from Fe, Cr, Ti, or O implant isolation in GaN.

(ii) GaN implanted with these species displays typical damage-related isolation behavior, with no evidence of chemically induced thermally stable isolation. (iii) Sheet resistances of ~ 1012 g2/square in n-GaN and "~101~ ~/square in p-GaN can be achieved by implantation of Cr, Fe, or Ti. (iv) The activation energies for the sheet resistance of the implanted GaN are in the range 0.2-0.49 eV in n-type and ,~0.44 eV for p-type.

10. DEVICES The best example of how ion implantation can directly impact the performance of group III-nitride transistors is illustrated in Figure 59. The figure shows four device structures that could be employed to fabricate A1GaN/GaN high electron mobility transistors (HEMTs). To date, the majority of the A1GaN/GaN HEMTs transistors have been fabricated in a planar structure as shown in Figure 16a, where the ohmic source and drain contacts are placed directly on the wide bandgap A1GaN layer without any increased local doping to reduce the contact or access resistance. This leads to a high access resistance, reduced current capability, and a high transistor knee voltage. This in turn reduces the transistor power gain, power-added efficiency, and linearity. Figure 59b and c shows two approaches that have been taken to reduce the access resistance. One is to selectively etch away the wide bandgap material in the contact regions and then regrow highly doped GaN to improved access resistance; however, the manufacturability of this approach, as with any regrowth process, is questionable. The recess gate approach of Figure 16c has been widely used in other mature compound semiconductors such as GaAs and InP. Although this type of structure has been demonstrated in GaN-based devices, the unavailability of controlled wet etching of GaN requires the use of a plasma recess etch. Use of a plasma etch introduces surface damage in the semiconductor in the region under Schottky gate that degrades the rectifying properties of the gate. Finally, the selfaligned ion implanted structure of Figure 59d is used to create

405

Fig. 59. Comparison of GaN-based HFET structures: (a) planar, (b) recessed gate, (c) regrown n + ohmic regions, and (d) self-aligned, implanted. Implantation is the most practical means to achieve the selective area doping required to reduce the transistor access resistance.

selective areas of highly doped regions for the source and drain contacts in a highly manufacturable fashion without any plasma etching of the gate region. To date, ion implantation has been used to realize a GaN junction field effect transistor but has not been applied to A1GaN/GaN HEMTs. As will be discussed later, one of the key challenges to applying ion implantation to A1GaN/GaN HEMTs is the avoidance of surface degradation that will negatively impact the Schottky gate formation during the high temperature implant activation anneal. Progress in GaN-based electronics has been remarkably rapid due to several factors. One of these is that the experience gained in GaAs/A1GaAs HEMTs has been quickly applied to the GaN/A1GaN system. At one time it was thought that MBE and related techniques would be the best choice for growth of electronic device structures, and this may still be the case if GaN substrates become available. However, for heteroepitaxial growth there is still a need to grow thick buffer or epitaxial lateral growth (ELO) structures, which are best done with MOCVD. The rapid advances in material purity, ohmic contact quality, and gate contact stability have fueled the progress in HFETs in the GaN/A1GaN system. Much work remains to be done on vertical device structures such as thyristors and HBTs, where minority carrier lifetime, interface quality, and doping control are important factors. As with GaAs electronics, much of the impetus for nitride electronics is coming from defense applications and there is as yet no commercialization of these devices. An example of how selective area implantation can be used to improve ohmic contact resistance on device structures is shown in Figure 60. In this case, W contact deposited on the implanted n-GaN showed minimum specific contact resistances of -~ 10 -4 ~ cm 2. After implantation of Si + followed by activation at 1100~ to produce n + GaN regions (n ~ 5 x 1020 cm -3), subsequently deposited W contacts show a contact resistance almost 2 orders of magnitude lower than on unimplanted material.

406

PEARTON 1 0 -3 -

W/Si-implanted GaN 30 second anneals

10-4 E o e

O

O

o

10_~

O O

10 -6

9 I

400

9

I

600

'

I

800

9

I

1000

=

1200

Anneal Temperature (~ Fig. 60. Contact resistance versus annealing temperature for W on Si-implanted GaN that was initially activated at 1100~ to produce n + GaN.

Acknowledgment

This work is partially supported by grants from DARPA/EPRI and NSF.

REFERENCES 1. J.C. Zolper, J. Cryst. Growth 178, 175 (1997). 2. J. C. Zolper, in "GaN and Related Materials, Optoelectronic Properties of Semiconductors and Superlattices," Vol. 2. Gordon and Breach, New York, 1997. 3. R.G. Wilson, Proc. Electrochem. Soc. 95-21,152 (1995). 4. H.P. Maruska, M. Lioubtchenko, T. G. Tetreault, M. Osinski, S. J. Pearton, M. Schurmann, R. Vaudo, S. Sakai, Q. Chen, and R. J. Shul, Mater. Rev. Soc. Symp. Proc. 483, 345 (1998). 5. J. C. Zolper, H. H. Tan, J. S. Williams, J. Zou, D. J. H. Cockayne, S. J. Pearton, M. H. Crawford, and R. E Karlicek, Jr., Appl. Phys. Lett. 70, 2729 (1997). 6. S. C. Binari, H. B. Dietrich, G. Kelner, L. B. Rowland, K. Doverspike, and D. K. Wickenden, J. Appl. Phys. 78, 3008 (1995). 7. C. Liu, B. Mensching, M. Zeitler, K. Volz, and B. Rauschenbach, Phys. Rev. B 57, 2530 (1998). 8. C. Ronning, N. Dalmer, M. Deicher, M. Restle, M. D. Bremser, R. E Davis, and H. Hofsass, Mater Res. Soc. Symp. Proc. 468, 407 (1997). 9. H. Kobayashi and W. M. Gibson, Appl. Phys. Lett. 73, 1406 (1998). 10. T. Suski, J. Jun, M. Leszczynski, H. Teisseyre, I. Grzegopy, S. Prorwski, J. M. Baranowski, A. Rockett, S. Strite, A. Stanert, A. Turos, H. H. Tan, J. S. Williams, and C. Jagadish, Mater Res. Soc. Symp. Proc. 482, 703 (1998). 11. S.J. Pearton, C. R. Abernathy, C. B. Vartuli, J. C. Zolper, C. Yuan, and R. A. Stall, Appl. Phys. Lett. 68, 2273 (1996). 12. J. C. Zolper, R. J. Shul, A. G. Baca, R. G. Wilson, S. J. Pearton, and R. A. Stall, Appl. Phys. Lett. 68, 2273 (1996). 13. J.C. Zolper, R. G. Wilson, S. J. Pearton, and R. A. Stall, Appl. Phys. Lett. 68, 1945 (1996).

14. J. C. Zolper, J. Han, S. B. Van Deusen, R. M. Biefeld, M. H. Crawford, J. Han, T. Suski, J. M. Baranowski, and S. J. Pearton, Mater. Res. Soc. Symp. Proc. 483,609 (1998). 15. H. H. Tan, J. S. Williams, J. Zou, D. J. H. Cockayne, S. J. Pearton, and R. A. Stall, Appl. Phys. Lett. 69, 2364 (1996). 16. J. Burm, K. Chu, W. A. Davis, W. J. Schaff, L. E Eastman, and T. J. Eustis, Appl. Phys. Lett. 70, 464 (1997). 17. J. C. Zolper, J. Han, R. M. Biefeld, S. B. Van Deusen, W. R. Wampler, D. J. Reiger, S. J. Pearton, J. S. Williams, H. H. Tan, and R. Stall, J. Electron. Mater. 27, 179 (1998). 18. J. C. Zolper, D. J. Reiger, A. G. Baca, S. J. Pearton, J. W. Lee, and R. A. Stall, Appl. Phys. Lett. 69, 538 (1996). 19. R.G. Wilson, E A. Stevie, and C. W. Magee, "Secondary Ion Mass Spectrometry." Wiley, New York, 1989. 20. R.G. Wilson, J. Electrochem. Soc. 138, 718 (1991). 21. J.P. Biersack, Nucl. lnstrum. Methods B 35, 205 (1988). 22. S.J. Pearton, C. R. Abernathy, C. B. Vartuli, J. C. Zolper, C. Yuan, and R. A. Stall, Appl. Phys. Lett. 67, 1435 (1995). 23. H. Kobayashi and W. M. Gibson, Appl. Phys. Lett. 73, 1406 (1998). 24. J.C. Zolper, R. G. Wilson, S. J. Pearton, and R. A. Stall, Appl. Phys. Lett. 68, 1945 (1996). 25. J. C. Zolper, J. Han, R. M. Biefeld, S. B. Van Deusen, W. R. Wampler, D. J. Reiger, S. J. Pearton, J. S. Williams, H. H. Tan, and R. Stall, J. Electron. Mater. 27, 179 (1998). 26. J. C. Zolper, D. J. Reiger, A. G. Baca, S. J. Pearton, J. W. Lee, and R. A. Stall, Appl. Phys. Lett. 69, 538 (1996). 27. M. Fu, V. Sarvepalli, R. K. Singh, C. R. Abernathy, X. A. Cao, S. J. Pearton, and J. A. Sekhar, Mater. Res. Soc. Symp. Proc. 483, 345 (1998). 28. X. A. Cao, C. R. Abernathy, R. K. Singh, S. J. Pearton, M. Fu, V. Sarvepalli, J. A. Sekhar, J. C. Zolper, D. J. Rieger, J. Han, T. J. Drummond, R. J. Shul, and R. G. Wilson, Appl. Phys. Lett. 73, 229 (1998). 29. M. S. Feng, J. D. Guo, and G. C. Chi, Proc. Electrochem. Soc. 95-21, 43 (1995). 30. C.C. Yi and B. W. Wessels, Appl. Phys. Lett. 69, 3206 (1996). 31. H. H. Tan, C. Jagadish, J. S. Williams, H. Zoa, D. J. H. Cockayne, and A. Sikorski, J. Appl. Phys. 77, 87 (1995). 32. J.C. Zolper, J. Han, S. B. Van Deusen, R. Biefeld, M. H. Crawford, J. Jun, T. Suski, J. M. Baranowski, and S. J. Pearton, Mater Res. Soc. Symp. Proc. 482, 618 (1998). 33. A.Y. Polyakov, M. Shin, M. Skowronski, R. G. Wilson, D. W. Greve, and S. J. Pearton, Solid-State Electron. 41,703 (1997). 34. J. C. Zolper, D. J. Rieger, A. G. Baca, S. J. Pearton, J. W. Lee, and R. A. Stall, Appl. Phys. Lett. 69, 538 (1996). 35. J.C. Zolper, M. H. Crawford, H. H. Tan, J. S. Williams, J. Zhou, D. J. H. Cockayne, S. J. Pearton, and R. E Karlicek, Jr., Appl. Phys. Lett. 70, 2729 (1997). 36. H. H. Tan, J. S. Williams, J. Zou, D. J. H. Cockayne, S. J. Pearton, and C. Yuan, J. Electrochem. Soc. 96-11,142 (1996). 37. H. Kobayashi and W. M. Gibson, Appl. Phys. Lett. 74, 2355 (1999). 38. P. Bogulawski, E. L. Briggs, and J. Bernholc, Phys. Rev. B 51, 17255 (1995). 39. C.R. Abernathy, J. D. MacKenzie, S. J. Pearton, and W. S. Hobson, Appl. Phys. Len. 66, 1969 (1995). 40. B. Mensching, C. Liu, B. Rauschenbach, K. Kornitzer, and W. Ritter, Mater Sci. Eng. B 50, 105 (1997). 41. J.S. Chan, N. W. Cheung, L. Schloss, E. Jones, W. S. Wong, N. Newman, X. Liu, E. R. Weber, A. Gassman, and M. D. Rubin, Appl. Phys. Lett. 68, 2702 (1996). 42. A. Pelzmann, S. Strite, A. Dommann, C. Kirchner, M. Kamp, K. J. Ebeling, and A. Nazzal, MRS Internet J. Nitride Semicond. Res. 2, 4 (1997). 43. S. Strite, A. Pelzmann, T. Suski, M. Leszczynski, J. Jun, A. Rockett, M. Kamp, and K. J. Ebeling, MRS Internet J. Nitride Semicond. Res. 2, 15 (1997). 44. E Bernardini, V. Fiorentini, and A. Bosin, Appl. Phys. Lett. 70, 2990 (1997).

ION IMPLANT DOPING 45. O. Brandt, H. Yang, H. Kostial, and K. Ploog, Appl. Phys. Lett. 69, 2707 (1996). 46. H. H. Tan, J. S. Williams, C. Yuan, and S. J. Pearton, Mater. Res. Soc. Symp. Proc. 395, 708 (1996). 47. H. H. Tan, J. S. Williams, J. Zou, D. J. H. Cockayne, S. J. Pearton, and R. A. Stall, Appl. Phys. Lett. 69, 2364 (1996). 48. C. Liu, B. Mecnsching, M. Zeitler, K. Volz, and B. Rauschenbach, Phys. Rev. B 57, 308 (1997). 49. C. Ronning, N. Dalmer, M. Deicher, M. Restle, M. D. Bremser, R. E Davis, and H. Hofsass, Mater. Res. Soc. Symp. Proc. 468, 407 (1997). 50. J.C. Zolper, M. H. Crawford, H. H. Tan, J. S. Williams, J. Zhou, D. J. H. Cockayne, S. J. Pearton, and R. E Karlicek, Jr., Appl. Phys. Lett. 70, 2729 (1997). 51. J.C. Zolper, in "GaN and Related Materials II" (S. J. Pearton, Ed.). Gordon and Breach, New York, 1998. 52. J. I. Pankove, E. A. Miller, and J. E. Berkeyheiser, "Luminescence of Crystals, Molecules and Solutions" (E Williams, Ed.), p. 426. Plenum, New York, 1973. 53. J. E Ziegler, J. P. Biersack, and U. Littmark, "The Stopping and Range of Ions in Solids," Vol. 1. Pergamon, New York, 1985. 54. S. Nakamura, M. Senoh, and T. Mukai, Appl. Phys. Lett. 62, 2390 (1993). 55. V. Swaminathan and A. T. Macrander, "Materials Aspects of GaAs and InP Based Structures." Prentice Hall, Englewood Cliffs, NJ, 1991. 56. D.E. Davies, Nucl. Instrum. Methods 7/8, 387 (1985). 57. K.G. Stevens, Nucl. Instrum. Methods 209/210, 589 (1983). 58. N. Nishi, T. Inada, and T. Saito, Japan. J. Appl. Phys. 122, 401 (1983). 59. J.D. Oberstar and B. G. Streetman, Thin Solid Films 103, 17 (1983). 60. B. Molnar, Appl. Phys. Lett. 36, 927 (1980). 61. C.A. Armiento and E C. Prince, Appl. Phys. Lett. 48, 1623 (1986). 62. S.J. Pearton and K. D. Cummings, J. Appl. Phys. 58, 1500 (1985). 63. R. T. Blunt, M. S. M. Lamb, and R. Szweda, Appl. Phys. Len. 47, 304 (1985). 64. A. Tamura, R. Uenoyama, K. Nishi, K. Inoue, and T. Onuma, J. Appl. Phys. 62, 1102 (1987). 65. T. E. Haynes, W. K. Chu, and S. T. Picraux, Appl. Phys. Lett. 50, 1071 (1987). 66. J.M. Woodall, H. Rupprecht, R. J. Chicotka, and G. Wicks, Appl. Phys. Lett. 38, 639 (1981). 67. S. Reynolds, D. W. Vook, W. C. Opyd, and J. E. Gibbons, Appl. Phys. Lett. 51,916 (1987). 68. W.H. Haydl, IEEE Electron. Device Lett. EDL-5, 78 (1984). 69. S.J. Pearton and R. Caruso, J. Appl. Phys. 66, 663 (1989). 70. S. Porowski and I. Grzegory, in "properties of Group III Nitrides" (J. Edgar, Ed.). INSPEC, London, 1994. 71. G.A. Slack and T. E McNelly, J. Cryst. Growth 34, 263 (1976). 72. J. Pastrnak and L. Roskovcova, Phys. Status Solidi 7, 331 (1964). 73. J.A. Van Vechten, Phys. Rev. B 7, 1479 (1973). 74. J. Karpinski, J. Jun, and S. Porowski, J. Cryst. Growth 66, 1 (1984). 75. J. R. Madar, G. Jacob, J. Hallais, and R. Fruchart, J. Cryst. Growth 31, 197 (1975). 76. C.D. Thurmond and R. A. Logan, J. Electrochem. Soc. 119, 622 (1972). 77. J. B. MacChesney, P. M. Bridenbaugh, and P. B. O'Connor, Mater. Res. Bull 5, 783 (1970). 78. R.D. Jones and K. Rose, J. Phys. Chem. Solids 48, 587 (1987). 79. A. M. Vorobev, G. V. Evseeva, and L. V. Zenkevich, Russian J. Phys. Chem. 47, 1616 (1973). 80. T. Matsuoka, H. Tanaka, T. Sasaki, and A. Katsui, Inst. Phys. Conf. Ser. 106, 141 (1990). 81. J. C. Zolper, M. Hagerott-Crawford, A. J. Howard, J. Rainer, and S. D. Hersee, Appl. Phys. Lett. 68, 200 (1996). 82. M. E. Lin, B. N. Sverdlov, and H. Morkoc, Appl. Phys. Lett. 63, 3625 (1993). 83. H. E Maruska andJ. J. Tietjen, Appl. Phys. Lett. 15, 327 (1969). 84. R. Groh, G. Gerey, L. Bartha, and J. I. Pankove, Phys. Status Solidi A 26, 363 (1974).

407

85. C.B. Vartuli, S. J. Pearton, C. R. Abernathy, J. D. MacKenzie, E. S. Lambers, and J. C. Zolper, J. Vac. Sci. Technol. B 14, 2761 (1996). 86. J. Karpinski, J. Jun, and S. Porowski, J. Cryst. Growth 66, 1 (1984). 87. J. C. Zolper, D. J. Rieger, A. G. Baca, S. J. Pearton, J. W. Lee, and R. A. Stall, AppL Phys. Lett. 69, 538 (1996). 88. J. R. Mileham, S. J. Pearton, C. R. Abernathy, J. D. MacKenzie, R. J. Shul, and S. P. Kilcoyne, Appl. Phys. Lett. 67, 1119 (1995). 89. T. Matsuoka, H. Tanaka, T. Susaki, and A. Kasui, Inst. Phys. Conf. Ser. 106, 141 (1990). 90. F. Roozeboom, in "Rapid Thermal Processing: Science and Technology" (R. B. Fair, Ed.), pp. 349-423. Academic Press, New York, 1993. 91. J.A. Sekhar, S. Penumella, and M. Fu, in "Transient Thermal Processing Techniques in Electronic Materials" (N. M. Ravindra and R. K. Singh, Eds.), pp. 171-175. TMS, Warrendale, PA, 1996. 92. S.J. Pearton, Internat. J. Mod. Phys. B 7, 4687 (1993). 93. J. Brown, J. Ramer, K. Zheng, L. F. Lester, S. D. Hersee, and J. C. Zolper, Mater. Res. Soc. Symp. Proc. 395, 702 (1996). 94. J.C. Zolper, J. Han, S. B. Van Deusen, R. Biefeld, M. H. Crawford, J. Jun, T. Suski, J. M. Baranowski, and S. J. Pearton, Mater Res. Soc. Symp. Proc. 482, 618 (1998). 95. J.A. Van Vechten, Phys. Rev. B 7, 1479 (1973). 96. J. Karpinski, J. Jun, and S. Porowski, J. Cryst. Growth 66, 1 (1984). 97. B.-C. Chung and M. Gershenzon, J. Appl. Phys. 72, 651 (1992). 98. M.D. Deal and H. G. Robinson, Appl. Phys. Lett. 55, 1990 (1989). 99. H.G. Robinson, M. D. Deal, and D. A. Stevenson, Appl. Phys. Lett. 58, 2000 (1991). 100. M. D. Deal, C. J. Hu, C. C. Lee, and H. G. Robinson, Mater Res. Soc. Symp. Proc. 300, 365 (1993). 101. H.G. Robinson, M. D. Deal, P. B. Griffin, G. Amaratunga, P. B. Griffin, D. A. Stevenson, and J. D. Plummer, J. Appl. Phys. 71, 2615 (1992). 102. S.J. Pearton and C. R. Abernathy, A ppl. Phys. Lett. 55, 678 (1989). 103. M. S. Feng, J. D. Guo, and G. C. Chi, Proc. Electrochem. Soc. 95-21, 43 (1995). 104. F. Ren, M. Hong, S. N. G. Chu, M. A. Marcus, M. J. Schurmann, A. Baca, S. J. Pearton, and C. R. Abemathy, Appl. Phys. Lett. 73, 3893 (1998). 105. M. Suzuki, T. Kawakami, T. Arai, S. Kobayashi, Y. Koide, T. Uemura, N. Shibata, and M. Murakami, Appl. Phys. Lett. 74, 275 (1999). 106. T. Suski, J. Jun, M. Leszczynski, H. Teisseyre, I. Grzegory, S. Porowski, J. M. Baranowski, A. Rockett, S. Strite, A. Stanert, A. Turos, H. H. Tan, J. S. Williams, and C. Jagadish, Mater Res. Soc. Symp. Proc. 482, 703 (1998). 107. S. Strite, P. W. Epperlein, A. Dommann, A. Rockett, and R. F. Broom, Mater. Res. Soc. Symp. Proc. 395,795 (1996). 108. J. Hong, J. W. Lee, C. B. Vartuli, J. D. MacKenzie, S. M. Donovan, C. R. Abernathy, R. Crockett, S. J. Pearton, J. C. Zolper, and F. Ren, Solid-State Electron. 41, 681 (1997). 109. J. Hong, J. W. Lee, C. B. Vartuli, C. R. Abernathy, J. D. MacKenzie, S. M. Donovan, S. J. Pearton, and J. C. Zolper, J. Vac. Sci. TechnoL A 15, 797 (1997). 110. J. Hong, J. W. Lee, J. D. MacKenzie, S. M. Donovan, C. R. Abernathy, S. J. Pearton, and J. C. Zolper, Semicond. Sci. Technol. 12, 1310 (1997). 111. S.J. Pearton, Mater Sci. Rep. 4, 313 (1990). 112. M. Orenstein, N. G. Stoffel, A. C. Von Lehmen, J. P. Harbison, and L. T. Florez, Appl. Phys. Lett. 59, 31 (1991). 113. K.L. Lear, R. P. Schneider, K. D. Choquette, S. P. Kilcoyne, J. J. Figiel, and J. C. Zolper, IEEE Photon. Tech. Lett. 6, 1053 (1994). 114. J.C. Zolper, A. G. Baca, and S. A. Chalmers, Appl. Phys. Lett. 62, 2536 (1993). 115. S.J. Pearton, M. P. Iannuzzi, C. L. Reynolds, Jr., and L. Peticolas, Appl. Phys. Lett. 52, 395 (1988). 116. J.C. Zolper, M. E. Sherwin, A. G. Baca, and R. P. Schneider, Jr., J. Electron. Mater. 24, 21 (1995). 117. D. Haase, M. Schmid, W. Kumer, A. Dornen, V. Harle, F. Scholz, M. Burkard, and H. Schweizer, Appl. Phys. Lett. 69, 2525 (1996). 118. A. Rebey, T. Boufaden, and B. E1Jani, J. Cryst. Growth 203, 12 (1999). 119. C. J. Sun, P. Kung, A. Saxler, H. Ohsato, E. Bigan, M. Razeghi, and D. K. Gaskill, J. Appl. Phys. 76, 236 (1994).

408

PEARTON

120. H. Tanaka and A. Nakadaira, J. Cryst. Growth 189/190, 730 (1998). 121. J. Han, T. B. Ng, R. M. Biefeld, M. H. Crawford, and D. M. FoUstaedt, Appl. Phys. Lett. 71, 3114 (1997). 122. Y. Kobayashi and N. Kobayashi, J. Cryst. Growth 189/190, 301 (1998). 123. S.J. Pearton, C. R. Abemathy, E W. Wisk, W. S. Hobson, and E Ren, Appl. Phys. Lett. 63, 1143 (1993). 124. J.C. Zolper, S. J. Pearton, C. R. Abemathy, and C. B. Vartuli, Appl. Phys. Lett. 66, 3042 (1995).

125. S.J. Pearton, C. R. Abemathy, M. B. Panish, R. A. Hamm, and L. M. Lunarfft, J. Appl. Phys. 66, 656 (1989). 126. J.C. Zolper, S. J. Pearton, C. R. Abemathy, and C. B. Vartuli, Mater Res. Soc. Syrup. Proc. 378, 408 (1995). 127. G. Harrington, Y. Hsin, Q. Z. Liu, P. M. Asbeck, S. S. Lau, M. A. Khan, J. W. Yang, and Q. Chen, Electron. Lett. 34, 193 (1998).

Chapter 8

PLASMA ETCHING OF GaN AND RELATED MATERIALS S. J. Pearton Department of Materials Science and Engineering, University of Florida, Gainesville, Florida, USA R. J. Shul Sandia National Laboratories, Albuquerque, New Mexico, USA Contents 1. 2.

3.

4. 5.

6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasma Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Reactive Ion Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. High-Density Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Chemically Assisted Ion Beam Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Reactive Ion Beam Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Low-Energy Electron-Enhanced Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasma Chemistries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. C12-Based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. 12- and Br2-Based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. CH4/H2/Ar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Etch Profile And Etched Surface Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasma-Induced Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. n-GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. p - G a N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Schottky Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. p-n Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Device Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Microdisk Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Ridge Waveguide Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Heterojunction Bipolar Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Field Effect Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. UV Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

409 410 410 410 412 412 412 413 413 418 422 424 425 426 430 434 438 441 441 441 443 446 448 450 450

as heterostructure field effect transistors (FETs), heterojunction bipolar transistors (HBTs), metal oxide semiconductor field effect transistors (MOSFETs), and diode rectifiers have all been realized in the A1GalnN system, with very promising hightemperature (>300~ and high-voltage performance. The applications for the emitter devices lies in full color displays, optical data storage, white-light sources, and covert communications, and electronic devices are suited to high-power switches and microwave power generation.

1. INTRODUCTION

GaN and related alloys are being used in applications such as fabrication of blue/greenAlV emitters (light-emitting diodes and lasers) and high-temperature, high-power electronic devices [ 1-15]. The emitter technology is relatively mature: lightemitting diodes have been commercially available since 1994, and blue laser diodes are also available. Electronic devices such

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

409

410

PEARTON AND SHUL

Because of limited wet chemical etch results for the group III nitrides, a significant amount of effort has been devoted to the development of dry etch processing [16-20]. Dry etch development was initially focused on mesa structures in which high etch rates, anisotropic profiles, smooth sidewalls, and equirate etching of dissimilar materials were required. For example, commercially available LEDs and laser facets for GaN-based laser diodes were patterned with the use of reactive ion etch (RIE). However, as interest in high-power, high-temperature electronics [21-24] increased, etch requirements expanded to include smooth surface morphology, low plasma-induced damage, and selective etching of one layer rather than. Dry etch development is further complicated by the inert chemical nature and strong bond energies of the group III nitrides as compared with other compound semiconductors. GaN has a bond energy of 8.92 eV/atom, InN a bond energy of 7.72 eV/atom, and A1N a bond energy of 11.52 eV/atom [25].

2. PLASMA REACTORS Dry plasma etching has become the dominant patterning technique for the group III nitrides, because of the shortcomings of wet chemical etching. Plasma etching proceeds by physical sputtering, chemical reaction, or a combination of the two, often referred to as ion-assisted plasma etching. Physical sputtering is dominated by the acceleration of energetic ions formed in the plasma to the substrate surface at relatively high energies, typically > 200 eV. Because of the transfer of energy and momentum to the substrate, material is ejected from the surface. This sputter mechanism tends to yield anisotropic profiles; however, it can result in significant damage, rough surface morphology, trenching, poor selectivity, and nonstoichiometric surfaces, thus minimizing device performance. Pearton and co-workers measured sputter rates for GaN, InN, A1N, and InGaN as a function of Ar + ion energy [26]. The sputter rates increased with ion energy but were quite slow, 500 A/min at - 4 0 0 V. Lin et al. reported similar results for GaN in BC13 and SIC14 plasmas with etch rates of 1050 ,~/min in BC13 at 150-W cathode (area 250 in 2) rf power [27]. Additional RIE results have been reported for HBr- [28], CHF3-, and CC12F2-based [29] plasmas with typical etch rates of

[]

H2

9

N2

133

(3-2 .

0

I

,

50

I

,

100

I

,

150

I

,

200

I

250

i

-4

300

-6

-4

-2

0

2

Voltage (V)

rf Power (W) 350 5

~

control

4 ~-" 250 (/) o...

rn m 2

to "13 t,i,-

"~ 150 oO

~

/x

N2

I

50

.

0

I

50

,

l

i

100

I

150

,

I

200

,

I

I

250

300

rf Power (W) Fig. 35. Variation of VB in GaN diodes (top) and dc chuck self-bias (bottom) as a function of rf chuck power in H2 or N2 plasmas (500 W source power, 5 mTorr).

by a transition to a stoichiometric but point defect-compensated region, and finally to unperturbed InP. The fact that plasma exposure severely degraded the surface is clear from the AFM data of Figure 37. Exposure to a source power of 500 W, a rf chuck power of 150 W (dc selfbias -221 V), and 5-mTorr N2 discharge increased the rms surface roughness from 0.8 to 4.2 nm. Subsequent photoelectrochemical etching restored the initial morphology. However, we observed the onset of increasingly rough surfaces for deeper etch depths [91], reducing a relatively inaccurate measure of how much of the surface had to be removed to restore the diode breakdown voltage to its original value. We were able to estimate this depth as ~600 + 150 A for the N2 plasma conditions mentioned above. Another method for trying to restore the electrical properties of the plasma-exposed surface is annealing. Figure 37 also shows AFM scan from samples after annealing at 550~ or 750~ with no significant change in rms values. I - V data from annealed samples are shown in Figure 38. At the top are characteristics from samples that were plasma exposed (N2, 500 W source power, 150 W rf chuck power, 5 mTorr) and then annealed and in which the contact was deposited. These samples

.

0

I

50

.

I

100

,

I

150

.,

I

200

,

I

250

,

300

Depth Removed (A) Fig. 36. I - V characteristics from N2 plasma-exposed GaN diodes before and after wet etch removal of different amounts of GaN before deposition of the Schottky contact (top) and variation of VB as a function of the amount of material removed (bottom).

show that increasing the annealing temperature to 750~ brings a substantial improvement in VB (Fig. 38, bottom). However, for annealing at 850~ the diode began to degrade, and this is consistent with the temperature at which N2 begins to be lost from the surface. In the case where the samples were exposed to the N2 plasma, and then the Pt/Au contact was deposited before annealing, the I - V characteristics show continued worsening upon annealing (Fig. 38, center). In this case, the Pt/Au contact is stable to 700~ on unetched samples. The poorer stability in etched samples could be related to the surface damage enhancing interfacial reaction between the Pt and GaN. The main findings of this study can be summarized as follows: 1. There is a severe degradation in the electrical quality of GaN surfaces after ICP H2 or N2 discharge exposure. Under all conditions there is a strong reduction of VB in diode structures to the point at which the Schottky contacts show almost ohmic-like behavior. These observations are consistent with the creation of a conducting n-type surface layer resulting from energetic ion bombardment. Heavier ions (N~-) create

430

PEARTON AND SHUL

9 o

control as-exposed 350oc 550~ ~C 750oC 850

A

0

< E

9

o

c o L_

o~

-2

-4 '-6

-4

-2

0

2

Voltage (V)

9 a A v

0

< E

control as-exposed 300 ~ 500 ~

r o L_

0

-4 - 10

-8

-6

-4

-2

0

2

Voltage (V) i

.

Fig. 37. AFM scans before and after N 2 plasma exposure (500 W source power, 150 W rf chuck power, 5 mTorr) and subsequent annealing or photochemical etching.

.

.

.

.

.

.

.

.

.

.

.

.

i

.

.

.

.

.

.

4 >3 m

more damage than lighter ions (H +) in this situation, where damage accumulates without any concurrent etching of the surface. 2. The depth of the damage is approximately 600 A, as judged by the return of the diode characteristics to their control values. 3. Annealing at 750~ is also effective in helping to remove the effects of plasma exposure. Higher temperatures lead to degradation in GaN diode properties for uncapped anneals.

5.2.

>

2

1 300

, ~

I 500

,

I 700

,, 900

Annealing T e m p e r a t u r e (~ Fig. 38. I - V characteristics from GaN diodes before and after N2 plasma exposure (500 W source power, 150 W rf chuck power, 5 mTorr) and subsequent annealing either before (top) or after (center) the deposition of the Schottky metallization. The variation of VB in the samples annealed before metal deposition is shown at the bottom of the figure.

p-GaN

The layer structure consisted of 1 /xm of undoped GaN (n 5 x 1016 cm -3) grown on a c-plane A1203 substrate, followed by 0.3 /zm of Mg doped (p ,~ 1017 cm -3) GaN. The samples were grown by rf plasma-assisted molecular beam epitaxy. Ohmic contacts were formed with Ni/Au deposited by e-beam evaporation, followed by lift-off and annealing at 750~ The GaN surface was then exposed for 1 min to ICP H2 or Ar plasmas in a Plasma-Therm 790 System. The 2-MHz ICP source power was varied from 300 to 1400 W, and the 13.56 MHz

rf chuck power was varied from 20 to 250 W. The former parameter controls ion flux incident on the sample, and the latter controls the average ion energy. Before to deposition of 250-#m-diameter Ti/Pt/Au contacts through a stencil mask, the plasma-exposed surfaces were either annealed under N2 in a rapid thermal annealing system or immersed in boiling NaOH solutions to remove part of the surface. As reported previously, it is possible to etch damaged GaN in a self-limiting fashion in hot alkali or acid solutions. The current-voltage (l-V) charac-

PLASMA ETCHING OF GaN AND RELATED MATERIALS

431

Fig. 39. Schematicof p-GaN Schottky diode structures.

Fig. 41. Variationof diode breakdown voltage in samples exposed to H2 or Ar ICP discharges (150 W rf chuck power) at different ICP source powers before deposition of the Ti/Pt/Au contact. The dc chuck self-bias during plasma exposure is also shown.

Fig. 40. I-V characteristics from samples exposed to either H2 (top) or Ar (bottom) ICP discharges (150 W rf chuck power) as a function of ICP source power before deposition of the Ti/Pt/Au contact.

teristics of the diodes were recorded on an HP 4145A parameter analyzer. A schematic of the final test structures is shown in Figure 39. The unetched control diodes have reverse breakdown

voltages of ~ 2 . 5 - 4 V, depending on the wafer--these values were uniform (4-12%) across a particular water. Figure 40 shows the I - V characteristics from samples exposed to either H2 (top) or Ar (bottom) ICP discharges (150 W rf chuck, 2 mTorr) as a function of source power. In both cases there is an increase in both the reverse breakdown voltage and the forward turn-on voltage, with these parameters increasing monotonically with the source power during plasma exposure. Figure 41 shows this increase in breakdown voltage as a function of source power and the variation of the chuck dc selfbias. As the source power increases, the ion density also increases and the higher plasma conductivity suppresses the developed dc bias. Note that the breakdown voltage of the diodes continues to increase even as this bias (and hence ion energy, which is the sum of this bias and the plasma potential) decreases. These results show that ion flux lays an important role in the change of diode electrical properties. The other key result is that Ar leads to a consistently greater increase in breakdown voltage, indicating that ion mass, rather than any chemical effect related to removal of N2 or NH3 in the H2 discharges, is important. The increase in breakdown voltage on the p-GaN is due to a decrease in hole concentration in the near-surface region through the creation of shallow donor states. The key question is whether there is actually conversion to an n-type surface under any of the plasma conditions. Figure 42 shows the forward turn-on characteristics of the p-GaN diodes exposed to different source power Ar discharge at low source power (300 W); the turn-on remains close to that of the unexposed control sample. However, there is a clear increase in the turn-on voltage at higher source powers, and in fact at >750 W the characteristics

432

PEARTON AND SHUL

Fig. 42. Forward turn-on characteristics of diodes exposed to ICP Ar discharges (150 W rf chuck power) at different ICP source powers before deposition of the Ti/Pt/Au contact.

are those of an n - p junction. Under these conditions the concentration of plasma-induced shallow donors exceeds the hole concentration, and there is surface conversion. In other words, the metal-p-GaN diode has become a metal-n-GaN-p-GaN junction. We always find that plasma-exposed GaN surfaces are N2-deficient relative to their unexposed state, and therefore the obvious conclusion is that nitrogen vacancies create shallow donor levels. This is consistent with thermal annealing experiments in which N2 loss from the surface produced increased n-type conduction. The influence of rf chuck power on the diode I - V characteristics is shown in Figure 43 for both H2 and Ar discharges at a fixed source power (500 W). A trend similar to that for the source power experiments is observed, namely the reverse breakdown voltage increases, consistent with a reduction in p-doping level near the GaN surface. Figure 44 plots breakdown voltage and dc chuck self-bias as a function of the applied rf chuck power. The breakdown voltage initially increases rapidly with ion energy (the self-bias plus ~25-V plasma potential) and saturates above ~ 100 W, probably because the sputtering yield increases and some of the damaged region is removed. Note that these are very large changes in breakdown voltage even for low ion energies, emphasizing the need to carefully control both flux and energy. We should also point out that our experiments represent worst-case scenarios, because with real etching plasma chemistries such as C12/Ar, the damaged region would be much shallower, because of the much higher etch rate. As an example, the sputter rate of GaN in a 300-W source power, 40-W rf chuck power, Ar ICP discharge is ~,40 t~ whereas the etch rate in a C12/Ar discharge under the same conditions is ~ 1100/~/min. An important question is the depth of the plasma-induced damage. We found that we were able to etch p-GaN very slowly

Fig. 43. I-V characteristics from samples exposed to either H2 (top) or Ar (bottom) ICP discharges (500 W source power) as a function of rf chuck power before deposition of the Ti/Pt/Au contact.

in boiling NaOH solutions, at rates that depended on the solution molarity (Fig. 45), even without any plasma exposure of the material. This enabled us to directly measure the damage depth in plasma-exposed samples in two different ways. The first method involved measuring the etch rate as a function of depth from the surface. Defective GaN resulting from plasma, thermal, or implant damage can be wet chemically etched at rates much faster than those for undamaged material, because the acid or base solutions are able to attack the broken or strained bonds present. Figure 46 shows the GaN etch rate as a function of depth in samples exposed to a 750-W source power, 150-W rf chuck power Ar discharge. The etch rate is a strong function of the depth from the surface and saturates between ~--425 and 550 A. Within this depth range the etch rate is returned to the "bulk" value characteristic of undamaged p-GaN. The second method of establishing the damage depth, of course, is simply to measure the I - V characteristics after different amounts of material are removed by wet etching before de-

PLASMA ETCHING OF GaN AND RELATED MATERIALS

Fig. 44. Variationof diode breakdown voltage in samples exposed to H2 or Ar ICP discharges (500 W source power) at different rf chuck powers before deposition of the Ti/Pt/Au contact. The dc chuck self-bias during plasma exposure is also shown.

433

Fig. 46. Wet etching rate of Ar plasma-exposed (750 W source power, 150 W rf chuck power) GaN as a function of depth in the sample.

Fig. 45. Wet etching rate of p-GaN in boiling NaOH solutions as a function of solution molarity.

position of the rectifying contact. Figure 47 (top) shows the I - V characteristics from samples exposed to 7 5 0 - W source power, 150-W rf chuck power ( - 1 6 0 V dc chuck bias) Ar discharges and subsequently wet etched to different depths with the use of 0.1 M N a O H solutions before deposition of the Ti/Pt]Au contact. Figure 47 (bottom) shows the effect of the amount of material r e m o v e d at the diode b r e a k d o w n voltage. Within the experimental error of + 1 2 % , the initial b r e a k d o w n voltage is reestablished in the range of 4 0 0 - 4 5 0 / ~ . This is consistent with the depth obtained from the etch rate experiments described above. These values are also consistent with the d a m a g e depths

Fig. 47. I-V characteristics from samples exposed to ICP Ar discharges (750 W source power, 150 W rf chuck power) and subsequently wet etched to different depths before deposition of the Ti/Pt/Au contact (top) and breakdown voltage as a function of depth removed (bottom).

434

PEARTON AND SHUL damage site density is larger than that needed to trap all of the free carriers, and trapped electrons or holes may move by hopping conduction. Annealing at higher temperatures removes some of the damage sites, but there are still enough to trap all of the conduction electrons/holes. Under these conditions the hopping conduction is reduced and the sample sheet resistance actually increases. At still higher annealing temperatures, the trap density falls below the conduction electron or hole concentration, and the latter are returned to their respective bands. Under these conditions the sample sheet resistance returns to its preimplanted value. The difference in the plasma-exposed samples is that the incident ion energy is a few hundred electron volts, compared with a few hundred kiloelectron volts in implant-isolated material. In the former case the main electrically active defects produced are nitrogen vacancies near the surface, whereas in the latter case there are vacancy and interstitial complexes produced in far greater numbers to far greater depths. In our previous work on plasma damage in n-GaN we found that annealing at ~750~ almost returned the electrical properties to their initial values. If the same defects are present in both n- and p-type material after plasma exposure, this difference in annealing temperature may be a result of a Fermilevel dependence of the annealing mechanism. The main conclusions of this study may be summarized as follows:

Fig. 48. I - V characteristics from samples exposed to ICP Ar discharges (750 W source power, 150 W rf chuck power) and subsequently annealed at different temperatures before deposition of the Ti/Pt/Au contact (top) and breakdown voltage as a function of annealing temperature (bottom).

we established in n-GaN diodes exposed to similar plasma conditions. The other method of removing plasma-induced damage is annealing. In these experiments we exposed the samples to the same type of plasma (Ar, 750-W source power, 150-W rf chuck power) and then annealed under N2 at different temperatures. Figure 48 (top) shows the I - V characteristics of these different samples and (bottom) the resulting breakdown voltages as a function of annealing temperature. On this wafer, plasma exposure caused an increase in breakdown voltage from ~2.5 to ~ 18 V. Subsequent annealing at 400~ initially decreased the breakdown voltage, but a higher temperature produced a large increase. At temperatures above 700~ the diode characteristics returned to their initial values and were back to the control values by 900~ This behavior is similar to that observed in implant-isolated compound semiconductors in which ion damage compensates for the initial doping in the material, producing higher sheet resistance. In many instances the

1. The effect of either H2 or Ar plasma exposure on p-GaN surfaces is to decrease the net acceptor concentration through the creation of shallow donor levels, most likely Nv. At high ion fluxes or ion energies there can be type conversion of the initially p-type surface. The change in electrical properties is more pronounced with Ar than with H2 plasmas under the same conditions. 2. Two different techniques for measuring the damage depth find it to be in the range of 400-500 A under our conditions. After the removed of this amount of GaN, both the breakdown voltage and wet chemical etch rates are returned to their initial values. 3. Postetch annealing in N2 at 900~ restores the initial breakdown voltage on plasma-exposed p-GaN. Annealing at higher temperatures degraded the electrical properties, again most likely because of N2 loss from the surface.

5.3. Schottky Diodes Contrary to initial expectations, the surface of GaN is relatively sensitive to energetic ion bombardment or thermal degradation encountered during device processing. In particular, it can preferentially lose N2, leaving strong n-type conducting regions. Whereas dry etching has been used extensively for patterning of photonic devices (light-emitting and laser diodes) and opto-electronic devices (UV detectors), there has been little work performed on understanding the electrical effects of ion-induced point defects or nonstoichiometric surfaces result-

PLASMA ETCHING OF GaN AND RELATED MATERIALS

Fig. 49.

435

Schematic of n- and p-GaN diode structures.

ing from the plasma exposure. Several groups have reported increases in the sheet resistance of GaN exposed to high-density plasmas, along with decreases in reverse breakdown voltage (VB) and reductions in Schottky barrier height (t~B) in diodes formed on n-type GaN. In this latter case, low-bias forward currents were increased by up to 2 orders of magnitude after exposure of the diode to pure Ar discharges. Conversely, whereas the rectifying contact properties were degraded by plasma exposure, the specific resistance of n-type ohmic contacts was improved. Similarly, in p-type GaN, the effect of Ar or H2 highdensity plasma exposure was to decrease the net acceptor concentration to depths of ~500 ~. At high ion fluxes or energies, there was type conversion of the initially p-GaN surface. Dry etching is needed for a range of GaN electronic devices, including mesa diodes, rectifiers, thyristors, and HBTs for hightemperature, high-power operation. These applications include control of power flow in utility grids, radar, and electronic motor drives. It is critical to understand the depth and thermal stability of dry etch damage in both n- and p-type GaN and its effect on the current-voltage (I-V) characteristics of simple diode structures. In this section we report on a comparison of the effects of C12/Ar and Ar ICP exposure on the electrical properties of nand p-GaN Schottky diodes. In some cases it was found that C12/Ar discharges could produce even more damage than pure Ar, because of the slightly higher ion energies involved. The damage saturates after a short exposure to either C12/Art or Ar discharges and is significant even for low ion energies. Annealing between 700~ and 800~ restored >70% of the reverse breakdown voltage on n-GaN, and the damage depth was again established to be "-~500/~ in p-GaN. The diode structures are shown schematically in Figure 49. The GaN layers were grown by rf plasma-assisted molecular beam epitaxy on c-plane A1203 substrates. The Ti/A1 (for n-type) and Ni/Au (for p-type) ohmic contacts were patterned by liftoff and annealed at 750~ The samples were exposed

Fig. 50. I - V characteristics from n-GaN samples exposed to ICP C12/Ar (top) or Ar (bottom) discharges (500 W source power) as a function of rf chuck power before deposition of the rectifying contact.

to either 10C12/5Ar or 15Ar (where the numbers denote the gas flow rate in standard cubic centimeters per minute) ICP discharges in a Plasma-Therm ICP reactor at a fixed pressure of 3 mTorr. We investigated a range of rf chuck powers (25250 W) and etch times (4-100 s), with a fixed source power of 500 W. In some cases, the samples were either annealed in N2 for 30 s at 500-800~ or wet etched in 0.1 M NaOH solutions at --~100~ after plasma exposure. The Schottky metallization (Pt/Au in both cases) was then deposited through a stencil mask (4~ = 70 or 90/zm) by e-beam evaporation. Current-voltage characteristics were recorded on an HP 4145A parameter analyzer, and we defined the reverse breakdown voltage as that at which the leakage current was 10 -3 A. The forward on-voltage (VF) was defined as the voltage at which the forward current was 100 A cm -2. In all cases the ideality factors increased from 1.3 to 1.6 on control samples to > 2 after plasma exposure, and thus we were unable to extract meaningful values of either bartier height or ideality factor. Figure 50 shows a series of I-V characteristics from n-type GaN diodes fabricated on samples exposed to either C12/Ar

436

PEARTON AND SHUL

Fig. 51. Variationsof VBand VF(top) and of n-GaN etching rate (bottom) as a function of rf chuck power for n-GaN diodes exposedto ICP C12/Ardischarges (500 W source power).

(top) or Ar (bottom) discharges at different rf chuck powers. There is a significant reduction in VB under all conditions, with Ar producing less damage at low chuck powers. This is probably related to two factors: the slightly higher chuck bias with CI2/Ar due to the lower positive ion density in the plasma (C1 is more electronegative than Ar) and the heavier mass of the C1+ ions compared with Ar +. This is consistent with our past data on the relative effects of N2 and H2 plasma exposure, in which ion mass was found to be more important in influencing the electrical properties of the GaN surface than any chemical effects. The variations of VB and VF with the rf chuck power during plasma exposure are shown in Figure 51 (top). At powers of < 100 W, the CI2/Ar creates more degradation of VB, as discussed above, whereas at higher powers the damage saturates. The average ion energy is the sum of dc self-bias (shown at the bottom of the figure) and plasma potential (which is about 2225 eV under these conditions). Thus for ion energies less than ~150 eV, Ar produces less damage than C12/Ar, even though

Fig. 52. I-V characteristics fromn-GaN samples exposed to ICP C12/Ar(top) or Ar (bottom) discharges (150 W rf chuck power, 500 W source power) as a function of plasma exposure time before deposition of the rectifying contact.

the etch rate with the latter is much higher. This is also reflected in the variation of VF with rf chuck power. Figure 52 shows a series of I - V characteristics from n-type GaN diodes fabricated on samples exposed to the two different plasmas for different times at fixed rf chuck power (150 W) and source power (500 W). It is clear that the damage accumulates rapidly, with the I - V characteristics becoming linear at longer times. It should be remembered that this is damage accumulating ahead of the etch front. Figure 53 shows the variations in VB and VF in n-type diodes with plasma exposure time to 500-W source power, 150-W rf chuck power C12/Ar or Ar discharges (top), together with the etch depth versus etch time (bottom). As is readily apparent, VB decreases dramatically after even short plasma exposures and then tends to recover slightly up to ~25 s. The VB values are < 1 V for basically all plasma exposure times for both C12/Ar and Ar. For VF, there was more degradation with CI2/Ar for short exposure times.

PLASMA ETCHING OF GaN AND RELATED MATERIALS

Fig. 53. Variationof VB and VF (top) and of n-GaN etch depth (bottom) as a function of plasma exposure time for n-GaN diodes exposed to ICP C12/Ar discharges (500 W source power, 150 W rf chuck power).

To examine the thermal stability of the etch damage, n-type samples were exposed to Ar or C12/Ar discharges at a fixed source power (500 W) and rf chuck power (150 W rf) and then annealed at different temperatures before deposition of the rectifying contact. Figure 54 shows I - V characteristics from control, plasma-exposed, and annealed diodes. The annealing produces a significant recovery of the electrical properties for samples exposed to either type of plasma. The VB values are shown in Figure 55, as a function of post-plasma exposure annealing temperature. Annealing temperatures between 700~ and 800~ restore more than 70% of the original VB value, but clearly annealing alone cannot remove all of the dry etchinduced damage. Annealing temperatures above 800~ were found to lead to preferential loss of N2 from the surface, with a concurrent degradation in VB. Turning to p-GaN diodes, Figure 56 shows I - V characteristics from samples that were wet etched to various depths in NaOH solutions after exposure to either C12/Ar or Ar discharges (500-W source power, 150-W rf chuck power, 1 min). For these plasma conditions we did not observe type conversion

437

Fig. 54. I-V characteristics from n-GaN samples exposed to ICP C12/Ar(top) or Ar (bottom) discharges (500 W source power, 100 W rf chuck power) as a function of annealing temperature before deposition of the rectifying contact.

of the surface. However, we find that the damaged GaN can be effectively removed by immersion in hot NaOH, without the need for photo- or electrochemical assistance of the etching. The VB values increase on p-GaN after plasma exposure because of introduction of shallow donor states that reduce the wet acceptor concentration. Figure 57 shows two methods for determining the depth of the damaged region in p-GaN diodes. At the top is a plot of the variation of VF and VB with the depth of material removed by NaOH etching. The values of both parameters are returned to their control values by depths of 500-600 A. What is clear from these data is that the immediate surface is not where the p-doping concentration is most affected, because the maximum values peak at depths of 300-400 ,~,. This suggests that Nv or other compensating defects created at the surface diffuse rapidly into this region, even near room temperature. This is consistent with results in other semiconductors, where damage depths are typically found to be many times deeper than the projected range of incident ions. The bottom part of Fig-

438

PEARTON AND SHUL

Fig. 55. Variation of VB in n-GaN diodes exposed to ICP C12/Ar or Ar discharges (500 W source power, 100 W rf chuck power) with annealing temperature before deposition of the rectifying contact.

ure 57 shows the wet etch depth in plasma-damaged p-GaN as a function of etching time. The etch depth saturates at depths of 500-600/~, consistent with the electrical data. It has previously been shown that the wet etch depth on thermally or iondamaged GaN was self-limiting. This is most likely a result of the fact that defective or broken bonds in the material are readily attached by the acid or base, whereas in undamaged GaN the etch rate is negligible. The main findings of our study may be summarized as follows: 1. Large changes in VB and VF of n- and p-GaN Schottky diodes were observed after exposure to both C12/Ar and Ar ICP discharges. In some cases the electrical properties are more degraded with C12/Ar, even though this plasma chemistry has a much higher etch rate. 2. The damage accumulates near the surface, even for very short exposure times (4 s). The damage depth was established to be 500-600/~ from both the changes in electrical properties and the depth dependence of the wet etch rate. 3. Annealing in the range 700-800~ partially restores VB in n-GaN diodes, but full recovery can only be achieved with an additional wet etch step for removal of the damaged material. The combination of annealing and a wet etch clean-up step looks very promising for GaN device fabrication.

5.4. p - n Junctions Layer structures were grown by metal organic chemical vapor deposition (MOCVD) on c-plane AleO3 substrates at 1040~ The structure consisted of a low-temperature (530~ GaN

Fig. 56. I - V characteristics from p-GaN samples exposed to ICP C12/Ar (top) or Ar (bottom) discharges (500 W source power, 150 W rf chuck power) and wet etched in boiling NaOH to different depths before deposition of the rectifying contact.

buffer, 1.2 # m of n (2 • 1017 cm -3, Si-doped) GaN, 0.5/zm of nominally undoped (n ~ 1016 cm -3) GaN, and 1.0/zm of p (NA ~ 5 • 1019 cm -3, Mg-doped) GaN. The p-ohmic metal (Ni/Au) was deposited by e-beam evaporation and liftoff and then alloyed at 750~ A mesa was then formed by BC13/C12/Ar (8/32/5 standard cm 3) ICP etching to a depth of 1.6/zm under different plasma conditions to examine the effect of ion energy and ion flux, respectively. The ICP reactor was a load-locked Plasma-Therm SLR 770, which used a 2-MHz, three-turn coil ICP source. All samples were mounted with a thermally conductive paste on an anodized A1 carrier that was clamped to the cathode and cooled with He gas. The ion energy or dc bias was defined by superimposing a rf bias (13.56 MHz) on the sample. The n-type ohmic metallization (Ti/A1) was then deposited, to produce the structure shown in Figure 58. Reverse I - V measurements were made on 300-/zm-diameter diodes with a HP 4145B semiconductor parameter analyzer. In this study the reverse leakage current was measured at a bias of - 3 0 V. Etch

PLASMA ETCHING OF GaN AND RELATED MATERIALS 10

20

439

1000

7000 - ~ R e v e ~ e Leakage -B- EtchRate

8

6OO0

100

15

5000 .m

~'~,

6

10 ~'~ 3000~

r

:rr,c,=l,-

4 .control !vF)" . l ~

5

,m

>

2000 ~ 0.1 1000

2

i.. 0

,

I . I . 200 400 Depth Removed (A)

i 600

0 0.01

t

I

t

I

1

t

~

50

100

150

200

250

300

350

0

400

dc-Bias (-Vt 103

9 9

Fig. 59. Reverse leakage current measured at - 3 0 V for GaN p-i-n junctions etched in ICP 32C12/8BC13/5Ar discharges (500 W source power, 2 mTorr), as a function of dc chuck self-bias.

Arexposed Ar/CI 2 etched

t-'. Q. ll)

a

tO

,,IN=.

UJ

0.1 M boiling NaOH

10 2

.

9 ....I

.

101

.

.

.....I

102Etching Time (s)

i

i

9 .

*..,

103

Fig. 57. Variation of VB and VF (top) with depth of p-GaN removed by wet etching before deposition of the rectifying contact, and wet etch depth versus etch time in boiling NaOH solutions for plasma-damaged p-GaN (bottom).

sist was removed. Etch profile and surface morphology were analyzed by SEM and AFM, respectively. Figure 59 shows the effect of dc chuck bias on the reverse junction leakage current, along with the corresponding GaN etch rates. There is little effect on the current below chuck biases of - 2 5 0 V. This corresponds to an ion energy of approximately - 2 7 5 eV, because this energy is the sum of chuck bias and plasma potential (about - 2 5 eV in this tool under these conditions). The reverse current decreases slightly as the dc self-bias is increased from - 2 5 to - 5 0 V. This may result from the sharp increase in etch rate, which leads to faster removal of near-surface damage. The reverse current increases rapidly above an ion energy of - 2 7 5 V, which is a clear indication of severe damage accumulating on the sidewall. The damage probably takes the form of point defects such as nitrogen vacancies, which increase the n-type conductivity of the surface. The total reverse current density, JR, is the sum of three components, namely diffusion, generation, and surface leakage, according to

( eDh eDe ) n 2 + eWni JR -- lhND + leNA Zg

Fig. 58.

Schematic of GaN p-i-n junction formed by dry etching.

rates were calculated from bulk GaN samples patterned with AZ-4330 photoresist. The depth of etched features was measured with an Alpha-step stylus profilometer after the photore-

+ JSL

where e is the electronic charge, De,h are the diffusion coefficients of electrons or holes,/e,h are the lengths of the n and p regions outside the depletion region in a p-n junction, ND,A are the donor/acceptor concentrations on either side of the junction, ni is the intrinsic carrier concentration, W is the depletion with rg the thermal generation lifetime of carriers, and JSL is the surface current component, which is bias-dependent. The latter component is most affected by the dry etch process and dominates the reverse leakage in diodes etched at high ion energies. GaN sidewall profiles and etch morphologies have been evaluated from previous results as a function of dc bias. The etch becomes more anisotropic as the dc bias increases from - 5 0 to - 1 5 0 V dc bias because of the perpendicular nature of the ion bombardment energies. However, at - 3 0 0 V dc bias a tiered etch profile with vertical striations in the sidewall was

440

PEARTON AND SHUL

1000

60O0

100

4000

Reverse l.e.akage - i - Etch Rate

3500

5000

100 3000

4000~

.m

~

~oo~

2000~ 1000 1000

0.1 500 1 0.01

I

t

I

I

t

200

400

600

800

1000

0 1200

ICP Power (W)

0

b

I

I

I

20

40

60

80

0 100

%C12 in a BCI3/CI2 Plasma Chemistry

Fig. 60. Reverse leakage current measured at - 3 0 V for GaN p-i-n junctions etched in ICP 32C12/8BC13/5Ar discharges ( - 1 0 0 V dc chuck self-bias, 2 mTorr), as a function of source power.

Fig. 61. Reverse leakage current measured at - 3 0 V for GaN p-i-n junctions etched as a function of C12 percentage in an ICP C12/BC13/Ar plasma. Plasma conditions were - 1 0 0 V dc chuck self-bias, 2 mTorr, 500 W ICP power, and 40 standard cm 3 total gas flow.

observed because of erosion of the mask edge under high ion bombardment energies. The physical degradation (both profile and morphology) of the etched sidewall at - 3 0 0 V could help explain higher reverse leakage currents above - 2 5 0 V dc bias. Under high bias conditions, more energetic ions scattering from the surface could strike the sidewalls with significant momentum, thus increasing the likelihood of increased damage and higher reverse leakage currents. Under low bias conditions, the sidewall profile is less anisotropic, implying increased lateral etching of the GaN (undercutting o f the mask). Under these conditions the etch process becomes dominated by the chemical component of the etch mechanism, which may account for the slightly higher reverse leakage observed at - 2 5 V dc bias. Figure 60 shows the effect of ICP source power on the junction reverse leakage current. The plasma flux is proportional to source power. In this experiment the ion energy was held constant at - 1 0 0 V dc bias. There is a minimal effect on leakage current for source powers of V

)C.9 n~'

ou

uJ 4 0 -

-Re

z

Ta**W pt

ILl tJ m

z

20

_

T i.~=FeoGe AId'Si ~/'r-Cu -ue Co

.Pd .Ag

__

I,,IJ

I

o 0

eAu

cMrn~ ,N i Z r..MO.Rh

20

I

I

40 60 ATOMIC NUMBER

I

8O

100

Fig. 12. Average kinetic energy of various atoms ejected from a target surface under 1200 eV krypton ion bombardment [65]. Reprinted from G. K. Wehner and G. S. Anderson, in "Handbook of Thin Film Technology" (L. I. Maissel and R. Glang, Eds.), p. 3-23. McGraw-Hill, New York, 1970, with permission.

of atoms with kinetic energy values in the distribution tail may also affect the characteristics of sputter-deposited films. A large fraction of sputtering ions striking the target surface are implanted in the target to an average depth of a few nanometers. Later, in the permanent sputtering regime, these atoms are ejected from the target surface together with target atoms with an average kinetic energy similar to those given in Figure 12. These atoms traveling through the plasma experience a kinetic energy loss caused by elastic collisions with gas phase species and these sputtering gas atoms impinge on the growing film surface with an average kinetic energy, Esga. A fraction of sputtering ions are neutralized and elastically backscattered from the target surface. The kinetic energy of these reflected neutral atoms impinging on the growing film surface may be as high as the kinetic energy of sputtering ions, i.e., more than 1 order of magnitude above the average kinetic energy of condensing atoms. The reflection coefficients in terms of ion flux, R0, and ion energy, )to, of ions used for sputter deposition of films are defined by R0 =

t~si

0 q~si Esi Y0 = 0

(31) (32)

Esi

where ~bsi and Esi are the flux and the kinetic energy of neutral sputtering gas atoms backscattered from the target surface, respectively; 4~s~ and Esi0 are the flux and the kinetic energy of sputtering ions striking the target surface, respectively. Usually, the initial kinetic energy of sputtering ions may vary in the range 0.5-2 keV. These reflection coefficients, R0 and F0, are dependent on the atom mass ratio, Mt/Mi, where Mt and Mi are the atomic masses of target atoms and sputtering ions, respectively. A strong dependence of the reflection coefficient, R0, on the atom mass ratio is observed in Figure 13; i.e., the fraction of ions reflected at the target surface may vary from 0.5 to 20%. The reflection coefficient in terms of energy, Y0, also depends on the atom mass ratio (Fig. 14). The neutral atom backscattered from the target surface can possess a relatively large kinetic energy in the range 0.08Es~ to 0.30E ~ with a typical kinetic energy of sputtering ions, Es~ of the order of 1 keV. In other words, these energetic neutral particles can impinge on the surface of growing films with an average kinetic energy of about 100 eV. The energy loss caused by elastic collisions in the gas phase can be minimized and even negligible under a sufficiently low sputtering gas pressure and with a short targetsubstrate distance. Under these conditions, the normalized momentum, Pn, for sputter deposition of films on grounded substrates can be expressed approximately as

Pn = v/2McEc +

+

RoCs~/

r

2MsiYoEsO

(1 -- R0)q~s0/2MsiEsga 4u

(33)

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS I

I,

0.2

'

I

1

!

-

0.7

469 '

'!

I

I

I

'

TheoreticoI to W i n t e r s

curves occordlng ond Horne

Sigmund's

t

h

e

o

r

1

1

~

't,'

0.5

0.1

0.4

,,...

0.3 ..

0.2

[i_ tL

w

..I tl ttl

&

~W& i ~

B

0

u

8

U

C.)

&

""-

~

9

%

0.1

Q

.,

M.i LI.

0.01

0.05

J

0.04

9 E o : 300 eV

ii

9 E o = 600eV .

0.005

q.

0.03

0.02

/ l

0.3

m Eo = 900eV l

i

0.5

, I,,

1

I , ,,1

l

l

2

4

5

3

10

Mt/Mi Fig. 14.

Reflection coefficient, }'0, as a function of the atomic mass ratio, The experimental data are compared with theoretical curves according to Sigmund [69], and Winters and Home [70]. The term, n, is the average collision number of the backscattering process and E0 is the kinetic energy of incident ions [71 ]. Reprinted from W. R. Gesang, H. Oechsner, and H. Schoof, Nucl. Instrum. Methods 132, 687 (1976), with permission.

Mt/Mi.

0.5

1

5

Mt/Mi

10

Fig. 13.

Reflection coefficient, R0, as a function of the atomic mass ratio, at a fixed reduced energy, e, of 0.2. The uppermost curve is calculated using a Thomas-Fermi cross section and the correction for surface effects on backscattering coefficients, the second curve is the same without the surface correction, and the third curve is the uncorrected curve. Inelasticity is neglected. Experimental data points: ( x ) from Bottiger et al. [66], (O) from Bmnne6 [67], (A) from Petrov [68]. Arrows indicate estimated extrapolations to e = 0.2 by Bottiger et al. [66]. Reprinted from J. Bottiger, J. A. Davies, E Sigmund, and K. B. Winterbon, Radiat. Effects 11, 69 (1971), with permission.

Mt/Mi,

In Eq. (33), the fluxes of particles impinging on the film surface are assumed to be similar to fluxes of particles reflected at the target surface; strictly speaking, these fluxes are proportional. The surface of films sputter deposited on negatively biased substrates is also bombarded with ions of charge q coming from the plasma. Therefore, the normalized momentum is given by Pn -- v/2McEc +

Ro4,s~

dPc /2MsiYoEsO

R0)r ~ + (1 - dpc

+ ~i

-~cV/2Msiyq VB

(34)

where 4)i is the flux of sputtering gas ions striking the growing film surface, }i is the energy transfer coefficient reflecting the efficiency of the energy transfer from incident ions to condensing atoms (7 can be calculated using Eq. (25)), and V8 is the substrate bias voltage. Various parameters involved in Eqs. (33) and (34) can be determined by computer calculation codes such as transport of ions in matter or TRIM code [72]. The values of

reflection coefficients, R0 and 70, can be estimated from data given in Figures 13 and 14.

2.4.4.3. Films Produced by Ion Beam Sputtering and Dual Ion Beam Sputtering The residual gas pressure effect on the kinetic energy of sputtered atoms is negligible using ion beam sputtering (IBS) processes. Ion-assisted growth of films can be accomplished by using an additional ion source. The surface of films produced by dual ion beam sputtering (DIBS) processes is exposed to energetic particles already mentioned for films deposited by sputtering on grounded substrates. An additional type of energetic particles (projectiles) coming from the ion source for ion-assisted deposition is involved in the DIBS process. The normalized momentum for DIBS processes can be written as

Pn-v/2McEc+

R~176 0EsO r V/2Msi

-+- (1 - ~ b c e 0 ) ~ s 0 / 2 M s i E s g a

-+- -~c dt)p v/ 2 M p y E p

(35)

where the first three terms in the fight-hand side member are similar to those given in Eqs. (33) and (34). The fourth term is similar to the second term of Eq. (30) where 4)p and 4u are the fluxes of incident ions (projectiles coming from the additional

470

PAULEAU

ion source for IAD) and condensing atoms on the film surface, respectively; Mp and E p are the atomic mass and the kinetic energy of incident ions, respectively.

3. MAGNITUDE OF RESIDUAL STRESSES IN PVD THIN FILMS Various methods for measuring the magnitude of residual stresses in thin films can be categorized on the basis of the physical phenomena or parameters involved in the experiments such as X-ray diffraction methods, optical, electrical, and electromechanical methods. Detailed information about the instruments needed for these measurements was already extensively reported in the literature [73-76]. The choice of the appropriate method depends on various factors or needs such as in situ or ex situ measurements, type of substrate materials, type of filmsubstrate structures. With a film tightly adherent to a thin substrate, a biaxial stress in the film of a sufficiently high intensity causes the substrate to bend elastically. A tensile stress (with a positive conventional sign) bends the film-substrate structure so that the film surface is concave whereas a compressive stress (with a negative conventional sign) bends the sample so that the film surface is convex. The most common methods for determining residual stresses in thin films are based on measurements of the deformation of film-substrate structures. The substrates can be in the form of either thin cantilevered beams or disks. Cantilevered beam type substrates are generally employed for in situ measurements of stresses in the films during deposition. The residual stresses are determined by measurements of the radius of curvature of the beam, the deflection of the free end of the beam, or by observing the displacement of the center of a circular disk type substrate. Then, the average value of residual stresses in the films can be calculated from the characteristic length value (radius of curvature, deflection, or displacement) using appropriate equations developed in the next sections. Alternatively, the residual stresses in polycrystalline and single crystal films can be determined by X-ray diffraction techniques. If the film is deposited on a single crystal substrate, X-ray measurements can be used to determine the bending of the lattice planes, and the average residual stresses are calculated from the radius of curvature of the substrate. Furthermore, the position of a diffraction peak in the X-ray pattern of the deposited material gives the interplanar spacing of the set of corresponding lattice planes, and the strain in the film can be deduced directly from the lattice parameter of the deposited material. Then, the average value of residual stresses in the film is calculated from the strain in the film using appropriate elastic constants and Hooke's law [77]. It is worthwhile to note that X-ray diffraction techniques give the strain, and hence the average residual stresses in a crystallite lattice. These stress values are not necessarily similar to those determined from substrate bending measurements since the stress at the grain boundaries may be different from the stress in the crystallite.

The strain distribution through the thickness of polycrystalline films can be deduced from analyses by X-ray diffraction techniques [78-81]. This aspect corresponds to the major advantage of X-ray diffraction measurements over the substrate curvature techniques for determination of residual stresses in polycrystalline films. However, PVD films exhibit in general amorphous or nanocrystalline structures and the determination of residual stresses by X-ray diffraction techniques is often difficult or even impossible. Therefore, the major advantage of the substrate bending techniques over X-ray diffraction measurements is that residual stresses can be determined even in amorphous films.

3.1. Determination of Residual Stresses from the Radius of Curvature of Substrates

The most common methods for the determination of residual stresses in thin films deposited on beam or disk type substrates are based on the measurements of the deformation of filmsubstrate structures. This approach can be used for a wide range of materials including elementary metal, semiconductor, and insulating films or multilayer structures deposited on various types of substrates such as metal, semiconductor, glass.

3.1.1. Relation between Residual Stresses and Radius of Curvature of Substrates The equation for stress can be derived on the basis of elementary considerations of the beam elasticity theory. First of all, it is necessary to clearly define various physical parameters involved in the calculations. The neutral axis is defined as that longitudinal axis of a beam which undergoes no additional strain, i.e., no change in length when the beam is bent (Fig. 15). Therefore, the neutral axis lies at the center of a simple beam. When a thin strip of metal (or other material) or a thin substrate restrained from bending is covered with a thin film, the strip is compressed by the tension in the film which is thereby also shortened and loses some of its stress. If the constraints are now released and the strip is allowed to bend, the stress in the film

, ,,

, ,,,

X

J

b

w

/

,/ a

NEUTRAL AXi S

,

SUBSTRA

Fig. 15. Distribution of stresses in the structure held rigid before contraction and bending of the substrate (the stresses in the nondeformed substrate are nil).

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS is still further relieved. These losses in stress depend on the dimensions of the substrate and, hence the final equilibrium stress in the film is not a constant quantity but depends on the experimental conditions. As a result, it is necessary to define the stress in the coating, S, which is independent of the mode of measurement. This stress referred to as the true stress is existing in the film when it is deposited on a rigid, incompressible surface or for practical purposes on a substrate thick enough to undergo no appreciable deformation. This term, S, is given by

S - fo tf tr (z) dz

o ts t s + tf

tfr

(36)

ts where tf is the thickness of the film and or(z) is the stress for a fiber at a distance z from the chosen axis. The average stress in the film can be calculated from the true stress and the thickness of the film: S cr = - -

Usually, the stress data given in the literature are the values of the average stress, or. Then, for a correct comparison of stress values obtained from samples with films of various thicknesses, it is necessary to verify that the stress is independent of the film thickness. Two basic conditions must be satisfied by the internal longitudinal fiber stresses of a beam in equilibrium,

F - - f cr(z) dA -- O --

f (z)z

THIN FILM NEUTRAL AXIS SUBSTRATE

otf

(37)

tf

M

471

dA

--

0

(38) (39)

These equations can be taken over any cross section of the beam. Equation (38) states that the sum, F, of the longitudinal forces within the beam is zero, i.e., that the internal compressive forces are equal to the internal tensile forces. Equation (39) states that at equilibrium the internal bending moment, M, of the beam is zero about any axis. The variable, z, is the distance of the fibers, of stress cr (z), from the chosen axis, and dA is the element of area of the cross section. Before considering the application of these general equations to the curvature of a substrate (typically, a strip of metal) covered with a thin film, various assumptions can be considered to simplify the calculations. It will be assumed that: (i) the properties of materials involved in the sample (substrate and thin film) fulfill the requirements for application of the mechanics of elastic, homogeneous, and continuous materials, (ii) elastic properties of the substrate and the film are isotropic, (iii) Young moduli of elasticity of the substrate and the film are equal approximately, (iv) the thickness of the film does not amount to more than a few percent of the thickness of the substrate, (v) the residual stresses are plane, biaxial, and isotropic (that means t Y x x ~ - t Y y y --- O" and azz = 0 (Fig. 15) since the film is free of any deformation or constraint along the z axis), (vi) during bending, the transverse cross sections remain plane and, (vii) the adherence of the film to the substrate surface is ideal; i.e., the film-substrate interface is free of any delamination.

ts+ tf Fig. 16. Distribution of stresses in the structure after lateral contraction of the substrate (the sum of forces is equal to zero).

In an initial approach, the film is deposited on a substrate rigidly held, i.e., neither contraction nor bending of the strip can occur. Since the substrate has not been allowed to deform, there is no resultant stress in the substrate as represented in Figure 15. The condition for mechanical equilibrium of the structure corresponds to the sum of forces equal to zero, ~ F = 0. Then, the constraints applied on the substrate are partially removed so that the strip is allowed to shorten but not to curve. The film also contracts and its stress is reduced; the stress in the substrate is increased by the same amount. The situation is schematically represented in Figure 16. A couple of longitudinal and opposite forces with equal intensities acting at a distance of (ts + tf)/2 appears in the structure. The bending moment is given by

M - F~

2

ts ) t f b ( ts+tf = cr(ts + tf 2 ) =or

(tstfb)

(40)

2

Now, the substrate is allowed to bend; as a result, a new distribution of the stresses occurs (Fig. 17). The new position at equilibrium is reached when the bending moment of the stresses is equal and opposite to the bending moment calculated previously and given by Eq. (40). In this situation, if the transverse cross section is assumed to remain plane according to the previous hypothesis (vi), the strain of a fiber at a distance z from the neutral axis is given by the following expression [82]:

ec =

Z

~

(41)

where R is the radius of curvature of the substrate. For elastically isotropic materials (hypothesis (ii)) and a state of plane, biaxial, and isotropic stress in the film (hypothesis (v)), the

472

PAULEAU or

Esb ft,/2 Esbt3s z 2 dz Mc = (1 - vs)R J-ts/2 12(1 - vs)R

tf

The bending moment given by Eq. (40) can be equated to the bending moment in Eq. (43b) since the structure is at mechanical equilibrium so that

,( )(ts

THI N FI LM NEUTRALAXIS

tsl V'-

a=-~

i

Fig. 17. Distribution of stresses in the structure after bending of the substrate (the sum of forces is still equal to zero).

THI N FI LM

NEUTRAL ts SUBSTRATE !

Fig. 18. Final distribution of stresses in the structure (the sum of forces and bending moments are equal to zero).

stress created in the structure by the curvature can be expressed by Hooke's law:

ac

1-v

~c "~

1-v

-R

(42)

The situation is schematically represented in Figure 17. The final distribution of stresses in the structure at equilibrium given in Figure 18 results from the superposition of stresses represented in Figures 16 and 17. According to previous hypotheses (iii) and (iv), i.e., tf

~

120

503

~,., .... 1 '"" "" . .I . '.' ' i

1 ''''1''''1

II

I

-3oo

N

80

-400

N

60

'~''-

Thermally-

"

Grown Si

"

" 9

40 - 500

~

-600

,,.,,,.,l

0.01

,,.

,,,,,,,;l

0.1

.... ,I

1

10

,,,,,,,.l

100

.,.,.,.,i

0

,~,...

1000

'

'"'"'I

'

'

r:"'l

~ ' " ' " I ''~ '"'"'i

''i ' " ' ~ '

E

- oo200-

~"

300 -i

'~" - 4 0 0

-

-500 0.01

&

9

, ,,,,,,,I , ,, .... 0.I 1

,,~ 10

I00

1.5

,, I,j,,

1.6

I,,,,

1.7

l,,,,

1.8

[i,

1.9

,,

1 |

2.0

f

, I , I t ,,'1',, 9

2.1

i

2.2

!

2.3

MASS DENS I T Y ( g / c m 3)

Fig. 53. Aging time effect on the residual stresses in SiO2 films deposited on Si substrates at 200~ under a base pressure of 2 x 10 -5 mbar (A) or under an oxygen pressure of 1 x 10 . 4 mbar (O), and 3 x 10 . 4 mbar (0); the mass density of these films was 2.03, 1.96, and 1.57 g cm -3, respectively [119]. Reprinted from H. Leplan, J. Y. Robic, and Y. Pauleau, J. Appl. Phys. 79, 6926 (1996), with permission.

~.,,.,,.I

",,,, , I,,

1.4

AGI NG TI ME (h)

I00

20

I000

A G I NG T I M E ( h ) Fig. 54. Aging time effect on the residual stresses in SiO 2 films deposited on Si substrates at 250~ under a base pressure of 2 x 10-5 mbar (A) or under an oxygen pressure of I x 10-4 mbar (O), and 3 x 10-4 mbar (0); the mass density of these films was 2.09, 1.98, and 1.64 g cm -3, respectively [I ]9]. Reprinted from H. Leplan, J. Y. Robic, and Y. Pauleau, J. Appl. Phys. 79, 6926 (1996), with permission.

The composition of SiO2 films deposited on Ge substrates was determined by IR spectroscopy after an aging time in room air of 15 min, 3 h, 3 and 4 days (Fig. 56a and b). As

Fig. 55. Relative variation of residual stresses versus mass density of SiO2 films after exposure of samples to room air for 1000 h [ 119]. Reprinted from H. Leplan, J. Y. Robic, and Y. Pauleau, J. Appl. Phys. 79, 6926 (1996), with permission.

the aging time increased, a progressive shift toward shorter wavelengths was observed for the absorption band at 9.3/zm (1080 cm -1) corresponding to the stretching vibration of S i - O - S i bonds. In addition, the IR spectra of films after an aging time longer than 15 min exhibited an absorption band at 10.7/zm (935 cm -1) ascribable to S i - O H groups [171,172]. The intensity of this absorption band increased with increasing aging time (Fig. 56b). The variation of residual stresses as the samples move.from vacuum to air, Aaw, and the time evolution of stresses resulting from exposure of films to room air constitute two distinct parts of the extrinsic stress. The first part was attributed to the effect of water molecules adsorbed in voids and pores of not fully dense SlOe films. The magnitude of this reversible compressive stress component was discussed in previous sections on the basis of the model proposed by Hirsch. The second part of the extrinsic stress resulting from exposure of samples to room air was found to vary irreversibly and may be ascribed to the instability of films to water vapor in room air. In addition to the increase in hydrogen concentration in films exposed to room air and detected by ERDA, the IR spectroscopic analyses revealed that the concentration of S i - O H atomic bonds increased with increasing aging time. A chemical reaction between water molecules and silicon dioxide occurring progressively as the aging time increases can be postulated on the basis of these experimental results. Porous SiO2 films deposited by evaporation can behave similarly to silica gel employed as a drying agent. The hydration of silica leads to the formation of various silicic acids such as Si(OH)4 or H8Si4012. Monosilicic acid, H4SiO4, would be the ultimate acidic com-

504

PAULEAU 0"501-~''' I ~' " "i " ~ " i' c i '"i" i';, I' i, i i ,", i , l ; " ' q

Si-OH F-

I

,,I-

sively in SiO2 films with increasing aging time (Figs. 52-54). New types of interactions appear in the material after partial hydration. Permanent electric dipole moments are associated with HO--Si--OH groups in silicic acids. As a result, the dipole interaction force may be invoked to explain the existence of tensile residual stresses in hydrated SiO2 films. The kinetics of hydration of films was discussed on the basis of a reaction mechanism composed of two successive elementary steps [119]: (i) Adsorption of water vapor molecules on the SiO2 surface,

(a)~ _.

/F-

o,o 0.30

Si O- S"

-

n20(g) + s ~-~ H20--s

(I)

k-1

(ii) Hydration of SiO2 with formation of silanol radicals,

0 . 1 0 I'' ' - ~ ' I ' - ' ' ' I_,_,_,, I,,,._, I,_,,, I , , , ~_i-~.,,~ !~,, :"

9

10

11

WAVELENGTH

IZ

H 2 0 - s -+- S i - O - S i -~ 2 S i - O H + s

(0 m )

/~ A/1,2 v..~or,

,

,~-,

!

,

, , ,

t~-''

.... ' - ~ '

i ~'

'

."

'

'

(b) !

,r

o.4s

ii i i t#

-,,: '

0.44

t

I I

~

'~' "

"_ :,

10

,,.:,.,

~, ',

",:

~176

SI-OH

,.~.e~"

',~ v.

.

,

,,t

~.

',

\ "' ',

!,.1 11 WAVELENGTH

(II)

where k i and k-1 are the rate constants of the direct and reverse reactions in step (I), respectively; k2 is the rate constant of step (II). In these elementary steps, the species, s, represents free adsorption sites at the SiO2 surface which can be Si or O atoms. Adsorbed water molecules, H z O - s , disappear via reaction (II), i.e., react with two neighboring species, Si and O - S i , belonging to an S i - O - S i group in which one of the S i - O atomic bonds is weakened. In fact, Si and O - S i species at the SiO2 surface may act as either adsorption sites or reactive species. The concentrations of Si and O - S i species decrease progressively as silica is converted into silicic acid. The adsorption of water molecules on the SiO2 surface (elementary step I) was assumed to be a rapid step while the formation of S i - O H radicals (elementary step II) was considered to be the rate-limiting step for the overall reaction. As a result, step (I) is considered to be at equilibrium and the concentration of adsorbed water molecules, qa, on the SiO2 surface is given by

12 qa -- K 1 P S

(p m )

Fig. 56. (a) Typical infrared absorption spectra of SiO2 films deposited on Ge substrates at ambient temperature under a base pressure of 2 x 10 -5 mbar after an aging time of 15 min ( I , solid line), 3 h (&, dashed line), 3 days (O, dashed and dotted line), and 4 days (0, dotted line); the mass density of films was 1.97 g cm -3. (b) Typical infrared absorption spectra in the wavelength range 10-12/zm for SiO2 films described in (a) [119]. Reprinted from H. Leplan, J. Y. Robic, and Y. Pauleau, J. Appl. Phys. 79, 6926 (1996), with permission.

pound formed by hydration of silica films (SiO2 + 2H20 --+ H4SiO4). The fixation of OH groups in the SiO2 lattice can occur via silicon dangling bonds but also may proceed by dissociation of S i - O - S i bonds [ 119]. The hydration of evaporated silica films leads to fragmentation and reduction of the degree of polymerization which result in the shrinkage of the SiO2 lattice and the reduction in residual stresses as the aging time increases. The hydration of the SiO2 lattice does not lead only to a stress relaxation but tensile residual stresses develop progres-

(149)

where K1 is the equilibrium constant of step (I), P is the partial pressure of water vapor, and S is the concentration of free adsorption sites at the SiO2 surface. Moreover, the concentration of S i - O - S i reactive species on the SiO2 surface is equal to S at a given aging time since these species may act as either adsorption sites in step (I) or reactive species in step (II). Assuming that step (II) is the rate-limiting step, the hydration rate of silica can be written as dS dt

= kzqa S

(150)

The rate of the elementary step (I) is given by dqa dt

= kl P S - k - l q a

(151)

The probability of desorption of water molecules from the oxide surface is believed to be very small at a given aging time;

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS hence, the rate of formation of adspecies via step (I) can be approximated to

dqa --kiPS dt

(152)

Therefore, Eqs. (149), (150), and (152) lead to

dS S

k2 = ~dqa

(153)

k-1

which integrates to S - So exp - ~ _ l q a

(154)

since initially (at t -- 0), qa "-- 0 and S = So. Consequently, the concentration of free adsorption sites on the oxide surface is found to decrease exponentially as the quantity of water molecules adsorbed on the surface increases. Equation (154) corresponds to the concentration of free adsorption sites given by the Elovich equation which can be derived for a uniform or a nonuniform surface when the activation energy of the adsorption step varies with the quantity of adspecies [173]. At the steady state, the rate of consumption of free adsorption sites is equal to the rate of hydration of silica which can be expressed as

dSdt - dqadt = klPS - k l P S o e x p ( - ff~2_lqa)

(155)

which integrates to k-1

qa = ~

k2

ln(k2KiSoPt + 1)

(156)

Equation (156) provides the amount of water molecules adsorbed on the SiO2 surface and consumed in step (II) for hydration of silica. In other words, this equation gives the hydration rate of silica. This logarithmic kinetic law may account for the linear decrease in extrinsic stress in evaporated SiO2 Table VII.

505

films with increasing the logarithm of the aging time. Furthermore, Eq. (156) predicts that the hydration rate decreases with decreasing water vapor pressure. This result is in good concordance with the reduced variation of the residual stresses observed when the samples were maintained under vacuum (Fig. 45).

6.2. Residual Stresses in Silicon Dioxide Films Produced by Ion-Assisted Deposition Silicon dioxide films have been deposited on various substrates at room temperature by direct electron beam evaporation of SiO2 using a high vacuum evaporation system equipped with a gridless ion source to produce high ion fluxes at low energy [ 174]. The kinetic energy and the flux of oxygen or argon ions can be adjusted by the source anode voltage, Va, and the current, la. The energy distribution and the current density of ions were measured at the substrate surface under experimental conditions similar to those used for ion-assisted deposition of films. A broad distribution of the ion energy was obtained around the nominal value fixed by the anode voltage, Ea : e Va. The maximum current density, Ja, measured at the center of the beam for each operating condition is listed in Table VII along with the experimental deposition conditions. The pressure in the deposition chamber was in the range 10 -4 mbar and was dependent on the gas flow rate required for the ion source to monitor the anode current. The optical properties (refractive index and extinction coefficient) and the thickness of SiO2 films deposited on glass substrates (BK7 Schott) were deduced from spectrophotometric measurements [ 175].

6.2.1. Characteristics of Silicon Dioxide Films Produced by lon-Assisted Deposition The refractive index and the mass density of SiO2 films produced by IAD under various conditions are given in Table VII.

Ion-assisted Deposition Parameters and Physical Properties for SiO2 Films Prepared in an Alcatel EVA 700 System and Assisted with a Gridless Ion Source

R

Va

Ia

Ja

Pn

p

n

cr

Atrw

Gas

(nm s - 1)

(V)

(A)

(mA cm - 2 )

(g eV m o l - 1) 1/2

(g cm - 3 )

at 600 nm

(MPa)

(MPa)

02

0.72

0

0

0

0

1.56

1.44

- 10

-64

02

0.76

150

1

0.37

117

1.80

1.46

-230

- 108

02

0.52

150

2

0.56

228

2.03

1.48

- 276

-40

02

0.52

150

3

0.75

284

2.21

1.48

-320

- 18

02

0.54

150

4

0.93

346

2.13

02

0.67

100

4

0.93

02

0.78

80

4

0.93

Ar

0.56

150

2

0.39

2.19

- 364

0

1.47

-230

-98

1.45

-100

-72

-470

0

Source: J. Y. Robic et al., Thin Solid Films 290-291, 34 (1996). The gas is the type of assistance gas; R is the deposition rate; Va is the anode voltage; la is the anode current; Ja is the maximum current density; Pn is the normalized momentum; n is the refractive index at 600-nm wavelength; p is the film mass density; s is the residual stress value in air; Acrw is the variation of residual stress value as the sample is moved from vacuum to air.

506

PAULEAU

1.49 .,,,,I

....

I ....

I ....

I ....

I ....

I ....

! ....

I ....

.

1.48 T

X I.IJ

a

z

1.47

"

1.46

-20

-

-

.

-

/k

"

/ Bulk"

i.1.1

>_

+

1.45-

~ 1.44

Silica-

60

80

m 1.43 1.42

,o

~. . . . ' . . . . i , , , . , , , , . , 1.4 1.5 1.6 1.7 MASS

.... , .... , .... , .... , .... 1.8 1.9 2.0 2.1 2.2 2.3 DENSITY

(g/cm 3)

120

Fig. 57. Refractive index at 600 nm versus mass density of SiO2 films deposited by evaporation in equipment I ([:3), and prepared either under ion beam bombardment or without any ion beam assistance in equipment II (O) [174]. Reprinted from J. Y. Robic et al., 290-291, 34 (1996), with permission.

ThinSolidFilms

The extinction coefficient for these films was below 10 - 4 . The refractive index of SiO2 films produced by direct evaporation exhibited the same linear correlation with the mass density as that of films prepared by ion-assisted deposition (Fig. 57). The residual stresses in lAD SiO2 films are also given in Table VII. The magnitude of residual stresses, or, measured in room air and the stress variation, Acrw, caused by adsorption of water molecules in the films were determined 1 h after deposition and exposure of films to room air. The compressive residual stresses in the films increased with increasing current and anode voltage. Films produced under argon ion bombardment exhibited more compressive stresses than films obtained with oxygen ion bombardment, i.e., - 4 7 0 MPa and - 2 7 6 MPa, respectively. The compressive stress variation, Aaw, corresponding to the transfer of samples from vacuum to air was reproducible and reversible; the value of Acrw was reduced to zero as the current or anode voltage was increased. This stress variation versus mass density of SiO2 films produced by direct evaporation and ion-assisted deposition is plotted in Figure 58. For both types of SiO2 films, the stress variation increases with increasing mass density, reaches a maximum value of about - 1 3 0 MPa as the mass density varies from 1.8 and 1.9 g cm -3, and decreases to zero for higher mass densities.

6.2.2. Normalized Momentum Effect on the Mass Density and the Residual Stresses of Silicon Dioxide Films Produced by lon-Assisted Deposition The normalized momentum is the relevant process parameter which governs the properties of films produced by ion-assisted deposition. For lAD of SiO2 films, the normalized momentum, Pn, is expressed as

en -- ~ccV/MiEi

-lOO

(157)

140 1.5

1.6

1.7 1.8 1.9 2.0 2.1 MASS DENSITY (g/cm 3)

2.2

2.3

Fig. 58. Residual stress variation as the sample is moved from vacuum to air as a function of the mass density of SiO2 films deposited on Si substrates using two different equipments: (fq) films prepared by thermal evaporation in equipment I and (O) films obtained under ion beam bombardment or without any ion beam assistance in equipment II [49]. Reprinted from H. Leplan, Ph.D. Thesis, National Polytechnic Institute of Grenoble, France, 1995.

where flfli/flflcis the ratio between the ion flux and the film atom flux at the substrate surface; Mi and Ei are the mass and the kinetic energy of incident ions, respectively. It is difficult to accurately estimate the value of Pn; hence, a functional parameter P* proportional to Pn was substituted for Pn,

/

p* -- r MiE* "gJa/e dp* DRpNAv/Mc

/ eMi Va

(158)

K

where DR is the deposition rate of films, p is the mass density of films, NAy is Avogadro's number, Mc is the molar mass of silica, e is the electron charge, Ja and Va are the maximum current density and the anode voltage of the ion source, respectively. The factor K is equal to unity and 2 for argon and oxygen ion assistance, respectively. The factor of 2 for oxygen is due to the dissociation of oxygen ions, O +, at the substrate surface [176]. A linear dependence of the mass density and the refractive index of IAD SiO2 films on the functional parameter, P*, is observed in Figure 59. This result is in good agreement with the prediction of models for film densification proposed in the literature. As mentioned in the model proposed by Windischmann [113], the densification of films can be achieved only by ions with a kinetic energy higher than the displacement energy of atoms in a crystal lattice, i.e., about 25 eV. Because of the broad energy scattering of the gridless ion source, it is difficult to evaluate the number of ions which have an energy above this threshold energy. Therefore, the comparison of results is possible only for films obtained with the same anode voltage, i.e., with an anode voltage of 150 V for data points reported in Figure 59.

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS ....

100

, ....

, ....

I ....

w. . . .

P"

,'"'","

2.3

9 . rm

0

toq n uJ

2.1

,,

~

v~ (/1

1~.

m

~

Z

1.9

Zm m ""

-300

"

. . m l . . . . I , , . , l , , , , I . , , | l . , , . I . . , . I . . .

50

''''~-

0 ~'"b"-.....

-100

13

9

-200 i

1.7

~

1,6

~

U Z (,,,,1

0

. . . . =. . . . I " ' " i

9

~

-400

t/)

m

-zoo s

. . . . I . . . . m. . . . j " " l " " =

'~

js

.~

100

507

1.5

100 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

NORMALIZED MOMENTUM (gl/Z morl/z eVl/Z) Fig. 59. Mass density and intrinsic stress of SiO2 films produced by IAD as a function of the normalized momentum. The films have been deposited under oxygen ion bombardment with Va = 150 V [174]. Reprinted from J. Y. Robic et al., Thin Solid Films 290-291, 34 (1996), with permission.

The thermal stress in these IAD SiO2 films deposited on substrates at room temperature are essentially nil. The extrinsic stress resulting from water adsorption in the films can be interpreted on the basis of the model proposed by Hirsch. For films with reduced mass densities (less than 1.5 g cm -3) and large pore sizes, the interaction forces between adsorbed dipoles are negligible and the extrinsic stress tends to be zero. For films of intermediate mass density values (between 1.5 and 1.9 g cm-3), the pore size is the major factor governing the water adsorption induced stress. For denser films with a mass density in the range 1.9 to 2.2 g cm -3, the number of open pores is the factor limiting the extrinsic stress caused by water adsorption. No water molecules can be adsorbed in films with the bulk density and the extrinsic stress becomes negligible. The values of the intrinsic stress in IAD SiO2 films were calculated from Eq. (1) using data given in Table VII. The intrinsic stress versus the functional parameter, P*, is plotted in Figure 59 for SiO2 films produced under oxygen ion bombardment. Similar to the mass density, a linear dependence of the intrinsic stress on P* is observed. A clear correlation appears between the mass density and the intrinsic stress in SiO2 films produced by direct evaporation and IAD (Fig. 60). The compressive intrinsic stress in these films increases with increasing mass density. For films produced by direct evaporation (without any ion assistance of the growth), the intrinsic stress was compressive although the kinetic energy of species condensed on the substrate was very low. Thermodynamic calculations for the system composed of SiO2 at equilibrium with gas species such as SiO, O2, O, SiO2, and Si at various temperatures under various oxygen pressures have shown that SiO molecules are the major species in the gas phase [49]. Therefore, the oxidation of the SiO species on the film surface is needed to produce stoichiometric SiO2 films by direct evaporation and by IAD as well. This oxidation process at the growing surface may generate compressive stress in the deposited material since oxidation results in an increase in molecular volume. On the basis of this possible oxidation which may be responsible for compressive

-300

....

==

-4oo

D',p -

9

9

m

-500

"J,==l

1.4

....

1.5

I ....

1.6

I,,,~1~,,=,i

1.7

1.8

....

1.9

I ....

2.0

I=,**1,,,

2.1

2.2

"~

2.3

MASS DENSn'Y (g/cm 3) Fig. 60. Intrinsic stress as a function of the mass density of SiO2 films deposited on Si substrates by: (D) thermal evaporation and (O) lAD [174]. Reprinted from J. Y. Robic et al., Thin Solid Films 290-291, 34 (1996), with permission.

intrinsic stress generation, it can be assumed that in films with a mass density lower than the bulk density the bombardment induced defects and atom displacements are not responsible for the compressive stress generation. Furthermore, for a given film density, the magnitude of the compressive intrinsic stress is lower in IAD films than in films deposited by direct evaporation (Fig. 60). This result suggests that a stress relief may be induced by ion bombardment of growing films.

6.3. Residual Stresses in Silicon Oxynitride Films Produced by Dual Ion Beam Sputtering The control of the refractive index of optical films between the refractive indices of silica and silicon nitride (1.46 and 2.05, respectively) can be achieved by silicon oxynitride films for optical applications which need discrete films as well as continuously variable films like rugate. Silicon oxynitride, SiOxNy, films of 0.5- to 1-/zm thick have been deposited using a high vacuum dual ion beam sputtering (DIBS) system equipped with two ion sources for sputtering and ion-assisted growth of films [177]. A silicon target of 35 cm in diameter was sputtered by ion beams using a Kaufman-type ion source of 15 cm in diameter operating with a mixture of argon and nitrogen of various compositions. A Kaufman-type ion source of 7.5 cm in diameter for ion beam-assisted deposition of films fed with nitrogen was focused on the rotating substrates which were bombarded with nitrogen ions in a discontinuous manner. Nitrogen was introduced into the deposition chamber through the ion sources while oxygen for oxidation of the deposited material was introduced directly into the chamber. The deposition rate of films was maintained at about 0.1 nm s -1. The substrate temperature and the pressure in the deposition chamber were fixed at 100~ and 2 • 10 -4 mbar, respectively. Oxynitride films of various nitrogen and oxygen contents were prepared under constant parameters of the ion sources (ion current, ion energy, gas flow rate, Ar/N2 ratio,

508

PAULEAU

etc.) while the flow rate of oxygen introduced in the chamber was varied in the range 0-22 cm 3 min -1. Two series of SiOx Ny films (referred to as conditions 1 and 2) corresponding to two different sets of parameters for the ion sources were investigated. The second set of deposition conditions was investigated to improve nitridation of films by reducing the sputtering rate of the silicon target and by increasing the nitrogen ion flux on the film surface. The refractive index, the extinction coefficient, and the thickness of films deposited on glass substrates (BK7 Schott or silica glass) were deduced from spectrophotometric measurements [ 175]. The mass density and the composition of films were determined by Rutherford backscattering spectroscopy (RBS) and nuclear reaction analysis (NRA). In addition, the residual stresses in films deposited on (111)-oriented Si substrates were determined from the change of the radius of curvature of substrates measured by interferometry.

6.3.1. Characteristics of Silicon Oxynitride Films Deposited by Dual Ion Beam Sputtering The composition of SiOxNy films produced with two sets of deposition conditions was found to vary with the oxygen flow rate introduced in the chamber as shown in Figure 61 in which the oxygen to silicon and nitrogen to silicon atom number ratios versus oxygen flow rate to deposition rate ratio, Do: / R are plotted. The variation of the composition with Do2/R is independent of the deposition conditions (conditions 1 or 2). The O/Si atom number ratio increases while the N/Si atom number ratio decreases with increasing Do2/R. For films deposited without oxygen in the deposition chamber, the N/Si atom number ratio in films obtained under conditions 2 is higher than that in films deposited under conditions 1 (1.4 and 1.1, respectively) while the N/Si atom number ratio is 1.33 in stoichiometric 2.0

~

' i'

w' i '

i'

I'

i'

i

'

~

2.0

f

Si3N4 films. The mass density of silicon oxynitride films was linearly dependent on the N/Si atom number ratio and varied from the mass density of silicon dioxide to the mass density of silicon nitride (Fig. 62). The refractive index of these films decreased from 2.09 to 1.54 with increasing Do:/R; the extinction coefficient of films in the range 10-4 decreased slowly with increasing Do: / R [ 177]. The optical properties of films were independent of the deposition conditions used (conditions 1 or 2) except for very low Do:/R values. The residual stresses in these silicon oxynitride films measured in room air were highly compressive (Fig. 63). A large decrease in the magnitude of the compressive residual stresses from - 1 4 8 0 to - 6 5 0 MPa and - 1 8 4 0 to - 6 4 0 MPa was observed in films deposited under conditions 1

A Oq

E O)

Ill {3 (/)

u~ < 2.4 =E

0.0

s

0.8

z

0.0 N /,

I,

0

I , ! , 1 , 1 .

4

8

I , i , I ,

12

1 , 1 , 1 , 1

16

20

Doz/R (cm 3 min"I/A s"1) Fig. 61. O/Si (open symbols) and N/Si (closed symbols) atom number ratios in silicon oxynitride films versus ratio between the oxygen flow rate and deposition rate of films produced under deposition conditions 1 (9 and 2 (7-1,II). The data point (0) corresponds to the N/Si atom number ratio in SiNy films deposited by IBS under conditions 1 without any ion bombardment and oxygen in the gas phase [177]. Reprinted from J. Y. Robic et al., in "Developments in Optical Component Coatings," Proceedings SPIE (I. Reid, Ed.), Vol. 2776, p. 381. SPIE, Bellingham, WA, 1994, with permission.

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Fig. 62. Mass density of silicon oxynitride films versus N/Si atom number ratio. The films have been deposited under conditions 1 (0) and 2 ( i ) [177]. Reprinted from J. Y. Robic et al., in "Developments in Optical Component Coatings," Proceedings SPIE (I. Reid, Ed.), Vol. 2776, p. 381. SPIE, Bellingham, WA, 1994, with permission.

-600

-1000

u~

-1200

I-03 ..J

. 1400

1/3 LId 03

< LU

'

"

'

S

'

'

''

'

"

'

'

'

'

'

'

'

S

~

$

-1 6 0 0

C~ tn

'

-800

v

u.I

~'0.0

0.2

N/Si ATOM NUMBER RATIO

~=

o.8

Si

2.2

a,.

1.z

.

2.8

~z 2.6

z

1.z

3.0

o

$

-1800

r~

-2000'

~''' 0

i,,,, 4

.... 8

I ,,, 12

,,,, 16

J , 20

Doz/R (cm 3 min'l/A s-1) Fig. 63. Residual stresses in silicon oxynitride films versus ratio between the oxygen flow rate and deposition rate of films produced under deposition conditions 1 (0) and 2 ([]) [177]. Reprinted from J. Y. Robic et al., in "Developments in Optical Component Coatings," Proceedings SPIE (I. Reid, Ed.), Vol. 2776, p. 381. SPIE, Bellingham, WA, 1994, with permission.

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS and 2, respectively. The residual stresses were independent of the environment. In other words, the residual stress value was unchanged when the samples were moved from room air to vacuum and no aging effect or evolution of stresses was observed for silicon oxynitride films stored for a long time (one year) in room air.

6.3.2. Origin of Residual Stresses in Silicon Oxynitride Films Deposited by Dual lon Beam Sputtering The oxidation process of silicon atoms or silicon-nitrogen species at the film surface is expected to depend on the flux ratio of oxygen and silicon atoms arriving at the surface. The value of this ratio is assumed to be proportional to the Do2/R ratio which was used as a process parameter. The data reported in Figure 61 suggest that the oxidation of silicon is the major reaction which controls the growth of silicon oxynitride films. Under deposition conditions (1 or 2) investigated, the nitrogen flux through ion sources was maintained constant for various Do2/R values; however, the nitrogen content in the films decreased with increasing Do2/R. Furthermore, except for low Do2/R values, the nitrogen content was similar in films deposited under conditions 1 or 2 although the nitrogen flux was higher for deposition of films under conditions 2. Therefore, silicon atoms are more or less oxidized depending on the Do2/R ratio and, then nitridation occurred on silicon sites unoccupied by oxygen up to saturation of the free silicon bonds. This dependence between nitrogen and oxygen contents in SiOxNy films is shown in Figure 64. The N/Si atom number ratio decreases from 1.33 (stoichiometric ratio in Si3N4) as the O/Si atom number ratio increases up to 2 (stoichiometric ratio in SiO2), except for low O/Si values under conditions 1 where the nitrogen flux is not sufficient for total nitridation of silicon atoms. Stoichiometric SiOxNy films were obtained by varying the Do2/R ratio (Figs. 62 and 64). The relative high extinction coefficient of films prepared under conditions 1 without oxygen in the deposition chamber resulted from a large deviation of stoichiometry (with respect to Si3N4) in these films. The mass density of silicon oxynitride films produced by DIBS was sufficiently high to avoid penetration or adsorption of water vapor molecules in the films and, thereby generation of extrinsic stress. The deposition temperature was 100~ as a result, thermal stress can be generated in the films during cooling down of samples and can be calculated using Eq. (105). The physical parameters such as Young's modulus, Poisson's ratio, and thermal expansion coefficient for these films are not known over the entire range of composition. To estimate the value of the thermal stress in oxynitride films, the calculation was performed for two limit compositions corresponding to SiO2 and Si3N4. Since the film density was nearly equal to the bulk density, the mechanical properties of bulk amorphous silica were adopted for calculation of thermal stress in SiO2 films. For Si3N4 films, relatively scattered data can be found for thermomechanical properties in the literature; the values proposed for dense silicon nitride films deposited by CVD at 800~ appear to be well adapted for dense films produced by DIBS. The thermal stress values for SiO2 and Si3N4 films calculated on the

1.61

,

,

,

,

,

,

,...,

SiN

0

3

1.2

509

,

,

,

,..,

,

I

,

,

,.,

.

,

,

,

,..,..,

~

,

,..

4

ILl

"~

0.8

z 0 bO

z

0.4 0.0 .

I

,

,

0.0

,

I

0.4

,

.

0.8

,

I

,

1.2

••O2" I

,

1.6

,

,

I

,

2.0

O/Si ATOM NUMBER RATIO Fig. 64. Nitrogen and oxygen contents of silicon oxynitride films produced by DIBS under deposition conditions 1 (O) and 2 (7]) [177]. Reprinted from J. Y. Robic et al., in "Developments in Optical Component Coatings," Proceedings SPIE (I. Reid, Ed.), Vol. 2776, p. 381. SPIE, Bellingham, WA, 1994, with permission. Table VIII.

Evaluation of Thermal Stress Values in SiO2 and Si3N 4 Films Deposited at 100~ on Si Substrates Biaxial modulus

Thermal expansion

E f / (1 - v f )

coefficient, c~

(GPa)

Film

Thermal stress (MPa)

(per ~

SiO 2

86

0.55 • 10 - 6

-14

Si3N 4

370

1.6 x 10 - 6

-27 i

Source: J. Y. Robic et al., SPIE, 1994.

basis of these data are given in Table VIII. The calculated values for silicon oxide and silicon nitride films are relatively low, i.e., - 1 4 MPa and - 2 4 MPa, respectively, so that the contribution of the thermal stress in the residual stresses for silicon oxynitride films deposited by DIBS can be neglected. On the basis of data obtained from the models proposed by Windischmann [ 113] and by Davis [ 141 ], the intrinsic stress in silicon oxynitride films was expressed as Gi

_

e:

,/Mi gi

(159)

where the first term in brackets is the biaxial modulus of the film material; Mt and Df are the molar mass and the mass density of the deposited material, respectively. The Mt/Df ratio is equal to 1/N where N is the atom number density of the deposited material. The term, ~i/~c, is the ratio between the ion flux and the film atom flux at the substrate surface; Mi and Ei are the mass and the kinetic energy of incident ions, respectively. Two terms, Q and Pn, can be distinguished in Eq. (159),

. (1

Ef

Mt

(1

Ef

1

(160)

510

PAULEAU

-600 t~

-600

-800

'

I

'

'

"

I

'

'

'

I

.

'

'

'

I

D

'

'

'

I

~,, ,''r

JD

'

I

'

,

I

,

[

t~ - 8 0 0 13.

- 1000 t.l.I 03

03 UJ t,r

u.I rr

ttl

to -1200

- 1000 DD

tn - 1 200 f,l,,

v-.. 1400 03

-1400

n'~,,

..I

< -1600

.-I

_ --~%

a m ILl - 1 8 0 0

~O z

"

:D

S i 3N4~~

er

-2000

,

I

,

,

I

,

,

,

I

,

,

,

l

, ,

,

I

,

,

,

I

,

,

,

I

,

,vt

I

,

Fig. 65. Residual stresses versus N/Si atom number ratio in silicon oxynitride films produced by DIBS (E3), or IBS ( I ) [49], and in SiNy films prepared by IBS (&) under similar deposition conditions according tothe results reported by Bosseboeuf [178]. Reprinted from H. Leplan, Ph.D. Thesis, National Polytechnic Institute of Grenoble, France, 1995.

which represents the stored elastic energy per mole and corresponds to the elastic response of the film to a volumetric distortion induced by defects (interstitial atoms) and

~i ~ M i Ei

-18oo

,

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 N/Si ATOM NUMBER RATIO

e" = E c.

-1600

c~

(161)

l

which is the normalized momentum. Since the pressure in the deposition chamber was always less than 2 • 10 -4 mbar and the path length of particles to reach the substrates was around 30 cm, the thermalization of energetic particles can be neglected. Thus, the normalized momentum was nearly constant for all experiments corresponding to data reported in Figure 63. As a result, in accordance with Eq. (159), the stress variation may originate essentially from the variation of the parameter Q which depends on the composition of films. The validity of this assumption seems to be confirmed by the direct correlation between residual stresses (or intrinsic stress since thermal and extrinsic stresses are negligible in these films) and the N/Si or O/Si atom number ratio (Figs. 65 and 66). The stress-nitrogen content correlation appeared more accurate than that with oxygen content and was also found for SiNy films produced by ion beam sputtering (IBS) under similar experimental conditions [ 178]. To compare the stress values predicted by the models and the experimental stress values, the parameter Q must be calculated using Eq. (160) for various SiOxNy films. Since the elastic constants for these films are not determined, the comparison can be only qualitative. For instance, for a SIO1.82N0.27 film produced by DIBS and an SIN1.4 film deposited by IBS, the intrinsic stress varied from - 6 9 0 MPa to - 1 8 4 0 MPa and, the atom number density, N, of these films determined by RBS was 2.6 • 1022 and 3.5 • 1022 at cm -3, respectively. Therefore, the variation of the atom number density is very small and, the stress variation with the composition of films reflects the variation of the biaxial modulus of films. It can be noted that this stress variation is compatible with the biax-

-2000

" "

0 ,

.l.t

0.0

" ,

~

I

,

,

,

I

,

,

,

I

,

,

,

I

0.4 0.8 1.2 1.6 O/Si ATOM NUMBER RATIO

,

,

"

2.0

Fig. 66. Residual stresses in silicon oxynitride films produced by DIBS versus O/Si atom number ratio [49]. Reprinted from H. Leplan, Ph.D. Thesis, National Polytechnic Institute of Grenoble, France, 1995.

ial modulus of silica and silicon nitride (Table VIII). The stress variation with the composition of films depends only on the parameter Q which is the elastic response of the film whereas the absolute value of the intrinsic stress for each composition is dependent on both Q and Pn factors according to Eq. (159). The effect of the normalized momentum is illustrated in Figure 65 where the intrinsic stress in silicon oxynitride films obtained by IBS (without any ion assistance) is also reported. The stress variation between IBS and DIBS films with identical N/Si atom number ratios may be attributed to the effect of the difference in the normalized momentum values, Pn, used in IBS and DIBS processes.

6.4. Amorphous Carbon Films Deposited by Conventional Magnetron Sputtering on Grounded Substrates Experiments were designed to estimate the flux and the kinetic energy of particles impinging on the surface of amorphous carbon (a-C) films produced by direct current (dc) magnetron sputtering from a graphite target in pure argon discharges [ 179]. The major objective of these experiments was to assess the contribution of various species to the energy deposited on the surface of growing films and to correlate the magnitude of residual stresses in a-C films to the kinetic energy and the flux of these species. The characteristics, in particular the plasma potential, of the argon discharge, the flux, and the kinetic energy of predominant energetic particles (neutral carbon atoms and argon ions) impinging on the growing film surface as well as residual stresses in a-C films were investigated as functions of the sputtering gas pressure at various sputtering powers. The films have been deposited on (100)-oriented Si substrates of 6 x 1 cm 2 at ambient temperature. The substrate temperature measured by a thermocouple inserted in the substrate holder during sputter deposition of films was less than 60~ under the experimental conditions investigated. The substrates were mounted on a grounded substrate holder located at 7 cm from the surface of the graphite target of 21 x 9 cm 2. The argon pres-

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS sure was varied in the range 0.1-2 Pa. The sputtering power was fixed at 0.5 or 2 kW. The thickness of a-C films (up to 1.8-/zm thick) was determined by profilometer measurements. The flux of carbon atoms, ~c, condensed on Si substrates was deduced from RBS data. The mass density of films was calculated from RBS data and film thickness values. The residual stresses in the films were determined from the change of the radius of curvature of Si substrates measured before and after deposition; the stress values were calculated using Eq. (45). The plasma potential, Vp, deduced from I (V) characteristics of a cylindrical Langmuir probe located at 6 cm from the target surface was investigated as a function of the argon pressure at a sputtering power of 0.5 and 2 kW. The flux of argon ions, ~Ar, impinging on the grounded substrates was calculated from the saturation ion current,/is, collected by the probe assuming that the flux of carbon ions was negligible with respect to the ion argon flux, i.e., ~Ar = lis/(eS) where e is the charge of Ar + ions and S is the surface of the grid electrode. Since the surface of the collector electrode was readily covered with carbon films, the current of secondary electrons emitted by the probe and resulting from the ion bombardment with a maximum energy of 100 eV was neglected for the calculation of the argon ion flux [ 180].

511

0.12 0.10 0.08 U b

~ 0.06

,

0.04 0.02

0.00 1 0.0

'

'

'

I

0.5

'

,1

'

l

I

. . . .

I

. . . .

I

. . . .

1.0 1.5 2.0 ARGON PRESSURE (Pa)

Fig. 67. Argon pressure effect on the ratio of the argon ion flux to the carbon atom flux for a sputtering power of 0.5 kW (O) and 2 kW (O) [ 179]. Reprinted from E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535 (1996), with permission.

0.0

2.4

-o.2

z.2

v

tael O Z

ttl

2.0 rn

u~ - 0 . 4

6.4.1. Characteristics of the Argon Discharge and the Amorphous Carbon Films The plasma potential reached a maximum value of 2.6 V under an argon pressure of 0.1 Pa and decreased progressively as the argon pressure increased up to 2 Pa before stabilization at about 1 V for high argon pressures [ 179]. The plasma potential was found to be independent of the sputtering power. The floating potential was equal to - 0 . 5 V under the experimental conditions investigated. The electron temperature and the electron density of 0.5 eV and about 2 • 109 cm -3, respectively, were in good agreement with values for argon magnetron discharges reported in the literature [ 181 ]. The flux of argon ions striking the surface of grounded substrates deduced from the saturation ion current was proportional to the sputtering power and was dependent on the argon pressure. The maximum value of this ion flux was reached under an argon pressure of 0.25 Pa. The uniformity of the film thickness was better than 8%. As a result, the flux of carbon atoms condensed on grounded Si substrates could be determined accurately by RBS measurements performed in the center of sampies. The flux of carbon atoms was also proportional to the sputtering power [ 182] and varied with the argon pressure [179]. The ratio of the argon ion flux to the carbon atom flux, q~Ar/~C, was found to vary from 0.10 to 0.05 as the argon pressure increased (Fig. 67). This flux ratio was nearly independent of the sputtering power, in particular under argon pressures higher than 1 Pa. Moreover, the flux of carbon atoms being independent of the sputtering gas pressure, the argon pressure dependence of the flux ratio was very similar to the dependence of the argon ion flux.

2.5

.-I

1.8

-o.6

-< to (3

~0

1.6 3

- 0 8 ~-i "

~ l ne

"

-1.0

0.0

0.5 1.0 1.5 2.0 ARGON PRESSURE (Pa)

1.4

2.5

Fig. 68. Argon pressure effect on the mass density of a-C films prepared with a sputtering power of 0.5 kW and residual stresses developed in films obtained with a sputtering power of 0.5 kW (&) and 2 kW (A) [179]. Reprinted from E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535 (1996), with permission.

The argon content in 30-nm-thick a-C films was less than the RBS detection limit evaluated to be about 0.5 at.%. The hydrogen content was less than 1 at.% with a base pressure in the deposition chamber lower than 4 x 10 -4 Pa which was currently reached prior to sputter deposition of films. The growth rate of films was in the range 10-60 nm min- 1 depending on the deposition conditions. Examinations of the cross section of a-C films by scanning electron microscopy revealed a densely packed structure for films deposited at low argon pressures while films produced at an argon pressure higher than 1 Pa exhibited columnar microstructures. The mass density of films depended on the sputtering gas pressure (Fig. 68); the maximum value was close to 2.2 g cm -3, i.e., nearly equal to the mass density of bulk graphite (2.25 g cm-3). The residual stresses were found to be

512

PAULEAU

compressive and the magnitude of stresses decreased progressively with increasing argon pressure (Fig. 68). In addition, the effect of the sputtering power on the stress value was negligible. The magnitude of residual stresses was also determined in a-C films sputter deposited with various substrate-target distances, d, at an argon pressure value fixed in the range 0.1--0.5 Pa. The compressive residual stress values decreased progressively as the distance d increased under a given argon pressure.

6.4.2. Energy of Carbon Atoms Ejected from the Graphite

Target The kinetic energy of carbon atoms condensed on S i substrates depends on both the energy of atoms ejected from the graphite target and the argon pressure. The experimental determination of the kinetic energy of sputtered atoms can be performed using relatively sophisticated techniques; however, this energy can also be estimated more readily from various models. In particular, the energy distribution of atoms ejected by ion sputtering can be determined from the theoretical model developed by Thompson [183] in which the ejection of atoms results principally from the generation of atomic collision cascades by the bombarding ions. This model was used to establish the velocity distribution of iron atoms sputtered from a magnetron target. The theoretical velocity distribution was found to agree with the distribution determined by laser-induced fluorescence measurements for a substrate-target distance, d, lower than the mean free path of sputtered atoms, )~Ar, colliding with sputtering gas atoms [184]; for a ratio, d/ZAr > 1, the thermalization of sputtered iron atoms caused by collisions in the gas phase became efficient. The kinetic energy of argon ions impinging on the surface of the graphite target is required for calculation of the energy distribution of carbon atoms ejected from the target surface. The argon ions experience an acceleration in the vicinity of the target surface caused by the potential drop in the cathode zone. The thickness of the cathode zone depends on the target voltage and the argon pressure; its value can be estimated to be less than about 1 cm under the experimental conditions investigated [ 185]. A number of accelerated argon ions may collide with argon atoms and a charge transfer process may occur with formation of a nonenergetic argon ion. This new argon ion experiences a lower acceleration in the cathode zone since the potential drop decreases as the distance from the target surface decreases [186]. The mean free path of argon atoms (in centimeters) at room temperature is given by ZAr = 0.7/P where P is the argon pressure expressed in Pascals. The value of ~.Ar varied from 7 to 0.35 cm as the argon pressure increased from 0.1 to 2 Pa. Furthermore, the mean free path for the charge transfer process, ~.CT, can be calculated from the following equation [ 187] ~.CT =

kT err(E)

(162)

12

10 8

"~

4 2 0

0 5 10 15 20 25 30 35 40 ENERGY OF SPUTTERED CARBON ATOMS (eV)

Fig. 69. Energydistribution of carbon atoms ejected from the graphite target biased to -680 V [179]. Reprinted from E. Mounier and Y. Pauleau,J. Vac.Sci. Technol. A 14, 2535 (1996), with permission.

where T and P are the absolute temperature and the pressure of the gas phase, respectively; k is Boltzmann's constant, and the charge transfer cross section, or(E), is equal to 3 x 10 -15 cm 2 for argon ions accelerated by a potential drop of 600-700 V [ 187]. Assuming that the gas temperature in the discharge is about 500 K, the value of the mean free path for the charge transfer process, ~.CT (in centimeters), at an argon pressure P (in Pascals) calculated from )~CT = 2 . 3 / P was found to vary in the range 23-1.1 cm as the argon pressure increased from 0.1 to 2 Pa. As a result, the thickness of the cathode zone was always lower than the mean free path for the charge transfer process and the mean free path of argon atoms. Therefore, the energy of argon ions colliding with the graphite target can be calculated directly from the target voltage since the energy loss caused by collisions in the cathode zone is expected to be negligible. According to the model developed by Thompson [ 183], the number of carbon atoms, d Nc, ejected from the target with a kinetic energy ranging from Ec to (Ec + d E c ) is proportional to 1 - [(MAr -t- MC)2(EB + EC)/(4MArMCEAr)] 1/2 E~(1 + E s / E c ) 3

(163)

where EAr is the kinetic energy of incident ions and E8 = 3.5 eV is the graphite surface binding energy [188]; MAr and ME are the masses of incident ions and target atoms, respectively. The energy distribution of Thompson for carbon atoms sputtered by argon ions from the magnetron discharge was determined for a target voltage of 680 V which corresponds to an average value of target voltages investigated (Fig. 69). The average value of the kinetic energy of carbon atoms deduced from the energy distribution up to 40 eV was found to be 10.1 eV. For this calculation, the analytical expression of the energy distribution was integrated up to 40 eV. Indeed, atoms with energies higher than 40 eV can be neglected since their number accounts for only a small fraction of the total population [ 189]. This limitation is justified on the basis of the comparison between the average kinetic energy of Cu atoms ejected from a

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS magnetron target determined experimentally and the average kinetic energy deduced from Thompson's distribution which revealed that the calculated energy value is overestimated [ 190].

6.4.3. Energy of Carbon Atoms Condensed on Silicon Substrates

(164)

The average diffusion angle of a carbon atom due to the collision with an argon atom is (0) - 78.46 ~ and the average distance traveled by the carbon atom making n collisions is given by [48] d-n~.~

cos(~)

(165)

where ~. is the mean free path of a carbon atom with mass Mc traveling through a gas consisting of a mixture of carbon atoms and argon atoms of mass MAr; the expression of ~. can be derived from the kinetic gas theory [ 191 ]. The value of ~. (in centimeters) can be calculated from Z = 2 . 2 / P where P is the argon pressure in Pascals. Therefore, the energy ratio, En/E1, after n elastic collisions is given by Es _ exp ( wd ) = exp(-0.205 d P ) E1 ~ . ~ c~s((0)/2)

(166)

where d and P are expressed in centimeters and Pascals, respectively. This ratio depends on the product (d x P), i.e., [(target-substrate distance) x (sputtering gas pressurg)] as shown in Figure 70. As a result, with a target-substrate distance of 7 cm and an average energy of sputtered carbon atoms, El, of 10.1 eV, the average kinetic energy of carbon atoms condensed on the substrate surface is approximately equal to the kinetic energy of argon atoms under an argon pressure higher than 2 Pa. In other words, above 2 Pa, the carbon atoms condensed on the substrate surface are thermalized because of elastic collisions with sputtering gas atoms. This thermalization state is reached after a number of collisions, nth, in the gas phase given by [48]

ln(En/E1) 1 (Eth) n t h - ln(E2/E1) = -w \--~1,]

1.00

ua" 0.10

The kinetic energy of carbon atoms traveling from the target to the substrates decreases progressively because of collisions in the gas phase. The scattering of sputtered atoms by the sputtering gas and the phenomena leading to kinetic energy losses of sputtered atoms in the gas phase have been modeled by Westwood [48]. A sputtered atom loses kinetic energy and changes direction on each elastic collision with an argon atom. The energy ratio, E2/E1, for carbon atoms is given by Eq. (9b) where E1 and E2 are the kinetic energies of a carbon atom before and after elastic collision with an argon atom, respectively. M is the atomic mass ratio, MAr/MC = 3.33. As a result, the terms w and E2/EI are equal to - 0 . 4 9 4 and 0.610, respectively. After n elastic collisions between a carbon atom and argon atoms, the energy ratio can be written as

En = exp(nw) E1

513

(167)

0.01 0.0

0.5 1.0 1.5 2.0 ARGON PRESSURE (Pa)

2.5

Fig. 70. Kineticenergy ratio, En/El, after n collisions versus argon pressure for various target-substrate distances [179]. Reprinted from E. Mounier and Y. Pauleau, J. Vac.Sci. Technol.A 14, 2535 (1996), with permission.

with E1 -- 10.1 eV and an average gas phase temperature of 500 K, i.e., Eth -- 0.065 eV, this number of collisions, nth, is equal to 10.

6.4.4. Energy of Argon Ions Impinging on the Surface of Growing Films The thickness of the sheath formed on the surface of grounded substrates can be calculated from the Child-Langmuir equation [192]; its value is much lower than 0.1 mm, i.e., much lower than the mean free path of argon atoms and the mean free path for the charge transfer process. In other words, the collision frequency of argon ions traveling through this cathode sheath was negligible. Therefore, the energy of argon ions colliding with the surface of a-C films grown on grounded substrates could be deduced directly from the value of the plasma potential. The kinetic energy of argon ions impinging on the surface of growing films was varied in the range 2.6-1 eV as the argon pressure increased from 0.1 to 2 Pa.

6.4.5. Origin of Residual Stresses in Amorphous Carbon Films Sputter Deposited on Grounded Substrates The residual stresses in a-C films sputter deposited on Si substrates may essentially result from thermal stress and intrinsic stress developed during the growth of films. The maximum substrate temperature for these sputter depositions of a-C films was less than 60~ As a result, the contribution of the thermal stress to the residual stresses may be neglected and the magnitude of intrinsic stress is approximately equal to that of residual stresses which was determined as a function of the argon pressure (Fig. 68). Intrinsic stresses are generated by energetic particle bombardment of the surface of growing films. The surface of films deposited by magnetron sputtering may sense four types of energetic particles, namely, (i) neutral target atoms sputtered from the target surface and condensed on the substrate, (ii) neutral sputtering gas atoms previously implanted in the target as

514

PAULEAU Table IX.

Residual Stresses in Amorphous Carbon (a-C) Films, Plasma Potential, and Characteristics of the Energetic Particles under Various Experimental Conditions

Sputtering power

Argon pressure

Residual stresses

Plasma potential

Flux ratio

Average energy of C atoms

(kW)

(Pa)

(GPa)

(V)

(PAr/~c

(eV)

0.5

0.1

-0.83

2.6

0.1~

8.7

0.5

0.25

-0.76

2

0.105

7

0.5

0.5

-0.51

1.7

0.082

4.9

0.5

1

-0.26

1.5

0.051

2.4

0.5

2

-0.11

1.1

0.053

0.6

2

0.1

-0.69

2.7

0.081

8.7

2

0.25

-0.65

1.9

0.088

7

2

0.5

m

1.7

0.06

4.9

2

1

-0.26

1.4

0.05

2.4

2

2

-0.19

1.2

0.~6

0.6

Source: E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535, 1996.

sputtering ions which are ejected from the target surface together with neutral target atoms, (iii) ions of the sputtering gas coming from the discharge, and (iv) neutralized sputtering ions backscattered from the target surface by elastic collisions. The flux of the second type of energetic particles is negligible with respect to the flux of carbon atoms ejected from the target. The reflection coefficients, R0 and Y0, corresponding to the flux and the energy of sputtering ions neutralized and backscattered from the target surface (fourth type of energetic particles) are dependent on the atomic mass ratio, MC/MAr (Figs. 13 and 14). For the carbon-argon system, the atomic mass ratio is equal to 0.3; hence, the reflection coefficients R0 and y0 are less than 10 -3 and 0.1, respectively. Therefore, for this system, the contribution of backscattered neutral argon atoms to the energy deposited on the surface of growing films is negligible with respect to the contribution of neutral carbon atoms and argon ions originating from the plasma. According to the model proposed by Windischmann [54], the magnitude of the compressive intrinsic stress in films produced by ion beam sputtering was material specific and scaled with elastic energy per mole defined by the parameter Q expressed by Eq. (121). Stress data reported in the literature for films produced by other deposition techniques involving ionpeening-induced stress show good correlation with Q for a wide range of materials (Fig. 71). The Q parameter value was found to be equal to 16 x 105 J mo1-1 for a-C films sputter deposited on grounded Si substrates using a biaxial modulus, Ef/(1 - vf), of 200 GPa [193]. These a-C films deposited at an argon pressure of 0.25 Pa and a sputtering power of 0.5 kW exhibited a mass density of 2.15 g cm -3 and a compressive residual (intrinsic) stress, ~r, o f - 0 . 7 8 GPa. The values of Q and cr for these a-C films represented in Figure 71 are in good agreement with the values reported in the literature for various materials. On the basis of this excellent correlation, the argon pressure effect on the intrinsic stress developed in sputterdeposited a-C films was analyzed using the forward sputtering model [54, 113]. The compressive intrinsic stress in a-C films

0.0

""

~A,''' ' ;d' I o ,N,- i

,

i i'

,

,'

!

'

''

'

i

'

'' -

-0.5

" .

O. V

-1.0

C ~~

oPt r Si

t/3

.s "

o Ti

-z.o

Cr O

Ta

U

.

O

m ~

z

,

-2.5

-3.o

O

-

AIN -3.5

i , , ,

! , , , , I , , , , I , , , ,

10

! , , , , I , , = , "

20 30 40 Q (x 10 s J mol "1)

50

60

Fig. 71. Variation of the intrinsic stress with the elastic energy per mole factor Q for films prepared by magnetron sputtering [179]. Reprinted from E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535 (1996), with permission.

is given by [179]

Ef

a =4.79(1 _vf)(K) x [2.79(EAr)l/Z~Ar + 2.64(Ec)l/2q~C]

(168)

where EAr and Ec are the argon ion and the carbon atom energies (in electron volts) on the surface of a-C films, respectively; (PAr and 4)c are the argon ion and the carbon atom fluxes (in particles cm -2 s -1) on the surface of growing films, respectively. K is a proportionality factor and N is the atom number density in the deposited material. The intrinsic stress in a-C films and the average kinetic energy of carbon atoms condensed on the surface of films grown under various conditions are given in Table IX. Moreover, the flux and the kinetic energy of argon ions impinging on the sur-

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS

0.0 ~=

-0.2

oq u~ I,M

-0.4

0 t,/') Z

'

'

'

'

i

'

'

'

"

I"

'

'

'

I

'

'"'"

'

I

'

'

515

Table X. Effect of the product (Target-substrate Distance) x (Argon Pressure) on the Residual Stresses in a-C Films Produced under Various Deposition Conditions

'''

Growth rate

Residual

Argon pressure, P

Target-substrate distance, d

d x P

of films

stresses

(Pa)

(cm)

(cm Pa)

(nm min-1)

(GPa)

4.36

-0.75

-0.6

.==.

"

-0.8 -1.0

..... 0.0

I ..... O.S

] ...... 1.0

I .... 1 .S

0.125

14

1.75

0.25

7

1.75

12.2

-0.75

0.5

3.5

1.75

27.6

-0.75

I .... 2.0

2.5

Source: E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535, 1996.

[2.79 (EAr)l/z (])Ar + 2.64 (Ec)l/z (]Dc] (X 1016 cm "z S"1 eV ~ Fig. 72. Dependence of the intrinsic stress in a-C films on the energetics of the deposition process; the solid line was deduced from a least-squares fit to the experimental data [ 179]. Reprinted from E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535 (1996), with permission.

face of grounded substrates were evaluated from the ion current and the plasma potential measurements [179]. These data are reported in the diagram intrinsic stress versus flux and energy of projectile particles plotted in Figure 72. The dependence of the intrinsic stress on energetics of the deposition process is in good agreement with the prediction of the model proposed by Windischmann. In this model, the projectile particles (argon ions and carbon atoms) are supposed to be sufficiently energetic to penetrate the surface and randomly displace carbon atoms from their equilibrium positions in the films through a series of primary and recoil collisions producing a volumetric distortion. The atom displacement energy in bulk materials is currently higher than 10 eV, i.e., higher than the average energy of carbon atoms condensed on Si substrates at low argon pressures and much higher than the energy of argon ions originating from the plasma. However, the displacement of carbon atoms located near the surface of the deposited material is expected to need less energy than the displacement of atoms in the crystal lattice of the bulk material. In addition, the carbon atoms displaced on the surface or in the outermost atomic layers are rapidly covered with other carbon atoms and are isolated from the flux of incident particles. As a result, these carbon atoms are frozen in nonequilibrium positions, leading to volumetric distortions and compressive intrinsic stress development. Furthermore, the energy distribution of carbon atoms ejected from the target shows that a small fraction of these atoms (in the distribution tail) can be sufficiently energetic to displace carbon atoms in the growing films from their equilibrium positions. These energetic carbon atoms may also contribute to the development of the compressive intrinsic stress in the films. The contribution of argon ions to the energy deposited on the film surface is relatively small compared to that of neutral carbon atoms, in particular, at low argon pressures when the thermalization phenomena of sputtered carbon atoms are not very efficient. In other words, in Eq. (168), at low argon pressures, the term 2.79(EAr)1/2~bAr is negligible with respect

to the term 2.64(Ec)1/2q~c. These thermalization phenomena involving collisions between sputtered carbon atoms and sputtering gas atoms play a major role in the deposition process. The number of collisions of carbon atoms in the gas phase and the thermalization of sputtered carbon atoms depend on the product (d • P) between the target-substrate distance and the argon pressure. This product is a relevant factor affecting the development of the intrinsic stress and governing their magnitude in sputter-deposited films as shown in Table X. The compressive intrinsic stress was found to remain at a constant value of -0.75 GPa in a-C films produced under various experimental conditions with the same value of the product (d • P).

6.5. Amorphous Carbon Films Deposited by Conventional and Unbalanced Magnetron Sputtering on Biased Substrates The magnetron target was placed in the center of a cylindrical magnetic coil of 23 cm in inner diameter and the unbalanced magnetron sputtering mode was operated by varying the current in the coil [ 194]. The water-cooled substrate holder was either grounded or biased to negative voltages up to 300 V. The characteristics of the deposition process such as substrate temperature, ion flux, ~PAr,and carbon atom flux, q~c, on the film surface were determined as functions of the substrate bias voltage for sputtering using conventional and unbalanced magnetron modes. The properties of sputter-deposited a-C films, in particular argon content, mass density, and residual stresses were correlated to the deposition parameters. The physical characteristics of the argon discharge (plasma potential, floating potential, electron density, and electron temperature) were deduced from I (V) characteristics of a cylindrical Langmuir probe placed 6 cm from the target surface. A grid probe was placed at the substrate holder position to determine the flux of ions impinging on the surface of growing films.

6.5.1. Characteristics of the Deposition Process The major characteristics of the argon discharge for sputter deposition of a-C films using the conventional and unbalanced magnetron modes have previously been reported [179, 182, 195]. The kinetic energy of ions striking the surface of growing

516

PAULEAU

films deposited on grounded substrates directly corresponds to the plasma potential which was independent of the sputtering power and the current in the magnetic coil. The plasma potential was found to vary in the range 2.5-1 V as the argon pressure was increased from 0.1 to 3.5 Pa. The kinetic energy of ions collected at the surface of films deposited on negatively biased substrates corresponds to the difference between the plasma potential and the substrate bias voltage. However, the value of the plasma potential was always negligible with respect to that of the substrate bias voltage. The flux of positive ions impinging on the film surface increased rapidly as the negative substrate bias voltage was varied from 0 to about 40-50 V [194]. In addition, the ion flux decreased with increasing argon pressure for both magnetron modes and increased with increasing current in the coil, i.e., with increasing unbalanced level of the magnetron target. The ion flux value was in the range (1-4) x 1014 ions cm -2 s -1 with the conventional magnetron mode and could be 20 times higher using the unbalanced magnetron mode [ 194]. The growth rate of a-C films up to 1.8-#m thick was in the range 10-160 nmmin -1 depending upon the deposition parameters and the magnetron modes used. The flux of carbon atoms condensed on Si substrates found in the range 10151016 atoms c m - 2 S-1 was proportional to the sputtering power and was essentially independent of the argon pressure and the negative substrate bias voltage [ 195]. In fact, the dependence of the growth rate of films (expressed in nanometers per minute) on the argon pressure resulted from the decrease in mass density of films with increasing argon pressure. Using the conventional magnetron mode at a sputtering power of 0.5 kW, the ratio of the ion flux to the carbon flux, ~bAr/q~C, was observed to vary from 0.05 to 0.17 with increasing negative substrate bias voltage [194]. The dependence of this ratio on the bias voltage applied to substrates was very similar to that of the ion flux since the carbon flux was approximately independent of the bias voltage. Using the unbalanced magnetron mode, the ratio, ~bAr/~bC, also increased with increasing negative substrate bias voltage; depending on the current in the coil and the substrate bias voltage, the flux ratio value could be higher by a factor of 10 to 20 than the ratio value obtained from the conventional magnetron mode [ 194]. The energetic particle bombardment of the surface of growing films is known to be a major factor affecting the compressive intrinsic stress in the films but also simultaneously the energy deposited on the film surface leads to a temperature rise which depends on the sputter-deposition conditions. Using the conventional magnetron mode with a sputtering power of 0.5 kW, the maximum substrate temperature was about 60~ The maximum temperature of grounded substrates decreased with increasing argon pressure. The energy deposited on the surface of grounded substrates was carried by carbon atoms condensed on the surface. The energy deposited on negatively biased substrates was carried by positive ions accelerated by the bias voltage applied to substrates. Using the unbalanced magnetron mode, the substrate temperature was stabilized more rapidly; however, the maximum substrate temperature was de-

pendent on the current in the coil and the substrate bias voltage. With a positive substrate bias voltage of +20 V, the substrate temperature can reach a relatively high value of 350~ [195]. Consequently, a water-cooled substrate holder must be utilized in particular with the unbalanced magnetron mode for sputter deposition of thermal stress-free a-C films under the experimental conditions investigated.

6.5.2. Characteristics of Amorphous Carbon Films Argon atoms were found as major impurities in the films. For a-C films sputter deposited on negatively biased substrates using the conventional magnetron mode at an argon pressure of 0.25 and 2 Pa, the argon concentration was proportional to the square of the bias voltage and became constant at a given bias voltage value which was dependent on the argon pressure [ 194]. The maximum amount of argon atoms incorporated in the films was 2 and 4 at.% under an argon pressure of 2 and 0.25 Pa, respectively, i.e., the maximum argon concentration increased with decreasing argon pressure. This dependence of the argon concentration on the negative bias voltage and the argon pressure is similar to that already observed for sputter-deposited metal films [ 196]. Argon atoms were also found as impurities in a-C films produced by unbalanced magnetron sputtering [ 194]. The argon concentration increased rapidly with increasing substrate bias voltage before stabilization at a value ranging from 1 to 1.4 at.%. However, the amount of argon atoms in the films was significantly lower than that incorporated in a-C films deposited by conventional magnetron sputtering. In addition, in this case, the linear dependence of the argon concentration on the square of the bias voltage was not observed. The mass density of argon containing a-C films deposited on negatively biased substrates by conventional magnetron sputtering at an argon pressure of 0.25 and 2 Pa increased linearly with increasing bias voltage up to 90-100 V; beyond this bias voltage value, the mass density of films was approximately constant (Fig. 73). The mass density of a-C films deposited on grounded substrates at an argon pressure of 0.25 Pa was nearly equal to the bulk graphite density (2.25 g cm-3). The variation of the mass density of a-C films with the substrate bias voltage is quite similar to the variation of the argon content; i.e., the mass density and the argon concentration were maxima for similar values of the bias voltage. Since the substrates were maintained at room temperature by the water-cooled substrate holder, the thermal stress contribution in the residual stress value can be neglected. As a result, the residual stress values deduced from measurements of the radius of curvature of Si substrates are the values of the intrinsic stress built up during sputter deposition of a-C films. The compressive intrinsic stress in films sputter deposited by conventional magnetron mode at an argon pressure of 0.25 Pa and a sputtering power of 0.5 kW increased progressively up to a maximum value o f - 2 . 8 GPa with increasing bias voltage (Fig. 73). This maximum value is about three times higher than that obtained from films sputter deposited on grounded substrates. By contrast, a-C films with a reduced mass density sputter deposited

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS 2.8[:

A"

-~

9

i

i

' w ....,

.--" 2 6 '

I

-o.s

?

uE

,_, >..

0.0

2.4

I ~

,

A,~

,

.

2.3

E, -1.0 In 15 ~

I,~ Z i,,iJ

-2.0

tn

i

w

i

i'

i

-0.2

i

tn -I~

;r

2.2

-0.3

i

Inrn 13 C

E 2.1 o

-0.4

o}

2.0

rn

r~ 2.0

SUBSTRATE TEMPERATURE (~ 50 190 210 250

~13

t"3

~2.2

517

-0.5

m 1.9 Z

--t ~ I"1'1

-0.6

(::3 1.8 1,o

oo

1.6

J ' -'--" 0 -100 -200 -300 SUBSTRATE BIAS VOLTAGE (V)

,,=I:

-s.o

~

1.6

Fig. 73. Substrate bias voltage effect on the mass density and the intrinsic stress for a-C films sputter deposited using the conventional magnetron mode at a sputtering power of 0.5 kW under an argon pressure of: 0.25 Pa (closed symbols) and 2 Pa (open symbols) [194]. Reprinted from E. Mounier and Y. Pauleau, Diamond Relat. Mater. 6, 1182 (1997), with permission.

2.8

L

t .....

i .....

!

"

i .......... i

9

9

i

E 2.6

Ai

-

9 Z

r

In -1.5 ~

~ 2.4 Z i11

m 2.2 < 5"

2.0

'-zs I_

l

i

I

1

I

,1

I

....

I

I

!

i

_

6 0 1 2 3 4 5 CURRENT INTENSITY IN THE COIL (A)

-o

-0.8

Fig. 75. Mass density of a-C films and magnitude of residual stresses in a-C films versus current density in the coil or the substrate temperature for sputter deposition with the unbalanced magnetron mode at a sputtering power of 0.5 kW under an argon pressure of 0.25 Pa [194]. Reprinted from E. Mounier and Y. Pauleau, Diamond Relat. Mater. 6, 1182 (1997), with permission.

-0.5

i

i

-07

1.7

-3.0

0 -10 -20 -30 -40 -50 SUBS'I'RATE BIAS VOLTAGE (V) Fig. 74. Substrate bias voltage effect on the mass density and the intrinsic stress for a-C films sputter-deposited using the unbalanced magnetron mode at a sputtering power of 0.5 kW under an argon pressure of 0.25 Pa with a current intensity in the coil of 6 A [ 194]. Reprinted from E. Mounier and Y. Pauleau, Diamond Relat. Mater. 6, 1182 (1997), with permission.

at an argon pressure of 2 Pa exhibited negligible compressive intrinsic stress whatever the bias voltage value although the argon concentration in these films was dependent on the substrate bias voltage. The mass density of a-C films produced by unbalanced magnetron sputtering increased from 2.2 to 2.4-2.5 g cm -3 with increasing negative substrate bias voltage before stabilization (Fig. 74). As already observed for films produced by conventional magnetron sputtering, the a-C films deposited on grounded substrates exhibited a mass density close to the bulk graphite density. In other words, the a-C films deposited on grounded substrates by conventional and unbalanced magnetron modes are quite similar in terms of mass density. The compressive intrinsic stress in a-C films produced by unbalanced magnetron sputtering also increased with increasing substrate bias voltage (Fig. 74). The films produced with a negative bias voltage higher than 50 V were not adherent to Si

substrates since the compressive intrinsic stress in these films was excessive, i.e., probably higher than 2.5 GPa. The value of the compressive intrinsic stress in a-C films produced on grounded substrates using the unbalanced magnetron mode was of the same order of magnitude as that for a-C films deposited by conventional magnetron sputtering, i.e., in the range - 0 . 8 to - 1 GPa. The compressive intrinsic stress in a-C films produced by unbalanced magnetron mode increased more rapidly with increasing bias voltage than the intrinsic stress in films deposited by conventional magnetron sputtering; however, the reverse trend was observed for the increase in argon concentration in films produced by unbalanced and conventional magnetron modes. The mass density and the residual stresses for a-C films deposited on grounded and nonwater-cooled Si substrates by unbalanced magnetron sputtering is plotted versus current in the coil in Figure 75; the substrate temperature increased with increasing coil current. The contribution of thermal stress in the residual stress value cannot be neglected for these films. The mass density and the residual stresses decrease with increasing substrate temperature. The characteristics of these a-C films are similar to those of films deposited on substrates heated at moderate temperatures by infrared lamps using the conventional magnetron sputtering process [197].

6.5.3. Origin of Residual Stresses in Amorphous Carbon Films Sputter Deposited on Biased Substrates The mass density of films and the concentration of argon atoms entrapped in the films are maximum for similar bias voltage values. This similarity suggests that the increase in mass density may be caused by the amount of argon atoms incorporated in the films rather than by the formation of really dense a-C films. In fact, the energy deposited on the film surface which increases

518

PAULEAU

with increasing bias voltage seems to have a negligible effect on the mass density of the deposited material. The energy available on the film surface essentially originates from the kinetic energy of positive ions created in the argon discharge and accelerated by the negative substrate bias voltage. The maximum value of the average kinetic energy of neutral carbon atoms condensed on the substrate is about 10 eV whereas the kinetic energy of positive ions is in the range 10-300 eV. The energy deposited on the growing films and resulting from the positive ion bombardment of the surface appears to be the relevant factor affecting the magnitude of the compressive intrinsic stress in a-C films deposited by conventional and unbalanced magnetron sputtering. Since the flux ratio, 4~Ar/4~C, is also dependent on the negative substrate bias voltage or energy of positive ions impinging on the film surface, this flux ratio can be considered as an additional factor affecting the value of the intrinsic stress in a-C films produced under the experimental conditions investigated.

-3.5 -3.0 '-2.5

~-2.0 -1.5 -1.0

-0.5

10

20 30 40 SO 60 70 80 4)," (E)l/2i (x 10 TM ions crn"2 s"1 eV 1/2)

Fig. 76. Effect of the flux and the energy of positive ions on the intrinsic stress in a-C films deposited with the conventional magnetron mode at a sputtering power of 0.5 kW under an argon pressure of 0.25 Pa; the substrate bias voltage values for sputter deposition of these films were in the range - 2 0 to - 3 0 0 V [194]. Reprinted from E. Mounier and Y. Pauleau, 6, 1182 (1997), with permission.

DiamondRelat.

Mater. 6.5.3.1. Applicability of the Forward Sputtering Model Proposed by Windischmann According to Windischmann's model, the compressive intrinsic stress is predicted to be proportional to the product of the particle flux, ~bp, and the square root of the particle energy, Ep (Eq. (120)); i.e., ~bp and Ep represent the flux and the kinetic energy of positive ions striking the surface of growing a-C films. For a-C films sputter deposited on Si substrates biased to a negative voltage in the range 20-300 V under an argon pressure of 0.25 Pa with a sputtering power of 0.5 kW, the intrinsic stress versus product is plotted in Figure 76. The experimental values of the compressive intrinsic stress are in good agreement with the prediction of Windischmann's model as the product [~bp • (Ep) 1/2] is less than 5 • 1015 ionscm -2 s -1 eV l/2. Beyond this value, a large deviation between experimental and predicted results can be observed. As a result, additional phenomena resulting in stress relaxation must be considered for interpreting and modeling the effect of the ion flux and energy on the intrinsic stress in a-C films deposited by sputtering under intense energetic particle bombardment.

[dpp(Ep)1/2]

6.5.3.2. Applicability of the Model Proposed by Davis On the basis of the model proposed by Davis [ 141 ], the compressive intrinsic stress in films for which the film surface is subjected to energetic particle bombardment during deposition can be calculated from Eq. (128). For sputter deposition of a-C films, the flux ratio ckc/cki was determined as a function of the energy Ei of Ar + ions striking the surface of negatively biased substrates. For a-C films sputter deposited with the conventional magnetron mode under an argon pressure of 0.25 Pa at a sputtering power of 0.5 kW, the expression of ckf/cki deduced from experimental data [ 194] is given by ~bc ~i

=

22.75 2.4 + 0.1

(Ef) 1/2

(169)

For a-C films produced with the unbalanced magnetron mode under an argon pressure of 0.25 Pa at a sputtering power of 0.5 kW with a current in the coil of 5 A, the ratio ckc/~i deduced from experimental data [194] is given by 4~c 22.75 = 4)i 26.6 -+- 5.72(Ef) 1/2

(170)

In Eqs. (169) and (170), the ion energy Ei in electron volts is equal to the absolute value of the substrate bias voltage expressed in volts. Finally, the compressive intrinsic stress in a-C films is related to the ion energy by

[

(Ef)l/2

]

cr -- x (22.75/(2.4 + O.l(Ef)l/2)) --I-ka(Ef) 5/3

[

(Ef)l/2

cr -- x (22.75/(26.6 + 5.72(Ef)]/2)) + ka(Ef) 5/3

(171)

] (172)

Equations (171) and (172) based on the model proposed by Davis [ 141 ] are valid for a-C films sputter deposited by conventional and unbalanced magnetron modes, respectively. These equations contain two undetermined parameters, tc and ka, which were used as fitting parameters for a least-squares fit to experimental results. The theoretical curves and the experimental values of the compressive intrinsic stress in the a-C films sputter deposited by conventional and unbalanced magnetron modes are represented in Figure 77. In addition, the values of parameters x and ka are given in Table XI. The experimental results and the predicted values of the intrinsic stress are in very good agreement for a-C films sputter deposited by conventional magnetron mode. For a-C films produced by an unbalanced magnetron mode, the theoretical curve also fits the experimental values; however, these values correspond to relatively low ion energies since the films produced under more energetic ion fluxes were found to be not adherent to Si substrates.

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS

-4

7. SUMMARY AND CONCLUSION

Ix. v

(/3 tr u.,I no'

I~-Z U %

Z ~' .,~.

,.=. ,-

I

0

I

I

.,,,..,,

.I

.

.

.

.

I

100 200 300 400 500 600 700 ION ENERGY (eV)

Fig. 77. Effect of the positive ion energy on the intrinsic stress in a-C films deposited at a sputtering power of 0.5 kW under an argon pressure of 0.25 Pa using: (@) the conventional magnetron sputtering mode, and ((3) the unbalanced magnetron sputtering mode with a current intensity in the coil of 5 A; the curves in solid and dashed lines represent the intrinsic stress values predicted from the model proposed by Davis [194]. Reprinted from E. Mounier and Y. Pauleau, Diamond Relat. Mater 6, 1182 (1997), with permission.

Table XI. Experimental Values of Fitting Parameters, K and ka, Included in Eqs. (171) and (172) Based on the Model Proposed by Davis

Fitting parameter

519

Conventional

Unbalanced

magnetron mode

magnetron mode

K

1.44

0.2

ka

2.54 • 10 - 4

3.45 x 10 -4

Source: E. Mounier and Y. Pauleau, Diamond Relat. Mater. 6, 1182, 1997.

The value of Ea which is an excitation energy required for release of the stress or for displacement of one carbon atom from a metastable position on the surface of the film can be deduced from the expression of ka, i.e., ka = O.O16p(Ea) -5/3 assuming that p = 1 (Eq. (126)). This energy was equal to 12 and 10 eV for films deposited by conventional and unbalanced magnetron modes, respectively. These excitation energy values are in concordance with those corresponding to various other materials [141]. The value of K are of the same order of magnitude for a-C films sputter deposited by conventional and unbalanced magnetron modes (Table XI). It is more difficult to verify the concordance between these values and those calculated from the literature data of various physical constants (Young's modulus, Poisson's ratio, and sublimation energy of the deposited material) included in the expression of K since these physical parameters are rather unknown for sputter-deposited a-C films. Nevertheless, the agreement between the experimental results and the predicted data as shown in Figure 77 contributes to assess the validity and to demonstrate the applicability of the mechanism proposed by Davis to explain the origin of the compressive intrinsic stress developed in a-C films deposited by magnetron sputtering.

Residual stresses in PVD films are the sum of: (1) thermal stress arising from the different thermal expansion coefficients of films and substrates combined with the difference between the deposition temperature and room temperature, (2) intrinsic stress developed as the films grow, and (3) extrinsic stress resuiting from interactions between the deposited material and the reactive agents present in film environment. Excessive residual stresses may cause mechanical damage which has a detrimental effect on the performance of films and devices utilized for various advanced technologies. The control of residual stresses together with a clear understanding of mechanisms involved in the development of stresses are required for reliable manufacturing techniques such as evaporation, sputtering, or ion plating currently used for preparation of thin films. The nucleation steps and the growth mechanisms of PVD films determine the microstructure or the morphology of the deposited materials which, in turn, affect the physical properties of films, in particular the mass or the packing density, the surface roughness, the microhardness, and the residual stresses. Therefore, it is important to investigate the microstructure and the growth mechanisms of films in combination with the nature and the magnitude of residual stresses as functions of experimental parameters related to the deposition equipment and the process. The major features of the microstructure of films which depend on the normalized growth temperature, Ts/Tm (where Ts is the absolute substrate temperature and Tm is the absolute melting point of the deposited material), are thoroughly described by structure-zone diagrams proposed for films deposited by evaporation and sputtering. The microstructure of films is related to the surface mobility of adatoms involved in the growth of films. The adatom mobility depends on the substrate temperature and the kinetic energy of species striking the growing film surface. Hence, the normalized growth temperature and the gas pressure in the deposition chamber are two major experimental parameters which affect the microstructure of PVD films and thereby the residual stresses. A wide variety of methods can be used for measuring the magnitude of residual stresses in PVD films. The residual stresses in amorphous, nanocrystalline, or polycrystalline films can be determined by measurements of the deformation of filmsubstrate structures. For thin films deposited on relatively thick substrates (beams), the nature and the average values of stresses are obtained from measurements of the radius of curvature of beams, the deflection of the free end of the beam, or by observing the displacement (sagitta) of the center of the beam or a circular disk type substrate. Alternatively, the residual stresses in polycrystalline and single crystal films can be determined by X-ray diffraction techniques. Various models can be invoked to explain the development of residual stresses, in particular the origin of intrinsic stress in PVD films. The intrinsic stress can be tensile or compressive depending on the deposition parameters. Tensile intrinsic stress is normally observed in films deposited on substrates at low temperatures by thermal evaporation in the

520

PAULEAU

absence of any energetic particle bombardment. These not fully dense films exhibit a zone 1 type microstructure represented in the structure-zone diagram and the grain boundary relaxation (GBR) model can explain the origin of the stress. Compressive intrinsic stress develops in films deposited at low temperatures under energetic particle bombardment. These films exhibit dense microstructures corresponding to zone T in the structurezone diagram and their compressive intrinsic stress results from the atomic peening mechanism which can be associated with thermal spikes causing displacement of the implanted atoms at relatively high energetic bombardment. The sudden tensileto-compressive stress transition may arise from a threshold phenomenon occurring at approximately the atomic displacement energy. Reduced intrinsic stress can be observed in PVD films deposited at relatively high temperatures since thermally activated atomic diffusion and stress relief phenomena may occur during deposition of films. In addition to thermal and intrinsic stresses, extrinsic stress may develop in thin films subsequently to the deposition process. Water vapor molecules may penetrate in porous films exposed to room air. Adsorption phenomena and adsorbed dipole interactions can be invoked to explain the origin of extrinsic stress. Furthermore, interactions between the deposited material and the adsorbed species can be responsible for a slow evolution of the extrinsic stress as the exposure time of samples to room air (aging time) increases. Stress data illustrating the applicability of models proposed for the origin of stresses have been obtained, in particular for silicon dioxide films prepared by thermal evaporation and ionassisted deposition, silicon oxynitride films produced by dual ion beam sputtering, and amorphous carbon films deposited by conventional and unbalanced magnetron sputtering. To assess the applicability of models, in particular to sputter-deposited films, numerous data regarding the plasma discharge, the flux, and the kinetic energy of particles impinging on the film surface must be collected using more or less complex experimental techniques. The magnitude of compressive intrinsic stress predicted from the models proposed by Windischmann and by Davis are clearly substantiated by experimental results obtained from SiO2, SiOxNy and a-C films produced by energetic deposition techniques.

REFERENCES 1. M.J. O'Keefe and J. M. Rigsbee, in "Materials and Processes for Surface and Interface Engineering" NATO-ASI Series, Series E: Applied Sciences (Y. Pauleau, Ed.), Vol. 290, p. 151. Kluwer Academic, Dordrecht, The Netherlands, 1995. 2. E. Klokholm, IBM J. Res. Develop. 31,585 (1987). 3. M. D. Drory, M. D. Thouless, and A. G. Evans, Acta MetalL 36, 2019 (1988). 4. L. van den Hove, J. Vanhellemont, R. Wolters, W. Claassen, R. De Keersmaecker, and G. Declerk, in "Proceedings of the 1st Symposium on Advanced Materials for VLSI" (M. Scott, Y. Akasaka, and R. Reif, Eds.), The Electrochemical Soc., Pennington, NJ, 1988. 5. J. Vanhellemont, S. Amelinckx, and C. Claeys, J. Appl. Phys. 61, 2176 (1987).

6. H. Awano and T. Sato, Japan. J. Appl. Phys. 27, L880 (1988). 7. K. Kolkholm and J. E Freedman, J. Appl. Phys. 38, 1354 (1967). 8. H.C.W. Huang, P. Chaudhari, and C. J. Kircher, Philos. Mag. A 54, 583 (1986). 9. C.-Y. Li, R. D. Black, and W. R. La Fontaine, Appl. Phys. Lett. 53, 31 (1988). 10. J. E. Greene, in "Multicomponent and Multilayered Thin Films for Advanced Microtechnologies: Techniques, Fundamentals and Devices," NATO-ASI Series, Series E: Applied Sciences (O. Auciello and J. Engemann, Eds.), Vol. 234, p. 39. Kluwer Academic, Dordrecht, The Netherlands, 1993. 11. J. K. Hirvonen, in "Materials and Processes for Surface and Interface Engineering," NATO-ASI Series, Series E: Applied Sciences (Y. Pauleau, Ed.), Vol. 290, p. 307. Kluwer Academic, Dordrecht, The Netherlands, 1995. 12. E B. Barna and M. Adamik, in "Protective Coatings and Thin Films: Synthesis, Characterization and Applications," NATO-ASI Series, Partnership Sub-Series 3: High Technology (Y. Pauleau and E B. Barna, Eds.), Vol. 21, p. 279. Kluwer Academic, Dordrecht, The Netherlands, 1997. 13. E.S. Machlin, "Materials Science in Microelectronics, The Relationships between Thin Film Processing and Structure," Chap. III, p. 49. Giro Press, Croton-on-Hudson, NY, 1995. 14. Y.W. Lee and J. M. Rigsbee, Surf. Sci. 173, 3 (1986). 15. J. P. Hirth and K. L. Moazed, "Thin Films Physics" (G. Hass and R. E. Thun, Eds.), Vol. 4, p. 97. Academic Press, New York, 1967. 16. C.A. Neugebauer, in "Handbook of Thin Film Technology" (L. I. Maissel and R. Glang, Eds.), Chap. 8. McGraw-Hill, New York, 1970. 17. R.S. Wagner and R. J. H. Voorhoeve, J. Appl. Phys. 43, 3948 (1971). 18. E. Krikorian and R. J. Sneed, Astrophys. Space Sci. 65, 129 (1979). 19. M. Marinov, Thin Solid Films 46, 267 (1977). 20. M.-A. Hasan, S. A. Barnett, J.-E. Sundgren, and J. E. Greene, J. Vac. Sci. Technol. A 5, 1883 (1987). 21. T. Narusawa, S. Shimizu, and S. Komiya, J. Vac. Sci. Technol. 16, 366 (1979). 22. K. Yagi, S. Tamura, and T. Tokuyama, Japan. J. Appl. Phys. 16, 245 (1977). 23. T. Tokuyama, K. Yagi, K. Miyaki, M. Tamura, N. Natsuaki, and S. Tachi, Nucl. Instrum. Methods 182-183, 241 (1981). 24. K.-H. MiJller, Phys. Rev. B 35, 7906 (1987). 25. K.-H. Miiller, Surf. Sci. 184, L375 (1987). 26. C.-H. Choi and S. A. Barnett, Appl. Phys. Lett. 55, 2319 (1989). 27. C.-H. Choi, L. Hultman, and S. A. Barnett, J. Vac. Sci. Technol. A 8, 1587 (1990). 28. C.-H. Choi, L. Hultman, R. Ai, and S. A. Barnett, Appl. Phys. Lett. 57, 2931 (1990). 29. S. A. Barnett, C.-H. Choi, and R. Kaspi, Mater. Res. Soc. Syrup. Proc. 201, 43 (1991). 30. D. K. Brice, J. Y. Tsao, and S. T. Picraux, Nucl. Instrum. Methods B 44, 68 (1989). 31. B. A. Movchan and A. V. Demchishin, Phys. Met. Metallogr. 28, 83 (1969). 32. H. T. G. Hentzell, B. Andersson, and S.-E. Karlsson, Acta Metall. 31, 2103 (1983). 33. A.G. Dirks and H. J. Leamy, Thin Solid Films 47, 219 (1977). 34. J. A. Venables and G. L. Price, in "Epitaxial Growth" (J. W. Matthews, Eds.). Academic Press, New York, 1971. 35. B.A. Movchan, A. V. Demchishin, and L. D. Kooluck, J. Var Sci. Technol. 11,869 (1974). 36. J.A. Thornton, J. Vac. Sci. Technol. 11,666 (1974). 37. J.A. Thornton, J. Vac. Sci. Technol. 12, 830 (1975). 38. J.A. Thornton and D. W. Hoffman, Thin Solid Films 171, 5 (1989). 39. J.A. Thornton, Annu. Rev. Mater. Sci. 7, 239 (1977). 40. C.R.M. Grovenor, H. T. G. Hentzell, and D. A. Smith, Acta MetaU. 32, 773 (1984). 41. E. Klokholm and B. S. Berry, J. Electrochem. Soc. 115, 823 (1968).

RESIDUAL STRESSES IN VAPOR-DEPOSITED THIN FILMS 42. C.C. Wong, H. I. Smith, and C. V. Thompson, Appl. Phys. Lett. 48, 335 (1986). 43. E.S. Machlin, "Materials Science in Microelectronics, The Relationships between Thin Film Processing and Structure," Chap. III, p. 57. Giro Press, Croton-on-Hudson, NY, 1995. 44. W. L. Brown and A. Ourmazd, MRS Bull. 6, 30 (1992). 45. E Jona, J. Phys. Chem. Solids 28, 2155 (1967). 46. S.D. Dahlgren, J. Vac. Sci. Technol. 11,832 (1974). 47. L. Eckertova, "Physics of Thin Films" Chap. 2, p. 3. Plenum, New York, 1977. 48. W.D. Westwood, J. Vac. Sci. Technol. 15, 1 (1978). 49. H. Leplan, Ph.D. Thesis, National Polytechnic Institute of Grenoble, France, 1995. 50. M. Xia, X. Liu, and E Gu, Appl. Opt. 32, 5443 (1993). 51. E Sigmund, Phys. Rev. 184, 383 (1969). 52. E M. d'Heurle, Metall. Trans. l, 725 (1970). 53. E Sigmund, in "Topics in Applied Physics: Sputtering by Particle Bombardment I" (R. Behrisch, Ed.), Vol. 47, Chap. 2. Springer-Verlag, Berlin, 1981. 54. H. Windischmann, J. Appl. Phys. 62, 1800 (1987). 55. G.H. Kinchin and R. S. Pease, Rep. Prog. Phys. 18, 1 (1955). 56. T.C. Huang, G. Lim, E Parmigiani, and E. Kay, J. Vac. Sci. Technol. A 3, 2161 (1985). 57. E. Kay, E Parmigiani, and E Parrish, J. Vac. Sci. Technol. A 5, 44 (1987). 58. H.H. Andersen and H. L. Bay, in '"ropics in Applied Physics: Sputtering by Particle Bombardment I" (R. Behrisch, Ed.), Vol. 47, p. 145. SpringerVerlag, Berlin, 1981. 59. W.D. Wilson, L. G. Haggmark, and J. E Biersack, Phys. Rev. B 15, 2458 (1977). 60. K.-H. Miiller, J. Vac. Sci. Technol. A 4, 184 (1986). 61. K.-H. Miiller, J. Appl. Phys. 59, 2803 (1986). 62. J.D. Targove and H. A. Macleod, Appl. Opt. 27, 3779 (1988). 63. H.A. Macleod, J. Vac. Sci. Technol. A 4, 418 (1986). 64. E Seitz and J. S. Koehler, Solid State Phys. 2, 307 (1956). 65. G. K. Wehner and G. S. Anderson, in "Handbook of Thin Film Technology" (L. I. Maissel and R. Glang, Eds.), p. 3-23. McGraw-Hill, New York, 1970. 66. J. Bottiger, J. A. Davies, E Sigmund, and K. B. Winterbon, Radiat. Effects 11, 69 (1971). 67. C. Brunne6, Z. Phys. 147, 161 (1957). 68. N.N. Petrov, Sov. Phys. Solid State 2, 857 (1960). 69. E Sigmund, Can. J. Phys. 46, 731 (1968). 70. H. E Winters and D. Home, Phys. Rev. B 10, 55 (1974). 71. W.R. Gesang, H. Oechsner, and H. Schoof, Nucl. Instrum. Methods 132, 687 (1976). 72. J. E Biersack and L. G. Haggmark, Nucl. Instrum. Methods 174, 257 (1980). 73. D. S. Campbell, in "Handbook of Thin Film Technology" (L. I. Maissel and R. Glang, Eds.), p. 12-21. McGraw-Hill, New York, 1970. 74. R. W. Hoffman, in "Physics of Non-Metallic Thin Films," NATO-ASI Series, Series B: Physics (C. H. Dupuy and A. Cachard, Eds.), Vol. 14, p. 273. Plenum, New York, 1976. 75. M.R. James and O. Buck, Crit. Rev. Solid State Mater. Sci. 9, 61 (1980). 76. S. Tamulevicius, L. Augulis, G. Laukaitis, and L. Puodziukynas, Medziagotyra 2, 40 (1998). 77. M. Murakami, T.-S. Kuan, and I. A. Blech, Treatise Mater Sci. Technol. 24, 163 (1982). 78. B. Borie, C. J. Sparcks, and J. V. Cathcart, Acta Metall. 10, 691 (1962). 79. C.R. Houska, J. Appl. Phys. 41, 69 (1970). 80. J. Unnam, J. A. Carpenter, and C. R. Houska, J. Appl. Phys. 44, 1957 (1973). 81. M. Murakami, Acta MetaU. 26, 175 (1978). 82. S. Timoshenko, "R6sistance des Mat6riaux" Vol. 1, p. 89. Librairie Polytechnique B6ranger, Paris. 83. G.G. Stoney, Proc. Roy. Soc. London Ser. A 82, 172 (1909). 84. A. Brenner and S. Senderoff, J. Res. Natl. Bur. Stand. 42, 105 (1949). 85. J.D. Wilcock and D. S. Campbell, Thin Solid Films 3, 3 (1969).

521

86. W.A. Brantley, J. Appl. Phys. 44, 534 (1973). 87. M.R. James and J. B. Cohen, in "Treatise on Materials Science and Technology, Experimental Methods" (H. Herman, Ed.), Vol. 19, Part A, p. 1. Academic Press, New York, 1980. 88. V.M. Hauk, Adv. X-Ray Anal. 27, 81 (1984). 89. E S. Prevey, in "Metals HandbookmMaterials Characterization" (R. E. Whan et al., Eds.), Vol. 10, p. 380. Am. Soc. Metals, Metals Park, OH, 1986. 90. I. C. Noyan and J. B. Cohen, in "Residual Stress Measurement by Diffraction and Interpretation," Materials Research and Engineering Series (B. Ilschner and N. J. Grant, Eds.). Springer-Verlag, Berlin, 1987. 91. R. E. Cuthrell, D. M. Mattox, C. R. Peeples, E L. Dreike, and K. E Lamppa, J. Vac. Sci. Technol. A 6, 2914 (1988). 92. H. D611e, J. Appl. Cryst. 12, 4598 (1979). 93. H. D611e and J. B. Cohen, Metall. Trans. Mater. A l l , 159 (1980). 94. Z.-C. Feng and H.-D. Liu, J. Appl. Phys. 54, 83 (1983). 95. E H. Townsend, D. M. Barnett, and T. A. Brunner, J. Appl. Phys. 62, 4438 (1987). 96. E. Suhir, ASME J. Appl. Mech. 55, 143 (1988). 97. M.D. Thouless, Thin Solid Films 181,397 (1989). 98. E. Suhir, ASME J. Appl. Mech. 53, 657 (1986). 99. E. Suhir, ASME J. Appl. Mech. 55, 143 (1988). 100. E. Suhir, ASME J. Appl. Mech. 56, 595 (1989). 101. G. Gille, in "Current Topics in Materials Science" (E. Kaldis, Ed.), Vol. 12. North-Holland, Amsterdam, 1985. 102. M.S. Hu and A. G. Evans, Acta Metall. 37, 917 (1989). 103. M. D. Thouless, H. C. Cao, and E A. Mataga, J. Mater. Sci. 24, 1406 (1989). 104. M.Y. He and J. W. Hutchinson, ASME J. Appl. Mech. 56, 270 (1989). 105. J.J. Prescott, "Applied Elasticity," p. 187. Dover, New York, 1961. 106. J. E. E. Baglin, in "Materials and Processes for Surface and Interface Engineering," NATO-ASI Series, Series E: Applied Sciences (Y. Pauleau, Ed.), Vol. 290, p. 111. Kluwer Academic, Dordrecht, The Netherlands, 1995. 107. A. Kelly, "Strong Solids." Clarendon, Oxford, 1976. 108. G.I. Barenblatt, Adv. Appl. Mech. 7, 55 (1962). 109. R.W. Hoffman, in "Physics of Thin Films--Advances in Research and Development" (G. Hass and R. E. Thun, Eds.), Vol. 3, p. 211. Academic Press, New York, 1966. 110. D. S. Campbell, in "Basic Problems in Thin Film Physics" (R. Niedermayer and H. Mayer, Eds.), p. 223. Vandenhoeck and Ruprecht, Gottingen, 1966. 111. K. Kinosita, Thin Solid Films 12, 17 (1972). 112. M. E Doerner and W. D. Nix, Crit. Rev. Solid State Mater. Sci. 14, 225 (1988). 113. H. Windischmann, Crit. Rev. Solid State Mater. Sci. 17, 547 (1992). 114. E.S. Machlin, "Materials Science in Microelectronics, The Relationships between Thin Film Processing and Structure," Chap. 6, p. 157. Giro Press, Croton-on-Hudson, NY, 1995. 115. H. Leplan, B. Geenen, J. Y. Robic, and Y. Pauleau, in "Optical Interference Coatings," Proceedings SPIE (F. Abel,s, Ed.), Vol. 2253, p. 1263. SPIE, Bellingham, WA, 1994. 116. H. Leplan, B. Geenen, J. Y. Robic, and Y. Pauleau, J. Appl. Phys. 78, 962 (1995). 117. I. Blech and U. Cohen, J. Appl. Phys. 53, 4202 (1982). 118. M. E Ashby and D. R. H. Jones, "Mat6riaux-1. Propri6t6s et Applications," p. 53. Editions Dunod, Paris, 1991. 119. H. Leplan, J. Y. Robic, and Y. Pauleau, J. Appl. Phys. 79, 6926 (1996). 120. E Jansen, M. A. Machonkin, N. Palmieri, and D. Kuhman, J. Appl. Phys. 62, 4732 (1987). 121. E Paduscheck, P. Eichinger, G. Kristen, and H. Mitlehner, Nucl. Instrum. Methods 199, 421 (1982). 122. E Paduscheck, C. Hopfl, and H. Mitlehner, Thin Solid Films 110, 291 (1983). 123. J. C. Knight, ~_n 'q'opics in Applied Physics: The Physics of Hydrogenated Amorphous Silicon ImStructure, Preparation, and Devices"

522

124. 125. 126. 127. 128. 129. 130.

131. 132. 133. 134. 135.

136.

137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148.

149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159.

160.

161. 162.

PAULEAU (D. Joannopoulos and G. Lucovsky, Eds.), Vol. 55, p. 5. Springer-Verlag, Berlin, 1984. J. P. Harbison, A. J. Williams, and D. V. Lang, J. Appl. Phys. 55, 946 (1984). H. Windischmann, R. W. Collins, and J. M. Cavese, J. Non-Cryst. Solids 85, 261 (1986). J. C. Angus, C. C. Hayman, and R. W. Hoffman, "Proceedings SPIE," Vol. 969, p. 2. SPIE, Bellingham, WA, 1988. H. Sankur and W. Gunning, J. Appl. Phys. 66, 807 (1989). G. Thurner and R. Abermann, Thin Solid Films 192, 277 (1990). E M. d'Heurle and J. M. E. Harper, Thin Solid Films 171, 81 (1989). J.D. Finegan and R. W. Hoffman, J. Appl. Phys. 30, 597 (1959). R.E. Rottmayer and R. W. Hoffman, J. Vac. Sci. Technol. 8, 151 (1971). E A. Doljack and R. W. Hoffman, Thin Solid Films 12, 71 (1972). R.W. Hoffman, Thin Solid Films 34, 185 (1976). H.K. Pulker, Thin Solid Films 89, 191 (1982). R. W. Hoffman, J. D. Finegan, E A. Doljack, and R. W. Springer, AEC Technical Report, Atomic Energy Commission, Case Western Reserve University, Cleveland, OH, 1961, p. 18; 1970, p. 64; 1971, p. 76; 1972, p. 79; 1975, pp. 82-83. R. Berger and H. K. Pulker, "Proceedings SPIE," Vol. 401, p. 69. SPIE, Bellingham, WA, 1983. H. Windischmann, G. E Epps, Y. Cong, and R. W. Collins, J. Appl. Phys. 69, 2231 (1991). H.K. Pulker and J. M~iser, Thin Solid Films 59, 65 (1979). M. Itoh, M. Hori, and S. Nadahara, J. Vac. Sci. Technol. B 9, 149 (1991). J.H. Rose, J. Ferrante, and J. R. Smith, Phys. Rev. Lett. 47, 675 (1981). C.A. Davis, Thin Solid Films 226, 30 (1993). E.A. Kenick and T. E. Mitchell, Philos. Mag. 32, 815 (1975). M.J. Makin, S. N. Buckley, and G. P. Waiters, J. Nucl. Mater 68, 161 (1977). J.E. Yehoda, B. Yang, K. Vedam, and R. Messier, J. Vac. Sci. Technol. A 6, 1631 (1988). B. Window and K.-H. Miiller, Thin Solid Films 171,183 (1989). O. Knotek, R. Elsing, G. Kramer, and E Jungblut, Surf. Coat. Technol. 46, 265 (1991). K.-H. Miiller, J. Vac. Sci. Technol. A 4, 209 (1986). E.S. Machlin, "Materials Science in Microelectronics, The Relationships between Thin Film Processing and Structure," Chap. 6, p. 179. Giro Press, Croton-on-Hudson, NY, 1995. H.P. Martinez and R. Abermann, Thin Solid Films 89, 133 (1982). A. Blachman, Metall. Trans. 2, 699 (1971). R.S. Wagner, A. K. Sinha, T. T. Sheng, H. J. Levinstein, and E B. Alexander, J. Vac. Sci. Technol. 11,582 (1974). R.D. Bland, G. J. Kominiak, and D. M. Mattox, J. Vac. Sci. Technol. 11, 671 (1974). D.W. Hoffman and J. A. Thornton, Thin Solid Films 40, 355 (1977). D.W. Hoffman and J. A. Thornton, Thin Solid Films 45, 387 (1977). J.A. Thornton, J. Tabock, and D. W. Hoffman, Thin Solid Films 64, 111 (1979). E.H. Hirsch, J. Phys. D: Appl. Phys. 13, 2081 (1980). W.R. Smythe, "Static and Dynamic Electricity," 3rd ed., p. 7. McGrawHill, New York, 1968. J. Topping, Proc. Roy. Soc. London Ser. A 114, 67 (1927). D.W. Hoffman and R. C. McCune, in "Handbook of Plasma Processing Technology" (S. M. Rossnagel, J. J. Cuomo and W. D. Westwood, Eds.), p. 483. Noyes, Park Ridge, NJ, 1990. E.S. Machlin, "Materials Science in Microelectronics, The Relationships between Thin Film Processing and Structure," Chap. 2, p. 21. Giro Press, Croton-on-Hudson, NY, 1995. J. A. Thornton, in "Semiconductor Materials and Process Technology Handbook" (G. E. McGuire, Ed.), p. 329. Noyes, Park Ridge, NJ, 1988. A.M. Haghiri-Goisnet, E R. Ladan, C. Mayeux, and H. Launois, Appl. Surf. Sci. 38, 295 (1989).

163. A.M. Haghiri-Goisnet, E R. Ladan, C. Mayeux, H. Launois, and M. C. Joncour, J. Vac. Sci. Technol. A 7, 2663 (1989). 164. E. Klokholm, J. Vac. Sci. Technol. 6, 138 (1969). 165. P. G. Shewmon, "Diffusion in Solids," p. 65. McGraw-Hill, New York, 166. 167. 168. 169. 170. 171. 172. 173. 174. 175.

176.

177.

178. 179. 180. 181. 182.

183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195.

196.

197.

1963. R.A. Holmwood and R. Glang, J. Electrochem. Soc. 112, 827 (1965). R.C. Sun, T. C. Tisone, andP. D. Cruzan, J. Appl. Phys. 46, 112 (1975). H. Windischmann, J. Vac. Sci. Technol. A 7, 2247 (1989). R.A. Roy, R. Petkie, and A. Boulding, J. Mater Res. 6, 80 (1991). S. Dushman, "Scientific Foundations of Vacuum Technique," 2nd ed., p. 460. Wiley, New York, 1962. W.A. Pliskin, J. Vac. Sci. Technol. A 4, 418 (1986). K. Ramkumar and A. N. Saxena, J. Electrochem. Soc. 139, 1437 (1992). D.O. Hayward and B. M. W. Trapnell, "Chemisorption," 2nd ed., p. 93. Butterworth, London, 1964. J. Y. Robic, H. Leplan, Y. Pauleau, and B. Rafin, Thin Solid Films 290291, 34 (1996). M. Ida, P. Chaton, and B. Rafin, in "Optical Interference Coatings," Proceedings SPIE (E Abel,s, Ed.), Vol. 2253, p. 404. SPIE, Bellingham, WA, 1994. D. Van Vechten, G. K. Hubler, E. P. Donavan, and F. D. Correl, J. Vac. Sci. Technol. A 8, 821 (1990). J. Y. Robic, H. Leplan, M. Berger, P. Chaton, E. Quesnel, O. Lartigue, C. Pel6, Y. Pauleau, and E Pierre, in "Developments in Optical Component Coatings," Proceedings SPIE (I. Reid, Ed.), Vol. 2776, p. 381. SPIE, Bellingham, WA, 1994. A. Bosseboeuf, Ph.D. Thesis, University of Paris-Sud, Orsay, France, 1989. E. Mounier and Y. Pauleau, J. Vac. Sci. Technol. A 14, 2535 (1996). K. Bewilogua and D. Wagner, Vacuum 42, 473 (1991). S.M. Rossnagel, M. A. Russak, and J. J. Cuomo, J. Vac. Sci. Technol. A 5, 2150 (1987). E. Mounier, E. Quesnel, and Y. Pauleau, in "New Diamond and DiamondLike Films," Proceedings of the Topical Symposium II on New Diamond and Diamond-Like Films of the 8th CIMTEC-World Ceramic Congress and Forum on New Materials, Advances in Science and Technology 6 (P. Vincenzini, Ed.), Vol. 6, p. 183. Techna srl, Faenza, Italy, 1995. M.W. Thompson, Philos. Mag. 18, 377 (1968). W.Z. Park, T. Eguchi, C. Honda, K. Muraoka, Y. Yamagata, B. W. James, M. Maeda, and M. Akasaki, Appl. Phys. Lett. 58, 2564 (1991). J. R. Roth, "Industrial Plasma Engineering," Vol. 1, Chap. 8, p. 281. Institute of Physics, Bristol, U.K., 1995. W.D. Davis and T. A. Vanderslice, Phys. Rev. 131,219 (1963). R. S. Robinson, J. Vac. Sci. Technol. 16, 185 (1979). Y. Lifshitz, S. R. Kasi, J. W. Rabalais, and W. Eckstein, Phys. Rev. B 41, 10,468 (1990). K. Meyer, I. K. Schuller, and C. M. Falco, J. Appl. Phys. 52, 5803 (1981). L.T. Ball, I. S. Falconer, D. R. McKenzie, and J. M. Smelt, J. Appl. Phys. 59, 720 (1986). E. W. McDaniel, "Collision Phenomena in Ionized Gases," Wiley, New York, 1964. J. R. Roth, "Industrial Plasma Engineering," Vol. 1, Chap. 9, p. 329. Institute of Physics, Bristol, U.K., 1995. A. Rouzaud, E. Barbier, J. Ernoult, and E. Quesnel, Thin Solid Films 270, 270 (1995). E. Mounier and Y. Pauleau, Diamond Relat. Mater 6, 1182 (1997). Y. Pauleau, E. Mounier, and P. Juliet, in "Protective Coatings and Thin Films: Synthesis, Characterization and Applications," NATO-ASI Series, Partnership Sub-Series 3: High Technology (Y. Pauleau and P. B. Bama, Eds.), Vol. 21, p. 197. Kluwer Academic, Dordrecht, The Netherlands, 1997. J.J. Cuomo and R. J. Gambino, J. Vac. Sci. Technol. 14, 152 (1977). E. Mounier, P. Juliet, E. Quesnel, Y. Pauleau, and M. Dubus, Mater Res. Soc. Symp. Proc. 383, 465 (1995).

Chapter 10

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES Victor Erokhin Fondazione El.B.A., Corso Europa 30, Genoa, 16132 Italy

Contents 1. 2.

3.

4.

5.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principles of the Langmuir-Blodgett Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Monolayers at the Air-Water Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Monolayer Transfer onto Solid Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Techniques for Studying Monolayers and LB Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Monolayers at the Air-Water Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. LB Films on Solid Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Protein Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Protein Monolayers at the Air-Water Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Monolayer Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Protein Layers on Solid Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Thermal Stability of Proteins in LB Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

523 524 524 526 528 528 529 533 533 538 538 543 544 545 545

at the beginning of the twentieth century [2, 3]. The behavior of insoluble floating monolayers at the air-water interface was investigated. From the fundamental point of view, the concepts of the two-dimensional gas, two-dimensional liquid, and two-dimensional crystal and of phase transitions between them were introduced for the first time. The Nobel Prize was given to Irving Langmuir in 1937 as a result of these works. The second stage of the investigations in this field was performed in the 1930s, when the collaboration of Irving Langmuir with Katrine Blodgett resulted in the development of the technique for monolayer transfer from an air-water interface to solid supports [4-8]. This invention opened more possibilities both from fundamental and applied points of view. On the one hand, more precise and quantitative methods of the investigation were available for the study of such objects. On the other hand, possibility of the manipulation with structures at the molecular level of resolution was established for the first time. The third stage in LB film studies was started in 1960s with the work of Hans Kuhn's group. In this period the LB technique

1. INTRODUCTION One of the essential parts of living organisms is the membranema thin layer that separates the intemal part of living unit from the surrounding space. Therefore, the membrane can be considered as the boundary between life and death. Moreover, it not only serves as a passive boundary, but several extremely important processes take place in it: photosynthesis, ion exchange and other biochemical and biophysical processes. However, the aim of this chapter is not to illustrate the state of the art in the field of biological membrane investigations, but to show possible ways of reconstructing membrane structures with artificial methods, namely, by the LangmuirBlodgett (LB) technique. The ancients knew of the ability of oillike compounds to form floating layers at an air-water interface. It was Lord Rayleigh who demonstrated for the first time that such layers can be one molecule thick [1]. Systematic investigations of floating monolayers began with work of Irving Langmuir

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

523

524

EROKHIN

was applied for the realization of molecular architectures [919]. Complicated structures, with designed alternation of different functional layers, were realized and investigated. Exciting work on energy transfer in artificial structures composed of donor, acceptor, and spacer layers attracted the interest of numerous research groups to the molecular manipulation possibilities provided by the LB technique. It is not surprising that the technique was applied for the investigation of biological objects practically as soon as it was discovered. In fact, a floating monolayer at an air-water interface can be considered as a model of half of a biological membrane. The surfactant molecules composing the layer are rather similar to lipid moleculesmthe main part of natural membranes. Thus, Langmuir and Schaefer published in 1938 the first work where the technique was applied for studying protein monolayers and multilayers [20]. This work was also important in that it introduced the horizontal deposition technique, which is widely used now for protein film deposition. Summarizing, the LB approach is very useful for studying membrane-like structures. First of all, several processes can be studied by injecting active molecules under the monolayer into the volume of the liquid subphase. The interaction of those molecules with the model membrane (monolayer) provides insight into the processes in biological membranes. Second, the technique allows one to deposit structures similar to the model membranes onto solid supports, where one can apply various modem and powerful tools for investigation of their structure and properties. Third, it allows one to realize complicated layered structures, which can be used for sensors, biocatalytical reactors, drug design, etc. The aim of this chapter is to give some ideas about the application of the LB technique for studying model systems of biological objects. The structure of the chapter is as follows. Section 2 gives some details on the LB method itself. Section 3 introduces several experimental techniques frequently used for studying monolayers at an air-water interface and LB films. This section gives some features of the techniques for subsequent reference. It does not give complete descriptions of the techniques, but describes their basic principles, ranges of application, and degrees of applicability for studying biological LB films. One graphic representation will be useful for illustrating the subject of the chapter. Figure 1 shows schematic representation of a biological membrane. It contains a lipid bilayer (object 1)--the main part of the membrane. Characteristic features of lipid LB films are considered in Sections 3 and 4. Lipid film studies have been performed for understanding fundamental mechanisms of the membrane structure, its phase transitions, and its interactions with ions and bioactive components. The main part of the chapter, Section 4, deals with proteins. As is seen in Figure 1, proteins in nature exist as integral membrane proteins (object 2), having large hydrophobic areas; partial membrane proteins (object 3), attached to the membrane by hydrophobic interactions of their restricted hydrophobic areas; and circulating hydrophilic proteins (object 4). Section 4 gives

Fig. 1. Schematic representation of the biological membrane: 1, lipid bilayer; 2, integral membrane protein; 3, partial membrane protein; 4, circulating hydrophilic protein; 5, DNA molecule; 6, valinomycin.

advice on how to proceed with film formation in each of these cases. In the conclusion (Section 5) are summarized the most important features of the application of the LB technique to lipid and protein layers. Some remarks on the applicability of the technique for studying some other biological objects, such as DNA (object 5 in Fig. 1) and valinomycine (object 6 in Fig. 1), which are not considered in detail in the text, will be presented.

2. PRINCIPLES OF THE L A N G M U I R - B L O D G E T T TECHNIQUE 2.1. Monolayers at the Air-Water Interface Salts of fatty acids are classical objects of the LB technique. The general structure of these molecules is CH3 (CH2)nCOOH Fatty acids that form stable monolayers, include stearic (n = 16), arachidic (n = 18), and behenic (n = 20) acid. Placed at an air-water interface, these molecules arrange themselves in such a way that the hydrophilic part (COOH) penetrates the water due to its electrostatic interactions with water molecules, which can be considered as electric dipoles. The hydrophobic part (aliphatic chain) faces the air, because it cannot penetrate water for entropy reasons. Therefore, if few enough molecules of this type are placed on the water surface, they form a two-dimensional system. Let us consider what will happen when the layer is compressed with some kind of barrier. We consider the surface pressure as a parameter describing the monolayer behavior. It is determined as Y~ = O'H20 -- O'ml

where O'H20 is the surface tension of pure water and ~rml is the surface tension of the monolayer-covered water surface. In

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES 50

525

FA

45 40 35

o$

30

$o

_

mg

:3 25 ~J

Fig. 3.

Measurement principle and force balance of the Wilhelmy balance.

20

~

15 1o 5

0

...................

8000

~.

.

10000

.

.

.

.

r ........

12000

a t

. . . . . . . . . . . . . . . . . . . . . . .

14000

16000

18000

barrier coordinate (mm) Fig. 2.

Pressure-area isotherm of a stearic acid monolayer.

other words, the surface pressure can be considered as the decrease of the water surface tension due to the presence of the monolayer on it. A compression isotherm of a stearic acid monolayer is presented in Figure 2. This important characteristic represents the dependence of the surface pressure upon the area per molecule, obtained at constant temperature. This dependence is usually called the zr-A isotherm [21 ]. Measurements of such isotherms are practically always performed for studying the behavior and phase transitions of the monolayers at the air-water interface [22-55]. L e t us now consider the isotherm in detail. Initially, the compression does not result in surface pressure variations. Molecules at the air-water interface are rather far from each other and do not interact. This state of the monolayer is referred to as a two-dimensional gas. Further compression results in an increase of the surface pressure. Molecules come closer one to another and begin to interact. This state of the monolayer is referred to as a two-dimensional liquid. For some compounds it is possible to distinguish also liquid-expanded and liquidcondensed phases. Continuation of the compression results in the appearance of a two-dimensional solid state phase, characterized by a sharp increase in the surface pressure for even a small decrease in the area per molecule. Dense packing of molecules in the monolayer is reached. Further compression resuits in the collapse of the monolayer. 2D structure no longer exists. Uncontrollable multilayers are formed at the water surface. Two instruments are usually considered for surface pressure measurements, namely, the Langmuir balance [56] and the Wilhelmy balance [57]. The Langmuir balance measures the surface tension directly. A barrier, separating the clean water sur-

face from that covered with the monolayer, is the sensitive element. This balance is used mainly when precise measurements are needed, and practically never when the monolayer is to be transferred onto solid substrates. There are several reasons for its restricted application. First of all, the utilization of the Langmuir balance requires that the compression of the monolayer be from one direction only. This can result in a gradient of the monolayer density (and thus the surface pressure), which is unacceptable in some cases. Second, the measurement of the surface pressure is not performed where the deposition takes place. This can result in weak control of the monolayer state during its transfer onto solid substrates. Third, there is rather large area of the monolayer that cannot be used. The first and the second drawbacks are critical when working with rigid monolayers. The third drawback is very important when working with expansive substances, as a significant part of the layer must be wasted. The Wilhelmy balance has found more applications, even though it does not provide a direct measurement of the surface pressure. It allows one to avoid all three of the mentioned drawbacks of the Langmuir balance [58-61 ]. The sensitive element of the Wilhelmy balance is a plate. The measurement principle is illustrated in Figure 3. The forces acting to the plate are: mg, the weight of the plate; FA, the Archimedean force; Fs, the surface-tension-induced force. The last force is just the product of the surface tension and the plate perimeter. The weight of the plate is constant, and Wilhelmy balances are now equipped with systems for maintaining the plate immersion depth in the water at the same level, and thereby keeping the buoyant force constant. Thus it is possible to attribute zero force to the clean water surface, and the differences from this value will directly yield the surface pressure. The construction of the balance allows one to perform measurements at a point exactly corresponding to the deposition point with respect to the barrier position. It provides precise control of the surface pressure value, maintained by ~ e feedback system. Another advantage of the Wilhelmy balance is the possibility of compressing the monolayer from both sides, achieving better homogeneity of the monolayer. An important consideration in using the Wilhelmy balance is connected with the necessity of maintaining constant plate po-

526

EROKHIN

sition with respect to the water surface level, in order to avoid variations in the buoyant force. Usually, it this is achieved by special construction of the balance. The Wilhelmy plate is connected to a magnet, which is inserted into a solenoid. Variations in the surface pressure displace the magnet, and electronics provides the current to the solenoid, which restores the initial magnet position. The position can be reset by optical methods. The value of the current is then proportional to the surface pressure value. Another parameter that can be controlled when working with monolayers at an air-water interface is the surface potential [62-87, 89]. This potential results from the orientation of molecular charges and dipoles during the compression of the monolayer. Three different regions are usually considered for its interpretation. The first one is due to the orientation of the C--H bonds in the hydrocarbon chains of the amphiphilic molecules during monolayer formation. The second one is connected with the regular arrangement of the polar head groups. And the third one is due to the dipole orientation of water molecules in the region just under the monolayer. The relative configuration of each of these regions can vary according to the nature of the molecules forming the monolayer. There are differences in behavior between the surface potential and the surface pressure. The variation of the surface potential begins long before the surface pressure begins to increase significantly. This behavior is due to the fact that molecules begin to aggregate, forming dimers, trimers, and small domains, at the initial stage of the monolayer formation. Being aggregated, molecules tend to orient themselves in energetically favorable positions, giving rise to variation in the surface potential. This happens while there is practically no increase of the surface pressure. In the later stages of the monolayer compression the variation of the surface potential is mainly due to the increase of the monolayer density. The Kelvin probe is the tool [90-93] that is usually used for surface potential measurements. The instrument is equipped with a vibrating electrode, placed near the water surface. The reference electrode is inserted into the water subphase. The electrode and water surface form a capacitor. The vibration of the electrode modulates the capacitance, resulting in an alternating current proportional to the surface potential. The surface potential of the monolayer can be either positive or negative; the sign is determined by the nature of the molecules in the monolayer.

2.2. Monolayer Transfer onto Solid Substrates A floating monolayer can be transferred onto the surface of a solid support. Two main techniques are usually considered for mon~layer deposition, namely, the Langmuir-Blodgett (or vertical lift) [4-8], and the Langmuir-Schaefer (or horizontal lift) [20, 94-97]. The scheme for Langmuir-Blodgett deposition is illustrated in Figure 4. A specially prepared substrate is passed vertically through the monolayer. The monolayer is transferred onto the

Fig. 4. Schemeof the Langmuir-Blodgettdeposition (vertical lift).

substrate surface during this passage. The important requirement for such deposition is to have the monolayer electrically neutral. If any charges in the monolayer molecule head groups are uncompensated, the deposition will not be performed because the electrostatic interaction of these charges with water molecules will be larger than the hydrophobic interactions of chains with the hydrophobized substrate surface. Let us consider again a monolayer of fatty acids in order to demonstrate the necessity of head-group neutrality. If the monolayer is formed at the surface of distilled water (pH about 6.0), it cannot be transferred onto a solid substrate. Its head group is dissociated and contains negative charge (COO-). There are two ways to enable deposition. The first one is protonation of the head groups. It requires a decrease of the pH of the subphase. In fact, the deposition begins to take place when the pH is less than 4.0. However, a monolayer of pure fatty acid is very rigid, and its transfer usually results in a defective LB film on a solid substrate. Therefore, usually fatty acid salt monolayers are deposited instead of fatty acids. In this case, bivalent metal ions are added to the water subphase. Normally, their concentration is of the order of magnitude of 10 -4 M. These ions attach themselves electrostatically to the dissociated fatty acid head groups, rendering them electrically neutral. In the deposited layer, the bivalent metal ion coordinates four oxygen atoms in two fatty acid molecules in adjacent monolayers. This coordination is illustrated schematically in Figure 5. The metal atom is at the center of the tetrahedron formed by the oxygen atoms. Such coordination implies that the metal ions are bound to the fatty acid molecules in the adjacent layers and their attachment is very likely to take place when the substrate passes through the meniscus during its upward motion.

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

527

Fig. 7. Situation on the solid substrate surface after touching the protein monolayer. Fig. 5. Tetrahedralcoordination of oxigen atoms by a bivalent metal ion in LB filmsof fatty acid salts.

Fig. 6. Schemeof the Langmuir-Schaefer(horizontal lift) deposition.

The other method of monolayer transfer from the air-water interface onto solid substrates is illustrated in Figure 6. It is called the Langmuir-Schaefer (LS) or horizontal lift technique. It was developed in 1938 by Langmuir and Schaefer for the deposition of protein layers. A specially prepared substrate touches the monolayer horizontally, and the layer transfers itself onto its surface. The method is often used for the deposition of rigid and protein monolayers. In both cases the application of LB method is not desirable, as it results in defective films. In the application of the LS method to rigid monolayers special care must be taken. The monolayer at the air-water interface must be divided into parts after reaching the desired surface pressure [98]. This must be done with a special grid with windows corresponding to the solid support sizes. The main reason for the grid is the following. If the monolayer is rigid, the removal of some part of it will result in the formation of empty regions in the monolayer. As the layer is rigid, these empty zones will be maintained for a very long time. Repeating the deposition will result in the formation of many defects in the monolayer, and the resulting transferred layer will be very inhomogeneous. The use of the grid also assures that only one monolayer is transferred during one touch. In the case of proteins the monolayer is soft. Therefore, the problems mentioned do not exist in this case and the use of the grid can be avoided [99]. In fact, the monolayer structure in the case of protein layers is practically amorphous, as it is easy to reveal by Brewster angle microscopy (to be considered later). Therefore, the removal of some monolayer regions can be rapidly compensated by the feedback system without the loss of the monolayer homogeneity. However, there is another problem when applying the LS technique for protein monolayer transfer. The situation on the solid support after the touching of the monolayer is schematically shown in Figure 7. A regular close-packed monolayer is on the surface of the solid support. Some amount of water, transferred together with the monolayer,

Fig. 8. Typesof Langmuir-Blodgett films.

forms a drop on the substrate. Some protein molecules form an irregular layer at the top of this drop. If the sample is dried in a usual way, these molecules will form an inhomogeneous layer in an uncontrollable way. Therefore, these additional molecules must be removed before the sample drying. The most effective way is to use a strong jet of inert gas, such as nitrogen or argon. It removes the water drop together with the randomly distributed protein molecules on its top, leaving only a regular layer facing to the substrate surface [ 100]. Deposited films are usually divided into three types, schematically shown in the Figure 8, namely, X, Y, and Z types [101]. As is clear from the figure, the Y type is a centrosymmetric one, while X and Z types are polar ones and they differ one from the other only by the orientation of the head groups and hydrocarbon chains with respect to the substrate surface. This difference is due to the fact that in some cases there is no monolayer transfer during upward or downward motion of the substrate in the case of LB deposition. In the case of the LS deposition, moreover, the layers seem to be always transferred in a polar manner. However, the X and Z types are practically never realized in practice. Even when some nonlin-

528

EROKHIN 70-

~ '~"

60

-

r~

50 -

g 9

~ 40 -

30 12

~

g

v

!

!

17

22

number of carbon atoms in the chain Fig. 9. Dependence of the spacing of the LB films of fatty acid complexes upon the length of hydrocarbon chains (expressed as the number of carbon atoms in the chain).

ear properties, such as pyroelectricity, realizable only in polar structures, were observed, and the structures were considered as polar ones [102-106], detailed investigations revealed that the films are of Y type but with unequal densities of odd and even layers [107]. Moreover, in the case of LS deposition of fatty acid films, it was shown that the last three transferred monolayers are involved in the structural reorganization during the passage of the meniscus, so as to realize the thermodynamically stable Y-type packing [ 108]. This reorganization provides the orientation of the hydrocarbon chains toward the air in the last-deposited monolayer. Normal packing of amphiphiles in LB films is characterized by head-to-head and tail-to-tail packing. The tilt angle of the hydrophobic chains with respect to the film plane can vary, but it must provide close packing of the chains. However, several examples of other packings with interdigitation of the hydrocarbon chains of adjacent layers were observed. Initially, such packing was observed on two objects, namely, substituted anthracene [109] and amphiphilic TCNQ complex [ 110]. It is interesting to note that in both cases the headgroup complex was rather large, and this fact was the first indication that the ratio of the head-group size to the hydrocarbon chain length is critical for the realization of such packing. However, this hypothesis was confirmed only after systematic study increasing the length of the aliphatic chain of a molecule with the same large hydrophilic head group. The head group used in this case was a fluorine metal complex, attached to the fatty acid molecule from the water subphase during the monolayer formation [ 111 ]. The complex layers were transferred onto solid substrates, and their structure was studied by small-angle X-ray scattering. The results of the study are presented in Figure 9. It is interesting to note that the spacings of all the films were less than those of LB films of the salts of the same acids with bivalent metals, even if the size of the head group was larger. It is clear from Figure 9 that there are

two linear branches in the dependence, with different slopes. In the case of arachidic acid, the X-ray pattern contained two systems of reflections, corresponding to different spacing values. Calculations of the electron density profile determined that for the short-chain fatty acids packing with interdigitation of hydrocarbon chains takes place, while for the longer chains, they are just packed tilted. The ratio of the head size to the hydrocarbon chain length was taken as the parameter indicating the realization of tilted or interdigitated packing. The value of the parameter for the arachidic acid layer was taken as the transition value (for coexistence of both phases). Application of the mentioned criterion for interdigitated packing confirmed its validity. Great interest in the LB method appeared after the works published by Kuhn's group [10-12, 14, 16, 18, 19, 112-121]. They had shown the possibility of realizing molecular architectures with this method. Complicated structures with alternation of layers of different molecules were realized. Such systems were used for studying energy transfer processes. Layers of donors and acceptors were separated by spacer layers of different thickness.

3. TECHNIQUES FOR STUDYING MONOLAYERS AND LB FILMS 3.1. Monolayers at the Air-Water Interface

The main technique for studying monolayers at an air-water interface is 7r-A isotherm measurement. It reveals the monolayer state and its phase transitions. The method was briefly described in the previous section, together with surface potential measurements. Therefore, let us here consider other methods useful for studying the monolayer at the air-water interface.

3.1.1. Fluorescence Microscopy This technique is based on the fluorescent light from a monolayer containing fluorescent molecules. It reveals the morphology of the layer. In most cases, small dye molecules are added to the monolayer. They cannot penetrate the regions with close packing of the monolayer molecules, and therefore reveal the variation of the domain structure during compression [122136]. However, the technique cannot be considered absolutely clean, as the monolayer under investigation contains additional dye molecules, the presence of which can vary the domain structure of the layer. Microscopy can also be used for revealing the attachment of protein or other fluorescently labeled molecules to surfactant monolayers from the water subphase [137-140]. The technique has been used for imaging the variation in domain structure, in particular, the growth of 2D streptavidin and enzyme crystals. It has been applied for studying phase transitions and chiral discrimination in monolayers. It has also been widely used for studying biorecognition processes between components with high affinity in monolayers.

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

Fig. 10. Brewsterangle microscopyimage of a bacteriorhodopsinmonolayer.

3.1.2. Brewster Angle Microscopy This method is based on the fact that p-polarized light does not reflect from an interface when it is incident at the Brewster angle q9 determined by the equation nl tan ~0 = - n2 where n 1 and n2 are the refractive indices of the two media at the interface. The value of this angle for an air-water interface is 53.1 o. Therefore, it is possible to adjust the analyzer's position in such a way that it will have a dark field when imaging the interface. Spreading of the monolayer varies the Brewster conditions for both air-monolayer and monolayer-water interfaces, making visible the morphology of the monolayer [ 141, 142]. A typical Brewster angle image of the monolayer at the air-water interface is shown in Figure 10. To some extent, the applications of fluorescence and Brewster angle microscopies overlap. Where they do, the application of Brewster angle microscopy is preferable as it does not demand adding anything to the monolayer, with the risk of disturbing it. Brewster angle microscopy was successfully applied for studying the morphology of monolayers [ 143-151 ], their phase transitions [ 131, 152, 153], their thickness and optical properties [154, 155], their 2D crystallization [156, 157] and 2D-3D transformations [158], and the miscibility of multicomponent monolayers [ 159-162].

3.1.3. X-Ray Reflectivity X-ray methods are very powerful for studying the structure of LB films. Mainly, they are used for investigation of films on solid supports and will be discussed later. However, there are some applications of the method for studying monolayers at the air-water interface [ 163-190]. Such experiments are rather complicated to perform. First, the Langmuir trough must be placed on a support that prevents vibrations and surface wave formation. Second, the X-ray

529

source must be powerful, as few molecules (one monolayer only) are involved in the scattering. For this reason synchrotron sources must be used. Third, the source of the incident beam must be attached to the tool so as to provide for scanning of the incident angle (when working with films on solid supports, this is achieved by rotation of the sample with respect to the beam). Modeling of the electron density profile in the direction perpendicular to the water surface is used for revealing the monolayer structure. The monolayer is divided into regions of fixed electron density. The experimental data are fitted by varying the length and relative positions of these regions. Usually the following regions are considered: bulk water; water just under the monolayer, which can be different from the bulk water due to the presence of ions or molecules attached to the monolayer by electrostatic or Van der Walls interactions; head-group region; hydrocarbon chain packing region; interface of the monolayer with air. Such measurements reveal differences in the monolayer packing upon compression as well as interactions of the monolayer with ions and active molecules distributed in the water subphase. 3.2. LB Films on Solid Supports

3.2.1. Electron Diffraction and Microscopy Electron diffraction is the most powerful technique for studying the in-plane structure of the layers. The technique was applied for the structural investigations of LB films at the end of 1930s [191, 192]. It is possible to apply the technique in both transmission and reflection modes. In the case of transmission the sample preparation is rather critical. The support must not significantly disturb the resulting diffraction pattern. In the most cases the supporting substrate is a thin organic layer [ 193]. However, some other methods have been used for the preparation of the supporting substrate. For example, a thin aluminum layer was anodically oxidized and used as a substrate [194, 195]. The layer was then chemically etched with weak HF solution. Cellulose acetate is another possibility for the supporting substrate [ 196]. The diffraction of this material is very diffuse and weak, and practically does not disturb the diffraction pattern of the layer under investigation. When the electron spot is large, the resultant diffraction pattern contains several tings. This is because several domains with different orientations are involved in the diffraction and the situation is rather similar to that of diffraction from a polycrystal powder. Such a diffraction pattern allows only a determination of the elementary cell size, giving no information about the symmetry. Good, reliable conclusions about the symmetry can be reached when the spot diameter is less than the domain sizes. In the case of reflected diffraction the supporting substrates are not so critical. Therefore, a larger variety of substrates have been used. Electron diffraction allows determining the type of symmetry and repetition units of the film elementary cell. LB films

530

EROKHIN

of fatty acid salts have been intensively studied [ 197-211 ]. Initially, their structure was attributed to hexagonal packing [193]. However, precise study using a decreased spot diameter revealed that this apparent hexagonal packing has nothing to do with the real packing, but is due only to the different orientations o f different film domains. Within the same domain the packing can be assigned to orthorhombic, monoclinic, or triclinic symmetry [212]. For electron microscopy the layers can be decorated with heavy atoms. This allows determination of the true structure (including defects) of LB films [213-216]. Both electron diffraction and electron microscopy have been applied even to single monomolecular layers [217-225]. The techniques have been widely applied for the investigation of the structure of lipid [226-231] and lipid-protein LB films [232-241 ].

3.2.2. Scanning Tunneling Microscopy STM is based on the phenomenon of electron tunneling. A sharp metal tip is connected to a piezo mover, which provides scanning of the sample surface. A feedback system maintains constant the tunneling current between the tip and the sample. As the tunneling current depends exponentially upon the tunneling distance, Z-motion of the tip reproduces the relief of the sample surface. STM allows one to obtain even atomic resolution when the sample is highly conductive and atomically flat. Freshly cut pirolytic graphite is an example of such samples. However, the technique has restricted application. The substrate must be conductive, and if the layer is insulating, its thickness must be not more than several angstroms. Otherwise, the tunneling current will be too small for effective measurements. Nevertheless, in some cases STM has been successfully applied for studying LB films of rather large molecules. In particular, good-quality images were obtained on LB films containing charge transfer salts, due to their rather high electrical conductivity [240-244]. Other successful imaging was performed on LB films of organic semiconductors [245-248] and inorganic clusters [249-253]. There are also publications on the successful STM imaging of LB films of large insulating molecules [97, 254-272]. One possible explanation of this success is the penetration of the tip into the layer during scanning. Image formation, in this case, can result from periodic disturbance of the tip by the film molecules. Finally, STM was also applied for protein LB film imaging [273-277]. Mechanisms of the image formation process in this case are still under discussion. However, it is clear that internal water can form passage ways for electrons in the protein films. Wide use of STM among research groups is due to the fact that the instrument allows not only imaging of surfaces and thin layers, but also manipulations of them [278-281]. In fact, it has been used for lithography at nanometer resolution. Moreover, the tip can be used as an ultrafine electrode for study and realization of point contacts for junctions involving single molecules. Such utilization of STM has made

possible room-temperature single-electron junctions, singlemolecule switches, molecular memory, etc.

3.2.3. Atomic Force Microscopy AFM is rather similar to STM. The difference is that in AFM the atomic forces are the parameters under control. A feedback system maintains constant the attractive or repulsive Van der Waals force according to the relative position of the tip and surface. The main advantage of AFM is the ability to study any kind of the surface regardless of its conductivity. However, it provides less resolution than STM. In fact, it is very hard to reach atomic resolution with AFM, due to the curvature of the tip. This is not the case for STM, due to the exponential dependence of the tunneling current upon tunneling distance. The AFM has been widely applied for the investigation of different kinds of LB films [200, 221, 261,266, 271, 281-289, 289-398]. The taping mode gives even more ability to the AFM for studying biological samples, as it is less affected by noise. In this case the tip is in vibration during the surface scanning [399402]. Like the STM, the AFM can be used as nanometer-scale instrument for realizing patterns in thin layers [403,404].

3.2.4. X-Ray Scattering Several methods based on the utilization of X-rays are used for studying the structure of the LB films. These methods were used even in the initial stages of LB film investigation [405412]. Diffractometry and reflectometry are the ones most often used. Diffractometry is mainly used when a well-ordered periodic structure is under the investigation and there are several Bragg reflections in the X-ray pattern [ 190, 209, 212, 282, 287, 413469]. The position of these reflections is determined by the Bragg equation 2D sin tO = nX where D is the thickness of the periodic unit (period or spacing), ~. is the wavelength of the incident X-ray beam, t0 is an incident angle, and n is the order of the reflection. Therefore, the thickness of the periodic unit (usually a bilayer) can be that obtained directly from the angular position of Bragg reflections. The other information that can be directly obtained from the X-ray pattern is the correlation length L. This parameter can be considered as the thickness up to which the film can be still considered as an ordered one, and it is determined by the following formula: L=

2Ato

where A to is the half-width of the Bragg reflections. More information can be obtained if several reflections are registered. Each Bragg reflection can be considered as a term in the Fourier series representing the electron density on the repeating unit of the film. Therefore, the electron density on a

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES period of the film can be expressed as

531

1600 .,~ 1400

p(1) ,,~ C An COS~n n

where An is proportional to the intensity of the Bragg reflection and (/9n is the phase of the harmonic. Fortunately, the most LB films have Y-type structure, and therefore the phases for them can be only 0 or rr, so that the typical crystallographic phase problem becomes a simpler sign problem. This problem is usually solved by fitting the electron density in some known regions--most often a region where close packing of hydrocarbon chains takes place. The resolution in the determination of the electron density profile in the case of diffractometry (R) is connected with the number of registered reflections and is determined by the formula

R=

D 2n

where D is the period and n is the number of registered reflection. Therefore, the resolution is half the wavelength of the harmonic determined by the last registered reflection. Reflectometry is the other approach for studying LB films with X-ray techniques [181,326, 470-500]. It allows one to study not very well ordered films and even monolayers. In reflectometry the whole registered scattering curve is considered. It can contain Bragg reflections and also Kiessig fringes. The latter correspond to the interference of the X-ray beams reflected from the air-film and film-substrate interfaces, and their angular position gives information about the total thickness of the LB film. The electron density profile in the case of reflectometry is calculated from models, fitting the whole experimental curve.

3.2.5. Infrared Spectroscopy Infrared spectroscopy is among the most powerful tools for studying the structure of LB films, both at the air-water interface and after deposition onto solid substrates. It allows one to determine the orientation of molecular chains [501-511 ], the structure and composition of layers [512-536], and the attachment and secondary structure of proteins [537-541 ]. It also allows one to visualize reorientation of the layers due to temperature [358-360, 542-547], substrate influence [548-551 ], and electron beam action [552]. The technique has also been used for studying water transport through layers, in particular, hydration of DNA containing LB films [455,553]. The main difficulty with IR experimental analysis of the LB films is connected with the small amount of the material in the sample. However, the good signal-to-noise ratio can be obtained if attenuated total reflection is used for the measurements of LB films [224, 554, 555].

3.2.6. Gravimetry A very useful technique is based on the fact that a piezoelectric oscillator changes its resonant frequency when additional

1200

~:~ lOOO ,~ 800 6OO

200 0,,~ 0

!

!

5

10

number of deposited bilayers Fig. 11. Dependence of the frequency shift of a quartz balance upon the number of bilayers of cadmium arachidate deposited on its surface.

mass is deposited onto its surface. Usually, quartz oscillators are used. The phenomenon is described by the Sauerbrey equation" Af Am = ----l

fo

Apt

where f0 is the initial resonant frequency, A f is the frequency shift, p is the density of the quartz, A is the electrode area covered by the film, and I is the oscillator thickness [566]. Calibration of the quartz balance can be performed by successive deposition of layers of fatty acid salts [567]. The typical dependence of the frequency shift upon the deposited layers is a straight line as presented in Figure 11. In many practical cases it is better to calibrate the balance in terms of surface density instead of mass changes. In this case it is also necessary to cover the quartz surface with layers of a material with known surface density (again, fatty acid salts, for example). Such calibration is useful for studying transferred layers of substances with unknown surface density. In the case of monolayer or bilayer transfer, it will be possible to determine the surface density of the film and, knowing the molecular weight of the compound, to determine the area per molecule in the layer [568]. This possibility is important for protein layers, as the area per molecule for them can almost never be found from zr-A isotherms, for reasons that will be discussed later. The technique was also applied for the investigation of the hydration of LB films [569-573], for the investigation of the attachment of ions [574, 575] and of other molecules [576579] to layers, for studying chemical reactions in LB films [580, 581], and for studying viscoelastic properties [582] and phase transitions [583, 584]. The technique also finds wide application in the field of gas sensors [585-592] and biosensors [593598].

3.2.7. Ellipsomerty This technique is based on the fact that linearly polarized light becomes elliptically polarized after reflection from the interface. The measured parameters are ~ (the amplitudes of oscillation of the electric field vector in the plane of incidence

532

EROKHIN

and perpendicular to it) and A (the difference of phase between them). They allow one to calculate with high accuracy the thickness and refractive index of the layer. The first time the technique was applied for LB film study was in 1934 for the investigation of properties of fatty acid layers on a mercury surface [599]. Since then, the technique has been successfully applied for studying films with increasing numbers of layers. In some cases, a three-layer model, including an intermediate layer (usually oxide) between the substrate (usually metal) and the LB film, is considered [600, 601 ]. Initial works considered the LB film as an isotropic system [602-617]. However, later the theory was extended to anisotropic LB films [618-620]. In this case, the difference in the refractive index in different directions with respect to the sample plane was measured. Such measurements made it possible to show that the dipping direction in the case of vertical lift deposition orients the layers, resulting in slight anisotropy of the LB films. Ellipsometric studies were also performed at the air-water interface, allowing study of the variation of the monolayer thickness during compression, and thereby revealing phase transitions of the monolayer [621-625]. Ellipsometry at the air-water interface is also very useful for studying the interactions of a monolayer with different compounds dissolved in the water subphase [626]. As an example, we can mention the successful application of the technique for studying lipid-protein interactions [ 138, 627]. Recently, microscopic ellipsometry was established, allowing one to determine the distribution of thickness and refractive index in 2D images [628,629].

3.2.8. Interference Methods The interference method of film thickness determination has been applied since the beginning of LB film investigations. For the normal incidence, the film thickness h can be determined from the formula h = m~/4n

where ~. is the wavelength, n is the film refractive index, and m is an integer. This simple technique is still used effectively for thickness determination [453,630-635]. It is interesting to note that one of the first practical applications of LB films was as thickness standards, using the high precision in the thickness of the resultant layers [8]. Another application of the technique is in the field of sensors [636]. In fact, any change that varies the thickness or refractive index of the layer can be revealed by interferometric methods. Finally, interferometry gave rise to very interesting and powerful method of thin-layer investigations, namely, scanning optical microscopy, where the thickness and refractive index patterning of the layer can be determined with rather high resolution [637].

3.2.9. Neutron Scattering

Neutron scattering is a complicated technique, demanding expensive, complicated equipment, which allows one to determine structural parameters of layers. There is one fundamental difference between neutron scattering and that of X-rays or electrons. In the case of neutrons, it is possible to observe socalled anomalous scattering, where the scattered beam changes its phase. Fortunately from the application point of view, one of the most widely distributed elements in nature, hydrogen, provides such anomalous scattering. Therefore, it is possible to vary the contrast of the measurements by using a mixture of ordinary and deuterated water (ordinaral water yields anomalous scattering; heavy water does not). Neutron scattering was used for studying the LB film structure at an air-water interface [ 166, 170, 638-667] and after deposition onto solid substrates [473, 481,484, 485,668-672]. At the air-water interface, the technique was used for the visualization of phase transitions, in particular, by registering the difference in the head-group hydration in different phases [27, 646, 673, 674], the attachment of protein molecules to the monolayer [667, 675-678], and the behavior of multicomponent mixtures [679, 670-687]. In the solid phase, the technique allows performing experiments on the lateral and interlayer motion of molecules in LB films, which cannot be determined with any other technique [490, 497,688]. Let us consider one example illustrating this statement [689, 690]. A multilayer barium stearate film was deposited. Each odd layer was deposited with ordinary stearic acid, while each even layer was deposited with deuterated stearic acid. The X-ray pattern revealed periodicity of about 5 nm, as is typical for stearic acid salt LB films. The neutron diffraction pattern, however, had a system of reflections with double that period. In fact, in the case of X-ray scattering measurements, there is no difference between normal and deuterated stearic acid, as their electron density is practically the same, while for the neutron scattering these layers are different and therefore the period was doubled. Quantitative analysis of the scattering curves showed that the layers are not uniform. Each deuterated layer contains about 70% of the deuterated and about 30% of the normal stearic acid. In the normal acid layer the situation was reversed. Therefore, this experiment showed that there is molecular exchange between adjacent layers in LB films. Very likely, this exchange takes place during deposition of the layers, when the solid substrate passes through the meniscus. In fact, there are other, indirect indications that monolayer molecules can be involved in flip-flop motion while passing a meniscus. This fact indicates once more that the resulting structure of the LB film can be different from the desired one, and that special structural investigations must be carried out to verify the real structure of realized films. Similar investigations were performed for analyzing the temperature and temporal effects on the LB film structure [417, 493, 691 ].

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

533

+50V

4. PROTEIN FILMS I

4.1. Protein Monolayers at the Air-Water Interface Protein molecules are complicated systems, composed of polypeptide chains organized into globules. Usually, interior of the globule is hydrophobic, while its surface is mainly hydrophilic. This fact about proteins leads to their instability at an air-water interface. In fact, the surface tension of the water (72 mN/m) is enough to exert significant forces on protein molecules, resuiting in most cases in denaturation. The time necessary for the denaturation depends upon the protein. In some cases it can be minutes, and in others, hours. Immunoglobulin, in particular IgG, is an example of the more stable proteins. The structure of this molecule is stabilized by covalent disulfide bridges. The presence of such strong bonds provides improved resistance to the action of the surface tension at the air-water interface. However, long exposition of IgG to surface tension leads to significant changes even in such a stable protein. There are some examples where protein solutions can be spread directly on the air-water interface. That is mainly true of membrane proteins, and it happens at interfaces even in nature. We will consider two examples of monolayers of such proteins. Other proteins demand the utilization of some variation of the LB technique for realization of films without denaturation.

4.1.1. Monolayers of Bacteriorhodopsin Bacteriorhodopsin (BR) is a light protein (12.5 kDa) providing light-induced transmembrane proton pumping. It is a main part (80%) of purple membranes. BR is very unstable in isolated form, while it is very stable in membranes. Therefore, a spreading solution is composed of membrane fragments. This makes it difficult to maintain a significant part of the protein at the air-water interface. In fact, the membrane fragments are about a micron in sizes. The top and bottom parts of these objects are hydrophilic, while only small lateral parts, about 5 nm high, are hydrophobic. Therefore, after the spreading on a pure water surface, most of the fragments penetrate the water volume and do not form a monolayer. In order to avoid this difficulty, the solubility of the membrane fragments must be decreased. This can be achieved by using concentrated salt solutions as a subphase. Usually, 1.5-2.0 M NaC1 or KC1 is enough to prevent leakage of the membranes from the surface to the volume of the liquid subphase [454]. A comparison of zr-A isotherms of membrane fragments at the surface of pure water and on 1.5 M KC1 clearly indicates that the presence of salt in the subphase allows one to maintain a significant amount of the sample in the monolayer. Usually, BR films are deposited onto the solid substrate by the horizontal lift technique. Some amount of water subphase is also transferred together with the monolayer. As the subphase contains concentrated salt solution, a significant amount of salt can remain at the substrate in the case of BR films. However, the salt can be removed from the sample. There are two ways to do so. The first one requires the use of special salts, which can be decomposed into gas compounds. Ammonium acetate is an

I'

......~ . . ~...: . . , . ~ . . . , . . . . . . - . : . . . , . . . . . . . . - . - . . . - . - . . . . . ~ i.i.iolololoi i.iololoir

I F i g . 12.

2_

Scheme for electric-field-assisted formation of a BR monolayer.

example. After the deposition, the BR LB film can be exposed to low vacuum, and the salt will be decomposed and removed from the sample. The second approach does not demand the use of special salts. The sample is simply washed with water after depositing each successive layer [454]. Many applications of BR films demand strong of the membrane fragments, with proton transfer vectors oriented in the same direction. However, that is not simple to realize in practice. The top and bottom parts of the fragment have nearly the same hydrophilic properties. Therefore, fragments are oriented in opposite directions, resulting in zero photopotential and photocurrent, as the proton displacements compensate each other in the adjacent fragments. This difficulty can be overcome by taking into consideration the charge distribution in the purple membranes: their interior is charged more positively than their exterior. The following modification of the LB technique was realized for obtaining highly oriented BR LB films [692]. The scheme of the modified procedure is shown in Figure 12. One electrode is immersed in the water subphase, containing the concentrated salt solution. The other electrode, with area about 70% or more of that of the opening in the barrier, is placed about 2 mm above the subphase surface. A voltage of 30-50 V is applied between the electrodes (the upper one is biased positively). Purple membrane solution is injected into the subphase volume. Membrane fragments begin self-assembling at the air-water interface, orienting themselves in the electric field in such a way that all proton pathways are oriented in the same direction. The process is analogous to electrochemical sedimentation in solution [693, 694]. The monolayer formation can be monitored by registering the increase of the surface pressure in time. Comparison of these dependences in the presence and absence of the electric field makes it clear that self-assembling of fragments into the monolayer takes place only if the electric field is applied. Moreover, if the polarity of the applied field is opposite (upper electrode is biased negatively), the dependence of the surface pressure upon the time is similar to that in the absence of the electric field. When the increase of the surface pressure with time becomes saturated (at surface pressure about 12 mN/m), the electric field can be switched off, the upper electrode removed, and

534

EROKHIN

Fig. 13. Scheme for the spreading of RC solution on the air-water interface using a hydrophilic plate.

the monolayer further compressed (25 mN/m) for higher density and transferred onto solid substrates. The proposed technique allows one to form much betteroriented mono- and multilayer BR films than the usual LB deposition. It also has significant advantages over the usual electrosedimentation technique, as it allows realizing structures at molecular resolution, while electrosedimented films are of about micron thickness. Investigations of BR monolayers at the air-water interface have allowed determining the role of the subphase composition [695-697], electrical and optical properties [698,699], and the structure of the monolayer [539, 700-702].

4.1.2. Films of Photosynthetic Reaction Centers A photosynthetic reaction center (RC) is a large protein (about 100 kDa), containing three subunits and performing lightinduced transmembrane electron transport. The electron transport chain of the protein contains a dimer of bacteriochlorophyll (primary donor), bacteriopheophetin, and two quinons. In nature the protein works together with multiheme cytochrome, which provides necessary electrons to the dimer of bacteriochlorophyll. Spreading solutions contain separated RC molecules. Each molecule is surrounded by a detergent, attached to a hydrophobic area that is embedded naturally in the membrane. The detergent appears during the extraction of RCs from the membrane. Therefore, the resulting complex is hydrophilic, and special care must be taken in placing such molecules on the air-water interface. There are two common methods to do this. The first method is based on the use of a hydrophilic glass plate inserted into the water subphase (Fig. 13). RC solution is dropped onto the plate and transfers itself to the subphase surface [698]. The second method is based on dropping small drops of RC solution onto the air-water interface [ 100, 703,704]. The spreading is good (small leakage into the subphase volume) if the drops remain for some time at the subphase surface, diminishing in size. Being placed on the air-water interface, the detergent-RC complex rearranges itself. Interaction of the detergent head groups with water results in their detachment from the RC molecules and transfer onto the water surface (Fig. 14). As a result, detergent-free RC molecules form a monolayer, and the space between them is filled by detergent molecules. Usually, detergent molecules have rather short hydrocarbon chains and cannot form a stable monolayer at the air-water interface them-

Fig. 14. face.

Rearrangment of the RC-detergent complex at the air-water inter-

selves. Therefore, dense RC packing in the monolayer with a reduced amount of detergent can be achieved by compressing the monolayer to high surface pressure. In this case, the detergent molecules can be pushed into the subphase volume in the form of micelles. They can also form local collapses. Therefore, at high surface pressure the monolayer is mainly composed of RC molecules. The compression of the RC monolayer must be rather fast in order to minimize the denaturing action of high surface tension on the RC molecules. In this regard, the chief weakness of the molecule is that it is composed of subunits. Therefore, it is easy to suppose that the surface tension will result first of all in the destruction of the quaternary structure of the protein. This suggestion is easy to check, as the two bacteriochlorophyll molecules in the dimer are attached to different subunits [705]. Absorption spectra of RC LB films deposited at different surface tensions have confirmed the splitting of the protein subunits. At surface pressures below 25 mN/m it is possible to see the absorbance of the monomer of bacteriochlorophyll (802 nm) and no absorbance of the dimer (860 nm). Increase of the deposition surface pressure results in the appearance of the dimer absorption peak, finally amounting to half the monomer peak intensity. Such behavior of the absorbance indicates that high surface tension at the initial stages of the monolayer compression splits the RC molecule into subunits. When the surface tension is reduced by monolayer compression, the spliting does not take place. As in the B R case, there is also great difficulty in orienting all RC molecules in the same direction in the monolayer, as the hydrophilic areas at the top and bottom of the molecule have similar properties. However, the approach used in the case of BR cannot be applied to the RC monolayers. In fact, the membrane fragments used in the case of BR monolayers cannot overturn after the switching off of the electric field. Their sizes are large, and overturning would demand significant energy. Instead, RC molecules, being separated one from the other, will reorient themselves, resulting in mutually compensating orientation of the electron pathways in the adjacent molecules. The following method was suggested to overcome this difficulty (Fig. 15). The monolayers were transferred onto the substrate, which was biased with respect to the liquid subphase [706-708]. Of course, the solid substrate must be conductive in this case. However, when the photoelectric proper-

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

535

Fig. 15. Schemefor the deposition of RC monolayersontoelectrically biased substrates.

ties of the RC monolayers are to be used, the substrates must be conductive ones anyway. Therefore, that is not a big disadvantage of the method. A more important problem is the prevention of electrical current flow between the substrate and water subphase, because such a current can have undesirable effects on the film. Therefore, it is best to deposit an insulating layer between the substrate surface and RC layers. The presence of such a layer will not create additional difficulties if optoelectronic measurements are used to probe the electron displacement in the RC molecules, but it will make practically impossible any measurements for which electron exchange must take place between the RC molecules and the substrate electrode. Another method, allowing better orientation of RC molecules in mono- and multilayers, was demonstrated on RC from Chromatium minutissimum [709, 710]. The cytochrome molecule is strongly attached to the RC molecule in these bacteria and is not lost during extraction from membranes. Therefore, the RC-cytochrome complex can be considered as a four-subunit aggregate in this case. The cytochrome subunit is charged positively. It is interesting to note that this charge on one subunit made it impossible to transfer the RC monolayer from the water surface to the solid substrate by the usual vertical or horizontal deposition techniques. The electrostatic interactions with the water were much stronger than that with the solid substrate surface. However, the presence of such a charged subunit is very useful for the realization of monolayer anisotropy. The cytochrome subunit is oriented into the water subphase. In order to keep this anisotropy in the deposited film, the RC monolayers must be transferred onto negatively charged substrates. Such deposition was realized by depositing heterostructures, with alternation of RC monolayers with arachidic acid monolayers (Fig. 16). A hydrophobized solid substrate was passed downward through an arachidic acid monolayer, formed at the subphase with pH 7.0. Head groups of the arachidic acid are mainly dissociated at this pH value and are charged negatively. During the subsequent upward motion, the substrate was passed through the RC monolayer. Electrostatic interaction of

Fig. 16. Schemefor the deposition of an RC-arachidic acid heterostructure.

the arachidic acid head groups with cytochrome subunit of RC took place at this stage. The process was repeated several times. An X-ray diffraction study performed on such hererostructures revealed the presence of seven Bragg reflections, indicating rather high ordering of the resultant film. Normally, monocomponent protein films do not allow registering more than one Bragg reflection [99]. The suggested approach seems to be rather general for obtaining highly ordered protein layers. Electrostatic interactions provide anisotropy of the film, while the presence of fatty acid interlayers results in improved layer packing.

4.1.3. Complex Lipid-Protein Monolayers The most natural way to eliminate the denaturing action of surface tension on protein molecules is to diminish it by spreading a lipid monolayer at the air-water interface and to attach proteins to it [237, 711-716]. A widely used example of such complex monolayers is based on biotin-streptavidin interactions, as the affinity of the resulting complex is extremely high [678, 717-727]. The streptavidin molecule has four binding sites where biotin can be attached. Several synthetic lipids with biotin molecules in the head group were synthesized, and their monolayer behavior at the air-water interface was studied. Streptavidin molecules were injected into the water subphase. When strike conditions of the biotinated lipid were chosen in the correct way, growth of 2D streptavidin crystals was observed by different methods. The proposed approach is very important for the realization of layer manipulation at the molecular level, called also molecular architecture. In fact, 2D crystals of streptavidin are attached with two biotin binding sites to the lipid monolayer, and two

536

EROKHIN

other binding sites are still available. The resulting 2D crystal of streptavidin can be used as a template for the next layer formation. This layer can be composed of any functional molecules, conjugated with biotin. Regular distribution of the binding in the temptate layer will make it possible to distribute desirable molecules in a quasi-crystallic manner, while attachment of the biotin at different positions will guarantee their preferential orientation. Therefore, combination of the LB technique with selfassembling, based on complexes with high affinity, allow one to form regular molecular systems with high ordering not only between monolayers, but also in each monolayer plane. The suggested procedure can be repeated to realize the organization of complicated structures of different layers. In this case, functional molecules must be conjugated with two biotin molecules. One of them will be attached to the template layer, while the other will provide the binding for the formation of the next streptavidin layer. The attached streptavidin will form a template layer for the formation of the next active layer, formed from different molecules. Another method to attach protein molecules to the lipid monolayer is based on the utilization of Coulomb interactions. From the realization point of view, the method can be considered as a simplified version of that based on specific affinity. Formation of cytochrome C monolayers can illustrate this method [442, 728-731 ]. Cytochrome C is a protein with molecular weight 30 kDa. It has charge +8 at neutral pH (7.0). Fatty acid molecules are dissociated at this pH value and contain negative charge. Therefore, a monolayer of stearic acid was formed and cytochrome C molecule solution was injected under it. Polarized absorbance measurements revealed the attachment of protein molecules to the monolayer with preferential orientation of heme groups in them parallel to the monolayer plane. A special tool for producing lipid-protein interactions at the air-water interface and transfer the resultant complex monolayers onto solid substrate is called the Fromherz trough [238,732, 733]. It is shown schematically in Figure 17. It is a circular trough divided into several sections (four are shown in the scheme, but their number can be varied). Two moving barriers allow one to compress monolayers in each section and also to transfer them from one section to another, maintaining the internal distances. The process of monolayer transfer from one section to another is schematically shown in Figure 18. Initially, the monolayer of desired lipid molecules is formed in section I by compressing it with the barriers up to the chosen surface pressure. Then, the monolayer can be transferred to section II by synchronous motion of both barriers. Section II can contain protein molecules with affinity (opposite charge) to the head groups of the formed monolayer. Then, the monolayer with attached protein molecules can be transferred to section III, containing reagents for detaching protein molecules adsorbed nonspecifically on the monolayer. Section IV can contain other protein molecules, which can be attached to the formed complex monolayer.

Fig. 17.

Scheme of the Fromhertz trough.

Fig. 18. Scheme for monolayer transfer from one section to another in a Fromhertz trough.

An important feature of the instrument is its ability to form the monolayer at the surface of one subphase and to produce the lipid-protein interaction, at the other. In fact, different conditions, such as composition, pH, or ionic strength, can be optimized for forming the monolayer and providing the interaction attachment. Moreover, in some cases the interaction can result in different protein attachment (density and orientation) to monolayers compressed to different surface pressure values. Therefore, the ability provided by Fromherz trough to perform protein attachment when the monolayer compression is finished is very important. Another instrument allowing the effective deposition of complex lipid-protein monolayers is based on a specially constructed sample holder [734]. The sample holder is equipped with a protective plate, located about 1 mm from the sample surface (Fig. 19). The plate is fabricated from hydrophilic materials. It can be in two positions: up (the sample surface is not protected by the plate) and down (the plate is near the sample surface, keeping a water layer between them by capillary forces).

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

Fig. 19. Schemeof the sample holder with protective plate for deposition of complex lipid-protein layers.

537

monolayer is transferred to its surface with active head groups exposed to water. At the lowest position of the substrate, the protective plates moved to the down position, and the sample holder begins to move up. The protective plate prevents the deposition of the next monolayer and preserves the orientation of the already deposited monolayer. After coming to the top, the sample holder can move horizontally to section a, containing the solution of protein molecules. After immersion in the section, the plate moves to the up position, allowing the attachment of the protein molecules to the monolayer. When the incubation is finished, the plate moves to the down position, and the sample holder transfers the sample to section b, containing the solution providing the detachment of nonspecifically attached proteins. After the washing, the sample can be transferred to section II. It passes the monolayer downward with the protective plate in the down position. At the bottom, the plate is moved to the up position and the sample passes the monolayer in upward motion. The monolayer in section II is transferred to the substrate. Finally, the protein molecules are encapsulated between two lipid monolayers. Such a structure is very useful for long-time storage of proteins without decrease of their activity. Lipid-protein interactions at the air-water interface have been studied for 2D protein crystal growth [235,436, 735-745], and for investigation of the interactions of model membranes with enzymes [746-763], with hydrophobic (membrane) proteins [140, 764-782], and with antibodies [579, 783-788].

4.1.4. Reversed MiceUe Monolayers

Fig. 20. Schemeof the trough for deposition of complex lipid-protein films.

The trough contains also two separated Langmuir sections and several sections where lipid-protein interactions take place. A scheme of the whole instrument is presented in Figure 20. The main task of the protective plate is to prevent the exposure of the monolayer to air during its transfer from one section to another. That is very important, as monolayers are not fixed systems, and they can reorient themselves for minimum energy in the environment where they are placed. In practice, it has been shown that last three monolayers in multilayer lipid LB films can perform flip-flop reorientation on passing the meniscus of the air-water interface [ 108]. The instrument works in the following way. Monolayers of two different lipids are formed in sections I and II. The hydrophobized substrate passes downward through the monolayer in section I with the protecting plate in the up position. The

The main difficulty in spreading proteins at the air-water interface, resulting in the penetration of a significant amount of protein molecules into the subphase volume, is connected with the fact that spreading solutions are aqueous rather than organic ones, and water is miscible with the subphase. This difficulty can be effectively overcome by using reversed micelles as spreading solutions [789-791 ]. Reversed micelles are complexes of proteins with surfactants, where proteins are incorporated into a vesicle formed by surfactant molecules. Proteins are in contact with polar head groups. The exterior of the complex is formed by hydrocarbon chains and is completely hydrophobic. This last fact makes the complex soluble in organic solvents. Usually, protein molecules enter the complex due to electrostatic interactions. As an example of this approach, let us consider micelles formed by cytochrome C and aerosol OT (AOT) [790, 791]. All stages of the monolayer formation are shown in Figure 21. Dropping of the micelle solution onto the air-water interface results in good spreading without penetration of the solution into the water subphase. Interaction with the water surface results in micelle reorganization such that surfactant molecules form a monolayer and cytochrome molecules remain attached to their charged head groups by electrostatic interactions. In fact, hydrocarbon chains of AOT molecules cannot penetrate the water volume, for entropy reasons. Therefore, the micelles

538

EROKHIN

f

4.2. Monolayer Transfer

J

Ow

I

i

Fig. 21. Scheme for monolayer formation using the reversed micelle approach. must be opened at the air-water interface. Just after the spreading, surfactant molecules cover all the trough surface, and protein molecules do not form a close packing; they are distant one from the other. This fact can be understood by simple geometrical consideration of the size of cytochrome C and the area of the monolayer after opening of the spherical surfactant neighborhood. The short hydrocarbon chains of AOT do not allow the formation of a stable monolayer of these molecules themselves. Therefore, compression of the monolayer to high surface pressure will push these molecules from the interface into the subphase volume in the form of normal micelles (their interior is hydrophobic, while the head groups are exposed to water). An AOT monolayer with cytochrome C molecules associated with it is more stable. Compression of such a monolayer to high surface pressure will result in a situation where the surfactant molecules form a densely packed layer at the air-water interface and cytochrome C molecules are also densely packed under it. Application of compression--expansion cycles to this complex monolayer can result in the formation of a densely packed layer. The first compression-expansion cycles result in a significant reduction of the area occupied by the monolayer during recompression to the same surface pressure, indicating pushing of the excess surfactant molecules from the monolayer into the water subphase. Further compression-expansion cycles do not change the monolayer properties, and the 7r-A isotherms are rather reproducible. X-ray patterns of LB films obtained from reversed micelles reveal Bragg reflections, indicating good ordering of the films [790]. Similar studies were performed using vesicles instead of micelles [559, 792-799].

In the most cases when dealing with pure protein monolayers, the area contacting the substrate surface is hydrophilic [99]. Therefore, the substrate surface must be hydrophilic also. Carefully washed glass or silicon surfaces are good for protein monolayer transfer. However, experience shows that fresh surfaces treated in weak oxygen-containing plasma are most suitable for protein monolayer transfer. In contrast, complex lipid-protein monolayers and those obtained using reversed micelles can be better transferred onto hydrophobic surfaces. The horizontal deposition technique is often used for protein monolayer transfer. The technique was used for the first time in 1937 by Langmuir and Shaefer for depositing urease layers, and therefore it is also referred to as the Langmuir-Shaefer (LS) technique [20]. Generally speaking, the LS technique can disturb the monolayer at the air-water interface during deposition. In fact, when a part of the monolayer is taken for transfer onto a solid substrate, a void can be formed in the place where the substrate touched the layer. Multilayer deposition will result in the formation of extremely defective monolayers, where voids are distributed in a random way. Such behavior is typical of rigid monolayers, where 2D quasi-crystals are formed. In the case of protein layers this situation is not frequent. When it takes place, however, special care must be taken. A simple and effective procedure is based on a special grid, whose cells must correspond to the substrate dimensions. The grid is placed over the compressed monolayer, dividing it into separate areas. After that, the feedback of the trough must be switched off, and the monolayer is transferred by touching with the substrate the layer in each grid cell. Such deposition results in the transfer of the monolayer in amounts corresponding to the substrate surface area, and protects the monolayer in all other cells from disturbance. When the monolayer is not rigid, as is true for the most protein films, the use of the grid can be avoided, as the transfer does not form serious defects, in view of the amorphous monolayer structure. 4.3. Protein Layers on Solid Substrates Most of the powerful techniques available for structure and property investigation can be applied to layers transferred onto solid substrates. Moreover, most practical applications of protein films also depend on their transfer onto solid substrates. Therefore, some examples of LB films of different important classes of proteins will be considered in this subsection. Their structure, properties, and possible practical applications will be described.

4.3.1. Light.Sensitive Protein Films Among light-sensitive proteins, bacteriorhodopsin (BR) and photosynthetic reaction centers (RC) have been widely studied by the LB technique.

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

539

Fig. 22. Schemeof the RC-arachidic acid heterostructure.

The layered structure of BR LB films was determined by X-ray diffraction measurements [454, 800]. Practically always the pattern contains at least one Bragg reflection, corresponding to a spacing of 4.8 nm. This spacing value corresponds well to the thickness of the purple membrane. This fact confirms that the BR structure is determined by the membrane fragment packing, which is the main component of the spreading solutions. In the case of RC the situation is rather different. Usually, LB films of RC do not display any Bragg reflections. In a few cases one Bragg reflection was registered [ 100, 661]. However, the ordering even in those cases was rather weak. The half-width of the reflection corresponded to only three monolayers within the ordering length. The ordering can be significantly improved by realizing heterostructures containing alternating layers of RC and fatty acid [709]. The resulting film structure is schematically shown in Figure 22. The X-ray pattern from such a film contained seven orders of Bragg reflections. Highly oriented interlayers of fatty acid maintained the order of the whole film. The in-plane structure of BR [274] and RC [801] films was investigated by STM. In both cases molecular resolution was obtained during measurements. It is still not very clear what is the mechanism of the STM image formation for such large molecules. However, very likely the electron pathways in these molecules are formed by internal water, associated with the protein molecules. It is interesting to mention that in the case of RC molecules effective STM imaging was obtained only in dark conditions, in light it was practically impossible to obtain any meaningful image. This behavior was attributed to the fact that an RC molecule transforms itself into an electrical dipole in light conditions, due to charge separation. This dipole interacts with the STM tip during scanning. This interaction results in molecular displacement during scanning, making structural investigations impossible. In order to check this suggestion, RC molecules in the monolayer were fixed with glutaraldehyde. This treatment provides intermolecular cross-linking, creating a rather rigid structure with fixed molecular positions. After the treatment, STM imaging was possible in both light and dark conditions, giving practically the same film structure. In the case of BR films the mentioned problem does not exist. The reason is that BR molecules are already rigidly fixed in 2D lattices in membrane fragments and cannot be moved by interaction with the STM tip.

Fig. 23. Schemeof a light-addressableelementbasedon an orientedBR layer.

Comparison of the behavior of RC and BR LB films under the STM allows us to reach rather general conclusions about the utilization of scanning tunnelling microscopy for the investigation of protein LB films. Large dimensions of the molecules do not create great problems, as there are always electron pathways formed by internal water associated with protein molecules. However, charges or dipoles of the protein molecules can interact with the STM tip during scanning, and this interaction can disturb the resultant image, and in some cases even make it impossible to obtain meaningful images. Such difficulty will be encountered when molecules in the layer do not form a rigid crystal-like structure. Therefore, special fixing techniques must be applied in such cases. The electro-optical behavior of BR and RC LB films is the most interesting property of these objects. It is determined by the charge transfer properties: electron in the case of RC, and proton in the case of BR. Of course, utilization of these properties demands uniaxial orientation of charge pathways of these molecules in the film. Methods of orientation were considered in Sections 4.1.1 and 4.1.2. The simplest setup for the photoresponse measurements is based on sandwich structures where RC [802-812] or BR [398, 813-828] LB films are placed between two electrodes, one of which is transparent or semitransparent. Measurements of the potential or current were performed during illumination of the layers by light of different wavelengths. Another interesting application of BR LB films is based on local light-driven proton transfer [829]. The element is based on an ultrathin film (ideally, one monolayer) of oriented BR molecules. The element must have similar properties to a lightaddressable potentiometric system (LAPS). A schematic representation of the element is shown in Figure 23. A BR LB film is deposited on a porous membrane, with holes of a size allowing unbroken film over it. The membrane separates two electrolyte solutions. Electrodes are inserted into these solutions. The cur-

540

EROKHIN Other applications of BR layers are connected with the optical bistability of this material [830-835]. For natural BR there are two stable states, one with the absorbance at 570 nm and the other at 410 nm. It is possible to switch one state to the other by optical illumination, by thermal action, or by pH variation. Moreover, there are already some mutants of the BR [836], providing increased stability of the excited state (410 nm). These properties are very useful for designing optical memory and Fourier optics elements based on BR layers. However, such applications do not demand molecular thickness of the layers, and therefore the application of the LB technique is not required in this case. Therefore, we will not consider these applications in this chapter.

Fig. 24. Scheme of the sensitive membrane for a multisensor based on oriented BR layers.

4.3.2. Antibody Films rent in each section is determined by the proton and ion conductivity. In the ideal case, there is no possibility for the electric current to pass from one section to the other, though in real conditions that situation cannot be achiewedmthere are always pathways for, at least, protons. Therefore, current will appear in the system only after the illumination of some BR film area with light of suitable wavelength. In this case, the BR molecules will begin proton pumping, providing the electric current between two sections. The value of the current will depend on the light intensity. However, this dependence will come to saturation when the number of incoming photons is sufficient to provide continuous proton transfer to each BR molecule. The other parameters responsible for the current value are the absolute value of the pH in each section and the pH gradient between sections. The system can be considered as a transducer for revealing pH variations. In fact, if the pH value in one section is maintained constant and the light intensity is also constant, the variation of the pH in the other section will be monitored as the variation of the current at the constant bias voltage. Such a scheme can be used for the construction of enzymatic sensors when the enzyme functioning results in the production or consumption of additional protons in the subphase volume (fortunately, most enzymes work in such a way). Moreover, more complicated devices, acting as artificial noses, can be based on the described principle. The scheme of the sensitive membrane of such a device is shown in Figure 24. The porous membrane is covered by the BR monolayer. A complex enzyme film is deposited on top of the BR monolayer. The enzyme monolayer contains different types of enzymes, covering different areas of the BR monolayer (pixels), providing a 2D matrix of sensitive units. The presence of different analytes in the solution will result in a pH gradient map in the area adjacent to the BR layer. This map will be revealed by registering the current variation on scanning a light beam over the matrix. The resolution and the degree of integration of such a sensitive matrix can be very high. In fact, its spatial resolution will be determined only by the dimensions of the light beam, and can be a micron scale.

Antibodies are a class of proteins responsible for the recognition and binding of specific antigens. There are several classes of antibodies. Here we will restrict ourselves to immunoglobulin G (IgG) antibodies, as most work using the LB technique has been performed on this class of antibodies. The IgG molecule is composed of two light chains and two heavy chains. These chains form one Fc fragment and two Fab fragments. IgG molecules are nearly identical. The only difference between them is in the Fab fragment, where there is a variable area, responsible for specificity to special groups in antigen molecules. Monoclonal antibodies have specificity of the variable area to a restricted group of antigen molecules, while polyclonal antibodies have specificity to different groups of antigens. The presence of numerous covalent S - S bridges makes the molecule very stable. In fact, it forms stable monolayers at the air-water interface [837]. Significant denaturation of IgG molecules in the monolayer at the air-water interface takes place only after some hours of exposure to the high surface tension [838]. Therefore, if the monolayer compression is performed immediately after spreading with high velocity, practically all the IgG molecules maintain their native structure and functional activity in LB films. The specific function of antibodies determines their field of applications. Their extremely high specificity is very important for sensor applications. The LB technique is very useful for their organization, one need have a layer only one molecule thick in order to provide sensing properties. Several types of transducers can be used for immunosensor fabrication. The easiest one, basing on the binding properties, is the gravimetric one. IgG LB films (monolayers) are deposited onto a quartz crystal resonator [593, 838-843]. Binding of the antigen will vary the frequency of the resonator, loaded into the driving circuit. Therefore, the element will monitor the binding event directly as an increase of the mass attached to the resonator surface. However, the technique has several limitations. First of all, the antigen must be a rather large molecule, in order to provide significant mass variation after the binding. Second, and

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES

541

Fig. 25. Scheme for gravimetric measurements in liquid using only one electrode of the resonator.

probably more important, there is always nonspecific physical adsorption of the antigen molecules to the film surface. This adsorption must be taken into account and subtracted from the binding signal in order to have an exact specifically bound mass value. The nonspecific binding can be taken into account by performing two crystal differential scheme measurements. For this, two quartz resonators must be covered with IgG LB film. The first (measuring resonator) must be covered with IgG molecules specific to the analyte under the investigation, while the second (reference resonator) must be covered with IgG molecules with no affinity to the analyte. The similarity of the two coveting molecules will lead to similar physical adsorption properties. Therefore, the registering electronics will monitor a differential signal, which will be proportional to the specifically attached mass. However, when the physical adsorption is intense, special washing must be performed after the binding. First studies of such immunosensors were performed in the air phase, drying the sensitive elements after each measurement in the liquid phase. That is not surprising, in that dipping of the resonator in liquid will provide contact of electrodes with the aqueous solution. That can be considered as the appearance of a resistor between the two electrodes of the resonator--a parasitic resistor in the vibrating circuit, which causes a decrease of the quality factor of the circuit. It means that the accuracy of the measurements will be significantly decreased. However, this difficulty was successfully overcome by using specially designed working chambers. These chambers provide the isolation of the working electrodes from each other [844]. In the simplest case (Fig. 25) only one electrode of the resonator is in contact with analyte solution and performs measurements. A simple modification will make both electrodes working, providing also inflow measurements. Other transducers are based on surface acoustic wave propagation [845]. The measuring parameters in this case will be not the frequency shift, but the difference in sound velocity and/or phases of the signals, tunelling through a surface covered by the sensitive layer and without it. There are several descriptions of successful application of such transducers, but they will hardly

Fig. 26.

Scheme of a sensor based on surface plasmon resonance.

be used for industrial applications. The main reason is the extremely high price of the surface acoustic wave generators and receivers without significant advantages in performance over other techniques. Different optical techniques can be used for fabrication of an immunosensor transducer. Up to now, fluorescence techniques are still the most widely used for medical applications [785, 846-858, 849]. The application of such a technique demands the initiation of a two-step reaction. The sensitive unit is the substrate covered by the antibody layer. This unit is exposed to the analyte solution. After incubation, the unit is immersed in a solution containing fluorescently labeled antibodies specific to the analyte under the investigation. Analysis of the fluorescence enables quantitation of the concentration of antigens in the analyte. Among the optical techniques for immunosensing registration, surface plasmon resonance is the more widely used in recent times [786]. The technique is based on the following principle. There is a particular angle where the energy of the incident light is practically all transferred into vibration of the electron plasma of the thin metal layer on which the light impinges. This angle is strongly dependent on the condition of the metal layer surface. Attachment of several molecules can vary it over several degrees. Therefore, this phenomenon can be used for an immunosensor transducer. A scheme of the sensor with typical binding curves is shown in Figure 26. Note that the sensor can be also used in the liquid phase, performing continuous measurements of the binding events. The technique can be used not only for transducer fabrication, but also as a measuring tool for the investigation of interactions of model membranes with different membrane-active compounds.

542

EROKHIN

There are some other optical techniques for investigating antigen-antibody interactions. However, all of them have currently rather restricted application and are rather far from incorporation into real sensors.

4.3.3. Enzyme Films The first work on protein films was performed by Langmuir and Schaefer on enzymes--pepsin and urease [20]. This work is interesting not only as the first use of the horizontal deposition technique, but also because it shows the possibility of preserving enzymatic activity in deposited layers. Wide interest in enzyme films is due to their specific properties, which can be used for the realization of biosensors with high specificity and of enzymatic bioreactors. The LB technique allows one to work with very small quantities of the proteins. Therefore, it is considered as a useful tool for realizing enzyme-active layers, as the cost of some enzymes is extremely high. The simpler and cheaper sensors are the enzymatic ones. Glucose oxidase (GOD) has been intensively studied by application of the LB technique, as its function can be easily detected, and GOD-based glucose sensors find wide application in medicine [860-874]. They are based on the following reaction: Glucose

GOD

~ gluconic acid + H202

A sensitive layer of GOD is deposited onto a platinum electrode. The measuring chamber contains also an Ag-AgC1 reference electrode. Voltage must be applied between the enzymatic and reference electrodes. The current in the circuit will be proportional to the concentration of H202 produced by the enzymatic oxidation of the glucose, and therefore proportional to the glucose concentration. In order to improve the sensor performance, GOD molecules can be associated with conductive polymer layers. Such a complex layer provides better a charge drain between electrode and reactive media. In all the cases, GOD layers are transferred to a solid substrate together with some amphiphilic molecules. However, selective removal of the lipid molecules after deposition has been shown to be possible. In particular, behenic acid molecules were removed from a film by isopropanol treatment of complex behenic acid-GOD LB films, deposited onto solid supports. Successful removal was confirmed by IR and AFM measurements. The possibility of the removal of fatty acid molecules (not salts) is well known, and is called skeletonization of the fatty acid salts [875]. Treatment of the fatty acid salt LB films with organic solvents results in the removal of fatty acid molecules not bound to metal ions, leaving only salt molecules, with reduced density of the layer. Another interesting example enzyme for LB films is luciferase [796, 876]. The main reason for the academic interest to this protein is its clear function, which is practically free from mistreatment and artifacts. The enzyme catalyzes oxidation of luciferin (L) by molecular oxygen in the presence of the ATP

Fig. 27.

Scheme of a sensor based on a complex luciferase and BR layer.

complex according to the following reaction: ATP + L + 02

luciferase

> OL + PPi + CO2 + AMP + hv(~.max = 562 nm)

where OL is oxyluciferin and Ppi is pyrophosphate. The activity of firefly luciferase, measured as light emission, was found to be preserved in LB films, but not stable in time. The position of the emission maximum in the case of the luciferase reaction corresponds well to that of the maximum absorbance of BR in its ground state (570 nm). Therefore, we consider a complex layer, containing a BR film covered with luciferase, deposited on a potential-sensitive support. A possible scheme of such a structure is shown in Figure 27. The functioning of luciferase will result in the emission of light that will be absorbed by BR molecules. Light absorption will result in the appearance of a photopotential, which will be registered by the potential-sensitive substrate. Another example of an enzyme successfully deposited with the LB technique is alcohol dehydrogenase (ADH) [877]. LB films of stearic acids with ADH were deposited and used as sensitive layers for ethanol monitoring. Detection of alcohol is based on the following reaction: CH3CH2OH + fl-NAD + ADH CH3CHO + NADH + H + The detectable substance in this case is the coenzyme NADH, which is reoxidized into fl-NAD + at the electrode. Like those of GOD, the properties of biosensors based on ADH LB films can be improved if the enzyme layers are associated with polymer sublayers. In this case, the polymer will

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES play a role of a mediator, transferring the electron from the enzymatic reaction to the electrode. Such complex ADH-polymer layers were deposited and investigated by AFM. In some cases the enzymatic activity in LB films can be registered by optical methods, if the absorbance of the reaction product is in a different wavelength range from that of the substrate and enzyme. Such measurements were performed for glutatione-S-transferase (GST) LB films [878-880]. GST catalyzes the conjugation of glutathione to electrophilic acceptors, such as quinones and organic peroxides. It has been shown that GST activity can be preserved in LB films. Moreover, thermal and temporal stability of the protein in the film were observed. Some work on LB films of polymers have been performed with enzymes. Enzyme molecules were added into the volume of the water subphase under the monolayer of monomers, performing enzyme-catalyzed polymerization at the air-water interface [881-884].

4.4. Thermal Stability of Proteins in LB Films Among the most interesting properties of the proteins organized in densely packed structures is their increased thermal stability. This property was described in 1993 for RC in LB films, in studying secondary structure variations by circular dichroism measurements [885, 886], and for BR self-assembled layers [887], in studying the structure by the X-ray method. Variations of the CD spectra of RC in solution, LB films, and layers produced by drying solution drops demonstrate that RC molecules begin to denature in the solution at temperatures of about 50~ and are denatured practically completely at about 70~ In the films prepared by solution drop drying the complete denaturation takes place at more elevated temperatures. However, the CD spectrum even at room temperature is different from that in the solution. Very likely, these variations are due to the mutual redistribution of the protein--detergent complex during drying, which can result in some penetration of the detergent molecules into the proteins, resulting in partial denaturation of RC molecules. In the case of LB film the situation was completely different. The initial spectrum is similar to that in the solution, indicating the preservation of the secondary structure of the protein after deposition onto solid substrates. The CD spectrum of the RC LB film is practically the same after heating to 150~ Small variations begin to take place only at about 200~ It is interesting to compare the RC data with the behavior of CD spectra of BR also in solution, LB films, and layers obtained by drop drying. The behavior in solution is rather similar to that of the RC. The same is true for the LB films. However, the situation is completely different in the case of films obtained by drop drying. The effect of heating in this case is very similar to that in the case of LB films. Comparison of the CD spectra allows one to state immediately that the water plays an important role in the thermal stability of proteins. In fact, variations of the secondary structure in

543

solutions begin at rather low temperatures. However, the comparison of the CD spectra in LB films and dried drops for RC and BR allows one to conclude that the absence of water is not the only condition responsible for the thermal stability of the secondary structure. In the case of BR, the microscopic organization of molecules in both LB films and dried drop layers is practically the same. As was described in Section 4.1.1 the elementary unit in the case of BR layers is a membrane fragment. Therefore, the difference between the LB film and the dried drop layer is only in the arrangement of these fragments. In the case of LB it is slightly more regular. However, inside these fragments the BR molecular packing is the same--regular close packing, as in the membrane. The situation is different in the case of RC films. The LB technique allows one to deposit regular close-packed'layers. Moreover, detergent molecules are removed from the layer during the monolayer formation at the air-water interface, as is described in Section 4.1.2. In contrast, simple drying of the solution drop does not provide either close packing of molecules or regularity of the layer. Comparison of the behavior of CD spectra for RC and BR films [888] allows one to suggest that the molecular close packing and regularity of the layers are the other conditions responsible for the increased thermal stability of protein secondary structure in LB films. However, the presence of the detergent molecules in the case of dried RC layers leaves some doubts about the last conclusion. In fact, the presence of detergent can vary the structure of the protein molecules during drying so significantly that it becomes impossible to make any comparison of such a sample with LB films. In this situation, our conclusion about the role of close packing and regularity in thermal stability cannot be strongly grounded, and the absence of water may be the only condition responsible for this phenomenon. In order to check this possibility, experiments on antibody layers were performed [889]. The first test was performed on the heating of the lyophilized powder. Heating of this powder to 100~ resulted in a significant variations of the CD spectrum, while the LB film was practically the same up to 150~ as with RC and BR LB films. Moreover, even boiling the LB film in water did not lead to so much denaturation as in the case of solution heating. The other interesting feature of the boiling of the LB sample is that there is practically no shift of the CD spectrum, but only a decrease of the peak values. This can be explained by the denaturation of the top layer (or layers), which forms (after the denaturation) a protective layer, preventing the penetration of water into the deep layers of the film. The above considerations allow us to conclude that, in fact, the absence of water is not the only condition responsible for the thermal stability of proteins in thin films, but also the dense packing of molecules and regularity of the layer must be taken into consideration. However, the preservation of the protein secondary structure does not always mean that the protein was not affected by the thermal treatment. Functional stability must be considered, as it

544

EROKHIN

Fig. 28. Schemeof the functional test of RC molecules using a Kelvinprobe.

is the most important characteristic from the application point of view. Let us consider RC films as the example of the stability of functional properties [890]. This choice is determined by the fact that the functioning of the protein, namely, light-induced electron transfer, can be rather easily detected. In the case of LB films, the detection was performed by light-induced electric potential measurements, using the Kelvin probe [889]. The scheme of the measurements is presented in Figure 28. The potential was measured at room temperature after heating to a fixed temperature for 10 min. The results of the experiment show that the functional properties of the RC in LB films are more affected by heating than by the secondary structure. Deactivation of the functional activity begins before significant changes in secondary structure, but later than in solution. It is also interesting to compare the stability of the functional properties of RC in LB films with that in dried solution samples. Unfortunately, the photopotential cannot be directly measured in this case. The unordered nature of the sample does not allow the preferential orientation of the protein molecules; therefore, electron displacements in adjacent molecules will compensate each other, giving no net potential. Therefore, functional activity was analyzed in this case by detecting the optical absorbance at 860 nm (dimer of bacteriochlorophyll). Though the presence of the bacteriochlorophyll dimer cannot be presumed to be absolutely without effect on the RC, we can use this method of investigation for comparison with LB films, as the disappearance of the peak will not take place before the deactivation of the protein. The results of this study show that the stability of the functional properties of RC in dried drops is much less than that in LB films, confirming once more the importance of close molecular packing and regularity of the layer for this property. However, the question still remainsmwhy is the functional activity destroyed if the secondary structure is preserved? The answer to this question can depend on the protein. As an example, we can consider RC again [891 ]. As was mentioned before, the protein contains three subunits. Heating to 110~ results in the splitting of the globule into its separate subunits. This fact was shown by STM investigationmthe size of the elementary unit of the film was reduced to that of the subunit. Therefore, the quaternary structure of the protein was the first element that was affected by the thermal treatment. The functional properties of the RC are strongly connected with its quaternary structure. The

two bacteriochlorophyll molecules of the dimer--the primary donor of the electron--belong to different subunits. Therefore, the loss of the quaternary structure destroys the initial electron donor, eliminating completely the functional properties of the RC molecule. It is interesting to note that STM images reveal not only the splitting of the RC into subunits, but also a significant improvement of the layer ordering after heating. The fact allows us to consider the heating as a rather general procedure (so long as it does not induce, for example, the destruction of the quaternary structure) for improvement of the protein LB film ordering. That statement was checked on different protein LB films, and in most cases was confirmed. The best results were obtained if the thermal treatment was performed not just on the finished multilayer film, but after each monolayer transfer [800]. Evaluation of the ordering-length improvement after thermal treatment of different protein LB films has been performed for antibodies, RC, BR, and cytochrome P450scc [800]. In some cases, such improvement of the film ordering resuited in improvement of the functional properties. Antibody films illustrate this statement [889, 891]. Increased antigenbinding ability was found for the thermally treated LB antibody monolayers, as represented both by the absolute value of the attached antigen (about 20% of the untreated value) and by the velocity of the reaction (about 5 times faster). It is difficult to suppose that this improvement is due to the variation of the individual protein molecule properties, caused by heating. More likely, it was due to the new organization of the layer. This suggestion was checked and confirmed by surface potential measurements of the antibody film before and after the heating. The increased value of the surface potential of the layer after the thermal treatment indicates improvement in the preferential orientation of molecules in the layer. This orientation can explain the improvement of the antigen-binding properties. Moreover, an electric potential can accelerate the reaction, providing additional driving force at its initial stage, when antigen must come close to the antibody layer surface. The nature of the thermal stability of the protein molecules in LB films is still not completely clear. Of course, the absence of water is important, but it is not the only condition. Close molecular packing and regularity of the layer play also an important role. One analogy can show this behavior very roughly. Let us consider some fragile objects, matches, for example. If they are in a closely packed regular group, it is very hard to break them. Probably, something similar takes place also in the case of protein LB films. Close packing and regularity demand some additional energy to be applied to the system in order to break the molecular packing and only then to act on individual molecules.

5. CONCLUSIONS The aim of this chapter has been to demonstrate the application of the LB technique for studying biological objects. Main attention was directed to protein LB films, as they are very important

LANGMUIR-BLODGETT FILMS OF BIOLOGICAL MOLECULES from the application point of view and it is rather difficult to work with them due to their fragile nature. Some biological objects were not considered in detail. However, we must mention the successful application of the LB technique for the formation of DNA-containing layers [553, 892-912] and for the incorporation of channel-forming molecules, such as valinomycin [679, 913-927]. The aim of the work, however, is to demonstrate the applicability of the technique for the fundamental investigation of the structure and processes in biological objects and for applied studies of thin active biological layers for applications in biosensors, transducers, and reactors.

ACKNOWLEDGMENT The author would like to thank Svetlana and Konstantin for their help in the figure preparation.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

19.

20. 21. 22. 23. 24. 25. 26.

27. 28. 29.

Lord Rayleigh, Proc. Lond. Math. Soc. 10, 4 (1879). I. Langmuir, J. Am. Chem. Soc. 39, 1848 (1917). I. Langmuir, Trans. Faraday Soc. 15, 62 (1920). K.B. Blodgett, J. Am. Chem. Soc. 57, 1007 (1935). K.B. Blodgett and I. Langmuir, Phys. Rev. 51,964 (1937). K.B. Blodgett, J. Am. Chem. Soc. 56, 495 (1934). K.B. Blodgett, J. Phys. Chem. 41,975 (1937). K.B. Blodgett, Phys. Rev. 55, 391 (1939). H. Kuhn and D. MObius, Angew. Chem. Int. Ed. EngL 10, 620 (1971). H. Kuhn, J. Chem. Phys. 53, 101 (1970). H. Kuhn, Pure Appl. Chem. 51, 341 (1979). H. Kuhn, Chem. Phys. Lipids 8, 401 (1972). H. Kuhn, Thin Solid Films 99, 1 (1983). H. Kuhn, Pure Appl. Chem. 53, 2105 (1981). H. Kuhn, Thin Solid Films 178, 1 (1989). H. Kuhn, Biosensors and Bioelectronics 9/10, 707 (1994). H. Kuhn, J. Photochem. 10, 111 (1979). H. Kuhn, D. M6bius, and H. Bticher, in "Physical Methods of Chemistry" (A. Weissberger and B. W. Rossiter, Eds.), Part III B, Chap. VII. Wiley, New York, 1972. H. Kuhn, D. MObius, and H. Biicher, in '"rechniques of Chemistry" (A. Weissberger and B. W. Rossiter, Eds.), Vol. I, Part IIIB, p. 577. Wiley, New York, 1972. I. Langmuir and V. J. Schaefer, J. Am. Chem. Soc. 60, 1351 (1938). G. L. Gaines, Jr., "Insoluble Monolayers at Liquid-Gas Interface." Wiley-Interscience, New York, 1966. R. C. Ahuja, P.-L. Caruso, and D. MObius, Thin Solid Films 242, 195 (1994). R.C. Ahuja and D. MObius, Thin Solid Films 243, 547 (1994). E. Ando, M.-A. Suzuki, K. Moriyama, and K. Morimoto, Thin Solid Films 178, 103 (1989). T. R. Baekmark, T. Wiesenthal, E Kuhn, T. B. Bayed, O. Nuyken, and R. Merkel, Langmuir 13, 5521 (1997). J. E Baret, H. Hasmonay, J. L. Firpo, J. J. Dupin, and M. Dupeyrat, Chem. Phys. Lipids 30, 177 (1982). T. M. Bayed, R. K. Thomas, J. Penfold, A. Rennie, and E. Sackmann, Biophys. J. 57, 1095 (1990). G. M. Bommarito, W. J. Foster, E S. Pershan, and M. L. Schlossman, J. Phys. Chem. 105, 5265 (1996). G. Brezesinski, C. BOhm, A. Dietrich, and H. MOhwald, Physica B 198, 146 (1994).

545

30. G. Brezesinski, E Bringezu, G. Weidemann, R B. Howes, K. Kjaer, and H. M0hwald, Thin Solid Films 327-329, 256 (1998). 31. G. Brezesinski, M. Thoma, B. Struth, and H. MOhwald, J. Phys. Chem. 100, 3126 (1996). 32. E Bringezu, G. Brezesinski, E Nuhn, and H. MOhwald, Thin Solid Films 327-329, 28 (1998). 33. R.S. Cantor and E M. McIlroy, J. Chem. Phys. 90, 4423 (1989). 34. M. K. Durbin, A. Malik, A. G. Richter, C.-J. Yu, R. Eisenhower, and E Dutta, Langmuir 14, 899 (1998). 35. C. Duschl, D. Kemper, W. Frey, E Meller, H. Ringsdorf, and W. Knoll, J. Phys. Chem. 93, 4587 (1989). 36. A. Fischer, M. LOsche, H. MOhwald, and E. Sackmann, J. Phys. (Paris) Lett. 45, L785 (1984). 37. A. Georgallas and D. A. Pink, Can. J. Phys. 60, 1678 (1982). 38. A. Jyoti, R. M. Prokop, and A. W. Neumann, Colloids Surf. B: Biointe~ 8, 115 (1997). 39. A. Jyoti, R. M. Prokop, J. Li, D. Vollhardt, D. Y. Kwok, R. Miller, H. MOhwald, and A. W. Neumann, Colloids Surf. A 116, 173 (1996). 40. C.M. Knobler and R. C. Desai, Annu. Rev. Phys. Chem. 43, 207 (1992). 41. D. Kramer and A. Ben-Shaul, Physica A 195, 12 (1993). 42. G. Lieser, B. Tieke, and G. Wegner, Thin Solid Films 68, 77 (1980). 43. M. LOsche, H.-E Duwe, and H. MOhwald, J. Colloid Interf. Sci. 126, 432 (1988). 44. V. Melzer, D. Vollhardt, G. Brezesinski, and H. MOhwald, J. Phys. Chem. B 102, 591 (1998). 45. V. Melzer, D. Vollhardt, G. Weidemann, G. Brezesinski, R. Wagner, and H. MOhwald, Phys. Rev. E 57, 901 (1998). 46. R.M. Mendenhall and A. L. Mendenhall, Jr., Rev. Sci. Instrum. 34, 1350 (1963). 47. R.M. Mendenhall, Rev. Sci. Instrum. 42, 878 (1971). 48. R. M. Mendenhall, A. L. Mendenhall, Jr., and J. H. Tucker, Ann. N. Y Acad. Sci. 130, 902 (1966). 49. K. Miyano, B. M. Abraham, J. B. Ketterson, and S. Q. Xu, J. Chem. Phys. 78, 1776 (1983). 50. G.A. Overbeck and D. MObius, J. Phys. Chem. 97, 7999 (1993). 51. I.R. Peterson, Phys. Scripta T45,245 (1992). 52. N. Sadrzadeh, H. Yu, and G. Zografi, Langmuir 14, 151 (1998). 53. E. ten Grotenhuis, R. A. Demel, M. Ponec, D. R. Boer, J. C. van Miltenburg, and J. A. Bouwstra, Biophys. J. 71, 1389 (1996). 54. V. Von Tscharner and H. M. McConnell, Biophys. J. 36, 409 (1981). 55. B.D. Casson and C. D. Bain, J. Phys. Chem. B 103, 4678 (1999). 56. I. Langmuir, J. Am. Chem. Soc. 39, 1848 (1917). 57. L. Wilhelmy, Ann. Phys. Chem. 119, 177 (1863). 58. G.L. Gains, Jr., J. ColloM Interf. Sci. 62, 191 (1977). 59. S. Sato and H. Kishimoto, J. Colloid lnterf. Sci. 69, 188 (1979). 60. B. Sun, T. Curstedt, and B. Robertson, Reproduction Fertility Devel. 8, 173 (1996). 61. P.B. Welzel, I. Weis, and G. Schwartz, Colloids Surf. A 144, 229 (1998). 62. N.K. Adam, J. E Danielli, and J. B. Harding, Proc. Roy. Soc. London Ser. A 147, 491 (1934). 63. M. Blank, L. Soo, R. E. Abbott, and U. Cogan, J. Colloid Interf. Sci. 73, 279 (1980). 64. H. Biimer, M. Winterhalter, and R. Benz, J. Colloid Interf. Sci. 168, 183 (1994). 65. G. Collacicco, Chem. Phys. Lipids 10, 66 (1973). 66. W.M. Heckl, H. Baumgiirtner, and H. MOhwald, Thin Solid Films 173, 269 (1989). 67. C.M. Jones and H. L. Brockman, Chem. Phys. Lipids 60, 281 (1992). 68. S.V. Mello, R. M. Faria, L. H. C. Mattoso, A. Riul, Jr., and O. N. Oliveira, Jr., Synth. Met. 84, 773 (1997). 69. J. Mingins and B. A. Pethica, Trans. Faraday Soc. 59, 1892 (1963). 70. D. MObius, W. Cordroch, R. Loschek, L. E Chi, A. Dhathathreyan, and V. Vogel, Thin Solid Films 178, 53 (1989). 71. A. Noblet, H. Ridelaire, and G. Sylin, J. Phys. E 17, 234 (1984). 72. O.N. Oliveira, Jr., A. Riul, Jr., and G. F. Leal Ferreira, Thin Solid Films 242, 239 (1994).

546

EROKHIN J

73. O.N. Oliveira, Jr., D. M. Taylor, C. J. M. Stirling, S. Tripathi, and B. Z. Guo, Langmuir 8, 1619 (1992). 74. O.N. Oliveira, Jr., D. M. Taylor, T. J. Lewis, S. Salvagno, and C. J. M. Stirling, J. Chem. Soc. Faraday Trans. 85, 1009 (1989). 75. J.G. Petrov, E. E. Polymeropoulos, and H. M6hwald, J. Phys. Chem. 100, 9860 (1996). 76. E Rustichelli, S. Dante, P. Mariani, I. V. Miagkov, and V. I. Troitsky, Thin Solid Films 242, 267 (1994). 77. D.M. Taylor, O. N. De Oliveira, Jr., and H. Morgan, J. Colloid Interf. Sci. 139, 508 (1990). 78. D.M. Taylor, O. N. Oliveira, Jr., and H. Morgan, Chem. Phys. Lett. 161, 147 (1989). 79. P. C. Tchoreloff, M. M. Boissonnade, A. W. Coleman, and A. Baszkin, Langmuir 11,191 (1995). 80. R.H. Tredgold and G. W. Smith, J. Phys. D 14, L 193 (1981). 81. R.H. Tredgold and G. W. Smith, Thin Solid Films 99, 215 (1983). 82. R.H. Tredgold, P. Hodge, Z. Ali-Adib, and S. D. Evans, Thin Solid Films 210/211, 4 (1992). 83. M. Winterhalter, H. Btirner, S. Marzinka, R. Benz, and J. J. Kasianowicz, Biophys. J. 69, 1372 (1995). 84. A. V. Hughes, D. M. Taylor, and A. E. Underhill, Langmuir 15, 2477 (1999). 85. A. Dhanabalan, L. Gaffo, A. M. Barros, W. C. Moreira, and O. N. Oliveira, Jr., Langmuir 15, 3944 (1999). 86. H. Kokubo, Y. Oyama, Y. Majima, and M. Iwamoto, J. Appl. Phys. 86, 3848 (1999). 87. M. Takeo, J. Colloid Interf. Sci. 157, 291 (1993). 88. B. Neys and P. Joos, Colloids Surf. A 143,467 (1998). 89. D.M. Taylor and G. E Bayers, Mater. Sci. Eng. C 8-9, 65 (1999). 90. N.A. Surplice and R. J. D'Arcy, J. Phys. E 3,477 (1970). 91. M. Yasutake, D. Aoki, and M. Fujihira, Thin Solid Films 273,279 (1996). 92. C. Goletti, A. Sgarlata, N. Motta, P. Chiaradia, R. Paolesse, A. Angelaccio, M. Drago, C. Di Natale, A. D'Amico, M. Cocco, and V. I. Troitsky, Appl. Phys. Lett. 75, 1237 (1999). 93. C. Di Natale, Sensors Actuators B 57, 183 (1999). 94. S. Lee, J. A. Virtanen, S. A. Virtanen, and R. M. Penner, Langmuir 8, 1243 (1992). 95. Z. Lu, S. Xiao, and Y. Wei, Thin Solid Films 210/211,484 (1992). 96. Y. Okahata, K. Ariga, and K. Tanaka, Thin Solid Films 210/211, 702 (1992). 97. R. M. Stiger, J. A. Virtanen, S. Lee, S. A. Virtanen, and R. M. Penner, Anal. Chim. Acta 307, 377 (1995). 98. O.A. Aktsipetrov, E. D. Mishina, T. V. Murzina, V. R. Novak, and N. N. Akhmediv, Thin Solid Films 256, 176 (1995). 99. Yu. Lvov, V. Erokhin, and S. Zaitsev, Biol. Membr. 4(9), 1477 (1991). 100. V. Erokhin, L. Feigin, R. Kayushina, Yu. Lvov, A. Kononenko, P. Knox, and N. Zakharova, Stud. Biophys. 122, 231 (1987). 101. G. G. Roberts, "Langmuir-Blodgett Films." Plenum Press, New York, 1990. 102. L.M. Blinov, A. V. Ivanschenko, and S. G. Yudin, Thin Solid Films 160, 271 (1988). 103. L.M. Blinov' L. V. Mikhnev, E. B. Sokolova, and S. G. Yudin, Sov. Tech. Phys. Lett. 9,640 (1983). 104. L.M. Blinov, N. N. Davydova, V. V. Lazarev, and S. G. Yudin, Sov. Phys. Solid State 24, 1523 (1983). 105. L.M. Blinov, N. V. Dubinin, and S. G. Yudin, Opt. Spectr. 56, 280 (1984). 106. L.M. Blinov, N. V. Dubinin, L. V. Mikhnev, and S. G. Yudin, Thin Solid Films 120, 161 (1984). 107. G.G. Roberts, Ferroelectrics 91, 21 (1989). 108. T. Kato, Japan. J. Appl. Phys. 26, L 1377 (1987). 109. P. Vincett and W. Barlow, Thin Solid Films 71,305 (1980). 110. B. Belbouch, M. Routliay, and M. Tournaric, Thin Solid Films 134, 89 (1985). 111. V. Erokhin, Y. Lvov, L. Mogilevsky, A. Zozulin, and E. Ilyin, Thin Solid Films 178, 111 (1989). 112. H. Kuhn and D. Mobius, Angew. Chem. Int. Ed. Engl. 10, 620 (1971). 113. H. Kuhn, Thin Solid Films 99, 1 (1983).

114. 115. 116. I 17. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152.

153. 154. 155. 156.

H. Kuhn, Thin Solid Films 178, 1 (1989). H. Kuhn, J. Photochem. 10, 111 (1979). B. Mann and H. Kuhn, J. Appl. Phys. 42, 4398 (1971). B. Mann, H. Kuhn, and L. v. Szenp~ily, Chem. Phys. Lett. 8, 82 (1971). E.E. Polymeropoulos, D. M6bius, and H. Kuhn, Thin Solid Films 68, 173 (1980). U. Schoeler, K. H. Tews, and H. Kuhn, J. Chem. Phys. 61, 5009 (1974). M. Sugi, K. Nembach, D. M6bius, and H. Kuhn, Solid State Commun. 15, 1867 (1974). M. Sugi, K. Nembach, D. M6bius, and H. Kuhn, Solid State Commun. 13, 603 (1973). L. E Chi, R. R. Johnston, and H. Ringsdorf, Langmuir 7, 2323 (1991). A.K. Dutta and C. Salesse, Langmuir 13, 5401 (1997). K. Fujita, S. Kimura, Y. Imanishi, E. Rump, and H. Ringsdorf, Langmuir 11,253 (1995). L. E Chi, R. R. Johnston, and H. Ringsdorf, J. Am. Chem. Soc. 109, 788 (1987). K. Y. C. Lee, M. M. Lipp, D. Y. Takamoto, E. Ter-Ovanesyan, J. A. Zasadzinski, and A. J. Waring, Langmuir 14, 2567 (1998). M. L6sche and H. M6hwald, Rev. Sci. Instrum. 55, 1968 (1984). M. L6sche, E. Sackmann, and H. M6hwald, Ber. Bunsenges. Phys. Chem. 87, 848 (1983). M. H. P. Moers, H. E. Gaub, and N. E van Hulst, Langmuir 10, 2774 (1994). E Mojtabai, Thin Solid Films 178, 115 (1989). S. Riviere, S. H6non, J. Meunier, D. K. Schwartz, M.-W. Tsao, and C. M. Knobler, J. Chem. Phys. 101, 10045 (1994). D.K. Schwartz and C. M. Knobler, J. Phys. Chem. 97, 8849 (1993). K.J. Stine and C. M. Knobler, Ultramicroscopy 47, 23 (1992). K.J. Stine and D. T. Stratmann, Langmuir 8, 2509 (1992). K.J. Stine, Microsc. Res. Technique 27, 439 (1994). R.M. Weis, Chem. Phys. Lipids 57, 227 (1991). D.W. Grainger, A. Reichert, H. Ringsdorf, and C. Salesse, Biochim. Biophys. Acta 1023, 365 (1990). J.N. Herron, W. Muller, M. Paudler, H. Riegler, H. Ringsdorf, and P. A. Suci, Langmuir 8, 1413 (1992). T. Kondo, T. Kakiuchi, and M. Shimomura, Thin Solid Films 244, 887 (1994). A. yon Nahmen, A. Post, H.-J. Galla, and M. Sieber, Eur. Biophys. J. 26, 359 (1997). D. H6nig and D. M6bius, J. Phys. Chem. 95, 4590 (1991). D. H6nig and D. M6bius, Thin Solid Films 210/211, 64 (1992). R. Castillo, S. Ramos, and J. Ruiz-Garcia, J. Phys. Chem. 100, 15235 (1996). W. J. Foster, M. C. Shih, and P. S. Pershan, J. Chem. Phys. 105, 3307 (1996). C. Lautz and T. M. Fischer, J. Phys. Chem. B 101, 8790 (1997). G.A. Overbeck, D. H6nig, L. Wolthaus, M. Gnade, and D. M6bius, Thin Solid Films 242, 26 (1994). T. Seki, H. Sekizawa, and K. Ichimura, Polymer 38, 725 (1997). M.-W. Tsao, T. M. Fischer, and C. M. Knobler, Langmuir 11, 3184 (1995). D. Vollhardt and T. Gutberlet, Colloids Surf. A: Physicochem. Eng. Aspects 102, 257 (1995). J.M. Rodriguez Patino, C. C. S~inchez, and M. R. R. Nifio, Langmuir 15, 2484 (1999). L. Wolthaus, A. Schaper, and D. M6bius, J. Phys. Chem. 98, 10809 (1994). W. J. Foster, M. C. Shih, and P. S. Pershan, in "Applications of Synchrotron Radiation Techniques to Material Science II" (D. L. Perry, G. Ice, N. Shinn, K. D'Amico, and L. Terminello, Eds.), Vol. 375, p. 187. Mater. Res. Soc. Proc., Pittsburgh, 1994. E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997). M.N.G. de Mul and J. A. Mann, Jr., Langmuir 14, 2455 (1998). Y. Tabe and H. Yokoyama, Langmuir 11,699 (1995). W. Frey, W. R. Schief, Jr., and V. Vogel, Langmuir 12, 1312 (1996).

LANGMUIR-BLODGETT

FILMS OF BIOLOGICAL MOLECULES

157. C. Lheveder, J. Meunier, and S. H6non, in "Physical Chemistry of Biological Interfaces" (A. Baszldn and W. Norde, Eds.). Marcel Dekker, New York, 1999. 158. A. Angelova, D. Vollhardt, and R. Ionov, J. Phys. Chem. 100, 10710 (1996). 159. A. Angelova, M. Van der Auweraer, R. Ionov, D. Volhardt, and E C. De Schryver, Langmuir 11, 3167 (1995). 160. Y. S. Kang, S. Risbud, J. Rabolt, and P. Stroeve, Langmuir 12, 4345 (1996). 161. M.M. Lipp, K. Y. C. Lee, A. J. Waring, and J. A. Zasadzinski, Biophys. J. 72, 2783 (1997). 162. J. M. R. Patino, C. C. Sfinchez, and M. R. R. Nifio, Langmuir 15, 4777 (1999). 163. P.-A. Albouy and P. Valerio, Supramol. Sci. 4, 191 (1997). 164. J. Als-Nielsen and K. Kjaer, in "Phase Transitions in Soft Condensed Matter" (T. Riste and D. Sherrington, Eds.), p. 113. Plenum Press, New York, 1989. 165. A. S. Brown, A. S. Holt, T. Dam, M. Trau, and J. W. White, Langmuir 13, 6363 (1997). 166. N. Dent, M. J. Grundy, R. M. Richardson, S. J. Roser, N. B. McKeown, and M. J. Cook, J. Chim. Phys. 85, 1003 (1988). 167. M. K. Durbin, M. C. Shih, A. Malik, P. Zschack, and P. Dutta, Colloids Surf. A: Physicochem. Eng. Aspects 102, 173 (1995). 168. M. Fukuto, K. Penanen, R. K. Heilmann, P. P. Pershan, and D. Vaknin, J. Chem. Phys. 107, 5531 (1997). 169. B. W. Gregory, D. Vaknin, T. M. Cotton, and W. S. Struve, Thin Solid Films 284-285, 849 (1996). 170. M.J. Grundy, R. M. Richardson, S. T. Roser, J. Penfold, and R. C. Ward, Thin Solid Films 159, 43 (1988). 171. H. Haas, G. Brezesinski, and H. M6hwald, Biophys. J. 68, 312 (1995). 172. C. A. Helm, H. M6hwald, K. Kjaer, and J. Als-Nielsen, Europhys. Lett. 4, 697 (1987). 173. M. Ibnelhaj, H. Riegler, H. M6hwald, M. Schwendler, and C. A. Helm, Phys. Rev. A 56, 1844 (1997). 174. K. Kago, H. Matsuoka, H. Endo, J. Eckelt, and H. Yamaoka, Supramol. Sci. 5, 349 (1998). 175. K. Kjaer, J. Als-Nielsen, C. A. Helm, P. Tippmann-Krayer, and H. M6hwald, Thin Solid Films 159, 17 (1988). 176. Z. Li, W. Zhao, J. Quinn, M. H. Rafallovich, J. Sokolov, R. B. Lennox, A. Eisenberg, X. Z. Wu, M. W. Kim, S. K. Sinha, and M. Tolan, Langmuir 11, 4785 (1995). 177. J. Majewski, T. L. Kuhl, K. Kjaer, M. C. Gerstenberg, J. Asl-nielsen, J. N. Israelachvili, and G. S. Smith, J. Am. Chem. Soc. 120, 1469 (1998). 178. M. L. Schlossman, D. K. Schwartz, E. H. Kawamoto, G. J. Kellogg, P. S. Pershan, M. W. Kim, and T. C. Chung, J. Phys. Chem. 95, 6628 (1991). 179. M. L. Schlossman, D. K. Schwartz, E. H. Kawamoto, G. J. Kellogg, P. S. Pershan, B. M. Ocko, M. W. Kim, and T. C. Chung, Mat. Res. Soc. Symp. Proc. 177, 351 (1990). 180. V. Skita, R. A. Butler, D. W. Chester, and R. F. Fishcetti, Biophys. J. 64, A259 (1993). 181. D. A. Styrkas, R. K. Thomas, and A. V. Sukhorukov, Thin Solid Films 243, 437 (1994). 182. D.A. Styrkas, R. K. Thomas, Z. A. Adib, E Davis, P. Hodge, and X. H. Liu, Macromolecules 27, 5504 (1994). 183. U. Vierl and G. Cevc, Biochim. Biophys. Acta Biomemb. 1325, 165 (1997). 184. U. Vierl, G. Cevc, and H. Metzger, Biochim. Biophys. Acta Biomemb. 1234, 139 (1995). 185. H. Yamaoka, H. Matsuoka, K. Kago, H. Endo, J. Eckelt, and R. Yoshitome, Chem. Phys. Lett. 295, 245 (1998). 186. C. Fradin, D. Luzet, A. Braslau, M. Alba, E Muller, J. Daillant, J. M. Petit, and E Rieutord, Langmuir 14, 7327 (1998). 187. R. Steitz, J. B. Peng, I. R. Peterson, I. R. Gentle, R. M. Kenn, M. Goldmann, and G. T. Barnes, Langmuir 14, 7245 (1998). 188. K. Kago, M. Ftirst, H. Matsuoka, H. Yamaoka, and T. Seki, Langmuir 15, 2237 (1999).

547

189. V.M. Kaganer, G. Brezesinski, H. M6hwald, E B. Howes, and K. Kjaer, Phys. Rev. E 59, 2141 (1999). 190. S. Leporatti, S. Akari, F. Bringezu, G. Brezesinski, and H. M6hwald, Appl. Phys. A 66, S1245 (1998). 191. E. Havinga and J. De Wael, Recl. Trav. Chim. Pays-Bas. 56, 375 (1937). 192. J. De Wael and E. Havinga, Recl. Trav. Chim. Pays-Bas. 59, 770 (1940). 193. L.H. Germer and K. H. Storks, J. Chem. Phys. 6, 280 (1938). 194. W. Walkenhorst, Naturwissenschaften 34, 375 (1947). 195. H.P. Zingsheim, Scanning Electron Microsc. 1,357 (1977). 196. D. Day and J. B. Lando, J. Polym. Sci. Polym. Chem. Ed. 16, 1431 (1978). 197. C. B6hm, R. Steitz, and H. Riegler, Thin Solid Films 178, 511 (1989). 198. T. Hayashi, S. Ito, M. Yamamoto, Y. Tsujii, M. Matsumoto, and T. Miyamoto, Langmuir 10, 4142 (1994). 199. T. Kato, K. Iriyama, and T. Araki, Thin Solid Films 210/211, 79 (1992). 200. T. Kato, N. Matsumoto, M. Kawano, N. Suzuki, T. Araki, and K. Iriyama, Thin Solid Films 242, 223 (1994). 201. V. V. Klechkovskaya, M. Anderle, R. Antolini, R. Canteri, L. Feigin, E. Rakova, and N. Sriopina, Thin Solid Films 284-285, 208 (1996). 202. E Kopp, U. P. Fringeli, K. Mtihlethaler, and H. H. Gtinthard, Biophys. Struct. Mech. 1, 75 (1975). 203. I.R. Peterson and G. J. Russell, Phil. Mag. A 49, 463 (1984). 204. H.E. Ries, Jr., and W. A. Kimball, Nature 181,901 (1958). 205. I. Robinson, J. R. Sambles, and I. R. Peterson, Thin Solid Films 189, 149 (1989). 206. E. Sheppard, R. P. Bronson, and N. Tcheurekdjian, J. Colloid Sci. 19, 833 (1964). 207. R. Steitz, E. Mitchell, and I. R. Peterson, MakromoI. Chem. Macromol. Symp. 46, 265 ( 1991). 208. I.R. Peterson, R. Steitz, H. Krug, and I. Voigt-Martin, J. Phys. France 51, 1003 (1990). 209. Yu. M. Lvov, V. I. Troitsky, and L. A. Feigin, Mol. Cryst. Liq. Cryst. 172, 89 (1989). 210. V.I. Troitsky, V. S. Bannikov, and T. S. Berzina, J. Mol. Electron. 5, 147 (1989). 211. V. I. Troitsky, in "Methods of Structure Analysis" (L. Feigin, Ed.), Vol. 272. Moscow, 1989. 212. L.A. Feigin, Y. M. Lvov, and V. I. Troitsky, Soy. Sci. Rev. A. Phys. 11, 287 (1989). 213. R.V. Sudiwala, C. Cheng, E. G. Wilson, and D. N. Batchelder, Thin Solid Films 210/211,452 (1992). 214. J.D. Jontes and R. A. Milligan, J. Mol. Biol. 266, 331 (1997). 215. G. Lieser, S. Mittler-Neher, J. Spinke, and W. Knoll, Biochim. Biophys. Acta 1192, 14 (1994). 216. A. Tanaka, M. Yamaguchi, T. Iwasaki, and K. Iriyama, Chem. Lett. 1219 (1989). 217. C. Flament, K. Graf, F. Gallet, and H. Riegler, Thin Solid Films 243, 411 (1994). 218. E.W. Kubalek, R. D. Kornberg, and S. A. Darst, Ultramicroscopy 35, 295 (1991). 219. J. Majewski, L. Margulis, D. Jacquemain, E Leveiller, C. B/3hm, T. Arad, Y. Talmon, M. Lahav, and L. Leiserowitz, Science 261,899 (1993). 220. H.E. Ries, Jr., and W. A. Kimball, J. Phys. Chem. 59, 94 (1955). 221. R. Rolandi, O. Cavalleri, C. Toneatto, and D. Ricci, Thin Solid Films 243, 431 (1994). 222. E. Sheppard, R. P. Bronson, and N. Tcheurekdjian, J. Colloid Sci. 20, 755 (1965). 223. R. Steitz and I. R. Peterson, in "Electron Crystallography of Organic Molecules" (J. R. Fryer and D. L. Dorset, Eds.), NATO ASI, Vol. C328, p. 365. Kluwer, Dordrecht, 1990. 224. F. Takeda, M. Matsumoto, T. Takenaka, and Y. Fujiyoshi, J. Colloid lnteof. Sci. 84, 220 (1981). 225. J.R. Fryer, R. A. Harm, and B. L. Eyres, Nature 313, 382 (1985). 226. W. Chiu, A. J. Avila-Sakar, and M. F. Schmid, Adv. Biophys. 34, 161 (1997). 227. W.M. Heckl, M. Thompson, and H. M/3hwald, Langmuir 5, 390 (1989). 228. S.W. Hui, M. Cowden, P. Papahadjopoulos, and D. F. Parsons, Biochim. Biophys. Acta 382, 265 (1975).

548

EROKHIN

229. M. Li, E. Zhou, X. Wang, and J. Xu, Thin Solid Films 264, 94 (1995). 230. E. Okamura, J. Umemura, K. lriyama, and T. Araki, Chem. Phys. Lipids 66, 219 (1993). 231. S.-X. Wang and S. Sui, Supramol. Sci. 5, 803 (1998). 232. A.J. Avila-Sakar and W. Chiu, Biophys. J. 70, 57 (1996). 233. W. Baumeister and M. Hahn, Cytobiologie 7, 244 (1973). 234. N. Braun, J. Tack, L. Bachmann, and S. Weinkauf, Thin Solid Films 284285, 703 (1996). 235. A. Brisson, A. Olofsson, P. Ringler, M. Schmutz, and S. Stoylova, Biol. Cell 80, 221 (1994). 236. A. Brisson, W. Bergsma-Schutter, E Oling, O. Lambert, and I. Reviakine, J. Cryst. Growth 196, 456 (1999). 237. D.G. Cornell and R. J. Carroll, Colloids Surf. 6, 385 (1983). 238. P. Fromherz, Nature 231,267 (1971). 239. P. Helme and P. M. Vignais, J. Mol. Biol. 274, 687 (1997). 240. M. Mule, E. Stussi, D. De Rossi, T. S. Berzina, and V. I. Troitsky, Thin Solid Films 237, 225 (1994). 241. T. Sawaguchi, E Mizutani, and I. Taniguchi, Langmuir 14, 3565 (1998). 242. P. Wang, J. L. Singleton, X.-L. Wu, M. Shamsuzzoha, R. M. Metzger, C. A. Panetta, J. W. Kim, and N. E. Heimer, Synth. Met. 57, 3824 (1993). 243. P. Wang, M. Shamsuzzoha, X.-L. Wu, W.-J. Lee, and R. M. Metzger, J. Phys. Chem. 96, 9025 (1992). 244. X.-L. Wu, M. Shamsuzzoha, R. M. Metzger, and G. J. Ashwell, Synth. Met. 57 (1993). 245. P. Quint, M. Hara, W. Knoll, H. Sasabe, and R. S. Duran, Macromolecules 28, 4019 (1995). 246. A. Zlatldn, S. Yudin, J. Simon, M. Hanack, and H. Lehman, Adv. Mater Opt. Electron. 5, 259 (1995). 247. S. Alexandre, A. W. Coleman, A. Kasselouri, and J. M. Valleton, Thin Solid Films 284-285, 765 (1996). 248. O.V. Kolomytkin, A. O. Golubok, D. N. Davydov, V. A. Timofeev, S. A. Vinogradova, and S. Y. Tipisev, Biophys. J. 59, 889 (1991). 249. P. Facci, A. Diaspro, and R. Rolandi, Thin Solid Films 327-329, 532 (1998). 250. M. Hara, H. Sasabe, and W. Knoll, Thin Solid Films 273, 66 (1996). 251. H. J. Schmitt, R. Zhu, G. Min, and Y. Wei, J. Phys. Chem. 96, 8210 (1992). 252. P. Facci, V. Erokhin, A. Tronin, and C. Nicolini J. Phys. Chem. 98, 13323 (1994). 253. P. Facci, V. Erokhin, S. Carrara, and C. Nicolini, Proc. Natl. Acad. Sci. U.S.A. 93, 10556 (1996). 254. N. Elbel, W. Roth, E. GiJnther, and H. von Seggern, Surf. Sci. 303, 424 (1994). 255. Y. Zhang, Q. Li, Z. Xie, B. Mao, B. Hua, Y. Chen, and Z. Tian, Thin Solid Films 274, 150 (1996). 256. C. Zhu, J. Shen, Z. Ma, S. Pang, A. Wang, and K. Hu, J. Chinese Electron Microsc. Soc. 10, 167 (1991). 257. H.-J. Butt, R. Guckenberger, and J. P. Rabe, Ultramicroscopy 46, 375 (1992). 258. H.C. Day, D. R. Allee, R. George, and V. A. Burrows, Appl. Phys. Lett. 62, 1629 (1993). 259. L. Eng, H. R. Hidber, L. Rosenthaler, U. Staufer, R. Wiesendanger, and H.-J. Guentherodt, J. Vac. Sci. Technol. 6, 358 (1988). 260. J.Y. Fang, Z. H. Lu, G. W. Ming, Z. M. Ai, Y. Wei, and P. Stroeve, Phys. Rev. A 46, 4963 (1992). 261. W. M. Heckl, Thin Solid Films 210/211,640 (1992). 262. M. Hibino, A. Sumi, and I. Hatta, Thin Solid Films 273, 272 (1996). 263. M. Hibino, A. Sumi, H. Tsuchiya, and I. Hatta, J. Phys. Chem. B 102, 4544 (1998). 264. J.-J. Kim, S.-D. Jung, H.-S. Roh, and J.-S. Ha, Thin Solid Films 244, 700 (1994). 265. C.A. Lang, J. K. H. H6rber, T. W. H~nsch, W. M. Heckl, and H. M6hwald, J. Vac. Sci. Technol. A6, 368 (1988). 266. R.M. Leblanc and J. A. DeRose, Surf. Sci. Rep. 22, 73 (1995). 267. R.M. Metzger and C. A. Panetta, Synth. Met. 41-43, 1407 (1991). 268. W.M. Sigmund, T. S. Bailey, M. Hara, H. Sasabe, W. Knoll, and R. S. Duran, Langmuir 11, 3153 (1995).

269. A. Stabel, L. Dasaradhi, D. O'Hagan, and J. P. Rabe, Langmuir 11, 1427 (1995). 270. C. Goletti, A. Sgarlata, N. Motta, P. Chiaradia, R. Paolesse, A. Angelaccio, M. Drago, C. Di Natale, A. D'Amico, M. Cocco, and V. I. Troitsky, Appl. Phys. Lett. 75, 1237 (1999). 271. L.C. Giancarlo and G. W. Flynn, Annu. Rev. Phys. Chem. 49, 297 (1998). 272. P. Facci, V. Erokhin, and C. Nicolini, Thin Solid Films 243, 403 (1994). 273. R. Garcia, J. Tamayo, J. M. Soler, and C. Bustamante, Langmuir 11, 2109 (1995). 274. H.E.-M. Niemi, M. Ikonen, M. Levlin, and H. Lemmetyinen, Langmuir 9, 2436 (1993). 275. A. Tazi, S. Boussaad, J. A. DeRose, and R. M. Leblanc, J. Vac. Sci. Technol. B, Microelectron. Nanometer Struct. 14, 1476 (1996). 276. E. P. Friis, J. E. T. Andersen, Yu. I. Kharkatz, A. M. Kuznetsov, R. J. Nichols, J.-D. Zhang, and J. Ulstrup, Proc. Natl. Acad. Sci. U.S.A. 96, 1379 (1999). 277. D. Erts, J. Dzelme, and H. Olin, Latv. J. Phys. Techn. Sci. 6, 57 (1996). 278. L. Stockman, G. Neuttiens, C. Van Haesendonck, and Y. Bruynseraede, Appl. Phys. Lett. 62, 2935 (1993). 279. K. Takimoto, H. Kawada, E. Kishi, K. Yano, K. Sakai, K. Hatanaka, K. Eguchi, and T. Nakagiri, Appl. Phys. Lett. 61, 3032 (1992). 280. R. Yang, D. E Evans, and W. A. Hendrickson, Langmuir 11, 211 (1995). 281. K. Yano, R. Kuroda, Y. Shimada, S. Shido, M. Kyogaku, H. Matsuda, K. Takimoto, K. Eguchi, and T. Nakagiri, J. Vac. Sci. Technol. B, Microelectron. Nanometer Struct. 14, 1353 (1996). 282. Z. Ali-Adib, P. Hodge, R. H. Tredgold, M. Woolley, and A. J. Pidduck, Thin Solid Films 242, 157 (1994). 283. S. Arisawa, T. Fujii, T. Okane, and R. Yamamoto, Appl. Surf. Sci. 60/61, 321 (1992). 284. C.E.H. Berger, K. O. van der Weft, R. P. H. Kooyman, B. G. de Grooth, and J. Greve, Langmuir 11, 4188 (1995). 285. E. Gy6rvary, J. Peltonen, M. Lind6n, and J. B. Rosenholm, Thin Solid Films 284-285, 368 (1996). 286. T. Imae and Y. Ikeo, Supramol. Sci. 5, 61 (1998). 287. N. Rozlosnik, G. Antal, T. Pusztai, and Gy. Faigel, Supramol. Sci. 4, 215 (1997). 288. A. K. Dutta, P. Vanoppen, K. Jeuris, P. C. M. Grim, D. Pevenage, C. Salesse, and F. C. De Schryver, Langmuir 15,607 (1999). 289. R. Lu, K. Xu, J. Gu, and Z. Lu, Phys. Lett. A 260, 417 (1999). 290. K. Ekelund, E. Sparr, J. Engblom, H. Wennerstr6m, and S. Engstr6m, Langmuir 15, 6946 (1999). 291. E. Sparr, K. Ekelund, J. Engblom, S. Engstr6m, and H. Wennerstr6m, Langmuir 15, 6950 (1999). 292. H. Sugimura and N. Nakagiri, J. Phys. A: Mater Sci. Process. 66, $427 (1998). 293. S. Morita, H. Wang, Y. Wang, K. Iriyama, and Y. Ozaki, Mol. Cryst. Liq. Cryst. 337, 325 (1998). 294. B. Lemkadem, P. Saulnier, E Boury, and J. E. Proust, Colloids Surf. B 13, 233 (1999). 295. W. Barger, D. Koleske, K. Feldma, D. Krtiger, and R. Colton, Polymer Preprints 37, 606 (1996). 296. G. K. Zhavnerko, V. N. Staroverov, V. E. Agabekov, M. O. Gallyamov, and I. V. Yaminsky, Thin Solid Films 359, 98 (2000). 297. K.S. Birdi and D. T. Vu, Langmuir 10, 623 (1994). 298. K. S. Birdi, D. T. Vu, L. Moesby, K. B. Andersen, and D. Kristensen, Surf. Coating Technol. 67, 183 (1994). 299. L. E Chi and H. Fuchs, NATO-Series, Workshop "Manipulations of Atoms in High Fields and Temperatures: Applications" (B. V. Thien, Ed.), p. 287. Kluwer Academic, 1993. 300. L. E Chi, H. Fuchs, R. R. Johnston, and H. Ringsdorf, J. Vac. Sci. Technol. B 12, 1967 (1994). 301. L. E Chi, M. Anders, H. Fuchs, R. R. Johnston, and H. Ringsdorf, Science 259, 213 (1993). 302. Y. Chunbo, L. Xinmin, D. Desheng, L. Bin, Z. Hongjie, L. Zuhong, L. Juzeng, and N. Jiazuan, Surf. Sci. Lett. 366, L729 (1996). 303. Y. Chunbo, W. Ying, S. Yueming, L. Zuhong, and L. Juzheng, Surf. Sci. 392, L 1 (1997).

LANGMUIR-BLODGETT

FILMS OF BIOLOGICAL MOLECULES

304. Y. Chunbo, W. Ying, Y. Xiaomin, L. Zuhong, and L. Juzheng, Appl. Surf. Sci. 103, 531 (1996). 305. L. Daehne, J. Tao, and G. Mao, Langmuir 14, 565 (1998). 306. J.A. DeRose and R. M. Leblanc, Surf. Sci. Rep. 22, 73 (1995). 307. L. Dziri, S. Boussaad, N. Tao, and R. M. Leblanc, Thin Solid Films 327329, 56 (1998). 308. J. Y. Fang, R. A. Uphaus, and E Stroeve, Thin Solid Films 243, 450 (1994). 309. M. F16rsheimer, A. J. Steinford, and E Giinter, Surf. Sci. Lett. 297, L39 (1993). 310. M. F1/Srsheimer, A. J. Steinford, and E Gtinter, Thin Solid Films 247, 190 (1994). 311. M. Fl6rsheimer, A. J. Steinfort, and E Giinter, Thin Solid Films 244, 1078 (1994). 312. R.A. Frazier, M. C. Davies, G. Matthijs, C. J. Roberts, E. Schatcht, S. J. Tendler, and E M. Williams, Langmuir 13, 4795 (1997). 313. M. Fujihira and H. Takano, Thin Solid Films 243,446 (1994). 314. I. Fujiwara, M. Ohnishi, and J. Seto, Langmuir 8, 2219 (1992). 315. J. Garnaes, D. K. Schwartz, R. Viswanathan, and J. A. N. Zasadzinski, Synth. Met. 57, 3795 (1993). 316. U.-W. Grummt, K.-H. Feller, E Lehmann, R. Colditz, R. Gadonas, and A. Pugzlys, Thin Solid Films 284-285, 904 (1996). 317. U.-W. Grummt, K.-H. Feller, E Lehmann, R. Colditz, R. Gadonas, and A. Pugzlys, Thin Solid Films 273, 76 (1996). 318. D.-E Gu, C. Rosenblatt, and Z. Li, Liq. Cryst. 19, 489 (1995). 319. A. E Gunning, E J. Wilde, D. C. Clark, V. J. Morris, M. L. Parker, and E A. Gunning, J. Colloid Interf. Sci. 183, 600 (1996). 320. J. Hu, M. Wang, H.-U. G. Weier, E Frantz, W. Kolbe, D. E Ogletree, and M. Salmeron, Langmuir 12, 1697 (1996). 321. S. W. Hui, R. Viswanathan, J. A. Zasadzinski, and J. N. Israelachvili, Biophys. J. 68, 171 (1995). 322. T. Imae and K. Aoki, Langmuir 14, 1196 (1998). 323. J. Y. Josefowicz, N. C. Maliszewskyj, S. H. J. Idziak, E A. Heiney, J. E McCauley, Jr., and A. B. Smith III, Science 260, 323 (1993). 324. T. Kajiyama, Y. Oishi, E Hirose, K. Shuto, and T. Kuri, Langmuir 10, 1297 (1994). 325. T. Kato, M. Kameyama, and M. Kawano, Thin Solid Films 272, 232 (1996). 326. E. A. Kondrashkina, K. Hagedorn, D. Vollhardt, M. Schmidbauer, and R. K6hler, Langmuir 12, 5148 (1996). 327. B. L. Kropman, D. H. A. Blank, and H. Rogalla, Thin Solid Films 327329, 185 (1998). 328. N. B. Larsen, T. Bjornholm, J. Garnaes, J. Larsen, and K. Schaumburg, NATO ASI Ser. Ser. E 292, 205 (1995). 329. M. V61ez, S. Vieira, I. Chambrier, and M. J. Cook, Langmuir 14, 4227 (1998). 330. N. C. Maliszewskyj, J. Y. Josefowicz, E A. Heiney, J. E McCauley, Jr., and A. B. Smith III, Mater. Res. Soc. Proc. 355, 147 (1995). 331. N.C. Maliszewskyj, E A. Heiney, J. Y. Josefowicz, J. E McCauley, Jr., and A. B. Smith III, Science 264, 77 (1994). 332. E. Mayer, L. Howald, R. M. Overney, H. Heinzelmann, J. Frommer, H.-J. Giintherodt, T. Wagner, H. Schler, and S. Roth, Nature 349, 398 (1991 ). 333. K. Meine, D. Vollhardt, and G. Weidemann, Langmuir 14, 1815 (1998). 334. O. Mori and T. Imae, Langmuir ll, 4779 (1995). 335. T. Nakagawa, K. Ogawa, and T. Kurumizawa, Langmuir 10, 525 (1994). 336. G. Nechev, M. Hibino, and I. Hatta, Japan. J. Appl. Phys. 36, L580 (1997). 337. N. Peachey and C. Eckhardt, Micron 25, 271 (1994). 338. J. Peltonen, M. Linden, H. Fagerholm, E. Gy6rvary, and E Eriksson, Thin Solid Films 242, 88 (1994). 339. J.B. Peng and G. T. Barnes, Thin Solid Films 284-285, 444 (1996). 340. B. Pignataro, C. Consalvo, G. Compagnini, and L. Licciardello, Chem. Phys. Lett. 299, 430 (1999). 341. X. Qian, Z. Tad, X. Sun, S. Xiao, H. Wu, Z. Lu, and Y. Wei, Thin Solid Films 284-285, 432 (1996). 342. H. Sato, Y. Ozaki, Y. Oishi, M. Kuramori, K. Suehiro, K. Nakashima, K. Uehara, and K. Iriyama, Langmuir 13, 4676 (1997).

549

343. E Sawunyama, L. Jiang, A. Fujishima, and K. Hashimoto J. Phys. Chem. B 101, 11000(1997). 344. E-J. Schrnitt, A. L. Weisenhorn, E K. Hansma, and W. Knoll, Makromol. Chem. Macromol. Syrup. 46, 133 (1991). 345. E-J. Schmitt, A. L. Weisenhorn, E K. Hansma, and W. Knoll, Thin Solid Films 210/21 l, 666 (1992). 346. D. K. Schwartz, J. Garnaes, R. Viswanathan, and J. A. N. Zasadzinski, Scanning 14, II-3 (1992). 347. D.K. Schwartz, J. Garnaes, R. Viswanathan, S. Chiruvolu, and J. A. N. Zasadzinski, Phys. Rev. E 47, 452 (1993). 348. D.K. Schwartz, R. Viswanathan, and J. A. N. Zasadzinski, Science 263, 1158 (1994). 349. N. Sigiyama, A. Shimizu, M. Nakamura, Y. Nakagawa, Y. Nagasawa, and H. Ishid, Thin Solid Films 331,170 (1999). 350. J.M. Solletti, M. Botreau, E Sommer, Tran Minh Duc, and M. R. Celio, J. Vac. Sci. Technol. B, Microelectron. Nanometer Struct. 14, 1492 (1996). 351. S.M. Stephens and R. A. Dluhy, Thin Solid Films 284-285, 381 (1996). 352. D.Y. Takamoto, E. TerOvanesyan, D. K. Schwartz, R. Viswanathan, A. J. Waring, and J. A. Zasadzinski, Acta Phys. Polon. 93, 373 (1998). 353. E. ten Grotenhuis, J. C. van Miltenburg, and J. E van der Eerden, Coll. Surf. A 105, 309 (1995). 354. M. Velez, S. Mukhopadhyay, I. Muzikante, G. Matisova, and S. Vieira, Langmuir 13, 870 (1997). 355. M. Velez, S. Vieira, I. Chambrier, and M. J. Cook, Langmuir 14, 4227 (1998). 356. R. Viswanathan, D. K. Schwarz, J. Gamaes, and J. A. N. Zasadzinski, Langmuir 8, 54 (1992). 357. D. Vollhardt, T. Kato, and M. Kawano, J. Phys. Chem. 100, 4141 (1996). 358. Y. Wang, K. Nichogi, K. Iriyama, and Y. Ozaki, J. Phys. Chem. 100, 374 (1996). 359. Y. Wang, K. Nichogi, K. Iriyama, and Y. Ozaki, J. Phys. Chem. 100, 17238 (1996). 360. Y. Wang, K. Nichogi, S. Terashita, K. Iriyama, and Y. Ozaki, J. Phys. Chem. 100, 368 (1996). 361. A.L. Weisenhom, D. U. Roemer, and G. P. Lorenzi, Langmuir 8, 3145 (1992). 362. A.L. Weisenhorn, F.-J. Schmitt, W. Knoll, and P. K. Hansma, Ultramicroscopy 42-44, 1125 (1992). 363. A.L. Weisenhorn, H. E. Gaub, H. G. Hansma, R. L. Kelderman, and P. K. Hansma, Scanning Microscopy 4, 511 (1990). 364. A. L. Weisenhorn, M. Egger, F. Ohnesorge, S. A. C. Gould, S.-P. Heyn, H. G. Hansma, R. L. Sinsheimer, H. E. Gaub, and P. K. Hansma, Langmuir 7, 8 ( 1991). 365. T.M. Winger and E. L. Chaikof, Langmuir 14, 4148 (1998). 366. H.-M. Wu and S.-J. Xiao, Jpn. J. Appl. Phys. 35, L161 (1996). 367. S.-J. Xiao, H.-M. Wu, X.-M. Yang, N.-H. Li, Y. Wei, X.-Z. Sun, and Z.-H. Tad, Thin Solid Films 256, 210 (1995). 368. H. Yamada, Y. Hirata, M. Hara, and J. Miyake, Thin Solid Films 243, 455 (1994). 369. K. Yamanaka, H. Takano, E. Tomia, and M. Fujihira, Jpn. J. Appl. Phys. 35, 5421 (1996). 370. X.-M. Yang, D. Xiao, Z.-H. Lu, and Y. Wei, Appl. Surf. Sci. 90, 175 (1995). 371. X.M. Yang, G. M. Wang, and Z. H. Lu, Supramol. Sci. 5, 549 (1998). 372. K. Yano, M. Kyogaku, R. Kuroda, Y. Shimada, S. Shido, H. Matsuda, K. Takimoto, O. Albrecht, K. Eguchi, and T. Nakagiri, Appl. Phys. Lett. 68, 188 (1996). 373. S. Yokoyama, M. Kakimoto, and Y. Imad, Synth. Met. 81,265 (1996). 374. C. Yuan, X. Yang, J. Liu, and Z. Lu, Surf. Sci. Lett. 355, L381 (1996). 375. M. Yumura, T. Nakamura, M. Matsumoto, S. Ohshima, Y. Kuriki, K. Honda, M. Kurahashi, and Y. F. Miura, Synth. Met. 57 (1993). 376. J.A. Zasadzinski, R. Viswanathan, D. K. Schwartz, J. Garnaes, L. Madsen, S. Chiruvolu, J. T. Woodward, and M. L. Longo, Colloids Surf. A 93, 305 (1994). 377. S. Terreyyaz, H. Yachibana, and M. Matsumoto, Langmuir 14, 7511 (1998).

550

EROKHIN

378. B. Cappella, P. Baschieri, M. Ruffa, C. Ascoli, A. Relini, and R. Rolandi, Langmuir 15, 2152 (1999). 379. O. I. Kiselyova, O. L. Guryev, A. V. Krivosheev, S. A. Usanov, and I. V. Yaminsky, Langmuir 15, 1353 (1999). 380. A. Komolov, K. Schaumburg, P. J. Mr and V. Monakhov, Appl. Surf. Sci. 142, 591 (1999). 381. C. Yuan, D. Ding, Z. Lu, and J. Liu, Colloids Surf. A 150, 1 (1999). 382. T. Geue, M. Schultz, U. Englisch, R. St6mmer, U. Pietsch, K. Meine, and D. Vollhardt, J. Chem. Phys. 110, 8104 (1999). 383. P. Qian, H. Nanjo, N. Sanada, T. Yokoyama, O. Itabashi, H. Hayashi, T. Miyashita, and T. M. Suzuki, Thin Solid Films 349, 250 (1999). 384. A.P. Gunning, A. R. Mackie, P. J. Wilde, and V. J. Morris, Langmuir 15, 4636 (1999). 385. F. Boury, P. Saulnier, J. E. Proust, I. Panaiotov, T. Ivanova, C. Postel, and O. Abillon, Colloids Surf. A 155, 117(1999). 386. A. Tazi, S. Boussaad, and R. M. Leblanc, Thin Solid Films 353, 233 (1999). 387. S.A. Evenson, J. P. S. Badyal, C. Pearson, and M. C. Petty, Adv. Mater. 9, 58 (1997). 388. C. Consalvo, S. Panebianco, B. Pignataro, G. Compagnini, and O. Puglisi, J. Phys. Chem. B 103, 4687 (1999). 389. N. Kato, K. Saito, H. Aida, and Y. Uesu, Chem. Phys. Lett. 312, 115 (1999). 390. Y. Chunbo, W. Ying, L. Zuhong, and L. Juzheng, J. Mater. Sci. Lett. 16, 227 (1997). 391. J. Yang, L. K. Tamm, T. W. Tillack, and Z. Shao, J. Mol. Biol. 229, 286 (1993). 392. R. Viswanathan, D. K. Schwartz, J. Garnaes, and J. A. N. Zasadzinski, Langmuir 8, 1603 (1992). 393. D.K. Schwartz, Curr. Opin. Colloid Interface Sci. 3, 131 (1998). 394. T. Mikayama, K. Uehara, A. Sugimoto, H. Maruyama, K. Mizuno, and N. Inoue, Mol. Cryst. Liq. Cryst. 310, 137 (1998). 395. Y. Wang, K. Nichogi, K. Iriyama, and Y. Ozaki, J. Phys. Chem. B 101, 6379 (1997). 396. H. Sato, Y. Oishi, M. Kuramori, K. Suehiro, M. Kobayashi, K. Nakashima, K. Uehara, and K. Iriyama, J. Chem. Soc. Faraday Trans. 93, 621 (1997). 397. J. P. K. Peltonen, P. He, and J. B. Rosenholm, J. Am. Chem. Soc. 114, 7637 (1992). 398. P. Hartley, M. Matsumoto, and P. Mulvaney, Langmuir 14, 5203 (1998). 399. A. IkaJ, Surf. Sci. Rep. 26, 261 (1997). 400. B.B. Sauer, R. S. McLean, and R. R. Thomas, Langmuir 14, 3045 (1998). 401. J. Yang, L. K. Tamm, A. P. Somlyo, and Z. Shao, J. Microscopy 171, 183 (1993). 402. H. Takano and M. Fujihira, Thin Solid Films 272, 312 (1996). 403. J.C. Kim, Y. M. Lee, E. R. Kim, H. Lee, Y. W. Shin, and S. W. Park, Thin Solid Films 327-329, 690 (1998). 404. H. E Knapp, W. Wiegr~ibe, M. Heim, R. Eschrich, and R. Guckenberger, Biophys. J. 69, 708 (1995). 405. C.L. Andrews, Rev. Sci. InstrtJm. 11, 111 (1940). 406. W.T. Astbury, E O. Bell, E. Gorter, and J. Van Ormondt, Nature 142, 33 (1938). 407. D.C. Bisset and J. Iball, Proc. Phys. Soc. London A 67, 315 (1954). 408. G.L. Clark and P. W. Leppla, J. Am. Chem. Soc. 58, 2199 (1936). 409. G.L. Clark, R. R. Sterrett, and P. W. Leppla, J. Am. Chem. Soc. 52, 330 (1935). 410. C. Holley and S. Bernstein, Phys. Rev. 49, 403 (1936). 411. C. Holley, Phys. Rev. 51, 1000 (1937). 412. D.S. Kapp and N. Wainfan, Phys. Rev. 138, 1490 (1965). 413. T. Amdt, A. J. Schouten, G. E Schmidt, and G. Wegner, Macromol. Chem. 192, 2219 (1991). 414. T.A. Barberka, U. H6hne, U. Pietsch, and T. H. Metzger, Thin Solid Films 244, 1061 (1994). 415. S.W. Barton, B. N. Thomas, E. B. Flom, S. A. Rice, B. Lin, J. B. Peng, J. B. Ketterson, and P. Dutta, J. Chem. Phys. 89, 2257 (1988). 416. A.S. Belal, M. M. SaUeh, and M. Yahaya, Supramol. Sci. 4, 535 (1997).

417. M.R. Buhaenko, M. J i Grundy, R. M. Richardson, and S. J. Roser, Thin Solid Films 159, 253 (1988). 418. M.W. Charles, J. Colloid Interf. Sci. 35, 167 (1971). 419. M.W. Charles, J. Appl. Phys 42, 3329 (1971). 420. J. Claudius, T. Gerber, J. Weigelt, and M. Kinzler, Thin Solid Films 287, 225 (1996). 421. S. Dante, M. De Rosa, E. Maccioni, A. Morana, C. Nicolini, E Rustichelli, V. I. Troitsky, and B. Yang, Mol. Cryst. Liq. Cryst. 262, 191 (1995). 422. S. Dante, M. De Rosa, O. Francescangeli, C. Nicolini, E Rustichelli, and V. I. Troitsky, Thin Solid Films 284--285,459 (1996). 423. M.K. Durbin, A. Malik, A. G. Richter, K. G. Huang, and P. Dutta, Langmuir 13, 6547 (1997). 424. V. Erokhin, L. Feigin, G. Ivakin, V. Klechkovskaya, Yu. Lvov, and N. Stiopina, Macromol. Chem. Macromol. Syrup. 46, 359 (1991). 425. N.P. Franks and W. R. Lieb, J. Mol. Biol. 133,469 (1979). 426. P. Ganguly, M. Sastry, S. Choudhury, and D. V. Paranjape, Langmuir 13, 6582 (1997). 427. R. Geer, R. Shashidhar, A. Thibodeaux, and R. S. Duran, Liq. Cryst. 16, 869 (1994). 428. D. B. Hammond, T. Rayment, D. Dunne, P. Hodge, Z. Ali-Adib, and A. Dent, Langmuir 14, 5896 (1998). 429. W. Jark, G. Comelli, T. P. Russel, and J. St6hr, Thin Solid Films 170, 309 (1989). 430. P. Lesieur, J. Mol. Struct. 383, 125 (1996). 431. W. Lesslauer, Acta Crystallogr. Sect. B 30, 1932 (1974). 432. H. Li, Z. Wang, B. Zhao, H. Xiong, X. Zhang, and J. Shen, Langmuir 14, 423 (1998). 433. Y.M. Lvov, D. Svergun, L. A. Feigin, C. Pearson, and M. C. Petty, Phil. Mag. Lett. 59, 317 (1989). 434. Yu. M. Lvov and L. A. Feigin, Stud. Biophys. 112, 221 (1986). 435. E. Maccioni, P. Mariani, E Rustichelli, H. Delacroix, V. Troitsky, A. Riccio, A. Gambacorta, and M. De Rosa, Thin Solid Films 265, 74 (1995). 436. W. MacNaughton, K. A. Snook, E. Caspi, and N. P. Franks, Biochim. Biophys. Acta 818, 132 (1985). 437. A. Malik, M. K. Durbin, A. G. Richter, K. G. Huang, and P. Dutta, Thin Solid Films 284-285, 144 (1996). 438. P. Mariani, E. Maccioni, E Rustichelli, H. Delacroix, V. Troitsky, A. Riccio, A. Gambacorta, and M. De Rosa, Thin Solid Films 265, 74 (1995). 439. H.J. Merle, Y. M. Lvov, and I. R. Peterson, Makromol. Chem. Macromol. Symp. 46, 271 (1991). 440. E. Milella, C. Giannini, and L. Tapfer, Thin Solid Films 293, 291 (1997). 441. H. Ohnuki, M. Izumi, K. Kitamura, H. Yamaguchi, H. Oyanagi, and P. Delhaes, Thin Solid Films 243,415 (1994). 442. J.M. Pachence and J. K. Blasie, Biochem. J. 59, 894 (1991). 443. J.B. Peng, G. J. Foran, G. T. Barnes, and I. R. Gentle, Langmuir 13, 1602 (1997). 444. M. Pomerantz and A. Segmiiller, Thin Solid Films 68, 33 (1980). 445. M. Pomerantz, A. Segmiiller, L. Netzer, and J. Sagiv, Thin Solid Films 132, 153 (1985). 446. M. Pomerantz, E H. Dacol, and A. Segmtiller, Bull. Am. Phys. Soc. 20, 477 (1975). 447. M. Prakash, P. Dutta, J. B. Ketterson, and B. M. Abraham, Chem. Phys. Lett. 111,395 (1984). 448. M. Prakash, J. B. Ketterson, and P. Dutta, Thin Solid Films 134, 1 (1985). 449. K. M. Robinson, C. Hernandez, and J. Adin Mann, Jr., Thin Solid Films 210/211, 73 (1992). 450. Y. Sasanuma and H. Nakahara, Thin Solid Films 261,280 (1995). 451. M. Seul, P. Eisenburger, and H. McConnell, Proc. Nat. Acad. Sci. U.S.A. 80, 5795 (1983). 452. V. Skita, M. Filipkowski, A. E Garito, and J. K. Blasie, Phys. Rev. B. 34, 5826 (1986). 453. V.K. Srivastava and A. R. Verma, Solid State Commun. 4, 367 (1966). 454. G. Sukhorukov, V. Lobyshev, and V. Erokhin, Mol. Mat. 1, 91 (1992). 455. G.B. Sukhorukov, L. A. Feigin, M. M. Montrel, and B. I. Sukhorukov, Thin Solid Films 259, 79 (1995).

LANGMUIR-BLODGETT

FILMS OF BIOLOGICAL MOLECULES

456. T. Takamura, K. Matsushita, and Y. Shimoyama, Japan. J. Appl. Phys. 35, 5831 (1996). 457. R. H. Tredgold, A. J. Vickers, A. Hoorfar, P. Hodge, and E. Khoshdel, J. Phys. D 18, 1139 (1985). 458. M. Von Frieling, H. Bradaczek, and W. S. Durfee, Thin Solid Films 159, 451 (1988). 459. B. Yang and Y. Qiao, Thin Solid Films 284-285, 377 (1996). 460. B. Yang and Y. Qiao, Thin Solid Films 330, 157 (1998). 461. J. Cha, Y. Park, K.-B. Lee, and T. Chang, Langmuir 15, 1383 (1999). 462. V.M. Kaganer, G. Brezesinski, H. M6hwald, P. B. Howes, and K. Kjaer, Phys. Rev. E 59, 2141 (1999). 463. W. MacNaughtan, K. A. Snook, E. Caspi, and N. P. Franks, Biochim. Biophys. Acta 818, 132 (1985). 464. Y. Shufang, Z. Huilin, and H. Pingsheng, J. Mater. Sci. 34, 3149 (1999). 465. P. Dutta, Cur. Opin. Solid State Mater. Sci. 2, 557 (1997). 466. R. A. Uphaus, J. Y. Fang, R. Picorel, G. Chumanov, J. Y. Wang, T. M. Cotton, and M. Seibert, Photochem. PhotobioL 65, 673 (1997). 467. M. K. Durbin, A. Malik, R. Ghaskadvi, M. C. Shih, P. Zschack, and P. Dutta, J. Phys. Chem. 98, 1753 (1994). 468. S. Arisawa, S. Hara, and R. Yamamoto, Mol. Cryst. Liq. Cryst. 227, 29 (1993). 469. B. Lin, J. B. Peng, J. B. Ketterson, P. Dutta, B. N. Thomas, S. W. Barton, and S. A. Rice, J. Chem. Phys. 90, 2393 (1989). 470. J.M. Chen, X. Q. Yang, D. Chapman, M. Nelson, T. A. Skotheim, P. D. Hale, and Y. Okamoto, Mol. Cryst. Liq. Cryst. 190, 145 (1990). 471. J. B. Peng, G. J. Foran, G. T. Barnes, M. J. Crossley, and I. R. Gentle, Langmuir 16, 607 (2000). 472. A. Asmussen and H. Riegler, J. Chem. Phys. 104, 8151 (1996). 473. A.S. Brown, A. S. Holt, P. M. Saville, and J. W. White, Austral J. Phys. 50, 391 (1997). 474. H. Franz, S. Dante, T. Wappmannsberger, W. Petry, M. de Rosa, and E Rustichelli, Thin Solid Films 327-329, 52 (1998). 475. V. Gacem, J. Speakman, A. Gibaud, T. Richardson, and N. Cowlam, Supramol. Sci. 4, 275 (1997). 476. C. Giannini, L. Tapfer, M. Sauvage-Simkin, Y. Garreau, N. Jedrecy, M. B. V6ron, R. Pinchaux, M. Burghard, and S. Roth, Thin Solid Films 288, 272 (1996). 477. C. Giannini, L. Tapfer, M. Sauvage-Simkin, Y. Garreau, N. Jedrecy, M. B. V6ron, R. Pinchaux, M. Burghard, and S. Roth, Nuovo Cimento D 19D, 411 (1997). 478. B. W. Gregory, D. Vaknin, J. D. Gray, B. M. Ocko, P. Stroeve, T. M. Cotton, and W. S. Struve, J. Phys. Chem. 101, 2006 (1997). 479. H. Kepa, L. J. Kleinwaks, N. E Berk, C. E Majkrzak, T. S. Berzina, V. I. Troitsky, R. Antolini, and L. A. Feigin, Physica B 241-243, 1 (1998). 480. A.P. Kirilyuk and V. N. Bliznyuk, Thin Solid Films 269, 90 (1995). 481. O. V. Konovalov, I. I. Samoilenko, L. A. Feigin, and B. M. Shchedrin, Crystallogr. Rep. 41,598 (1996). 482. O. V. Konovalov, L. A. Feigin, and B. M. Shchedrin, Crystallogr. Rep. 41,592 (1996). 483. O. V. Konovalov, L. A. Feigin, and B. M. Shchedrin, Crystallogr. Rep. 41,629 (1996). 484. O. V. Konovalov, L. A. Feigin, and B. M. Shchedrin, Crystallogr. Rep. 41,640 (1996). 485. O. V. Konovalov, L. A. Feigin, and B. M. Shchedrin, Crystallogr. Rep. 41,603 (1996). 486. E Leveiller, C. B6hm, D. Jacquemain, H. M6hwald, L. Leiserowitz, K. Kjaer, and J. Als-Nielsen, Langmuir 10, 819 (1994). 487. A. Momose, Y. Hirai, I. Waki, S. Imazeki, Y. Tomioka, K. Hayakawa, and M. Naito, Thin Solid Films 178, 519 (1989). 488. G. Reiter, C. Bubeck, and M. Stamm, Langmuir 8, 1881 (1992). 489. M. Schaub, K. Mathauer, S. Schwiegk, P.-A. Albouy, G. Wenz, and G. Wegner, Thin Solid Films 210/211,397 (1992). 490. A. Schmidt, K. Mathauer, G. Reiter, M. D. Foster, M. Stamm, G. Wegner, and W. Knoll, Langmuir 10, 3820 (1994). 491. J. Souto, E Penacorada, M. L. Rodriguez-Mendez, and J. Reiche, Mater Sci. Eng. C 5, 59 (1997). 492. A. Henderson and H. Ringsdorf, Langmuir 14, 5250 (1998).

551

493. T. R. Vierheller, M. D. Foster, H. Wu, A. Schmidt, W. Knoll, S. Satija, and C. E Majkrzak, Langmuir 12, 5156 (1996). 494. H.-Y. Wang, J. A. Mann, Jr., J. B. Lando, T. R. Clark, and M. E. Kenney, Langmuir 11, 4549 (1995). 495. D.G. Wiesler, L. A. Feigin, C. E Majkrzak, J. E Ankner, T. S. Berzina, and V. I. Troitsky, Thin Solid Films 266, 69 (1995). 496. S. Yu. Zaitsev, and Y. M. Lvov, Thin Solid Films 254, 257 (1995). 497. U. Englisch, E Pefiacorada, L. Brehmer, and U. Pietsch, Langmuir 15, 1833 (1999). 498. R. K. Thomas and J. Penfold, Curr. Opin. Colloid Interface Sci. 1, 23 (1996). 499. K.N. Stoev and K. Sakurai, Spectrochim. Acta B 54, 41 (1999). 500. Y.-K. See, J. Cha, T. Chang, and M. Ree, Langmuir 16, 2351 (2000). 501. D.J. Ahn and E. I. Franses, J. Phys. Chem. 96, 9952 (1992). 502. D. Blaudez, T. Buffeteau, B. Desbat, N. Escafre, and J. M. Turlet, Thin Solid Films 243, 559 (1994). 503. E Kimura, J. Umemura, and T. Takenaka, Langmuir 2, 96 (1986). 504. P.A. Chollet and J. Messier, Chem. Phys. 73, 235 (1982). 505. P.A. Chollet, Thin Solid Films 52, 343 (1978). 506. P.A. Chollet, J. Messier, and C. Rosilio, J. Chem. Phys. 64, 1042 (1976). 507. Y. Fujimoto, Y. Ozaki, and K. lriyama, J. Chem. Soc. Faraday Trans. 92, 419 (1996). 508. D. D. Popenoe, S. M. Stole, and M. D. Porter, AppL Spectrosc. 46, 79 (1992). 509. L.H. Sharpe, Proc. Chem. Soc. 461 (1961). 510. T. Takenaka, K. Nogami, and H. Gotoh, J. Colloid lnterf. Sci. 40, 409 (1972). 511. T. Takenaka, K. Nogami, H. Gotoh, and R. Gotoh, J. Colloid Interf. Sci. 35, 395 (1971). 512. T. Wiesenthal, T. R. Baekmark, and R. Merkel, Langmuir 15, 6837 (1999). 513. T.L. Marshbanks, H. K. Jugduth, W. N. Delgass, and E. I. Franses, Thin Solid Films 232, 126 (1993). 514. Y.P. Song, A. S. Dhindsa, M. R. Bryce, M. C. Petty, and J. Yarwood, Thin Solid Films 210/211,589 (1992). 515. X. Du and Y. Liang, Chem. Phys. Lett. 313, 565 (1999). 516. N. Katayama, Y. Ozaki, T. Seki, T. Tamaki, and K. Iriyama, Langmuir 1O, 1898 (1994). 517. T. Kawai, J. Umemura, and T. Takenaka, Langmuir 6, 672 (1990). 518. R. Azumi, M. Matsumoto, S. Kuroda, and M. J. Crossley, Langmuir 11, 4495 (1995). 519. V.A. Burrows, Solid State Electron. 35, 231 (1991). 520. M. A. Chesters, M. J. Cook, S. L. Gallivan, J. M. Simmons, and D. A. Slater, Thin Solid Films 210/211,538 (1992). 521. B. Desbat, L. Mao, and A. M. Ritcey, Langmuir 12, 4754 (1996). 522. J.W. Ellis and J. L. Pauley, J. Colloid Sci. 19, 755 (1964). 523. S.A. Francis and A. H. Ellison, J. Opt. Soc. Am. 49, 131 (1959). 524. T. Hasegawa, J. Umemura, and T. Takenaka, J. Phys. Chem. 97, 9009 (1993). 525. H. Hui-Litwin, L. Servant, M. J. Dignam, and M. Moskovits, Langmuir 13, 7211 (1997). 526. T. Kamata, J. Umemura, T. Takenaka, K. Takehara, K. Isomura, and H. Taniguchi, J. Mol. Struct. 240, 187 (1990). 527. L. Mao, A. M. Ritcey, and B. Desbat, Langmuir 12, 4754 (1996). 528. N. Nakahara and K. Fukuda, J. Colloid lnterf. Sci. 69, 24 (1979). 529. J. E Rabolt, E C. Bums, W. E. Schlotter, and J. D. Swalen, J. Chem. Phys. 78, 946 (1983). 530. H. Sakai and J. Umemura, Langmuir 14, 6249 (1998). 531. T. Takenaka, K. Harda, and M. Matsumoto, J. Colloid Interf. Sci. 73, 569 (1980). 532. Y. Urai, C. Ohe, and K. Itoh, Langmuir 14, 4873 (1998). 533. D.A. Myrzakozha, T. Hasegawa, J. Nashijo, T. Imae, and Y. Ozaki, Langmuir 15, 3595 (1999). 534. D.A. Myrzakozha, T. Hasegawa, J. Nashijo, T. Imae, and Y. Ozaki, Langmuir 15, 3601 (1999). 535. Ya. I. Rabinovich, D. A. Guzanas, and R.-H. Yoon, J. Colloid Interf. Sci. 155, 221 (1993).

552

EROKHIN

536. J. Yang, X.-G. Peng, Y. Zhang, H. Wang, and T.-S. Li, J. Phys. Chem. 97, 4484 (1993). 537. J. Buijs, W. Norde, and J. W. T. Lichtenbelt, Langmuir 12, 1605 (1996). 538. H. Ancelin, D. G. Zhu, M. C. Petty, and J. Yarwood, Langmuir 6, 1068 (1990). 539. M. M6thot, F. Boucher, C. Salesse, M. Subirade, and M. P6zolet, Thin Solid Films 284-285,627 (1996). 540. I. M. Pepe, M. K. Ram, S. Paddeu, and C. Nicolini, Thin Solid Films 327-329, 118 (1998). 541. E. Bramanti, E. Benedetti, C. Nicolini, T. Berzina, V. Erokhin, A. D'Alessio, and E. Benedetti, Biopolymers 42, 227-237 (1997). 542. Y. Tian, X. Xu, Y. Zhao, X. Tang, T. Li, J. Sun, C. Li, and A. Pan, Thin Solid Films 284-285,603 (1996). 543. J. Umemura, S. Takeda, T. Hasegawa, and T.Takenaka, J. Mol. Struct. 297, 57 (1993). 544. T. Hasegawa, T. Kamata, J. Umemura, and T. Takenaka, Chem. Lett. 1543 (1990). 545. E Hoffmann, H. Huhnerfuss, and K.J. Stine, Langmuir 14, 4525 (1998). 546. Y. Wang, K. Nichogi, K. Iriyama, and Y. Ozaki, J. Phys. Chem. 100, 17232 (1996). 547. Z. Zhang, A. L. Verma, K. Nakashima, M. Yoneyama, K. Iriyama, and Y. Ozaki, Thin Solid Films 326, 211 (1998). 548. Y. Sakata, K. Domen, and T. Onishi, Langmuir 10, 2847 (1994). 549. T. Hasegawa, J. Nishijo, Y. Kobayashi, and J. Umemura, Bull. Chem. Soc. Jpn. 70, 525 (1997). 550. N. Katayama, Y. Fujimoto, Y. Ozaki, T. Araki, and K. Iriyama, Langmuir 8, 2758 (1992). 551. J.L. Dote and R. L. Mowery, J. Phys. Chem. 92, 1571 (1988). 552. E Yano, V. A. Burrows, M. N. Kozicki, and J. Ryan, J. Vac. Sci. Technol. A11,219 (1993). 553. B. I. Sukhorukov, M. M. Montrel', G. B. Sukhorukov, and L. I. Shabarchina, Biophysics 39, 273 (1994). 554. N. Katayama, Y. Ozaki, T. Araki, and K. Iriyama J. Mol. Struct. 242, 27 (1991). 555. T. Hasegawa, J. Umemura, and T. Takenaka, Thin Solid Films 210/211, 583 (1992). 556. T. Kamata, A. Kato, J. Umemura, and T. Takenaka, Langmuir 3, 1150 (1987). 557. T.L. Marshbanks, D. J. Ahn, and E. I. Franses, Langmuir 10, 276 (1994). 558. E. Okamura, J. Umemura, and T. Takenaka, Biochim. Biophys. Acta 812, 139 (1985). 559. P. Wenzl, M. Fringeli, J. Goette, and U. P. Fringeli, Langmuir 10, 4253 (1994). 560. D. J. Ahn, P. Sutandar, and E. I. Franses, Macromolecules 27, 7316 (1994). 561. T.I. Lotta, L. J. Laakkonen, J. A. Virtanen, and P. K. J. Kinnunen, Chem. Phys. Lipids 46, 1 (1988). 562. T. Hasegawa, J. Umemura, and T. Takenaka, Appl. Spectrosc. 47, 379 (1993). 563. T. Kamata, J. Umemura, and T. Takenaka, Bull. Inst. Chem. Res. Kyoto Univ. 65, 170 (1987). 564. T. Kamata, J. Umemura, and T. Takenaka, Bull, Inst. Chem. Res. Kyoto Univ. 65, 179 (1987). 565. E Kopp, U. P. Fringeli, K. MiJhlethaler, and H. H. Gtithard, Z. Naturforsch. 30c, 711 (1975). 566. G.Z. Sauerbrey, Z. Phys. 178, 457 (1964). 567. P. Facci, V. Erokhin, and C. Nicolini, Thin Solid Films 230, 86 (1993). 568. C. M. Hanley, J. A. Quinn, and T. K. Vanderlick, Langmuir 10, 1524 (1994). 569. K. Ariga and Y. Okahata, Langmuir 10, 2272 (1994). 570. K. Ariga and Y. Okahata, Langmuir 10, 3255 (1994). 571. Y. Ebara, K. Itakura, and Y. Okahata, Langmuir 12, 5165 (1996). 572. Z. Lin, R. M. Hill, H. T. Davis, and M. D. Ward, Langmuir 10, 4060 (1994). 573. Y. Okahata and K. Ariga, J. Chem. Soc. Chem. Commun. 1535 (1987). 574. Y. Ebara, H. Ebato, K. Ariga, and Y. Okahata, Langmuir 10, 2267 (1994).

575. S. J. Roser and M. R. Lovell, J. Chem. Soc. Faraday Trans. 91, 1783 (1995). 576. T. Hasegawa, J. Nishijo, and J. Umemura, J. Phys. Chem. B 102, 8498 (1998). 577. H. J. Kim, S. Kwak, Y. S. Kim, B. I. Seo, E. R. Kim, and H. Lee, Thin Solid Films 327-329, 191 (1998). 578. Y. Okahata, X. Ye, A. Shimuzi, and H. Ebato, Thin Solid Films 180, 51 (1989). 579. I. Vikholm, W. M. Albers, H. V~ilim~d, and H. Helle, Thin Solid Films 327-329, 643 (1998). 580. D. N. Furlong, R. S. Urquhart, H. Mansur, E Grieser, K. Tanaka, and Y. Okahata, Langmuir 10, 899 (1994). 581. P. Facci, V. Erokhin, A. Tronin, and C. Nicolini, J. Phys. Chem. 98, 13323 (1994). 582. D. Johannsmann, E Embs, C. G. Willson, G. Wegner, and W. Knoll, Makromol. Chem. Macromol. Symp. 46, 247 (1991). 583. E J. B. Kremer, H. Ringsdorf, A. Schuster, M. Seitz, and R. Weberskirch, Thin Solid Films 284--285,436 (1996). 584. Y. Okahata, K. Kimura, and K. Ariga, J. Amer. Chem. Soc. 111, 9190 (1989). 585. Z.-K. Chen, S.-C. Ng, S. E Y. Li, L. Zhong, L. Xu, and H. S. O. Chan, Synt. Met. 87, 201 (1997). 586. M. Furuki and L. S. Pu, Thin Solid Films 210/211,471 (1992). 587. J.-D. Kim, S.-R. Kim, K. H. Choi, and Y. H. Chang, Sensors Actuators B: Chem. 40, 39 (1997). 588. S.-R. Kim, S.-A. Choi, J.-D. Kim, K. J. Kim, C. Lee, and S. B. Rhee, Synth. Met. 71, 2027 (1995). 589. K. Matsuura, Y. Ebara, and Y. Okahata, Langmuir 13, 814 (1997). 590. S.C. Ng, X. C. Zhou, Z. K. Chen, P. Miao, H. S. O. Chan, S. E Y. Li, and P. Fu, Langmuir 14, 1748 (1998). 591. Y. Okahata, K. Matsuura, and Y. Ebara, Supramol. Sci. 3, 165 (1996). 592. S. Zhang, Z. K. Chen, G. W. Bao, and S. E Y. Li, Talanta 45,727 (1998). 593. T. Dubrovsky, V. Erokhin, and R. Kayushina, Biol. Mem. 6(1), 130 (1992). 594. V. Erokhin, R. Kayushina, and P. Gorkin, Biochemistry 45, 1049 (1990). 595. V. Erokhin, R. Kayushina, P. Gorkin, I. Kurochkin, B. Popov, and S. Chernov, J. Anal. Chem. 45, 1446 (1990) (in Russian). 596. C. Nicolini, M. Adami, T. Dubrovsky, V. Erokhin, P. Facci, P. Paschkevitch, and M. Sartore, Sensors Actuators B. Chem. 24-25, 121 (1995). 597. E Patolsky, M. Zayats, E. Katz, and I. Willner, Anal. Chem. 71, 3171 (1999). 598. C. Nicolini, V. Erokhin, P. Facci, S. Guerzoni, A. Rossi, and P. Paschkevitsch, Biosensors Bioelectron. 12, 613 (1997). 599. C. G. P. Feachem and L. Tronstad, Proc. Roy. Soc. London Ser. A 145, 127 (1934). 600. A. Tronin and V. Shapovalov, Thin Solid Films 313-314, 786 (1998). 601. A. Yu. Tronin and A. E Konstantinova, Phys. Chem. Mech. Surf. 8, 722 (1993). 602. J.P. Cresswell, Langmuir 10, 3727 (1994). 603. D. den Engelsen and B. de Koning, J. Chem. Soc. Faraday Trans. 1 70, 2100(1974). 604. D. den Engelsen, J. Phys. Chem. 76, 3390 (1972). 605. D. den Engelson and B. de Koning, J. Chem. Soc. Faraday Trans. 70, 1603 (1974). 606. M.J. Dignam, M. Moskovits, and R. W. Stobie, Trans. Faraday Soc. 67, 3306 (1971). 607. E.P. Honig and B. R. de Koning, Surf. Sci. 56, 454 (1976). 608. H. Knobloch, E Penacorada, and L. Brehmer, Thin Solid Films 295, 210 (1997). 609. W. Knoll, J. Rabe, M. R. Philpott, and J. D. Swalen, Thin Solid Films 99, 173 (1983). 610. V.N. Kruchinin, S. M. Repinsky, L. L. Sveshnikova, E. M. Auvinen, I. N. Domnin, and N. P. Sysoeva, Phys. Chem. Mech. Surf. 7, 2899 (1992). 611. H. Motschmann, R. Reiter, R. Lawall, G. Duda, M. Stamm, G. Wegner, and W. Knoll, Langmuir 7, 2743 (1991). 612. M. Paudler, J. Ruths, and H. Riegler, Langmuir 8, 184 (1992). 613. T. Smith, J. Colloid Interf. Sci. 26, 509 (1968).

LANGMUIR-BLODGETT 614. 615. 616. 617. 618. 619. 620. 621. 622. 623. 624. 625. 626. 627. 628. 629. 630. 631. 632. 633. 634. 635. 636. 637. 638. 639.

640. 641. 642. 643. 644. 645. 646. 647. 648. 649. 650. 651.

FILMS OF BIOLOGICAL

T. Smith, J. Opt. Soc. Am. 58, 1069 (1968). R. Steiger, Hevl. Chim. Acta 54, 2645 (1971). M.S. Tomar and V. K. Srivastava, Thin Solid Films 12, $29 (1972). J. G. Petrov, T. Pfohl, and H. M6hwald, J. Phys. Chem. B 103, 3417 (1999). D. den Engelsen, J. Opt. Soc. Am. 61, 1460 (1971). B. Lecourt, D. Blaudez, and J. M. Turlet, Thin Solid Films 313-314, 791 (1998). M.S. Tomar and V. K. Srivastava, Thin Solid Films 15, 207 (1973). D. den Engelsen and B. de Koning, J. Chem. Soc. Faraday Trans. 1 70, 1603 (1974). D. Ducharme, C. Salesse, and R. M. Leblanc, Thin Solid Films 132, 83 (1985). D. Ducharme, J.-J. Max, C. Salesse, and R. Leblanc, J. Phys. Chem. 94, 1925 (1990). L. Gambut, J.-P. Chauvet, C. Garcia, B. Berge, A. Renault, S. Rivi~re, J. Meunier, and A. Collet, Langmuir 12, 5407 (1996). S.R. Goates, D. A. Schofield, and C. D. Bain, Langmuir 15, 1400 (1999). M.W. Kim, B. B. Sauer, H. Yu, M. Yazdanian, and G. Zografi, Langmuir 6, 236 (1990). S.W.H. Eijt, M. M. Wittebrood, M. A. C. Devillers, and T. Rasing, Langmuir 10, 4498 (1994). M. Harke, M. Stelzle, and H. R. Motschmann, Thin Solid Films 284-285, 412 (1996). R. Reiter, H. Motschmann, H. Orendi, A. Nemetz, and W. Knoll, Langmuir 8, 1784 (1992). F. Kajzar, J. Messier, J. Zyss, and I. Leboux, Opt. Commun. 45, 133 (1983). R.D. Mattuck, J. Opt. Soc. Am. 46, 782 (1956). R.D. Mattuck, J. Opt. Soc. Am. 46, 621 (1956). G.D. Scott, T. A. McLauchlan, and R. S. Sennet, J. Appl. Phys. 21,843 (1950). V.K. Srivastava and A. R. Verma, Proc. Phys. Soc. 80, 222 (1962). S. Tolansky, "Multiple-Beam Interferometry of Surfaces and Films." Clarendon Press, London, 1948. G. Gauglitz, A. Brecht, G. Kraus, and W. Nahm, Sensors Actuators B 11, 21 (1993). H. Shiku, J. R. Krogmeier, and R. C. Dunn, Langmuir 15, 2162 (1999). G.J. Ashwell, G. M. S. Wong, D. G. Bucknall, G. S. Bahra, and C. R. Brown, Langmuir 13, 1629 (1997). H.D. Bijsterbosch, V. O. de Haan, A. W. de Graaf, M. Mellema, E A. M. Leermakers, M. A. Cohen Stuart, and A. A. van Well, Langmuir 11, 4467 (1995). A. Eaglesham, T. M. Herrington, and J. Penfold, Colloids Surf. 65, 9 (1992). S. K. Gissing, B. R. Rochford, and R. W. Richards, Colloids Surf. A 86, 171 (1994). J.A. Henderson, R. W. Richards, J. Penfold, and R. K. Thomas, Macromolecules 26, 65 (1993). J. A. Henderson, R. W. Richards, J. Penfold, and R. K. Thomas, Acta Polymer. 44, 184 (1993). J. A. Henderson, R. W. Richards, J. Penfold, C. Shackleton, and R. K. Thomas, Polymer 32, 3284 (1991). P. Hodge, C. R. Towns, R. K. Thomas, and C. Shackleton, Langmuir 8, 585 (1992). M.E. Lee, R. K. Thomas, J. Penfold, and R. C. Ward, J. Phys. Chem. 93, 381 (1989). Z.X. Li, J. R. Lu, and R. K. Thomas, Langmuir 13, 3681 (1997). Z.X. Li, J. R. Lu, R. K. Thomas, and J. Penfold, Progr. Colloid Polymer Sci. 98, 243 (1995). M. L6sche, M. Piepenstock, D. Vaknin, and J. Als-Nielsen, Thin Solid Films 210/211,659 (1992). J.R. Lu, E. A. Simister, R. K. Thomas, and J. Penfold, J. Phys. Condens. Matter 6, A403 (1994). J.R. Lu, E. A. Simister, R. K. Thomas, and J. Penfold, J. Phys. Chem. 97, 6024 (1993).

MOLECULES

553

652. J.R. Lu, E. M. Lee, R. K. Thomas, J. Penfold, and S. L. Flitsch, Langmuir 9, 1352 (1993). 653. J. R. Lu, M. Hromadova, E. A. Simister, R. K. Thomas, and J. Penfold, J. Phys. Chem. 98, 11519 (1994). 654. J.R. Lu, Z. X. Li, J. Smallwood, R. K. Thomas, and J. Penfold, J. Phys. Chem. 94, 8233 (1995). 655. J.R. Lu, Z. X. Li, R. K. Thomas, and J. Penfold, J. Chem. Soc. Faraday Trans. 92, 403 (1996). 656. D.J. Lyttle, J. R. Lu, T. J. Su, R. K. Thomas, and J. Penfold, Langmuir 11, 1001 (1995). 657. G. Ma, D. J. Barlow, J. R. P. Webster, J. Penfold, and M. J. Lawrence, J. Pharm. Pharmacol. 47, 1071 (1995). 658. K.B. Migler and C. C. Han, Macromolecules 31,360 (1998). 659. S. K. Peace, R. M. Richards, M. R. Taylor, J. R. P. Webster, and N. Williams, Macromolecules 31, 1261 (1998). 660. J. Penfold, E. M. Lee, and R. K. Thomas, Mol. Phys. 68, 33 (1989). 661. J. Penfold, R. M. Richardson, A. Zarbakhsh, J. R. P. Webster, D. G. Bucknail, A. R. Rennie, R. A. L. Jones, T. Cosgrove, R. K. Thomas, J. S. Higgins, P. D. I. Fletcher, E. Dicknson, S. J. Roser, I. A. McLure, A. R. Hillman, R. W. Richards, E. J. Staples, A. N. Burgess, E. A. Simister, and J. W. White, J. Chem. Soc. Faraday Trans. 93, 3899 (1997). 662. I. Reynolds, R. W. Richards, and J. R. P. Webster, Macromolecules 28, 7845 (1995). 663. R.W. Richards, B. R. Rochford, and J. R. P. Webster, Faraday Discuss. 98, 263 (1994). 664. P.M. Saville, I. R. Gentle, J. W. White, J. Penfold, and J. R. P. Webster, J. Phys. Chem. 98, 5935 (1994). 665. E.A. Simister, E. M. Lee, R. K. Thomas, and J. Penfold, J. Phys. Chem. 96, 1373 (1992). 666. E. A. Simister, R. K. Thomas, J. Penfold, L. Aveyard, B. P. Binks, P. Cooper, P. D. I. Fletcher, J. Rin, and A. Sokolowski, J. Phys. Chem. 96, 1383 (1992). 667. J.R. Lu and R. K. Thomas, in "Physical Chemistry of Biological Interfaces" (A. Baszkin and W. Norde, Eds.). Marcel Dekker, New York, 1999. 668. U. Englisch, T. A. Barberka, U. Pietsch, and U. Hohne, Thin Solid Films 266 (1995). 669. R.R. Highfield, R. K. Thomas, P. G. Gummins, D. P. Gregory, J. Mingins, J. B. Hayter, and O. Sch~xpf, Thin Solid Films 99, 165 (1983). 670. H. Kepa, L. J. Kleinwaks, N. E Berk, C. E Majkrzak, T. S. Berzina, V. I. Troitsky, R. Antolini, and L. A. Feigin, Physica B 241-243, 1 (1998). 671. R.M. Nicklow, M. Pomerantz, and A. Segmtiller, Phys. Rev. B 23, 1081 (1981). 672. R. Stommer, U. Englisch, U. Pietsch, and V. Holy, Physica B 221,284 (1996). 673. J. R. Lu, E. A. Simister, E. M. Lee, R. K. Thomas, A. R. Rennie, and J. Penfold, Langmuir 8, 1837 (1992). 674. C. Naumann, T. Brumm, A. R. Rennie, J. Penfold, and T. M. Bayeri, Langmuir 11, 3948 (1995). 675. P.J. Atkinson, E. Dickinson, D. S. Home, and R. M. Richardson, J. Chem. Soc. Faraday Trans. 91, 2847 (1995). 676. P. J. Atkinson, E. Dickinson, D. S. Home, and R. M. Richardson, Am. Chem. Soc. Symp. Ser. 602, 311 (1995). 677. S. Petrash, A. Liebmann-Vinson, M. D. Foster, L. M. Lander, and W. J. Brittain, Biotechnol. Prog. 13, 635 (1997). 678. A. Schmidt, J. Spinke, T. Bayerl, E. Sackmann, and W. Knoll, Biophys. J. 63, 1185 (1992). 679. A. Eaglesham and T. M. Herrington, J. Colloid Interface Sci. 171, 1 (1995). 680. J.D. Hines, G. Fragneto, R. K. Thomas, P. R. Garrett, G. K. Rennie, and A. R. Rennie, J. Colloid Interface Sci. 189, 259 (1997). 681. L.T. Lee, E. K. Mann, O. Guiselin, D. Langevin, B. Farnoux, and J. Penfold, Macromolecules 26, 7046 (1993). 682. J. R. Lu, J. A. K. Blondel, D. J. Cooke, R. K. Thomas, and J. Penfold, Progr. Colloid Polym. Sci. 100, 311 (1996). 683. J. R. Lu, R. K. Thomas, B. P. Binks, P. D. I. Fletcher, and J. Penfold, J. Phys. Chem. 99, 4113 (1995).

554

EROKHIN

684. J. R. Lu, R. K. Thomas, R. Aveyard, B. P. Binks, P. Cooper, P. D. I. Fletcher, A. Sokolowski, and J. Penfold, J. Phys. Chem. 96, 10971 (1992). 685. J. Penfold, E. Staples, L. Thompson, and I. Tucker, Colloids Surf. A: Physicochem. Eng. Aspects 102, 127 (1995). 686. J.Y. Wang, D. Vaknin, R. A. Uphaus, K. Kjaer, and M. L6sche, Thin Solid Films 242, 40 (1994). 687. P.C. Griffiths, M. L. Whatton, R. J. Abbott, W. Kwan, A. R. Pitt, A. M. Howe, S. M. King, and R. K. Heenan, J. Colloid Interf. Sci. 215, 114 (1999). 688. U. Englisch, S. Katholy, E Pefiacorada, J. Reiche, and U. Pietsch, Mater. Sci. Eng. C 8-9, 99 (1999). 689. L. Feigin, O. Konovalov, D. G. Wiesler, C. E Majkrzak, T. Berzina, and V. Troitsky, Physica B 221, 185 (1996). 690. D.G. Wiesler, L. A. Feigin, C. E Majkrzak, J. E Ankner, T. S. Berzina, and V. I. Troitsky, Thin Solid Films 266, 69 (1995). 691. A. Bolm, U. Englisch, E Penacorada, M. Gerstenberg, and U. Pietsch, Supramol. Sci. 4, 229 (1997). 692. C. Nicolini, V. Erokhin, S. Paddeu, and M. Sart6re, Nanotechnology 9, 223 (1998). 693. A.V. Maximychev, A. S. Kholmansky, E. V. Levin, N. G. Rambidi, S. K. Chamorovsky, A. A. Kononenko, V. Erokhin, and L. N. Checulaeva, Adv. Mater Opt. Electron. 1, 105 (1992). 694. A. V. Maximychev, S. K. Chamorovsky, A. S. Kholmanskii, V. V. Erokhin, E. V. Levin, L. N. Chekulaeva, A. A. Kononenko, and N. G. Rambidi, Biol. Mernbr. 8, 15 (1996). 695. B. E Li, Y. C. Song, J. R. Li, J. A. Tang, and L. Jiang, Colloids Surf. B: Biointerf. 3, 317 (1995). 696. H. Lavoie and C. Saiesse, Mater. Sci. Eng. C 10, 147 (1999). 697. A. Shibata, J. Kohara, S. Ueno, I. Uchida, T. Mashimo, and T. Yamashita, Thin Solid Films 244, 736 (1994). 698. D.M. Tiede, Biochim. Biophys. Acta 811,357 (1985). 699. T. Miyasaka and K. Koyama, Chem. Lett. 1645 (1991). 700. S.B. Hwang, J. I. Korenbrot, and W. Stoeckenius, J. Membr. Biol. 36, 115 (1977). 701. G. Dencher and M. Ltische, J. Mol. Biol. 287, 837 (1999). 702. Y. Sugiyama, T. Inoue, M. Ikematsu, M. Iseki, and T. Sekiguchi, Thin Solid Films 310, 102 (1997). 703. V. Erokhin, R. Kayushina, Yu. Lvov, N. Zakharova, A. Kononenko, P. Knox, and A. Rubin, Dokl. Akad. Nauk SSSR 299, 1262 (1988). 704. J. Y. Fang, D. E Gaul, G. Chumanov, and T. M. Cotton, Langmuir 11, 4366 (1995). 705. P. Facci, V. Erokhin, S. Paddeu, and C. Nicolini, Langmuir 14, 193 (1998). 706. Y. Yasuda, H. Sugino, H. Toyotama, Y. Hirata, M. Hara, and J. Miyake, Bioelectrochem. Bioenerget. 34, 135 (1994). 707. Y. Hiram and J. Miyake, Thin Solid Films 244, 865 (1994). 708. Y. Yasuda, H. Toyotama, M. Hara, and J. Miyake, Thin Solid Films 327329, 800 (1998). 709. V. Erokhin, J. Sabo, N. Zakharova, R. Kayushina, A. Kononenko, Yu. Lvov, E. Lukashev, and P. Knox, Biol. Membr. 2(6), 1125 (1989). 710. V. Erokhin, R. Kayushina, A. Dembo, J. Sabo, P. Knox, and A. Kononenko, Mol. Cryst. Liq. Cryst. 221, 1 (1992). 711. M. Ahlers, W. Mtiller, A. Reichert, H. Ringsdorf, and J. Venzmer, Angew. Chem. Int. Ed. Engl. 29, 1269 (1990). 712. H. Mohwald, Annu. Rev. Phys. Chem. 41, 44 1 (1990). 713. R. Verger and E Pattus, Chem. Phys. Lipids 30, 189 (1982). 714. H. Brockman, Curr. Opin. Struct. Biol. 9, 438 (1999). 715. G. Colacicco, J. Colloid Interf. Sci. 29, 345 (1969). 716. M. Saint-Pierre-Chazalet, C. Fressign6, E Billoudet, and M. P. Pileni, Thin Solid Films 210/211,743 (1992). 717. R. Blankenburg, P. Meller, H. Ringsdorf, and C. Salesse, Biochemistry 28, 8214 (1989). 718. L. A. Samuelson, Y. Yang, K. A. Marx, J. Kumar, S. K. Tripathy, and D. L. Kaplan, Biomimetics 1, 51 (1992). 719. S. A. Darst, M. Ahlers, P. H. Meller, E. W. Kubalek, R. Blankenburg, H. O. Ribi, H. Ringsdorf, and R. D. Kornberg, Biophys. J. 59, 387 (1991).

720. Z. Liu, H. Qin, C. Xiao, S. Wang, and S. E Sui, Eur. Biophys. J. 24, 31 (1995). 721. L.A. Samuelson, P. Miller, D. M. Galotti, K. A. Marx, J. Kumar, S. K. Tripathy, and D. L. Kaplan, Langmuir 8, 604 (1992). 722. J.N. Herron, W. Muller, M. Paudler, H. Riegler, H. Ringsdorf, and P. A. Suci, Langmuir 8, 1413 (1992). 723. S. Koppenol, L. A. Klumb, V. Vogel, and P. S. Stayton, Langmuir 15, 7125 (1999). 724. V. Vogel, W. R. Schief, Jr., and W. Frey, Supramol. Sci. 4, 163 (1997). 725. L. Samuelson, P. Miller, D. Gaiotti, K. A. Marx, J. Kumar, S. Tripathy, and D. Kaplan, Thin Solid Films 210/211,796 (1992). 726. L.A. Samuelson, D. L. Kaplan, J. O. Lim, M. Kamath, K. A. Marx, and S. K. Tripathy, Thin Solid Films 242, 50 (1994). 727. K.A. Marx, L. A. Samuelson, M. Kamath, S. Sengupta, D. Kaplan, J. Kumar, and S. K. Tripathy, in "Molecular and Biomolecular Electronics" (R. R. Birge, Ed.), Vol. 240, Chap. 15. American Chemical Society, 1994. 728. J.M. Pachence, S. M. Amador, G. Maniara, J. Vanderkooi, P. L. Dutton, and J. K. Blasie, Biophys. J. 58, 379 (1990). 729. P.L. Edmiston and S. S. Saavedra, Biophys. J. 74, 999 (1998). 730. J. Peschke and H. M6hwald, Colloids Surf. 27, 305 (1987). 731. S. Boussaad, L. Dziri, R. Arechabaleta, N. J. Tao, and R. M. Leblanc, Langmuir 14, 6215 (1998). 732. P. Fromhertz, Biochim. Biophys. Acta 225,382 (1971). 733. P. Fromhertz and D. Marcheva, FEBS Lett. 49, 329 (1975). 734. V. I. Troitsky, M. Sartore, T. S. Berzina, D. Nardelli, and C. Nicolini, Rev. Sci. Instrum. 67, 4216 (1996). 735. E.E. Uzgiris, Biochem. Biophys. Res. Commun. 134, 819 (1986). 736. E.E. Uzgiris, Biochem. J. 242, 293 (1987). 737. M. Egger, S. P. Heyn, and H. E. Gaub, Biophys. J 57, 669 (1990). 738. L. Lebeau, S. Olland, P. Oudet, and C. Mioskowski, Chem. Phys. Lipids 62, 93 (1992). 739. N. Dubreuil, S. Alexandre, D. Lair, E Sommer, T. Duc, and J. Valleton, Colloids Surf. B: Biointerf. 11, 95 (1998). 740. L. Lebeau, E. Regnier, P. Schultz, J. C. Wang, C. Mioskowski, and P. Oudet, FEBS Lett. 267, 38 (1990). 741. M. A. Requero, M. Gonzalez, E M. Goni, A. Alonso, and G. Fidelio, FEBS Lett. 357, 75 (1995). 742. E.E. Uzgiris, J. Cell. Biochem. 29, 239 (1985). 743. A. Brisson, W. Bergsma-Schutter, E Oling, O. Lambert, and I. Reviakine, J. Cryst. Growth 196, 456 (1999). 744. R.H. Newman and P. S. Freemont, Thin Solid Films 284-285, 18 (1996). 745. R. D. Kornberg and H. O. Ribi, in "Protein Structure, Folding and Design" (D. L. Oxender and A. R. Liss, Eds.), p. 175. Plenum Press, New York, 1987. 746. K.M. Maloney, M. Grandbois, D. W. Grainger, C. Salesse, K. A. Lewis, and M. E Roberts, Biochim. Biophys. Acta Biomemb. 1235, 395 (1995). 747. J.P. Slotte, Biochim. Biophys. Acta Lipids Lipid Metab. 1259, 180 (1995). 748. G. Zografi, R. Verger, and G. H. de Haas, Chem. Phys. Lipids 7, 185 (1971). 749. D. M. Goodman, E. M. Nemoto, R. W. Evans, and P. M. Winter, Chem. Phys. Lipids 84, 57 (1996). 750. I. Arimoto, M. Fujita, H. Saito, T. Handa, and K. Miyajima, Colloid Polymer Sci. 275, 60 (1997). 751. T.Z. Ivanova, I. Panaiotov, E Boury, J. E. Proust, and R. Verger, Colloid Polymer Sci. 275,449 (1997). 752. V. Raneva, T. Ivanova, R. Verger, and I. Panaiotov, Colloids Surf. B: Biointerf. 3,357 (1995). 753. A. Alsina, O. Vails, G. Pi6roni, R. Verger, and S. Garcia, Colloid Polymer Sci. 261,923 (1983). 754. G. Pi6roni and R. Verger, Eur. J. Biochem. 132, 639 (1983). 755. T.O. Wieloch, B. Borgstr6m, G. Pi6roni, E Pattus, and R. Verger, FEBS Lett. 128, 217 (1981). 756. G. Pi6roni and R. Verger, J. Biol. Chem. 254, 10090 (1979). 757. T. Wieloch, B. Borgstr6m, G. Pi6roni, E Pattus, and R. Verger, J. Biol. Chem. 257, 11523 (1982). 758. A. Verger, J. Biol. Chem. 258, 5477 (1983).

LANGMUIR-BLODGETT

FILMS OF BIOLOGICAL MOLECULES

759. C. Souvignet, J. M. Pelosin, S. Daniel, E. M. Chambaz, S. Ransac, and R. Verger, J. BioL Chem. 266, 40 (1991). 760. S. Yokoyama and E J. Kezdu, J. Biol. Chem. 266, 4303 (1991). 761. M. Grandbois, B. Desbat, D. Blaudez, and C. Salesse, Langmuir 15, 6594 (1999). 762. M. Grandbois, J. Dufourcq, and C. Salesse, Thin Solid Films 284-285, 743 (1996). 763. M.C.E. van Dam-Mierac, A. J. Slotboom, H. M. Verheij, R. Verger, and G. H. de Haas, in "Structure of Biological Membranes" (S. Abrahmsson and I. Pascher, Eds.), p. 177. Plenum Press, New York, 1977. 764. S. Taneva, T. McEachren, J. Stewart, and K. M. W. Keough, Biochemistry 34, 10279 (1995). 765. M.C. Phillips, H. Hauser, R. B. Leslie, and D. Oldani, Biochim. Biophys. Acta 406, 402 (1975). 766. W.M. Heckl, M. L/Ssche, H. Scheer, and H. M/Shwald, Biochim. Biophys. Acta 810, 73 (1985). 767. W.M. Heckl, B. N. Zaba, and M. H. Mohwald, Biochim. Biophys. Acta 903, 166 (1987). 768. S. G. Taneva and K. M. W. Keough, Biochim. Biophys. Acta Biomembr. 1236, 185 (1995). 769. P. Kernen, W. I. Gruszecki, M. Matuta, P. Wagner, U. Ziegler, and Z. Krupa, Biochim. Biophys. Acta Biomembr. 1373, 289 (1998). 770. C.R. Flach, A. Gericke, K. M. W. Keough, and R. Mendelsohn, Biochim. Biophys. Acta Biomembr. 1416, 11 (1999). 771. J. P6rez-Gil, K. Nag, S. Taneva, and K. M. W. Keough, Biophys. J. 63, 197 (1992). 772. K. Y. C. Lee, M. M. Lipp, J. A. Zasadzinski, and A. J. Waring, Biophys. J. 72, 368 (1997). 773. K. Nag, S. Taneva, J. P6rez-Gil, A. Cruz, and K. M. W. Keough, Biophys. J. 72, 2638 (1997). 774. M. L. E Ruano, K. Nag, L.-A. Worthman, C. Casals, J. P6rez-Gil, and K. M. W. Keough, Biophys. J. 74, 1101 (1998). 775. K. Y. C. Lee, M. M. Lipp, J. A. Zasadzinski, and A. J. Waring, Colloids Surf. A 128, 225 (1997). 776. R.B. Weinberg, J. A. Ibdah, and M. C. Phillips, J. Biol. Chem. 267, 8977 (1992). 777. A. Chfivez, M. Pujol, I. Haro, M. A. Alsina, and Y. Cajal, Langmuir 15, 1101 (1999). 778. M. M. Lipp, K. Y. C. Lee, J. A. Zasadzinski, and A. J. Waring, Science 273, 1196 (1996). 779. E. Ladanyi, I. R. Miller, D. M6bius, R. Popovits-Biro, Y. Marikovsky, P. von Wichert, B. Mtiller, and K. Stalder, Thin Solid Films 180, 15 (1989). 780. B. Lu, Y. Bai, and Y. Wei, Thin Solid Films 240, 138 (1994). 781. X. Caide, Z. Liu, Q. Gao, Q. Zhou, and S. Sui, Thin Solid Films 284-285, 793 (1996). 782. R. Maget-Dana, Ch. Hetru, and M. Ptak, Thin Solid Films 284-285, 841 (1996). 783. E.E. Uzgiris, Biochem. J. 272, 45 (1990). 784. M.M. Timbs, C. L. Poglitsch, M. L. Pisarchick, M. T. Sumner, and N. L. Thompson, Biochim. Biophys. Acta 1064, 219 (1991). 785. S. Tanimoto and H. Kitano, Colloids Surf B: Biointerf. 4, 259 (1995). 786. B. Fischer, S. P. Heyn, M. Egger, and H. Gaub, Langmuir 9, 136 (1993). 787. I. Vikholm, E. Gy/Srvary, and G. Peltonen, Langmuir 12, 3276 (1996). 788. M. Piepenstock and M. L6sche, Thin Solid Films 210/211,793 (1992). 789. V. Erokhin, S. Vakula, and C. Nicolini, Progr. Colloid Polymer Sci. 93, 229 (1993). 790. V. Erokhin, S. Vakula, and C. Nicolini, Thin Solid Films 238, 88 (1994). 791. L. V. Belovolova, T. V. Konforkina, V. V. Savransky, H. Lemmetyinen, and E. Vuorimaa, Mol. Mater 6, 189 (1996). 792. S. Wang and S. Sui, Acta Biophys. Sinica 8, 148 (1992). 793. I. Vikholm, J. Peltonen, and O. Teleman, Biochim. Biophys. Acta Biomembr. 1233, 111 (1995). 794. K. Nag, J. Perez-Gil, A. Cruz, N. H. Rich, and K. M. W. Keough, Biophys. J. 71, 1356 (1996). 795. V. Marchi-Artzner, J.-M. Lehn, and T. Kunitake, Langmuir 14, 6470 (1998).

555

796. L. Marron-Brignone, R. M. Mor61is, J.-E Chauvet, and E R. Coulet, Langmuir 16, 498 (2000). 797. S. Sui and S. Wang, Thin Solid Films 210/211, 57 (1992). 798. E. Kalb and L. K. Tamm, Thin Solid Films 210/211,763 (1992). 799. V.S. Kulkarni and R. E. Brown, Thin Solid Films 244, 869 (1994). 800. V. Erokhin, S. Carrara, S. Guerzoni, P. Ghisellini, and C. Nicolini, Thin Solid Films 327-329, 636 (1998). 801. P. Facci, V. Erokhin, and C. Nicolini, Thin Solid Films 243,403 (1994). 802. G. Alegria and P. L. Dutton, Biochim. Biophys. Acta 1057, 239 (1991). 803. G. Alegria and P. L. Dutton, Biochim. Biophys. Acta 1057, 258 (1991). 804. C. C. Moser, R. J. Sension, A. Z. Szarka, S. T. Repinec, R. M. Hochstrasser, and P. L. Dutton, Chem. Phys. 197, 343 (1995). 805. K. Iida, A. Kashiwada, and M. Nango, Colloids Surf. A 169, 199 (2000). 806. Y. Yasuda, M. Hara, J. Miyake, and H. Toyotama, Japan. J. Appl. Phys. Lett. 36, L557 (1997). 807. J. Goc, M. Hara, T. Tateishi, J. Miyake, A. Planner, and D. Frackowiak, J. Photochem. Photobiol. A 104, 123 (1997). 808. J. Miyake, T. Majima, K. Namba, M. Hara, Y. Asada, H. Sugino, S. Ajiki, and H. Toyotama, Mater. Sci. Eng. C1, 63 (1994). 809. T. Ueno, J. Miyake, T. Fuju, M. Shirai, T. Arai, Y. Yasuda, and M. Hara, Supramol. Sci. 5, 783 (1998). 810. M. Fujihira, M. Sakomura, and T. Kamei, Thin Solid Films 180, 43 (1989). 811. Y. Yasuda, Y. Hiram, H. Sugino, M. Kumei, M. Hara, J. Miyake, and M. Fujihira, Thin Solid Films 210/211,733 (1992). 812. Y. Yasuda, Y. Kawakami, and H. Toyotama, Thin Solid Films 292, 189 (1997). 813. M. Ikonen, A. Sharonov, N. Tkachenko, and H. Lemmetyinen, Adv. Mater Opt. Electron. 2, 115 (1993). 814. M. Ikonen, A. Sharonov, N. Tkachenko, and H. Lemmetyinen, Adv. Mater Opt. Electron. 2, 211 (1993). 815. J. P. Wang, J. R. Li, P. D. Tao, X. C. Li, and L. Jiang, Adv. Mater. Opt. Electron. 4, 219 (1994). 816. H. H. Weetall, A. B. Druzhko, L. A. Samuelson, A. R. de Lera, and R. Alvarez, Bioelectrochem. Bioenerget. 44, 37 (1997). 817. A. A. Kononenko, Y. P. Lukashev, D. S. Broun, S. K. Chamorovskii, B. A. Kruming, and S. A. Yakushev, Biophysics 38, 1025 (1993). 818. C. Steinem, A. Janshoff, E Hohn, M. Sieber, and H. Galla, Chem. Phys. Lipids 89, 141 (1997). 819. B.-E Li, J.-R. Li, Y.-C. Song, and L. Jiang, Mater. Sci. Eng. 3,219 (1995). 820. E T. Hong, Mater Sci. Eng. C 4, 267 (1997). 821. E.P. Lukashev, S. Yu. Zaitsev, A. A. Kononenko, and V. P. Zubov, Stud. Biophys. 132, 111 (1989). 822. T. Miyasaka and K. Koyama, Thin Solid Films 210/211, 146 (1992). 823. J.R. Li, J. P. Wang, T. E Chen, L. Jiang, K. S. Hu, A. J. Wang, and M. Q. Tan, Thin Solid Films 210/211,760 (1992). 824. H.H. Weetall and L. A. Samuelson, Thin Solid Films 312, 314 (1998). 825. J. Min, H.-G. Choi, J.-W. Choi, W. H. Lee, and U. R. Kim, Thin Solid Films 327-329, 698 (1998). 826. L. Yuan, B. Li, and L. Jiang, Thin Solid Films 340, 262 (1999). 827. H. Lemmetyinen and M. Ikonen, Trends Photochem. Photobiol. Res. Trends 3, 413 (1994). 828. H. Lemmetyinen, M. Ikonen, A. Sharanov, and N. Tkachenko, "Laser Spectroscopy of Biomolecules," Proc. SPIE 1921,209 (1993). 829. C. Nicolini, V. Erokhin, S. Paddeu, and M. Sartore, Nanotechnology 9, 223 (1998). 830. V. Volkov, Y. P. Svirko, V. F. Kamalov, L. Song, and M. A. E1-Sayed, Biophys. J. 73, 3164 (1997). 831. A. S. Alexeev, S. I. Valiansky, and V. V. Savransky, ICPAS Mater 38, 209 (1992). 832. A. V. Kir'yanov, I. A. Maslyanitsyn, V. V. Savranskii, V. D. Shigorin, and H. Lemmetyinen, Quantum Electron. 29, 85 (1999). 833. T. Miyasaka, K. Koyama, and I. Itoh, Science 255, 342 (1991). 834. Y. Okada-Shudo, I. Yamaguchi, H. Tomioka, and H. Sasabe, Synth. Met. 81,147 (1996). 835. J. Yang and G. Wang, Thin Solid Films 324, 281 (1998). 836. T.V. Dyukova and E. P. Lukashev, Thin Solid Films 283, 1 (1996).

556

EROKHIN

837. V. Erokhin, in "Thin Protein Films" (Yu. Lvov and H. M6hwald, Eds.). Marcel Dekker, New York, 1999. 838. T. Dubrovsky, A. Tronin, and C. Nicolini, Thin Solid Films 257, 130 (1995). 839. T. Dubrovsky, A. Tronin, S. Dubrovskaya, O. Guryev, and C. Nicolini, Thin Solid Films 284-285,698 (1996). 840. T. Dubrovsky, A. Tronin, S. Dubrovskaya, S. Vakula, and C. Nicolini, Sensors Actuators B: Chem. 23, 1 (1995). 841. H. Ebato, C. A. Gentry, J. N. Herron, W. Mtiller, Y. Okahata, H. Ringsdorf, and P. A. Suci, Anal. Chem. 66, 1683 (1994). 842. V. Erokhin, R. Kayushina, Yu. Lvov, and L. Feigin, Nuovo Cimento 12D, 1253 (1990). 843. I. Turko, I. Pikuleva, and V. Erokhin, Biol. Membr. 4(10), 1745 (1991). 844. Z. Lin, R. M. Hill, H. T. Davis, and M. D. Ward, Langmuir 10, 4060 (1994). 845. V. Chernov, P. Monceau, M. Saint-Paul, L. Galchenkov, S. Ivanov, and I. Pyataikin, Solid State Commun. 97, 49 (1996). 846. A. Ahluwalia, D. De Rossi, and A. Schirone, Thin Solid Films 210/211, 726 (1992). 847. A. Ahluwalia, D. De Rossi, C. Ristori, A. Schirone' and G. Serra, Biosensors Bioelectron. 7, 207 (1992). 848. A. Ahluwalia, D. De Rossi, M. Monici, and A. Schirone, Biosensors Bioelectron. 6, 133 (1991). 849. T. B. Dubrovsky, M. V. Demecheva, A. P. Savitsky, E. Yu. Mantrova, A. I. Yaropolov, V. V. Savransky, and L. V. Belovolova, Biosensors Bioelectron. 8, 377 (1993). 850. D. Izhaky and L. Addadi, Adv. Mater. 10, 1009 (1998). 851. I. Vikholm, T. Viitala, W. M. Albers, and J. Peltonen, Biochim. Biophys. Acta Biomembr. 1421, 39 (1999). 852. G.K. Chudinova, A. V. Chudinov, V. V. Savransky, and A. M. Prokhorov, Thin Solid Films 307, 294 (1997). 853. K. Owaku, M. Goto, Y. Ikariyama, and M. Aizawa, Anal. Chem. 67, 1613 (1995). 854. A. Ahluwalia, G. Giusto, and D. De Rossi, Mater. Sci. Eng. C 3, 267 (1995). 855. I.V. Turko, G. I. Lepesheva, and V. L. Chashchin, Thin Solid Films 230, 70(1993). 856. I.V. Turko, I. S. Yurkevich, and V. L. Chashchin, Thin Solid Films 205, 113 (1991). 857. I. V. Turko, I. S. Yurkevich, and V. L. Chashchin, Thin Solid Films 210/211,710 (1992). 858. G.I. Lepesheva, I. V. Turko, I. A. Ges', and V. L. Chashchin, Biokhimiya 59, 939 (1994). 859. G. I. Lepesheva, T. N. Azeva, V. N. Knyukshto, V. L. Chashchin, and S. A. Usanov, Sensors Actuators B 68, 27 (2000). 860. Y. Okawa, H. Tsuzuki, S. Yoshida, and T. Watanabe, Anal. Sci. 5, 507 (1989). 861. H. Tsuzuki, T. Watanabe, Y. Okawa, S. Yoshida, S. Yano, K. Koumoto, M. Komiyama, and Y. Nihei, Chem. Lett. 1265 (1988). 862. E Q. Tang, J. S. Yuan, and L. Jiang, Chem. Sensors 10, 26 (1990). 863. G. Dai, J. Li, and L. Jiang, Colloids Surf. B 13, 105 (1999). 864. Anicet, A. Anne, J. Moiroux, and J.-M. Saveant, J. Am. Chem. Soc. 120, 7115 (1998). 865. N. Dubreuil, S. Alexandre, C. Fiol, and J. M. Valleton, J. Colloid Interf. Sci. 181,393 (1996). 866. A. Baszkin, M. M. Boissonnade, V. Rosilio, A. Kamyshny, and S. Magdassi, J. Colloid Interf. Sci. 209, 302 (1999). 867. V. Rosilio, M.-M. Boissonnade, J. Zhang, L. Jiang, and A. Baszkin, Langmuir 13, 4669 (1997). 868. S.Y. Zaitsev, Sensors andActuators B: Chem. 24, 177 (1995). 869. A. J. Guiomar, S. D. Evans, and J. T. Guthrie, Supramol. Sci. 4, 279 (1997). 870. P. Zhu, Y. Li, L. Wang, W. Zhang, X. Ma, and Z. Zhu, Thin Film Sci. Technol. 4, 70 (1991). 871. Y. Okahata, T. Tsuruta, K. Ijiro, and K. Ariga, Thin Solid Films 180, 65 (1989).

872. C. Fiol, J.-M. Valleton, N. Delpire, G. Barbey, A. Barraud, and A. Ruaudel-Teixier, Thin Solid Films 210/211,489 (1992). 873. C. Fiol, S. Alexandre, N. Dubreuil, and J. M. Valleton, Thin Solid Films 261,287 (1995). 874. J.-r. Li, Y.-k. Du, P. Boullanger, and L. Jiang, Thin Solid Films 352, 212 (1999). 875. Skeletization. 876. L. Marron-Brignone, R. M. Morelis, and P. R. Coulet, Langmuir 12, 5674 (1996). 877. P. Pal, D. Nandi, and T. N. Misra, Thin Solid Films 239, 138 (1994). 878. E Antolini, S. Paddeu, and C. Nicolini, Langmuir 11, 2719 (1995). 879. S. Paddeu, E Antolini, T. Dubrovsky, and C. Nicolini, Thin Solid Films 268, 108 (1995). 880. S. Paddeu, V. Erokhin, and C. Nicolini, Thin Solid Films 284-285, 854 (1996). 881. E Bruno, K. A. Marx, S. K. Tripathy, J. A. Akkara, L. A. Samuelson, and D. L. Kaplan, J. Intelligent Mater. Syst. Struct. 5, 631 (1994). 882. E E Bruno, J. A. Akkara, L. A. Samuelson, D. L. Kaplan, B. K. Mandal, K. A. Marx, J. Kumar, and S. K. Tripathy, Langmuir 11,889 (1995). 883. E E Bruno, J. A. Akkara, L. A. Samuelson, D. L. Kaplan, K. A. Marx, and S. K. Tripathy, MRS Proc. 292, 147 (1993). 884. E Bruno, J. Akkara, L. A. Samuelson, B. K. Mandal, D. K. Kaplan, K. A. Marx, and S. Tripathy, Polym. Prep. (Am. Chem. Soc., Div. Polym. Chem.) 32, 232 (1991). 885. V. Erokhin, E Antolini, P. Facci, and C. Nicolini, Progr. Colloid Polymer Sci. 93, 228 (1993). 886. C. Nicolini, V. Erokhin, E Antolini, P. Catasti, and P. Facci, Biochim. Biophys. Acta 1158, 273 (1993). 887. Y. Shen, C. R. Safinya, K. S. Liang, A. E Ruppert, and K. J. Rothshild, Nature 336, 48 (1993). 888. V. Erokhin, P. Facci, A. Kononenko, G. Radicchi, and C. Nicolini, Thin Solid Films 284-285, 805 (1996). 889. V. Erokhin, P. Facci, and C. Nicolini, Biosensors Bioelectron. 10, 25 (1995). 890. E Antolini, C. Nicolini, and M. Trotta, Thin Solid Films 254, 252 (1995). 891. P. Facci, V. Erokhin, E Antolini, and C. Nicolini, Thin Solid Films 237, 19 (1994). 892. V. Erokhin, B. Popov, B. Samori, and A. Yakovlev, Mol. Cryst. Liq. Cryst. 215,213 (1992). 893. Y. Fang and J. Yang, J. Phys. Chem. 101, 441 (1997). 894. M. A. Frommer, I. R. Miller, and A. Khaiat, Adv. Exp. Med. Biol. 7, 119 (1970). 895. K. Ijiro, M. Shimomura, M. Tanaka, H. Nakamura, and K. Hasebe, Thin Solid Films 284-285,780 (1996). 896. R. Ionov, J. De Coninck, and A. Angelova, Thin Solid Films 284-285, 347 (1996). 897. M. A. Karymov, A. A. Kruchinin, A. Yu, A. Tarantov, L. A. Balova, L. A. Remisova, N. G. Sukhodolov, A. I. Yanklovich, and A. M. Yorkin, Sensors Actuators B 6, 208 (1992). 898. E Nakamura, K. Ijiro, and M. Shimomura, Thin Solid Films 327-329, 603 (1998). 899. C. Nicolini, V. Erokhin, P. Facci, S. Guerzoni, A. Rossi, and P. Paschkevitsch, Biosensors Bioelectron. 12, 613 (1997). 900. Y. Okahata and K. Tanaka, Thin Solid Films 284-285, 6 (1996). 901. Y. Okahata, T. Kobayashi, and K. Tanaka, Langmuir 12, 1326 (1996). 902. M. Shimomura, E Nakamura, K. Ijiro, H. Taketsuna, M. Tanaka, H. Nakamura, and K. Hasebe, J. Am. Chem. Soc. 119, 2341 (1997). 903. C. Xiao, M. Yang, and S. Sui, Thin Solid Films 327-329, 647 (1998). 904. R. Vijayalakshmi, A. Dhathathreyan, M. Kanthimathi, V. Subramanian, B. U. Nair, and T. Ramasami, Langmuir 15, 2898 (1999). 905. S. Huebner, E. Politsch, U. Vierl, and G. Ceve, Biochim. Biophys. Acta Biomembr. 1421, 1 (1999). 906. K. Kago, H. Matsuoka, R. Yoshitome, H. Yamaoka, K. Ijiro, and M. Shimomura, Langmuir 15, 5193 (1999). 907. M. Liu, J. Lang, and H. Nakahara, Colloids Surf. A 175, 153 (2000). 908. M. Shimomura, O. Karthaus, N. Maruyama, K. Ijiro, T. Sawadaishi, S. Tokura, and N. Nishi, Rep. Prog. Polym. Phys. Jpn. 40, 523 (1997).

LANGMUIR-BLODGETT

FILMS OF BIOLOGICAL MOLECULES

909. M. M. Montrel, A. I. Petrov, L. I. Shabarchina, B. I. Sukhorukov, and G. B. Sukhorukov, Sensors Actuators B: Chem. 42, 225 (1997). 910. G. Sukhorukov, G. Ivakin, V. Erokhin, and V. Klechkovskaya, Physica B 198, 136 (1994). 911. G. Sukhorukov, V. Erokhin, and A. Tronin, Biophysics 38, 243 (1993). 912. G. B. Sukhorukov, M. M. Montrel, A. I. Petrov, L. I. Shabarchina, and B. I. Sukhorukov, Biosensors Bioelectron. 11, 913 (1996). 913. B.M. Abraham and J. B. Ketterson, Langmuir 1,461 (1985). 914. T. Berzina, V. Troitsky, S. Vakula, A. Riccio, A. Morana, M. De Rosa, L. Gobbi, F. Rustichelli, V. Erokhin, and C. Nicolini, Mater. Sci. Eng. C 3, 33 (1995). 915. T.L. Fare, K. M. Rusin, and P. P. Bey, Jr., Powder Technol. 3, 51 (1991). 916. V. A. Howarth, M. C. Petty, G. H. Davies, and J. Yarwood, Langmuir 5, 330(1989). 917. V. A. Howarth, M. C. Petty, G. H. Davies, and J. Yarwood, Thin Solid Films 160, 483 (1988). 918. C. Nicolini, E Rustichelli, T. S. Berzina, V. I. Troitsky, V. V. Erokhin, S. Vakula, A. Riccio, A. Morana, M. De Rosa, and L. Gobbi, Mater Sci. Eng. C 3, 33 (1995).

557

919. C. Nicolini, T. S. Berzina, V. I. Troitsky, A. Riccio, S. Vakula, and M. De Rosa, Mater. Sci. Eng. C 5, 1 (1997). 920. S. Pathirana, L. J. Myers, V. Vodyanoy, and W. C. Neely, Supramol. Sci. 2, 149 (1995). 921. J.B. Peng, B. M. Abraham, P. Dutta, J. B. Ketterson, and H. E Gibbard, Langmuir 3, 104 (1987). 922. H.E. Ries, Jr., and H. S. Swift, J. Colloid Interf. Sci. 64, 111 (1978). 923. M. Shimomura, E. Shinihara, S. Kondo, N. Tajima, and K. Koshiishi, Supramol. Chem. 3, 23 (1993). 924. V. Vodyanoy, S. Pathirana, and W. C. Neely, Langmuir 10, 1354 (1994). 925. S.Y. Zaitsev, V. P. Zubov, and D. M6bius, Colloids Surf. A: Physicochem. Eng. Aspects 94, 75 (1995). 926. S. Yu. Zaitsev, V. P. Vereschetin, V. P. Zubov, W. Zeiss, and D. M6bius, Thin Solid Films 284-285,667 (1996). 927. S.M. Amador, S. D. Myers, V. Vodyanoy, and W. C. Neely, Biophys. J. 74, A371 (1998).

Chapter 11 STRUCTURE FORMATION DURING ELECTROCRYSTALLIZATION OF METAL FILMS V. M. K o z l o v

Department of Physics, National Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine L. P e r a l d o Bicelli

Dipartimento di Chimica Fisica Applicata del Politecnico, Centro di Studio sui Processi Elettrodici del CNR, Milan, 20131 Italy

Contents 1. 2. 3. 4. 5. 6.

7. 8.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of the Structural Defects in Electrodeposits . . . . . . . . . . . . . . . . . . . . . . . . . Mechanism of Formation of Structural Defects during Noncoherent Nucleation . . . . . . . . . . . . . Classical Theory of Noncoherent Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atomistic Analysis of Noncoherent Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factors Influencing the Structure of Electrodeposits (Theoretical and Experimental Results) . . . . . . 6.1. Influence of the Crystallization Overvoltage on the Structure of Electrodeposits . . . . . . . . . . 6.2. Influence of the Foreign Particle Adsorption on the Structure of Electrodeposits . . . . . . . . . . 6.3. Influence of the Nature of Metals on the Formation of the Polycrystalline Structure of the Deposit during Electrocrystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanism of Multitwinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

559 560 563 566 570 574 574 576 580 582 584 585 585

more of a present interest. A solution to this important practical problem can be found on the basis of a deep and complex investigation of a whole series of fundamental questions, those related to the structure of deposits and to the mechanism of its formation included. Indeed, by means of the structure it is possible to realize the connection between the electrodeposition conditions of metals and the properties of the obtained deposits. The need to investigate the structure of the deposits is suggested not only for practical reasons, but also for theoretical ones. As a matter of fact, the deposit structure is the end product of the crystallization process. Therefore, the experimental results of a structural research contain the information which may be utilized to deepen and to enlarge our knowledge of the details of the real crystal growth process. It may also be useful

1. INTRODUCTION Metal deposits are largely employed in microelectronics, for optical devices, in cosmic and atomic technology, in galvanotechnique, and in other fields. Their numerous practical applications are based on the possibility to deposit metal films with a favorable combination of their functional properties. In addition, there is also the possibility to prepare metal deposits with particular physical and mechanical properties which substantially differ from those of the same metals in their usual massive state. These possibilities offer the opportunity for improving the physical and technical parameters of materials and devices and for promoting new technical branches. It may well be understood that the problem to obtain metal deposits with a foreseeable set of their properties becomes even

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

559

560

KOZLOV AND PERALDO B ICELLI

to create physical models of the formation of a deposit with either a single-crystal structure or a polycrystalline structure and to elaborate the mechanism of formation of the different types of crystallographic defects in deposits. To more or less reproduce the overall mechanism of formation of the structure of the deposits, it is necessary to examine all the consecutive steps of their growth. In the case of the heterogeneous crystallization on a foreign substrate, two main growth steps of the deposits may be considered in connection with the formation of the different structural defects. They are: the initial nucleation step and the subsequent deposit growth step "in thickness." The initial crystallization step includes the formation of the nuclei on the substrate, their lateral growth until a thin compact deposit layer is produced. The laws regulating the initial step as well as the type and the quantity of the structural defects which are formed during this step are first of all determined by the degree of interaction at the interphase between the substrate and the deposit. For this step, two main growth mechanisms of the deposit may be distinguished: the Volmer-Weber [ 1, 2] and the Frank-van der Merwe [3, 4] mechanism. The former describes the case of a weak interaction between the substrate and an atom of the deposit. It implies the formation of the deposit through the nucleation of three-dimensional isolated nuclei, their subsequent growth tangentially to the substrate surface until their coalescence. The Frank-van der Merwe mechanism occurs owing to a strong interaction of the atoms of the deposit with the substrate. In this case, the layer-by-layer growth takes place by a two-dimensional nucleation as a consequence of the oriented influence of the crystalline substrate on the depositing metal layer (epitaxial growth). In agreement with the numerous experimental results, the main types of crystal defects which are formed during the initial step of heterogeneous crystallization are: low- and high-angle grain boundaries, twin boundaries, dislocations, and stacking faults. It is acknowledged that their main mechanism of formation is related to the process of coalescence of the isolated nuclei of the condensed phase during their tangential growth. Furthermore, it is important to point out the mechanism of formation of the mismatch dislocations during the epitaxial growth of the deposit. Such formation occurs when at a critical thickness of the depositing metal layer a relaxation of the accumulated elastic deformation takes place through the formation of dislocations at the substrate-deposit interphase to compensate the mismatch between the parameters of the two coordinating crystalline lattices. At the end of the formation of a thin and complete layer of the condensating phase, the further growth of the deposit occurs in thickness, i.e., in the direction perpendicular to the substrate surface (the second growth step). During this step, the substrate does practically not influence the crystallization process any more and, correspondingly, the formation of the structural defects of the deposit. Hence, during the second growth step, the mechanism of formation of crystal defects has to depend on the typical characteristics of the elementary steps of the deposit growth process in thickness.

It may be concluded that the structural aspect plays an important role in the general problem of crystallization and growth of metal deposits. In the present chapter, the structural problem is discussed taking as an example the electrocrystallization of metals, although several of the problems which are examined may completely be applied to deposits obtained in other ways, first of all by deposition from the vapor phase. Furthermore, the main attention is devoted to the formation of structural defects during the second step of the growth of the electrolytic deposits.

2. CLASSIFICATION OF THE STRUCTURAL DEFECTS IN ELECTRODEPOSITS According to the modern ideas of solid-state physics, the defects in crystals (structural defects) are classified on the basis of their geometric characteristics, i.e., of their extent in the three-dimensional space. Among them, the main role from the point of view of the influence of these defects in the majority of the metals properties is played from the two-dimensional (surface) defects such as the boundaries among near fragments of a crystal which are disoriented the one with respect to the other. This type of structural defect was investigated in detail for the first time in metals of metallurgical origin. In a simple case, when such a boundary among parts of the grain is a screw boundary, its crystallographic characteristic is the azimuth angle of disorientation among the single parts, 0, while its energetic characteristic is the free energy per unit area of the boundary, y, which depends in the general case on the value of the angle 0. The value of y may be determined from the well-known Read-Shockley relationship [5], y = E00(1 + lnO/Om)

(1)

where Eo = Gb/4~r(1 - v)

G is the shear modulus, b is the absolute value of the Burgers vector of the dislocation, and v is the Poisson's ratio. This relationship gives the variation of y in the range of the 0 values between zero and the maximum value Om, which for the greatest part of the metals has a value in the order of 10 to 15 ~ [6]. Figure 1 shows the dependence of )I on 0 evaluated for three metals which substantially differ by their physicomechanical parameters, in particular, heat of sublimation, melting point, and elastic constants. In agreement with the theory of dislocations [7], the boundaries between the different fragments of the crystal are classified as low-angle boundary (of dislocations), if the disorientation angle 0 < On, and high-angle boundary, if 0 > On. In the former case, y increases to its maximum value, Ym, when the value of 0 increases from zero to Om and each part is called subgrain; in the latter case, ), is equal to Ym, and generally does not depend on the value of 0 while each part is called grain.

STRUCTURE FORMATION OF METAL FILMS In addition to these types of boundaries, it is necessary to consider the twin boundaries which are characterized by the well-defined twinning plane typical of each crystalline lattice and by the value of the specific free energy, Ytw. In the case of two parallel twin boundaries which are at an interatomic distance, a stacking fault is formed and its specific free energy is more than two times Ytw. According to the results of numerous investigations obtained by means of the modem methods of metal structure examination, such as optical microscopy, X-ray diffraction, and transmission electron microscopy (TEM), the different types of structural surface defects previously mentioned have been recognized in metal electrodeposits. The quantity and the distribution of the structural defects in the bulk of the deposit depend on both the nature of the deposited metal as well as on the electrocrystallization conditions, in particular, on the current density, the acidity of the electrolyte, and the concentration of the surface-active additives which are present in the solution [8-14]. First of all, it may be noted that as a rule polycrystalline metal deposits are formed during electrodeposition. The single-

Fig. 1. Specific free energy of the dislocation boundary, y, as a function of the azimuth disorientation angle, 0. Reprinted from [70] with kind permission from Elsevier Science.

561

crystal structure of the deposits is formed only during the deposition of a metal on its own single-crystal substrate or even on foreign substrates but in particular electrolysis conditions. The quantitative parameter which characterizes the polycrystalline microstructure of the deposits and strongly influences their properties is the average grain size, D. Its value is inversely proportional to the extension of the high-angle boundaries in the volume unit of the polycrystalline deposit. As to their dependence on the D value, the electrodeposits are conventionally divided into three types: large-crystalline (when D > 10 #m), thin-crystalline (1 # m < D < 10/zm), and ultrathin-crystalline deposits (D < 1/zm). The microstructure of the deposits cross section of the first and second crystal types was investigated in detail by Fischer [8, 15, 16] through optical microscopy. Particular attention was devoted to the character of the electrodeposits microstructure from the point of view of the shape of the grains. According to the experimental results, a classification was performed of the different types of the deposits microstructure. Here, we mention the two main types of the microstructure of compact electrodeposits which differ in principle one from the other. The first type of microstructure (columnar or FT-type according to Fischer's classification) is characterized by the columnar shape of the grains, as shown in Figure 2a [17]. As a rule, such type of microstructure is formed when electrodeposition is carried out at a constant current from simple aqueous electrolytes without additives. The second type (homogeneous or RD-type) is characterized from the size of the grains which is nearly equal in the different directions, Figure 2b. The microstructure of these types of deposits is usually observed when electrodeposition occurs from electrolytes containing surface-active addition agents in a sufficiently high concentration and when the processes of surface adsorption of the foreign molecules strongly influence the growth of the electrodeposits. It is easy to understand that the possibilities offered from the optical microscopy methods to study the deposits structure are rather limited and that such methodology does not allow to obtain experimental data on the bulk structure of the grains. On the other hand, these data are extremely necessary for the

Fig. 2. Microstructure of the cross section of Cu electrodeposits obtained (a) in the absence and (b) in the presence of thiourea at a concentration of 15 mg L-1. Reprinted from [ 17] with kind permission from Elsevier Science.

562 Table I.

KOZLOV AND PERALDO BICELLI Electrolyte Composition, Electrodeposition Conditions, and Deposit Thickness Electrolyte

Metal

composition

Current density pH

(Adm -2)

Thickness t (~

(/zm)

Ni

NiSO4-400 g L -1

4.0

1-5

45-70

80

Cu

CUSO4-500 g L - 1

m

1-3

30--60

120

H 2 SO4-50 g L - 1 Fe

FeSO4-500 g L - 1

2.0

1-6

50-70

100

Zn

ZnSO4-400 gL -1

3.0

1-6

30-50

80

Reprinted from [29] with kind permission from Elsevier Science.

development of a theory of the growth of the deposits in real conditions. More complete information on the structural defects in electrolytic deposits has been obtained by the methods of the transmission electron microscopy (TEM) [ 18-29]. In particular, there is the possibility to investigate such structural defects as dislocations and twins. As generalized results of this topic, we first of all consider our experimental data relevant to electrodeposits with different types of crystalline lattice (Ni, Cumface-centered cubic (fcc), Fembody-centered cubic (bcc), Zn~hexagonal close packed (hcp)). Electrodeposition of the former metals has been carried out from concentrated acid sulfate baths not containing organic addition agents, at relatively low overvoltages (see Table I). These are the favorable conditions to obtain deposits which are practically free from macrostresses known to be at the origin of plastic deformation and to produce deformation defects (in particular dislocations and twins). Therefore, the structural defects of these deposits observed during our TEM investigation may be classified from the point of view of their nature as defects formed during the growth process of the same deposits, only. Moreover, care was taken to exclude the formation of structural defects due to the direct influence of the substrate. To reach this goal, first, the electrodeposition of these metals was performed on an indifferent substrate which had to assure a weak adhesion and, therefore, an insignificant influence on the formation of the deposits structure. For this purpose, electrodeposition was carried out on a mechanically polished stainless steel substrate from which the deposit could easily be detached. Second, the deposits were thick (see Table I) and were analyzed following the TEM methodology. The samples to be submitted to TEM analysis were obtained by anodic polishing of the deposits in orthophosphoric acid. In this way, we investigated the layers of the deposited metals which were at a relatively high distance from the substrate. So, it could be assumed that the structural defects observed in these layers had been formed according to the mechanism relevant to the growth process of the deposits. The investigation of the TEM micrographs showed that the deposits had the polycrystalline structure and that from the point of view of the average size of their grains those of Ni, Cu,

and Fe were thin crystalline, while those of Zn were large crystalline. As to the details of the intemal structure of the grains, TEM investigation showed that they were composed of subgrains set as layers. Figure 3a and b shows the substructure of a Cu and Ni deposit when the planes of the subgrain boundaries were perpendicular to the deposit surface. The type of these boundaries was determined by a crystallographic analysis of the electron diffraction pattem of the regions containing them (e.g., the M and N areas in Fig. 3a and b, respectively). It was observed that in some cases the subgrain boundaries were twin boundaries, the octahedral (111) plane being the twin plane (Fig. 3c and e). In other cases, the angular separation of the diffraction spots (Fig. 3d and f) allowed us to evaluate the azimuth disorientation angle between neighboring subgrains. For example, such an angle was small, around 5 to 6 ~ as shown in Figure 3d. Consequently, the subgrain boundary in N (Fig. 3b) is a low-angle boundary, i.e., a dislocation boundary. The presence of dislocation boundaries in the bulk of the grains was confirmed by direct observation when the boundary surface was parallel to, or only a little tilted toward, the deposit surface. In this case, it was possible to observe the dislocation boundaries as typical dislocation networks (Fig. 4). The dislocation density was proportional to the mean disorientation angle between the subgrains. Such an angle increased with the current density and at decreasing the electrodeposition temperature, that is, it increased with the cathodic overvoltage. For example, in the case of Cu deposits, such an angle increased from 1-2 ~ to 5-6 ~ increasing the current density from 1 to 3 A dm -2. It was found that growth twins were present in large quantities in Ni and Cu deposits (fcc lattice, (111) twin plane, and [ 117.] shear direction) but in small quantities in Fe deposits (bcc, (112), and [111], respectively) and in Zn deposits (hcp, (1012), and [1011 ]) and only when they were obtained at current densities higher than 4 A dm -2. Moreover, it resulted that the deposits with an fcc lattice (Cu and Ni) had the specific structure for twinning: in addition to twins inside the same grain with parallel { 111 } planes, twinning with intersecting octahedral planes also took place. This was confirmed by direct observation of the grains with the (110) zone axis in TEM micrographs where the points of intersection of some twin boundaries were observed which were perpendicular to the surface of the deposit (Fig. 5). In addition to dislocation boundaries and twinning, stacking faults (Fig. 6) were observed in Cu and Ni deposits obtained at high current densities (3 Adm -2 and 5 A dm -2, respectively). In conclusion, the experimental results of the investigation of the electrodeposits structure are the basis for stating that the main types of structural defects which are formed during the growth step when the substrate does not influence the process any more are high-angle boundaries of the grains, dislocation boundaries, twins, and stacking faults. As already stated, their presence and quantity depend on the nature of the deposited metal and on the electrocrystallization conditions.

S T R U C T U R E FORMATION OF METAL FILMS

~

m

111

200

O

X

563

x

O

111

000

111

2~0

200

220

0

0

0

0

0

0

020

000

020

0

0

0

200

O

111

0

X

x i

zone axis [011] (e)

zone axis [001] (f)

Fig. 3. TEM micrographs of (a) Cu and (b) Ni electrodeposits; (c) and (d) diffraction patterns of the M and N regions; (e) and (f) related schemes. (o) Reflexes of the matrix; (x) reflexes of the twins. The deposition conditions are: current density 2 A dm-2" t = 60~ Reprinted from [29] with kind permission from Elsevier Science.

3. M E C H A N I S M O F F O R M A T I O N O F S T R U C T U R A L DEFECTS D U R I N G N O N C o H E R E N T NUCLEATION The mechanism of formation of structural defects in electrodeposits is based on the one side on the generalized experimental data resulting from the deposits structure investigation, which was considered in the previous section and, on the other side,

is based on the theoretical data resulting from crystal growth science. Regarding the results of structural research, it is worth underlining that the main types of crystallographic defects in electrodeposits (high-angle grain boundaries, subgrain boundaries of dislocations, and twins) have the same general character from the geometrical point of view; i.e., they belong to the group of two-dimensional surface defects. They sepa-

564

KOZLOV AND PERALDO BICELLI

Fig. 4. TEM micrographs showing the dislocation networks in the grains of (a) Ni, (b) Cu, (c) Fe, and (d) Zn electrodeposits. The deposition conditions are: Ni has a current density 2 A dm-2; t = 60~ Cu has a current density 1 A dm-2; t -- 45~ Fe has a current density 3 A dm-2; t = 60~ Zn has a current density 3 A dm-2; t = 30~ Reprinted from [29] with kind permission from Elsevier Science.

Fig. 5. TEM micrographs showing the multitwinning of intersecting octahedral planes of (a) Cu and (b) Ni electrodeposits with a (110) orientation axis. The deposition conditions are: Cu has a current density 2 A dm-2; t -- 30~ Ni has a current density 3 A dm-2; t = 60~

rate nearby parts of a deposit which are in a determined different relative crystallographic orientation one with respect to the other. Hence, it may be expected that even the mechanism of their formation has a general unique character and has to be related to a determined elementary step of the electrodeposit growth process in thickness. Here and in the following, only structural defects are considered which are formed when the substrate does not influence the process any more.

Moreover, it must be evidenced that the considered structural defects in electrodeposits are not in t h e r m o d y n a m i c equilibrium and, therefore, that their process of formation during crystal growth is expected to present typical fluctuations which are also typical of the nucleation step, one of the elementary step of metal electrocrystallization. Taking account of the previously m e n t i o n e d (geometrical and t h e r m o d y n a m i c ) factors relevant to defects in deposits, it may be assumed that the m e c h a n i s m of formation of the main

S T R U C T U R E FORMATION OF METAL FILMS

565

Fig. 6. TEM micrographs showing the stacking faults of (a) Cu and (b) Ni electrodeposits. The deposition conditions are: Cu has a current density 3 A dm-2" t = 30~ Ni has a current density 5 A dm-2" t = 45~

Fig. 7. Schemeof a two-dimensional nucleus of four atoms on the top of a {100} plane of an fcc metal (a) in a normal position, and (b) in a disoriented position. structural defects is unique and is connected with the step of nuclei formation. In agreement with the classical theory, crystal growth occurs through the continuous formation of two-dimensional nuclei [ 1, 4, 30-32]. It is necessary to stress that the classical theo r y assumes that the two-dimensional nuclei which are formed on their own substrate plane are in a normal (regular) position from the geometrical point of view. It is obvious that in this case, i.e., in the case of normal nucleation, no crystal defects are formed on the plane of the interface between the nucleus and the substrate. Another possible situation may occur if we assume that, in addition to normal nuclei with a defined probability, noncoherent nuclei are also formed. These nuclei lie in an irregular crystallographic position of the growing surface and their growth forms a disordered layer which is bound to the underlying plane by the two-dimensional (surface) structural defect. Figure 7a shows the disposition of a two-dimensional normal nucleus of four atoms on the top of a { 100 } plane of an fcc crystal and Figure 7b the simplest model of a noncoherent nucleus having an azimuth disorientation angle, 0, with respect to its own substrate plane.

Fig. 8. Atomspositions (a) in the {111 } plane and (b) section parallel to the {110} plane for an fcc crystal. The actual type of a two-dimensional defect which is formed owing to noncoherent nucleation depends on the value of the disorientation angle. More precisely: 1. if the value of 0 is smaller than 10-15 ~ a dislocation boundary is formed; 2. if it is greater than 10-15 ~, the usual high-angle grain boundary is formed. It is necessary to draw attention to the third case which may occur, that is when nucleation takes place on a crystallographic plane which is the typical twinning plane of the crystal. As an example, an fcc crystal may be considered whose twinning plane is the octahedral { 111 } plane. This plane typically has two stable equilibrium positions for the growth of the next atomic plane, the normal (regular) N and the twin positions T (Fig. 8a). If this plane grows in the direction perpendicular to its surface through a subsequent normal nucleation, i.e., when the atoms of the nuclei occupy exactly the normal positions N, the usual stacking of the octahedral planes without defects A B C A B C A . . . takes place. A different situation occurs when the atoms of one of the nuclei occupy the twin position T. In this case, a twin is formed and the stacking of the closepacked planes will be A B C A C B A . . . .

566

KOZLOV AND PERALDO BICELLI

A particular case is observed when the nuclei are formed two times in sequency in the twin position and as a result a stacking fault is formed. This process will be examined considering as an example the case of an fcc crystal which has been formed through a continuous nucleation on octahedral planes (Fig. 8b). The figure shows that the octahedral atomic planes 1 to 4, 7, 8 are formed through normal nucleation, while planes 5 and 6 are formed by nuclei which have occupied twin positions. Hence, the stacking of the close-packed planes will be ABCACABC... and the crystal will contain a stacking fault. From the crystallographic point of view, while noncoherent nuclei of types (1) and (2) may be formed on any plane, twin nuclei may be formed on a twin plane, only. Therefore, the quantity of growth twins in the electrodeposits must depend not only on the thermodynamic factor (oversaturation value) but also on the crystallographic habitus of the growing crystals. In agreement with literature data, Kern [33] was the first who suggested a twinning mechanism for the nucleation of twodimensional nuclei on a twin plane of the growing crystal. Applying classical thermodynamics for phase transformation, he determined the nucleation work of the normal and twin nucleus, analyzing the influence of the electrodeposition conditions on their relative rate of formation. Kern's theory had an evolution by Pangarov [34] who followed the method of the average work of separation [35]. The theoretical analysis of the equations he obtained for the work of formation of nuclei in normal and twin positions showed that the twin nuclei may be formed only when the value of the oversaturation is higher than a threshold value. Then, increasing the oversaturation values strongly increases the relative probability of the formation of the twin nuclei and for relatively high oversaturation values it is already equal to the probability of the formation of normal nuclei. The fundamental ideas of the previous theory of twin formation during deposits growth were confirmed by the numerous research works investigating fcc metals (Ag, Ni, and Cu) [3643]. As to the formation of dislocation boundaries in deposits, Sears was the first who suggested that such formation is connected to that of noncoherent two-dimensional nuclei [44]. The determination of the probability of formation of noncoherent nuclei was performed on the basis of the classical theory of nucleation. The mechanism of formation of structural defects in the deposits which is also connected to the process of noncoherent nucleation was considered in Refs. [45-47]. It may occur when two or more nuclei are formed on a growing crystal plane which are casually disoriented with respect to this plane. These same nuclei will be disoriented among them. Therefore, as a result of their lateral growth and coalescence, structural defects between near atomic layers must be formed. The actual type of these defects (high-angle grain boundary, dislocation boundary, twin boundary) will depend on the value of the disorientation angle between the nuclei. Hence, the formation of the main crystal defects in the deposits may be examined from the point of view of the noncoher-

ent nucleation process which may take place during the growth of the deposit crystals. Therefore, the step of formation of noncoherent nuclei must be analyzed in detail to determine the general laws concerning the influence of the electrocrystallization conditions on the structure of metal deposits.

4. CLASSICAL THEORY OF N O N C O H E R E N T NUCLEATION Since the formation of the main types of structural defects in deposits is related to the nucleation step during crystal growth, the process of formation of noncoherent nuclei will first of all be examined according to classical theory of heterogeneous nucleation [48, 49]. It will be assumed that the noncoherent nucleus presenting an azimuth disorientation angle with respect to the substrate plane of its same nature is three-dimensional with a well-defined shape, e.g., it is a cylinder. For the thermodynamic analysis of noncoherent nucleation, as an example, a close-packed plane of an fcc lattice will be examined (Fig. 8a). A noncoherent nucleus may be obtained by rotation of the normal nucleus around the axis perpendicular to the octahedral plane by an angle 0. During the rotation of the nucleus by an angle in the range 0 ~ < 0 < 60 ~ and also 60 ~ < 0 < 120 ~ each atom of the nucleus crosses a series of unstable positions characterized by an excess free energy which depends on the azimuth disorientation angle of the same nucleus. The value 0 = 60 ~ corresponds to the stable equilibrium position of the twin nucleus and the value 0 = 120 ~ to the case of a normal nucleus occupying the regular stable position. Contrary to the normal and twin nucleus, the noncoherent nucleus is not stable and, therefore, tends to decrease its free energy by spontaneously reorienting itself to the normal or twin position. However, in the actual electrocrystallization conditions, foreign atoms and/or molecules adsorbed on the surface of the growing crystal hinder such reorientation. For the thermodynamic evaluation of the work of nucleation of a noncoherent nucleus, the excess free energy of the nucleus, Es, must be considered, which depends on the azimuth disorientation angle, 0, Es = Sy(O)

(2)

where S is the contact area of the nucleus with the surface of the underlying plane and y (0) is the free energy per unit area of the noncoherent bond between nucleus and substrate. According to the dislocation theory, the azimuth disorientation of contiguous crystal layers with an angle not greater than the value Om 10-15 ~ causes the formation of a dislocation boundary in the plane in between these layers. Taking into account that the disoriented layers of the deposits are produced by noncoherent nucleation, in first approximation, it may be assumed that y (0) is also equal to the free energy per unit area of the dislocation boundary which may be evaluated by the ReadShockley relationship [Eq. (1)]. When the 0 values are greater than On, y (0) may be assumed to be constant and equal to the free energy per unit area of the usual grain boundary, Ym. Let us =

STRUCTURE FORMATION OF METAL FILMS 0.3

567

15 12

A

qE 0.2

09 2: "r" 6

.-j v

"~ 0.1

0

0

0

20

40

60

80

100

120

0.01

0.02

0.03

Fig. 9. Free energy per unit area, y, of the noncoherent bond between the nucleus and the octahedral plane of an fcc lattice as a function of the azimuth disorientation angle, 0. The data refer to Cu.

take these considerations into account and also that the atoms of the noncoherent nucleus periodically occupy the normal, N, and the twin, T, positions during their rotation around the axis perpendicular to the octahedral plane (Fig. 8a). Then, the dependence from the azimuth disorientation angle of the free energy per unit area of the noncoherent bond between the nucleus and the { 111 } plane of an fcc lattice is expected to follow the trend shown in Figure 9. The data employed for the calculations refer to copper. Hence, it may be underlined once again that the types of structural defects which are formed during the metal deposition process owing to noncoherent nucleation depend on the azimuth disorientation angle of the nucleus. More precisely, as already stated: 1. if the value of 0 is smaller than 10-15 ~ a dislocation boundary is formed; 2. if it is greater than 10-15 ~, the usual grain boundary is formed; 3. if the nucleus is in a favorable position for twinning, a twin boundary is formed. To analyze the formation of three-dimensional noncoherent nuclei, we utilize the general Gibbs equation for heterogeneous nucleation taking into account that the nucleus has a cylindrical shape, with radius R and height H, and also Eq. (2),

7rR2 H = - ~ A / z

Vo

+

27rRHcr +

yrR2F(0)

(3)

where A G3 is the Gibbs free energy of formation of the noncoherent nucleus, Vo is the atom volume, cr is the (lateral) surface free energy per unit area of the nucleus, and A/z is the variation of the chemical potential due to the phase transition which depends on the oversaturation of the system [50],

Alz = kT In C/Co

0.05

0.06

,~(v)

e ( degree )

AG3

0.04

(4)

k is the Bolzmann constant, T is the absolute temperature, C and Co are the adatoms concentration in the oversaturation and equilibrium state, respectively.

Fig. 10. Relative height of the noncoherent Cu nucleus, H/Ho, as a function of the crystallization overvoltage, Aqg. Disorientation angle of the nucleus: 3 ~ (curve 1) and 10 ~ (curve 2). tr = 1 J m -2.

In the case of metals electrocrystallization, A/x is equal to zeoA~O, z is the number of charges transferred during the charge-transfer process, eo is the electron absolute charge, and Aq9 is the absolute value of the crystallization overvoltage characterizing the deviation of the system from the equilibrium state. Considering the minimum of Eq. (3), that is the conditions owing to which the nucleus assumes its equilibrium size, we obtain the dimensions and the nucleation work of the noncoherent three-dimensional critical nucleus, R3 =

/43 = A3 --

2Vocr zeoAq9 2Voy(O) ZeoAq9 4n'tr2 V2y (0) (zeoAqg) 2

(5)

(6) (7)

According to Eqs. (5) and (6), the nucleus radius and the height decrease at increasing overvoltage. However, contrary to the R3 value, the //3 value depends on the disorientation angle of the noncoherent nucleus and not on the value of the surface free energy per unit area of the nucleus. Moreover, in any case, the nucleus height has a minimum value, Ho, equal to the atom diameter (Fig. 10). This means that the noncoherent nucleation process may be analyzed from the point of view of a three-dimensional nucleation process only in the limit of the H3 values not smaller than 2Ho. In the opposite case, it is necessary to utilize the Gibbs equation for the heterogeneous two-dimensional nucleation, AG2 = -

7r R2 Ho ~

Vo

AlZ + 2rcRx + 7rR2F(0)

(8)

where A G2 is the Gibbs free energy of formation of the noncoherent two-dimensional nucleus and X is the linear free energy per unit length of the nucleus boundary, equal to Hotr. From the minimum of Eq. (8), the radius and nucleation work of the noncoherent two-dimensional critical nucleus are

568

KOZLOV AND PERALDO B ICELLI

0.06

Table II. Estimated Values of the Work of Formation (• 10-19 j) of a Noncoherent, Anc, and Normal, Ao, Cu Nucleus and of Their Difference, A n c - Ao, for Different Values of the Crystallization Overvoltage, A~0, and of the Disorientation Angle, 0

0.04

L

0

2~

4~

6~

8~

Anc

106

Ao Anc - Ao

10 ~

159

192

213

224

21

21

21

21

21

85

138

171

192

203

56

Aq9 = 0.02 V

"~ 0.O2

0

, I

I

I

I

I

A~o = 0.04 V

0

2

4

6

8

10

12

e(~) Fig. 11. Value of the critical crystallization overvoltage, A~0o, as a function of the azimuth disorientation angle, 0, of the noncoherent nucleus of Cu. cr = 1 Jm -2.

obtained:

R2 = A2 =

(Vo/Ho)X zeoA~o- (Vo/Ho)y(O) 7rx2(Vo/no) zeoA~o- (Vo/Ho)y(O)

Ao =

(Vo/ Ho) X zeoA~p rc x 2 ( Vo/ Ho) zeoAq9

(10)

Vo• zeoHo

38

46

52

10

10

10

10

10

Anc - Ao

16

28

36

42

46

Anc

12

16

19

21

22

Ao

7

7

7

7

7

Anc - Ao

5

9

12

14

15

Anc

7.7

9.9

11.6

13.1

14.1

Ao

5.2

5.2

5.2

5.2

5.2

Anc - Ao

2.5

4.7

6.4

7.9

8.9

A~0 = 0.06 V

Aq9 = 0.1 V Anc

5.8

6.9

7.7

8.4

8.9

Ao

4.1

4.1

4.1

4.1

4.1

Ant - Ao

1.7

2.8

3.6

4.3

4.8

0.12

0.15

c r = l J m -2.

[x 10"19]

(11)

4Or-(12)

30

Hence, the overvoltage values may be divided into two ranges, from 0 to A~oo (the critical value) where noncoherent three-dimensional nucleation takes place, and for values greater than A~0o where noncoherent two-dimensional nucleation occurs. The critical overvoltage may be obtained either from Eq. (6) assuming Ha = 2Ho, or from Eq. (10) assuming the denominator equal to zero, i.e., [zeoA~p - (Vo/Ho)y(O)] = O, A~0o --

26

Ao

A~0 = 0.08 V

(9)

Since crystal growth occurs through the formation not only of noncoherent (two-dimensional or three-dimensional) but also of normal (two-dimensional) nuclei, introducing the condition y(0) = 0 into Eqs. (9) and (10), the radius and nucleation work of the normal two-dimensional critical nucleus are obtained"

Ro --

Anc

(13)

In agreement with Eq. (13), increasing the disorientation angle of the noncoherent nucleus, A~po increases reaching its maximum value when 0 = Om, that is when y(0) = Ym (Fig. 11). Such curve A~oo as a function of 0 divides the field of existence of the two-dimensional and three-dimensional noncoherent nuclei. So, increasing the crystallization overvoltage, the range of 0 values for the two-dimensional nuclei increases and, vice versa, that for the three-dimensional nuclei decreases. For example, as shown in Figure 11 when the crystallization process occurs with overvoltages greater than 0.055 V, the noncoherent nucleation process with the different 0 values occurs through two-dimensional nucleation.

A

.
Eo. On the basis of the results of these calculations, the following conclusions were drawn: (1) the cluster's mechanism of formation of pentagonal nuclei with veritable-five symmetry may occur when the conditions of crystallization favor the three-dimensional nucleation [86, 87]; (2) when during its growth the dimension of the pentagonal nucleus reaches a few thousands of angstroms, its structure has to change either into the usual close-packed structure [78, 82, 93] or into the structure with pseudo-five symmetry (four twin boundaries and one high-angle boundary) [94]. According to the second point of view relevant to the mechanism of formation of the pentagonal crystals, their formation is explained by a repeated twinning process during the growth step of the crystals [72, 75]. Pangarov and his co-workers [34, 79, 98] assumed this mechanism to interpret their experimental results regarding the electrocrystallization of fcc metals. The substantial points of the mechanism of a repeated twinning process may be explained as in the following. Let us suppose that during the electrodeposition of an fcc metal there is a separate crystal having a tetrahedral shape (tetrahedron 1 in Fig. 34a). On its octahedral plane, the formation of a nucleus in the twin position may occur which then increases forming a second tetrahedron. As a result of this process, the first twin boundary between tetrahedra 1 and 2 is formed (Fig. 34a). Then, on the octahedral plane of tetrahedron 2, a nucleus is formed in the twin position and, as a consequence, tetrahedron 3 is formed and, correspondingly, the twin boundary between tetrahedra 2 and 3. Tetrahedra 4 and 5 are subsequently formed with the same mechanism. It is evident that the first and the last tetrahedron (1 and 5 in Fig. 34a) are not in the twin position between them. Therefore, with the filling of this corner split between tetrahedra 1 and 5 by the atoms of the deposit, the high-angle boundary of the grains is formed (Fig. 34b). Hence, as a result of the successively repeated twinning process, a crystal with pseudo-five symmetry is obtained presenting the shape of the decahedron (Fig. 33). In the same way, it is possible to explain the formation of the pentagonal crystal having the shape of the icosahedron.

584

KOZLOV AND PERALDO BICELLI

Fig. 35. (a) TEM micrograph showing the multitwinning of intersecting octahedral planes of Cu electrodeposits with a (110) orientation axis and (b) schematic where the twin boundaries (continuouslines) and the high-angle boundaries of the grains (dashedlines) are reported.

Similar configurations of intersecting twin boundaries have also been observed in [89, 91, 92]. In agreement with the opinion of the authors of the article reported in [99], the formation of the points of multitwinning where several twin boundaries intersect (from two to four) may be explained by a repeated twinning process during the growth step of the crystals. In this case, the so-called cluster's mechanism can explain the formation of the points of one type, only; i.e., the point where four twin boundaries and one high-angle boundary of the grains (the pseudo-five symmetry point O1, in Fig. 35b) intersect but not the formation of the points where three or two twin boundaries (02, 03, and 04, in Fig. 35b) intersect. Let us now consider the formation of all the points of multitwinning in agreement with the schematic shown in Figure 35b. For example, crystal 1 is first formed which has the four octahedral planes perpendicular to the { 110 } plane, that is the plane of the drawing. Then, nuclei are formed on the four octahedral planes in the twin positions and fragments 2, 5, 7, and 8 will be in the twin position relative to fragment 1. Subsequently, fragments 3, 4, 6, and 9 may be formed in the same way with the formation of twin boundaries. After the connection of fragments 4 and 5, 6 and 5, 7 and 8, 9 and 8, the usual high-angle boundaries of the grains are formed. So, it may be concluded that the separated crystals of the fcc metals with the pentagonal shape which are observed during the initial step of heterogeneous electrocrystallization are probably formed by the cluster's mechanism when the conditions of crystallization favor three-dimensional nucleation. This is related to the lower internal energy of the nuclei having the decahedral and icosahedral shape. On the other hand, the formation during the subsequent growth step of the different configurations of the intersecting twin boundaries of the fcc metals is probably connected to a repeated twinning process.

8. CONCLUSIONS In the real case, during the inital deposition step of the fcc metals, both mechanisms of the formation of the pentagonal crystals may occur. We have a particular situation when the multitwinning of intersecting octahedral planes of electrodeposited fcc metals is observed not in the initial layers but in the layers which are formed at a distance of some tens of microns from the substrate (as shown in Fig. 5). In this case, the points of multitwinning are observed where two or more twin boundaries intersect. The crystallographic analysis shows that, if in the point of multitwinning n boundaries intersect (with n = 3, 4, 5), then (n - 1) of them will be twin boundaries while one boundary will be the high-angle boundary of the grains. We analyze this last case in detail considering as an example the TEM micrograph shown in Figure 35a. Figure 35b reports the scheme of this TEM micrograph. We observe the four points of the multiplying twinning, O1, 02, 03, and 04, where 5, 4, 3, and 4 boundaries intersect, respectively. In the figure, the twin boundaries are represented by the continuous lines whereas the high-angle boundaries of the grains are represented by the dashed lines.

The elaboration of the mechanism of formation of the different types of crystallographic defects in metal deposits is important both for practical and theoretical reasons. In the present chapter, the problem of the structure formation of deposits was discussed taking the electrocrystallization of metals as an example, although several aspects which have been examined may completely be applied to metal deposits obtained in other ways, first of all by deposition from the vapor phase. As the basis of this investigation, we considered the model of noncoherent (disoriented) nuclei, which are formed with a defined probability besides the normal nuclei during the growth of the deposit in thickness at the end of the initial crystallization step including the formation of the nuclei on the substrate, their lateral growth, and the formation of a thin compact deposit layer. The application of this model allowed us to explain from a unique point of view the formation of the main types of structural defects in electrodeposits (high-angle grain boundaries, subgrain boundaries of dislocations and twins). In agree-

STRUCTURE FORMATION OF METAL FILMS ment with our ideas, the effective type of crystallographic twodimensional defect which is formed owing to noncoherent nucleation depends on the value of the azimuth disorientation angle, 0, with respect to its own substrate plane. More precisely: 1. if the value of 0 is smaller than 10-15 ~ a dislocation boundary is formed; 2. if it is greater than 10-15 ~, the usual high-angle grain boundary is formed. It is necessary to draw attention to the third case which may occur, that is when nucleation takes place on a crystallographic plane being the typical twinning plane of the crystal (for example, the octahedral { 111 } plane of fcc crystals). In this case, if the atoms of the nucleus occupy twin positions; i.e., the electrodeposition conditions are favorable to twinning, then a twin is formed in the deposit (Kern's mechanism). The classical thermodynamic analysis of the noncoherent nucleation step performed during our research has confirmed that there is a unique mechanism of formation of the main structural defects during metal electrocrystallization. On the basis of the calculations of the work of formation of noncoherent and normal nuclei, the influence of the crystallization overvoltage (oversaturation) and of the surface free energy per unit area on the relative probability of noncoherent nucleation which qualitatively characterizes the degree of crystal imperfection of the electrodeposits was investigated. In more detail, the mechanism of formation of the main structural defects in the deposits was investigated according to a thermodynamic-statistical analysis of the noncoherent nucleation step from the atomistic point of view. This allowed us to determine the quantitative relationship between the main structural parameters of the deposits (dislocation density, p, and average grain size, (L)) and the conditions of electrocrystallization. First of all, we theoretically analyzed the influence of the crystallization overvoltage, A~0, and of the surface coverage with adsorbed foreign particles, O, on the values of p and (L) of the deposits. These results were interpreted in connection with the growth in thickness of the electrodeposits initially having either a polycrystalline structure or a monocrystalline structure and they were confirmed by a structural research (principally following the TEM method) of electrodeposited metals with different types of crystalline lattice (Cu, Ni--fcc, Fe--bcc, Zn--hcp). The proposed model of noncoherent nucleation explained not only the mechanism of formation of the main structural defects but also the structural changes occurring by modifying the electrolysis conditions. In particular, it was possible to explain the well-known transition from the single-crystalline to the polycrystalline structure observed in metals deposited on single crystals at increasing cathodic overvoltage, current density, concentration of surface-active agents, or deposit thickness. Moreover, the transition of the microstructure of the polycrystalline electrodeposits from the columnar to the homogeneous type when the concentration of surface-active agents in the electrolyte was increased was also explained.

585

A thermodynamic-statistical analysis of the noncoherent nucleation step was also carded out to investigate the influence of the nature of metals on the formation of the electrodeposits polycrystalline structure. Considering the traditional classification of metals into three groups according to their increasingly slower kinetics during electrodeposition from aqueous solutions, we theoretically analyzed Cd, Cu, and Ni, they being typically representative metals of each group. The theoretical results were confirmed by the experimental results obtained during Cd, Cu, and Ni electrodeposition. Particular attention was devoted to the phenomenon of multitwinning with intersecting octahedral planes in the fcc electrodeposited metals and in particular to the formation of the pentagonal crystals with a geometrical pseudo-five symmetry. In agreement with the results of the crystallographic analysis and of the generalization of the numerous literature data, some conclusions could be drawn regarding the mechanism of the multitwinning process in electrodeposits. The proposed mechanism of the formation of the structure of electrodeposits certainly does not exclude other possible mechanisms, however, from our point of view, the major contribution to the formation of the main crystallographic defects during the growth in thickness of the electrodeposits is due to the noncoherent nucleation step. In any case, the series of problems connected to the structure of the electrodeposits could be explained just considering noncoherent nucleation.

ACKNOWLEDGMENT

V. M. Kozlov kindly acknowledges the Cariplo Foundation, "A. Volta" Center for Scientific Culture, for financial support.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16. 17. 18. 19.

M. Volmer and A. Weber, Z. Phys. Chem. 119, 277 (1926). E. Bauer, Z. Kristallogr. 110, 372 (1958). F.C. Frank and J. H. van der Merwe, Proc. R. Soc. A 198, 205 (1949). J.H. van der Merwe, Cryst. Interfaces 34, 117 (1963). W.T. Read and W. Shockley, Phys. Rev. 78, 275 (1950). H. Gleiter and B. Chalmers, "High-Angle Grain Boundaries," Pergamon, New York, 1972. J.P. Hirth and J. Lothe, "Theory of Dislocation," Plenum, New York, 1966. H. Fischer, "Elektrolytische Abscheidung und Elektrokristallisation von Metallen," Springer-Verlag, Berlin, 1954. S. Steinemann and H. E. Hintermann, Schweiz. Archiv Angew. Wiss. Tech. 26, 202 (1960). Y.M. Polukarov and Y. D. Gamburg, Elektrokhimiya 2, 487 (1966). K.R. Lawless, Phys. Thin Films 4, 191 (1967). V.M. Kozlov, L. Peraldo Bicelli, and E. A. Mamontov, Ann. Chim. (Italy) 63,405 (1973). M. Froment and G. Maurin, Electrodep. Surface Treat. 3, 245 (1975). E. Budevski, G. Staikov, and W. J. Lorenz, "Electrochemical Phase Formation and Growth," VCH, Weinheim, New York, 1996. H. Fischer, Z. Elektrochem. 54, 459 (1950). H. Fischer, Electrodep. Surface Treat. 1,319 (1973). V.M. Kozlov and L. Peraldo Bicelli, Mater. Chem. Phys. 62, 158 (2000). L. Reimer, Z. Metallkd. 47, 631 (1956). S. Ogawa, J. Mitzumo, D. Watanabe, and E E. Fujita, J. Phys. Soc. Jpn. 12, 999 (1957).

586

KOZLOV AND PERALDO BICELLI

20. R. Weil and H. C. Cook, J. Electrochem. Soc. 109, 295 (1962). 21. E.M. Hofer and Ph. Javet, Microtecnic 17, 168 (1963). 22. T. G. Stoebe, E H. Hammad, and M. L. Rudee, Electrochim. Acta 9, 925 (1964). 23. H.J. Read and E. J. Oles, Plating 52, 860 (1965). 24. E. M. Hofer, L. E Chollet, and H. E. Hintermann, J. Electrochem. Soc. 112, 1145 (1965). 25. M. Froment and A. Ostrowiecki, Metaux 41, 83 (1966). 26. G. Maurin and M. Froment, Metaux 41, 102 (1966). 27. E.A. Mamontov and V. M. Kozlov, Elektrokhimiya 5, 1158 (1969). 28. V.M. Kozlov, Elektrokhimiya 18, 1353 (1982). 29. V.M. Kozlov and L. Peraldo Bicelli, J. Cryst. Growth 165, 421 (1996). 30. H. Brandes, Z. Phys. Chem. 126, 196 (1927). 31. R. Kaischev, Izv. Bulg. Akad. Nauk, Ser. Fis. 1,100 (1950). 32. I. Markov and R. Kaischev, Thin Solid Films 32, 163 (1976). 33. R. Kern, Bull. Soc. Franc. Miner. Cryst. 84, 292 (1961). 34. N.A. Pangarov, Phys. Status Solidi 20, 371 (1967). 35. I.N. Stranski and R. Kaischev, Ann. Phys. 23, 330 (1935). 36. T.H.V. Setty and H. Wilman, Trans. Faraday Soc. 51,984 (1955). 37. Th. H. Orem, J. Res. Natl. Bur. Stand. 60, 597 (1958). 38. S.C. Barnes, Acta Metall. 7, 700 (1959). 39. G. Poli and L. Peraldo BiceUi, Met. Ital. 51,548 (1959). 40. Y.M. Polukarov and Z. V. Semionova, Elektrokhimiya 2, 184 (1966). 41. M. Lazzari and B. Rivolta, "Proceedings of the Symposium on Sulfamic Acid," Milan, 1966. 42. N.A. Pangarov and V. Velinov, Electrochim. Acta 13, 1909 (1968). 43. J.B. Cusminsky and H. Wilman, Electrochim. Acta 17, 237 (1972). 44. G.W. Sears, J. Chem. Phys. 31,157 (1959). 45. G.A. Bassett, "Proceedings of the European Regional Conference on Electron Microscopy," Delft, 1960. 46. J.W. Matthews and D. L. Allinson, Philos. Mag. 8, 1283 (1963). 47. R. Weil and J. B. C. Wu, Plating 60, 622 (1973). 48. I.N. Stranski, Z. Phys. Chem. 136, 259 (1928). 49. M. Volmer, "Kinetik der Phasenbildung," Steinkopf, Dresden-Leipzig, 1939. 50. T. Erdey-Gruz and M. Volmer, Z. Phys. Chem. 157A, 165 (1931). 51. D. Walton, J. Chem. Phys. 37, 2188 (1962). 52. D. Walton, T. N. Rhodin, and R. W. Rollins, J. Chem. Phys. 38, 2698 (1963). 53. S. Stoyanov, Thin Solid Films 18, 91 (1973). 54. V.M. Kozlov and L. Peraldo Bicelli, J. Cryst. Growth 177, 289 (1997). 55. I.N. Stranski and R. Kaischev, Z. Phys. Chem. 35B, 27 (1937). 56. E Hirsh, Prog. Metal. Phys. 6, 236 (1956). 57. G. Williamson and R. Smallman, Philos. Mag. 1, 34 (1956). 58. S.C. Barnes, Electrochim. Acta 5, 79 (1961). 59. G. Poli and L. Peraldo Bicelli, Met. ltal. 54, 497 (1962). 60. L. Peraldo Bicelli and G. Poli, Electrochim. Acta 11,289 (1966).

61. V.M. Kozlov, L. Peraldo Bicelli, and V. N. Timoshenko, J. Cryst. Growth 183, 456 (1998). 62. V.V. Povetkin, Izv. Akad. Nauk SSSR Met. 3, 187 (1985). 63. S. Nakahara and R. Weil, J. Electrochem. Soc. 120, 1462 (1973). 64. R. Weil, G. J. Stanko, and D. E. Moser, Plating Surf. Finishing 63, 34 (1976). 65. R. Piontelli, "Proceedings IX Congress IUPAC," London, 1947, p. 785. 66. T. Erdey-Gruz, "Kinetics of Electrode Processes," Higler, London, 1972. 67. P.L. Cavallotti, D. Colombo, U. Ducati, and A. Piotti, Proc. Electrochem. Soc. (Electrodeposition Technol. Theory Practice) 87-17, 429 (1987). 68. P.L. Cavallotti, B. Bozzini, L. Nobili, and G. Zangari, Electrochim. Acta 39, 1123 (1994). 69. R. Winand, Hydrometallurgy 29, 567 (1992). 70. V.M. Kozlov and L. Peraldo Bicelli, J. Cryst. Growth 203, 255 (1999). 71. A.J. Melmed and D. O. Hayward, J. Chem. Phys. 31,545 (1959). 72. H. Schlotterer, Metalloberfliiche 18, 33 (1964). 73. M.A. Gedwill and C. J. Altstetter, J. Appl. Phys. 35, 2266 (1964). 74. E Ogburn, B. Paretzkin, and H. S. Peiser, Acta Crystallogr. 17,774 (1964). 75. R.W. De Blois, J. Appl. Phys. 36, 1647 (1965). 76. R.L. Schwoebel, J. Appl. Phys. 37, 2515 (1966).

77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.

J.G. Allpress and J. V. Sanders, Surface Sci. 7, 1 (1967). S. Ino and S. Ogawa, J. Phys. Soc. Jpn. 22, 1365 (1967). N.A. Pangarov and V. Velinov, Electrochim. Acta 13, 1641 (1968). E. Gillet and M. Gillet, Thin Solid Films 4, 171 (1969). I. Epelboin, M. Froment, and G. Maurin, Plating 56, 1356 (1969). Y. Fukano and C. M. Wayman, J. Appl. Phys. 40, 1656 (1969). E. Gillet and M. Gillet, Thin Solid Films 15,249 (1973). S. Kamasaki and Y. Tanabe, Met. Finish. Soc. Jpn. 25, 75 (1974). K. Yagi, K. Takayanagi, K. Kobayashi, and G. Honjo, J. Cryst. Growth 28, 117 (1975). M. Froment and J. Thevenin, Metaux N594, 43 (1975). J. Thevenin, J. Microsc. Spectrosc. Electron. 1, 7 (1976). C. Digard, G. Maurin, and J. Robert, Metaux N611, 255 (1976). J.W. Faust and H. E John, J. Phys. Chem. Solids 25, 1407 (1964). S. Ino, J. Phys. Soc. Jpn. 21,346 (1966). J. W. Faust, E Ogburn, D. Kahan, and A. W. Ruff, J. Electrochem. Soc. 114, 1311 (1967). J. Smit, E Ogburn, and C. J. Bechtoldt, J. Electrochem. Soc. 115, 371 (1968). T. Komoda, Jpn. J. Appl. Phys. 7, 27 (1968). E. Gillet, M. Gillet, and A. Renou, Thin Solid Films 29, 217 (1975). S. Ino, J. Phys. Soc. Jpn. 26, 1559 (1969). S. Ino, J. Phys. Soc. Jpn. 27, 941 (1969). M.R. Hoare and P. Pal, J. Cryst. Growth 17, 77 (1972). V. Velinov and N. Pangarov, Izv. Otd. Him. Nauk Bulg. Akad. Nauk 5, 207 (1972). E. A. Mamontov, V. M. Kozlov, and L. A. Kurbatova, Elektrokhimiya 15, 257 (1979).

Chapter 12

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS Michael Huth Institute for Physics, Johannes Gutenberg-University Mainz, 55099 Mainz, Germany

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MBE Growth of Intermetallic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Intermetallic Compounds: Definition of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. General Considerations in Compound Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Phase Stabilization and Orientation Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Epitaxial Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Morphological Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selected Applications in Basic and Applied Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Superconductivity in UPd 2AI 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Magnetoelastic Coupling Effects in RFe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Magnetization Reversal of Ultrathin Co-Pt Heterostructures . . . . . . . . . . . . . . . . . . . . 3.4. Intermetallic Compounds for Magnetooptics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Exchange Anisotropy with Metallic Antiferromagnets . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Antiferromagnetic Order Parameter Nucleation on a Thin Film Surface . . . . . . . . . . . . . . 3.7. Order-Disorder Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. INTRODUCTION

587 588 588 588 593 594 601 604 608 608 611 615 618 618 619 620 623 623 624

with respect to their applicability as magnetooptically active layers, to give just one example. In this context, the large variety of MBE techniques and in situ characterization methods, even though originally set up mainly for research on semiconductors, establishes a sound basis for the preparation of epitaxial metallic structures. Many guiding principles can be taken from the growth in the semiconductor knowledge base, but there are also salient differences in metallic systems. To give only two examples: first, the maintenance of epitaxial strain in metallic systems is difficult because there is no appreciable activation barrier for dislocation formation, whereas in semiconductors the Peierls barrier, due to directed covalent bonding, helps to sustain strain far beyond the critical film thickness. Particularly in magnetic systems exhibiting sufficient magnetoelastic coupling effects, "strain tailoring" is often necessary to generate desired magnetic properties, such as the orientation of the axis of easy magnetization. Second, the influence of impurity lev-

The potential of epitaxial thin films of intermetallic compounds in basic and applied research is only just emerging. Although the growth of semiconductor heterostructures and compounds based on molecular beam epitaxy (MBE) and related methods has come through a 30-year history of ongoing refinement and sophistication, still much has to be learned concerning the growth and characterization of even moderately complex metallic thin film structures. One of the main reasons for this used to be the lack of strong driving forces for possible industrial applications in metals epitaxy that is surely present in semiconductor science and technology. (It should be stressed here that investigations focused on the optimization of metallization layers based on silicides for semiconductor devices will not be considered in this chapter.) Nevertheless, this is changing now. At present, various intermetallic compounds are being investigated

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

587

588

HUTH

els on the characteristic properties (e.g. the electronic structure) of metals is far less pronounced because of strong screening effects. This is in obvious contrast to semiconductors, the electronic structure of which can be appreciably changed, even by residual gas trace impurities introduced during the deposition process in a vacuum of 10 -11 mbar. This means, in some instances, that reasonably decent metallic layers can be grown in a less stringent vacuum of 10 -8 mbar. MBE represents a well-defined crystallization technique based on the reactions between molecular or atomic beams of the constituent elements on a substrate or template at elevated temperatures in an ultrahigh vacuum (UHV) environment. Owing to the UHV environment, various surface sensitive characterization techniques, like electron diffraction in grazing and normal incidence, can be used to monitor and/or control the growth process. The appreciably improved control of beam fluxes and growth conditions, as compared with conventional physical vapor deposition techniques, allows the realization of synthetic structures on the atomic layer scale. This includes superlattice structures as well as metastable (ordered) alloys or intermetallic compounds. The growth process is much more driven than in near-equilibrium techniques because of an enhanced supersaturation that may be as large as 10 to 40. As a consequence, the growth of any compound, even if the constituent elements have vastly differing vapor pressures, is possible in principle. In the following some general considerations conceming the growth of intermetallic compounds as epitaxial thin films will be given. This will comprise a short overview of different systems that show specific aspects of metallic compound growth employing MBE techniques. A detailed account of the technical side of MBE growth itself lies beyond the scope of this chapter. Only a short overview is given conceming specific instrumental aspects of MBE growth of metals. For recent publications conceming conceptional details of MBE and related techniques, the growth process, and relevant characterization techniques, the reader is referred to [ 1]. An appreciable part of this review will be devoted to the applications of thin films of intermetallic compounds in basic and applied research, which, more than anything else, spurs the growth of the field. This overview will certainly not be complete. It rather represents a subjective selection of investigations on intermetallic compounds and ordered alloys that either highlight specific aspects relevant to the field or are examples that are highly interesting in their own fight.

2. MBE GROWTH OF INTERMETALLIC COMPOUNDS

2.1. lntermetallic Compounds: Definition of Terms When should an ordered intermetallic alloy be designated an intermetallic compound? The physical reason for the formation of an ordered phase can give some guidance in the formulation of an answer to this question.

In the Helmholtz free energy of an alloy it is the entropy of mixing that favors the formation of mixed alloys. Only when the pair formation of unequal next neighbors results in an energy gain does the formation of an ordered phase tend to become advantageous. Consider, for example, the phase diagram of a binary alloy. With increasing negative energy of mixing the phase diagram will change, eventually showing the formation of an intermetallic phase out of the melt. Such a compound can be formed at high temperatures, with the liquidus and solidus curves forming a common maximum, resulting in a congruently melting compound. The compound can also form peritectoidically. For moderate negative mixing energies the formation of an ordered phase can also take place out of a disordered solid alloy phase. Cu3Au can be considered one of the best-studied examples. Cu3Au forms from the disordered phase by a congruent transformation at the stoichiometric composition and at the Au-rich limits by an eutectoid transformation. In this respect, one cannot discriminate between the terms "ordered alloy" and "intermetallic compound," at least below the order-disorder transition temperature. We therefore also include aspects of ordered alloys in this review. These are from growth studies that deal with the influence of interfaces and film morphology on the onset of long-range chemical order. We will also discuss some recent investigations conceming stabilization techniques for specific stacking variants in intermetallic compounds with fcc structure grown in (111) orientation.

2.2. Equipment 2.2.1.

Preparation

Many aspects of modem MBE systems for metals epitaxy are analogous to the technology used in semiconductor growth. Figure 1 shows a state-of-the-art MBE system custom designed by Omicron Vacuumsystems. The general setup of such a system is based on a modular concept that helps to sustain excellent vacuum conditions in the growth and analytic chambers. A small load lock with multiple sample cassette and heating capabilities permits the necessary preconditioning of the substrates. This can comprise outgassing, ion beam cleaning, and cleaving. The commonly used sample size is in the millimeter to centimeter range. For growth at high substrate temperatures, substrate carriers made from refractory metals (Mo, Ta) are often used, to which the substrate is attached by various clamping techniques or tungsten wires spot-welded over the edges, or with silver paint or ceramic adhesives. If the substrate is glued, care should be taken to degas the cartier and substrate before transfer into the MBE or analytic chambers because organic solvents can interfere with delicate components, like hair filaments of electron guns. The distribution chamber forms the central part of a modular system design, allowing the delivery of samples to the different attached chambers. The MBE chamber itself can be equipped with conventional Knudsen cells, high-temperature cells for refractory metals fitted with special liners (usually made from W, Ta, Mo, and pyrolytic graphite), and electron beam or electron

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS

Distribution Chamber

589

Load Lock LEED/AES

UHV-STM

RHEED

Analytic Chamber

/ Quadrupol Mass "-'----~ Spectrometer

E-Beam Evaporator Effusion Cells

Fig. 1. MBE systemconsisting of load lock, distribution chamber, growth chamber, and analytic chamber with UHV-STMas indicated.

impact evaporators. The use of high-temperature effusion cells relies on an open cell design to reach sufficient flux at acceptable cell temperatures, which can be as high as 2100 K. The heat transfer is then completely governed by radiation, which has to be taken into account for cell design and thermocouple placement. An accurate measurement of the source material's temperature can be difficult. However, the important parameters for compound growth are the rate ratios of the constituent components, rate stability, and the overal growth rate. Therefore, in some instances an exact knowledge of the absolute temperature of the source material is not mandatory. Because of the high mobility of metal adatoms, the MBE sample heater should be able to sustain temperatures in the low-temperature regime (N2 lq. or 4He lq.). On the other hand, for the growth of refractory metals, often used as templates or buffer layers, temperatures as high as 1400 K can be needed. Such high temperatures are also mandatory for the preconditioning of some substrate materials, like sapphire. Hightemperature annealing is necessary here to form highly ordered surfaces with a well-defined step-edge distribution. These demands can result in a complex sample stage design. Typical growth rates in metals epitaxy vary from about 0.1 ML/s to 5 ML/s (ML: monolayer) but can be much slower in dedicated growth studies focusing on interface effects, pseudomorphism, or surface diffusion. To estimate the residual gas incorporation risk for a given background base pressure, we assume a growth rate of 0.1 ML/s. Especially for reactive metals with high oxygen affinity, like the rare earths or actinides, one

would want to keep the maximum oxygen impurity concentration below the 100 ppm level. Because the maximum growth rate of adsorbants from the residual gas is about 0.5 ML/s at 10 -6 mbar, this puts the upper limit for the base pressure at 5 • 10-11 mbar. On the other hand, in many instances even the incorporation of 0.1% gas impurities in metals is only weakly deteriorating of the characteristic electronic properties of the layers, because of the excellent screening characteristics in metals. Moreover, comparable impurity levels can be present in the source material. These can be enriched or depleted in the growing epilayer, depending on their respective vapor pressure, as compared with the base source material. As a result, even at a higher base pressure, metal layers can be grown that are of high quality structure and electronic properties. Nevertheless, for nucleation, surface diffusion, and morphology evolution, the residual gas pressure will in general exert a strong influence. Furthermore, in semimetallic systems screening is reduced, and the growth at elevated background pressure can result in severe changes in the electronic properties of the epilayersl as compared with bulk crystals. The most common procedure for achieving base pressures in the low 10-11 mbar range is to bake the systems at about 170~ for about 24 h if the interior was exposed to air. Water readily desorbs from the walls at this temperature. An accurate monitoring of the residual gas composition during the bakeout process by mass spectroscopy is desirable. To sustain a low level of background pressure during the growth process, the desorption of adsorbants from the chamber surfaces has to be reduced.

590

HUTH '

i

9

i

9

I

,

I

lowing dependence:

0.30

d

-

T . di 9 -Di -.

IO

0.25

E =

0.20

~'~ ..

r

~\~'-'~~;~,,J~!~~~,~.~,~,,,~'~i~..s,..~ , .',

~

w~'~

~."

~.

' - , '

.:. : "

.....

7"

,

,

. ~ . : . ~ . . . . .r

i-

i]~

~ u ............... Pd ........ A1

9

0.15

0.10

500

1000 time ( s )

1500

2000

Fig. 2. Typical rate protocol for the growth of a UPd2A13 thin film. For clarity, the rates for Pd and A1 are vertically displaced by 0.1 nm/s and 0.2 nm/s, respectively.

This can be achieved by removing excessive heat loads created by the evaporation sources and sample heater, with the use of water cooling shrouds for the evaporation sources and cryopanels for liquid nitrogen cooling, predominantly in the sample region. The individual evaporation sources have to be properly screened from each other. Cross-talk prevention is especially important if materials with vastly different vapor pressures are used. Evaporation control can be realized with various degrees of sophistication, depending on the desired precision in rate control. Oscillating quartz monitors are commonly used with feedback control for electron beam evaporators. Accuracies in the 0.01 nrn/s range at overall growth rates of 0.1 nm/s can easily be achieved. Nevertheless, cross-talk of the evaporation sources in compound growth has to be avoided by proper shielding of the individual rate monitors. More flexibility and rate precision can be realized if a quadrupole mass spectrometer with cross-beam source and channel multiplexing for multiple source control is used. In either case, the monitoring of the actual growth rates over time is advantageous because it offers a direct means of judging the rate stability with regard to short-term fluctuations and long-term drift. Short-term rate instabilities are a drawback of electron-beam evaporators, whereas long-term drift is likely to happen when effusion cells are employed. In Figure 2 the rate protocol for the deposition of a UPd2A13 thin film is presented. The rate control was performed with the use of three shielded, independent vibrating quartz monitors for the constituent elements U, Pd, and A1. On a short time scale the rates fluctuate by about 7%. With a typical deposition rate of 0.2 ML/s this reduces to about a 2.5% standard deviation averaged over the deposition time for one complete monolayer. The reproducibility of the respective rates can be judged by taking the average over 10 film depositions. Standard deviations below 0.7% can easily be obtained. For a given thicknesses di of an individual component, as measured by the vibrating quartz monitors, the resulting thickness of the compound layer d is given by the fol-

Z j cjMj ci Mi

(1)

Pi, mi, and ci denote the density, molar mass, and concentration of the components, p is the density of the compound. 7" stands for the tooling factor, that is, the ratio of arrival rates of evaporant at the substrate and at the thickness monitors (assumed here to be the same for all components). For sticking coefficients below unity this relationship has to be adapted accordingly. To ensure an accurate average rate and stoichiometry calibration, independent measurements of the film thickness and composition should be peformed. This can be achieved by X-ray diffraction in grazing incidence and Rutherford backscattering (RBS), respectively. Because of backscattering from the substrate the application of energy-dispersive X-ray analysis for composition analysis is less straightforward for thin films. Analytic equipment integrated with the MBE process mainly comprises electron reflection in grazing (RHEED) or normal incidence (LEED); the latter is often combined with Auger electron spectroscopy (AES) in retarding field mode. This can be augmented by various spectroscopic methodes in dedicated analytic chambers, such as photoelectron spectroscopy (PES) and scanning probe microscopy (SPM). RHEED has to be regarded as especially helpful for in situ growth analysis. It readily yields information about the various growth stages, such as nucleation and phase formation processes, epilayer orientation, strain evolution, and morphological changes. In situ patterning capabilities based on shadow-mask techniques can be of practical use for electronic transport and tunneling investigations, thus avoiding air exposure of the interfaces. In this context, portable detachable sample chambers for transfer to other experiments under ultra-high-vacuum conditions may be needed. All of these requirements put some demands on the construction of the sample holder stages, heaters, and transfer system with respect to reliability, heat stability, and compatibility. In metals epitaxy the substrates used cover a broad range of materials, ranging from 3d and refractory metals to different semiconductors and insulators, depending on the aim of the research. Dedicated growth studies tend to rely on highly oriented single-crystal metal substrates. But insulating substrates selected for minimal misfit and chemical inertness are also used. In many instances epitaxial-grade sapphire in various crystallographic orientations is preferred, on which excellent epitaxialquality refractory metal buffer layers can be grown. 2.2.2. Characterization

In the following, two valuable tools for structural and chemical characterization are briefly outlined: RHEED and RBS. RHEED offers a very direct means for in situ studies of the growing epilayer with respect to phase formation and crystallographic orientation. Moreover, strain relaxation phenomena and the influence of annealing processes on the films' crystalline coherence and morphology can be analyzed in great de-

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS tail. However, the interaction of the electrons with the crystal surface is strong and nonlinear. As a consequence, the diffraction patterns are often rather complex, with diffuse background, Kikuchi lines, diffraction spots, and streaks all of significant intensity. Even with advanced computational methods the calculation of the RHEED pattern for a given surface is a difficult task [2]. We will therefore limit the discussion to the kinematic approach to RHEED and refer to the literature for a more complete account [3]. RBS offers in many respects a simple means of analyzing sample composition in conjunction with depth profiling. Segregation and interface reaction processes can thus be identified. It is an especially valuable tool for composition calibration of thin films of intermetallic compounds.

2.2.2.1. RHEED The information Obtained in a RHEED experiment represents an averaging process over the longitudinal and transversal coherence length of the electron beam. For an estimate of these lengths, the influence of the energy spread of the electrons and the spatial extent of the electron emitter have to be considered. For a thermoelectric emitter operating at about 2600 K, the resuiting energy spread amounts to AE = 2.45kBT = 0.59 eV, assuming a Maxwell distribution for the emitted electrons. After acceleration of the electrons to an energy E, the resulting spatial extent Axt of the wave packet due to the finite temporal coherence is given by E --

h2 k 2 2me

=~

Ak = k

AE 2E

;

Axt =

2re Ak

(2)

For k the component parallel to the film surface has to be used which amounts to 27r k = kll = --~ cos q~

(3)

where 4~ is the incidence angle of the electron beam on the film surface. Assuming a typical energy of 9 keV and an angle of incidence of 1~ the resulting longitudinal extent of the wave packet is about xt -~ 400 nm. The spatial coherence length is determined by the area of the virtual electron source (crossover region) as seen from the film surface. A sketch of the geometry appears in Figure 3. Any wave packet emitted from a given point of the virtual electron source is coherent and will result in an interference pattern on the screen. Figure 3 shows the travel

591

distance of two wave packets being emitted from the same point of the virtual electron source for a film region of lateral extension Ax. Consider now the two most distant points on the electron source. The interference pattern on the screen will disappear if the difference in the travel distances amounts to ~./2. According to Figure 3 one obtains Ax
io

(13)

the availability of vacant nearest-neighbor sites. Nevertheless, assuming that D(Tm) -- DO exp (

Hd ) "~const. kBTm

(16)

still holds, inserting Eq. (16) into (15) leads to the following linear relationship between T* or Te and Tm"

Tc Tm

ln(D(Tm)/Do) _~ const. ln(c~o/ Do)

(17)

Inspection of Table I shows that such a Te-to-Tm relationship can indeed be identified for all simple metal layers and intermetallic compounds related to the author's work. As can be expected, the epitaxial temperature for intermetallic compounds is enhanced as compared with simple metal films, because for compounds diffusion is slower because of inequivalent adatom sites. For a new metallic system to be grown, the relationship given here might be used to choose an appropriate substrate temperature for epitaxy before growth.

T* and Te are then determined by the following condition" - c*k0 c*

and

or

~ "-- Ce/;0

Ce =

const. > 1

2.4.2. Early Growth Stages

with (14)

Rearranging the terms leads to

( cio'] =

lid

Ink, D0 J

kB Tc

c = (c*, Ce)

and

with Tc -- (T*, Te)

(~5)

Quite accurately, for self-diffusion in metals the diffusion coefficient D(Tm) at the metal's melting point amounts to 10 -8 cm2/s [22]. For surface diffusion the activation barrier for jump processes is reduced as compared with bulk diffusion. This is due to the reduced binding energy at a surface site and

As a recent example of in situ growth studies in the early stages of film growth we discuss the near-interface alloy formation process of the Gd-Fe system. Employing MBE growth and scanning tunneling microscopy (STM) with atomic resolution, Pascal et al. investigated the influence of the W (110) substrate on the formation and crystallographic structure of the cubic Laves phase compound GdFe2 [23, 24]. Alloys and compounds of 3d transition metals and the rare earths are of high technological interest because they offer a wide variety of magnetic properties, ranging from strong magneto-optical active systems to magnetostrictive materials with record strictive distortions at room temperature.

596

HUTH

Fig. 8. Comparisonof the growth of (a) Fe and (b) Gd on W (110) in the submonolayer coverage regime (coverage about 0.25 ML). Scan area 70 x 70 n m 2. Structure modelsbelow the STM images highlight the different growthmodes. Image courtesy of M. Getzlaff. Reprinted with permission from [24], 9 1999, American Physical Society. The experiments were carried out in a two-chamber UHV system. The background pressure during growth did not exceed 4 x 10 -10 mbar. The STM investigations were performed in a separate analysis chamber used to maintain a base pressure below 10 -11 mbar. All measurements were performed in the constant-current mode. Because of the different ionic radii of Gd and Fe, the coverages are given in substrate units. In these units, the first closed Gd layer holds 0.64 monolayers and the first closed Fe layer holds 1 monolayer because of the pseudomorphic growth of Fe on W (110). The first important aspect of the growth of Gd and Fe on W is their widely differing growth morphologies for coverages below one monolayer. Fe forms one-monolayer-high patches on the terraces and stripes along the substrate's step edges, indicating step-flow growth. The Gd atoms, on the other hand, tend to cover the substrate by forming quasi-one-dimensional fingered superstructures [25, 26]. The formation of dipole moments on the Gd atoms induced by a charge transfer from the Gd atoms

to the substrate results in repulsive dipolar interactions. These trigger the formation of the stripe pattern. The surface morphologies for submonolayer Fe and Gd growth are compared in Figure 8. As a consequence of the difference in the layer morphology of the constituent elements in the early growth stages, the formation of GdFe2 is not initiated in the C15 bulk structure of this compound. In a first step the Gd-to-Fe ratio was selected to be approximately 1 : 1. The deposition was performed at room temperature, followed by a 5-min annealing step at 700 K. The resulting film morphology appears in Figure 9. It consists of two regions formed by smooth areas and the Gd-typical onedimensional finger structure. With the Fe content increased to the stoichiometric mixing ratio for GdFe2, the nominal deposition of one monolayer does indeed result in a completely closed and smooth first GdFe2 monolayer on W (110). The corresponding STM image is shown in Figure 10.

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS Subsequent LEED and STM analysis with atomic resolution led Pascal et al. to suggest the following structure model. The Fe and Gd atoms are assumed to occupy the W (110) bridge sites, which were previously shown to be the energetically preferred sites for Fe atoms on top of W (110) [27]. The resulting

Fig. 9. STM image of Gd-Fe alloy with approximately 0.3 ML of Gd and 0.4 ML of Fe. The image was taken in constant current mode. The striped areas represent the Gd superstructure. The stripes are aligned along the [001 ] direction of the W substrate. The smooth areas correspond to an alloy of GdFe2. The scan range is 70 • 70 nm 2, sample bias U = 0.2 V, tunneling current I = 0.3 nA. Image courtesy of M. Getzlaff. Reprinted with permission from [24], 9 1999, American Physical Society.

597

arrangement of atoms is reproduced in Figure 11. Proceeding to the second monolayer, this structure is repeated as shown in Figure 12. As compared with the geometrical arrangement of the Fe and Gd atoms in the bulk C15 structure, the observed layer structure resembles the (111) plane being laterally compressed by 14% in the [110] direction of the W (110)substrate and strained by 5.3% in the [001] direction. Nevertheless, the atomic arrangement of the Fe atoms with respect to the Gd atoms does not correspond to the C15 (111) lattice plane. Because the growth of the isostructural TbFe2 on Mo (110) to larger film thicknesses (to be discussed next) shows the formation of the bulk C 15 structure, a structural phase transition as a function of the film thickness in GdFe2 on W (110) is likely to take place. These STM studies are very well corroborated by RHEED studies of the growth of TbFe2 on Mo (110) [13]. Although RHEED cannot give a comparable degree of information concerning the atomic arrangement of the growing layers, it is very well suited for the study of time-dependent phenomena and relaxation effects. Because of the large magnetostriction in TbFe2, monitoring the strain evolution during growth is essential for assessing the reasons for residual strain present after film growth. This residual strain directly influences the overall magnetic ansiotropy, as will be discussed in the second part of this chapter. The film deposition was performed in a Perkin-Elmer 430 MBE system. After the growth of the Mo buffer layer on sapphire (117.0), the samples were cooled to a temperature range of 450~ to 680~ for deposition of TbFe2 (111). This was accomplished at a growth rate of 0.02 nm/s for film thicknesses of 40 nm to 150 nm, with a background pressure of 1.1 • 10 -1~ mbar. For the RHEED investigation a 10-kV beam with an incidence angle of about 0.5 ~ was used.

Fig. 10. (a) Completely closed and smooth first ML of GdFe2 on W (110). (b) Atomic resolution obtained on this sample (U = 0.18 V, I = 3 nA). (c) Photograph and (d) sketch of the (2, 1; 1, 2) LEED pattern. Image courtesy of M. Getzlaff. Reprinted with permission from [24], 9 1999, American Physical Society.

598

HUTH

Fig. 11. Structure model for the first ML of GdFe2 on W (110). Gd is represented by the large, Fe by the small balls. In the upper part atomic diameters are scaled down by a factor of 2. An atomically resolved STM image is overlaid. In the structure model shown in the lower part the atomic diameters are to scale. Image courtesy of M. Getzlaff. Reprinted with permission from [24], 9 1999, American Physical Society.

The initial growth forms well-defined diffraction streaks. The spacing with the electron beam aligned along [211] indicates that the films are under - ( 1 . 5 + 1.0)% compressive strain, whereas with the beam alignment along [011] a compressive strain of - ( 1 2 . 0 4- 1.5)% is observed. The orthorhombic distortion of the TbFe2 (111) surface amounts to +0.5% and -9.1%, respectively, assuming a perfect accommodation of the Mo (110) template at a typical growth temperature of 550~ It can then be concluded that the TbFe2 surface is not fully pseudomorphic, most probably because of the large elastic strains involved. The epitaxial relationship and registry of the TbFe2 (111) surface on the Mo (110) surface in the strained and relaxed states are depicted in Figure 13d. As shown in the STM studies on GdFe2, the established Fe-to-Gd atomic arrangement is in fact different from the C15 (111) arrangement of the bulk. As the thickness is increased to the 0.8-1.0-nm range, specular intensity shifts into the diffuse background, indicating a loss of long range coherence of the film surface. The RHEED image eventually recovers to show spots along the original diffraction streaks. This evidence for 3D scattering is accompanied by a relaxation of the streak spacing toward the lattice constants of unstrained TbFe2 (111). This roughening transition most probably

Fig. 12. (a) Atomic resolution on the first and second ML GdFe2 on W (110) (U = 55 mV, I = 3 nA). The grating and balls are used to determine the registry between the atoms of the first and second ML. (b) Structure model (top and side views) of the first and second ML of GdFe 2 deduced from the STM images. Image courtesy of M. Getzlaff. Reprinted with permission from [24], 9 1999, American Physical Society.

occurs at the onset of dislocation formation. However, a structural phase transition as a function of film thickness cannot be excluded, as was suggested by Pascal et al. [24]. With increasing film thickness the diffraction pattern evolves back to streaks, which become well-defined at 8 nm. For film thick-

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS

599

Fig. 13. (a-c)RHEEDstudy of the TbFe2 (111) growthon Mo (110) for the filmthickness indicated. The beam was aligned along the [031] direction. (d) Schematic diagram showing the orthorhombic lattice distortion of the TbFe2 (111) surface in the initial pseudomorphic growth stage (dashed lines). Reprinted with permission from [13], 9 1998, American Physical Society.

nesses of 40 nm and more, the diffraction pattern reveals that the surface is flat on the length scale of the longitudinal coherence of the electron beam, namely several hundred nanometers. The RHEED patterns corresponding to the three growth stages are shown in Figure 13a-c. The TbFe2 surface reconstructs through the sequence of 1 x 1, 3 • 3, and then 2 • 2 reconstructions as the temperature is increased from 520~ to 580~ The surface also exhibits (110) faceting, as made evident by RHEED and atomic force microscopy (AFM) measurements. A discussion of these morphological aspects is deferred to the next section.

2.4.3. High Vapor Pressure Materials From the technological point of view, semimetallic pnictides, particularly MnBi, hold some promise for applications in magnetooptical data storage because of their large Kerr rotations [28]. Very large Kerr rotations of up to 90 ~ at low temperatures and in large magnetic fields were also reported for the Kondo semimetal CeSb [29, 30]. However, the main interest here lies in the investigation of the interplay between crystal field effects and Kondo-like electronic correlations despite the low charge carrier density of 0.02 holes per Ce ion. This results in a complex magnetic phase diagram including at least 15 different phases [31, 32]. Thin film investigations currently con-

centrate on the low charge carrier density aspect [33, 34]. The modulation of the charge carrier concentration in a well-defined fashion, employing an electric field effect structure with thin CeSb layers, represents a unique opportunity to vary the typical energy scales, namely the Kondo temperature TK and the N6el temperature TN, without disturbing the coherent nature of the Kondo lattice. Investigations of the growth characteristics presented here for CeSb show striking similarities to III-V semiconductor growth. This is mostly related to the vastly different vapor pressures of the constituent elements. In the following, some aspects of the phase formation and orientation selection mechanisms in MBE-grown CeSb layers are discussed. The growth was carried out by coevaporation of Sb from a Knudsen cell with a p-BN liner and Ce by means of electron impact evaporation from a tungsten crucible onto heated A1203 (112.0). Ce was supplied as monomers from the liquid with a fixed evaporation rate. The availability of adsorbed Sb in various molecular forms on top of the growing epilayer represents the main controlling parameter in the formation of CeSb. At Sb cell temperatures of about 820 K, which resulted in a stoichiometric S b : C e ratio on the growing epilayer, the Sb vapor is predominantly formed by Sb4 [35]. With increasing temperature, thermal dissociation tends to increase the dimer fraction in the Sb flux with equal vapor pressures of the tetramer and

600

HUTH

dimer molecules at cell temperatures of about 1160 K [35]. At these cell temperatures the Sb :Ce ratio is about 100. Before the details of the phase formation and orientation selection processes for CeSb are discussed, a short review of homoepitaxial III-V semiconductor growth is given, with emphasis on GaAs. If the supply of As consists primarily of dimers, the growth proceeds through a physisorbed precursor state with a large desorption probability of the dimers. In the presence of Ga, dissociative chemisorption results in the formation of G a - A s bonds. Stoichiometric GaAs growth is ensured because excess As2 readily desorbs from the surface, even at substrate temperatures as low as 200~ For a dominantly tetramer supply, a transition to a chemisorbed As4 pair state was proposed before the dissociation process sets in on adjacent Ga sites. Desorption of excess As results again in the formation of stoichiometric GaAs. This transient behavior in the phase formation process was studied in great detail by means of modulated beam mass spectrometry [36]. For CeSb some similarities can be noted with regard to the following observations. If Ce-Sb intermetallics form on A1203 (1120), regardless of the Sb:Ce flux ratio, only CeSb is stabilized analogously to III-V compound growth. This was checked by RBS with 4He+ ions at 2 MeV. Nevertheless, the influence of the Sb molecular state and evaporation rate on the phase formation is more complex than in III-V materials. First, for the heteroepitaxial growth on A1203, CeOx formation appears to be a competitive process. In contrast to Ga, Ce is a highly reactive metal. Second, the preferential CeSb orientation for stoichiometric Sb supply is (111), despite the lack of symmetry adaption to the A1203 (1120) surface. The (111) orientation is suppressed and (100) growth is favored for increased Sb dimer supply. As a result, the phase formation-orientation diagram shows re-entrant-like behavior for the CeSb phase formation and a change in the preferential orientation, depending on the Sb molecular state. This is presented in Figure 14.

Fig. 14. (a) Sb tetramer-to-dimer ratio as a function of the Sb cell temperature. (b) Comparison of CeSb growth rates in the different growth regimes as indicated. The Ce evaporation rate and substrate temperature were fixed.

As a first step in analyzing this growth behavior, the following model for the phase formation process is suggested. (In all cases discussed here the Ce evaporation rate was fixed and the substrate temperature was held constant at 1200 K.) The re-entrant behavior for the CeSb phase formation and the orientational preferences are governed by two factors that are inseparably connected for the Sb supply process employed here. These factors are the Sb tetramer-to-dimer ratio and the respective overall Sb evaporation rate. For pBN liner material a catalytic Sb4-to-Sb2 dissociation can be neglected [35]. The molecular distribution is therefore determined by the cell temperature alone, as indicated in Figure 14. The rock-salt structure of CeSb implies a tetrahedral next-nearest-neighbor configuration of equivalent atoms. The geometrical arrangement of adatoms in (111) orientation then suggests that Sb4 can transfer from a precursor state (or even a Sb4 pair state, as proposed for As in GaAs) to a chemisorbed state in the CeSb surface. The triangular base layer of Sb4 can align parallel to the surface, leaving the pyramidal top atom for dissociation as an Sb monomer. Alternatively, two or four next-neighbor pyramidal atoms might form dimerized or tetramerized states, which will then desorb or occupy an available nearby triple site. Ce monomers fill in accordingly to complete the (111) stacking sequence, provided that the Ce-to-Sb ratio is close to 1. This will then proceed without significant CeSb (100) and CeOx formation and represents the dominant growth process in the low-flux and large tetramerto-dimer ratio region of the phase diagram. The other limiting case is given by Sb2-to-Sb4 ratios close to 1 in conjunction with an Sb arrival rate that exceeds the Ce rate by about two orders of magnitude. In this case, Sb dimers in the precursor state can proceed to a chemisorbed state on the (100) surface. The formation of CeOx is suppressed because Ce adatoms will very probably find Sb next neighbors because of the large arrival rate of Sb on the surface. Moreover, the overall growth rate for CeSb is reduced because the inclusion of tetramers in the formation of the (100) surface is kinetically limited as a competitive process to direct inclusion of dimers. Two-thirds of Sb adatoms will therefore tend to desorb. Furthermore, RBS experiments showed that the Ce-to-Sb ratio in these films is still 1. This implies that the sticking coefficient of Ce is also significantly reduced. As a result, the growth rate is reduced to about one third of the growth rate observed for (111) growth. This corresponds very well to the experimental observation as presented in Figure 14b. The geometrical adatom arrangements for the two limiting cases described above are shown in Figure 15 for reference. In the high-flux regime the crystal quality tends to degrade because the large Sb arrival rate hinders surface diffusion. Between these limiting cases the overall Sbx supply is too large to allow sufficient formation probability for the (111) stacking sequence, which necessarily contains pure Ce layers. No shortrange ordered state of either (111) or (100) character can readily be formed. As a result, an increased tendency toward CeOx formation is observed. For further investigations, and to evaluate the present model, which is based mainly on geometrical considerations, the sep-

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS

601

Fig. 15. Scenario for the geometrical adatom arrangement on the CeSb (100) surface (left) and CeSb (111) surface (right).

aration of the tetramer-to-dimer ratio from the overall Sb evaporation rate is desirable. This suggests the use of a cracker cell, thus allowing the increase of the dimer contribution to the flux by catalytic Sb4 dissociation in a separate hot zone. Keeping the overall Sb evaporation rate fixed, this could be used to tailor the orientation of the growing phase to be either (111) or (100). Very likely, these observations are relevant for the growth of manganese pnictides as well. They might offer a means of controlling epitaxy in these technologically promising materials.

2.5. Epitaxial Strain Strain exerts several influences during epilayer growth. It can influence the energy balance in the phase formation process so that the growth of metastable phases becomes possible. The growth of metastable Fe layers on various substrate materials and in a variety of orientations represents a prominent example [37]. Strain, furthermore, can drive morphological instabilities that result in uniaxial or bidirectional corrugation effects (mound formation) that allow the relaxation of strain energy balanced against an increase in surface energy [38]. It can cause phase segregation effects that result in regular stripe domain patterns, as was recently demonstrated for the Fe/Co-Ag system [39]. The natural limit for these phenomena is given by the onset of dislocation formation. Isotropic metallic bonding resuits in very small activation barriers for dislocation formation. Consequently, for homogeneous epilayers strain can hardly be sustained beyond the critical film thickness beyond which strain relaxation sets in by the formation of interfacial dislocations [40]. Dislocation formation will generally result in an increase in rotational disorder; for example, small-angle grain boundaries are formed when glissile dislocations arrange on top of each other. The mosaicity and long-range coherence of the crystal are correlated with its strain state.

In semiconductor and metal epitaxy the establishment of a specific strain state can be desirable. Most often, this is not so with regard to the morphological changes strain can cause, because these frequently result in an unwanted increase of roughness. Nevertheless, the better our understanding of straininduced roughening phenomena becomes, the better are the chances of finding specific applications of these effects in a controlled way. This can be considered a means of patterning on the nanometer scale based on self-organization effects. Below are several examples of strain relaxation phenomena. RHEED and X-ray diffraction studies of the growth of Ti (0001) layers on large and small misfit substrates will serve to discuss some aspects related to strain relaxation phenomena and the critical thickness. We also briefly discuss the correlation between rotational disorder and the film's strain state.

2.5.1. Growth of Ti Layers on Large and Small Misfit Substrates

This study focuses on hcp Ti (0001) grown by MBE on symmetry-compatible MgO (111) with the rock-salt structure, and on A1203 (0001), which is quasi-hexagonal [41 ]; these represent small ( - 1 % ) and large (+6.8%) misfit substrates, respectively. The initial stages of the film growth were monitored by RHEED, and the characterization was augmented by X-ray diffraction and AFM. The morphological aspects are postponed to the next section. The thin films were deposited by electron beam evaporation of Ti in a Perkin-Elmer 430 MBE system with a base pressure of 2.5 x 10 -11 mbar, which increased to about 6.5 x 10 -1~ mbar during growth, mainly because of hydrogen release from the Ti melt. Deposition was maintained at 0.03 nrn/s to overall film thicknesses of 30 nm or 80 nm. Before deposition the substrates were heated to 1000~ in 1 h, kept there for 30 min, and then cooled to the growth temperature. RHEED measurements were

602

HUTH

Fig. 16. (a) RHEED intensity oscillations for a Ti thin film sample grown on MgO at 600~ The intensity was integrated over a rectangular region around the specular spot. RHEEDimages were taken after deposition of one monolayerof Ti on (b) MgO and (c) A1203. (d) RHEED image taken after growth, showing the 2 x 2 surface reconstruction (beam I1[1120]). Reprinted with permission from [41], 9 1997, AmericanInstitute of Physics. performed at 9 keV with an incidence angle of about 0.5 ~ Film growth was monitored by RHEED imaging and intensity measurements. A computerized data acquisition system was used to integrate the intensity of the specular beam over a predefined integration window. X-ray measurements were later performed ex situ with the use of a two-circle diffractometer with Cu-K~ radiation, and an in-plane resolution Aqll/ql I -- 1.6 x 10 -3. RHEED measurements following the completion of one monolayer Ti on MgO reveal well-defined diffraction streaks characteristic of two-dimensional growth, as shown in Figure 16b. Layer-by-layer growth is also suggested by the appearance of intensity oscillations of the specular reflection for substrate temperatures in the range 400~ _< T _< 600~ (see Fig. 16a). These oscillations are caused by periodic variations in the step-edge density and are believed to occur only in regimes of strong surface diffusion between terraces [42]. Throughout the entire deposition period no damping of the oscillation amplitude was observed. The oscillation period corresponds to the full c axis spacing of hcp-titanium, as determined by comparison with an independent thickness calibration by RBS. After about six monolayers the intensity breaks down, but it recov-

ers after another two monolayers. For lower growth temperatures the amplitude of the intensity oscillations is reduced, most probably as a consequence of reduced interterrace adatom diffusion. For the highest growth temperature of 650~ a step edge flow growth mode with constant step edge density can account for the observation that the intensity oscillations are suppressed [43]. Within the instrumental resolution of the RHEED experiment, no lattice parameter relaxation of the growing Ti film was observed. However, X-ray diffraction studies showed that the Ti lattice constants were completely relaxed to their bulk values for the 30-nm- and 80-nm-thick films, regardless of growth temperature from 340~ to 650~ Based on these RHEED results it can be concluded that the Ti growth on the low-misfit substrate MgO (111) starts in a layer-by-layer mode until a critical thickness is reached. This is followed by the nucleation of dislocations that allow the Ti lattice constants to relax to their bulk values. With the use of the Matthews and Blakeslee model [44-46], the critical film thickness tc for dislocation formation based on the (112,0) {0001} slip system of Ti for perfect edge dislocations is given by tc - (aTi/8zr(1 + v)E)ln(ottc/aTi)

(18)

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS where ot is the dislocation core energy parameter, E = -0.01 is the lattice misfit at growth temperature, v -- 0.33 Poisson's ratio, and the basal plane lattice parameter of Ti is awi. Assuming that the break in the specular reflection at 2.8 nm signifies the critical thickness, this results in a deduced dislocation core energy parameter of c~ = 2.5. This value represents rather an upper limit because the activation energy for formation of dislocations can result in a sustained supercritical state of strain. In contrast, Ti growth on A1203 (0001) was observed to proceed through three-dimensional nucleation, as deduced from the spot-like intensity enhancements on the RHEED diffraction streaks after completion of one monolayer, as shown in Figure 16c. No RHEED oscillations were observed, nor were any pronounced damping or recovery effects in the specular beam intensity, so no evidence exists for a crossover regime in the surface morphology in this case. Independently of the substrate material, RHEED images taken after growth at room temperature revealed no appreciable differences for the different growth conditions. In each case well-pronounced surface resonance features in the form of Kikuchi lines indicate a well-ordered surface (see Fig. 16d). At the highest growth temperature of 650~ or with heating of the films above 620~ after growth, a stable 2 • 2 surface reconstruction was observed. The high intensity of the superstructure reflections tends to indicate a reconstruction of the Ti top layer itself, as opposed to a possible regular arrangement of a surface adsorbate. However, the high adsorption probabilities for the residual gases N2, O2, and H2 on the Ti surface suggest, to the contrary, an adsorbate-induced reconstruction. This question must remain for future resolution. According to the X-ray diffraction analysis the epitaxial relationship between Ti (0001) and the substrates MgO (111) and A1203 (0001) is compatible with an adatom geometric arrangement of minimal misfit with Ti [ll,20]llMgO [101] and Wi [ 112.0] 11A1203 [ 1 i00]. Films of various thicknesses showed a sharp specular and a broad diffusive component in transverse scans (rocking curve) at the Bragg positions (0002) and (0004) for films of 30-nm thickness. This is shown for Ti grown on MgO and A1203 in Figure 17. The respective rocking curve widths of the sharp components are resolution limited. The broad components are characteristic of rotational disorder, with fixed angular width independent of the magnitude of the perpendicular component of the scattering vector. The width of the broad component for films grown on sapphire is independent of growth temperature with FWHM ~ 0.45 ~ whereas for films on MgO the width follows a nearly linear dependence on the growth temperature and decreases from 0.25 ~ to 0.16 ~ for growth temperatures ranging from 340~ to 650~ As can be seen in the inset of Figure 17b, the Bragg scan of the (0002) reflection of Ti on sapphire is shifted to a lower scattering angle. Thus a 1.7% increase in the c lattice parameter of Ti is caused by clamping to the substrate. The asymmetric shape of the thin film oscillations visible on the high-angle side of the (0002) reflection might indicate that a strain field gradient exists along the Ti c axis as a consequence of incomplete strain

10000

~-

I

'

I

'

I

603 '

I

'

Ti on M g O (1 1 l)

I

'

I

'

I

(OOO2)

1000

&

ca~ 100

(a) I0

I

,

-0.4 5 1 0 0 0 0

,

Ti ~

I

,

-0.10 ,

I

,

-0.05

I

,

,

0.00

I

,

I

0.05

,

i

0.10

0.4 5

~i, 0002)10000.[ . . . ~A ...... A1203 ( 0 0 0 1 ~ ~ ,

,

,

t

1000

,

,

,

.

,

,

,

~,:oo4~~ 100r "

.Jr'

. l,IWltk

,,~f

rl. lo"'

,~,~'llbJ

~I 6

~ '

9 ,

~'

,

",Irl ....

I. . . .

"

~

~o,

to)

100

10

-0.15

.

-~

I

,

-0.10

I

-0.05

,

I

0.00

,

I

0.05

,

I

0.10

,

I

0.15

0.20

Aq,(A ) Fig. 17. Rocking curves for 30-nm-thick Ti on (a) MgO and (b) A1203, grown at 650~ The inset in (b) is a Bragg scan through the Ti (0002) reflection. The dashed vertical line corresponds to the peak position for the c lattice constant of bulk Ti. Reprinted with permission from [41 ], 9 1997, American Institute of Physics.

relaxation toward decreasing c at the film surface. For films of 80-nm thickness the peak position corresponds to a fully relaxed film. No evidence for residual strain was found for films of 30-nm and 80-nm thickness on MgO. The occurrence of a two-component line shape in transverse scans of metal [47-49] and semiconducting [50] films with weak disorder was observed only recently. In the present case it can be inferred that long-range structural coherence in the film plane gives rise to the narrow component; the broad background component is characteristic of rotational disorder or mosaicity [51 ]. Both components can be described by introducing a displacement-difference correlation function, 2crZ(r) = ( [ u z ( r ) - Uz(0)] 2)

(19)

that describes displacements Uz along the film normal ~" for any given in-plane distance r. The resulting differential cross section separates into two Debye-Waller-like contributions that represent the narrow and broad components [51, 52]. Because

604

HUTH

of an exponential damping the narrow component is visible only for weak disorder and is most pronounced for small momentum transfer qz. If the reduction of the in-plane structural coherence is ascribed to dislocations in the film, the more pronounced sharp component for films grown on MgO is a consequence of the small lattice misfit. The curves shown are not corrected for qz-dependent instrumental resolution.

2.5.2. Strain and Crystalline Coherence in Epitaxial UPt3 Layers on SrTi03 Strain is an important parameter for heavy-fermion systems, because the hybridization of f-orbitals with itinerant states sensitively determines the electronic properties of the material [ 10]. In heavy-fermion thin films strain can be used to alter the heavy-fermion characteristics in a controlled way, but it might also be an unwanted effect. The investigation of the strain state of a given thin film sample is therefore an integral part of the characterization process. As an example, the correlation between biaxial strain and the long-range crystalline coherence in UPt3 (0001)-oriented films on symmetry-adapted SrTiO3 (111) is briefly discussed. As was already shown for the growth of Ti (0001) on MgO and A1203, the concept of a simple mosaic crystal for epitaxial thin film samples has to be revised. The correlation length for rotational disorder in thin films is reduced as compared with bulk samples. This is due to the fact that reduced interfacial displacements are a consequence of epitaxy. A sharp component in transverse X-ray scans then arises from a structurally coherent contribution that is not present in the simple mosaic model. This narrow component is overlaid by a broad mosaic contribution. The more dislocations that are formed during the strain relaxation process, the more pronounced the mosaic contribution becomes. An example of this is shown in Figure 18

.5

.....

"

I

"

I

"

I

' 4 UPt 3 (0002)

0.0 ",~

~

3

.'=

2

=

1

A "

-0.5 ~. -1.0

"'.~

-1.5

.

0

J

J 17

"-.

1'8 ' 19 co ( d e g )

" ' " - .

20

-2.0 -2.5 9

0.0

I

0.1

,

I

0.2

,

I

0.3

,

I

0.4

~

I

0.5

,

I

0.6

A n a r r o w /A m o s a i c Fig. 18. Strain-coherence correlation of (0001)-oriented UPt3 films on SrTiO3 (111). The normal contraction is shown versus the area ratio of the coherent and mosaic component of the (0002) rocking curve of UPt3. Inset: A typical (0002) rocking curve of UPt3 on SrTiO3 (111) for reference.

for c axis-oriented UPt 3 layers on SrTiO3 as the relative normal lattice contraction versus the area ratio of the narrow and broad component of the (0002) reflection of UPt3. Despite the strong scatter in the data, owing to the different defect structures present in different samples, the correlation is obvious. Larger strain or, equivalently, less dislocation formation results in a more pronounced long-range coherence of the lattice. The functional relationship between residual strain fields and the mosaic structure is very specific to the system under investigation. It is analyzed in more detail by lateral mosaicity studies that allow the identification of the dominant relaxation process [53].

2.6. Morphological Aspects The evolution of surface morphology is governed by several processes, which are often interrelated. The substrate or template surface microstructure (miscut, step-edge distribution, defect types, impurities, etc.) strongly determines the onset of dislocation formation and its lateral distribution. The resulting surface morphology of the growing epilayer will therefore vary, depending on the substrate preprocessing [54]. Furthermore, kinetically driven surface instabilities, like mound formation, can result if there is a diffusion barrier (Ehrlich-Schwoebel barrier) at the step edges. Moreover, the visitation frequency of the diffusing adatoms at the step edges has to be low to obtain an increased probability for the formation of stable islands on the terraces [38]. Mound instabilities can therefore be avoided if substrates with a large miscut (i.e., a high step edge density) are employed or, alternatively, surfactant assisted growth can be realized. Substrate temperature increase, although an additional possible path to the stabilization of step-flow growth instead of mound formation, may very often be impracticable because of interface alloying or other degradation effects. Because, loosely speaking, compressive strain tends to enhance surface mobility whereas tensile strain lowers diffusion, the epilayer's strain state and the appearance of surface instabilities will in general be mutually dependent [38]. These aspects of surface morphology evolution are common to all metal layers. Specific to alloys and intermetallic compound thin films are segregation phenomena that can create regular chemical and morphological patterns [39, 55]. In the following a small selection of surface morphologies that can be found in metal epitaxy is given. First, the influence of the substrate's microstructure on the film morphology is discussed. The influence of strain and its relaxation is presented next. Finally, a new promising pathway for the selection of one specific stacking variant of (111) oriented fcc layers is outlined.

2.6.1. The Influence of the Substrate and Template Morphology One of the most often employed insulating substrate materials is A1203. Epitaxial-grade sapphire is widely used in rare earth epitaxy in conjunction with adquate buffeting [56, 57], but it is also an indispensable substrate material for the semiconductor industry. The necessary mechanochemical polishing

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS

605

Fig. 19. Atomic force microscopy analysis ofA1203 (0001) (a)as supplied and (b) annealed in air. Ta layers grown on A1203 (0001) substrates (c) as supplied and (d) annealed in air. Data were acquired in contact mode.

process results in a topmost layer with an irregular corrugation and crystallographic defects. To enhance the epitaxial growth on these substrates, flatness on the atomic scale and a wellordered step edge distribution on vicinal surfaces are desirable. Vacuum annealing above 1000~ is known to improve the crystallinity of (0001), (11),0), and (1102) surfaces [56], whereas it results in faceting of A1203 (1100) [58]. Moreover, annealing in air at temperatures between 1000~ and 1400~ results in the formation of atomically flat terraces separated by a regular arrangement of step edges [59]. The step edge height is uniformly 0.22 nm, showing a tendency toward step bunching at elevated annealing temperatures. An AFM analysis in air, presented in Figure 19, shows the result of 12 h of annealing of A1203 (0001) in air at 1200~ Ta (110) template layers grown

on as-supplied and on annealed A1203 (0001) exhibit a pronounced change in surface morphology (see Fig. 19c and d). Because the epilayer morphology strongly depends on the template, the controlled preparation of the substrate surface before growth offers one pathway to the realization of different surface morphologies. As an example, the microstructure of TbFe2 (111) surfaces on Mo (110) templates can be varied by changing the molybdenum morphology. This can be achieved by inserting an additional Ta (110) buffer layer before the Mo growth. The resulting alteration of the TbFe2 morphology is presented in Figure 20. The percolation network in which Mo grows on sapphire is reproduced in the magnetic layer. When the magnetic layer is grown on the much smoother Mo-Ta template, however, the structure is dominated by largely isolated

606

HUTH

Fig. 20. AFM images of (a) 40 nm of Mo (110) grown on 30 nm of Ta (110) on sapphire (112.0); and (b) 40 nm of Mo (110) grown directly on sapphire (112.0). The arrow indicates the Mo [001] direction. (c) and (d) show the surface morphologies of TbFe2 (111) grown on these templates. The film thickness is 50 nm in both cases. The arrows indicate the TbFe2 [112.] direction. Reprinted with permission from [13], 9 1998,American Physical Society.

islands that reflect the symmetry of the TbFe2 (111) surface. In both cases the grooving between TbFe2 islands is pronounced, with a depth that is 60% of the nominal film thickness. The microstructure shows no dependence on the miscut of the sapphire substrates, which varied in the present case from 1.5 ~ to 0.2 ~ The pronounced island structure of TbFe2 films grown on Mo-Ta templates exerts an important influence on the magnetic hysteresis, as will become evident in the next section.

2.6.2. The Influence of Temperature and Strain The sequence of AFM images shown in Figure 21 reveals a pronounced morphological change as Ti (0001) is grown on MgO (111) at various substrate temperatures. The strong in-

fluence of substrate defects blocking the propagation of the Ti growth fronts, causing step edges to bend, is strongly reduced with increasing substrate temperature. The direction of the step edges corresponds to the directions of substrate miscut. At the highest temperature the step edges follow the sixfold symmetry of the Ti (0001) surface. The growth is dominated by strong interlayer diffusion, which points to a reduced importance of the Schwoebel-Ehrlich barrier [60, 61 ] at the step edges as the thermal energy increases with substrate temperature. The surface free energy of the films is reduced by the formation of welldefined facets with step edges along the hexagonal symmetry directions. Unlike these results for MgO, the surface morphology for Ti grown on A1203 (0001) is stable against changes in the substrate temperature and exhibits reduced island diameters

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS

607

Fig. 21. Sequence(a-d) of AFM images for Ti on MgO (a-c) and A1203 (d) grown at the different substrate temperatures shown. The substrate miscut was 0.6-0.8~ for MgO in directions shown by white arrows and 0 and antiferromagnetic order for x < 0 [135, 136]. The magnetic ordering temperature varies with x, reaching a maximum Nrel temperature of TN = 270 K in the antiferromagnetic region and a maximum Curie temperature of Tc = 385 K in the ferromagnetic region. Recent investigations on (110)-oriented textured thin films with a composition close to x = 0 showed evidence for a FM-AFM phase separation process resulting in a large effective FM-AFM surface area [137]. Exchange-bias effects were observed in these films at low temperature, as presented in Figure 34. Proceeding now to the preparation of epitaxial FM-AFM heterostructures on sapphire substrates with varying step edge density, it might be possible to identify the individual control parameters for the exchange-bias effect in a systematic fashion. Neither interface strain nor chemical incompatibilities should play a role in this layer system. 3.6. Antiferromagnetic Order Parameter Nucleation on a Thin Film Surface

Information about phase transitions on a microscopic scale can be gained from scattering experiments. This is due to the fact

619

that the scattering cross section is proportional to a two-site correlation function [ 138]. In this and the following section two examples are given that might help to illustrate this fact. For the interpretation of diffraction experiments on synchrotron light sources the probe coherence volume has to be taken into account. In particular, when the probe coherence volume approaches that of microscopically ordered regions in the sample, information about the location of the source of scattering below the sample surface can be obtained. In an experiment performed by Bernhoeft and collaborators [ 139] on the beamline ID20 at the European Synchrotron Radiation Facility, coherence effects in conventional high-resolution diffraction with partially coherent illumination were studied. The experiment utilized the fact that close to an absorption edge the absorption length can be made significantly smaller than the dimension of the coherently diffracting volume. In such circumstances the beam attenuation has to be taken into account at the level of the scattering amplitude instead of the scattered intensity. A technique of resonant magnetic X-ray scattering was employed that relies on the enhancement of the magnetic scattering cross section as the photon energy is tuned to an absorption edge. To be more specific, (001)-oriented thin film samples of the heavy-fermion compound UPd2A13 were analyzed. UPd2A13 shows antiferromagnetic order below TN = 14 K. The uranium moments are ferromagnetically aligned in the hexagonal basal plane, and they are stacked antiferromagnetically in the c axis direction. The beam line energy was tuned to the M4 absorption edge of uranium at 3.73 keV. At the M4 edge the absorption length is about 200 nm. Consequently, the change of the probe wave amplitude within the diffracting volume has to be taken into account because the longitudinal coherence length of the beam is generally larger than 1 /zm. As a result, the line shape of an energy scan I (E) about the absorption edge at the magnetic Bragg peak (0 0 1/2) depends on the number N of coherently scattering lattice planes. Basically, the observed broadening in the I (E) line shape with increasing N can be understood to arise from a reduction in the effective scattering volume at the resonant energy. This was studied systematically by analyzing the I (E) profile on a series of UPd2A13 films of varying thicknesses ranging from 10 nm to 160 nm. In a quantitative analysis the necessity to include the absorption in the scattering on the amplitude level could be beautifully verified. This is shown in Figure 35. Furthermore, a microscopic scenario for the nucleation of the antiferromagnetic order parameter in the films could be derived from an analysis of the temperature dependence of the magnetic Bragg peaks [140]. Transverse 0-scans and longitudinal L-scans were performed at the magnetic Bragg peaks (001/2) and (00 3/2). From longitudinal scans the magnetic correlation length c/AL in the c axis direction could be deduced from the observed peak width AL. At sufficiently low temperatures the longitudinal magnetic correlation length was shown to be identical to the structural correlation length as deduced from the respective scan at the (001) reflection. However, transverse scans revealed an enhanced peak width A0 as compared with the structural reflection at all temperatures be-

620

HUTH i

_

_

i

i

t

i

I

i

I

i

U P d AI films 2 a

9 ..... ~

>

i

i

i

1

i

i

i

i

I

bulk value

expt coh calc l i n e a r calc

~

/

~'

~

-

i

i

i

i

1

i

1

1

~. ~-~''~'''-'-"--~ -

(001/2)

aa~ ~1600 A

_

E l--

_

'

l--

(003/2)

_

800

(001/2)

800 A

,,

A

t

\

_

"

~

~(003/2) 1600 A (001/2) 75 A 2 100

I

(001/2) 350 A

(001/2) 240 A [

i

I

I

I

I

I [

1

1

I

I

I

1000

I

I

I

]

104

I

i

i

i

t

i

i

i

Without going into too much detail, two examples are given below that highlight order-disorder phenomena on surfaces of ordered alloys grown in situ by an MBE process. Thin film studies of these phenomena offer the advantage of freshly prepared crystal surfaces available before to the investigation. Furthermore, the combination of surface sensitive diffraction techniques can be applied to study the order-disorder transformation in great detail. As a first example, resonant RHEED studies of the surface order of Cu3Au (111) films performed by Bonham and Flynn are briefly reviewed [143]. Second, a recent investigation of critical phenomena at FeCo (100) surfaces by Krimmel et al. is taken up, which employed an advanced X-ray scattering technique [ 145, 146].

,

10 s

t/sin(e) [A] Fig. 35. HWHM of energy profiles vs the optical path of the antiferromagnetic peaks of various UPd2A13 thin films taken at T = 4 K (t: film thickness, 0: Bragg angle for a reflection). The scans were performed at the uranium M4 absorption edge. The dashed line is the numerical simulation in the coherent approximation, and the solid line corresponds to a classical (incoherent) summation, as discussed in detail in [ 139]. Image courtesy of N. Bernhoeft.

low TN. This deduced lateral magnetic correlation length was shown to be considerably smaller then the structural correlation length of about 1 /zm. Taking the width A0ch of the (001) reflection as a measure of the mosaic spread of the films and the diffractometer resolution, a simple quadratic deconvolution was used to obtain the lateral magnetic correlation length 2c/AO. At low temperatures 2c/A0 corresponded to the film thickness. With increasing temperature the energy width AE, 2c/A0, and c~AL increased, whereas the ratio AL/A0 remained constant. This behavior is consistent with the assumption that the magnetic order initially develops on the film surface and penetrates into the bulk as the temperature is lowered. In the same framework we consider next order-disorder phenomena on surfaces of thin films of ordered alloys. 3.7. Order-Disorder Phenomena Surfaces modify the symmetry and dimensionality of orderdisorder phenomena and can significantly alter phase transitions and their associated critical behavior [141,142]. In a discussion of critical behavior, the appearance of novel universality classes can be parameterized by an additional scaling field that quantifies the extent to which the interactions at the surface are changed with regard to their value in the bulk. If this interaction is reduced, order at the surface sets in at a temperature below the bulk critical temperature Tc(b). In contrast, for enhanced interactions an ordered surface layer will be established above Tc(b), which is then floating on the disordered bulk. This surface layer, being a natural two-dimensional system, will show a 2D phase transition whose critical exponents will, in general, be very different from the 3D transition in the bulk.

3.7.1. Surface Order of Cu3Au (111) Films The order-disorder transformation in bulk Cu3Au takes place at about Tc(b) - 395~ above which the crystal exhibits an fcc order, with the Cu and Au atoms occupying the sites at random. Below Tc(b) the Au atoms segregate to one of the four possible fcc sites. Consequently, the formation of a single-domain ordered crystal must proceed through a two-step process. The fast nucleation of four equivalent ordered domains is followed by a slower ripening process in which one domain grows at the expense of others [143]. The order parameter, ranging from zero to unity as the order increases, can be specified as follows [147]: 69 -- p - Pd Po -- Pd

(28)

in which p signifies the actual propability of finding the Au atom at the correct site. Pd is the occupation probability in the disordered state, and Po is the probability in the ordered state. To be able to measure the order with surface sensitive probes, the selected surface orientation should not exhibit strong segregation of one constituent element. In this respect, Cu3Au (111) is ideally suited, because the unperturbed (111) planes have the same stoichiometry as the bulk crystal. Inherent composition changes during the phase transformation are therefore not to be expected. RHEED investigations of order phenomena are advantageous because of their extreme surface sensitivity with regard to the average periodicity of the surface net. The average penetration depth at about 10 keV under grazing incidence, as was discussed earlier, is only a few atomic layers. Nevertheless, highly complex diffraction patterns comprising contributions from the main Laue reflections, surface resonance features (Kikuchi lines), diffraction spots, and diffuse background scattering render any quantitative analysis very difficult. Furthermore, the interaction of electrons with the crystal surface are strong and nonlinear. In some instances, as is the case in the work reviewed here, a quasi-kinematical approach is sufficient to model and interpret the results. In the quasikinematical approach the kinematical description of RHEED is augmented by a temperature-independent correction that takes dynamical phenomena, such as surface resonance effects, into

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS

621

Fig. 36. RHEED diffraction patterns taken under surface resonance conditions, as a gray scale image and surface plot. The beam is aligned along the [150] axis. (a) 4-2 resonance. (b) -t-3/2 resonance. Reprinted with permission from [ 143], 9 1998, American Physical Society.

account. For details we refer to the orginal work by Bonham and Flynn [ 143]. The samples used in this research were grown by MBE onto epitaxial-grade A1203 (11,20) with Nb (110) buffer layers of 50 nm thickness that act as a template for the nucleation of Cu3Au (111). The RHEED investigations were performed with a Perkin-Elmer 10-keV electron gun and a computerized data acquisition system. The electron beam was aligned parallel to the [110] direction. Independently of the order parameter, the structural refections for the (111) surface are (00), (10), and (10). If the surface is chemically ordered, the most prominent superstructure reflexions are (1/2 0) and (1/2 0), which were used for the order-disorder analysis. The intensities of these superstructure reflections are proportional to the square of the surface order parameter Os. A typical diffraction pattern appears in Figure 36. As the central result of this work, the critical exponent for the temperature dependence of the order parameter was deduced from the temperature-dependent evolution of the superstructure scattering intensity at and below the ordering temperature Tc. For a second-order transition (i.e., a continuous evolution of the order parameter), Os(T) is predicted to follow a power law

Fig. 37. Normalized RHEED superstructure peaks as a function of temperature for three different data sets. The intensities are proportional to the square of the surface order parameter. The empty and filled circles are taken from the (1/2 0) and (1/2 0) diffraction spots, respectively. The value of the critical exponent 13 is determined from the fits. + and x represent the data from the diffraction spots not used in the fit. The surface order reaches saturation at about 150 K below the transition temperature. Reprinted with permission from [ 143], 9 1998, American Physical Society.

behavior below the critical temperature: Os(T) oc

Tc- T Tc

(29)

The bulk order-disorder transformation of Cu3Au has to be of first order for symmtry reasons [148]. However, the crystal symmetry is broken at the surface, which can result in a different order of the phase transition. Indeed, the research reviewed here unambiguously finds a critical exponent of 0.51 4- 0.03, which is in excellent correspondence with the mean field value 0.5 (see Fig. 37).

3. 7.2. Critical Phenomena at FeCo (100) Surfaces In the work by Krimmel et al. [144, 145], to be discussed next, X-ray scattering using synchrotron radiation was employed to

622

HUTH

Fig. 38. (a) Structure model of ordered FeCo. (b) Order parameter profiles associated with surface-enhanced order for T > Tc and T < Tc (surface order parameter Os, bulk order parameter Ob, lattice constant a). (c) Schematics of the temperature dependence of the bulk and surface order in the presence of a surface field hs. See text for details.

study the continuous B2-A2 order-disorder transition of the FeCo (100) surface. In this work the authors could clarify two aspects specific to this surface phase transition. First, the surface layer undergoes a order--disorder transition at a temperature Tc > T(b). Second, the critical behavior of this surface layer is not caused by an enhanced surface coupling but is induced by surface segregation. The binary alloy FeCo undergoes a continuous orderdisorder transition from the B2 (CsC1) structure below Tc~b) _~ 920 K to the A2 (bcc) structure above Tc~b) in a wide composition range [149]. In the B2 structure the normal direction of FeCo (100) consists of alternating A- or B-type layers. Because Fe-Co nearest-neighbor configurations are favored by the internal interactions, the surface segregation of either Fe or Co will induce an alternating layering into the bulk, starting with a second layer of the other type. This corresponds to a non-zeroorder parameter. According to Monte Carlo simulations [ 150] and field-theoretical studies [ 151 ], an alternative scenario, besides enhanced surface interactions, can induce the surface order transformation before bulk ordering sets in. This scenario is based on a surface field hs induced by the segregation of one atomic species, which stabilizes an order parameter profile as indicated in Figure 38. As a result, the temperature dependence of the order parameter should not follow the behavior indicated in Eq. (29), but should show a leading temperature dependence of the form

j,

(30)

with y = O.33. Experimentally, the onset of surface order can be observed in X-ray scattering by the appearance of a broad feature related to the associated asymptotic (00s Bragg rod at the position of the superlattice reflection. This is indicated schematically in

Fig. 39. (a) Reciprocal lattice map of FeCo with bcc points (full symbols) and superlattice points (empty symbols). The dashed vertical lines indicate the asymptotic Bragg scattering from the free (001) surface. (b) Schematic of asymptotic Bragg scattering intensity along the (001) reflection for surfaceenhanced order.

Figure 39. Performing a detailed analysis of the Bragg intensity as a function of temperature, Krimmel et al. could show that even though the order is driven by a segregation-induced surface field, the order parameter in a 15-nm thin surface sheet still belongs to the ordinary universality class. It follows the temperature dependence given in Eq. (29) with/3 = 0.79 4- 0.10. The crossover to extraordinary behavior, according to Eq. (30), may only occur very close to Tc. A selection of asymptotic Bragg profiles as function of temperature appears in Figure 40. The short review of investigations concering order-disorder phenomena presented here represents only a small fraction of the research going on in this field. The interested reader is referred to recent reviews on this topic [ 141 ].

EPITAXIAL THIN FILMS OF INTERMETALLIC COMPOUNDS 2.0xlO 4

i ~

0.0

-

-0.4

0.0 H [r.l.u.]

0.4 9

9

10 5

T~-0 8 K ~ .

log.

[

~

9

104

"~

U II

log.

9

103

T-0.6 t

T+0.7

4000

jr. T o+ 1.8

2000

T+4.2

0 "

,

!

0.6

,

I

0.8

i

I

1.0

,

I

1.2

.

1.4

L [r.l.u.] Fig. 40. Selected asymptotic Bragg profiles along (001) as observed at various temperatures below and above Tc. The two upper curves for T < Tc are shown on a logarithmic scale. The full lines are theoretical curves. The inset shows a typical H-scan profile taken at L = 0.98 for T = Tc + 0.7 K (arrow). Image courtesy of W. Donner [145].

4. O U T L O O K It should be appararent from the foregoing sections that thin films of intermetallic compounds offer the possibility to tackle problems in basic and applied research in new and sometimes unique ways. Because of the consequences of the nonequilibrium phase formation process and various epitaxial constraints, the properties of such grown layers need not be in full correspondence with what is known from the respective bulk single crystals. This concerns purely crystallographic aspects, the defect structure, strain, and morphological variations, as well as the electronic and magnetic properties of the films. On the one hand, this can be an annoyance if the investigator wishes to study specific aspects known to be present in bulk crystals. An example is the strong strain dependence of the electronic properties of heavy-fermion materials, which have to be taken into account if thin films are to be employed. Very recent electron spectroscopy investigations CeNi2Ge2 and CePd2Si2 grown in situ show the wealth of electronic structural informa-

623

tion that can be gained with the use of thin films [152]. Yet, the interpretation of the results suffered from the lack of corresponding structure and strain information. On the other hand, in particular, the constraints imposed by the thin film form are exactly what are needed and can be used to tailor specific material aspects, as was shown for magnetostrictive layers. Moreover, patterning or the preparation of heterostructures is only feasible in thin film form. In any event, materials science has to go hand in hand with any research concerning the electronic and magnetic structure of the films under investigation. In this respect detailed studies of the microstructure evolution down to the atomic scale during the growth of alloy and compound films can give valuable insight into the early stages of nucleation and strain relaxation. This has to be augmented by theoretical studies of the growth of alloys and compounds in the form of thin films. Ultimately, it would be highly desirable to be able to judge the compatibility of certain substrate/templateepilayer combinations before film growth. Accompanying the current rise of designer materials, the understanding of the nature of film growth from first principles presents an important challenge for basic and applied research. Such theoretical studies are still in their infancy. The current main stream of research seems to go along the lines of kinetic Monte Carlo studies of alloy formation, mostly in binary form [ 153]. These investigations, combined with first-princicple calculations of the diffusion coefficients deduced from all of the relevant atomic processes, such as terrace diffusion, corner crossing, and king breaking, might eventually lead to a more detailed understanding of surface morphology evolution and the formation of ordered alloys and compounds. In this respect recent densityfunctional calculations of the self-diffusion of A1 on A1 (111) have to be mentioned [ 154]. The scope of issues that are accessible to thin film investigation on intermetallic compounds and ordered alloys is wide. The availability of topics of broad scientific interest is not the limiting factor in this field. Rather, the development and adaptation of adequate real-time rate monitoring and control for compound growth and an improved understanding of phase nucleation and orientation selection phenomena are needed. The elucidation of mechanisms for selecting the stacking variants in (111) growth of fcc metals is but one example of the research still to be done.

Acknowledgments

I cannot conclude without thanking all of the colleagues and students I had the pleasure to work with over the last few years. Specifically, I thank Hermann Adrian for his continuous support and C. P. Flynn, from whose knowledge I benefited during my time at the Physics Department and Materials Research Laboratory at the University of Illinois at Urbana-Champaign. I am also especially grateful to Martin Jourdan, Patrick Haibach, and Holger Meffert. Part of their work is presented in this chapter.

624

HUTH

REFERENCES 1. M. A. Herman and H. Sitter, "Molecular Beam Epitaxy," 2nd ed. Springer-Verlag, Berlin, 1996. 2. Z. Mitura and P. A. Maksym, Phys. Rev. Lett. 70, 2904 (1993). 3. W. Braun, "Applied RHEED," Springer Tracts in Modern Physics, Vol. 154. Springer-Verlag, Berlin, 1999. 4. P.J. Dobson, "Surface and Interface Characterization by Electron Optical Methods" (A. Howie and U. Valdr~, Eds.), NATO ASI Serie B 191, 1987. 5. C.J. Humphreys, Rep. Prog. Phys. 42, 1825 (1979). 6. M.P. Seah and W. A. Dench, Surf. Interface Anal. 1, 2 (1979). 7. L.C. Feldman and J. W. Mayer, "Fundamentals of Surface and Thin Film Analysis." Appleton & Lange, New York, 1986. 8. Rutherford Backscattering Data Analysis, Plotting and Simulation Package. Computer Graphics Service, Ithaca, NY. 9. D. Lederman, D. C. Vier, D. Mendoza, J. Santamaria, S. Schultz, and I. K. Schuller, Appl. Phys. Lett. 66, 3677 (1995). 10. N. Grewe and E Steglich, "Handbook on the Physics and Chemistry of Rare Earths," Vol. 14 (K. A. Gschneidner, Jr., and L. Eyring, Eds.), p. 343. North-Holland, Amsterdam, 1991. 11. G. Bruls, B. Wolf, D. Finsterbusch, P. Thalmeier, I. Kouroudis, W. Sun, W. Assmus, B. Ltithi, M. Lang, K. Gloos, E Steglich, and R. Modler, Phys. Rev. Lett. 72, 1754 (1994). 12. K. Ishida, Y. Kawasaki, K. Tabuchi, K. Kashima, Y. Kitaoka, K. Asayama, C. Geibel, and E Steglich, Phys. Rev. Lett. 82, 5353 (1999). 13. M. Huth and C. P. Flynn, Phys. Rev. B: Condens. Matter 58, 11526 (1998). 14. A. Masson, J. J. Metois, and R. Kern, "Advances in Epitaxy and Endotaxy" (H. G. Schneider and V. Ruth, Eds.), p. 103. VEB Deutscher Verlag ftir Grundstoffindustrie, Leipzig, 1971. 15. J.C.A. Huang, R. R. Du, and C. P. Flynn, Phys. Rev. Lett. 66, 341 (1991). 16. V. Oderno, C. Dufour, K. Dumesnil, Ph. Mangin, and G. Marchal, J. Cryst. Growth 165, 175 (1996). 17. M. Huth and C. E Flynn, J. Appl. Phys. 83, 7261 (1998). 18. M. Jourdan, Preparation and Thermoelectric Power of Thin Films of the Heavy-Fermion Superconductors UPd2AI 3 and UNi2A13, Diploma Thesis, TH Darmstadt, 1995. 19. B.W. Sloope and C. O. Tiller, J. Appl. Phys. 36, 3174 (1963). 20. J.E. Cunningham, J. A. Dura, and C. E Flynn, "Metallic Multilayers and Epitaxy" (M. Hong, S. Wolfe, and D. Gubser, Eds.), p. 75. Publics Metall Soc. Inc., 1988. 21. C. E Flynn, I. Borchers, R. T. Demers, R. Du, J. A. Dura, M. V. Klein, S. H. Kong, M. B. Salamon, E Tsui, S. Yadavaki, X. Zhu, H. Zabel, J. E. Cunningham, R. W. Erwin, J. J. Rhyne, "MRS International Meeting on Advanced Materials," 1989, Vol. 10, p. 275. 22. C. E Flynn, "Point Defects and Diffusion." Clarendon, Oxford, 1972. 23. M. Getzlaff, R. Pascal, H. Trdter, M. Bode, and R. Wiesendanger, Appl. Surf. Sci. 142, 543 (1999). 24. R. Pascal, M. Getzlaff, H. Trdter, M. Bode, and R. Wiesendanger, Phys. Rev. B: Condens. Matter 60, 16109 (1999). 25. J. Kolaczkiewicz and E. Bauer, Surf. Sci. 175,487 (1986). 26. R. Pascal, Ch. Zarnitz, M. Bode, and R. Wiesendanger, Phys. Rev. B: Condens. Matter 56, 3636 (1997). 27. E.D. Tober, R. X. Ynzunza, C. Westphal, and C. S. Fadley, Phys. Rev. B: Condens. Matter 53, 5444 (1996). 28. U. Rudiger, J. Kohler, A. D. Kent, T. Legero, J. Kubler, E Fumagalli, and G. Gtintherodt, J. Magn. Magn. Mater. 199, 131 (1999). 29. E Salghetti-Drioli, K. Mattenberger, E Wachter, and L. Degiorgi, Solid State Commun. 109, 687 (1999). 30. E Salghetti-Drioli, E Wachter, and L. Degiorgi, Solid State Commun. 109, 773 (1999). 31. J. Rossat-Mignod, P. Burlet, S. Quezel, J. M. Effantin, D. Delacrte, H. Bartholin, O. Vogt, and D. Ravot, J. Magn. Magn. Mater. 31-34, 398 (1983). 32. T. Chattopadhyay, P. Burlet, J. Rossat-Mignot, H. Bartholin, C. Vettier, and O. Vogt, Phys. Rev. B: Condens. Matter 49, 15096 (1994).

33. H. Meffert, J. Oster, R Haibach, M. Huth, and H. Adrian, Physica B 259261,298 (1999). 34. H. Meffert, M. Huth, J. Oster, P. Haibach, and H. Adrian, Physica B 281282, 447 (2000). 35. Landolt-Brrnstein, lI/2a, 6th ed. Springer-Verlag, Berlin/Grttingen/ Heidelberg, 1960. 36. C. T. Foxon, in "Principles of Molecular Beam Epitaxy," Handbook of Crystal Growth 3a (D. T. J. Hurle, Ed.), p. 155. North-Holland, Amsterdam, 1994. 37. M. T. Kief and W. Egelhoff, Phys. Rev. B: Condens. Matter 47, 10785 (1993). 38. E Family, Physica A 266, 173 (1999). 39. E. D. Tober, R. E C. Farrow, R. E Marks, G. Witte, K. Kalki, and D. D. Chambliss, Phys. Rev. Lett. 81, 1897 (1998). 40. C. R Flynn, J. Phys. Chem. Solids 55, 1059 (1994). 41. M. Huth and C. E Flynn, Appl. Phys. Lett. 71, 2466 (1997). 42. E I. Cohen, G. S. Petrich, E R. Pukite, G. J. Whaley, and A. S. Arrott, Surf. Sci. 216, 222 (1988). 43. P.J. Dobson, B. A. Joyce, J. H. Neave, and J. Zhang, J. Cryst. Growth 81, 1 (1987). 44. J.W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974). 45. J.W. Matthews, J. Vac. Sci. Technol. 12, 126 (1975). 46. J.W. Matthews and A. E. Blakeslee, J. Cryst. Growth 32, 265 (1976). 47. E M. Reimer, H. Zabel, C. E Flynn, and J. A. Dura, Phys. Rev. B: Condens. Matter 45, 11426 (1992). 48. A. Gibaud, R. A. Cowley, D. E McMorrow, R. C. C. Ward, and M. R. Wells, Phys. Rev. B: Condens. Matter 48, 14463 (1993). 49. A. Stierle, A. Abromeit, N. Metoki, and H. Zabel, J. Appl. Phys. 73, 4808 (1993). 50. E E Miceli, C. J. PalmstrCm, and K. W. Moyers, Appl. Phys. Lett. 58, 1602 (1991). 51. P. E Miceli and C. J. PalmstrCm, Phys. Rev. B: Condens. Matter 51, 5506 (1995). 52. E F. Miceli, J. Weatherwax, T. Krentsel, and C. J. Palmstr~m, Physica B 221,230 (1996). 53. V. Srikant, J. S. Speck, and D. R. Clarke, J. Appl. Phys. 82, 4286 (1997). 54. G. L. Zhou and C. E Flynn, Phys. Rev. B: Condens. Matter 59, 7860 (1999). 55. G.L. Zhou and C. E Flynn, Appl. Phys. Lett. 72, 34 (1998). 56. S. M. Durbin, J. E. Cunningham, M. E. Mochel, and C. P. Flynn, J. Phys. F 11, L223 (1981). 57. J. Kwo, E. M. Gyorgy, D. B. McWhan, M. Hong, E J. DiSalvo, C. Vettier, and J. E. Bower, Phys. Rev. Lett. 55, 1402 (1985). 58. K.A. Ritley and C. E Flynn, Appl. Phys. Lett. 72, 170 (1998). 59. M. Yoshimoto, T. Maeda, T. Ohnishi, H. Koinuma, O. Ishiyama, M. Shinohara, M. Kubo, R. Miura, and A. Miyamoto, Appl. Phys. Lett. 67, 2615 (1995). 60. G. Ehrlich and E G. Hudda, J. Chem. Phys. 44, 1039 (1966). 61. R.L. Schwoebel, J. Appl. Phys. 40, 614 (1969). 62. C. E Flynn and W. Switch, Phys. Rev. Lett. 83, 3482 (1999). 63. S.W. Bonham and C. E Flynn, Phys. Rev. B: Condens. Matter 58, 10875 (1998). 64. G. L. Zhou, S. W. Bonham, and C. P. Flynn, J. Phys.: Cond. Matter 9, 671 (1997). 65. R. J. Fisher, N. Chand, W. E Kopp, H. Morkoq, L. E Erikson, and P. Youngman, Appl. Phys. Lett. 47, 397 (1985). 66. H. Kroemer, J. Cryst. Growth 81, 193 (1987). 67. E Haibach, J. Krble, M. Huth, and H. Adrian, Thin Solid Films 336, 168 (1998). 68. E Haibach, J. Krble, M. Huth, and H. Adrian, J. Magn. Magn. Mater. 198-199, 752 (1999). 69. P.W. Tasker, J. Phys. C: SolidState Phys. 112, 4977 (1979). 70. D. Wolf, Phys. Rev. Lett. 68, 3315 (1992). 71. A. Pojani, E Finocchi, J. Goniakowski, and C. Noguera, Surf. Sci. 387, 354 (1997). 72. R. H. Heffner and M. R. Norman, Comm. Cond. Matter Phys. 17, 361 (1996).

EPITAXIAL THIN FILMS OF INTERMETALLIC 73. N. D. Mathur, E M. Grosche, S. R. Julian, I. R. Walker, D. M. Freye, R. K. W. Haselwimmer, and G. G. Lonzarich, Nature (London) 394, 39 (1998). 74. S.C. Zhang, Science 275, 1089 (1997). 75. W. Hanke, R. Eder, and E. Arrigoni, Phys. Bl. 54, 436 (1998). 76. H.v. L6hneysen, Physica B 218, 148 (1996). 77. K. Gloos, C. Geibel, R. Mueller-Reisener, and C. Schank, Physica B 218, 169 (1996). 78. N. Metoki, Y. Haga, Y. Koike, and Y. Onuki, Phys. Rev. Lett. 80, 5417 (1998). 79. N. Bernhoeft, B. Roessli, N. Sato, N. Aso, A. Hiess, G. H. Lander, Y. Endoh, and T. Komatsubara, Phys. Rev. Lett. 81, 4244 (1998). 80. M. Jourdan, M. Huth, and H. Adrian, Nature (London) 398, 47 (1999). 81. C. Geibel, C. Schank, S. Thies, H. Kitazawa, C. D. Bredl, A. B6hm, M. Rau, A. Grauel, R. Caspary, R. Helfrich, U. Ahlheim, G. Weber, and E Steglich, Z Phys. B: Condens. Matter 84, 1 (1991). 82. A. Krimmel, E Fischer, B. Roessli, H. Maletta, C. Geibel, C. Schank, A. Grauel, A. Loidl, and E Steglich, Z. Phys. B: Condens. Matter 86, 161 (1992). 83. H. Ikeda and Y. Ohashi, Phys. Rev. Lett. 81, 3723 (1998). 84. T. Petersen, T. E. Mason, G. Aeppli, A. P. Ramirez, E. Bucher, and R. N. Kleinman, Physica B 199-200, 151 (1994). 85. N. Sato, N. Aso, G. H. Lander, B. Roessli, T. Komatsubara, and Y. Endoh, J. Phys. Soc. Jpn. 66, 1884 (1997). 86. N. Metoki, Y. Haga, Y. Koike, N. Aso, and Y. Onuki, J. Phys. Soc. Jpn. 66, 2560 (1997). 87. N. Bernhoeft, B. Roessli, N. Sato, N. Aso, A. Hiess, G. H. Lander, Y. Endoh, and T. Komatsubara, in "Itinerant Electron Magnetism: Fluctuation Effects" (D. Wagner, W. Brauneck, and A. Solontsov, Eds.). Kluwer, Dordrecht, 1998. 88. N. Bernhoeft, B. Roessli, N. Sato, N. Aso, A. Hiess, G. H. Lander, Y. Endoh, and T. Komatsubara, Physica B 259-261, 614 (1999). 89. N. Bernhoeft, Eur Phys. J. B 13, 685 (2000). 90. M. Jourdan, M. Huth, and H. Adrian, Physica B 259-261, 621 (1999). 91. M. Huth and M. Jourdan, in "Advances in Solid State Physics," Vol. 39, p. 351. Vieweg, Braunschweig/Wiesbaden, Germany, 1999. 92. M. Huth, M. Jourdan, and H. Adrian, Eur Phys. J. B 13,695 (2000). 93. M. Huth, M. Jourdan, and H. Adrian, Physica B 281-282, 882 (2000). 94. M. Huth, A. Kaldowski, J. Hessert, Th. Steinboru, and H. Adrian, Solid State Commun. 87, 1133 (1993). 95. M. Huth, Transport Phenomena and Coherence in Epitaxially-Grown Heavy-Fermion Thin Films, Ph.D. Thesis, TH Darmstadt, 1995. 96. M. Jourdan, Tunneling Spectroscopy of the Heavy-Fermion Superconductor UPd2A13, Ph.D. Thesis, University of Mainz, 1999. 97. R.C. Dynes, V. Narayanamurti, and J. E Garno, Phys. Rev. Lett. 41, 1509 (1978). 98. K. Gloos, R. Modler, H. Schimanski, C. D. Bredl, C. Geibel, E Steglich, A. I. Buzdin, N. Sato, and T. Komatsubara, Phys. Rev. Lett. 70, 501 (1993). 99. J. Hessert, M. Huth, M. Jourdan, H. Adrian, C. T. Rieck, and K. Scharuberg, Physica B 230-232, 373 (1997). 100. G. Varelogiannis, Z Phys. B: Condens. Matter 104, 411 (1997). 101. D. C. Jiles, "New Materials and their Applications" (D. Holland, Ed.). IOP, Bristol, 1990. 102. V. Koeninger, Y. Matsumara, H. H. Uchida, and H. Uchida, J. Alloys Compounds 211-212, 581 (1994). 103. A. E. Clark, "Handbook of the Physics and Chemistry of Rare Earth" (K. A. Gschneidner and L. Eyring, Eds.), Vol. 2, reprint. North-Holland, Amsterdam, 1982. 104. E Tsui and C. P. Flynn, Phys. Rev. Lett. 71, 1462 (1993). 105. C. T. Wang, B. M. Clemens, and R. L. White, IEEE Trans. Magn. 32, 4752 (1996). 106. E. C. Stoner and E. E Wohlfarth, Philos. Trans. R. Soc. London, Set A 240, 599 (1948). 107. E.W. Lee and J. E. L. Bishop, Proc. Phys. Soc., London 89, 661 (1966). 108. Etienne du Tr6molet de Lacheisserie, "Magnetostriction." CRC Press, Boca Raton/Ann Arbor/London/Tokyo, 1993.

COMPOUNDS

625

109. A. E. Clark, in "Ferromagnetic Materials" (E. E Wohlfarth, Ed.), Vol. 1. North Holland, Amsterdam/New York/Oxford, 1980. 110. R. S. Beach, A. Matheny, M. B. Salamon, C. E Flynn, J. A. Borchers, R. W. Erwin, and J. J. Rhyne, J. Appl. Phys. 73, 6901 (1993). 111. D.C. Jiles and J. B. Thoelke, J. Magn. Magn. Mater 134, 143 (1994). 112. H. Uchida, M. Wada, K. Koike, H. H. Uchida, V. Koeninger, Y. Matsumura, H. Kaneko, and T. Kurino, J. Alloys Comp. 211-212, 576 (1994). 113. V. Koeninger, Y. Matsumura, H. H. Uchida, and H. Uchida, J. Alloys Comp. 211-212, 581 (1994). 114. E Schatz, M. Hirscher, M. Schnell, G. Flik, and H. Kronmtiller, J. Appl. Phys. 76, 5380 (1994). 115. S. E Fischer, M. Kelsch, and H. Kronmtiller, J. Magn. Magn. Mater 195, 545 (1999). 116. H. Yamamoto, S. Matsumoto, M. Naoe, and S. Yarnanaka, Trans. Inst. Electrical Eng. Jpn. 98, 31 (1978). 117. M. Huth and C. E Flynn, J. Magn. Magn. Mater 204, 203 (1999). 118. W.B. Zeper, E J. A. M. Greidanus, E E Garcia, and C. R. Fincher, J. Appl. Phys. 65,4971 (1989). 119. L. Uba, S. Uba, A. N. Yaresko, A. Ya. Perlow, V. N. Antonov, and R. Gontarz, J. Magn. Magn. Mater 193, 159 (1999). 120. J. Pommier, E Meyer, G. P6nissard, J. Ferr6, E Bruno, and D. Renard, Phys. Rev. Lett. 65, 2054 (1990). 121. E Haibach, M. Huth, and H. Adrian, Phys. Rev. Lett. 84, 1312 (2000). 122. U. Nowak, J. Heimel, T. Kleinefeld, and D. Weller, Phys. Rev. B: Condens. Matter 56, 8143 (1997). 123. M. Jost, J. Heimel, and T. Kleinefeld, Phys. Rev. B: Condens. Matter 57, 5316 (1998). 124. E Grtitter and U. T. Dtirig, Phys. Rev. B: Condens. Matter 49, 2021 (1994). 125. R. S. Tebble and D. J. Craik, "Magnetic Materials." Wiley-Interscience, London, 1969. 126. A. E Andresen, W. Halg, E Fischer, and E. Stoll, Acta Chem. Scand. 21, 1543 (1967). 127. X. Guo, X. Chen, Z. Altounian, and J. O. Strom-Olsen, J. Appl. Phys. 73, 6275 (1993). 128. E R. Bandaru, T. D. Sands, Y. Kubota, and E. E. Marinero, Appl. Phys. Lett. 72, 2337 (1998). 129. A. Borgschulte, D. Menzel, T. Widmer, H. Bremers, U. Barkow, and J. Schoenes, J. Magn. Magn. Mater 205, 151 (1999). 130. J. Nogu6s and I. K. Schuller, J. Magn. Magn. Mater 192, 203 (1999). 131. A.E. Berkowitz and K. Takano, J. Magn. Magn. Mater 200, 552 (1999). 132. W.H. Meiklejohn and C. E Bean, Phys. Rev. 102, 1413 (1956). 133. W.H. Meiklejohn and C. P. Bean, Phys. Rev. 105, 904 (1957). 134. R.D. Hempstead, S. Krongelb, and D. A. Thompson, IEEE Trans. Mag. 14, 521 (1978). 135. T. Nakamichi, J. Phys. Soc. Jpn. 25, 1189 (1968). 136. E. F. Wassermann, B. Rellinghaus, Th. Roessel, and W. Pepperhoff, J. Magn. Magn. Mater 190, 289 (1998). 137. J. Koeble and M. Huth, "European Conference on Magnetisma and Magnetic Applications (EMMA)," Kiev, 2000, Materials Science Forum. Transtech Publications, Zurich, Switzerland. 138. L. van Hove, Phys. Rev. 95,249 (1954). 139. N. Bernhoeft, A. Hiess, S. Langridge, A. Stunault, D. Wermeille, C. Vettier, G. H. Lander, M. Huth, M. Jourdan, and H. Adrian, Phys. Rev. Lett. 81, 3419 (1998). 140. A. Hiess, N. Bernhoeft, S. Langridge, C. Vettier, M. Jourdan, M. Huth, H. Adrian, and G. H. Lander, Physica B 259-261,631 (1999). 141. K. Binder, "Phase Transitions and Critical Phenomena" (C. Domb and J. L. Lebowitz, Eds.), p. 1. Academic Press, London, 1983. 142. H. Dosch, "Critical Phenomena at Surfaces and Interfaces," Springer Tracts in Modern Physics, Vol. 126. Springer-Verlag, Heidelberg, 1992. 143. S.W. Bonham and C. P. Flynn, Phys. Rev. B: Condens. Matter 57, 4099 (1998). 144. B. Nickel, W. Donner, H. Dosch, C. Detlefs, and D. Grtibel, Phys. Rev. Lett. 85, 134 (2000). 145. S. Krimmel, W. Donner, B. Nickel, H. Dosch, C. Sutter, and G. Grubel, Phys. Rev. Lett. 78, 3880 (1997).

626

HUTH

146. C. Era, W. Donner, A. Ruhm, H. Dosch, B. R Toperverg, and R. L. Johnson, Appl. Phys. A 64, 383 (1997). 147. B.E. Warren, "X-Ray Diffraction." Addison-Wesley, Reading, MA, 1969. 148. E. Domany, Y. Shnidman, and D. Mukamel, J. Phys. C: Solid State Phys. 15, IA95 (1982). 149. M. E Collins and J. B. Forsyth, Philos. Mag. 8, 401 (1963). 150. E Schmid, Z. Phys. B: Condens. Matter 91, 77 (1993). 151. A. Drewitz, R. Leidl, T. W. Burkhardt, and H. W. Diehl, Phys. Rev. Lett. 77, 1090 (1997).

152. G. H. Fecher, B. Schmied, and G. Sch6nhense, J. Electron. Spectrosc. Relat. Phenom. 103,771 (1999). 153. Y. Shim, D. E Landau, and S. Pal, J. Phys.: Condens. Matter 11, 10007 (1999). 154. A. Bogicevic, J. Str6mquist, and B. I. Lundqvist, Phys. Rev. Lett. 81,637 (1997).

Chapter 13

PULSED LASER DEPOSITION OF THIN FILMS: EXPECTATIONS AND REALITY Leonid R. Shaginyan Institute for Problems of Materials Science, Kiev, 03142 Ukraine

Contents 1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.

Composition of Pulsed Laser-Deposited Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 2.1. Dependence of the Composition of PLD Films on Laser and Deposition Processing Parameters . 630 2.2. Dependence of the Composition of PLD Films on the Evaporating Material . . . . . . . . . . . . 631 2.3. Experimental Details of Pilyankevich et al . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 2.4. Formation of P L D Film Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 2.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650 Structure of P L D Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 3.1. Factors Influencing the P L D Film Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 3.2. Role of Molecules and Larger Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 3.3. Gas-Phase Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 3.4. Crystallization Temperature as an Index of Film Structure "Perfection" . . . . . . . . . . . . . . 653 3.5. Influence of Laser Parameters and Substrate Temperature on Epitaxial Growth of PLD Films . . 655 3.6. Ways to Control the PLD Film Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658 3.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 Polymorphism in P L D Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 4.1. Polymorphism of P L D Carbon Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 4.2. Polymorphism of Boron Nitride Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660 4.3. Polymorphism of Silicon Carbide Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 4.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 Macrodefects in P L D Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 5.1. Mechanisms of Splashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 5.2. Elimination of Particulates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662

3.

4.

5.

6.

7.

627

5.3. Determination of Vapor Portion in Products of Laser-Ablated Metals . . . . . . . . . . . . . . . . 5.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Influence of Target Properties on Some Features of PLD Compound Films . . . . . . . . . . . . . . . . 6.1. Role of Target Thermal Conductivity in Compound Film Property Formation . . . . . . . . . . . 6.2. Powder Targets: Mechanisms of Particulate Generation . . . . . . . . . . . . . . . . . . . . . . . 6.3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

662 666 666 667 668 670 670 671 671

surface) determine the composition, structure, and properties of the resulting films. The composition of FFS generated by evaporation or sputtering of any substance during the preparation of the film by physical vapor deposition (PVD) methods depends primarily on

1. INTRODUCTION

Three constituents of the deposition process (composition of the film-forming species (FFS), composition of the of medium where the FFS propagate, and conditions on the condensation

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 1: Deposition and Processing of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512909-2/$35.00

627

628

SHAGINYAN

the composition of the initial substance (target). However, the transfer of the substance from the target surface to the substrate includes several processes, which can substantially change its composition. These changes can start on the target surface, depending on the method of generation of the film-forming flux. The next step, in which the composition of the generated film-forming flux can be changed, is its transfer from the surface of the target to the condensation surface. This can be affected by interaction between FFS in a gas phase and interaction between FFS and particles of the medium, where FFS propagate. Another mechanism that can influence the composition of evaporated (sputtered) species during their transfer from target to substrate is a scattering of these species by atoms or molecules of the medium. The scattering depends on several factors. The greater the working gas pressure during the deposition, the more probable are the collisions between the propagating species and the gas particles; and the greater the difference between the atomic masses of FFS and medium particles, the more probable is the deviation of the FFS from the initial direction of their movement. Both processes can substantially change the composition of the FFS deposited on the substrate (and hence the film composition) from the initial composition of the target. The composition of the FFS can also be changed directly at the condensation surface. There are several reasons for this. The first is the difference in the sticking coefficients for different atoms. Metal atoms have sticking coefficients of ~ 1 at substrate temperatures in the range of -195~ to several hundred degrees Celcius; the sticking coefficients of gas atoms at room temperature are between 0.1 and 0.5 [1 ]. Another possible reason is the ion or energetic particle bombardment of the condensation surface. If this is the case, the film composition can change drastically, especially if atoms of volatile component are present. Qualitative and quantitative composition of FFS can influence not only the composition of the film, but its structure as well. A striking example of the influence of quantitative FFS composition on the structure of the resulting condensate can be the fabrication of diamond-like films. A diamond-like carbon (DLC) film with a high (up to 90%) content of s p 3 bonds can be obtained only from the atomic flux of carbon atoms with a certain amount of carbon ions with a certain energy. If the flux of sputtering from graphite target species contains clusters of several carbon atoms, the resulting condensate exhibits graphite-like properties [2]. All of the above considered stages (FFS formation, their transport, and condensation) of the pulsed laser deposition of thin films exhibit significant differences from those for other PVD methods. The interaction of the high power pulse of laser irradiation with the target surface can heat it to such a temperature that all of the target constituents can be evaporated simultaneously and with the same velocity. This peculiarity of pulsed laser deposition (PLD) allows to assume that the composition of the generated vapor and the resulting condensate will be similar to that of the initial target.

Another peculiarity of the interaction of a high power density laser pulse with the condensed phase is the generation of high-density vapor just above the target surface. The supersonic expansion of the vapors during the initial hydrodynamic flow accompanies the effect of segregation of the atomic, molecular and micro-sized particulates due to their collisions in the laser plume. The clusters arising in such a process may contain several or hundreds of atoms [3, 4]. If the evaporation occurs in a gas medium the clusterization effect in PLD is substantially enhanced [5]. In this case, along with the clusters formed from the evaporated species, molecular clusters synthesized from the gas atoms and the evaporated species appear [6]. The other important peculiarities of the species generated by pulsed laser evaporation are their high kinetic energy and the presence of charged species among them. These factors result in the bombardment of the condensation surface by these species. Each of the above considered peculiarities make the PLD method substantially different from other methods of physical vapor deposition. Conventional methods of physical vapor deposition that use ion sputtering, electron bombardment, or resistive heating of a substance to genere the vapor phase yield a much lower vapor pressure compared with the instantaneous pressure of the vapor generated by laser pulse. The low vapor pressure almost excludes the interaction between the species in a vapor phase. The energy of sputtered and, in particular, evaporated particles is lower by orders of magnitude than that of the species generated by laser radiation. The amount of charged species in the filmforming flux generated by other PVD methods is also much smaller. So it is natural to expect the properties of films fabricated by laser evaporation to be different from those obtained by other methods of physical deposition. It is assumed that, owing to the above considered peculiarities of pulsed laser evaporation, the target composition has to be easily reproduced in the film. It is expected that the structure of PLD film is more perfect than that deposited by any other PVD technique at lower substrate temperatures. The absence of the heating elements and discharging electrodes inside the vacuum chamber and the short time pulse duration contribute to the high purity of the deposited film. The history of PLD started in 1964, when the first papers devoted to the application of laser to film deposition appeared. Even at that time discrepancies between the actual and predicted properties of condensates had been detected. The composition of the films of different compounds deviated from their initial target composition. Macroscopic defects (macrodefects) like solidified droplets and solid particles were present in the majority of condensates. Many investigations directed toward the development of the PLD method as well as the elimination of the aforementioned drawbacks have been carried out since that time. More attempts have been made to improve PLD than that for other film deposition techniques. Major efforts have been made to eliminate the presence of macrodefects in a condensate. Different approaches had been

PULSED LASER DEPOSITION used for the solution of this problem. One of them was related to improvements of the laser itself. The main directions here have been the improvement of the spatial and temporal homogeneity of the laser pulse [7, 8] and the search for optimal pulse duration and the optimal frequency of the pulse variation of radiation wavelength [9]. Other approach was to manipulate the target properties to improve the effectiveness of absorption of laser radiation energy and to enhance the vapor phase fraction in the products ejected from the target. For this purpose the evaporation of different types targets, such as alloys, single crystals, and freefalling and pressed powders has been investigated. One more method, widely used in PLD technology to lower the number of macrodefects in films is the mechanical separation of film-forming particles [10-12]. According to the majority of publications related to PLD, the most important advantage of this method is the possibility of obtaining films of complex compounds with a composition identical to that of a target (see, e.g., [12, 13]). One may notice that the variety of the films fabricated by PLD was much wider in the early history of the method. Many investigations related to the fabrication of nitride, boride, carbide, and oxide films were carried out during the 1970s and the beginning of the 1980s. However, many of them were not successfully deposited with the correct stoichiometric composition. By the middle of the 1980s, after all merits and drawbacks of the method had been clarified, the activity in this field had declined. By the end of the 1980s PLD had been given new stimulus due to success in the laser deposition of high-temperature superconducting (HTSC) films. At the moment most research and development in PLD is concerned with the deposition of oxides and high-temperature superconductors. This is due to the fact that the composition of the films deposited by pulsed laser evaporation of these materials is very close to that of the initial target. Another reason for the rebirth of PLD is the development of accessible and relevant excimer lasers. In recent years a number of systematic studies giving very detailed accounts of the ablation mechanism under typical PLD experimental conditions have appeared. This is related to the inspiration of the successful PLD deposition of HTSC films as well as the necessity to search for a solution to long-standing PLD problems, such as the presence of macrodefects and the nonstoichiometry of condensates composition. The effect of ambient background gases on YBCO plume propagation under film growth conditions was studied with the use of various analytical techniques, such as optical spectroscopy, ion probing, time-of-flight analysis, and gated high-speed CCD photography [4]. This study reveals features of laser-target interaction and plume transport that cannot be predicted otherwise. Our analysis of the publications regarding PLD shows that despite of extensive past experience with PLD deposition of films from a wide variety of materials, the mechanisms of film formation and structure are still not completely clear; the main drawbacks of the method are still present. Furthermore, there are no definite answers to the following questions:

629

9 Which materials are most promising for the PLD fabrication of films? 9 Which material properties provide effective evaporation with identical (i.e., without loss of stoichiometry) transfer of composition to the film? 9 Why, despite the prerequisites for fabrication of PLD films with more perfect structure at a lower substrate temperature (that is, high energy of evaporated FFS) usually not occur? Rather, the substrate temperature turns out to be even higher for the fabrication of laser condensates of the same structural perfection as those obtained by other methods. 9 What properties of the target material determine the portion of vapor phase in the products ejected from the target under the laser pulse action? Let us mention that this parameter determines the effectiveness of absorption of laser radiation. The presence of the macrodefects in the film also depends on it. 9 Which physical mechanisms govern the evaporation of targets of different types? What targets are optimal for the deposition of films with the required characteristics? The answers to some of the above questions can, in principle, be found in the literature. However, we were not able to find a systematic survey of all of the aforementioned problems, despite a huge literature devoted to PLD. Hence, the aim of this chapter is to give a systematic survey of aforementioned problems, based on literature sources and the author's own investigations.

2. COMPOSITION OF PULSED LASER-DEPOSITED FILMS One of the most important problems of film materials science is the fabrication of films with a specific composition. A short pulse of high-density optical radiation generated by a laser gives so great a thermal spike on the irradiated surface of the solid that all of its components should be evaporated similarly. If the sticking coefficients of each component are equal to each other, one can expect that obtained from such a flux condensate should have a composition similar to that of the initial target. This physical idea inspired the appearance of many experimental articles dedicated to the investigation of rules governing the formation of the aforementioned laser condensate composition. Analysis of those papers has shown that there are many factors influencing the composition. These factors can be divided into two groups: those related to the laser operation parameters and those related to the properties of both the evaporated substance and the medium where this evaporation occurs. The density of laser radiation power, the radiation wavelength, the duration of a pulse and its spatial and temporal homogeneity, and the diameter of the radiation spot on the target surface can be related to the first group of factors.

630

SHAGINYAN

The chemical composition of a target, its thermophysical characteristics, and the medium where evaporation occurs (vacuum, gas, its chemical properties) can be related to the second group of factors. The method of laser deposition determines a great number of technological parameters influencing films properties. Because experimental investigations of laser deposition of the films were carried out by different scientists under different deposition conditions and with different sources of laser radiation, the analysis of the results of such investigations is quite complicated. This is why the conclusions provided here, while of a pretty general nature, cannot be regarded as final. Let us consider the influence of the aforementioned groups of factors on the composition of laser condensates.

2.1. Dependence of the Composition of PLD Films on Laser and Deposition Processing Parameters Film composition depends on the composition of the FFS. There are two main differences between species fluxes generated by laser radiation and those generated by other methods. These peculiarities are complex composition of the flux (the flux contains different particles, from multiply charged ions to multiatomic clusters and larger particles) and angular distribution of particles in the flux [14-16]. Both of these parameters depend essentially on the laser operation regime as well as on the deposition conditions (ambient medium, distance to target, etc.) [7]. It is obvious that the more inhomogeneous the composition and spatial distribution of the flux of FFS are, the less satisfactory is the quality of the resulting film. Laser fluence (q), wavelength (~.), pulse duration (r), targetto-substrate distance, laser spot size, and ambient medium (vacuum, gas) have been investigated for their influence on the plume angular distribution. Few general conclusions are possible, because even the laser fluence, the best studied of these parameters, has been examined in detail for only a few materials. Another consideration is the complication of data interpretation by the fact that variation of a single parameter may influence several aspects of the ablation process simultaneously. For example, a change in laser wavelength while the other laser parameters are kept constant may change both the initial density and energy of the plume, because of wavelength-dependent changes in the target and laser plume optical properties. Experimental data and theoretical analysis show that there are two regions of laser power density with quite different compositions of ejecta. For flux densities of 106 < q < 108 W/cm 2, the ejecta consist mainly of the vapor in the form of neutral species and liquid phase. If q > 109 to 1010 W/cm 2, the amount of the ejecta is much less, but the charged particle fraction appears and increases rapidly with increasing laser power density [7, 14]. The angular distribution of ionized and neutral components of the laser plume defines the uniformity and physical properties of the film-forming flux. It is known that the angular, energy, and velocity distributions of different components of the laser plume are quite different [ 17, 18]. The angular distribution

of the laser generated flux is often much more strongly forward peaked than the flux obtainable from effusive sources. This forward peaking phenomenon for depositions in vacuum is now generally agreed to arise from collisions of the plume species among themselves. The axis of the laser generated plume is always oriented along the target surface normal for normal and nonnormal angles of laser incidence [ 19]. In addition to spatial separation, the time separation of the species in laser plumes has also been observed. The fast electrons are moving ahead of other species, and ions of maximal charge follow them. Ions of minimal charge are at the tail of the ion component of the flux. The slowest part of the flux is neutral. The ions of maximal charge have the narrowest angular distribution (0max ~ 30~ AS the ion charge decreases, the angular distribution widens so that neutral particles have the widest angular distribution. The energy distribution of laser plasma components follows their angular distribution. The ions with a maximal charge have the largest kinetic energy (up to tens of kiloelectron volts at a laser radiation density q ~ I011 to 1012 W/cm2). The neutral atoms has the smallest kinetic energy (tens of electron volts) [ 18]. A general examination shows that the absorption coefficients of insulators and semiconductors tend to increase as one moves to the short wavelength (200-400 nm), whereas metals absorb more or less efficiently in a wide range of radiation wavelength (10 #m to 100 nm). The influence of wavelength on ion energy distribution was investigated in [18], where Ti was evaporated by excimer laser (308 nm, r = 20 ns) and by CO2 laser (10.6 /zm, r = 100 ns) at a constant energy density q = 15 J/cm 2. The energy spectrum of the ions was in the region of 0 eV to 2000 eV for a CO2 laser, whereas for an excimer laser the spectrum was narrower and expanded up to "~ 1000 eV. The mean ion energy for both cases was 100-400 eV. These resuits correlate with the data obtained for the plume angular distribution for Se [ 18]. These data suggest that the angular distributions produced with IR wavelengths are significantly broader than those produced with visible and UV wavelengths [19]. The laser pulse length also has great influence on the plume composition and the angular distribution of its components. At a relatively long laser pulses (~ms) and low fluences (q 105 W/cm 2) the energy of evaporated particles is much less than the dissociation energy of the molecules, and these conditions are suitable for obtaining stoichiometric films of polycomponent materials with a high energy of dissociation. At a short pulse duration (~ns) the laser-produced plasma contains a significant amount of high-energy particles, especially ions [18], which can greatly influence film properties, particularly their composition, because of the ion bombardment effect [20-23]. The influence of the pulse duration on the composition of Y-Ba-Cu-O films was observed when the films deposited at r = 150 ns were more compositionally uniform then those deposited at r = 15 ns [24]. Angular distribution also affects to such deposition conditions as the target-substrate distance, laser spot dimensions, and ambient gas presence. Noninteracting particles emitted in a vacuum from a small-area source are expected to have an angular

PULSED LASER DEPOSITION distribution that does not change with distance from the source. Contrary to expectations, measurements for the deposition of some materials in a vacuum suggest that the angular distribution of the source may change with the distance from the source. The carbon data suggested a broader angular distribution close to the target that ceased at distances far from the target. These findings were attributed to scattering of the incident flux, with particles reflected and resputtered from the substrate [ 16]. The frequently observed effect of laser spot dimensions on the angular distribution of the evaporated species is that the smaller the spot dimensions are the more uniform is the film thickness. These effects arise because the number of intraplume collisions increases with the laser spot dimensions. The angular distribution of evaporated material in a vacuum is determined by collisions among the plume species. Most of these collisions take place close to the target, while the plume is small. The angular distribution of the evaporated material changes if the evaporation occurs in ambient gas. Under these conditions the evaporated species experience additional collisions with the gas molecules that scatter the plume particles from their original trajectories and broaden the angular distribution. For a given background gas mass and plume species velocity, one qualitatively expects the dispersive effects of collisions to vary with the mass of the species: the higher the mass of the evaporated species, the lower the collision effect, and vice versa. Hence the background gas pressure at which this effect may be observed depends on the ratio of masses of evaporated species to a mass of the gas particles. Because the different plume species have their own angular distributions, one may expect that each of the considered laser and deposition parameters may influence the composition of the film. Measurements of laser film composition confirm that the film stoichiometry varies with the deposition angle [16]. The reason for this effect (see also above) is the different angular distributions of the plume component species. The latter may be associated with the difference in species charge (ions or neutrals) as well in their mass (heavy or light). For instance, the ions and neutrals in the plume have been observed to have distinctly different angular distributions. Measurements of film composition produced by PLD in a vacuum from multicomponent targets sometimes indicate contradictory results. Higher on-axis light-to-heavy ratios were observed both for YBCO films [25] and for PbZrxTil-xO3 films [26]. However, for YBCO films this effect became less pronounced at higher fluences, whereas in contrast to YBCO films, composition inhomogeneities in PbZrxTil-xO3 films were enhanced as the fluence increased from 0.2 to 5 J/cm 2. In [27] film composition homogeneity was investigated with variation in laser fluence, spot size, oxygen pressure, and the substrate-to-target distance. Slight on-axis enrichment of Cu and Ba was found in the films deposited in a vacuum, whereas the films deposited in oxygen were on-axis enriched in Y because of the gas-scattering effect. The last effect was increased with increasing of substrate-to-target distance. The authors concluded that the deposition of compositionally uniform films at

631

intermediate substrate-to-target distances results from cancellation of the intrinsic (in a vacuum) composition inhomogeneity by gas scattering effects. Studies of laser plume composition established a very important effect that can significantly influence the film composition. It is the existence of two distinct components in the laserproduced fragments at the target surface [ 12, 25, 28]. One of the components with a weaker angular dependence was identified as a nonstoichiometric thermal evaporation. The other component, highly peaked in the forward direction, was identified as a stoichiometric component produced in a nonlinear evaporation process, such as a shock wave or highly excited dense plasma. The ratio of material emitted in the two different components depended upon the laser energy density. At lower energy densities (typically for Y-Ba-Cu-O below 0.9 J/cm 2, 248 nm, 30-ns laser pulses) the thermal evaporation component dominated. As a result the composition of deposited films deviated from the proper stoichiometry. At higher laser energy densities the propensity for deposition of laser-produced debris increased so that optimal energy density was required. Our brief examination shows that PLD film composition is sensitive to the laser and deposition processing parameters. The sensitivity may be different for different evaporating materials. The main reasons for these effects are the multicomponent composition of the laser plume and the nonuniformity of the spatial distributions of each of the components.

2.2. Dependence of the Composition of PLD Films on the Evaporating Material The main reason for the deviation of film stoichiometry during the evaporation of complex compounds by conventional methods is the difference in the vapor pressures of constituents of the compound. This is why the deposition of the film of a complex compound with the correct stoichiometry by conventional evaporation is possible in three cases: in the case of molecular evaporation of the compound; when the compound constituents evaporate congruently; when the volatilities of the constituents are similar. However, if the energy input to the evaporating compound is sufficient to instantly raise its temperature significantly above the temperature of evaporation of its less volatile component, one can expect that the composition of the condensate will be close to that of the initial compound. The flashing method (method of discrete evaporation) of thin compound film deposition is based on this principle [ 1]. Concentration of the laser radiation energy in a small volume for a short time interval gives rise to conditions suitable for the fabrication of complex compound films. The main aim of the majority of studies since the inception of the PLD method was to establish the proper laser operation regime and deposition conditions to obtain a film with a composition identical to that of the target. More than 100 compounds have been investigated [ 16] over more than 30 years of PLD film deposition and investigation. These compounds fall into four groups: low-melting-point semiconductor compounds of AIIB vI, AIIIBv, and AIVBTM

632

SHAGINYAN

types; oxides and perovskites, including HTSC; and refractory compounds---carbides, silicides, and nitrides. The majority of compounds had been investigated during the first 15 years of the application of PLD. During these years a large number of papers dedicated to PLD had appeared. The peculiarity of recent investigations of PLD is the reduction of the number of materials deposited by this method. These materials are mainly binary and multicomponent oxides, including HTSC and ferroelectrics, as well as an amorphous carbon and carbon nitride. At the same time, much attention had been paid to different forms of reactive PLD [6] because of the necessity to correct the oxygen deficiency in oxide condensates.

2.2.1. Mechanisms of Formation of Low-Melting.Point Semiconductor Compounds and Oxides To understand the mechanisms of laser condensate formation, let us consider the main results from investigation of the composition of the films, obtained by a pulse evaporation of compounds. Some data are reported in Table I. Although they are from quite a small number of articles about laser film fabrication, these data reflect a wide variety of film materials, obtained by PLD. Their analysis allows some conclusions about the properties of the compounds that can be obtained as films with proper composition by laser evaporation in a vacuum. Note that here we intentionally avoid discussion of HTSC films (like YBa2Cu307-x) obtained by PLD, because much attention has been paid to these materials in the literature (see, e.g., [ 16 and references therein]). A group of materials that can be deposited by PLD without serious deviation of the stoichiometry is low-melting-point semiconductors of AIIBVI, AIIIBv, and AIVBIV types. These substances incorporate components with a low melting temperature and a high pressure of saturation vapor at relatively low temperatures. This means that one may expect to obtain a film with the correct stoichiometry if the temperature achieved on the evaporation surface is substantially higher than those necessary for intensive evaporation of the compound components. Because the temperature in a laser spot reaches several thousand degrees, it is sufficient for the complete evaporation of all components of low-melting-point compounds. It is essential to note that because of such thermophysical properties of components, the majority of considered semiconductor compounds can also be obtained as a films of stoichiometric composition by conventional evaporation [ 1]. Another group of materials that can be obtained by PLD with stoichiometric composition, includes some two-component (ZrO2, A1203 [44], SiO2 [31]) and multicomponent (BaTiO3, SrTiO3 [30], CaTiO3 [31]) oxides. The main feature of the evaporation of many two-component oxides (BaO, BeO, A1203, SnO2, In203, TiO2, ZrO2, SiO, SiO2, and some others) is their preferential evaporation in a molecular form [ 1]. This peculiarity makes it possible, to obtain them in a stoichiometric form by both conventional and laser evaporation at relatively low power densities (q -- 105 to 106 W/cm 2) [18]. The principal

mechanism of composition formation of multicomponent oxides films is most probably the same for conventional evaporation and PLD. During their evaporation, multicomponent oxides dissociate to the molecules of the MeOx (Me = Ba, Ca, Sr) and TiOy types, which during their condensation on the substrate form the stoichiometric compound. Most probably, such a mechanism of evaporation makes it possible to obtain the films of BaTiO3, CaTiO3, and SrTiO3 not only by PLD but also by a flashing method (for instance, BaTiO3 [ 1]). The other evaporation mechanism (e.g., complete dissociation of a compound with subsequent condensation and reaction between its components on a substrate) is less likely to occur because oxygen atoms have a sticking coefficient several times smaller than that of metal atoms [1 ], and the deposition occurs in a vacuum (see, e.g., [30]). In our view, the formation of the films of complex HTSC oxides exhibits the elements of a mechanism discussed for BaTiO3, CaTiO3, and SrTiO3. That is, the action of a laser beam on ceramics does not lead to complete dissociation of a compound to separate chemical elements, but rather to the molecules of stable oxides of YxOy and BaxOy types. The second element of formation of the films of these compounds is a reaction between free metal atoms and oxygen in a gas phase [6]. This is due to the fact that the process takes place in an oxygen atmosphere at a relatively high pressure. The two aforementioned mechanisms make it quite easy to obtain the stoichiometric HTSC films by PLD. The oxides of the MexOy type can be attributed to the third group. The films of these oxides have been obtained by laser evaporation of their powders or sintered powders. Some of these oxide films were reduced completely (Cu20 [29], ZnO [31], PbO, Fe203 [43]) during laser evaporation in vacuum or had an oxygen deficiency (TiO2 [46], In203 + SnO2 [47], RuO2 [48]), which have been corrected by evaporation in an oxygen ambient. At the same time, in [18] the successful deposition of a whole series of stoichiometric oxide films by pulsed laser evaporation of BeO, A1203, SnO2, TiO2, and ZrO2 powders in a vacuum has been reported. The author emphasizes that this was possible because of the use of relatively long laser pulses (~ms) and low fluences (q ~ 105 W/cm2). These conditions are suitable for obtaining stoichiometric films of multicomponent materials with high dissociation energies and for oxides in particular. The data from Table I show that the oxides in [46-48] had been evaporated with higher power density, by nanosecond pulses and by short wavelength radiation. These conditions are favorable for the dissociation of oxides due to the higher absorption of laser radiation by the target material and by the generated vapor phase. The latter leads to an oxygen deficiency in the condensate. To eliminate this deficiency, the target evaporation should be carried out in an oxygen medium. The evaporation in an oxygen ambient provides the interaction of evaporated species with gas particles and the formation of oxide molecules in a gas phase. The other mechanism is the reaction between oxygen and metal atoms on the substrate. The stoichiometric composition of the PLD deposited films is due, presumably, to the aforementioned mechanisms. Let us note that the formation of oxide molecules

PULSED

Table I.

LASER

DEPOSITION

633

Deposition Conditions, Composition, and Structure of Thin Film Materials Deposited by PLD Laser processing parameters

Film

Ambient gas

Film composition

structure

pressure (torr)

Reference

CdTe, ZnTe stoichiometric; PbTe(?);

P/C

Vac. 10 . 4

[29]

Stoichiometric

P/C

Vac. 10 -7

[30]

GaP, GaSb, GaAs, InAs; ZnS, ZnSe,

AiiiB v, AiiB v

Vac. 10 - 6

[31]

ZnTe, CdTe, CdSe, CaTiO 3

P/C;

A1203, SiO2, CaTiO 3, MgA1204,

stoichiometric;

residuary A

CdCrS4 (P)

ZnO reduction to Zn Vac. 10 - 6

[32, 33]

Vac. 10 -5

[18]

Vac. 10 -7.

[34]

Target (composition, type) CdTe, ZnTe, PbTe, InAs, ZnO,

(q, J/cm2; r; Z) 106

ms

Ruby

Cu20 (P)

As/In = 35; Cu 2 0 reduction to Cu

ZnS, Sb2S3, SrTiO3, BaTiO3 (fine P) GaP, GaSb, GaAs, InAs;

(?)

ms Nd:YAG

107-108 ms

Ruby

ZnS, ZnSe, ZnTe, ZnO, CdTe, CdSe;

In2Te 3, Cu2Te (crystals)

108

ns

Nd:YAG

In2Te3, Cu2Te; depending on Ts

A; P/C; Epi; depending on Ts

GaAs, CdS, PbS, PbSe, PbTe,

105-106 ms Nd:YAG

Stoichiometric

Pb-Cd-Se (crystals) A1N, GaN, InN (PP)

P/C; Epi depending on Ts

108

ns

KrF

AIN stoichiom.; GaN, InN partial

Epi ~500~

reduction to Ga and In A1N (C)

~ 108

ns Nd:YAG, 0.95 < N/A1 < 1.2 depending on PN2

PN2 = 5 • 10 -3 Epi 1000 ~C

5 • 10 -5 < PN2 ~ 10 -1

[35]

266 nm h-BN

-~ 108

ns

KrF

Stoichiometric in N 2

P/C c-BN (main)

PN 2 = 5 • 10 - 2

[36]

TiN (SP)

"~ 108

ns

XeCI

Stoichiometric in N2

P/C

5 • 10 - 4 < PN 2 < 10 -3

[37]

TiC (SP)

~ 108

ns

XeC1

Stoichiometric

Nanocrystal

Vac. 10 -5

[38]

Vac. 10 -5

[39]

Vac. 10 -5

[40]

(Ts = 300 ~C) SiC (SP)

"~ 108

ns

XeC1

Stoichiometric

P/C; 3C-SiC (Ts = 800 ~C)

WC (SP)

"~ 107

ms

ruby

(?)

A (Ts = 400~

MoSi 2 (free,falling P)

"~108

ns

CO2

Si/Mo = 11

(?)

Vac. 10 -5

[41]

SiO2, HfO2, ZrO2 (C)

"~108

ns CO2, KrF

SiO2 stoichiom. (CO2" inO2)

(?)

Poe = 10-4

[42]

Reduction to metals

(?)

Vac. 10 -5

[43]

Stoichiometric

A (Ts = RT); P/C

Vac. 10 -5

[44]

PO2 -- 10-4

[45]

10-4 < POe < 10-1

[46]

103 < PO2 < 5 x 10 - 2

[47]

0.2 < PO2 < 5 x 10 - 4

[48]

HfO2, ZrO2 stoichiom, under O~bombardment PbO2, Fe203 (PP)

~107

ms Nd:YAG

ZrO2, A1203 (C)

~107

Ns

CO2

(Ts = 300 ~C) ZnO (SP)

~ 107

ns

KrF

Stoichiometric in 02

Epi (Ts -- 800~

TiO2 (SP)

~108

ns

Nd:YAG

Stoichiometric in 02

A (Ts = RT); P/C (Ts > 500~

95% In203 + 5% SnO2 (SP)

RuO2 (SP)

~108

"~108

ns

ns

KrF

XeC1

Stoichiometric in 02 (resistivity,

A (Ts = RT); P/C

optical measurements)

(Ts > 200~

Stoichiometric in 02

P/C (Ts < 500~ Epi (Ts > 500~

Abbreviations: (P), powder; (PP), pressed powder; (C), ceramics; (SP), sintered powder; A, amorphous; P/C, polycrystalline; Epi, epitaxial; (?), no data.

634

SHAGINYAN

in a gas phase is not peculiar to the composition formation of the films deposited by other PVD techniques.

2.2.2. Mechanisms of Formation of Refractory Materials Films The next large group of materials that can be deposited as films by pulsed laser evaporation are the refractory nitrides, carbides, borides, and silicides. To discuss a mechanism of formation of the aforementioned condensates, it is appropriate to consider separately the materials with volatile components, such as nitrogen. The fabrication of stoichiometric nitride films is difficult because of their dissociation during heating to high temperatures and the large difference in the sticking coefficients of nitrogen and the solid component. The majority of nitrides dissociate under evaporation. This may be due to the smaller binding energy of M e - N in the nitrides than of in M e - O in oxides. Examples are films of gallium and indium nitrides, where a noticeable number of droplets of indium and gallium metals have been detected after the evaporation of their pressed powders. These droplets were present both for evaporation in a vacuum and in nitrogen [34]. At the same time, stoichiometric films of aluminum [34, 35], boron [36], and titanium nitrides [37] could be obtained with substantially lower amounts of metal impurities from their laser evaporation in nitrogen. The authors of [34] mention a correlation between the growth of a number of metal droplets in A1N, GaN, and InN films and decrease in Me--N binding energy. A1N is stable up to its melting point of 2150~ as opposed to GaN, which sublimes at 800~ or especially to InN, which dissociates at ~600~ [34]. Note that some nitrides, like oxides (e.g., aluminum nitride), can be obtained by conventional evaporation without essential dissociation [1 ]. This means that the mechanism of nitride film formation during laser evaporation of a nitride target is principally similar to that of oxides (see above). This is why the stoichiometric films of aluminum nitride could be (similar to some oxides) obtained by evaporation without pronounced deviation from stoichiometry and even without adding nitrogen as a working gas [34]. It should be noted that laser operating parameters can influence the probability of compound dissociation. This factor may lead to a drastic change in the final condensate composition. This phenomenon will be discussed below in more detail for the example of aluminum nitride. It is of value to discuss the possibility of the fabrication of stoichiometric films from the other refractory compounds (carbides, silicides) with respect to the difference in the temperature of intensive evaporation (the temperature at which the vapor pressure is about 10 -2 to 10-1 torr) of their constituents. If the volatilities of the constituents differ greatly, the film might be enriched by an element with a higher volatility. For instance, molybdenum silicide (MoSi2) films contained 11 times more Si than the initial powder [41 ]. The reason for such silicon enrichment is the large difference in the volatilities of silicon and molybdenum vapors. For example, whereas the vapor pressure

of Si achieves the value of 10 -2 torr at ~1900 K, the same vapor pressure of Mo is reached at "~2800 K only. Films of titanium and silicon carbides had a stoichiometric composition during the laser evaporation of these targets in a vacuum [38, 39] despite the large difference in their components' volatilities. It is probable in such cases that the important role belongs to the molecular nature of the evaporation of these carbides. It is known that vapors generated during the conventional evaporation of silicon carbide contain a large number of SiC2 and SizC molecules [49], wereas titanium carbide evaporates coherently [ 1]. The regularities of the formation of PLD films had been investigated in [50]. This paper covers the deposition and investigation of a broad spectrum of materials, including alloys and compounds. The results of the paper are of some interest because the deposition and investigation of all films were carried out under similar conditions. A more detailed consideration of the results of [50], along with those from Table I is of value with regard to getting a clearer idea of the mechanisms of the formation of PLD condensates.

2.3. Experimental Details of Pilyankevich et al. A Nd:YAG laser (~. = 1064 nm, pulse duration -~1 ms, power 1000 J per pulse) was used by Pilyankevich et al. [50]. The scheme of a PLD system used in [50] is presented in Figure 1. The dependence of the film composition on the laser power density was investigated for two values, q = 1.5 • 106 W/cm 2 (defocused regime) and q = 5 • 107 W/cm 2 (focused regime). The power density was varied by variation of the laser spot size at a constant power of 1000 J/pulse. The vacuum conditions were maintained by diffusion pump, and the process was carried out at 5 x 10 - 6 torr. Polished ceramic plates based on (SiO2-TiO2-A1203) oxides and fresh cleaves of NaC1 or KC1 crystals were used as substrates. The substrates were located in two positions relative to the target. One substrate was clamped to the substrate holder that was parallel to the target (line-ofsight position), and the other was placed on the holder positioned at the periphery of the target (off-axis position) (Fig. 1). The substrate-target distance for both substrates was ~50 mm. The temperature of the substrates placed on the holder in the off-axis position can be varied from the liquid nitrogen temperature to 450~ The upper limit of the substrate temperature was defined by the sublimation temperature of the NaC1 or KC1 single crystals used as a substrates. Such substrates are convenient for further investigation of films by transmission electron microscopy (TEM). Such an arrangement of the substrates relative to the target made it possible to estimate roughly the influence of the angular distribution of different species in the laser plume on the composition, structure, and macrodefects of films. Discs of alloys, ceramics (hot pressed powders of compounds), and single crystals were the targets for the evaporation. The composition of the films that did not contain the light constituent was investigated by electron probe microanalysis (EPMA). Because the analysis of light elements by the methods used was impossible, the conclusion about the

PULSED LASER DEPOSITION Table II.

635

Compositionand Structure of Films Deposited by PLD of Alloys and Compounds

Target composition

Film composition

50Fe-50Co 80Fe- 17Ni-3Cr 50Fe-50Si

Coincides with target comp. Coincides with target comp. Coincides with target comp.

50Zr-50Ni 80Fe-20B

FilmmNi, dropletsmZr Not investigated

75Nb-25Si

Si/Nb ~ 2.5-3

LaB6

Not investigated

WSe2 SiC

Coincides with target comp. Not investigated

CdSe CrSi2

Coincides with target comp. Not investigated

FeSi2

Not investigated

TiSi2

Not investigated

TaSi2

Coincides with target comp.

WSi2

Coincides with target comp.

BN A1N Si3N4

Not investigated Not investigated Not investigated

90W- 10Cu (cold-pressed) 90W- 10Cu (hot-pressed)

Strongly enriched with Cu Strongly enriched with Cu

Film structure: initial; after annealing in electron diffraction column

Total mass of ejected products (g); average film thickness (nm) (q = 1.5 • 106 W/cm2)

Total mass of ejected products (g); average film thickness (nm) ( q = 5 x 107W/cm2)

0.1406; ,-~110

0.1399; "-~70

0.0591; 200

0.0779; 70

0.1237; 160

0.1359; 90

0.7834; 130

0.3267; 50

0.1324; 170

0.1094; 70

0.0412; 220

0.0191; 170

0.2484; 130 0.0220; 20

0.1624; 90 0.0340; 20

c~-Fe Coincides with target structure As-deposited amorphous; coincides with target structure at Ts -- 300~ Ni As-deposited amorphous; ot-Fe at Ts = 300~ Amorphous at Ts = 300~ transition to NbSi2 after heating to 800~ As-deposited amorphous; transition to LaB6 after heating to 700~ Not identified As-deposited amorphous; transition to 3C-SiC after heating to 850~ As-deposited polycrystalline CdSe As-deposited amorphous; transition to CrSi2 after heating to 550~ As-deposited amorphous; transition to FeSi2 after heating to 450~ As-deposited amorphous; transition to TiSi2 after heating to 750~ As-deposited amorphous; transition to TaSi2 after heating to 750~ As-deposited amorphous; transition to WSi2 after heating to 800~ Main h-BN; locally c-BN AI As-deposited amorphous; transition to Si after heating to 850~ Not established Not established

Deposition conditions: substrate-target distance 5 cm; substrate is at off-axis position; Ts = RT. (After [50, 86].)

composition of several c o m p o u n d s is based on their structural

Such an approach to the investigation of a wide class of laser

analysis (LAB6, SiC, BN, A1N, Si3N4). The structure of the films was studied by high-energy electron diffraction (HEED)

regard the results obtained to be fair indicators of the mecha-

and selected area electron diffraction (SAED), and the target structure was investigated by X-ray diffraction (XRD). Com-

nisms of their composition formation. The materials under investigation were divided into three

parison of these data made it possible to come to a conclu-

groups. The first group consisted of two types of alloys. The al-

condensates, deposited under similar conditions, permits us to

sion about the correlation between film structure and compo-

loys of the first type, namely, 50Fe-50Co, 70Fe-17Ni-3Cr, and

sition. The a m o r p h o u s condensates were annealed in situ in the

50Fe-50Si, have c o m p o n e n t s with close melting temperatures

electron diffraction c o l u m n until the initiation of the transition from the amorphous to the crystalline state, and the results obtained made it possible to judge their c o m p o s i t i o n and structure.

and temperatures of the intensive evaporation (temperature at which Ps - 10 -1 torr) (Table III). For the alloys of the second type, namely, 50Ni-50Zr, 80Fe-20B, and 75Nb-25Si, these characteristics differ strongly from each other.

636

SHAGINYAN

Fig. 1. A schematic of a pulsed laser deposition system. 1, vacuum chamber; 2, laser (Nd:YAG, 1064 nm, 1000 J/pulse, 1 ms); 3, focusing system; 4a, line-of-sight substrates; 4b, off-axis substrates; 5, target; 6, gas inlet; 7, pumping. (After [50].)

Table III.

Element B

A1 In Cd Sn Co Cr Cu Fe La Mo Nb Ni Se Si Ti W Zr After [1].

Melting Point and Temperatures at Which Saturated Vapor Pressure is Ps = 10-1 torr

Melting point (K)

Temperature at which Ps = 10-1 torr

2360 933 430 594 505 1768 2176 1300 1809 1193 2890 2770 1725 490 1685 1850 3650 2128

2520 1640 1355 593 1685 1960 1820 1690 1920 2200 3060 3170 1970 570 2090 2210 3810 2930

The second group incorporates refractory compounds, chosen by the same principle as alloys (CdSe, CrSi2, FeSi2, TiSi2 m c o m p o u n d s with close c o m p o n e n t melting temperature and volatility, whereas WSi2, TaSi2, WSe2, LAB6, and SiC are compounds with very different c o m p o n e n t melting temperatures and volatility). The third group contains the nitrides BN, A1N, and Si3N4 with a volatile nitrogen component. The results of composition and structure investigations of obtained condensates are reported in Table II; the micrographs represent the characteristic structures of condensates.

2.3.1. Results: Alloy Evaporation The majority of the results of investigations of composition and microstructure have been obtained for films deposited on the substrates located in an off-axis position. This is due to the fact that the much smaller n u m b e r of large particles present in them made composition investigations difficult. The point is that E P M A gives the film composition as an average over the area under analysis. The presence of droplets with a mass larger than that of the entire film in this area shifts the results of such an analysis toward the excess of the droplet c o m p o n e n t in the film. In the cases where analysis was possible for the films deposited in both positions, no difference in their composition has been detected. The mean thickness of the films of alloys, deposited by one laser "shot" on the off-axis substrate, was 3 0 - 1 4 0 nm/pulse

PULSED L A S E R DEPOSITION

637

Fig. 2. Microstructure and corresponding SAED patterns of 50Zr-50Ni alloy films deposited at two different power densities. (a) q = 1.5 x 106 W/cm2 (defocused regime). (b) q = 5 • 107 W/cm2 (focused regime). (c, d) Corresponding SAED patterns.

Fig. 3. Microstructure (a) and diffraction pattem (b) of the 70Fe-17Ni-3Cr alloy film.

when a laser was operated in the defocused regime, whereas the thickness of the films was ~ 10-50 nm/pulse in the case of a laser operating in the focused regime. The role of power density can be demonstrated by the example of films obtained by the evaporation of the alloy 50Zr-50Ni (Fig. 2a-c). For evaporation in the defocused regime when the laser spot diameter on the target was ~ 6 mm, the crater depth was less than its diameter and the number of defects (droplets and punctures) was much smaller than that for the case of focused regime evaporation. When the evaporation was carried out in the focused regime the depth of the crater was 1.2-1.5 times larger than its

diameter. In this case the traces of solidified melt that splashed out of the crater were present at the crater edges. The micrographs of the films obtained by the evaporation of alloys 70Fe- 17Ni-3Cr, 50Fe-50Co, and 80Fe-20B are presented in Figures 3-5. Such a microstructure was inherent to the alloy films deposited on the substrate at room temperature. The main difference in the morphology of the films of alloy deposited at room temperature was the different mean grain size. The micrographs and electron diffraction patterns of Zr film deposited simultaneously on line-of-sight and off-axis substrates are shown in Figure 6a,b. It is seen that the film deposited

638

SHAGINYAN

directly from the laser plume (line-of-sight substrate, Fig. 6b) has a large number of defects, like punctures and droplets. The structure of the latter film was always polycrystalline (Fig. 6c), whereas the regions with quasi-amorphous (or fine-grained) structure (Fig. 6d) were present in the film deposited on the off-axis substrate. The films deposited by evaporation of the alloys with silicon or boron constituents (50Fe-50Si, 80Fe-20B, 75Nb-25Si ) on the substrate at room temperature were amorphous. The EPMA investigations of the films deposited by the evaporation of 80Fe-17Ni-3Cr, 50Fe-50Co, and 50Fe-50Si alloys,

containing the elements with close thermophysical parameters discussed above, have shown that the film composition coincided with that of corresponding targets (Table II). The structural analysis of targets and films confirmed the similarity of their structures. If the components with strongly different volatilities were contained in an alloy, then the corresponding condensates were enriched in the element with the larger volatility. The films obtained by the evaporation of the 75Nb-25Si alloy were amorphous regardless of their deposition on cold or heated (300~ substrates. Heating of the films to 800~ in an electron diffrac-

Fig. 4. Microstructureof the film deposited from 50Fe-50Co alloy target.

Fig. 5. Microstructureof the film deposited from 80Fe-20B alloy target.

Fig. 6. Microstructureof Zr films deposited on substrates located at (a) off-axis position and (b) line-of-sightposition. (c, d) Corresponding SAED patterns.

PULSED LASER DEPOSITION

639

Fig. 7. Microstructureof CrSi2 filmsdeposited at two different power densities. (a) q = 1.5 x 106 W/cm2. (b) q = 5 x 107 W/cm2. (c, d) SAED patterns from the film presented in a and b, respectively.

tion column promoted the formation of the crystalline structure of the film with the NbSi2 lattice. The analysis of the composition of as-deposited films by EPMA confirmed that the silicon amount in the film was 2.5-3 times higher than that in the target. The structure of condensates obtained by the evaporation of the 80Fe-20B target was similar to that of c~-Fe, whereas the target material consisted of two phases, Fe2B and Fe. The SAED investigation of the structure of films, obtained by the evaporation of the 50Zr-50Ni alloy, was hindered by the presence of many Zr droplets of different sizes (Fig. 2a, b). But in a few cases when it was possible to take the diffraction pattern from a film area free of droplets, its structure corresponded mainly to that of nickel.

2.3.2. Results: Evaporation of Compounds with Nonvolatile Components The micro- and crystalline structures of the films obtained by pulsed laser evaporation of the refractory materials targets (LAB6, YbB6, SiC, CrSi2, TiSi2, TaSi2, WSi2) exhibit peculiarities different from those of films deposited by alloy evaporation. These films have significantly smaller amounts of macrodefects in the form of droplets and punctures. Those films were amorphous for the deposition on unheated substrates. The variation in laser power density has a weaker influence on the amount of macrodefects in these films, in contrast to that deposited

from the alloy targets. It is seen from a comparison of the microstructure of CrSi2 and WSi2 films deposited by the irradiation of corresponding targets in focused and defocused regimes (Figs. 7a-d and 8a, b). The large average thickness of the film deposited per laser pulse (100-200 nm/pulse) is a noticeable peculiarity of laser evaporation of these materials. Another important peculiarity is that the average thickness of the film deposited per pulse of focused radiation was 1.5-3 times smaller than that deposited by defocused radiation. This regularity was not observed for the average mass of the products ejected under the focused and defocused laser radiation what was revealed by the target weighting before and after laser "shot" (Table II). The depth of the crater left on these targets by the laser "shot" was usually less than its diameter, even for the case of focused radiation. No traces of molten materials have been detected on the crater edges. The peculiar defects of films deposited by pulsed laser evaporation of the refractory materials were rarely encountered large droplets (0.1-10 #m), punctures, and traces of reflected droplets. The composition of droplets depends on the evaporated compound composition. For instance, the droplets on rare-earth metal hexaborides usually had the structure of the corresponding hexaboride (Figs. 9a-c, and 10). At the same time the droplets on the films obtained by the evaporation of hot pressed powders of silicides and single crystals of silicon

640

SHAGINYAN

Fig. 8. Microstructure o f W S i 2 films deposited at two different power densities. (a) q = 1.5 • 106 W/cm 2. (b) q = 5 • 10 7 W/cm 2. Solidified silicon droplets, pinholes and traces of reflected droplets are clearly seen in b.

Fig. 9. Microstructure and corresponding SAED patterns of LaB 6 film. The right side of micrograph (a) corresponds to the film microstructure. (b) S A E D pattern from film area. The left side of micrograph (a) corresponds to the microstructure of a solidified LaB 6 droplet on the film. (c) Corresponding SAED pattern from the droplet.

Fig. 10. Solidified droplet of YbB 6 on a film deposited by pulsed laser evaporation of YbB 6.

Fig. 11. TiS2 film with silicon droplets and pinholes. The film was deposited at a laser power density q -- 1.5 • 10 6 W/cm 2.

carbide (6H-SiC) were the droplets of pure silicon (Figs. 11 and 12). The film structure in the close vicinity of a droplet was crystalline. The heat produced during freezing of the molten droplet was sufficient to crystallize the amorphous film in the droplet vicinity. This is seen from Figs. 9b and c, where S AED patterns, taken from the droplet itself and from the film area remote from the droplet, are presented. The structure of the droplet and the film in its close vicinity (the region of the film

adjacent to the droplet, see Fig. 9a) corresponds to LAB6, and the structure of the film far from the droplet is amorphous. The films of LaB6 and other hexaborides (YbB6, DyB6) deposited on the substrates at a temperature below 400~ were amorphous. The in situ annealing of these films in the electrondiffraction column up to ~700~ leads to their crystallization. The composition of the condensates was similar to the initial hexaboride in all of the cases considered.

PULSED LASER DEPOSITION The structure of condensates deposited on substrates at a temperature below 400~ by the evaporation of single-crystal 6H-SiC was amorphous. The heating of these condensates in the electron diffraction column to ~850~ promoted their crystallization in the 3C-SiC phase. Electron microscopy and selected area electron diffraction studies of as-deposited amorphous silicon carbide films reveal the presence in the amorphous matrix of small areas with a clearly seen crystalline structure (Fig. 13) corresponding to the 3C-SiC phase.

Fig. 12. PLD.

Solidified silicon droplet on the surface of SiC film, deposited by

Fig. 13. Microstructure of as-deposited SiC film. The structure of the upper left side of the film corresponds to polycrystalline 3C-SiC. Most of the film area is amorphous.

641

Droplets have also been detected in films obtained by the evaporation of silicide (CrSi2, TiSi2, TaSi2, WSi2) targets. But the mean size of the droplets was smaller and their number was larger than those for hexaborides and carbides (Figs. 7 and 8). The structural analysis of the droplets was hindered because of their small size. But in a few cases where the analysis was possible, it was revealed from SAED patterns that the droplets have a structure peculiar to that of silicon. At the same time the silicide condensates in some cases were slightly enriched by a silicon, as was shown by EPMA. The as-deposited amorphous silicide films transited into the crystalline state after their annealing in the electron-diffraction column, and the structure of annealed films coincided with that of the target. The study of the temperature of the transition from the amorphous to the crystalline state for different silicide films deposited under similar conditions shows that it is different for different silicides. For instance, the transition from the amorphous to the crystalline state for a CrSi2 film occurred at a temperature of ~420~ whereas for WSi2 it was ~650~ The temperature of crystallization initiation of amorphous silicide films also depends on the radiation power density. On average this temperature was ~ 100-150~ less when the film was deposited under a larger radiation power density (in the focused regime). For example, the crystallization of WSi2 films deposited at q -- 5 • 107 W/cm 2, was initiated at ~650~ whereas the crystallization of those deposited at q = 1.5 x 10 6 W / c m 2 w a s initiated at ~750~ (Table IV). The films obtained by the evaporation of a cold-pressed powder of low-melting-point CdSe are thick (~200 nm/pulse) and structurally and morphologically inhomogeneous. When deposited on a substrate at room temperature, they have a polycrystalline structure with frequently observed single crystal inclusions (Fig. 14). The composition and the structure of these films coincides with those of the target. The condensation of the film did not occur on the substrates heated to over ~400~ becuse of its reevaporation. The films obtained by laser evaporation of a WSe2 target were also thick (~ 150-200 nm/pulse) and on average had more macrodefects than the other films of this group of materials (Fig. 15). Their structure consists of two phases, amorphous

Fig. 14. Microstructure of CdSe film. Regions with different grain sizes are clearly seen. The SAED pattern confirms the film microstructure inhomogeneity.

642

SHAGINYAN

Fig. 15.

(a) Microstructure of a WSe2 film. (b) Halos on the SAED patterns are the evidence of an amorphous film structure.

Fig. 16. (a) Microstructure of a film deposited by laser ablation of an A1N ceramic target. (b) The crystal structure of the film corresponds to that of aliuminum, as follows from the SAED pattern.

Table IV. Temperature of Amorphous to Crystalline Phase Transition for Silicide Films, Deposited at Two Power Densities by PLD and Obtained by Magnetron Sputtering Temperature of amorphous to crystalline transition (~ Silicide film

PLD;

PLD;

Sputtered

q = 106 W/cm 2

q -- 5 x 107 W/cm 2

[71] --~300

CrSi 2

-~560

~420

WSi 2

~750

~650

TaSi 2

--,750

~600

--~380

TiSi2

--~750

"~600

~300

and polycrystalline. These phases were revealed in the films deposited on the substrate at room temperature and on that heated to 400~ Unambiguous identification of the structure of the crystalline phase of this film was impossible. However, interplanar distances neither of WSe2 nor of W and Se were revealed. EPMA analysis of these films showed the coincidence of the composition of the film and that of the target. The general feature of all condensates deposited by pulsed laser evaporation of refractory compounds is the coincidence, to first order, of the film composition with that of the target.

2.3.3. Results: Evaporation of Compounds with Volatile

Components Micro- and crystalline structures of the films obtained by the evaporation of nitride (A1N, Si3N4, and BN) targets were different. The films deposited in the temperature range from room temperature to 500~ by the evaporation of an A1N target were homogeneous and coarse-grained. Droplets and other macrodefects were almost absent in these films. These films have a crystalline structure with a lattice constant peculiar to aluminum. The microstructure of a film deposited by the evaporation of an A1N target on a substrate heated to Ts < 500~ is shown on the micrograph in Figure 16. The patterns on the condensate surface are the consequence of decoration by aluminum of thermally etched regions of a single-crystal NaC1 substrate surface during its preheating before film deposition. The variation of laser power density and substrate temperature has no influence on the film composition. The thermal etching patterns of the single-crystal NaC1 surface have also been observed on the microstructure of films deposited by evaporation of a Si3N4 target on substrates heated to over 450~ (Fig. 17a). However, the films remained amorphous, even at this substrate temperature (Fig. 17b). Droplets of solidified silicon are present on the surface of such films (Fig. 18a). When the droplet was large, then the structure of

PULSED LASER DEPOSITION

643

Fig. 17. (a) Microstructure of the film deposited by laser ablation of a Si3N4 ceramic target. (b) The film structure is amorphous, as is evident from the SAED pattern.

Fig. 18. (a) Solidified silicon droplet on the surface of a film deposited by laser ablation of a Si3N4 ceramic target. The structure of the film adjoining the droplet corresponds to silicon (spotty tings on SAED pattern b), whereas the main film area is amorphous(halo in SAED pattem b).

the film in the vicinity of the droplet was crystalline and its structure coincided with that of silicon (Fig. 18b). The density of the laser pulse power had no essential influence on the film structure. The in situ annealing of amorphous films obtained by Si3N4 evaporation provides the transition of amorphous film to the crystalline state, where the structure coincided with that of silicon. It should be noted that the crystallization temperature (850~ for these films is higher than that for amorphous silicon films of the same thickness. This fact was established by pulsed laser evaporation of single-crystal silicon targets under similar conditions. The silicon films obtained by this method were also amorphous. Their crystallization during in situ annealing occurs at 650~ The most probable reason for the higher thermal stability of the amorphous phase in the films deposited from a Si3N4 target as compared with that deposited from a Si target is the nitrogen impurity they contain. Films obtained by laser evaporation of the graphite-like boron nitride had a substantially higher density of macrodefects and were inhomogeneous as compared with those of the above considered nitrides (Fig. 19a). The HEED studies of these films had shown that they are amorphous if deposited on substrates heated to 450~ (Fig. 19c). The SAED investigations revealed small areas of the film with polycrystalline structure. These

polycrystalline areas consisted mainly of graphite-like h-BN, although sometimes the areas with c-BN structure have also been observed (Fig. 19b). The irradiation of a h-BN target at a lower power density (q -- 1.5 • 10 6 W/cm 2) resulted in the formation of BN film with larger areas of the polycrystalline h-BN phase together with amorphous areas. In this case the polycrystalline phase was revealed not only by SAED but also during the HEED investigations. The amorphous phase in boron nitride films (similar to that of silicon nitride) consists, most probably, of boron with nitrogen admixture. This phase evidently arises because of incomplete boron nitride dissociation under the laser impact. The composition of the films deposited by laser evaporation of A1N and Si3N4 targets in nitrogen gas ambient at PN2 : 10 -2 torr was similar to that deposited in a vacuum.

2.4. Formation of PLD Film Composition

2.4.1. Role of the Target Type and Chemical Bonding The above studies have shown that the film composition depends on the chemical bonding of target constituents (alloys or compounds), on the target type (cast or pressed powder), and

644

SHAGINYAN

Fig. 19. (a) Microstructure of a BN film obtained by laser ablation of a h-BN target. The main part of the film has an amorphous structure (SAED in c). Rarely observed small polycrystalline film areas correspond to the c-BN phase (SAED in b).

on the laser radiation power density [50]. If target components are not chemically bonded or are weakly bonded (as in some alloys), the resulting film composition depends greatly on the thermophysical properties of each of the components. If the target material is a compound in which the constituents are chemically bound, the resulting film composition does not depend for the most part on the thermophysical properties of each of the components. The film composition weakly depends on the radiation power density for the case of pulsed laser evaporation of the compound targets with nonvolatile constituents. Let us consider the mechanism of the influence of the above noted target features on laser film composition formation. Physically the difference between the target types is determined by their thermal conductivity. The thermal conductivity of a cast target is substantially larger than that of a nonpressed or even a hot-pressed powder. The thermal conductivity of a material is one of the most important characteristics defining the effectiveness of laser evaporation. The thermal conductivity coefficient linearly enters the expression for the effectiveness of substance evaporation by laser radiation. This expression gives the relation between the thermophysical and optical characteristics of a substance and radiation energy [3]: B

Ka Hv I (1 - R ) C p

where B is a dimensionless parameter, K is the thermal conductivity, ct is the absorption coefficient, Hv is the heat of evaporation, I is the laser power density, R is the reflectivity, and Cp is the heat capacity. The dimensionless absorption parameter B can be regarded as a ratio of the heat (per unit area) required to evaporate a layer with a certain thickness and the deposited heat (per unit area) from laser irradiation. In general, for a smaller value of B ( 1), particulates are the dominant form of material removal. The material dependence of the B factor is reflected in various physical parameters: K, ct, R, Cp. Under similar conditions the share of the vapor phase depends on the target material thermal conductivity, which in turn depends on the target type. The

lower the thermal conductivity, the higher is the share of vapor in ablated products. From this point of view the maximal temperature will be achieved at the surface of free (nonpressed) powder, and the temperature at the surface of a cast alloy target (at the same laser power density) will be minimal because of its high thermal conductivity. This means that the probability of total evaporation of all target constituents will be higher in the case of a target with low thermal conductivity. The second reason for the difference in the composition of laser films deposited by evaporation of alloy and compound targets is the difference between the binding energies of the atoms in an alloy or compound. The atoms in an alloy are weakly bound or are not bound at all, whereas the binding energy in a compound is on the order of electron volts. Therefore during the conventional evaporation of the alloy the resulting film composition has to depend on the thermodynamic characteristics of each of the components because the evaporation occurs as an independent vaporization of each component according to Raul's law [ 1]. The atoms in compounds are bound by chemical interaction with the energy, depending on the particular properties of the compound components. This energy value and crystalline lattice symmetry determines whether the evaporation of a compound is accompanied by its complete dissociation or partial dissociation or occurs without dissociation [1]. It is clear that if the vaporized compound does not dissociate, then it is quite possible to obtain a condensate with a composition similar to that of the initial substance. In the case of evaporation with dissociation, the condensate composition depends on the volatilities of the compound components. The composition is similar or close to the initial composition in the case of close volatilities of compound components. If the initial compound involves a gas component as a constituent and the evaporation is accompanied by dissociation, it is impossible to obtain a stoichiometric condensate from its evaporation in a vacuum.

2.4.2. Target Effects during Excimer Laser Evaporation Some problems related to the target effects influencing the film composition can arise during the use of an excimer laser oper-

PULSED LASER DEPOSITION ated in the frequency regime. One of the important problems related to target surface effects of low-power and low-pulselength frequency laser (excimer laser) ablation was the texturing of the target by the incident laser beam, which makes a nonnormal incidence angle with the target. Because of the shadowing effects, as the target is irradiated, surface features are enhanced via cone formation [51]. The cone formation leads to a shift in the angle of the emitted evaporant toward the laser beam. Because the composition and the thickness of the film are optimal when the film is deposited from the peak of the plume emitted from the target surface, a shift of the plume direction is a serious problem for the deposition of stoichiometric films. Another problem related to target surface changes under low-power frequency irradiation is surface segregation [52]. Surface segregation is the preferential enrichment at a surface or grain boundary of one or more components of a multicomponent target. The model of this process incorporates both the propagation into and withdrawal from the bulk target of a melt front. As resolidification begins, higher-melting-point components of the liquid freeze first, driving lower-meltingpoint liquid components toward the surface. This type of process is used to explain the compositional changes in YBCO PLD films in [52]. As Cu-rich material segregates to the top of the melt, it is removed by evaporation during laser pulses, leaving behind an yttrium-enriched surface. As Y enrichment proceeds, the laser begins interacting with increasingly transparent material~Y203 is transparent enough to allow a greater melt depth. However, the process is self-limiting, because the distance over which Cu must diffuse toward the surface becomes large. As a result, changes in the PLD (1 J/cm 2, KrF excimer laser) YBCO films were observed. These films were initially copper and barium rich until (at 40 shots/site) a steady-state composition was reached [53]. One more effect that is able to influence PLD film composition is the postevaporation from the hot target after termination of the pulse. This effect was experimentally established by high-speed photography of the film thickness during laser evaporation of a ZnS target with a millisecond pulse duration [54]. The duration of the postevaporation time can vary from one to hundreds of milliseconds, depending on the thermal conductivity of the target and melting point of the target constituents. Evidently the postevaporation mechanism in this case still has the same drawbacks of composition formation that are intrinsic to conventional evaporation. The results described in [50] were obtained by the evaporation of the target with a high power laser pulse (1000 J/pulse) of sufficiently large duration (~1 ms). The thickness of the film deposited per pulse under these conditions can be sufficient for its potential applications, so the second "shot" has to be aimed at another location on the target. Therefore the above described problems inherent to frequency excimer laser evaporation are not urgent for lasers operating in a high pulse power regime.

645

2.4.3. TargetEffects during High.Power-Long-Pulse Laser

Evaporation Our investigations of metal and alloy target surfaces had shown that two significantly differing zones appear after laser irradiation. The first zone (zone I) is a zone of direct laser influence. This zone is the bottom of the crater and appears as a smooth surface with rarely encountered solidified "bubbles" of metal. The bubbles are probably the result of subsurface boiling [10]. The second zone (zone II) adjoins the first and has a typical dendritic pattern formed during cooling of the melt of metals or alloys. The second zone is separated from the first by an intermediate region combining the features of the first and second zones (Fig. 20). It is clear that the temperature in zones I and II is quite different during the laser pulse action. The heating of zone I (up to the highest temperature) occurs by direct laser power transfer to the target. The size of zone I (zone of complete evaporation) is approximately equal to the laser spot diameter. The temperature in zone II is lower than that in zone I because of losses of radiation power to the heating and melting of the target. Whereas the size of zone I depends mainly on the laser spot diameter, the zone II dimensions depend on the temperature in zone I and the thermal conductivity of the target material. The composition of the film can be identical to that of the target in the case of the saturation vapor pressure balance of different target constituents. Vapor pressure balance is possible in two cases: when the saturation vapor pressure of different target constituents is equal at different temperatures, or when the temperature of the evaporation surface is so high that the

Fig. 20. Crater on the surface of an 50Fe-50Co alloy target after a laser "shot." Three temperature zones are clearly seen. The higher temperature zone is the smooth area with few bubbles at the bottom of the crater (the upper left corner of the picture). The minimum temperature zone is the edge of the crater with dendritic patterns formed during the melt splashing cooling (the lower right corner of the picture). The zone with the intermediate temperature is situated between the above two zones and corresponds to crater walls with partially crystallized melt.

646

SHAGINYAN

difference between the saturation vapor pressures of different constituents disappears. The highest temperature of an evaporation surface can be achieved in zone I. Therefore one can expect that the composition of a PLD film will be identical or close to that of the target when the film is formed only by the vapors from zone I. However, the effect of postevaporation [54] from zone I can somehow change the composition of the film deposited from vapors of zone I. The deviation of the film composition depends on the thermophysical properties of constituents of the target and its thermal conductivity. The evaporation mechanism from zone II is quite different from that of zone I, and it is similar to that at evaporation by conventional heating. Therefore the composition of the deposit from the vapors from zone II can deviate significantly from that of the evaporant [ 1]. Thus the effectiveness of PLD (with respect to the film composition formation) depends on the ratio of the sizes of zones I and II. The larger zone I is in comparison with zone II, the closer the film composition is to that of the target. This argumentation confirms the results of our investigations of the ablated targets and correlates with the data of [ 12, 25, 28]. The authors of these papers described the appearance of two components in the laser plume. One component has a stoichiometric composition of vapors and is formed by a nonlinear evaporation process at optical irradiation, and the other component is the result of conventional evaporation. It was shown in [28] that at lower energy densities the thermal evaporation component dominates. The consequence of this is the deviation of the composition of the deposited film from the proper stoichiometry. The ratio of zone I and zone II sizes depends on the ratio of parts of laser power consumed both by the evaporation and by the heating of the target material by thermal conductivity. One can increase the part of the laser power consumed by the evaporation by decreasing the time of its input (decreasing the pulse duration) and by increasing the absorption coefficient. The latter parameter can be optimized by using a laser with the relevant wavelength. Excimer lasers provide the possibility of variation of the wavelength and a pulse duration a few orders of magnitude shorter than that of lasers working in a free-running regime. However, at a nanosecond pulse length the power density of an excimer laser achieves values of 101~ to 1011 W/cm 2. Moreover, in this operating regime the absorption (by vapors) of laser radiation becomes significant [7]. In this case the deposition rate drops because of decreased evaporation effectiveness. Simultaneously the properties of the FFS change significantly. The number of charged species in the FFS increases drastically, and the process of molecule dissociation is also enhanced [ 18]. These effects can negatively influence the composition and the structure of the laser condensates. Now let us consider the mechanisms of composition formation of laser films. This will be done according to the papers from Table I and [50]. For the sake of simplicity, we will base the subsequent discussion mainly on our results regarding laser alloy and compound films [50].This is because all experiments in this work were carried out on a wide class of materials and

under identical deposition conditions. The latter means that the rate of laser power input is similar for different targets, and the rate of its dissipation depends on the individual target material properties, such as the absorption coefficient and thermal conductivity.

2.4.4. Mechanism of Composition Formation of Alloy Films The diameter of the craters appearing on alloy targets after a laser "shot" was 4-5 times larger than the laser spot. One could observe the signs of molten and crystallized substance (Fig. 20) on the edges of the craters. This indicates that a zone heated to high temperatures because of thermal conductivity (zone II) significantly exceeds a zone of direct influence of laser radiation (zone I). We should remember here that because the temperature in zone I is much higher than the evaporation point of most refractory alloy components, all initial alloy components in this zone are evaporated simultaneously. But, in zone II, the temperature is much lower (than that in zone I), so that the actual evaporation point of each alloy component becomes important from the point of view of the resulting film composition. Hence, one may conclude that the film composition is mainly due to the vapor pressure of the alloy components (because the film is formed from almost all of the vapors from zone II). This means that the mechanism of evaporation of alloys by a laser operating in free-running mode is close to the conventional evaporation of alloys and obeys the Raul law. That is, the alloy constituents evaporate independently of each other like pure metals and predominantly as separate atoms [ 1]. In fact, if the alloy is composed of elements with equal vapor pressures (e.g., 10-1 torr) at close temperature, the composition of the condensates coincides with that of the target as it is observed for the alloys 80Fe-17Ni-3Cr, 50Fe-50Co, and 50Fe-50Si (see Table II). When these thermophysical characteristics of alloy constituents are significantly different, the film is enriched in elements with lower temperatures of intensive evaporation (more volatile element), as was observed for 75Nb-25Si and 80Fe-20B alloys. An important effect for the laser evaporation of alloys was revealed during an investigation of a film obtained by laser ablation of the 50Zr-50Ni alloy. The large amount of droplets was revealed in the films deposited both in focused and defocused evaporation regimes. The films deposited in the focused regime contain relatively large amount of droplets (Fig. 2a, b). EPMA investigations had shown that the films are enriched in zirconium. Simultaneously, as shown by SAED investigations, the main phase in these films was nickel. Taking into account that the mass of the droplets per film area is larger than the mass of the film of the same area, and keeping in mind the peculiarities of EPMA and SAED methods, one can suppose that the droplets in the film are mainly composed of zirconium. This effect can be explained as follows. The difference between the melting point and the temperature at which the vapor pressure P = 10 -1 torr is significantly lower for nickel than that for zirconium. At the same time, the temperature at which P -- 10-1 torr for nickel is close to the melting point of zirconium.

PULSED LASER DEPOSITION Therefore the nickel on the evaporation surface is mainly present as a vapor, whereas the zirconium is present mainly as a melt. The recoil pressure of nickel vapors ejects the molten zirconium from the evaporation zone, and zirconium is transported to the condensation surface in the form of droplets. In the focused evaporation regime, when the narrow and deep crater forms, the vapors accumulated in the crater absorb laser irradiation and transfer the excessive heat energy to the crater walls. Because the molten evaporation area in this regime is larger, one can expect an increased number of zirconium droplets in the condensate deposited in this regime. Just this effect is observed in the micrographs (Fig. 2a, b), reflecting the microstructure of Zr-Ni condensates obtained under two deposition regimes. The EPMA investigation of the surface of the crater on the 50Zr-50Ni alloy target showed that it was slightly enriched in zirconium compared with the proper composition. This is quite understandable, because the evaporation rate of nickel is higher than that of zirconium. The results obtained during the study of laser evaporation of the 50Zr-50Ni alloy confirm the above discussed laser evaporation mechanism of the alloys and simultaneously reveal the thermophysical parameters of the target material responsible for the droplets in PLD films. A more detailed study is made below of the influence of thermophysical parameters of metals on the particulates in PLD films. The difference in the structure of the films deposited on the substrates at the same temperature in the range of 20-350~ by laser evaporation of alloys is striking. If the alloys are composed only of metals (e.g., 80Fe- 17Ni-3Cr, 50Fe-50Co), the deposited films have a polycrystalline structure, whereas the films deposited from the alloys with nonmetal constituents like silicon or boron (e.g., 50Fe-50Si, 80Fe-20B, 75Nb-25Si) were amorphous. Most likely this effect has something to do with the partial formation of silicide or boride molecules in a gas phase and their condensation at the growth surface. The formation of molecules in a gas phase in a dense laser plasma is firmly established [3, 5]. At the same time the probability of the formation of metal molecules or clusters in a gas phase is low because of weak chemical bonding of metal atoms [5]. The surface mobility of molecules is lower than that of the atoms, and the crystallization temperature of silicides or borides is higher than that of the corresponding metals. These two factors hinder the formation of the crystalline phase in the films of such alloys on a substrate at a low temperature. Note that such an effect is typical for films of high-melting-point materials deposited by other PVD methods. This observation permits us to suggest yet another probable composition formation mechanism for PLD films of alloys containing elements with higher (than metals) chemical bonding energies. This issue is discussed below.

2.4.5. Mechanisms of Composition Formation of Compound Films

The thermal conductivity of compound targets (A1N, BN, Si3N4, LAB6, YbB6, CdSe, WSe2, SiC, CrSi2, TiSi2, TaSi2, WSi2) in the form of hot-pressed powders (ceramic targets) was

647

significantly lower than that of the melting-cast alloy targets. Note that such targets have been used in many of the works cited in Table I. The craters that appeared on such targets after a laser "shot" had dimensions close to the laser spot diameter and showed no signs of melting. There is one more important effect observed during laser evaporation of ceramic targets. This effect demonstrates the difference between the evaporation mechanism of alloys and compounds and consists of the difference in the mean thickness of the film deposited per pulse. The mean thickness of the film deposited per laser pulse during evaporation of the ceramic target was 100-200 nm, and this value was 30-140 nm for alloy targets. These facts indicate that the effectiveness of laser evaporation of compound targets is higher. This means that the share of laser power expended on the evaporation is larger for this type of target. The temperature in a zone of direct laser pulse action in the case of a ceramic target is significantly higher, and the evaporation was mainly from this zone (zone I). Therefore under these conditions the evaporation mechanism approaches that expected for laser evaporation. That is, it was expected that the temperature of the target in a zone of direct pulse action is so high that the difference in saturation vapor pressures for compound constituents disappears. In this case the composition of the condensate coincides with that of the target. Analysis of BN, CdSe, LAB6, YbB6, WSe2, SiC, CrSi2, TiSi2, TaSi2, and WSi2 films confirmed the coincidence or similarity of the target and film composition despite the fact that these compounds have significantly different dissociation energies and are formed of components with substantially different volatilities. At the same time, some silicide films (e.g., TaSi2, CrSi2) were slightly enriched in silicon, and an excess of silicon was also revealed on the surface of the crater of a CrSi2 target. The surplus of the silicon in these films was concentrated in solidified silicon droplets on the film surface. This implies that despite a more effective input of laser optical radiation (due to lower thermal conductivity of the target), some deviation of the film composition from stoichiometry still takes place. The reason for this effect is the difference in the thermophysical properties of the target constituents. The influence of this factor is similar to that proposed above in the discussion of film composition formation by laser evaporation of a 50Zr-50Ni alloy. That is, the difference between the temperature at which the vapor pressure P = 10-1 torr and the melting point of chromium is negative ( - 5 0 6 K), whereas the same difference for silicon is substantially larger (265 K). This means that when the temperature of the surface becomes so high that chromium begins to evaporate intensively, silicon only melts. The recoil pressure of chromium vapors ejects the molten silicon from the evaporation zone, so that silicon is transported to the condensation surface as droplets. This process can be realized at the very beginning of the pulse action, when the temperature at the target surface is not sufficiently high as well as after the pulse action during the cooling of the target. Therefore abundant silicon was revealed both on the surface of the crater

648

SHAGINYAN

on the CrSi2 target and as droplets in the corresponding film (Fig. 7a). The evaporation of a single-crystal 6H-SiC target also occurred with some dissociation that was revealed by the presence of solidified silicon droplets on the film surface (Fig. 12). The other indication of the dissociation of silicon carbide under laser irradiation was the structure of annealed SiC films that corresponds to the 3C-SiC phase. It is known that the presence of an over-stoichiometric silicon in silicon carbide stabilizes the cubic 3C-SiC phase [49]. Similar results were obtained in [39]. It should be noted that SiC target types were different in [39] and [50]. The SiC target in [39] was ceramic (sintered SiC powder); the target in [50] was 6H-SiC single crystal. The thermal conductivity of a single-crystal target is much larger than that of ceramics. Therefore if the evaporation mechanism of SiC was mainly dependent on the thermal conductivity of the target but not on the atomic bonding, the composition and structure of the films deposited in [39] and [50] would be different. The above consideration shows that the mechanism of conventional low-temperature evaporation has also been realized under laser evaporation of compounds, but to a lesser degree than in the case of alloys. Aforementioned investigations of the composition of laser plasma during YBCO target evaporation with an excimer laser (~. = 248 nm, q ,~ 1 J/cm 2, r = 30 ns) confirm this conclusion. The presence of two components in laser plasma has been revealed in these investigations. The composition of one of these components corresponds to the vapor generated under conventional evaporation. This was the reason for the deviation of the film composition from stoichiometric [28]. Ultrafast photography techniques have been used to observe the temporal evolution of the fragments of laser ablation of YBCO in an oxygen background gas [55]. It was established that the time interval over which material is evaporated from the target surface may be significantly longer than the laser pulse length. The authors also established that the temperature of the target surface was close to the melting point of YBCO (--~1400 K) for a rather long time after the laser pulse ceased. These results correlate well with the data obtained in [54] for ZnS laser evaporation with a millisecond pulse length. The coincidence of the results obtained for different compounds deposited by laser evaporation with quite different power densities indicates that the processes occurring under such different conditions have the same nature and tend to suggest the important role of the mechanism of conventional evaporation in film composition formation during PLD. Indirect confirmation of this conclusion is provided by the fact that most of the films deposited by PLD with stoichiometric composition can also be obtained by conventional evaporation of the same compounds. Among them are the compounds AIIB vI, A1203, ZrO2, In203, SnO2, SiO, SiO2, TiO2, BaTiO3 [ 1], SiC [49], LAB6, and YbB6 [56, 57], the evaporation of which occurs congruently, coherently, or molecularly. From Table I it is seen that the films of just these compounds with stoichiometric composition were successfully deposited by PLD.

2.4.6. Composition Formation Mechanism of PLD Films Compounds with Volatile Components The mechanism of formation of a film with complex composition includes at least two processes. One is film composition formation from separate chemical elements on the growth surface, and the second is formation of a film from the molecules of a compound. The generation of FFS by conventional PVD methods occurs during the evaporation or sputtering of the target. In this case the source of separate atoms and molecules is the condensed matter (target). It is clear that the composition of the film is closer to that of the target in the case of molecular sputtering or evaporation of the condensed phase. For pulse laser evaporation there is one more source of molecules, which is the gas phase. As was already mentioned, the formation in a gas phase of clusters, containing two or more atoms is one of the significant peculiarities of PLD. Let us consider the role of this effect in the formation of the composition of PLD films. Formation of molecules or polyatomic clusters in a gas phase can occur during pulse laser evaporation in a vacuum and in a chemically active background gas. The ability of the evaporant to aggregate is one of the main conditions of gas-phase cluster generation under direct laser evaporation of a material in a high vacuum. Some chemical elements such as sulfur, silicon, and carbon can easily aggregate, and their clusters have been produced by direct laser ablation of a solid target under high vacuum conditions. For typical metals the laser plasma is composed mostly of atomic species. Because of their weak bonding forces, metal clusters are not as easily formed by direct laser ablation as are silicon and carbon clusters. Aluminum is the exception to this rule. Aluminum clusters ranging from A13 to A150 were generated by direct laser ablation of an aluminum disk in a high vacuum [5]. The other metal clusters, like Fe, Ni, and Ti, were produced by laser ablation of these metals only in argon or helium background gas in a pressure range of 1-1500 torr. The decrease in the ambient gas pressure resulted in a decrease in size and a narrower cluster size distribution [3]. The study of laser ablation of YBCO in a vacuum has shown that clusters of nearly every combination of Y, Ba, Cu and O were observed, except for Y1Ba2Cu307. The majority corresponded to Y203 or YBa. On the basis of experimental results it was assumed that gas-phase condensation dominated over the direct ejection of these clusters [58]. The interaction of the laser plume with a reactive background gas plays an important role in the formation of compound thin films like oxides and nitrides because of the concomitant production of atomic and molecular precursors required for the growth of the compound phase. Note that such an effect is not typical for other PVD methods. To facilitate the growth of an oxide film it is usually necessary to maintain an oxidizing environment during the deposition process. The laser ablation of some pure metals in an ambient of reactive gas can change the film composition because of the gas-phase formation of molecules containing the atoms of ablated material and gas atoms. The effect of formation of YO2 molecules in the gas phase and Y203 film deposition was ob-

PULSED LASER DEPOSITION served during the laser evaporation of Y into 02 [59]. Nonetheless there are some oxides that are extremely stable even at high temperatures, and their molecules can be easily generated in a vacuum by direct ablation of an oxide target [6]. Although generally successful, the effectiveness of molecular oxygen as an oxidizing agent is somewhat limited because its low activity requires the use of relatively high pressures and deposition temperatures for the growth of high-quality HTSC films. For example, PLD deposition of YBCO films usually requires the use of 0.1-0.2 torr background O2 and a deposition temperature of 700-750~ [12, 78]. The fact that a relatively high background O2 pressure is required to obtain HTSC films with good quality shows that the oxidation during the growth of YBCO is kinetically limited by the instantaneous flux of species impinging onto the substrate [6]. The use of atomic species like O or N, which are extremely reactive and form much more efficient corresponding molecules, adsorbed on the surface, makes it possible to deposit the stoichiometric oxide and nitride films at lower background pressures. But it should be kept in mind that the efficiency of producing N atoms is significantly lower than that of O atoms, all other conditions being equal. Maybe this is why there are only a few reports of reactive deposition of nitride films by direct laser evaporation of metal in nitrogen [6]. One more element of the composition formation mechanism of PLD condensates distinguishing this film deposition method from other PVD methods has already been mentioned: noncontrollable postevaporation after cessation of the laser pulse. Confirmation of an established effect of postevaporation from a ZnS target after the and of pulse action [54] was recently obtained for YBCO and BN targets. The appearance of visible emission from laser-ablated particulates after 2.5 J/cm 2 248-nm irradiation of YBCO in a vacuum was observed. The emission is very weak, begins at the hot target surface at early times, and continues long after emission (to 500 #s) from the plasma has ceased. The same effect was also observed for a BN target [4]. The effect of postevaporation can play a negative role in the composition formation of the film. If the flux of postevaporated species is of a molecular nature, as was observed for a B N target, the film composition will not be deteriorated. But in the case of incongruent postevaporation, the film composition will deviate from the stoichiometric. The relative contribution of this effect in the film composition formation depends on many factors, including the properties of the compound, the thermal conductivity of the target, laser operation parameters, the deposition duration time, and the working gas pressure. The existing experimental data about the conditions of cluster generation are very poor, despite the great importance of this detail in the mechanism of PLD film formation. It is known that the number of clusters that presumably form in the gas phase increases with increasing laser power density. The increasing of cluster amount with increasing laser power density was experimentally observed during mass spectrometric investigation of the laser ablation of YBCO in a vacuum [58]. Another general observation is that the probability of gas-phase molecule generation increases with increasing vapor density during the laser evaporation of the solid and with increasing pressure of

649

the ambient gas [5, 6]. Existing experimental results allow us to consider that the gas-phase formation of two- or few-atom molecules, all other conditions being equal, is more probable than the appearance of larger clusters. Obtaining such experimental results is hindered by the difficulties in distinguishing between the clusters ejected from the target and those generated in a gas phase. During the deposition of films with a volatile component the most important role plays the formation of film-forming species (molecules or clusters) in a gas phase. It is known that the sticking coefficient of gas atoms on the substrate at room temperature ranges from 0.1 to 0.5 whereas this coefficient for most molecules containing metal and gas atoms is close to 1 [1]. Therefore the probability of formation of a film with the correct stoichiometry is substantially higher in the case of filmforming species containing oxide or nitride molecules or clusters, compared with the film forming flux containing individual gas and metal atoms. This is especially important for PLD, because the desorption probability of condensed gas adatoms increases sharply because of the increased energy of FFS bombarding the growth surface. However, molecules and clusters are not generated under any deposition conditions of PLD. For example, in [50] it was found that the films deposited by pulsed laser evaporation (1064 nm, 1 ms, 106 to 107 W/cm 2) of an A1N ceramic target consisted completely of aluminum, and their composition did not depend both on the deposition conditions and on the ambient medium (vacuum or nitrogen background gas at PN = 10-2 tort). At the same time in [34, 35, 70] A1N films with the correct stoichiometry were produced by frequency laser (248, 266 nm, 3-10 ns, 1-3.5 J/cm 2) evaporation of an A1N ceramic target both in a vacuum and in nitrogen background gas. These films had a structure with parameters close to that of bulk A1N, and only small amount of little ( N/A1 > 1 was found in the film deposited in a nitrogen pressure range of 10 -2 > PN2 > 10-4 torr. Increased the nitrogen pressure to over 10 -4 torr was accompanied by the appearance of over-stoichiometric nitrogen in the film and by deterioration of the film structure. Authors associate both of these effects with the formation of nitride clusters in a gas phase, which in tum is the result of enhancement of the interaction between ablated species and ambient gas at higher nitrogen pressures. Thus the third constituent of the composition formation mechanism of PLD films can be realized where an excimer laser is used for thin film deposition. Namely, apart from the growth of a film directly from molecules evaporated from a target and the formation of the film composition from the individual atoms on the growth surface, the third component is the formation of a film of molecules and larger clusters generated in a gas phase. At the same time we would like to note the negative role of gas phase clustering during A1N film formation. In [34, 70] the presence of a small amount of little A1 droplets on the film surface was explained by clustering of A1 atoms in a gas phase. This means that A1 atoms that appear because of dissociation of A1N under laser impact interact more easily with each other than with nitrogen atoms. This conclusion follows directly from the fact that the influence of the nitrogen ambient gas on (i) the film composition and (ii) the amount of A1 droplets was not revealed in [34, 70]. A possible reason for this effect is the low concentration of atomic nitrogen compared with the concentration of molecular nitrogen, the chemical activity of which is significantly lower than that of atomic nitrogen [6]. Thus, the Clustering of A1 atoms in a gas phase on one hand weakens the microstructure of the film because of the presence of the droplets in it, and, on the other hand, it reduces the growth rate of the film. Unsuccessful attempts to deposit silicon nitride film by laser evaporation (1064 nm, 1 ms, 107 W/cm 2) of a Si3N4 ceramic target also relate to the almost complete dissociation of nitride and the very low probability of nitride molecule formation in the gas phase under these conditions [50]. However, the dissociation of silicon nitride was not complete, as in the case of an aluminum nitride target. The higher crystallization temperature of these films compared to that for silicon films deposited under the same conditions indicates the presence of a small amount of nitrogen in these films. The less complete dissociation of silicon nitride compared to aluminum nitride during their laser evaporation under similar conditions [50] can be related to the lower binding energy in the A1N molecule (3.7 eV) compared to that of the SiN molecule (5.2 eV) [60].

The degree of dissociation of the boron nitride target under the laser impact was lower than that of aluminum nitride and silicon nitride. This indicates the presence of crystalline h-BN and c-BN phases along with an amorphous phase in the films deposited in these experiments [50]. The amorphous phase relates to the boron, with a low nitrogen content. The degree of dissociation of boron nitride decreases with decreasing laser power density (evaporation in defocused regime, q = 106 W/cm2). This conclusion follows from the observation of decreasing amorphous phase areas in the films deposited at a lower power density in comparison with that obtained at q = 5 • 107 W/cm 2. Partial dissociation of boron nitride was also observed during evaporation by excimer laser (248 nm, 2.7 J/cm2). This conclusion follows from the deposition conditions of these films, which included the presence of a nitrogen background gas (PN2 = 0.05 torr) as a necessary condition [36]. An investigation of the film morphology indicated the presence of two types of particulates in an otherwise smooth matrix. Spherical particles with diameters up to 1/zm were composed of boron. Irregularly shaped particles about 350 nm in size consisted of h-BN and were presumed to be ejecta [36]. If one assumes that the boron particles in these films are the result of gas-phase clustering of boron atoms, as was observed for aluminum atoms during the evaporation of A1N targets in [34, 35, 74], then it is necessary to agree that boron atoms more readily interact with each other than with the nitrogen. In [61 ] c-BN films were deposited by laser ablation (248 nm, 1.5 J/pulse) of a h-BN target in the presence of Ar-N2 ambient gas. The films were deposited on Si substrates that had been heated to ~450~ and which were electrically biased. The laser plume was further excited by an electric discharge ignited in the nitrogen background gas. This mode of deposition was chosen to produce additional nitrogen atoms in the substrate region because the chemical efficiency of nitrogen molecules is quite low. The authors do not mention finding any particulates in their films. The above results indicate that boron nitride is also dissociated under a laser impact, although the degree of dissociation of this nitride is much lower than that of aluminum nitride or silicon nitride. The degree of dissociation of boron nitride depends on the deposition conditions and laser parameters.

2.5. Conclusions The above problems of composition formation of PLD films and related questions led us to the following conclusions. 1. The composition formation mechanism of the films de, posited by pulse laser evaporation of targets with complex chemical composition includes at least three constituents: (i) the growth of the film due to chemical reaction of monoatomic components on the condensation surface being evaporated from the target; (ii) the formation of the film directly from molecules or clusters evaporated from the target; (iii) the formation of the film from molecules or clusters appearing in the gas phase due to the reaction of evaporated atoms with the background gas

PULSED LASER DEPOSITION atoms. The portion of each constituent in the composition formation mechanism depends on the properties of the evaporant, the deposition medium (vacuum, background gas), and the laser parameters. 2. If the evaporation of the compound by conventional methods occurs without dissociation, congruently or coherently, then it is reasonable to obtain a film of stoichiometric composition by PLD. Nevertheless there is the probability of compound dissociation, depending on the laser operation regime. 3. The clustering effect of atoms in a gas phase, which is possible under the proper laser operation parameters and at certain deposition conditions, is able to influence the film composition, especially for compounds with volatile components. 4. The mechanisms of composition formation of the films deposited by pulsed laser evaporation of alloys and compounds are quite different. The laser evaporation of alloys composed of metals only (i) occurs mainly in monatomic form. (ii) The evaporated atoms do not interact with each other in the gas phase. (iii) The evaporation of cast alloys occurs both from the spot of direct laser impact and from the indirectly heated zone. These peculiarities of pulsed laser evaporation of alloys approach wthat is typical of conventional evaporation. Let us recall that the composition formation of alloy films deposited by conventional evaporation methods obeys the Raul law [ 1]. The laser evaporation of compounds can occur (i) directly in molecular form. (ii) The formation of molecules of compound can take place in a gas phase. (iii) The effectiveness of laser evaporation of compounds is higher than that of alloys because of the lower thermal conductivity of compound targets and because of their higher atomic binding energy. These differences in the evaporation mechanisms of alloys and compounds promote the laser deposition of compound films with compositions close to that of the target more frequently than that of the alloys.

3. STRUCTURE OF PLD FILMS Perfection of the crystalline structure of a film depends on the nucleation and growth conditions. The most important of these are the arrival rate of FFS on the growth surface, substrate temperature, the energy and the composition (atoms, molecules, or clusters) of FFS, and the crystalline structure of the substrate. 3.1. Factors Influencing the PLD Film Structure A high deposition rate leads to a high rate of nucleation and, as a result, the formation of small islands with high density. On one hand these processes lead to the formation of continuous films with a lower average thickness, but, on the other hand, such films have a smaller grain size. Therefore, to obtain a film with more perfect crystalline structure under such deposition conditions, a higher substrate temperature is required [62]. The increased energy of the species arriving at the substrate increases their sticking coefficient and surface mobility. These

651

factors make it possible to deposit a film with greater structural perfection. However, if the energy of condensed species exceeds the optimal value (5-10 eV [63]), they promote the surface and bulk defects in the film, the creation of additional nucleation sites [64] and a decrease in the grain size of the film [65]. The presence of charged species also contributes to the increase in the number of nucleation sites (i.e., nuclei density) [621. All of these effects negatively influence the film structure. Each of the factors considered is present in the PLD process. Actually, instantaneous deposition rates during laser evaporation are very high and can be varied from 1014 to 1022 cm -2 s-l; at a pulse duration of a nanosecond, the energy spectrum of the ions is in the region of 0-2000 eV, with a mean energy of 100-400 eV, depending on the experimental conditions. The energy of the neutral component of the laser plasma flux is about 10 eV; the ionization degree of the plasma is between 10% and 70% and depends strongly on the energetic and spectral laser parameters [ 18]. The composition of the flux of FFS is very complex and includes particles from ions to polyatomic clusters [5, 16, 18]. All of these factors are present simultaneously during the growth of the film. 3.2. Role of Molecules and Larger Clusters Nucleation sites of different dimensions and different compositions, in the form of molecules or clusters, can be a noticeable limiting factor of the growth of crystallites in a film, even at a rather high surface mobility of adatoms. This means that the structure of a film deposited from the atomic flux onto the substrate with the same temperature has a more perfect crystalline structure than that formed of mixed film-forming particles (atoms, molecules, clusters). For example, whereas the structure of a film formed by atomic flux is polycrystalline, a film grown from a mixed film-forming flux has a fine-grained or amorphous structure at the same substrate temperature. The epitaxial growth of a film grown from mixed film-forming flux has to start at a higher substrate temperature than that of a film deposited from atomic flux. The role of the composition offilmforming flux in the formation of film structure has received little attention in the literature. Evidently this is related to the experimental difficulties encountered in creating a film-forming flux with a controlled composition. We presume, however, that the composition of the FFS (namely, atoms, molecules, clusters) plays an important role in the formation of the film structure. In [68] the correlation between the composition of the vapor phase and the structure of simultaneously deposited films was studied. The composition of vapors generated by conventional and laser evaporation of a wide class of compounds (CdS, CdSe, ZnSe, SnTe, GeTe, GeSe, GeS, GaSe, InSe, SbeS3, AseS3) was investigated by mass spectrometry. Structural studies of the corresponding films show that the presence of > 10% polyatomic clusters in a vapor phase results in the formation of a film with an amorphous structure. If the vapor is predominantly composed of atomic species, as is the case of evaporation

652

SHAGINYAN

of CdS, CdSe, ZnSe, and SnTe, then the deposited films are polycrystalline. The authors also noticed an unexpected similarity in the composition of vapors generated by conventional evaporation and pulsed laser evaporation. Another example of the role of the composition of FFS in film structure formation are the results of investigations carried out in [69]. In this paper the authors also reported on a mass spectrometric investigation of vapor generated by pulse laser evaporation of GaAs single crystal and the structure of the films deposited from this vapor. It was revealed that the vapor contained charged GaAs, As3, As4, and Ga2 molecules and neutral clusters containing three to five atoms of different types. The deposited films had a quasi-amorphous structure and were composed of very fine GaAs crystallites. The authors believe that such a superfine structure of the film is determined by a large number of nucleation sites created by condensed molecules and clusters. Our investigations of the influence of laser power density on silicide film structure also indirectly demonstrate the dependence of the film structure on the properties of FFS. CrSi2, WSi2, TaSi2, and TiSi2 silicide films were deposited by PLD (1064 nm, ms, 1000 J/pulse) in two power density regimes, q = 106 and q = 5 x 107 W/cm 2 which were varied by focusing and defocusing of the laser beam. The films were deposited on the substrates at room temperature and had amorphous structure. During their in situ annealing in an electron diffraction column it was established that each silicide underwent its proper temperature transition into the crystalline state. At the same time there a common feature in the structures of these films was revealed. That is, the silicide film deposited in the defocused regime had a ~100-150~ higher phase transition temperature than that deposited in the focused regime (Table IV). Note that the transition from the amorphous to the crystalline state for similar silicide films with close thickness, deposited by magnetron sputtering, occurs at a temperature that is 150-200~ lower [71] than that for PLD films deposited in the focused regime (Table IV). The results obtained for PLD silicide films suggest that the structure of the films deposited in the focused regime was more "perfect" than that of films deposited in the defocused regime. There are two possible reasons for this effect. One of them is that the effective substrate temperature was higher during the deposition in the focused regime. In other words, the arrival energy of the FFS generated in this regime was higher what is reasonable for such power density irradiation. Simultaneously, the dissociation of the silicide is more probable for higher power density, and thus the film deposited in this regime could be grown mostly from atoms. This effect can also provide a more "perfect" film structure [66, 68]. On the other hand, the FFS generated during low power density evaporation of matedais with strong chemical bonding were mostly composed of molecules [18], the mobility of which is lower than that of the atoms [66, 67]. So it is reasonable to expect the film formed of molecules to be more amorphous than that grown from atomic flux. The lower transition temperature for similar silicide films deposited by sputtering supports this idea, because the flux of

species generated by sputtering is compositionally uniform and is mainly composed of atoms [ 13], and this is the reason for the more "perfect" structure of these films. One more observation indirectly confirms the idea of a leading role for FFS composition in the structure formation of PLD films. The structure of Zr films was investigated with respect to the location of the substrate. Zr films were deposited in the defocused regime simultaneously on the substrates; one of these was placed at an off-axis position, and the other at a line-ofsight position (see Fig. 1). The structure of the main part of the film deposited on the substrate at the off-axis position was finegrained, and the film deposited on the substrate placed at the line-of-sight position had a normal polycrystalline structure, as seen from diffraction patterns (Figs. 6c and d). Because the formation of molecules or clusters in a gas phase is not peculiar for the PLD evaporation of metals [5], the reason for the more "perfect" structure of Zr films deposited from the central region of the laser plume is the higher kinetic energy of Zr atoms arriving at the substrate from this region of the plume. The higher energy of the species from the central zone of the laser plume is an experimentally established fact [ 17, 18]. Higher energy provides a higher mobility to Zr adatoms, and, correspondingly, Zr film deposited on the substrate at the line-of-sight position had a more perfect structure. Because the silicide films were deposited on the substrates located at the line-of-sight position for both focused and defocused regimes, one can assume that the energy upon arrival at the substrate species is high. Therefore it is reasonable to expect to obtain the films with similar structures deposited in the two regimes. As this was not the case, it is reasonable to assume that the difference in the structural quality was conditioned by the lower surface mobility of FFS generated in the defocused regime. Because the energies of FFS generated in the two regimes are nearly equal, it is valid to associate the lower surface mobility of species generated in the defocused regime with their larger dimensions. In other words, it is reasonable to assert that the FFS generated in the defocused regime consist mainly of molecules and larger clusters, in contrast to mainly atomic flux generated in the focused regime. The difference in the compositions of fluxes generated in the two laser operation regimes is the main reason for the more disordered structure of the films deposited from the species of larger dimension.

3.3. Gas-Phase Clustering When PLD is used for the deposition of films containing volatile constituents such as oxygen or nitrogen, the process is typically performed in a chamber with a background gas pressure of a few tenths of a torr. This means that interaction between the gas particles and evaporated species is inevitable. The interaction between these species has few effects that are expected to influence film formation. It reduces the energy of FFS and excludes ions. For example, during magnetron sputtering of WTi alloy, the concentration of Ar + ions with an energy Ei > 80 eV showed more than an order of magnitude decrease, and the average energy of sputtered atoms de-

PULSED LASER DEPOSITION creased from ~ 4 to 1.5 eV when PAr was increased from 10 - 4 to 10-1 torr [ 100]. Thus in the case of PLD in an ambient of gas, factors that negatively influence the film structure, like noncontrollable bombardment of the growth surface by energetic particles and charged species, are excluded. But the probability of formation of large-scale FFS (clusters) in gas phase increases in the presence of background gas. Because the mobility of clusters is low, one may expect that the substrate temperature during PLD in a gas ambient has to be higher for deposition of a film with high structural quality. The last assertion can be confirmed by the results obtained in [34, 35, 70], where epitaxial A1N films of similar or close structural perfection were produced by PLD in a vacuum or in nitrogen as the background gas. These A1N films were produced by frequency pulsed excimer laser evaporation (248 and 266 nm, 30 ns) of an A1N ceramic target. The films were deposited on sapphire single crystal substrates and had a highly oriented structure with a basal plane parallel to the substrate. However, such universal parameters as the substrate temperature and working gas pressure were quite different for different deposition methods. In [35] the films were deposited on the substrate at Ts - 1000~ (q = 1 J/cm 2, target-substrate distance 3 cm, repetition rate 10 Hz), and the dependence of the film structure on the nitrogen pressure in the chamber was investigated. It was established that the epitaxial films with the most perfect structure (X-ray rocking curves with minimum full width at half-maximum, FWHM) could be deposited only at PN2 --< 10-4 torr. The increase in nitrogen pressure in the chamber promoted rapid deterioration of the film structure (fast increase of FWHM). The authors relate the degradation of film crystallinity with increasing PN2 to the increased number of collisions between the evaporated species and the gas particles in a gas phase. They assume the result of interaction is that the vapor species lose energy as they migrate on the substrate and form clusters with low surface mobility. In [70] the substrate temperature needed for epitaxial growth of A1N films in a vacuum (q = 2 J/cm 2, target-substrate distance 4 cm, growth rate per pulse 0.025 nm/pulse, average growth rate Vg ~ 1.25 nrn/s, repetition rate 50 Hz) was Ts -- 670~ which is substantially lower than that determined in former investigations. If the process was carried out in nitrogen background gas at PN2 = 5 x 10 -2 torr then films of similar crystallographic orientation and structural perfection were obtained at Ts = 500~ As the nitrogen pressure was increased to PN2 = 0.4 torr the structure of the film deteriorated, which was indicated by the simultaneous appearance of two different crystallographic orientations of film crystallites. The most probable reason for increased epitaxial temperature during the deposition in a vacuum in comparison with that in nitrogen (PN2 = 5 x 10 -2 torr) is the high instantaneous rate of vapor condensation and the high laser repetition rate, which was noted in particular. As already mentioned, the nuclei are smaller, and their densities are higher at high deposition rates [62]. Therefore a higher substrate temperature is needed for the formation of epitaxial films with perfect structures. If the

653

deposition is carried out in a gas background, then the instantaneous condensation rate is reduced because of the scattering of evaporated species on the gas particles. The reduced condensation rate makes it possible to deposit epitaxial films of the same perfection at lower substrate temperatures. At the same time, the deterioration of the film structure with increasing nitrogen pressure was noted both in [35] and [70]. In the latter, the indicator of film structure deterioration was the appearance of crystallites with one more crystallographic orientation. In [34] (q = 3.5 J/cm 2, target-substrate distance 3 cm, average growth rate Vg = 0.015 nm/s, laser repetition rate 1 Hz) epitaxial A1N films were deposited on a substrate in a vacuum at Ts = 500~ Such a reduction of the epitaxial temperature in comparison with that used in [70] can be explained by the substantially lower deposition rate and lower pulse repetition rate used in [34]. However, it is difficult to explain the fact that the perfection of A1N films deposited on a substrate at Ts = 500~ in a nitrogen background (PN2 = 5 • 10 -3 torr) was the same as that of films deposited in a vacuum in [70]. It is also impossible to understand why the growth rate of A1N film deposited in [70] was almost two orders of magnitude higher than that in [34], whereas the power density was higher and the target-to-substrate distance was lower in the latter case. While considering the structure formation of A1N films in [34, 35, 70], we assumed that the main FFS are the particles that are not smaller than molecules. The following discussion provides basis for this assumption. In [35] the dependence of the composition of A1N films on nitrogen pressure was investigated. It was shown that the relative nitrogen content in films deposited in a vacuum is N/A1 ~ 0.95. At the same time, it is known that there are such laser operation regimes in which the evaporation of A1N occurs with complete dissociation of the compound, and as a result a pure aluminum film is deposited [50]. It is also known that it is possible to deposit stoichiometric A1N films through the evaporation of A1N by conventional methods [ 1]. Keeping in mind these experimental facts, one can assume that the evaporation of A1N by excimer lasers with the operation parameters used in [34, 35, 70] occurs almost without dissociation. Therefore the main FFS in these experiments were A1N molecules and possibly even larger molecular clusters. With this in mind, it is natural to expect that the epitaxial temperature of these films has to be higher than that of the film deposited from atomic aluminum and nitrogen fluxes. The latter assumption might be confirmed by the data presented in Table V. Information on the structures of different materials films deposited by different PVD methods is presented in this table. 3.4. Crystallization Temperature as an Index of Film Structure ~ Perfection 99 The preceding discussion shows that one of the significant factors influencing the structure of films is the composition of the film-forming flux, which may include atoms, molecules, and larger clusters. We have already seen that the film-forming flux

654

SHAGINYAN Table V.

Temperatures of Crystallization and Epitaxial Growth of Films Deposited by PLD and Other PVD Techniques

Film

Deposition

composition

technique

A1N

PLD; excimer

A1N

PA MBE

A1N

Film structure;

Working gas pressure (torr)

Reference

SC; 500; 670; 1000;

N2, 10-4; vac.

[34, 35, 70]

SC; 500

Vac.

[72]

S

SC; 350

Ar-N2, "-~10-1

[73]

GaN

PLD; excimer

T/PC; 500

Vac.

[34]

GaN

PA MBE

SC; 500

Vac.

[72]

SiC

PLD, excimer

PC; 800

Vac.

[39]

SiC

PLD, Nd:YAG, ms

A; 450

Vac.

[50]

SiC

e-beam evaporation

Fine-grained PC; unheated

Vac.

[74]

LaB 6 LaB 6

PLD, Nd:YAG, ms S

A; 450 PC; 200

Vac. Ar; ~,10 -2

[50] [75]

substrate temperature (~

LaB 6

e-beam evaporation

PC; 350

Vac.

[76]

In-Sn-O

PLD; excimer

PC; 200

02, ~ 10-2

[47]

In-Sn-O

S

PC; RT

02, "~10-2

[77]

YBCO

PLD; excimer

T/PC; 700-750

02, ~10 -1

[12, 78]

YBCO

S

SC; 550-730

Ar-O2, ,~ 103-10 -1

[99]

GaAs

PLD, Nd glass, ns

SC; 600

Vac.

[ 101 ]

GaAs

RF ion-beam epitaxy

SC; 400

Vac.

[ 102]

Abbreviations: PA MBE, plasma activated molecular beam epitaxy; S, sputtering; SC, single crystal; PC, polycrystalline; T/PC, textured polycrystalline; A, amorphous.

generated by pulsed laser evaporation of compounds frequently has a complex composition, including ions, atoms, molecules, and larger particles. At the same time it is known that the surface mobility of large particles is lower than that of atoms. It is also known that the film-forming flux generated by such PVD techniques as molecular beam epitaxy or sputtering is mostly homogeneous and mainly contains atomic species. Therefore it is reasonable to assume that the substrate temperature for the deposition of films of identical composition and with similar structural perfection has to be lower in the case of PVD methods in comparison with PLD. The particular experimental conditions can noticeably influence the temperature of crystallization or of epitaxial growth, as was seen, for instance, from a comparison of the results obtained in [34] and [70]. Nevertheless there is a certain temperature interval typical for the deposition of a film of a certain composition and of a certain structural perfection by a certain technique. With this in mind, let us try to compare the structural quality of the films deposited by PLD and by other PVD methods. Let us choose substrate temperature as a performance criterion of the method. The lower is the substrate temperature for deposition of a film with higher structural perfection, the more optimal are the deposition conditions and deposition method for film production. The important condition for a comparison of deposition techniques is the equality or the closeness of the pressures of working gas during the film deposition. Table V contains information about the structure of the films of some compounds deposited by different PVD methods and

the values of the substrate temperature at which the films were obtained. It follows from these data that the substrate temperature at which films of the same composition and structural perfection were deposited by PLD was not lower and frequently was even higher compared with the temperature of deposition by other PVD methods. One more criterion of the degree of perfection of the structure of as-deposited films may be the temperature of transition of initially amorphous film to the crystalline state (crystallization temperature). The lower is the transition temperature for the film of the same composition from the amorphous to the crystalline state, the closer is the structure of the film to the crystalline state. In other words, if the crystallization temperature of the amorphous film deposited by one of the PVD methods is lower than that for the film deposited by PLD, it is of value to consider that the former film structure has a greater degree of perfection. As an example, the crystallization temperatures of some amorphous silicide films deposited by PLD and by magnetron sputtering are listed in Table IV. From these data it follows that the temperature of transition from the amorphous to the crystalline state for silicide films deposited by PLD in our investigations was, on average, noticeably higher than that for similar films of close thickness deposited by magnetron sputtering. All examples given indicate that the crystallization of films grown from the film-forming flux generated by laser pulse is impeded in comparison with that for films deposited by other deposition techniques.

PULSED LASER DEPOSITION

3.5. Influence of Laser Parameters and Substrate Temperature on Epitaxial Growth of PLD Films Analysis of the investigations devoted to the peculiarities of epitaxial growth of PLD condensates presented below confirms the conclusions of the previous section. The epitaxial growth of the film is determined by the following conditions: (i) The substrate temperature cannot be lower than a certain value. This requirement provides the advantage of epitaxial nucleation and growth compared with nonoriented nucleation. (ii) The supersaturation of the condensed vapor has to be of a low value, at which the nucleation occurs only on the preferred centers, providing epitaxial growth. (iii) Increased supersaturation of the vapor enhances the possibility of chaotic nucleation exponentially. A high substrate temperature activates the attachment of adatoms at a particular site of crystal lattice of the substrate and enhances the surface and bulk diffusion. The surface diffusion smooths the mismatch during the coalescence of nuclei. The temperature of film epitaxial growth is linearly related to the rate of FFS condensation: the logarithm of the condensation rate is proportional to the inverse substrate temperature [62]. The upper limit of the deposition rate is determined by the kinetics of atomic rearrangement. A certain time is needed for adatoms migrating along the substrate surface to reach thermodynamically stable sites. The kinetics of epitaxial growth is determined by the substrate temperature and by the kinetic energy of fast atoms and ions supplied to the growth surface. Epitaxial growth is an energetically limited process and is highly material dependent. For example, in molecular beam epitaxy of GaAs, the typical rate of deposition is about 1 #m/h. The temperature is chosen to be high enough to provide the surface atom mobility needed to form the film layer by layer. The epitaxial film could be grown faster by raising the temperature to accelerate the rearrangement process, but this results in the decomposition of GaAs by the evaporation of As and bulk diffusion of Ga or As into the substrate. In general, the temperature window will vary according to the material properties, including the surface mobility of the constituents of the compound, their bulk diffusivity, and the thermal stability of the compound. As was mentioned several times, the characteristic features of pulsed laser evaporation are the pulses of instantaneous vapor fluxes of high density (which are separated by periods of the absence of vapor flux in the case of frequency deposition) and the relatively high arrival energy of vapor species. These peculiarities influence the epitaxial growth of PLD films. Special in-depth investigations of the epitaxial growth of PLD films of different materials were carried out at the Moscow Engineering Physical Institute [ 101 ]. Because of the great importance of these investigations for the comprehension of the structure formation of PLD films, we consider the most interesting of them in more detail. The influence of laser parameters and substrate temperature on perfection of the crystal structure of GaAs and PbTe films was investigated by both ex situ and in situ depositions. The ex situ depositions were carried out in a vacuum chamber, with

655

subsequent structural investigations by RHEED (reflection high energy electron diffraction), HEED, and TEM. Depositions in situ were carried out in an electron diffraction or electron microscope column with simultaneous observation of the structural evolution during the film growth. The laser systems used for evaporation were based on Nd glass ()~ = 1064 nm) and could operate in two different irradiation modes: in an ordered running regime with q ,~ 105 to 106 and in Q-switch mode, with q ~ 108 to 109 W/cm 2. Pulse duration in the ordered pulse regime was 0.5 ms, while in Q-switch mode it was 30 ns. Single-crystal plates of cleaved NaC1 and polished GaAs were used as substrates. Ex situ investigations of the temperature dependence of the structure of the films with thickness of about 30 nm deposited in two regimes revealed the following results. The structure of the films deposited at q ~ 105 W/cm 2 on a NaC1 substrate at room temperature was amorphous. The films deposited at 250~ had structures composed of amorphous and polycrystalline phases. The increase in the substrate temperature to 300~ promoted the refinement of the film structure up to textured polycrystalline, but a further increase of the substrate temperature to 350~ led to a drastic degradation of the structure. The structure of the films deposited at q ~ 108 W/cm 2 in the same temperature interval was more perfect than that of films deposited at lower q. Films deposited at 250-350~ had a mosaic crystal structure with a different range of ordering. The films with the best crystalline structure were grown at 300~ and had highly oriented crystallites of a large size. In situ monitoring of the growth of a GaAs film on a GaAs substrate, with respect to the film thickness per pulse di at different substrate temperatures, was carried out at q 108 W/cm 2. It was revealed that the films deposited at Ts < 300~ and di ~ 0.8-1.0 nm/pulse were polycrystalline. The oriented crystallization of the film began at Ts = 350~ and epitaxial films with a highly oriented structure could be grown at Ts = 500-600~ Increasing di to ,~4 nm at Ts = 600~ revealed the effect of the structure evolution for a few minutes after the pulse decay. Immediately after the pulse decay slightly diffuse diffraction tings were observed, indicating the formation of a fine-grained polycrystalline structure. One minute later diffraction spots appeared on the diffraction tings, the intensity of which decreased simultaneously with the appearance and increased intensity of the spots. At the end of the third minute only diffraction spots were seen on the electron diffraction screen. Highly oriented epitaxial layers up to ~50 nm in thickness could be grown at di ~ 4 nm only over an interval larger than 3 min between the depositing laser pulses. However, the structural perfection of these films was lower than that of films deposited at the same substrate temperature but with di ,~ 0.8-1.0 nm/pulse. This indicated the Kikuchi lines on the diffraction patterns of the GaAs films deposited at di ~ 0.81.0 nm and Ts = 600~ After the structural transformations ceased, the diffraction patterns of the films deposited at di ,~ 6-7 nm and Ts = 600~ contained diffusive diffraction tings with barely visible spots. The films deposited at di > 10 nm/pulse and the same substrate

656

SHAGINYAN

temperature were amorphous. Special investigations had shown that orienting substrate influence extended no farther than 4-5 nm over the interface in the case of di > 10 nm/pulse. The deposition of a GaAs film at the substrate with Ts > 650~ promoted the re-evaporation at first of As and later the Ga, which was indicated by structural transformation of the film surface. To discuss the results described above, we will start with a comparison of the structures of films deposited at two different laser power densities, q ~ 105 W/cm 2 and q ~ 108 W/cm 2, keeping in mind that the power densities were changed by variation of the laser irradiation mode, not by simply changing the laser spot size. The structural perfection of the films deposited at q 105 W/cm 2 and millisecond pulse duration was lower compared with that deposited at q ~ 108 W/cm 2 and nanosecond pulse duration while other conditions were equal. The authors attributed this to the presence in the ejected products of large amounts of molecular clusters. Such clusters were found by the mass spectrometric investigation of laser plasma during the evaporation of GaAs by laser [69] operated in a regime (,~105 W/cm 2, ms pulse) close to that used here. Clusters, because of their lower mobility at the growth surface, hinder the ordering of the nuclei for epitaxial growth. The postdeposition structural transformations of these films also occurred more slowly, and such films did not achieve as great a structural perfection as the films deposited at q ~ 108 W/cm 2. These findings confirm two important ideas: (i) the laser operation mode can sufficiently influence the composition of FFS, and (ii) the presence of molecules or molecular clusters at the condensation surface can notably hinder the structural ordering of the film. The dependence of the structured perfection of the film on the thickness of the layer deposited per pulse, di, was explained in the following way. The layer formed at the substrate from highly supersaturated vapors and from laser plasma may exist in a nonequilibrium state for a certain time. The processes developing in the layer during this period depend on two factors: the thermal motion of the atoms in the layer and the orienting influence of the substrate surface energy. As the temperature decreases, the solid-melt interface moves from the interface to the outer film surface. The crystallization proceeds fast and completely if the layer is thin, as was observed for di ~ 0.8-1.0 nm/pulse. In the case of a layer with a large thickness, the accumulation of structural defects in the bulk of the film takes place during the movement of the solid-melt interface. The stored structural defects inside the layer disrupt the oriented crystallization of the film and freeze the amorphous structure, as was observed for di > 10 nm/pulse. Estimations based on RHEED investigations have shown that the orienting influence of the substrate (Ts = 600~ extended no farther than 4-5 nm over the substrate. So one of the factors discussed earlier that hinders epitaxial growth is readily seen from this series of experiments, that is, the high level of supersaturation of vapors and laser plasma. Taking this factor into account, the authors came to the conclusion that high-quality epitaxial GaAs films can be obtained only under conditions adequate for crystallization: (i) thickness per pulse di < 0.8-1.0 nrn/pulse,

(ii) time between laser pulses > 1 s, and (iii) substrate temperature Ts = 600~ Let us now compare the results of the deposition of epitaxial GaAs films by PLD with that deposited by rf ion beam epitaxy [102]. In this work the structures of GaAs films prepared by an ion beam epitaxial system with two ion sources and an rf coil have been studied. The films were deposited on cleavage surfaces of rock salt by the separate evaporation of gallium and arsenic from two ion sources. The deposition rate was about 1 nm/s, and the mean film thickness was 300 nm. It was established that epitaxial GaAs films with high structural quality could be grown on NaC1 and GaAs substrates at Ts - 400~ whereas the substrate temperature and growth rate needed for the deposition by conventional MBE of GaAs films of the same structural quality are about 550-570~ and 0.3 nm/s. Murayama [102] emphasizes that the main factors needed to obtain epitaxial films with good structure at a decreased growth temperature and increased growth rate are the ionization of the vapor beam, rf excitation, and dc bias of the substrate, with strong control of the bias voltage. This means that the film deposited under such conditions during the growth was exposed to continuous bombardment with ions at a certain energy. In this case the ion bombardment facilitated the epitaxial growth because of the enhancement of adatoms surface mobility. A reasonable question arises: Why didn't the presence of the ions and the ion bombardment of the growth surface during PLD of GaAs films facilitate the epitaxial growth of this film? The answer to this question can be found by considering the next series of experiments, devoted to the study of the epitaxial growth of PLD PbTe and (Bi,Sb)2Te3 films in [ 101 ]. In this series a Nd:glass laser operating in Q-switch mode (30ns pulse duration) was used. The power density was varied in the range of q = 2 • 1011 to 109 W/cm 2 by variation of the pulse energy. The substrate-target distance was 3 cm, the rock salt-cleaved surfaces served as substrates. Simultaneously with the deposition, mass spectrometric investigations of the laser plasma composition were carried out. Oilless pumping of the vacuum chamber provided a vacuum better than 10 -6 torr. The mass spectrometric investigations of the energy distribution of charged particles inside the laser plume have shown that it is quite inhomogeneous spatially, both energetically and in number of charged particles. The species with maximal energy (-~5 keV) and maximal charge ( Z m a x - - 3) were distributed in a narrow (~30 ~ spatial angle along the axis of the laser plume. The mass spectrometric analysis showed a fast decrease in the numbers of the energetic and charged species as the analysis angle was increased. The decrease in the power density from 1011 tO 109 W/cm 2 promoted a decrease of the maximal charge of the ions from Zmax - 3 to Zmax = 1. An estimation showed that the total ion current to the substrate at q - 1011 W/cm 2 and a 3-cm target-substrate distance can reach --~103 A/cm 2. The TEM investigations of the films deposited on unheated substrates at q - 2 x 1011 W/cm 2 revealed a zone with the traces of re-evaporation and/or re-sputtering of the film. The center of this zone was located on the axis of the laser plume,

PULSED LASER DEPOSITION

657

Fig. 21. Schemeof the structure formation of PbTe and (Bi,Sb)2Te3 films deposited by pulsed laser evaporation. Deposition conditions: ~. -- 1064 nm, r = 30 ns, q = 1011 W/cm2, laser spot dimensions 4 mm2; target-to-substrate distance 3 cm. The scheme is drawn according to the results of [101].

where the densities of most energetic and charged species were maximal. Both PbTe and (Bi,Sb)2Te3 films deposited at this zone had structures with maximal perfection. PbTe films were highly textured, whereas the (Bi,Sb)2Te3 films had a polycrystalline structure with a large grain size. The film structure became less ordered further from this zone and was completely amorphous at the periphery of the film. The films deposited at lower power densities (q ~ 101~ W/cm 2) had less ordered structure and were completely amorphous at q - 109 W/cm 2 for both materials. A scheme of the structural formation of PbTe and (Bi,Sb)2Te3 films drawn according to these results is depicted in Figure 21. The tendency of the structure to deteriorate toward the periphery of the film remained constant with the reduction in laser power density. The authors emphasized that the most important factor in the formation of the film structure is not the film thickness but the distance from the central zone. The thickness of the film was the same for regions with different structures. An investigation of the influence of the specific energy of the laser plume on the film structure was carded out by depositing double-layered films of both materials. The upper layer of one of the double-layered films was deposited at a lower (q = 7 x 101~ W/cm 2) power density, and the lower layer was deposited at a higher power density (q = 2 x 10 ll W/cm2). The sequence order of the layers in one double-layered film was opposite that of the other. For both materials it was revealed that if

the upper layer was deposited at lower q, its structure was more ordered than that in the opposite case, where the upper layer was deposited at higher q. At the same time the structure of a single-layered film deposited at lower q (thickness -~ 7 nm) was more ordered than that of the layer deposited at higher q (thickness ~ 20 nm), as was already observed for GaAs films. The structure of a threelayered film with layers of equal thickness (with a total thickness of 20 nm) was less ordered than that of a single-layered film. In discussing the results described above, the authors stated that the main reason for the structural perfection of the films is the transformation of the specific energy of laser plasma into the crystallization heat. Undoubtedly this effect plays an important role in film structure formation. The deterioration of the film structure away from the center of the film and toward its periphery might be explained just by this effect. In fact, as follows from mass spectrometric investigations, the energy of FFS deposited at a peripheral regions of the film is lower than that of species deposited in the central zone. Another argument supporting this idea is the deterioration of the film structure as the laser power density decreases which results in a decrease in the energy of ejected species. Nevertheless there may be another reasonable explanation for these effects. As is known from [62], the gas phase generated by conventional evaporation of PbTe mainly consists of

658

SHAGINYAN

PbTe molecules. In the case of pulsed laser evaporation of PbTe, the composition of generated species depends on the opening angle of laser plume and heavy species with low kinetic energy usually observed at larger angles (see the results of mass spectrometric investigations described above and [ 16]). So it could be expected that the more distant regions of the film are formed mostly of condensed PbTe molecules. Because the mobility of molecules is significantly lower than that of atoms, it might be concluded that the latter is the reason for the low-order structure of the peripheral regions of the film (Fig. 21). However, it is difficult to explain other results by discussing investigations based only on these aspects of laser plasma. For example, one could assume that the structure of upper layer in double-layered film is more ordered in the case of its deposition at a higher power density of q = 2 • 1011 W/cm 2. This is reasonable on one hand, because of the orienting effect of the lower layer, which has an ordered structure, and on the other hand, because of the higher specific energy of the laser plume at higher q. However, the result is just the opposite of what is expected. The more ordered structure has the upper layer deposited at a lower power density (q = 7 • 101~ W/cm 2) on the layer with the lower structural quality. This effect can be explained if one takes into account another aspect of laser plasma, namely the intense and noncontrollable bombardment of the condensation surface by energetic neutrals and ions. The higher the intensity of the bombardment, the higher the damage of the growth surface and growing layer, which prevents the ordering of the film structure. If the upper layer is deposited from a flux of species with lower energy, then the possibility of damaging to the growing film is lower. Because the thickness of the layer deposited at lower q is small, the possibility of annealing of the structural defects is higher. Another cause for the more ordered structure of the upper layer is the lower level of the supersaturation of the vapors generated at lower power density. This effect was also observed during GaAs film deposition. All of these factors provide the more ordered structure of the layer deposited at lower q. Because the deposition conditions of GaAs were close to that for PbTe and the growing film and growth surface were bombarded by energetic neutrals and ions, it is reasonable to assume that the higher epitaxial temperature of GaAs films (600~ compared to that deposited by rf ion beam epitaxy (400~ relates to the noncontrollable bombardment. In fact, despite the decreased vapor supersaturation resulting from the reduced GaAs layer thickness deposited per pulse and the increased time interval between pulses, the optimal epitaxial temperature remained as high as 600~ This hints at some other factor hindering the epitaxial growth of GaAs film under these conditions. In the case of deposition of GaAs films by ion beam epitaxy, the energy of ions bombarding the growing film could easily be controlled by the substrate bias voltage [ 101 ], whereas the energy distribution of neutral and ion species bombarding the growing film during PLD is rather wide and can hardly be controlled. Therefore a species with an energy that exceeds the permissible limit of 5-10 eV can damage the film structure [63].

3.6. Ways to Control the PLD Film Structure After the preceding discussion it could be concluded that such peculiarities of the PLD as (i) inhomogeneity of the FFS, (ii) the wide energy spectrum of a deposited species with a high average energy per particle, and (iii) a high instantaneous supersaturation of condensed vapors (deposition rate) significantly affect the structure of PLD condensates. As was shown, these factors may frequently negatively influence the film structure. Efficient control of parameters and properties of FFS by the variation of deposition conditions is difficult task. The most easily controlled parameter is the deposition rate, which can be changed by variation of the laser power density and pulse duration. It is possible to decrease the amount of the evaporated volume and thus decrease the instantaneous vapor supersaturation by decreasing the power density and shortening the pulse length. The control of the composition of FFS is a much more complicated problem because atomic clusters and molecules are generated by at least two mechanisms. One is the direct evaporation of molecules from the target, and the second is the creation of the molecules and clusters in a gas phase. Moreover, the two of mechanisms are independent of each other and depend on the deposition conditions and the laser operation regime in different ways. For example, the evaporation of the target by a lower power laser pulse can yield mostly molecules in the case where the dissociation energy of the molecules of the target material is higher than the thermal energy of the evaporated particles [ 18]. At the same time, increasing the power density per pulse and/or carrying out deposition in a gas ambient will promote the clustering of evaporated species in the gas phase [3, 5]. The laser wavelength can also influence the composition of the evaporated particles. For example, the evaporation of a ceramic A1N target by a Nd:YAG laser (1064 nm) is accompanied by the formation of pure aluminum film [50], whereas the use of excimer lasers (248 and 266 nm) makes it possible to deposit films of pure aluminum nitride both in vacuum and in a nitrogen ambient [34, 35, 70]. Regulation of the energy of FFS bombarding a condensation surface is also a very complex problem because of the wide energy spectrum of the particles and because of their nature (neutrals and ions). The most efficient methods for the reduction of the energy of fast particles are to decrease the laser power density and to carry out the deposition in a gas ambient [6]. However, deposition in a gas ambient promotes clustering in the gas phase, which again can negatively influence the film structure. Evidently the negative influence of noncontrollable bombardment of a growing film during PLD is greater than its positive effect, which is frequently defined as one of the important advantages of PLD. In fact, most of above considered investigations of PLD films show that the substrate temperature has a key influence upon their structure. As was shown earlier, the temperature of crystallization or epitaxial growth of PLD films is frequently higher than that for films obtained by other deposition techniques (Table IV). At the same time, if the positive effect of transferring tens of electron volts per atom by energetic particles to the growing film were high, then the energetic

PULSED LASER DEPOSITION influence of the substrate temperature (~ 10 -2 eV/atom) upon the film structure would be negligible against the background of the energy transferred to the growing film by fast particles. In practice, the role of the substrate temperature in the case of PLD is found to be even larger than that for the other PVD methods. In general, separation and hence the control of the influence of simultaneously acting factors during PLD, such as the inhomogeneity of FFS, the bombardment of the growth surface by energetic particles, and a high instantaneous deposition rate, are impossible.

3.7. Conclusions The crystalline structure of PLD films on average is less perfect than that of the films deposited at the same substrate temperature by the other methods of PVD. The reasons for this effect are weakly controlled factors: the inhomogeneity of the composition of FFS and bombardment of the growing film by energetic particles. Both of these factors are the result of an intrinsic feature of pulsed laser evaporation, which is the high nonequilibrium of the processes taking place during the interaction of a high-power short laser pulse with the condensed matter. These peculiarities of PLD are sufficient to limit the possibility of deposition of high-quality epitaxial films.

4. POLYMORPHISM IN PLD FILMS The interaction of a high-power laser pulse with condensed matter supposes the simultaneous appearance of an instantaneous pulse of high temperature and high pressure on the target surface. Such conditions are favorable for the origin of metastable structural states at the point of interaction of the laser beam with the target. The bombardment of the condensation surface by energetic particles generated under a laser pulse impact with the target can also be the reason for the generation of metastable structural phases. In the latter case the nucleation of the metastable phase occurs on the growth surface. Most frequently the effect of the formation of metastable phases is observed in the case of laser evaporation of substances like carbon or polymorphous compounds.

4.1. Polymorphism of PLD Carbon Films The properties of amorphous carbon films depend on the type of atomic bonding of carbon atoms. If s p 2 bonding prevails, then the film has graphite-like properties. When the prevailing bonding type is s p 3, then the hardness and elasticity of the film are similar to those of a diamond. DLC films with "-~90% s p 3 bonding can be produced only with the use of a mass- and energy-filtered carbon ion or atomic source adjusted to give the required energy (about 100 eV per carbon atom) and when the substrate temperature Ts < 100~ [2]. Because the laser plume generated by pulsed laser evaporation of carbon materials contains carbon ions and atoms with an energy of hundreds of electron volts, it is possible to obtain DLC films by choosing the

659

proper laser operation regime (power density, wavelength, pulse duration) and other technological conditions [79-81 ]. The analysis of many publications devoted to the deposition of carbon films by pulsed laser evaporation of graphite led Voevodin et al. [80] to conclude that the probability of DLC film formation increases with decreasing laser wavelength and with increasing power density per pulse. Simultaneously, the shorter the laser wavelength is, the lower the power density can be in the production of an amorphous carbon film with diamond-like properties. An increase in the laser wavelength and a reduction of the power density promote the formation of amorphous graphite-like or graphite condensates. These observations can be supplemented by the results obtained in [81, 82]. In [81] it was shown that at a given laser wavelength there exists an optimal power density of laser irradiation at which the DLC films obtained had a maximal concentration of s p 3 bonding. If the power density deviates from a certain value, the proportion of s p 3 bonded carbon atoms decreases. At the same time, from the results of [82] it follows that the s p 3 content in the film may be increased by using a laser with a shorter wavelength. The role of laser wavelength and power density in the deposition of carbon film with a high concentration of s p 3 bonded carbon atoms can be understood on the base of the preceding discussion. It is known that evaporated graphite can exist in the vapor phase in the form of separate atoms and as atomic clusters, because of the high anisotropy of atomic bonding in graphite [ 1]. It is also known that the substance absorption coefficient tends to increase as one moves to the short wavelength end, and the depth of penetration into the target materials is correspondingly reduced [9]. This means that the amount of laser power absorbed by a target volume unit increases with decreasing laser wavelength. In other words, the amount of laser power per evaporated atom increases as the laser wavelength decreases. The probability of graphite evaporation in graphitelike cluster form decreases, and the energy of evaporated carbon atoms and ions increases because of this effect. Hence the probability of DLC film formation has to be enhanced by a decrease in the laser wavelength, which was experimentally observed in [84]. The existence of an optimal combination of power density and laser wavelength (q-)~) for the formation of a carbon film with maximal s p 3 content is explained as follows. The amount and energy of evaporated carbon atoms and ions are not sufficient for the formation of a DLC film at low q. If q exceeds the optimal level, the energy of evaporated species is also enhanced, which negatively influences the s p 3 concentration in the condensate [2]. The carbon films deposited at relatively lower power density and larger wavelength (1000 J/pulse, 107 W/cm 2, ~ = 1064 nm) consist of two phases, amorphous carbon and crystalline graphite (Fig. 22), in contrast to DLC films, which are deposited by the irradiation of a graphite target by an excimer laser with lower power (0.1-0.3 J/pulse) but a higher power density per pulse (q = 108 to 1011 W/cm 2, ~. -- 248 nm) [79-81 ]. This means that the concentration of carbon atoms and ions of a certain energy in a laser plume is insufficient for formation of a film with any s p 3 concentration in the former case.

660

SHAGINYAN

Sometimes crystalline particles of different sizes were found embedded in amorphous carbon film (Fig. 23). Selected area electron diffraction investigations showed that these particles are the crystals of metastable carbon phase carbine [83]. Carbine phase was recently revealed in graphite subjected to laser irradiation and in simultaneously deposited condensate [84]. The appearance of this metastable carbon phase can be explained by the simultaneous action of an instantaneous pulse of high pressure and temperature induced by laser pulse on the graphite surface. Part of the carbine crystals that originated on the target were transported to the condensation surface by the recoil pressure of evaporated carbon. It is unlikely that the formarion of such large particles could occur in the gas phase.

4.2. Polymorphism of Boron Nitride Films Currently the growth of boron nitride (BN) films is one of the most attractive areas for the application of different PVD techniques. It is known that BN is stable in three crystallographic structures: a hexagonal graphite-like structure (h-BN), a cubic zincblende structure (c-BN), and a wurtzite structure analogous to hexagonal diamond (w-BN) [103]. Up to now BN films have been obtained only in two structure modifications, h-BN and c-BN, both by PLD and by other PVD methods. There is no

Fig. 22. Microstructure of graphite film deposited by laser ablation of a graphite target. (Nd:YAG laser, q = 5 x 107 W/cm 2, 1 ms).

information on how to obtain w-BN films. A short review of some properties of PLD BN films appears in [104]. In a majority of the works devoted to the PLD of BN films, excimer lasers operating in a frequency regime with a low power density per pulse ( ~ 3 - 4 J/cm 2) are used. The depositions were carfled out in a nitrogen gas ambient, c-BN films could be successfully deposited by additional excitation of nitrogen by the electric discharge conditions [61 ], or from a separate source of nitrogen ions and atoms [104]. In a survey devoted to the review of deposition methods and the mechanisms of formation of c-BN films, it is emphasized that the necessary condition for c-BN film production is the bombardment of the growing film by ions with energies in a narrow range (80-120 eV for PVD methods and 200--400 eV for plasma-activated CVD) [ 105]. For the successful production of c-BN films by PLD, either deposition with electrical biasing of the substrate [61 ], or employment of an ion source to bombarding the substrate during the deposition [104] was also necessary. Hence it is reasonable to assume that the formation mechanism of BN films with cubic structure during their deposition under the above-described conditions by excimer laser is close to that realized during the deposition of c-BN films by other PVD techniques. The distinguishing feature of this mechanism is the formation of the c-BN phase on the condensation surface. It should be emphasized that such a mechanism can be realized during the PLD of BN films in the case of excimer lasers operating in frequency mode with a low power density per pulse. However, a quite different mechanism of the formation of the c-BN phase during pulsed laser evaporation of an h-BN target is also possible. This mechanism was realized during the evaporation of an h-BN target with the use of a Nd:YAG laser (~. = 1064 nm) with high power per pulse (1000 J/pulse) and a millisecond pulse length [50]. The areas with a c-BN phase that were revealed in the films deposited under these conditions most possibly are the products of the phase transition that took place on the h-BN target surface under the influence of a laser pulse and were then transferred in the film. Such a mechanism is similar to that of carbine phase origination in a carbon film during pulsed laser evaporation of graphite under the same ex-

Fig. 23. (a) Carbine particle embeddedin an amorphous carbon film deposited by laser ablation of a graphite target. (b) Spots on the SAEDpattern correspond to the particle, and halos relate to the amorphous carbon film.

PULSED LASER DEPOSITION perimental conditions. That is, the appearance of a c-BN phase is related to the simultaneous action of a pulse of high temperature and high pressure on a h-BN surface induced by laser pulse. It is known that the phase transition of h-BN to c-BN in bulk occurs only under conditions of simultaneous high temperature and high pressures [103]. However, the creation of c-BN nuclei in the gas phase due to the interaction of nitrogen and boron atoms evaporated from the target cannot be excluded.

4.3. Polymorphism of Silicon Carbide Films The formation of a 3C-SiC phase in films deposited during the evaporation of a ceramic silicon carbide (SIC) target or a 6H-SiC single crystal has quite different causes. This result was obtained both in a majority of the works in which SiC films were obtained by the evaporation of a ceramic SiC target by excimer lasers [39], and by evaporation of a 6H-SiC single crystal with a Nd:YAG laser with a high power per pulse [50]. It is worth mentioning that ceramic SiC targets mostly have a structure of cubic SiC (3C-SiC) that relates to the peculiarities of the fabrication of this material. SiC ceramic material always contains an excess of silicon. And it is known that even an extremely small excess of the silicon in SiC stabilizes the 3C-SiC phase both in a single crystal [85] and in polycrystalline ceramic material. Solidified droplets of silicon were revealed in SiC films deposited by pulsed laser evaporation of 6H-SiC single crystal during TEM investigations (Fig. 12). This fact indicates that during pulsed laser evaporation of SiC partial dissociation of the composition occurs. At the same time it is known that the volatility of silicon is noticeably higher than that of carbon, so the appearance of some excess of silicon in the film is not surprising. Evidently just this effect plays the main role in the formation of the cubic 3C-SiC phase in SiC films deposited by pulse laser evaporation of 6H-SiC single crystal or a ceramic SiC target. The same mechanism of 3C-SiC phase formation is typical for the other deposition methods of SiC films. As follows from the above consideration of polymorphism in PLD films, the mechanisms of formation of polymorphous phases are different for different compounds. However, the mechanisms of formation of metastable phases during the deposition of films by excimer laser with a short pulse length and low power per pulse are similar to that realized in other deposition methods. The mechanism of formation of such phases, however, can differ from what is typical for other deposition techniques, with the use of laser irradiation with high power per pulse. In this case the simultaneous action of pulses of high temperature and pressure that arise at the target surface under the influence of a laser pulse can induce new phases. Nuclei and particles of a new structural phase formed by this means then are transferred to the condensation surface. The formation of new phases apart from this mechanism can occur directly on the condensation surface because of its bombardment by particles with high energy. Each of these kinetic factors (pulses of high temperature

661

and pressure bombarding a growing film) can shift the thermodynamic balance on the condensation surface or on the target in the direction of the formation of a metastable or new phase.

4.4. Conclusions The phase transitions in bulk polymorphic substances can occur under the influence of high temperatures and pressures (carbon, BN, and some others) or may be related to the concentration variations in the compound. In the latter case the phase transition can be observed even at minor (almost at stoichiometry limits) variations of the concentration of one of the constituents (AUB vI compounds, SiC, and some others). The mechanisms of origination of structural phases in PLD films that are different from that intrinsic to the target depend on the peculiarities of the target substance and on the laser operation regimes. The influence of the laser irradiation directly on the target surface and indirectly on the growing surface can induce a new structure phase in the film due to the concentration changes in the film composition and under the simultaneous action of a pulse of high temperature and pressure. The compositional changes in the film inducing the formation of a new phase can take place on the target surface and on the growth surface, and this mechanism can be realized in other deposition methods. The induction of a new phase in the film by the transfer of the nuclei and particles of the new phase from the target to the growth surface is inherent only in the PLD method.

5. MACRODEFECTS IN PLD FILMS One of the major drawbacks of PLD is the macrodefects in PLD films. We use the term "macrodefect" to designate a microstructure inhomogeneity in a PLD film that appears not due to condensation of the vapor phase. The origin of macrodefects in PLD films is an intrinsic problem of pulse laser interaction with condensed matter; therefore it is much more difficult or may even be impossible to overcome.

5.1. Mechanisms of Splashing There are two major sources of macrodefects in PLD films. One source is the splashing that occurs during interaction of the laser pulse with the target, and this effect has many causes. The second source of macrodefects is the generation of particulates due to condensation of vapor species in the gas phase. The size of particulates formed from the vapor phase tends to be in the nanometer range, whereas their counterparts are in the micron and submicron ranges. Particulates formed by splashing effects tend to be spherical, whereas the particulates formed from the solid ejecta tend to be irregularly shaped. Particulates formed from vaporized species mainly have a spherical shape. Splashing includes a few mechanisms that lead to the deposition of particulates on the substrate [ 10]. For a given material splashing can include any one or a combination of these mechanisms.

662

SHAGINYAN

One of these splashing mechanisms is subsurface boiling. It occurs if the time required to transform laser energy into heat is shorter than that needed to evaporate a surface layer with a thickness on the order of a skin depth. Under this condition the subsurface layer is superheated before the surface itself reaches the vapor state. Under this process micron-sized molten ejecta will be removed to the substrate. In the second mechanism of splashing the force that causes expulsion of liquid droplets comes from above the liquid layer in the form of recoil pressure exerted by the shock wave of the plume. Because the droplets originating from this process also contain micron-sized balls, it is impossible to distinguish the last mechanism from the first. The magnitude of this effect can be reduced as in the previous case by lowering of the laser power density. The third type of macrodefect observed in PLD films is the solid ejecta originating more during the evaporation of brittle material systems, particularly sintered ceramic targets. The mechanism of their generation relates to the formation of long, needle-shaped microstructures a few microns in dimension on the target surface as a result of erosion during laser beam forcing. These microdendritic structures are very fragile and can be broken by thermal shock induced during intense laser irradiation. This debris is carried toward the substrate by the rapidly expanding plume and condense on the growth surface. 5.2. Elimination of Particulates There are a few approaches to the problem of particle deposition. One concems the improvement of laser systems. It includes the improvement of the spatial and temporal homogeneity of the pulse structure [7, 8]; searching for optimal wavelength and pulse duration [9], and using the frequency evaporation regime. As a result of many years of investigations of laser development for film deposition, an ideal laser system was proposed [12]. This system is likely to have a pulse energy of < 1 J at a repetition rate of 200 Hz with a beam homogeneity and pulse-to-pulse energy stability of better than 10%. The lower laser pulse energy makes it possible to reduce the particulate generation, because of the lowered condensation of vapor species in the gas phase and the decreased amount of liquid phase on the target and the lower magnitude of recoil pressure. Evaporation of a nonmetal target by irradiation with a shorter wavelength also decreases the possibility of clustering of evaporated species because of more efficient conversion of energy of shorter electromagnetic waves into heat for nonmetal materials [3]. Another approach to reducing the macrodefects in PLD films is the manipulation of the thermophysical properties of the targets to increase the efficiency of conversion of laser power into a heating-evaporating process and to increase by this means the portion of vapor phase in the ejecta. For this purpose the evaporation of different types of the targets like cast metals and alloys, single crystals, cold pressed and hot pressed powders [86], and free-falling powders [41] was investigated. These effects are considered in detail in Section 6.

One more widely used PLD technique for lowering the number of microparticles in films is the mechanical separation of the particles ejected from the target. These methods are widely treated elsewhere in surveys [3, 10, 12], and we will omit this question. A quite different approach to enhancing the efficiency of laser irradiation in material evaporation is to establish the correlation between the thermophysical properties of the evaporant and the portion of a vapor phase in laser ablation products. In this case the efficiency of laser evaporation can be determined as the ratio of vapor mass to the total mass of the products, produced by laser irradiation of the target. One can enhance the evaporation efficiency and decrease or avoid the particulates in the film either by changing the thermophysical properties of the target (e.g., its thermal conductivity) or by choosing a relevant target composition. In this context the problem of the efficiency of laser evaporation and splashing is tightly bound up with the problem of the determination of the portion of the vapor phase in laserablated products. The larger is the vapor portion in products ejected from the target by laser pulse, the greater is the film thickness and the more efficient is the utilization of laser radiation. The portion of the vapor in the ablated products depends on the laser parameters and on the thermophysical properties of the target material. Because there are very few publications devoted to this problem, we consider it in more detail in view of its importance for PLD. 5.3. Determination of Vapor Portion in Products of Laser-Ablated Metals A few works have been devoted to the determination of the vapor portion in products ejected from the metal target during pulsed laser evaporation [87-90]. In [88] the efficiency of metal evaporation was estimated from the depth of the crater on the metal target that appeared after the impact of the laser pulse and from the mass of the products ejected from the crater. Using these criteria, the authors concluded that there is no correlation between the thermophysical properties of the metals and the amount of vapor produced by laser pulse impact. However, because the mass of the ejected products mainly consists of the liquid phase [7], the mass of the ejected products and the depth of the crater are not relevant parameters for the characterization of the efficiency of the evaporation of the metal by laser irradiation. The ratio of vapor to liquid components in the ejected products during laser pulse impact with some metals was estimated and a correlation between the amount of vapor and the value / Q, where ~. and Q are the specific energies of melting and vaporization, accordingly, was established in [87]. The authors determined the portion of the vapor component mv/m (mv, mass of the vapor, m, total mass of the products ejected by the pulse laser irradiation at q = 5 x 107 W/cm 2) by two methods. In the first method m v was calculated from the equation of the energy balance, where the total mass of ejecta m was the single experimentally determined parameter. However, in the equation of the

PULSED LASER DEPOSITION energy balance the laser power was considered to be consumed only by the evaporation, and the unproductive losses of optical power on heating and melting of the metal were not taken into account. In the second method mv was determined from the recoil momentum, inasmuch as the liquid fraction momentum in the total recoil momentum is negligible, because the velocity of the liquid droplets is 1)1

. ~ ", ^o ~icd

-4.5-

/

-6.0 ,~ 1200

689

w i,,,,

i,,

9

,,

i,

1300 1400 1500 Temperature(K)

,,,

1600

Fig. 19. Equilibrium vapor pressures in the (K0.9Li0.1)2CO3, (K0.9Li0.1)C1, and (K0.9Li0.1)-fltt-A1203 systems in air and low oxygen partial pressure.

however, the upper K20 limit of K-/3-A1203 solid solutions extends as far as K20.4.9A1203, i.e., over the solid solution compositions generally accepted for the fl"-A1203 phase. The growth of K-/3"-A1203 on A1203 was pursued with the use of chloride (KC1 + LiC1), carbonate (K2CO3 + Li2CO3), and /3"-A1203 (K-/3"-A1203 + Li-flf1-A1203) vaporization sources. Ceramic substrates were used instead of sapphire in the preliminary tests. The results can be summarized as follows: 1. K-flII-A1203 forms on A1203 with carbonate, chloride, and (K,Li)-/3"-A1203 sources. The equilibrium vapor pressures of the K species are plotted in Figure 19. 2. The chloride and carbonate systems generated no A1 species, so formation of fl"- or/3-A1203 must be from vapor-substrate reactions. ]3II-A1203 first appeared at temperatures as low as 950-1000~ because of the high chemical reactivity and vapor pressures of the K20 species. The yield of f11'-A1203, however, was low in the chloride system because of the high potassium pressure and a deficiency of oxide. 3. A K20-rich aluminate phase (in most cases K20.A1203) was found to coexist with/3 II- or fl-A1203. This was assumed to be a reaction product of the high K vapor pressure or to be produced by a reaction between the K species and the/31I- or/3-A1203 formed. Potassium aluminate was very hygroscopic and severely corroded the ceramic substrate. 4. K-/3"-A1203 single-crystal films only grew on sapphire substrates. Growth started at 1040~ ~50~ lower than that of Na-/3"-A1203. A continuous film formed above 1100~ The K-/3"-A1203/sapphire epitaxial partnership has a crystallography identical to that of the Na isomorph.

/3'I-A1203 single-crystal films ion exchange like bulk crystals [48]. The ion exchange ability of/3- and fl'-A1203 arises from the loose-packed crystal structure. Cations on the conduction planes are exchangeable with ions of different sizes and valences. The extent of the exchange depends on the chemical potentials of the exchanging and exchanged ions in the solid and the ion exchanging medium. It therefore varies with the temperature of the exchange and the concentration and nature of the anion associated with the exchanging cation. The rate of exchange is diffusion-controlled and can be accelerated by applied electrical or ultrasonic fields. In some cases it is decelerated by the "mixed-cation effect." The facility of ion exchange of the fl(f111)-A1203 family provides a number of chemical and electrochemical paths to new isomorphs. In general, the temperature of ion exchange is lower than that of solid synthesis (or crystal growth), facilitating the preparation of isomorphs of (or doping with) cations unstable at higher processing temperatures. This facility offers control of the valence state of optically active, transition-metal and rare-earth ions. Over 50 isomorphs of/3-and fl'-A1203 have been prepared by ion exchange (Appendix, Tables X-XV). Na-fl'-A1203 is the commonly used precursor because of its high diffusivity (conductivity) and availability, fl"-A1203 single-crystal films have been exchanged into Li, K, Cu, Ag, and Ca isomorphs. Because the isomorphs have similar ao lattice constant values, the film-substrate interface is subjected to low stress. The film is free to extend vertically, so stresses associated with c axis dimension changes are released. This is not true for polycrystalline ceramics, and the stresses developed during ion exchange destroy them. The conditions for the ion exchange of fl'-A1203 singlecrystal films are summarized in Table VI. Partial or complete exchange was identified by EDX (Fig. 20). The associated X-ray patterns are given in Figure 21. The calculated diffraction intensities for the exchanged isomorphs, based on the atomic occupation of bulk crystals, are presented in Table VII. A distinct intensity change is observed for silver-/3"-A1203. The intensity of reflections (001) was simulated and found to be sensitive to the atomic scattering factor but insensitive to the ionic occupation site. Conventional ion exchange is carried out in fused salts. The melting temperature of solid mixed salts is high enough for ionic diffusion and substitution, and ion replacement is complete in a few hours. An aqueous ion exchange method [60] was designed to avoid sealing corrosion problems associated with fused-salt media at high temperatures. Aqueous electrochemical cells were constructed to create ion distribution profiles in/3"-A1203 single-crystal films for luminescence patterning (Section 6.2). Aqueous-solution ion exchange was conducted on a single-crystal Na-f111-A1203 film in a 0.2-0.3 M AgNO3

690

KUO AND NICHOLSON Conditions for Ion Exchange and Cu + Doping in/~'-A1203 Single-Crystal Films

Table VI. Starting phase

Medium

Ag-/3~t-A1203 Na-/~-A120 3 Na-/~-A1203 Na-/3~CA1203 Na-/3tr-A1203 Na-/3rZ-A1203 Na-/3ZCA1203 Na-/3Zt-A1203 Na-/3~t-A1203 Na-/3t~-A1203

LiC1 (exchanging) KNO3 (exchanging) AgNO3 (exchanging) CaC12 (exchanging) 0.75CuC1-0.25NaC1 (doping) 0.70CuC1-0.30KC1 (doping) 0.80CuC1-0.20LiCI (doping) 0.67CuC1-0.33RbC1 (doping) 0.936CuC1-0.064CaC12 (doping) 0.70CuC1-0.30BaC12 (doping)

Time (h)

Temperature (~

10.5 87 46 24 2-4 2-4 3-6 4--6 7 10.5

650 405 270 800 410-450 420-470 470 450 485 650

Observed and Calculated X-ray Diffraction Intensities of/~-A1203 Isomorphs

Table VII. Na-/3~-A1203 0.42(6c), 1.18(18h)

Li-/3"-A1203 0.42(6c), 1.18(18h)

K-/3~t-A1203 0.56(6c), 1.04(18h)

Ag-/3~t-A1203 1.60(6c), 0.0(18h)

(hkl)

Obs.

Calc.

Obs.

Calc.

Obs.

Calc.

Obs.

Calc.

(003) (006) (009)

100 79 2

100 59 3

100 45 4

100 58 5

84 1 93

23

17

20

9

100 67 12 30

11 3 86

(00,12)

100 67 3 54

100

100

(00,15)

36

13

21

9

66

26

49

77

The figures indicate the occupation on 6c and 18h sites used for the diffraction-intensity calculation.

o

to

o

AI

o

""--" 13")

d

Q Q

O v

~

Ca-Exchanged .

.

.

.

k__

.

Ca _,ik .._

._~

_

. . . . . . . . . ~ __ ..

_

A..._.__~

:

ki_13,,_Ai20 3

Ag-Exchanged Ag

K-Exchanged

........ i,,,,i,i,,l/,,,i,,,,i,,,,I,,,,I,,,,I,,,, 5 10 15 20 25

K A_

t

,-

,

1.0

2.0

.

.

35

40

I 45

20(0)

Fig. 21. The X-ray diffraction pattern of Na-/3tt-A1203 and ion-exchanged single-crystal films.

Na-I]"-AI203

0.0

30

L,,,..,. Ag_I3,,_AI203

i

I

3.0

4.0

keV

Fig. 20. The EDX spectrum of Na-/3t~-A1203 and ion-exchanged singlecrystal films.

solution. Na + and Ag + have high diffusivity and mobility in /3"-AleO3. E x c h a n g e d fractions were d e t e r m i n e d via w e i g h t gain, m i c r o b e a m , and X-ray diffraction analyses. The increases in relative intensities of reflections (009) and (00,12) are asso-

691

SINGLE-CRYSTAL fl"-ALUMINA FILMS

A

8o _

1

,~

j

g

. . . . . . . .

.

.

.

.

.

.

.

.

.

.

_ ~J,_..... .

lb

s

1.0

I

15

20

25

~~ _

30

35

40

45

2O(O)

A

1

o

~ I o.8

[

m 04

.......1

e,,.

!

i

,

0.8

~

!

.

" 13l =

"

ct (cation) =

....

i 80 time (h)

-

-

-

5

10

,

,,_,L

....

i

1'5 20

3R 4zrNA

R "-AI O3 = E R(oxide =

Ooi-'[I I[ !

where VM and WM a r e the mole-volume and mole-weight; NA and Nf are Avogadro's number and the number of formulae per unit cell, respectively; d is the density; and n is the geometric mean refractive index from the ordinary and extraordinary refractive indices, a0 and co are the lattice constants of the unit cell. The molar refractivity of Na-, Li-, K- and Ca-fl"-A1203 is given in Table VIII. Refractivity increases with increasing size and charge of the exchanged cation. Previous investigations have shown that the refractivities of fitt_ and fl-A1203 compounds obey the additivity principle [61] and are correlated with the bond ionicity [62]. The refractivity of A1203 in fl"- and fl-A1203 is estimated to be approximately equal to that of y-A1203 rather than c~-A1203. The polarizability (c~) is

~

|,l

.

.

i

2's 30 2O(o)

.

.

i

3'5 4o

1

~[

4s

Fig. 22. The ion exchange of Na-fl"-A]203 in AgNO3 aqueous solution at 92~ (the X-ray diffraction patterns were taken at 0.00, 0.43, and 0.86 exchange fractions). The relative intensity changes are distinct.

ciated with a decrease in intensity of (003) and (006) as Ag + replaces Na + (Fig. 22). Nearly complete Ag exchange was obtained below 90~ The reaction rate decreases with time, as expected for a diffusion-controlled process.

a(O 2) -

R(cation + E R(O -t

3R(cation) 4zrNA 3R(O -2) 47rNA

where the molar refractivity is summed from the refractivity and polarizability of the cation and oxygen anion components as correlated with bond ionicity. The calculated polarizability is included in Table VIII. This suggests a heterogeneous bonding pattern for the fl"-A1203 crystals. There are two types of chemical bond, (conduction ion) - (oxygen), and A1-O. As given in [62], the ionicities of the two oxide components are estimated as 0.63-0.65, and >_0.90, respectively. The low ionicity of the A1203 component is attributable to the strong polarizing power of trivalent A13+, which increases the proximity of the valence electrons shared with the oxygen. The conducting cations have low field strengths, so their valence electrons are less attracted, thus increasing the oxide ionicity and the oxide-ion polarizability. The additivity principle was used to estimate the mean refractive index of fl"- and fl-A1203 via molar volume. The resuits are summarized in the Appendix, Tables XVII and XVIII.

8. LUMINESCENCE INVESTIGATION OF

Cu+-DOPED, SINGLE-CRYSTAL ~"-A1203 FILMS 8.1. Luminescence

7.2. The Optical Refractivity of [3"-A1203 Isomorphs The Lorentz-Lorenz molar refractivity (R) was determined from the measured lattice constants and refractive indices for fl"-AlzO3 single-crystal films and crystals, i.e., R - VM(n2 -- 1)/(n 2 + 2)

VM -- WM/d n

--(n2ne)1/3

or

NA/Nf{a~co sin(27r.3)}

Luminescence in activated/3"- and fl-A1203 hosts has been verified. Active ions can be doped into the spinel block or onto the conductiont plane. Cations on the conduction plane are mobile and weakly bonded and are believed to be responsible for environmental effects. Cu + was doped into single-crystal films via ion exchange in CuC1 melts in dry nitrogen atmospheres (see Table VI). The luminescence and spectra for Cu+-doped/31t-A1203 singlecrystal films excited by ultraviolet radiation (254 nm) are shown

692

KUO AND NICHOLSON Table VIII.

Composition

Optical Refractivity of/~//-AI20 3 and Ion Polarizability of Ions Derived via Single-Crystal Film Data

a0 (/~)

co (/~)

no

Na1.6Li0.3A110.7017

5.61

33.565

Li 1.6Li0.3A110.7017

5.605

33.67

5.60

34.126

Ag 1.6Li0.3A110.7017

5.604

33.46

Ca0.8Li0.3All0.7017

5.607

33.47

K 1.6Li0.3A110.7017

ne

R

Rbasic oxide

1.687

1.637

68.6

8.95

0.192

2.79

1.662

1.627

67.1

7.05

0.069

2.62

1.697

1.642

70.2

10.92

0.647

2.67

1.702

1.672

70.1

0.594

2.97

9.143

Table IX.

Creation (/~)3

t~oxygen anion (]k)3

Emission Bands of the Cu+-Doped fl//-A1203 Spectrum Emission (nm) (fraction)

Cation

Fig. 23. The luminescence of Cu+-doped diated with ultraviolet light (254 nm).

fltt-ml203

Blue

Green

Red 600 (0.053)

Na +

438 (0.100)

535 (0.847)

K+ Ba 2+

440 (0.266) 440 (0.539)

495 (0.734) 485 (0.461)

Na +

442 (0.053)

540 (0.776)

625 (0.172)

Ag +

442 (0.255)

505 (0.046)

606 (0.699)

single-crystal films irra-

in Figures 23 and 24. The emission bands and their contributions are summarized in Table IX. Activated Na +-, K +-, and Ba-/~-A1203 exhibited green-blue luminescence. The spectra were resolved into three emitting bands at 440, 485-540, and 600-625 nm, respectively, i.e., in blue, green, and red visible. The transition in the Cu+-doped/~'t-A1203's can be assigned as 3d 1~ --+ 3d94s, where the blue and green emissions are assumed to arise, respectively, from cuprous ion monomers and dimers, as compared with the spectral data for Cu + in various phosphors [4, 63-65]. The band shifts and the efficiency vary with site occupation and crystal field. The wide shift of the emitting band observed in the Cu+-activated fl'~-A1203 bulk crystals is explained by the crystal field changes associated with the expansion and contraction of the host lattice. However, the crystal field explanation is inapplicable to the blue and red shifts for the Ba and Ag hosts, where the emission energy increased with increasing lattice constant (co) and decreasing crystal field. The blue band activated in the singlecrystal film host emits an identical ~440-nm wavelength in the different isomorphs, whereas the green band varies in the wavelength range 485-540 nm, shifting to short wavelengths from Na- to K- and to the Ba-fl~-A1203 hosts. This abnormality in the crystal field effect is explained by the Cu + and 0 2 - ligand interaction with the codoped, matrix cations. The 0 2 - is less deformed with increasing polarizability of the matrix ions and so contributes more to the bond with Cu 2+ ions and enhances the environmental field, increasing the emission energy. As a result, green luminescence shifts to shorter wavelengths from sodium to potassium to barium. This suggests that the Cu +

dimers are more flexibly affected by the host environment as compared with the stable blue emission. The contribution of the blue emission was enhanced in the same sequence of increasing polarizability from Na + to K + to Ba 2+. The increase in polarizability of the matrix cations strengthens the bonding between Cu 2+ and 0 2 - and suppresses the tendency of ions to cluster. These results suggest that cations of high polarizability are preferred for blue luminescence in a flt~-A1203 host. The red emission band of the Na-fl~t-A1203 host is enhanced in Ag/Na-fl"-A1203. Polarizability (or refractivity) data are unavailable for silver fl~-A1203, so further calculations are not possible. However, the high electronic polarizability of Ag + is expected because of the non-inert gas electronic configuration. The increased covalency of the bonding in the Ag-fl~-A1203 isomorph may account for the red-band enhancement.

8.2. Luminescence Patterning of Single-Crystal [3"-A1203 Films Single-crystal films patterned into green and purple luminescent domains (Fig. 23) were obtained via ion exchange in an aqueous, electrochemical cell. A Cu+-doped Na-fl1~-A1203 single-crystal film was the electrolyte separator, and Na- and Ag-nitrate solutions were the electrodes [64]: ( - ) NaC1 aq. I Na-fl"-A1203

] AgNO3 aq. (+)

An electrical potential was imposed on the cell to accelerate ion migration. The chemical potential of Na + and Ag + ions was dominated by the NaNO3 and AgNO3 solutions. The solution electrodes are reversible to Na- and Ag-fl~t-A1203, respectively, under low current density at moderate temperatures. During

693

SINGLE-CRYSTAL/3"-ALUMINA FILMS

c

400

450

500 550 600 Wavelength (nm)

650

19

I

700

400

450

500 550 600 Wavelength (nm)

(a)

650

700

(b)

,

~ 1 400

450

I I I 500 550 600 Wavelength (nm)

I 650

I 700

(c) Fig. 24.

Emission spectra excited by 254-nm radiation. (a) Cu+-activated Na-/~"-A1203. (b) Cu+-activated K-/~"-AI203. (c) Cu+-activated Ba-/~"-A1203.

charging with the AgNO3 compartment positively charged against NaNO3, Ag + ions are forced toward the /3"-A1203-, and Na + ions exit therefrom into the NaNO3 solution. The charged Ag + are expelled from the/~"-A1203 electrolyte into the NaNO3 solution because of the extremely low Ag + concentration therein. On the other hand, Ag + ions are strongly held in the electrolyte soaked in the AgNO3, as [Ag +] is much higher than [Na +]. The difference in chemical potential in the electrode compartments determines the Na + and Ag + concentrations in the/3"-A1203 electrolyte. Figure 25 shows the emission spectrum for the two halves of the luminescent fl"-AlaO3 single-crystal film electrolyte and the EDX analysis

thereof. The latter indicates the Na and Na/Ag content of the separate domains. The emission spectra of the ion-patterned/~"-A1203 film consists of blue, green, and red emission bands. The green and purple luminescences (Fig. 23) are the result of the ionic distribution. For the Na-rich part, a strong spectral peak is positioned at 540 nm, emitting green luminescence. The green emission is greatly depressed in the Ag-rich part of the film, and the red band is intensified. The Ag domain appears purple. A sharp green-to-purple luminescence boundary builds in the Na/Ag-/3"-A1203 single-crystal film. The chemical potential of the solution electrodes dominates the Na + and Ag +

694

KUO AND NICHOLSON Table X.

2.0"

Ion

Startingmaterial

Li K Rb

Ag-fl-A12 03 Na-/3-A12 03 Na-fl-Al203 Ag-/~-A1203 Ag-fl-A1203 Na-fl-Al203 Na-fl-A1203 Na-fl-A1203 Na-fl-A12 03 Ag-fl-A1203 Na-/3-AI203 Ag-fl-A1203 Ag-fl-A1203 Na-fl-A1203 Na-fl-Al203 Na-fl-Al203

Ag

m

i

t_ ~

..Q m v

4.0

,,,=,R

keV

Cs Ag Cu

L _

"

t

\

t-.

l l l

t...

~'1 I I /

T1 Ga In

/\ I I %

NO H H30 NH4

% ,,,,

MonovalentIon Exchange in/3-A1203 Preparation conditions

Reference

LiC1 saturated LiNO3 melt KNO3 melt RbNO3 melt RbC1-RbNO3melt CsC1 melt, 54% exchange AgNO3 melt CuC1 + Cu, 527~ 24 h, Ar CuC1 melt + Cu, electrolysis T1NO3 melt (Ga iodide + Ga) melt InI, 400~ no exchange In metal, 350~ 3 days NOC1-A1C13 melt, 197~ 23 h H2, 300~ Boiling in concentrated H2SO4 NH4NO3 melt, 170~

[1] [1] [1] [1] [1] [1] [2] [2] [1] [1] [1] [1] [4] [5] [6] [1]

9 ,,,...,_,.,r-,--

2.0-

.e

4.0

v

AI

.i

w

-,.,.,.

I

. . . .

~,: ,~

l 400

I 450

I 500

I 550

~) . . . . .

I - I 600 650

I 700

2. Ion-exchanged fl'-A1203 single-crystal films doped with the cuprous ion have been prepared and employed as luminescent hosts. The emission spectrum observed includes blue-, green-, and red-emitting bands. The band position and emission contribution are associated with the polarizability of codoped cations. Blue emission is enhanced by codoping with ions of high polarizability. 3. Luminescence patterning was achieved with the use of an electrochemical cell. A Cu+-doped, Na-fl'-A1203 single-crystal film was used as an electrolyte separator, and NaNO3 (aq.) and AgNO3 (aq.) were used as the solution electrodes. Green and purple luminescent emission areas were patterned into the Na- and Ag-rich domains of the electrolyte.

Wavelength (nm) Fig. 25. The emission spectrum and EDX analysis of a luminescencepatterned/311-A1203 single-crystal film.

10. A P P E N D I X 10.1. 13"- and 13-A1203 Isomorphs

concentrations in the luminescence-patterned ]3"-A1203 singlecrystal films.

9. S U M M A R Y 1. Na-/3"-A1203 single-crystal films have been grown on (001) sapphire substrates via chemical-epitaxial reaction between sapphire and alkali vapors. The two phases have identical c axes and 30~ a axes. The film area achieved is 6.5 cm 2, the thickness, 1 and the interaction between film atoms is stronger for W < 1. The energy axis is a relative axis between the two states, clustered and uniform film. It is given by (E (n) - E (0) - lXcn) with/Zc being the chemical potential of a bulk piece of the material forming the film, and n is the number of monolayers in the film. Thus, when the slope of a curve in the plot is positive, /Zfilm 1 to the oscillations shown in Figure 2, where unpaired bonds, edgeand corner-arrangements cause the increase in energy between complete layers. Whenever the system can alternatively lower its energy through a phase separation, the real growth follows the alternate route. In the current model, this is the case be-

CLASSIFICATION OF CLUSTER MORPHOLOGIES

(a)

3

(b)

/

/ surfoce term

Z

riSK

Wl

I

F(r) n (ML)

/

/

/

/

/

/

/

n (ML)

Fig. 2. (a) Energy relative to that of the bulk crystalline state, plotted versus the film thickness for a film-substrate interaction strength larger (W > 1) and smaller (W < 1) than the film-film interaction. The dashed line represents the minimum energy configuration for a single-phase system, the solid line includes two-phase regimes between full layers. (b) Chemical potentials relative to the bulk chemical potential for the same system, nSK labels the Stranski-Krastanov layer thickness and nmd labels the critical thickness for misfit dislocations.

tween the completion of full layers where a two-phase regime can be traversed (represented by the common-tangent of two subsequent energy minima) by growing the new layer in form of large two-dimensional islands, avoiding unpaired bonds, edgeand corner-arrangements (dashed line to n = 3 ML). Three-dimensional clustering can be established in Figure 2 based on the same argument. It occurs when the chemical potential//,film exceeds # c , i.e., the slope of the common-tangent curve becomes positive (dashed line beyond n = 3 ML). Instead of following the dashed line toward higher energy, the system follows the dashed-dotted line, defining a wetting transition [12]. The resulting film morphology, consisting of a few uniform layers and clustering of subsequently deposited material is referred to as a Stranski-Krastanov (SK) growth condition [ 13]. Based on the thermodynamic equilibrium arguments applied to Figure 2, two growth models are distinguished: if the structure grows with the formation of three-dimensional clusters on the bare substrate, the system is called a Volmer-Weber system [ 14] and if the growth results initially in a uniform layer the system is either a Frank-van der Merwe or a Stranski-Krastanov system. The latter is distinguished by the occurrence of clusters beyond a given coverage above one monolayer, as illustrated in Figure 2. This coverage is called the SK-layer thickness. During the growth of a film, however, clustering usually does not occur immediately after exceeding the SK-layer thickness due to a kinetic barrier toward clustering. The reason for this observation is illustrated in Figure 3. The figure shows the Gibbs free energy of a three-dimensional cluster as a function of its radius (assuming for simplicity a spherical cluster shape). At small radii, the energy gain due to the formation of bulk material, which is essentially proportional to the cube of the radius times the difference between the chemical potential of bulk film material and the chemical potential of free adatoms on the sub-

\

\ \

\ "~.volumeterm

\

,

Fig. 3. Sketch illustrating the Gibbs free energy differential for a cluster on a surface. Reprinted with permission from [ 181 ], @ 1992, Elsevier Science.

strate, (/zc - / Z a d ) 9 r 3, is exceeded by the energy loss due to the surface of the cluster, which is essentially proportional to the square of the cluster radius, y r~, with y the surface tension of the cluster material. With increasing radius, the volume term begins to dominate, establishing a critical radius in Figure 3 with a maximum of the Gibbs free energy Fc(r). Applying the condition d F c ( r ) / d r = 0 allows us to calculate the critical cluster size for which the increasing surface energy and the decreasing volume free energy are balanced. This critical radius can be interpreted in two ways, (i) in experiments with variable deposition rates and variable free adatom concentrations, the critical radius identifies the size of a cluster which needs to form before it can become stable with the addition of a single adatom. Such clusters may require cluster sizes of the order of several tens of nanometers to be energetically favored. (ii) For a cluster with a given radius r a vapor pressure can be calculated such that this cluster grows and decomposes with the same probability. This leads to the Gibbs-Thomson equation defining the equilibrium concentration of a cluster of radius r [15-19], c(r) = cooexp

rkT

~ c~

1+

rkT

(1)

4

LI AND ZINKE-ALLMANG

where c ~ is the equilibrium concentration for an infinitely large cluster, y is the surface tension, vc is the atomic volume of the cluster material, and k is the Boltzmann constant. The second equation in Eq. (1) applies when r > 5 nm. For large clusters, the exponent in Eq. (1) vanishes and c(r) approaches cc~. In this form, the Gibbs-Thomson equation is applied to cluster growth under zero deposition rate conditions in part 2 of this chapter. Thus, uniform layer growth often continues beyond the SKlayer thickness, forming coherently strained but metastable layers. The decay of such metastable structures occurs along different kinetic pathways, separately discussed earlier: The traditional model allows a metastable uniform film to grow to a thickness where local regions start to exceed a critical thickness for misfit dislocations. In these regions, homogeneous strain relaxes. Gettering mobile adatoms at these sites results in the nucleation of clusters and a decay of the metastability by approaching the bulk chemical potential. Nucleation mechanisms and the resulting cluster distributions are discussed in Section 1.1.2. Another mechanism possible for approaching the bulk chemical potential is through spinodal decomposition [20]. This mechanism is expected for states deep in the miscibility gap shown in Figure 1. The formation of well-defined clusters by nucleation is replaced in these cases by long-wavelength instabilities in the supersaturation leading to a network of denser and more dilute areas. This perturbation then increases, forming sharp concentration steps. Spinodal decomposition is seldomly seen in thin film growth situations as indicated already when discussing Figure 1. We still discuss it briefly in Section 1.1.3 as a few examples of the resulting morphologies can be given. A third kinetic pathway was identified. Before the supersaturation reaches the onset point of nucleation of relaxed clusters, coherently strained clusters can form in some systems [21-23]. These clusters still represent an energetically more favorable state than a uniform, strained film as the corrugation of the surface allows for some strain relief. However, these structures are only metastable as a fully relaxed cluster is the energetically most favorable state for all systems [3, 20]. Since the coherent clusters have received a lot of interest lately, a more detailed discussion is provided in a separate section (Section 1.2). When studying clustered structures, it should also be noted that at all nonzero temperatures a free concentration of adatoms must be present between the clusters. This is already implicitly indicated in the Gibbs-Thomson equation (Eq. (1)) where each cluster on a surface requires a specific adatom concentration to be in thermodynamic equilibrium. However, in any experimental system, there is a range of cluster sizes on the surface, and most of them are not in thermodynamic equilibrium. Thus, this concentration cannot be derived from Eq. (1) alone, although this equation indicates which two contributions to the free concentration have to be included: (i) the temperature-dependent solubility term c ~ and (ii) the additional contribution associated with the exponential factor for a representative cluster in the cluster size distribution. The second contribution depends obviously on the actual cluster size distribution and thus on the growth processes leading to the cluster morphology of interest. In general, however, this contribution is a small correction (in

the range below 1%) of the contribution due to c~. This term is discussed in the present context as it establishes a free adatom concentration in the range of up to a few tenths of a monolayer for all systems discussed in this chapter. For a two-phase system with both phases in thermodynamic equilibrium, in our case the dense cluster phase and the dilute adatom phase on a surface, thermodynamics requires that the chemical potential between both phases is balanced [24], lzc(T) = /Zad(T), where the index ad refers the free adatom phase and C refers to the dense cluster phase. If we neglect for simplicity the dependence on the number of atoms in a cluster, we derive from the balance condition of the chemical potential a Clausius-Clapeyron type of equation [25], In(coo(T)) cx

Ef kT

(2)

where E f is the energy of formation of a cluster (i.e., the energy difference for a film atom between being a free adatom and an integral part of a larger cluster). The temperature dependence of c~ has been verified [25] in a direct measurement of the adatom concentration as a function of temperature using scanning Auger microscopy in which the surface concentration between clusters is directly determined.

1.1.2. Nucleation

The time evolution of cluster formation is divided into three stages [20]: nucleation, early stage growth, and late stage growth, as sketched in Figure 4. Random nucleation and spinodal decomposition (see Section 1.1.3) are the dominant processes in the first stage. While nucleation is continuing, the first nuclei start to grow, capturing atoms from the supersaturated adatom phase. When the supersaturation is mostly reduced the nucleation process ceases. Clusters will continue to grow but other processes dominate, such as ripening, i.e., growth of larger clusters at the expense of smaller clusters which dissolve (Lifshitz-Slyozov-Wagner (LSW) model [26, 27], discussed in Section 2.2), and coalescence, i.e., clusters growing into each other [28, 29] (see Section 1.3). The early stage of growth is a transition stage between nucleation and late stage growth regime. In the early stage, the development of the cluster morphology depends primarily on the deposition rate. If deposition ceases, cluster nucleation ends and the clusters grow individually from the surrounding supersaturation which far exceeds the equilibrium concentration c~ while growth becomes a global phenomenon in the late stage with the entire cluster distribution interacting. If deposition continues during the early stages of cluster growth, the system asymptotically approaches a coalescence state. During the formation of precoalescence morphologies, i.e., structures where the merging of clusters does not yet dominate the morphology, coherent clustering may lead to novel structures which are discussed in Section 1.2.

CLASSIFICATION OF CLUSTER MORPHOLOGIES

INITIAL

0

radius has formed, the addition of one further atom stabilizes this cluster, i.e., then the cluster does not decay anymore. The main quantity besides the critical radius to be determined is the nucleation rate J which is the number of stable clusters formed per unit time and unit area on the substrate. The nucleation rate of stable clusters is given by the areal density of critical clusters, and the rate at which these clusters gain an additional atom. The nucleation rate is then deduced from the principle of detailed balance with the key equation given in the form [32],

\

J 0 o

0

LU 0

>,

=o < wO

/

ilij!il

COALESCENCE~

0

J-

..-

,._.-

T

,,,

9 _J o

,---,

o

{ o,, ~

DIFFUSIVE

BREAK-UP

GROWTH I11

0 q) LU

O O

N(rc)N(1)6in(rc)

(3)

SPINODAL

NUCLEATION

T

5

o O

OSTWALD RIPENING

Fig. 4. Sketch of the different stages of phase formation and phase separation. Indicated are random nucleation and spinodal decomposition in the cluster formation regime, diffusive growth, coalescence, and breakup of spinodal networks in the early stage and coalescence and Ostwald ripening in the late stage. Reprinted with permission from [ 181 ], 9 1992, Elsevier Science.

1.1.2.1. Fundamental Concepts of Nucleation Essentially, two approaches for nucleation and early stage growth have to be distinguished, (i) a model based on analytical formulations requiring usually restrictive assumptions such as a strict separation of the different stages of growth and (ii) a model based on kinetic rate equations with fewer assumptions, allowing the inclusion of growth modifications such as variable deposition rates or competing early stage coalescence [30, 31 ]. The kinetic rate equation approach has been chosen most frequently in the literature since it allows studing a wider range of cases. Thus, the concepts used in analytical models are only summarized briefly and the kinetic rate equations model is discussed in more detail. In this section, we assume that a system, consisting of a homogenous adlayer on a substrate surface, is brought into a two-phase coexistence regime by a sudden change in supersaturation, e.g., by a temperature quench or during a deposition process. We also assume that an energy barrier exists toward formation of instabilities, i.e., a small fluctuation in the surface concentration does usually decay, i.e., the adlayer can exist as a metastable configuration. In the thermodynamic limit, the energetic situation for a randomly formed small aggregation of atoms is described by the total Gibbs free energy. For a specific critical radius in Figure 3, the positive contribution due to surface increase and the negative bulk contribution is balanced. After a cluster of critical

where N (1) is the monomer adatom concentration, N (rc) is the areal density of clusters of critical radius, and gin is a collision factor describing the likelihood of a monomer to enter a cluster. The three factors in Eq. (3) are obtained as follows: (1) N (1) is calculated from the deposition rate and certain assumptions about the time constant for adatoms to remain in the free concentration as opposed to joining a cluster at low temperatures or possibly desorbing at higher temperatures. (2) The number density of critical nuclei N (rc) is estimated by analyzing Figure 3 quantitatively. It is assumed that the densities of all subcritical clusters reach a steady state. (3) The collision factor contains two major contributions: direct impingement from the vapor phase by the deposition process and surface diffusion of monomers (neglecting mobility of larger clusters). The diffusion mechanism dominates in most experimental cases [33, 34]. The collision factor then depends exponentially on the activation energy for diffusion. For condensation in most three-dimensional systems, e.g., rain clouds, the critical cluster contains more than 100 atoms and an analysis based on the continuum thermodynamic model is justified [35]. On surfaces however, critical clusters often contain only a few atoms [36] or even a single atom, as discussed later in greater detail. Atomic level quantifies, such as the binding energies of atoms at different sites on the surface or at the cluster, have to be used replacing macroscopic thermodynamic quantities [37]. The applicability of this approach suffers, however, from the same restrictions mentioned above. A qualitative advantage of the atomic approach is given for nucleation of crystalline nuclei, when Eq. (3) is modified to reflect the equilibrium shape of the cluster. In the atomic approach, a sequence of nucleation steps toward this shape can be described. Still, both approaches cannot deal with major factors in experimental studies, e.g., a spatial gradient of the free adatom concentration N(1) including diffusion effects on the surface. To rectify these shortcomings, an independent model was developed by Zinsmeister [31] and Venables [30], called the kinetic rate equations approach. Frankl and Venables also gave the first comprehensive discussion of the applicability of these equations in the analysis of nucleation experiments [38]. In the rate equation model for each cluster size (represented by j atoms in the cluster), the change of number of the clus-

6

LI AND ZINKE-ALLMANG

ters is written as a function of all processes contributing to the change of this number. To keep the model transparent, surface mobility is restricted to single atoms in this section. Further, coalescence phenomena are neglected and are discussed later. The kinetic rate equations are then given by dN(1)

dt

N(1)

=R

ra

2N(1)26in(1) + N(2)3out(2)

cx:)

-t- E [ 3 o u t ( j ) -- N(1)3in(j)]N(j) j=2

dN(2)

dt

= N(1)[3in(1)N(1) - 3in(2)N(2)]

(4)

+[6out(3)N(3) - 3out(2)N(2)]

dN(j) = N ( 1 ) [ 3 i n ( j - 1 ) N ( j - 1 ) - 3in(j)N(j)] dt +[3out(j + 1)N(j + 1 ) - 3out(j)N(j)].

1.1.2.2. Applications of the Fundamental Nucleation Concepts

where 3in is the collision factor for monomer capture and 6out is the collision factor for the release of a monomer; both factors are cluster size-dependent proportionality factors. The first equation describes the change in the number of single atoms, which is equivalent to changes of the free adatom concentration. It contains five terms: the first term is the deposition rate R, the second term represents losses due to reevaporation (where ra is a time constant for evaporation), and the third and fourth terms describe loss and gain due to charge in the number of dimers. The first term in the bracket of the sum corresponds to capture of single atoms by clusters and the second term corresponds to release of single atoms from a cluster. Each of these rates is given by the product of the number of relevant species and the collision factor which depends on the size of the cluster. The second and all following equations give the number change of clusters with j atoms, losses (negative terms) due to capture or release of single atoms, and gains (positive terms) due to growth of the next smaller cluster or decomposition of the next larger cluster. Nucleation for the case of a constant deposition rate allowed Venables [39] to simplify Eq. (4) by separating three groups of formulas: a formula for single adatoms, a formula combining all stable clusters, and a formula for the nonstable clusters (j < i*, where i* represents the number of atoms in a cluster of critical radius). Assuming a steady state for these sizes, the simplified set of kinetic rate equations reads: dN(1)

dt

=R

dN(j) =0 dt

N(1) Ta

forl <j

d(Nxjx) dt Fig. 11. Island size distribution for i* = 0 for 4 < 0 < 30% and D/F > 109 from Monte Carlo simulations. (Data taken from Amar and Family [75]. Reprinted with permission from [75], @ 1996, Elsevier Science.)

form N(j)(j)2/O) are shown in Figure 11. The distributions are distinguished because no peak occurs at finite cluster size. An interesting intermediate case between i* = 1 and i* -- 0 emerges for vicinal surfaces in homoepitaxial systems. When steps are present, an additional sink for monomers is created through irreversible attachment of mobile monomers. Bales [78] studied the case of irreversible nucleation (i* = 1) with both the kinetic Monte Carlo simulations and the rate equation models with a new parameter representing the competition between monomers attaching to the steps and monomers attaching to existing islands or forming new islands. As a function of this new parameter, a crossover from scaling is observed toward a new scaling form in the limit of strong step influence (i.e., monomer depletion due to attachment to steps). Resulting size distributions are quite similar to the case discussed earlier for i* -- 0. This may arise from the similarity of the effects of monomer exchange with substrate atoms [77] and the attachment of a monomer to a step. In both cases, the monomer is immobilized and leaves behind a stable structure object to further monomer attachment. (iii) Irreversible Nucleation in Reduced Dimensional Subspaces (i* = 1). The influence of imperfections of the substrate surface, such as steps or random point defects, can vary the nucleation dynamics significantly. Nucleation in heteroepitaxy is affected differently as monomers do not disappear completely when incorporated in a step. Mulheran and Blackman [79, 80] studied the case of irreversible nucleation on a stepped surface. Monomers cannot detach from steps after diffusive attachment. Subsequent diffusion along the step is possible and leads to nucleation when

11

a second monomer is encountered or leads to aggregation if a larger island is met. This reduces the irreversible nucleation model to one dimension. Monte Carlo simulations and rate equation calculations have been performed for point islands and circular shaped, extended islands. Their island size distributions show that the use of a finite island shape in the calculations has a noticeable effect. Spatial correlations are demonstrated in the form of nonrandom nearest neighbor distance distributions. Nucleation is not expected to be spatially random if cluster formation is diffusion controlled since the probability to nucleate a new island between existing islands is proportional to the square of the monomer concentration at each position which in turn is determined by the diffusion profile. Heteroepitaxial nucleation at random point defects has been investigated by Venables [64] and by Heim et al. [81 ]. The point defects are introduced as traps with an areal density and a trapping energy. A local equilibrium in the form of a Langmuir adsorption isotherm is established on the surface between the density of monomers in traps and monomers on the perfect surface because adsorbed monomers block further monomers from adsorbing at the same site. For large values of the trapping energy, all defects are decorated with a monomer and nucleation is strongly favored at the defect site. A consequence of this model is that the nucleation density is temperature independent over a wide range of substrate temperatures. Depending on the trapping energy relative to competing activation energies, such as the pair bond energy and the surface diffusion activation energy, this temperature interval may coincide with typical substrate temperatures in nucleation experiments. (iv) Reversible Nucleation with Monomer Detachment from Stable Islands. Ratsch et al. [82] studied the opposite case where two-dimensional island formation is reversible. This scenario is particularly interesting as it contradicts the assumption of a well-defined value for i* as all islands can decompose. The reversibility of islanding is introduced in the Monte Carlo simulation by steadily decreasing a single pair bond energy barrier Epair for atom detachment from islands. Varying the pair bond energy by a factor of 3 leads immediately to a deviation from the expected behavior from the kinetic rate equations (Eq. (5)) for Nx as the exponent of the term D / R varies continuously between 1/3 and 3/5, the discrete values expected for i* = 1 and i* = 3. This behavior has been interpreted as a crossover between two different stable island sizes [72, 83] but has been used to question the concept of a discrete i* value by Ratsch et al. [84]. Figure 12 illustrates the resulting size distributions. The data set represents six different coverages between 7.5 and 25%. Thus, reversible nucleation leads to sharper size distributions with a significant reduction of the number of islands of sizes near zero. A slightly more complicated system was studied by Nosho et al. [66] including strain in their model of a system with significant anisotropy. The strain is incorporated through a modification of the monomer attachment probability in one orthogonal surface direction. The strain coefficient, 0, is given such that no islands wider than 20 monomer units in this di-

12

LI AND ZINKE-ALLMANG

ml' 9

scaling is only expected when both of these rates are smaller than the rate at which dimers aggregate with larger islands as a result of their diffusive motion [89]. For irreversible nucleation with significant dimer mobility, several Monte Carlo simulations have been performed to obtain island size distributions. For hopping rates between 1 and 100% of the monomer hopping rate, size distributions become narrower with a more distinct peak near the average size. In addition, in some studies [88] a separate peak toward small island sizes is reported. Furman and Biham [87] extended the studies to systems with mobile trimers finding an even narrower size distribution.

9

, j ~ 9 JI,,Dm eq, t, '~t w

"".61 ,

1.0 A V Z

0.5

1.1.2.4. Novel Experimental Aspects in Nucleation

0

"7

0

1

2

3

jl<j> Fig. 12. Island size distributions collapsed for six areal coverages (between 7.5 and 25%) for reversible nucleation. Reversibility is included by varying the pair binding energy in the Monte Carlo simulations. Reprinted with permission from [82], 9 1994, American Physical Society.

rection are allowed. This additional strain leads to stronger anisotropy of the island shape. The additional strain effect modifies the size distribution more significantly than the energy anisotropies alone when compared with the isotropic system. Further, scaling is not achieved in the direction of the uniaxial stress where no broadening of the length distribution occurs with increasing coverage. (v) Irreversible Nucleation with Mobile Islands. In many systems, island mobility, particularly dimer mobility at low temperatures where i* -- 1, is expected due to low barriers for twisting motion on (100) metal surfaces where one monomer moves around the other in the dimer configuration [85]. Other mechanisms of cluster motion include the motion of dislocations across the island which leads to a significant increase in island mobility at certain sizes [86]. Modifications to the properties of irreversible nucleation have been studied in several simulations [85, 87-89] based on the initial rate equation study by Villain et al. Villain et al. [58] limited the mobility to dimers and derived a modified scaling form for the stable island density where Nx c~ (D1/R) -1/3 is replaced by Nx c~ (D1D2/R2) -2/5, with D1 the diffusion rate of monomers and D2 the diffusion rate of dimers. However, for this type of scaling to occur, the rates for three fundamental processes have to be compared: (i) if the dimer immobilization through incorporation of mobile monomers dominates, the dimer mobility does not contribute significantly to the process and scaling of immobile dimers of the irreversible nucleation model is reproduced. (ii) If the dissociation rate of dimers dominates, then the classical nucleation scenario as described by the kinetic rate equations (5) for i* > 1 applies [39, 90, 91]. (iii) The novel

Experimental systems are grouped by substrate material, including (i) element semiconductors, (ii) compound semiconductors, (iii) metals, and (iv) insulators. . (i) Semiconductor Surfaces: Silicon and Germanium. Only a few studies connect experimental nucleation data to kinetic Monte Carlo simulations or the rate equation model on semiconductor surfaces. The complexity of these systems leads to a large number of parameters which limit the usefulness of data simulation by numerical methods [64]. In addition to the basic activation energies of adsorption-desorption, diffusion, and island formation which are required in the rate equation model, several new processes play a significant role, including crossing of step edges, diffusion along island edges, reconstructions of the substrate and adlayer islands. Only some of these processes can be studied with STM [92, 93]. The homoepitaxial system Si/Si(100) is of particular interest due to technological relevance. Mo et al. [59, 60] analyzed the number density of Si islands in STM to obtain surface diffusion data for this system. In the temperature range 350 K < T < 500 K, island coalescence did not interfere with the data and dimers are stable, but larger islands showed a significant anisotropy of the two-dimensional island shape (long needlelike structures of mostly dimer-length width). The experimental data were analyzed using a Monte Carlo simulation with random walk diffusion and random deposition with an activation energy of diffusion of Ea = 0.67 4- 0.08 eV and a preexponential factor of 10 -4 < Do < 10 -2 cm2/s. To model the data properly, a combination of anisotropy of diffusion and attachment to stable islands has to be taken into account. Anisotropic bonding (sticking limited to the ends of islands) is found to affect the model less than anisotropic diffusion (jump rate along substrate dimers 1000 times higher than across the rows, i.e., quasi-one-dimensional diffusion). This anisotropy also alters the relation between island density and diffusion rate [58]. Two other complications arise in the homoepitaxy of silicon. The first problem is associated with steps. Monomers can attach to steps like to large islands. This leads to denuded zones near step edges [60] with widths depending on several factors including Ehrlich-Schwoebel energy barriers [94]. A second complication is the lack of observations of small islands which

CLASSIFICATION OF CLUSTER MORPHOLOGIES are slightly larger than dimers. This draws in question whether a dimer is indeed the smallest stable island and establishes the kinetic pathway to larger islands. For a SiGe alloy layer on Si(100) chains of adatom pairs have been observed which are terminated at both ends by buckled dimers [95]. The adatom pairs are not dimers as the distance between the two atoms in the pair is too large. These structures are metastable and convert into stable dimer chains in a transition with a positive activation energy. This process is not affected by isolated dimers concurrently observed on the surface. Direct experimental evidence exists for critical two-dimensional island sizes of the order of 650 dimers for Si(100) homoepitaxy at 925 K (typical epitaxy growth temperature). In a low-energy electron microscopy experiment (LEEM). Theis and Tromp [96] studied the step-terrace exchange kinetics of a surface growing at R = 0.0017 ML/s to R = 0.033 ML/s with chemical vapor deposition of silane and disilane. They found nucleation at this growth temperature to occur much closer to thermal equilibrium than previously assumed, with the deposition rate varying the intrinsic monomer concentration on the surface by less than 2%. The data can be extrapolated to lower temperatures at the same deposition rate and can predict a minimal stable island size of a dimer for temperatures below 775 K for R = 0.017 ML/s. Heteronucleation on silicon is often complicated due to chemical interaction with the highly reactive, clean silicon surface, e.g., in form of silicide formation for many metals. Temperature thresholds for chemical processes vary and may interfere with the nucleation experiment. Cobalt, as an example, clusters as a metal on Si(100) at temperatures below 650 K [97] but forms silicide at higher temperatures. At 595 K, reactive epitaxy of cobalt on Si(111) leads to monolayer thick islands of triangular shape which nucleate at the faulted side of the Si 7 • 7 reconstruction and grow in length in multiples of the 7 • 7 cell size [98]. Two studies on Ge(111) surfaces [99, 100] extend previous studies of Ag on Si(111) [ 101 ]. The experiments are based on the widening of a silver deposit through a 20 • 100-#m mask, studied by biased secondary electron imaging (b-SEI) and scanning Auger microscopy (SAM). Nucleation starts after a uniform, reconstructed ~ structure of 1-ML thickness is formed. The nucleation density as a function of temperature for A g / G e ( l l l ) in the temperature range from 525 to 725 K is shown in Figure 13 (full symbols) in comparison with a measurement for Ag/Si(111) (open symbols [ 102]). Both data sets were obtained for similar deposition rates close to R = 1.3 ML/min. Note that the analysis of the Ag/Si(111) data led to large critical nucleus sizes, with up to several hundred atoms. To extract the microscopic activation energies involved in the nucleation process, the broadening at the edges of the deposited patch have been observed. In this regime, an instability of the ~ structure for Ag/Ge(111) is observed with the formation of a new (4 • 4) reconstruction with a thickness between 0.25 and 0.375 ML [100]. The patch width for a 6.7-ML deposit varies with temperature as shown in Figure 14 (full circles for

13

T[~ lO 6

500

400

I

300

I

I

10 5 z

104 ~

1.2

I

!

I

1.4

1.6

1.8

2.0

1 / T [ 1 0 " 3 K "1] Fig. 13. Nucleation density for Ag/Ge(111) as a function of inverse deposition temperature (full circles), compared with data for Ag/Si(111) (open circles). The simulation (solid line) is based on a pair bond energy of 0.05 eV, on activation energy for diffusion of 0.4 eV, and on activation energy for adsorption of 2.55 eV. Reprinted with permission from [99], @ 1996, Elsevier Science.

structure and open circles for 4 x 4 structure, compared with data for a 5-ML deposition of Ag/Si(111), open squares). These data can be modeled with the rate equation model. In addition using a two-dimensional diffusion equation, reasonable values for the activation energy of surface diffusion, the pair binding energies, and the activation energies for adsorption are obtained. The activation energy for adsorption is higher for Ag/Ge(111) which results in a higher monomer concentration. (ii) Semiconductor Surfaces: Compound Semiconductors. Systematic nucleation studies are rare on III-V semiconductor surfaces since most films are grown by chemical vapor deposition (CVD) which is incompatible with most in situ analytical tools. Often, studies focus on practical aspects, for example, the control of the island density with ion presputtering to achieve smoother growth surfaces. Wang et al. [103] showed that significantly increased nucleation densities are obtained for Ge on in situ cleaved GaAs(110) when the substrate is exposed to a 2-keV Xe beam prior to Ge deposition at 695 K. The studies selected in this section focus on specific properties of nucleation on GaAs surfaces. Nucleation, coalescence, and layer-by-layer growth for the system Ge on cleaved GaAs(110) was studied with STM by Yang, Luo, and Weaver [104, 105]. The first article focuses on nucleation at 695 K with a deposition rate of roughly R -- 1 ML/min and a total deposition of 0.2 and 0.4 ML. For both final coverages, the nearest neighbor distance distributions are compared with random simulations in Figure 15. Although the random simulation does not take areal exclusions into account to prevent overlapping of islands, the deviation from the simulation is sufficiently

14

LI AND ZINKE-ALLMANG

T[~ 5OO !

0.3

400

300

!

!

1

I

1---

10

15

a)

200 I

t

0.2 "O

150

13_ 0.1

E e-

100

"r',

t-

"*"

I

13

r-,

t

[]

t

I I I

0.2

[]

tiII

"0

[]

t

% % %

%%%

13.

E!

50

0.1

13 13 !

I I

I

I

I

I

I

1.5

I

I

I

2.0

1/T[10"3K "1] Fig. 14. Width of a deposited patch of Ag on Ge(111) (open and full circles) and Ag on Si(111) (open squares). The Ge(111) data split in two branches with the open circles linked to the 4 x 4 reconstruction and the solid circles linked to the ~/3 surface structure. The Ag coverage for Ge(111) is 6.7 ML and the coverage for S i ( l l l ) is 5 ML. Reprinted with permission from [99, 102], 9 1992, Elsevier Science.

large to indicate that nucleation does not occur random, rather with depletion zones around existing clusters. This is due to the fact that an adsorbed monomer attaches easier to an existing nearby cluster instead of nucleating a new cluster with other free monomers. These data do not allow an unambiguous m e a surement of the depletion zone width, however, as parameters such as the mobility of small clusters are not known. The depletion zone around clusters is easier to be seen for clusters nucleating at substrate steps. Preferred nucleation at steps leads to increased cluster densities at the steps with corresponding depletion zones of the order of 10-nm width on the adjacent terraces. Nucleation at steps is only kinetically favored since cluster ripening during postnucleation annealing at 825 K leads to a reduction of the cluster density at steps [ 104]. Homoepitaxial nucleation has been studied for metalorganic vapor-phase epitaxy (MOVPE) for GaAs by Kasu and Kobayashi [ 106]. The islands have anisotropic shapes (factor of 2 longer in (110) direction) due to a difference in the attachment probability for mobile monomers of a factor of 3 for the two perpendicular directions. In addition, a variation of the width of denuded zones near step edges was observed, indicating a significant role of steps with different attachment probabilities

5 dnn [ nm ]

Fig. 15. Nearest neighbor cluster distance distribution for (a) 0.2-ML coverage and (b) 0.4-ML coverage of Ge on cleaved GaAs(001) at 695 K. The dashed line connects the data points and shows a significant depletion of shorter cluster distances in comparison to a random simulation (solid line). The random simulation did not include an areal exclusion provision to avoid cluster overlap. Reprinted with permission from [ 104], 9 1992, American Physical Society.

(favoring the descending steps for monomer incorporation by a factor of 10-300). Bressler-Hill et al. [107] studied island scaling for InAs growth on an As rich GaAs(001)-(2 x 4) surface at 725 K. Total coverages ranged from 0 -- 0.15 ML to 0 = 0.35 ML. Data analysis was done on areas with low step density and parallel to the (110) direction as steps along (110) (B-type steps) influence the island shape while steps perpendicular to (110) (A-type steps) have no influence. The island size distribution, obtained from STM images, is shown in Figure 16. The size distribution clearly disagrees with the simulation in Figure 8 for an unstrained system, but agreement is also not reached for strained system simulations. If the same system is grown with chemical vapor deposition (CVD) techniques [108], stable island densities are much smaller than those predicted by the standard nucleation models [91 ]. Stoyanov [109] predicted such reduced nucleation densities with a modified model based on a two-species nucleation. This model predicts a dependence on the indium flux and the partial arsenic pressure which is observed in the experiments for the InAs island density on GaAs(001).

CLASSIFICATION OF CLUSTER MORPHOLOGIES I

I

15

1.5

I

a)

12

CD



1.0

A

0

+

I

t-

Z

A

A~o +

~

Oo L~

oo

0.5 o

.I-

I

0

1

2

3

4

j / <j> Fig. 16. Island size distributions for nucleation of InAs on GaAs(001) at 725 K studied by STM. The data represent varying coverages (0.15 ML < 0 < 0.35 ML). The solid lines are smooth fits to the data. Reprinted with permission from [ 107], @ 1995, American Physical Society.

CD

~ ,~ ~ t ~

I



b)

Z

0 0

oO -3

1.0

In N x

/



(iii) Metal Substrates. Cluster formation has been studied on a wide range of metal surfaces. In most cases, good agreement with the kinetic Monte Carlo simulations and the solutions of the rate equation model has been found. A data set frequently compared to theoretical models is Fe on Fe(001) whiskers [ 110]. Fe nucleation occurs irreversibly at room temperature with i* - 1. Scaling of the island size distribution is demonstrated in Figure 17. The island size distribution is shown for the temperature range of 293 to 480 K with 106 < D / F < 109 in Figure 17a. In Figure 17b, the island size distribution is shown for two higher temperatures (at 575 K with D / F -- 8 x 109 and at 630 K with D / F -- 1.7 x 101~ The inset of Figure 17b shows an Arrhenius plot for the stable cluster density, indicating a transition of i* with i* - 1 for T < 520 K and i* - 3 above. These data should be compared with simulations for irreversible nucleation at the lower temperatures (T < 480 K) and the classical rate equation model for i* > 1 at the higher temperatures, assuming i* -- 2 at 520 K and i* -- 3 at T > 575 K [72, 110], as well as with simulations for reversible nucleation [84]. Due to the scatter of the size distribution, a definite choice of the appropriate model is however not possible. Bott et al. [ 111 ] studied the homoepitaxial system Pt/Pt(111) with STM. A comparison with kinetic Monte Carlo simulations is undertaken to provide an independent test of the rate equation model. Figure 18 presents this comparison for the saturation island density versus inverse substrate temperature. The experimental data were obtained with a deposition rate of R - 6.6 4- 0.7 x 10 -4 ML/s and a temperature quench to 20 K immediately following deposition. The kinetic Monte Carlo simulations require just two free parameters, the diffusion coefficient and the diffusion prefactor. The best agreement with the data is obtained for Ed -- 0.26 eV and v0 - 5 x 1012 Hz. A further Monte Carlo simulation result from Bales and Chrzan [67] is included in the figure as a dash-dotted line. The two numerical solutions for the rate equations model (dashed lines)

.....

-2

0

/

-4



0

2i

O

0.5

|

3,

1/r[,O-3K -~]

O



0

o

0

Oo 0 0

0

I 1

~.", I

2

3

j / <j>

Fig. 17. Island size distribution and island separation distribution for Fe on Fe(001) whiskers. (a) Low-temperature size distributions for T < 480 K and (b) high-temperature data for T > 575 K. The inset of (b) shows the stable cluster density as a function of substrate temperature. The solid and the dashed lines indicate i* = 1 at low temperatures and i* = 3 at high temperatures. Reprinted with permission from [52, 53, 56], @ 1999, Elsevier Science.

are based on i* -- 1 with immobile stable islands and negligible evaporation. These simulations are limited by the accuracy of assumptions for the collision factors gin [76, 112-115]. The experimental data are also somewhat uncertain as STM tip effects on the mean displacement of surface atoms were observed [111]. Brune et al. [114] investigated Ag on Pt(111) at low temperatures (50-120 K) with STM. The nucleation density was measured as a function of coverage in the range 0 < 14%. The variation of coverage leads to an order of magnitude difference in nucleation density. Figure 19 shows the nucleation density as a function of coverage at 75 K. The dashed line indicates the low coverage limit for a model with i* = 1. The solid line is the best fit using the classical rate equation model with the collision terms gin obtained from the gradient of the monomer concentration at the island surface [39]. The good agreement between rate equation model and experimental data indicates the applicability of the classical rate equation model in this case. The monomer diffusion activation energy for Ag on Pt(111) is de-

16

LI AND ZINKE-ALLMANG l t, ,x,,

/lw-]---]-----"t

II} t,,,,)

i

'

~

I'

i

11

m

_,.i

p

o

t"" :3

,_._, X

"l

z

O ,_.__,

2

z" 0

0

a)

I

I

0.05

0

!

I

0.1

0.15

O [ML] .= I

I

l

z

v

/,/

/

t i,

i 4

/

b)

tt i 5

i 6

I

7

1 / T [10 "3 K -1]

Fig. 18. Comparison of STM nucleation data for Pt/Pt(111) (full squaresi with kinetic Monte Carlo simulation (solid line) and numerical solutions of rate equation model with i* = 1 (dashed lines) using Ed = 0.26 eV and v0 = 5 x 1012 Hz. The rate equation model curves are based on two different assumptions for the capture cross-sections tr. The plots show the saturation island density at 0.1-ML coverage as a function of substrate temperature. Reprinted with permission from [ 111], 9 1996, American Physical Society.

rived as Ed = 0.16 4- 0.01 eV. A molecular dynamic simulation study for the same system was unfortunately limited to substrate temperatures above 400 K [ 116]. In that regime, the system behaves differently as the deposited atoms are always embedded in a metallic environment as suggested by photoemission measurements [ 117]. The Ag on the Pt(111) system was further studied by Brune et al. [118] in comparison with Ag on Ag(111) and a single monolayer of Ag on Pt(111), focusing on the influence of strain on the nucleation process. An Ag monolayer on Pt(111) is under 4.2% compressive strain leading to a significant number of dislocations in the film. Dislocations and strain have a significant effect on the nucleation properties of Ag adatoms, e.g., a lowering of the surface diffusion activation barrier (40% compared to Ag/Ag(111)) as derived from the saturation island density as a function of temperature from STM data. In general, reduction of diffusion barriers are expected for compressive strain while tensile strain increases the diffusion barrier. In a

I

0

,,,

I

I

I

I

0.1

0.05

Et [ML] Fig. 19. Ag/Pt(111) nucleation STM images on island density as a function of coverage at 75 K with lines for the low coverage limit for i* = 1 (dashed line) and full data simulation (solid line) based on the classical rate equation model. Reprinted with permission from [ 114], (g) 1994, American Physical Society.

subsequent study, R6der et al. [ 119] varied the temperature between 130 and 300 K. The temperature increase leads to an increased layer thickness for the initial two-dimensional layer. This behavior is also attributed to the compressive strain of the Ag film which reduces the energy barrier toward interlayer mass transport (Ehrlich-Schwoebel barrier). The dependence of the average island spacing on the deposition rate has been studied for Cu/Cu(100) by high-resolution low-energy electron diffraction (HRLEED) [120]. The average island spacing, (d), is related to the island density, Nx, in the form (d) oc ~/Nx for two-dimensional nuclei. Thus, the classical rate equation approach predicts (d) cx i*/2(i* + 2). The experimental data for island separation versus inverse deposition flux, l / R , are shown in Figure 20 for two substrate temperatures and two coverages. In the double logarithmic representation, an i* - constant behavior is reflected in linear curve segments. For low deposition rates, the low temperature data agree with a slope of 0.165 4- 0.015 indicating irreversible nucleation with i* - 1, while the high temperature data are fitted with a slope of 0.29 4- 0.01 leading to i* = 3 [121,122]. Another mechanism is proposed for the system Fe/Cu(100) [123-125] studied the room temperature by STM. A monotonously decreasing cluster size distribution with cluster size was found. This suggests a model with i* -- 0. The mechanism apparently involves the exchange of an Fe monomer with a Cu substrate atom leading to an embedded Fe inclusion. This mechanism had been proposed initially by Kellogg and Feibelman [ 126] for Pt on Pt(100). Subsurface growth of nuclei is also observed for Cu on Pb(111) [ 127]. That monomer exchange with the substrate does not automatically cause i* - 0 as shown in an HRLEED study for Fe on Au(001) [128]. Submonolayer Fe deposition at 315 K leads to a direct exchange with the substrate, displaying a 1 x 1 LEED pattern for coverages above 0.2 ML [129]. The island size distributions for coverages in the range 0.15 ML < 0 < 0.6 ML were compared with simulations by Amar, Family, and Lam [76] leading to the conclusion that i* - 1 best describes the data. Coalescence terminates nucleation only above 0.6 ML, which has been established for this system through a steep in-

CLASSIFICATION OF CLUSTER MORPHOLOGIES 200

'

I

'

'

'

'

I

'

'

-

T= 2 6 3 K 0.28 + 0.01 0.30 + 0.01 100 ,---,

,/

^ "o v

0.16 + 0.01 ~

A

"

~

T= 2 2 3 K

el9~

~

9

50

9

o

.

0.17 __+0.01 0.17

"

O

Oo O

O

17

sion electron microscope (UHVSTEM). The nucleation density is independent of the deposition temperature in the range from 295 to 575 K and decreases with coverages larger than 20% due to coalescence. The density of nuclei is much higher than for metal systems. These observations have been simulated with the rate equation model modified to include point defects on the surface [64]. The simulations suggest i* -- 1 for the studied temperature regime with i* increasing as incomplete condensation occurs at the highest temperatures. The trap density is roughly 1% of fluor-binding sites on the surface and must interact with the monomers chemically due to the large trapping energy (e.g., fluor vacancies or oxygen-hydroxyl groups). Deposition of Ag on the same surface under the same conditions led to lower nucleation densities in agreement with the standard rate equation nucleation model, i.e., not requiting trapping sites on the surface or allowing only for sites with detrapping energies below 0.1 eV. Point defects in combination with mobility of small islands also affect the spatial island distribution in the Au/NaCI(100) system [ 131 ].

O

o I

100

I

I

I

I

I,

I

~

,

I

I

i

1000 .... 1IF [ s / M L ]

Fig. 20. Average island spacing as a function of inverse deposition rate for nucleation on Cu(100) at two temperatures (T = 263 K: open and solid triangles, and T = 223 K: open and solid circles) and two coverages (0 -- 0.3-ML open symbols and 0 ~ 0.7-ML solid symbols). The straight line segments are simulations using Venables' rate equation model for i* = 1 at the lower temperature and i* = 3 at the higher temperature. Deviations from the classical behavior occur at high deposition rates. Reprinted with permission from [121], 9 1992, American Physical Society.

crease in the average island size and a corresponding decrease in the density of stable clusters. A metal system with strong anisotropy effects is Au on Au(100) due to a surface reconstruction with a dense quasihexagonal top layer on the square bulk lattice [ 130]. The density of rectangular islands is found to vary with the deposition flux in the form predicted by the classical rate equation model, i.e., Nx c~ (D/R) -x but with the exponent given in the form X -- 0.37 + 0.03. Assuming isotropic diffusion, only i* - 1 with ) - 1/3 would be in agreement with the data. The anisotropy of the morphology would still have to be explained with anisotropic edge diffusion and monomer attachment rates. However, Monte Carlo simulations with these parameters predict absolute values for the stable nuclei density of a factor of almost 10 higher than the experimental data [54, 57]. Assuming strongly anisotropic diffusion, i* - 1 leads to X - 1/4 which does not agree with the experimental data either. Thus, i* > 2 is required and i* - 3 leads to the best agreement with the stable island density in the experiment. (iv) Insulator Surfaces. On insulators, defect trapping becomes a major issue in nucleation studies. Heim et al. [81] investigated nucleation of Fe and Co on C a F 2 ( l l l ) films grown on Si(111) in an ultrahigh vacuum scanning transmis-

1.1.3. Spinodal Decomposition The nucleation models discussed before apply only to a shallow regime inside the coexistence curve, i.e., the dashed area in Figure 1. At temperatures close to the critical point, the correlation length of density fluctuations starts to diverge and the classical picture of a cluster as a homogenous and sharply confined atom aggregation becomes meaningless. However, no universal model exists for the entire range. Cluster formation through spinodal decomposition in a mean-field approach is usually illustrated using the CahnHilliard theory [132, 133]. A qualitative discussion of the changes, which are expected when a system crosses over from the nucleation to the spinodal decomposition regime, is given based on Figure 21 [36]. The first panel shows the development of a system toward equilibrium in the metastable limit and the last panel shows the same process in the unstable limit. The second and third panels study the situation adjacent to the spinodal line where the Cahn-Hilliard model predicts diverging critical cluster sizes. In the figure, the local density profiles and the morphological representations are compared. For a classical cluster (Fig. 21 a) with the concentration of the system c just inside the coexistence line of Figure 1, the density drops from the value in the well-defined cluster, cc to the free adatom concentration coo at a sharp edge over a length defined as a coexistence length )~coex. Far in the spinodal regime (Fig. 21 d), density fluctuations in the length regime of the order of )~coex occur. Close to the spinodal, the correlation length for the critical cluster (Fig. 2 lb) and the wavelength of the critical fluctuation diverge. The reshaping of the cluster surface toward the equilibrium shape may dominate the processes in the spinodal regime [ 134]. For a two-dimensional unstable fluid of Lennard-Jones atoms, Amar, Sullivan, and Mountain [135] observed spinodal decay of the supersaturation by isothermal molecular dynamics simulations. Characteristic of the end of the spinodal regime is the time dependence of the size of the largest cluster crossing a

18

LI AND ZINKE-ALLMANG

p(r) f Cc ;

"

hcoex ~

a,

..... a,[~

i : o ol

.... !i im

p(r)

,

Cc 1

R

Acoex

E1

r

[

b)

$ b) o

/

p(x)

Cct

Coo

*

~

~

o X~o~x~ 0 ~

ii

[

~

~

)kcoex R

.

,

.

.

.

,

p(x) # Xcoex R Cct_ _

r

o o o

~

0 0

o ,--,~o

.

.

.

_

.

.

.

r ___d) d)

o *~-~(b o 0 hcoex ~ 0 0 o0~

Oo

E3

R2

I

R3

,,i

SK1

ol

FM

o 0 (::3 I ~ ~ 01

0 o | ~o01

VW 0 i

0.0 v

hcoex

$

~1

c) c) , ooOoo o I .

E2

oI

oG I

,.. o 'Go o

$

1

Iv

0.1

J 0.2

E

r

Fig. 21. Schematic of the density profile of thermal fluctuations against which the system is unstable according to the Cahn-Hilliard theory. (a) At densities close to the coexistence curve the unstable fluctuation is a spherical critical cluster. (b) At densities close to the spinodal curve the critical cluster becomes very diffuse with the density in the interior only slightly higher than outside, but the radius diverges. (c) At densities slightly higher than the spinodal density the unstable fluctuation is weak. (d) Far in the unstable region all fluctuations are unstable and grow. Snapshots of the corresponding density fluctuations are shown on the right side. Reprinted with permission from [36], (g) 1976, Taylor & Francis Ltd.

maximum. This is due to the wave type of fluctuations forming highly interconnected and thus large clusters. Breaking up of this network leads to smaller clusters which are closer to the equilibrium shape. The authors report an r (x t 1/5 dependence of the average cluster size in the spinodal regime for two-dimensional clusters after eliminating short-range order effects.

1.2. Coherent Clustering Morphologies Coherent clustering in heteroepitaxial systems was first observed at the beginning of the 1990s in the growth of Ge on Si(001) [20, 22], and was later confirmed for other systems (InGaAs [23, 136] and InAs [137] on GaAs(001), and GeSi on Si(001) [138]). Although it affects only a few systems up to now, the coherent clustering attracts a great deal of attention because of the new physical concepts raised, including materials self organization. Also important are the potential applications for growth of nanoscaled structures, e.g., quantum dots (QDs) for electronic and optoelectronic devices [139, 140]. With selforganized clustering, we expect to take advantage of fabricating damage-free QD structures in situ without the help of expensive lithographic processes, possibly allowing a higher sample throughput [ 141 ]. A significant number of theoretical studies have been published discussing the coherent clustering mechanism based on energetic and kinetic models. In experimental investigations, details of the growth have been explored, e.g.,

Fig. 22. Equilibrium phase diagram in a function of the coverage h and the misfit e. The small panels on the top and the bottom illustrate the morphology of the surface in the six growth modes. The small empty clusters indicate the presence of stable s, while the large ones refer to ripened clusters. The phases are separated by the following phase boundary lines: Hcl (e): FM-R 1, F M SKI; Hc2(e): SK1-R2; Hc3(e): SK2-SK1; Hc4(e): VW-SK2, VW-R 3. The parameters used to obtain the phase diagram are a - 1, C = 40E 0, ~AA -- EO, ~AB -- 1.27E0, g = 0.7, p = 4.9, b = 10, and y = 0.3. Reprinted with permission from [143], 9 1997, American Physical Society.

the controlling of the size, the shape, and the spatial distributions of QDs. For heteroepitaxial systems, there are three equilibrium growth modes as discussed in Section 1.1: (i) the Frank-van der Merwe (FM) growth mode (two-dimensional layer by layer growth), (ii) the Volmer-Weber (VW) mode (formation of three-dimensional clusters on the bare substrate), and (iii) the intermediate Stranski-Krastanow (SK) mode (two-dimensional layer growth followed by three-dimensional cluster formation) [13, 14, 142]. A more detailed phase diagram has been developed in a study [143] using an equilibrium theory, distinguishing the main growth modes as a function of the layer thickness and the lattice constant misfit between film and substrate (see Fig. 22). The key features of this phase diagram are: (i) at a lattice misfit ~, which is smaller than a critical value E2 and the equivalent film thickness H (in monolayers) which is smaller than a critical value Hcl (E), the heteroepitaxial system will undergo FM or pseudomorphic growth, with the latter defining a wetting layer for which the lattice mismatch between the epitaxial layer and the substrate is completely accommodated by elastic strain; (ii) for el < E < E3 and H smaller than another critical value Hce(E), the system grows in the SK mode growth; (iii) for a system with E larger than a certain value E2,

CLASSIFICATION OF CLUSTER MORPHOLOGIES the system grows in the VW mode; (iv) with H larger than certain critical values Hc(~), cluster ripening occurs in either cases with or without the existence of the wetting layer. (All the critical values shown here are determined through a minimization of the system energy.) Based on this equilibrium picture, coherent clustering is found to be closely related to the SK growth mode. Threedimensional clusters appear in both cases on the supersaturated wetting layer as a means of reducing the strain built in the wetting layer as the epilayer thickness reaches a critical value. The critical value is associated with the extension to which the lattice mismatch between the deposited material and the substrate can be accommodated fully by elastic strain (pseudomorphic epilayer). Subsequent deposition leads to a supersaturated epilayer. Growth often continues layer-by-layer, however, as the increasing strain energy in the film disfavors the uniform epilayer energetically, but kinetic barriers prevent the immediate formation of relaxed clusters. The propensity of the metastable film toward a stabilized structure causes the system to relax to a state of lower total free energy along any possible kinetic path; i.e., any strain relief mechanism for the accumulated strain energy has to be considered. The conventional mechanism is now called the classical SK model, as distinguished by Seifert et al. [144]. When the strain energy is high enough to overcome the energy barrier for the introduction of misfit dislocations, nucleation and growth of three-dimensional relaxed clusters occurs across the surface. Coherent clustering is introduced as an alternative pathway for the strain relief, and it will be observed in systems where the kinetic threshold for the process occurs at a lower film thickness than the threshold for the formation of dislocations. The mechanism is based on a roughening of the film under strain with a subsequent diffusive aggregation of monomers at elevated points representing a lower total strain energy. This transition from two-dimensional layer to three-dimensional coherent clustering is defined [ 145] as a morphological phase transition, and the origin of the total strain relief in this process was identified by Eaglesham and Cerullo [21 ] as illustrated in Figure 23. Figure 23a and b schematically compare two possible structures of a commensurate cluster on a lattice mismatched substrate. The sketches indicate two sources of strain relief; first, partial lateral relaxation within the cluster, and second, elastic local adjustment of the substrate lattice parameter. The latter process may accommodate an equivalent amount of strain energy as the cluster itself [ 146]. Figure 23c is a cross-sectional TEM micrograph of a large coherent Ge cluster on Si(100) grown at 775 K with a deposition rate of 6 x 10 -3 nm/s. As shown, the substrate is a bend below the defect-free cluster.

1.2.1. Equilibrium Theories Ratsch and Zangwill [147] developed an equilibrium theory based on minimizing the total energy of an adlayer system. They used a rigid crystalline substrate and they describe the film such that both elastic and plastic strain can be accommodated (Frenkel-Kontorova model). This model is particularly suited

19

Fig. 23. (a) and (b) Sketch of a commensurate cluster on a crystalline, lattice mismatched surface. The structure in (a) allows for a partial lattice relaxation within the cluster and therefore represents a system with a lower energy than a strained film of uniform thickness. An additional, local lattice adjustment of the substrate below the cluster can lower the energy of the system further (b). Both effects are observed in cross-sectional TEM for Ge on Si(100) grown at 775 K with a deposition rate of 0.006 nrn/s (c). The Ge island is 50-nm high and 140 nm in diameter, representing a coherent island near the threshold for misfit generation. Note the strong strain contrast around the island. Reprinted with permission from [21], (~ 1990, American Physical Society.

to compare uniform films with coherent and relaxed clusters. For diamond-like materials, the analysis results in a phase diagram allowing for coherent clusters. The stability window for coherent clusters depends on lattice mismatch, surface energy, and total number of particles in the film; in Figure 24 the phase diagram is shown as a function of misfit and total number of atoms in the film with a fixed dimer binding energy of 1.7 eV. A minimum of 2% lattice mismatch is required for the coherent cluster phase (CC), and this phase narrows significantly for misfits larger than 5% due to dominance of the formation of

20

LI AND ZINKE-ALLMANG i

I

"

the size of an cluster, L, is determined

I

AEel -- -fl

(~b0)~,e2L 3 - f 2 ( ~ b o ) e ' r L 2

- ' 3 (4~0)r2/)~L In ( 2 n - ~ )

RC ffl .m

UF O0

I

I 2500

1

5000

# Atoms

relaxed clusters (RC). For a misfit of 3%, the coherent cluster phase disappears for binding energies larger than 2.0 eV where the uniform film phase (UF) is stable. There is also an upper limit of the number of atoms in the system for a stable coherent cluster phase. The picture developed by Ratsch and Zangwill is more detailed since the actual surface energy of relaxed clusters is taken into account, which favors the stability of uniform films or coherent clusters for smaller lattice mismatch or small particle numbers in the film. The authors note however that their model required several simplifications such as neglecting strain nonuniformity in the substrate surface. Thus, only a qualitative comparison with experimental data should be possible. Shchukin et al. [148, 149] treat the energetics of coherent clustering based on the evaluation of the change of the total energy of a heterophase system, with a uniformly strained film of thickness Ha on a (001) substrate, due to formation of a single cluster. This energy change is written in the form, Efac + Eed + A Eel

where fl, f2, and f3 are coefficients which depend on the facet tilt angle 4~, )~ is the elastic modulus, 4~0 = tan -I (k/l) with k and 1 Miller indices for a (kOl) facet. The formula shows that A Eel also depends on the strain field factors due to the lattice mismatch, E = Aa/a, and the discontinuity of the intrinsic surface stress tensor, "gij at the edges. Equation (8) represents a relation between the elastic energy and the cluster size. A square-based pyramid, or "quantum dot," is energetically more favorable than an elongated prism, or "quantum wire," because it provides for a larger elastic relaxation. Substituting Eq. (8) in Eq. (7) and using an additional term for the elastic interaction between clusters (anticipating high cluster densities) the cluster size-dependent energy density (per unit surface area) is found

E(L) -- Eo[-2X-21 ln(el/2x)--t-.2ote-1/2X-1 +413e-3/4X-3/2 ]

Fig. 24. Phase diagram for thin crystalline films grown on a diamond lattice with a dimer binding energy of 1.7 eV. As a function of misfit and a total number of atoms in the film (coverage), three distinct phases have been identified, a coherent cluster phase (CC), a uniform film phase (UF), and a relaxed cluster phase (RC) [192], with only the latter two considered in classical StranskiKrastanov growth of lattice mismatched systems. Reprinted with permission from [20], 9 1999, Elsevier Science.

A Eisl = A

(8)

(7)

where AEfac is the surface energy of a tilted facet, Eed is the short-range energy of edges, and A Eel is the change of the strain energy due to an elastic relaxation. With the facet energy included of the minimum of A Eisl corresponds to an cluster bounded by low index facets, e.g., a pyramid or a prism, essentially defining the shape of the coherent clusters. From the equilibrium elasticity theory [ 150], the dependence of A Eel on

(9) where E0 is the characteristic energy per unit area, X -- L/Lo is the dimensionless length, and L0 is the characteristic length. c~ and /3 are parameters containing the surface energy and the cluster interaction energy, respectively. The first term in Eq. (9) represents the contribution from the edges to the elastic relaxation energy, the second and third terms represent the contribution from the surface and the cluster interactions. Equation (9) gives a representative expression of the energy density for a coherent clustering system that has widely been cited by later studies. A phase diagram results from this formula based on the energy minimum for variables c~ and/3. A key result of this model is that a minimum of the total energy exists at a finite cluster size L when the elastic relaxation energy at cluster edges exceeds the surface energy. In this case, clusters resume their optimum size and do not have a propensity to grow. Another equilibrium theoretical model with two-dimensional platelets as a precursor for three-dimensional coherent SK clustering was presented by Priester and Lannoo [151, 152]. This model also provides an explanation for the initial nucleation and narrow size distribution of the coherent clusters. For distant and noninteracting islands, the authors applied the mass action law to obtain a thermal equilibrium distribution in relation to the reduced energy of the system (the energy per atom in the island). This allows islands to grow or to decompose. An absolute minimum of the reduced energy should exist in the equilibrium distribution for physically interesting cases of thermal equilibrium. Based on continuous elasticity theory, the total system energy was studied with a valence force field approach to include the elastic properties of the system. Separately, the surface energy is included. The study allows one to estimate the reduced energy for three-dimensional clusters versus the cluster sizes, in the form, e ( n ) - - ~:ps --

Ar -Jr-Asn -1/3

(10)

CLASSIFICATION OF CLUSTER MORPHOLOGIES where 6ps is the energy per atom of the corresponding pseudomorphic layer, Ar and As are two positive constants representing the relaxation and surface energies respectively, and n is the number of atoms in the cluster. By testing this expression with experimental data for heteroepitaxial growth on GaAs, the authors found that the reduced energy does not vary with the surface coverage for clusters larger than 1000 atoms. This led them to conclude that direct formation of threedimensional clusters cannot explain the existence of a critical coverage and the narrow distribution in the three-dimensional cluster sizes. For a two-dimensional system with noninteracting square platelets, they further determined the reduced energy from classical elasticity theory as a function of the platelet size in the form, ~(n) -- ~ p s -

Brn-l~2 ln(n 1/2) 4- Bsn-l~2

(11)

where Br and Bs are positive constants representing the relaxation and surface energies, respectively. Based on this expression, a Gaussian size distribution is obtained for the twodimensional platelets in cases where the equilibrium can be reached, and the resulting distribution curve, together with the two-dimensional and three-dimensional clustering energy, are shown in Figure 25 as a function of clusters size. At coverage smaller than a critical value and cluster sizes smaller than 20,000 atoms, the two-dimensional platelets have a lower energy thus grow as stable prenuclei, and this remains the case as long as the two-dimensional platelets do not interact; when the coverage reaches a critical value, three-dimensional clusters have lower energy and become more stable than the two-dimensional platelets. Thus, the authors expect that the islands undergo a spontaneous transition from two-dimensional platelets to coherent three-dimensional clusters. They conclude further that the corresponding size distribution of the threedimensional clusters must be narrow as well, like that of the two-dimensional platelets. Several groups used Monte Carlo techniques to identify the kinetic pathways for coherent SK mode clustering. Such studies were initiated by Orr et al. [153] who first discussed how to incorporate elasticity more realistically in Monte Carlo simulations. In addressing the question of the kinetic pathway, Ratsch et al. [ 154] simulated thin film growth with Monte Carlo methods as a random deposition on a square lattice. The effects of lattice misfit in the heteroepitaxial system was included through strain relaxation at the edges of clusters and through a reduction of the detachment barrier with an increasing number of lateral neighbors. Neither vacancies nor overhangs were allowed in the direction perpendicular to the substrate surface, thus excluding misfit dislocations and limiting the model to a comparison of uniform film versus coherent clustering. Monomers had decreasing mobility with an increasing number of neighbor atoms to allow for surface diffusion. Results of the model simulations showed that up to a coverage of 0 = 0.25 ML, two-dimensional islanding is observed with the clusters growing in size, covering an increasing fraction of the surface. At higher coverage, three-dimensional clusters form. In this stage, the areal coverage increases only

21

56.0 I.

55.5 r

>

55.0

54.5 0.0

;/,, /

......

.................................

2.5

5.0

N x (10 4 atoms)

Fig. 25. Representation of the relative variations of three-dimensional (full line) and two-dimensional (dotted and dashed lines) reduced energy curves versus the number of atoms in the island, referred to the corresponding ideally fiat reduced energy (horizontal full line). The two-dimensional dashed line corresponds to a coverage lower than the critical coverage, and the twodimensional dotted line to a coverage greater than the critical coverage. The three-dimensional curve does not depend on the coverage. The chain-dotted curve gives the size distribution for noninteracting two-dimensional platelets at 500~ Reprinted with permission from [51], 9 1995, American Physical Society.

slightly and the additional material deposited (up to 0.5 ML) is used to build the clusters up. This growth in the third dimension continues and clusters of about four layers of thickness are obtained at 1-ML coverage. During the growth of the threedimensional clusters, some two-dimensional islands dissolve. Seifert et al. [144, 155] use a picture closer to classical nucleation theory for the transition from the two-dimensional supersaturated phase to three-dimensional clusters. Stress plays an important role in their model as the first nuclei, formed through film thickness fluctuations, lead to a lateral strain profile as illustrated in Figure 26. Within the cluster, the local strain energy density is lowered due to the partial relaxation associated with the finite lateral size of the cluster. In turn, a maximum strain exists at the edge of the cluster which may accelerate the decomposition of the supersaturated layer in the vicinity of the cluster. These strain field predictions have been quantified in a combined analytical and computational two-dimensional continuum model of partially spherical, coherent clusters by Johnson and Freund [156]. The enhanced strain at the cluster edge leads to forced growth of the nuclei with high initial growth rates. The resulting clusters have kinetically controlled shapes, i.e., are bound by low index planes which grow slowest. Like in classical nucleation studies, the temperature does influence the diffusion process and the growth rate of facets, which alter the nucleation density. The transition to three-dimensional clusters should occur on a timescale much shorter than the deposition process and thus

22

LI AND ZINKE-ALLMANG

Fig. 26. Sketch of a coherent cluster nucleated within a two-dimensional, supersaturated wetting layer. The top graph shows the local strain energy density profile across the coherent cluster, with strain relaxation inside the cluster and a strain increase at the cluster edge. Reprinted with permission from [144], 9 1996, Elsevier Science.

E2,~ E .~ E3 I

1.5 /

~

1.01-

does not directly depend on the deposition rate. However, the deposition rate has been shown to play a major role in experimental studies. This may be explained by reaching a higher supersaturation with a higher deposition rate which in turn may shorten the time period between onset and completion of the nucleation process [ 155]. In the model given by Shchukin et al. [148], as discussed above, the existence of the wetting layer was neglected in the total energy, thus (i) the actual growth mode, (ii) the cluster sizes and the densities, and (iii) the wetting layer thickness as a function of the deposited material cannot be predicted. These quantities can be measured experimentally, however, with great accuracy. With this argument, Daruka and Barabasi [ 143] present an equilibrium model for strained heteroepitaxial growth to address these problems. The model incorporates the growth of the wetting layer, dislocation-free cluster formation, and ripening, which results in the phase diagram of strained heteroepitaxial systems as shown in Figure 22. For such a system where H monolayers have been deposited, of which n 1 monolayers are incorporated in the wetting layer and the rest of the material (n2 = H - n l) is distributed in the clusters, this model expresses the energy density of the system as u ( H , n l , n 2 , ~.) = E m l ( n l ) + n 2 E i s l + ( H - n l - n 2 ) E r i p

I

/

n"n

I

~,.~L

V W__.i,~____SK2 ~ _ ~

/

~

,/J" l

0.5~

o oh

I

,i. . . . . . .

s/

--I I

,i

,'Y,

!

_..-"T- . . . . .

_..--"-

-I~ ~

/nl

I

0

7

~ ~i

t /

He41

b~ I

I

SK,--+--I

,

a2--;

i

Hc3 2

=

!

I

,

He2

3

0.4 t

I

i

I I I

1.5

Xo

1.4~ I

//

/ rl

i

I P

I

I I I _~

I ~

I

~ ~

.......

i -

L! I "~ " v^ 0

0.2

i

I

I

,

-

b)

I

W

0

~

I

i

1

i

I

i

2

t

,

3

0.0

(b) Fig. 27. (a) Wetting film thickness (nl), cluster coverage (n2) (top), cluster size (X0), and cluster density (p) (bottom) as a function of H for e = 0.08. At Hcl, there is a transition from the FM to the SKI phase, the cluster size jumping discontinuously. In the R 2 phase, present for H > Hc2, ripening takes place; (b) same as (a) but for e = 0.12. At Hc4, there is a transition from the VW to the SK2 phase followed by the SKI phase at Hc3. Finally, at Hc2 the system reaches the R2 phase. Reprinted with permission from [143], 9 1997, American Physical Society.

(12)

where Ern](n 1) is the energy contribution of the strained wetting layer (given as an integral over the binding and the elastic energy densities), Eisl is the corresponding contribution of the clusters (in the form of Eq. (7) as given by Shchukin et al. [148]), and Erip is the ripening energy which is obtained from the limit of infinitely large clusters. Minimization of Eq. (12)

with respect to n 1, n2, and X (the normalized cluster size as defined in Eq. (9)) determines the equilibrium properties of the system. From this minimization, different growth modes (or phases) are found as shown in Figure 22. In addition the phase diagram, the model also predicts some criteria for the formation of coherent clusters and ripening as shown in Figure 27.

CLASSIFICATION OF CLUSTER MORPHOLOGIES For strain induced clustering, a critical strain E1 exists such that for any value E > E1 stable clusters are possible. On the other hand, for any E value there exists an upper limit to the number of layers in the film, Hc2, beyond which ripening occurs. Thus, the stability of the coherent clusters is sensitively dependent on the coverage. To grow stable clusters, thin deposition layers must be used. For small coverage and small values of E, the formation of the pseudomorphic wetting layer should become a general feature of strained layer formation. The obtained phase diagram shows that the critical thickness of the wetting layer for initial nucleation of three-dimensional coherent clusters decreases with increasing lattice misfit E, in agreement with experimental measurements [143, 157]. Uniform clustering occurs after the critical thickness has been reached, and in the vicinity of the critical thickness, He1, the cluster density increases linearly with (H - He1). The equilibrium model also shows that unlike the cluster density, the equilibrium cluster size does not increase continuously near He1, but jumps discontinuously from zero, again in agreement with the results of experimental observations [144, 158]. From the above studies, we emphasize that (i) equilibrium theories are successful in describing the energetics of the heteroepitaxial systems with a two-dimensional to threedimensional transition; (ii) the classical continuity theory is a good approximation for strained epilayer growth in the initial SK stage and for the coherent cluster growth; (iii) the origin of coherent clustering is attributed to the mismatch strain induced by the. lattice misfit between the film and the substrate material, causing the strain energy in the initial twodimensional wetting layer to overcome the barrier for formation of three-dimensional coherent clusters which is observed as a two-dimensional to three-dimensional SK mode transition. Two-dimensional platelets are possibly a precursor stage; (iv) the surface facets of the coherent clusters, their edges, and the elastic strain within the cluster establish additional energies which determine the shapes and the sizes of the threedimensional coherent cluster.

1.2.2. Kinetics Considerations The foregoing discussion indicates that coherent SK mode clustering in heteroepitaxial growth is based on the assumption of a thermodynamic equilibrium: the free energy of a "macroscopic" three-dimensional cluster competing with that of an epitaxial film. On the other hand, kinetic processes such as thermal fluctuation and diffusion, the existence of possible intermediate phases, and mass transfer in the two-dimensional to three-dimensional transition, must also contribute to the formation of coherent cluster morphologies. Various studies have been conducted [147, 159-163] to address the kinetics issues of the coherent clustering morphologies in heteroepitaxial growth. In thin film growth, surface diffusion is critically important since it allows the deposited material to be redistributed that may significantly affect the final morphology of the film. For the initial stage of the coherent clustering, such surface diffusion effect may accelerate or delay the nucleation process

23

by allowing sufficient or insufficient material to reach particular positions on the surface. After the initial nucleation, the competition between formation of new nuclei and growth of an existing nucleus may also be altered. Thus, diffusion can affect the critical thickness in coherent clustering and alter the cluster size and density distributions. Snyder, Mansfield, and Orr [ 159] presented an early work on the kinetics of the coherent clustering morphologies with an experimental investigation and model study for the InxGal_xAs/GaAs(O01) system. In the study, they demonstrated a temperature dependence of the critical thickness for the coherent cluster formation. STM and RHEED measurements showed that at 520~ the critical thickness for the two-dimensional to three-dimensional transition increases with decreasing lattice misfit. At a fixed lattice misfit, the critical thickness increases with decreasing temperature, and the transition from the two-dimensional wetting layer to the three-dimensional clusters becomes more gradual as shown in Figure 28. Thus, a suppression of the two-dimensional to three-dimensional transition occurs at lower temperatures. In addition, they observed that planar films grown at moderate and low temperatures are unstable against cluster formation at subsequent high-temperature annealing, in agreement with the theoretical prediction that the strain-relieved three-dimensional cluster morphology is the lower energy configuration. A model incorporating the surface diffusion was proposed in which the kinetic diffusion barriers delay or hinder the morphological transformation to coherent clusters at lower temperature. This model uses the surface diffusion length x/Dr as a characteristic length on the two-dimensional surface L = x/Dr, where r is taken as the time to deposit a monolayer. The volume of the deposited material, V -- Ld, either in the form of a uniform film with thickness d or in a cluster, raises the system energy due to the strain and the surface energies, which is expressed as [ 159],

V

= tc62f(x) + FFV,/~__ VV

(13)

where x is the bulk modulus, E is the misfit, ~ w is the surface tension, x is the aspect ratio of the cluster height to width (with x -- 0 for a uniform film), and f (x) is an empirical function incorporating the strain relaxation. In this equation, it is assumed that elastic strain is built in both the substrate and the clusters. Minimizing this system energy with respect to the cluster aspect ratio and comparing it to the energy of the uniform film, . 2 ~ K 2 E 4 L), at a critical thickness criterion is obtained (dc ~ , YFV/ which the aspect ratio jumps from zero to a finite value, thus predicting the formation of coherent clusters. From this study, it is clear that the critical thickness is inversely dependent of the diffusion length, and consequently, dependent of the growth temperature in the same fashion. Further, with decreasing misfit or increasing surface tension, the onset for coherent clustering increases, which is consistent with the energetic models. In addition to the surface diffusion, mass transfer in the two-dimensional to three-dimensional transition of the coherent clustering has been reported by Ramachandran et al. [160]. Considering the experimental results for both Ge/Si [138, 161] and InGaAs/GaAs [136, 137] systems, a partial

24

LI AND ZINKE-ALLMANG

Fig. 28. RHEED data characterizing (a) the high-temperature (T -~ 520~ and (b) the low-temperature (T ~ 320~ growth of In0.sGa0.sAs (3.5% lattice mismatch) on GaAs(001). Both the intensity oscillations of the specular beam (top curve) and the corresponding surface lattice constant (bottom curve) are plotted as a function of epilayer thickness. Reprinted with permission from [ 159], 9 1992, American Physical Society.

breakup of the two-dimensional layer in the formation of threedimensional clusters is expected. The authors conducted a systematic study of the two-dimensional to three-dimensional morphology change for InAs on GaAs(100) focusing on the material transfer in the process. Using in situ STM to obtain the micrographs in Figure 29, they observed four main structures (small (50 nm) two-dimensional islands, small quasi-three-dimensional and three-dimensional clusters) in the morphological evolution from a purely twodimensional surface to the final three-dimensional structures as the InAs coverage varies (in the range of 1.35-2.18 ML). By plotting the density (Figure 30a) and total volume (Figure 30b) of each type of the structures versus the surface coverage of InAs, they found that the two-dimensional to three-dimensional transition occurs over a range of coexisting two-dimensional islands, small quasi-three-dimensional and three-dimensional clusters. The quasi-three-dimensional clusters only exist as a mediate structure in the transition regime but play a significant role in the material redistribution. They also found that after the formation of the first three-dimensional clusters and below a critical coverage, the total volume of each of the three structures (two-dimensional islands, small quasi-three-dimensional, and three-dimensional clusters) increase with increasing coverage. This indicates that three-dimensional structures initially form as a result of the local strain-driven kinetics but not as a straight shape transition from two-dimensional platelets to three-dimensional clusters, contrary to the equilibrium model prediction given by Priester and Lannoo [151, 152]. Beyond the critical coverage, the total volume of two-dimensional islands decreases accompanying with the increase of the volume of the three-dimensional clusters, indicating a pure mass transfer from two-dimensional islands to three-dimensional clusters. The analysis further shows that with a subsequent increase of the coverage, the small quasi-three-dimensional clusters gradually disappear with their mass redistributed into the threedimensional clusters, indicating a ripening-like growth of the three-dimensional clusters. Another kinetic process identified in coherent clustering is related to the so-called cooperative nucleation as studied by Jes-

Fig. 29. In situ UHVSTM images for InAs depositions on GaAs(001) of (a) 1.35 ML, (b) 1.45 ML, and (c) 1.61 ML. The observed structural features are labeled as follows: A-small two-dimensional islands (1 ML ~ 0.3-nm high, lateral size 50 nm), Csmall quasi-three-dimensional clusters (0.6-1.2-nm high), D-three-dimensional clusters (~2-4-nm high), S-steps of 1-ML high, and H-holes of 1-ML deep. Note the completely two-dimensional morphology in (a), the appearance.of small quasi-three-dimensional clusters in (b), and the presence of all features A-D in (c). Reprinted with permission from [160], 9 1997, American Institute of Physics.

son et al. [ 162]. In an experimental investigation of the strain induced two-dimensional to three-dimensional transition in the SixGel_x/Si(lO0) system, they recorded with atomic force microscopy (AFM) the formation of a ripple morphology through a gentle postdeposition annealing step at about 590~ of a 5nm thick alloy layer which was grown at a lower temperature. The annealed surface region shows a well-defined and continuous ripple geometry shown in Figure 3 l a. At a surface region annealed at 570~ isolated ripple domains, consisting of alternating clusters and pits, were observed with intermittent planar regions of the strained layer as shown in Figure 3 lb. The latter morphology indicates a direct transformation from a strained planar film to a ripple morphology, while the continuous ripple in Figure 3 l a is considered to be the coalesced stage of a cooperative nucleation process involving clusters and pits. As the elastic interaction between clusters and pits is negative (they attract each other), the nucleation of clusters and pits in a cooperative manner may reduce the activation barrier for this type of nucleation. With a simple model, the authors estimated the energy change, A G N, which is associated with the nucleation of N pits and clusters for various simultaneous and sequential configurations. The resulting nucleation energy barrier is shown in Figure 32 with the data normalized with the energy barrier A G 1 for nucleation of an cluster with N -- 1. The figure indicates that for simultaneous nucleation of a domain consisting of N pits and clusters the activation barrier increases linearly with N.

CLASSIFICATION OF CLUSTER MORPHOLOGIES

25

Fig. 31. AFM image of a 5-nm thick Si0.sGe0. 5 alloy layer grown on Si(001) and annealed for 5 min at (a) 590~ where a regular surface ripple pattern is formed at the center of the wafer, and (b) 570~ where the cooperative nucleation of surface ripple domains is captured. Clusters (A) and pits (B) nucleate adjacent to each other as indicated, with substantial planar regions of the film remaining in (b). Note that in both images, the cluster and the pits are bounded by (501) facets. Reprinted with permission from [162], 9 1996, American Physical Society.

(b) Fig. 30. (a) Density of various InAs structural features on GaAs(001) as a function of InAs delivery, 0. The open symbols indicate a density of 2 x 10 -3 ML/s at 145 K with D/R < 104. In these cases, the evolution of the morphology is dominated by the monomer concentration at the time of termination of the deposition process and the island density is independent of the substrate temperature, resembling distributions for i* - 0 in Section 1.1. (ii) Direct Ripening. The reduction of the initial supersaturation is the main effect during early stage growth. Direct diffusional growth slows down and the area around the clusters defined by the diffusion length A start to overlap. As the to-

45

tal overlap approaches the entire surface, the late stage growth regime starts as described in the next section. For a short intermediate time interval, a growth process becomes possible which is called "direct ripening" [262]. This process is characterized by a local interaction between two neighboring clusters of slightly different size. The smaller cluster starts to decompose to maintain the concentration gradient toward the larger cluster due to the Gibbs-Thomson effect. The appearance of such processes is critically dependent on the initial conditions, especially the fraction of spatially close cluster pairs. The process is part of the early stage growth since it is a local effect. Hirth [263] used this picture to describe nonrandom spatial distributions of clusters on the substrate surface, i.e., that very close clusters are less likely to survive into the late stage. Physically, this shows up in SEM or TEM pictures as a denuded zone around larger clusters. These zones may be due to a diffusive dissolution of small clusters in the neighborhood of a larger cluster (direct ripening). Alternatively, a reduced probability of nucleation due to the decreased supersaturation around large clusters may lead to the denuded zones (direct growth from the supersaturated phase). (iii) Coalescence. Although coalescence, i.e., the growth of clusters into each other, is normally considered part of the late stage growth, it may also be important in the early stages. This process depends strongly on the cluster density on the surface and becomes dominant when the fraction of the surface covered by the cluster increases. This is the case during the nucleation regime, when the number of nuclei increases or when continuous deposition of monomers steadily increases the average size of existing clusters. A semiquantitative argument on the relative contribution of single atoms (ripening) or stable clusters (coalescence) in the early growth regime is given by Kern [264] by comparing the monomer concentration on the surface and the number of stable clusters when nucleation reaches the maximum density. The latter value is usually about 109-1011 cm -2. In the particular study, the monomer concentration is estimated from the difference of the heat of adsorption and evaporation, e.g., for Au on KCI(100) or C(0001) (graphite) as 103 monomers/cm 2 at 1100 K and for Au on MgO(100) or S i ( l l l ) as 1011 monomers/cm 2 at 1100 K. Thus, a lower monomer concentration favors coalescence growth. For Ge on Si(100) at typical heteroepitaxial growth temperatures (550~ the monomer concentration is estimated by molecular dynamic simulations to be of the order of 0.1 ML [265] which is confirmed by an experimental scanning Auger microscopic study [266].

2.3. Late Stage R i p e n i n g M o r p h o l o g i e s

2.3.1. Experimental Tests of the Basic Ripening Theory on Surfaces 2.3.1.1. The Two-Dimensional-Two-Dimensional Case A detailed experimental study for two-dimensional-two-dimensional ripening has been presented by Krichevsky and Stavans

46

LI AND ZINKE-ALLMANG ,, .

, I

I

i

I 200

I

2

1.5

% E

_y.aP

O

v

,_.._,

o3

1

n,' A V

0.5

0 0 0

500

1000

t [min] Fig. 64. Dependence of the third power of the radius of succinonitrile solid droplet growth in its melt near 320 K in a quasi-two-dimensional arrangement between two glass slides. Data represent different volume fractions, ~ -- 19% (open circles), ~ = 40% (solid circles), and 9 = 54% (triangles). Reprinted with permission from [268], 9 1995, American Physical Society.

[267, 268]. A thin layer of succinonitrile with solid droplets surrounded by their melt was prepared between glass slides 25 /zm apart. Since the droplet sizes exceeded 25 /xm, the system essentially behaves two dimensional. The solid fraction can be controlled with an impurity in a coexistence region near 320 K. Volume fractions of the solid phase were varied between r - 13% and 9 - 54%. For all concentrations, the growth power-law R cx t a was determined with exponent ot = 0.335 4- 0.005 (Fig. 64). The predicted power law was also studied for an amphiphiles mixture forming a monolayer at an air-water interface (Langmuir film) [269]. For r = 25%, the components were miscible at 292 K but become immiscible through a rapid mechanical expansion (10% areal increase). The analysis of the average domain area as a function of time leads to an exponent of ot = 0.28 4- 0.01 slightly below the expected value at ot - 1/3. Step edge attachment-detachment limited ripening has been observed for 0.1-ML Si on Si(001) at 945 and at 1135 K [270, 271 ]. By imaging the evolution of individual islands with low energy electron microscopy (LEEM [272]) the time dependence of the average island area (Fig. 65) was followed. The solid line illustrates a linear dependence, corresponding to ot - 0.5, in agreement with the exponent expected [ 181 ]. Another case of attachment-detachment controlled island growth has been observed by Cavalleri et al. [273,274]. During the formation of a uniform thiol layer (H2S derivates with an organic (CH3-[CH2]x-) ligand) on an Au(111) surface, erosion of the gold surface led to thiol covered, nanometer sized depressions of monolayer depth. The annealing process of these holes at about 635 K was followed by STM. The holes coarsen in an Ostwald ripening mechanism with ot varying between ot = 0.48 and ot = 0.52 (error margin < 4-0.1) for three chain lengths with x - 5, 9, and 17. The interface barrier dominated process is linked to breaking and forming interchain bonds between the

i

......

400

t(s) Fig. 65. Time dependence of the average island area during ripening of 0.1ML Si on Si(001). The plot shows the growth of an average sized island on a terrace at 945 K. Reprinted with permission from [270], 9 1996, American Physical Society.

thiol molecules. This interpretation is supported by a faster annealing for molecules with shorter organic ligands. Observation of deviating power laws requires special considerations. For example, Ernst, Fabre, and Lapujoulade [275] observed low-temperature islanding in the system Cu on Cu(100) with a 0.5-ML coverage using helium atom beam scattering. Deposition at 100 K was followed by ripening in the temperature range of 212-266 K for annealing times of 5-165 min. Due to the high coverage, strongly interlinked structures are expected on the surface. The time evolution of the characteristic length scale at four temperatures in this interval showed slopes that varied between 0.17 and 0.25. These values imply an asymptotic exponent of 1/4 which can only be explained with diffusion limited ripening along the edges of the interlocked morphology as predicted by Mullins based on scaling arguments [ 184]. 2.3.1.2. Three-Dimensional-Two-Dimensional Case

The 1/4 power law for a three-dimensional-two-dimensional system was first experimentally observed for the system Sn on Si(111) and Si(100) [260, 276]. The difficulty to establish a power law in such experiments is illustrated by comparing linearizations with a third- and a fourth-power assumption for the cluster height versus time. Figure 66 shows such a comparison for 22.3- and 3.8-ML Sn on Si(100) at 795 K [277]. The fourthpower law agrees with the data better if a transient regime for cluster sizes up to radii of 100 nm is included. This transient regime coincides with estimates of the transition from early stage growth to late stage growth for this system [260]. Figure 67 shows a similar measurement for 2.9-ML Sn on Si(111) at 525 K. The same conclusions apply, supported in this figure with a double-logarithmic plot in the inset of the figure. The inset illustrates that the fourth-power law is indeed the best fit to the data after an initial period representing early stage growth [277]. The activation energies for clustering as obtained from such measurements have been included in Table I.

CLASSIFICATION OF CLUSTER MORPHOLOGIES

1.0 MeV L'He§ '

o)

I

'

I

'

I

'

T=795Kn=223 .HLI

Si (10 0)- ( 2x 1)/Sn

I

'

I

b) T=795K

2

47

'

'

n=3.BML

'

T

i!

2

l/,/ 1 -.a" i,,d e--

/ [r , ~

0

0

I

20

i

I

~

,

I

,

60

I

0

80

'

0

2O

l,O

60

t(rnin) Fig. 66. Power-law dependence of the height of clusters as a function of time at 795 K for two different coverages on Si(001) 2 • 1, (a) 22.3-ML and (b) 3.8-ML equivalent coverage of Sn. The solid line corresponds to the fourth-power dependence of the cluster height and the dashed line to the cube of the cluster height. Technique: ion scattering (RBS). Reprinted with permission from [260], 9 1991, Elsevier Science.

Rogers et al. [278] measured the growth exponent for a liquid-liquid (succinonitrile-water) two-phase system at 315 K. The experiment was carried out in a quartz test cell with clustering of partial spherical caps on the walls of the cell. Clustering was observed for times up to 4 months. Figure 68 shows in double-logarithmic representation the average cluster radius as a function of time. The late stage is described by a power law with coefficient ot = 0.247 (solid line in Fig. 68) in good agreement with the theoretical value of 1/4.

2.3.2. Finite Areal Fraction and Volume Fraction Effects Although the power-law exponent of cluster growth is not affected by the volume or the areal fraction of clusters, two other main properties depend on the volume fraction as has been shown for three-dimensional-three-dimensional systems: (i) the cluster size distribution function broadens and becomes more symmetric with increasing volume fraction, and (ii) the absolute growth rate of clusters increases by a factor of 2 to 3 between 9 = 0% and 9 = 50% [ 181,228-231].

2.3.2.1. Two-Dimensional-Two-Dimensional Systems: Analogy to Three-Dimensional-Three-Dimensional Systems Areal fraction effects have been predicted for two-dimensionaltwo-dimensional systems by Marqusee [234]. Both aspects have been investigated rigorously during the last few years due

to the related problems with the diffusion process in two dimensions. Yao et al. [238-240] compared two-dimensional-two-dimensional and three-dimensional-three-dimensional systems in a series of mean-field analytical and numerical studies of many droplet systems with screening effects. The resuits are summarized in Figure 69 for the absolute cluster growth rate and in Figure 70 for the size distributions. Figure 69 compares absolute rates of cluster growth, K ( ~ ) , defined by Rc = [K(ap)t] 1/3, which is the suitable power law for both three-dimensional-three-dimensional and twodimensional-two-dimensional systems. Note that the data are shown as absolute values [234, 236, 238, 239, 243]. The data agree on an increase of cluster growth rates with increasing volume fraction. Marder [235] attributed this to the increased direct ripening [279, 280] between neighboring clusters which accelerates the growth of the larger cluster in a binary pair. Figure 70 illustrates the changes of the normalized size distribution for various areal fractions in the range from 9 -- 0% to 9 = 8.5% for two-dimensionaltwo-dimensional systems. For comparable volume fractions the changes of the cluster size distributions are comparable with three-dimensional-three-dimensional predictions, with the shown two-dimensional-two-dimensional distribution broadening slightly stronger. Cluster size distributions are quantitatively compared using the different moments of the distributions. Most frequently, the standard deviation and the skewness (a measure for the

48

LI AND ZINKE-ALLMANG I w ~.10 3 -

.~

I I

I

i

I

1.0 HeM ~He*--

Si (111)-(7x7)

ISn

T = 525K

g= 2.gilL

2.10 3 "

I

I

!

I

I

"'

I

I

1.0

-

r r i ~

~

f,=.

lO3

,@

8" 10 2

v

0.5 t 1 1 1 w

4." 10l

I 2

1

i 4.

i 10

i ZO

i 4O

-

t(min)

/

A

/

/

0

_

I 0

""0

I 2

i

I, 4

I

i 6

i

i 8

4>.[%]

r"

,F

-

Fig. 69. Plots of ripening rates K, in Rc = (Kt) 1/3, versus areal coverage fraction in a two-dimensional-two-dimensional system. The data are taken from Ardell [243] (long dashed line), Marqusee [234] (short dashed line), Zheng and Gunton [236] (dash-dotted line), and Yao et al. [238-240] (solid line and solid circles). Reprinted with permission from [20], 9 1999, Elsevier Science.

M 10

20

30

"9 ia i ,,"x | / / s

t,O

(min)

t

A

Fig. 67. RBS measurement of the cluster height as a function of time for 2.9ML equivalent coverage of Sn on Si(111) deposited at room temperature and held at 525 K. The solid line corresponds to the fourth-power dependence of the cluster height and the dashed line corresponds to the cube of the cluster height. The inset shows the same data in double-logarithmic form. Technique: RBS. Reprinted with permission from [260], (~) 1991, Elsevier Science.

I'

I

I

I

"

'1

I

! I, / it~

v

~l

I

Q

0

E -I A n,' V t-

1

Fig. 70. Scaled normalized size distributions for two-dimensional-twodimensional system with variable areal-volume fractions. The short dashed line corresponds to 9 = 0%, the long dashed line corresponds to 9 = 1%, the dashdotted line corresponds to 9 = 4% and the solid line corresponds to 9 = 8.5%. Reprinted with permission from [239], 9 1993, American Physical Society.

3.5

'

10

I

I

12

I

14

,,,

I

I

a s y m m e t r y o f the distribution) are r e p o r t e d w h i l e the k u r t o -

16

sis (a m e a s u r e o f the s y m m e t r i c d e v i a t i o n f r o m a G a u s s i a n

In t [ s ]

shape) and h i g h e r m o m e n t s c a r r y too large e r r o r m a r g i n s in e x p e r i m e n t s . M o m e n t s for t w o - d i m e n s i o n a l - t w o - d i m e n s i o n a l

Fig. 68. Double-logarithmic representation of the clustering in a binary liquid mixture of water and succinonitrile (clusters are succinonit_rile rich phase) on a quartz surface at 315 K. The linear regression to the late stage yields a powerlaw coefficient of c~ = 0.247 in good agreement with the theoretical value of = 1/4. Reprinted with permission from [278], 9 1994, Minerals, Metals, and Materials Society.

and t h r e e - d i m e n s i o n a l - t h r e e - d i m e n s i o n a l s y s t e m s are s h o w n in F i g u r e 71 ( s t a n d a r d d e v i a t i o n ) and F i g u r e 72 ( s k e w n e s s ) . T h e relative i n c r e a s e o f the s t a n d a r d d e v i a t i o n is s h o w n t w i c e as a f u n c t i o n o f @, w i t h a linear 9 axis in F i g u r e 7 l a a n d as a loga r i t h m i c @ axis in F i g u r e 7 1 b to h i g h l i g h t v a r i a t i o n s at s m a l l

CLASSIFICATION OF CLUSTER MORPHOLOGIES 80

'

I

'T /

I

'

I

'"

!

1.5

'

'

I'

'

49 I

'

I

'

40

'

o Ga/Si In/Si

1.0

~

I

9 G e l Si

t

Ks

D3

0.0 1 . . . . 20

E3 -0.5

0

0.0

I 0.1

I

t

I 0.2

I

t

0.3

0.4

I

I

|

I

I

I

T

1

/

O

LSW

--

0,0

m

l

I 0.1

i

I 0.2

i

I 0.3

I

I

,

0.4

0.5

Fig. 72. Skewness of cluster size distribution for ripening systems as a function of areal-volume fraction ~. Notations of experimental and theoretical data are the same as in Figure 71. Reprinted with permission from [283], 9 1996, Elsevier Elseviel Science.

60-

"-"

C

0.5

(a) 80

M2 M3

I

40-

:=-~...,-~

H

..~-~

!~:~."--~9 ~ ~ q~.?.,, ~"~-tH"bl u

H

H

b2u

":-:~

Fig. 30. A schematic representation of the benzene molecular orbitals. Figure adapted from [387] and W. L. Jorgensen and L. Salem, "The Organic Chemist's Book of Molecular Orbitals," p. 257. Academic Press, San Diego, 1973.

the molecular plane parallel with the surface. This compelling further refinement of the benzene adsorption site is not, however, in agreement with the expected theoretical binding site of the benzene bonding atop a nickel atom [427]. In spite of the compelling STM [385] and NEXAFS [418] results, benzene on Cu(110) appeared to be tilted out of the plane of the surface in HREELS and angle-resolved photoemission [425]. These conflicting results for benzene on Cu(110) may be reconciled by

85

distortion of the benzene planar ring structure, as suggested by theory [428]. The degeneracy of the benzene 2elu orbitals (schematically shown in Figure 30) is lifted in photoemission, resulting in the formation of two bands, the bl and b2 bands (at 7.5 and 7.9 eV binding energy) on Ni(110) [384]. The same is true of the lelg orbitals (bl and b2 bands at 4.3 and 4.6 eV) and the 2e2g orbitals (al and a2 bands at 5.5 and 6.1 eV) [384] also shown in Figure 30. The reduction of the symmetry to C3v for benzene on Ni(111) [414] may result in two 2e2g orbitals (at 5.9 and 6.5 eV binding energy). For benzene on Ni(111), the preferential orientation apparent in angle-resolved photoemission [387, 414] has been confirmed by photoelectron diffraction [416]. Low energy electron diffraction structural studies [417] suggest that benzene on Ni(111) is also placed with the molecular plane parallel with the surface, although there is a slight molecular distortion. (This distortion is somewhat similar to that postulated for benzene on Ni(110) [386].) There is buckling of the Ni(111) substrate induced by the chemisorption of benzene [417]. When the Ni(111) surface is covered by only a monolayer of copper, the angle-resolved photoemission [429] suggests that the adsorbed benzene loses azimuthal orientation and becomes much more weakly bound, like benzene on Cu(111) [419]. Similarly, benzene on AI(111) is also weakly bound, with the molecular plane seen to be parallel with the surface in angle-resolved photoemission and HREELS [413]. The C6v molecular symmetry of benzene is preserved on AI(111) [413 ] and, in spite of some preferential orientation for adsorbed benzene on Rh(111), the C6v molecular symmetry also appears to be preserved in angle-resolved photoemission [392]. Angle-resolved photoemission suggests a strong preferential orientation for benzene on Rh(111) [392, 406] and Pt(111) [399], but it is clear that almost undetectable amounts of coadsorbed CO can induce a preferential orientation for benzene on the very flat surfaces like Rh(111) [392]. However, there is a fairly convincing case to be made [430] that the Jahn-Teller effect in the photoemission process itself leads to a "double peak structure" for the 2e2g from adsorbed benzene. This lowering of symmetry in the photoemission process is also observed in NEXAFS in the core excitation to the l e2u unoccupied molecular orbitals (shown in Figure 30) for benzene on Pt(110) [389], on Mo(110) [431], and in condensed molecular films [432]. For benzene on Pd(ll0) [364, 391], the selection rules applied to the angle-resolved photoemission measurements suggest that, instead of lying "fiat," the adsorption geometry is slightly tilted. A tilt geometry of 10 ~ to 20 ~ was proposed [391 ], reducing the overall symmetry to Cs. This result is fairly compelling in spite of early HREELS data that suggest a "fiat" orientation [433, 434]. Similarly, benzene on Pt(ll0) (reconstructed to the 1 x 2 structure) is also seen to be tilted, with the overall symmetry of Cs, by angle resolved photoemission [389]. With NEXAFS [389], a tilt angle of about 30 ~ in the (001) direction is deduced, placing the benzene almost planar with the (111) facets on this platinum surface, as shown in Figure 31. This tilted orientation is a consequence of the

86

DOWBEN ET AL.

Fig. 31. The proposedbondingconfigurationfor benzene in the 4 x 2 structure on Pt(110) 1 x 2. The adsorption sites are chosen somewhatarbitrarily, but the tilt is indicated. Reprintedwithpermissionfrom [389], copyright1998,Elsevier Science.

surface structure and is not like the tilting of phenylacetylene on Pt(111) (the phenyl ring is tilted by 34 ~ to 37 ~ out of the plane of the surface as observed in NEXAFS) caused by the end group [435]. The reduction of symmetry in the photoemission final state can make unequivocal assignment of the bonding configuration difficult: without angle-resolved measurements, assigning benzene adsorption on Si(111) to a Diels-Alder like addition [436] on the basis of the photoemission bands alone is uncertain. Benzene chemisorbed on Si(100)-2 • 1 appears to lose much of its aromatic character in infrared adsorption and NEXAFS [437]. The majority of the benzene, in the simple overlayer, chemisorbs to the surface with a Diels-Alder like configuration, resembling that of 1,4-cyclohexadiene tilted with respect to the surface by about 30 ~ [437]. The closely related molecule pyridine does not lie fiat as readily as benzene. Angle-resolved photoemission measurements show quite clearly that the molecule bonds through the N atom on Ir(111) [412]. The molecule stands up (i.e., uptight), occupying a relatively high point group symmetry in this bonding configuration, with the molecular axis along the surface normal [412]. Angle resolved photoemission results for pyridine on Pd(111) suggest a tilted configuration (neither "flat" nor "uptight" in bonding configuration) with the molecule interacting with the surface through both the nitrogen lone pair electrons and the Jr electrons [397, 438]. While angle-resolved photoemission band studies have been undertaken for pyridine on Cu(111) [439], the assignment of the bands has been questioned [438, 440].

Pyridine on Pd(110) appears from angle-resolved photoemission to bond in a "flat" configuration [441]. This is quite different from many of the results for the pyridine bonding configuration on Cu(110), where the pyridine is again observed, by photoelectron diffraction [442], to bond atop the copper atoms and to have its molecular plane tilted with respect to the surface. Angle-resolved photoemission from Pd(110) has also provided unusual results for benzene, as just noted. Surprisingly, while benzene generally bonds with the molecular plane parallel with most surfaces, benzene has also been observed to bond on Pd(110) in a tilted configuration [364, 391]. The slightly larger benzotriazole (C6HsN3) is found, by NEXAFS, to adsorb (at submonolayer coverages) with the molecular plane nearly perpendicular to the CU(100) surface [443], a more "uptight" configuration than even pyridine. The preferential orientation of the molecule in the multilayer is much closer to a configuration with the molecular plane parallel with the surface [443]. The related benzimidazole (CTH6N2) and 1-methyl benzotriazole (C7H7N3) do not appear to have a strong preferential orientation on Cu(100) [443]. Dimethyl. pyridine, as well as 1,3 dimethylbenzene, adsorb on Pd(111) with the molecular plane parallel with the surface [397]. The absence of a strong preferential orientation for benzimidazole and 1-methyl benzotriazole and the "flat" bonding configuration of dimethyl pyridine may be due to steric hindering of the bonding with the surface through a protruding N lone pair that may be characteristic of both pyridine and benzotriazole bonding. The unsaturated bonds of phenyl (C6H5) and benzyne (C6H4) [398, 422] are also probably responsible for the slightly tilted bonding configuration of these species [425]. The ligand cyclopentadienyl (C5H5) has also been studied by angle-resolved photoemission on Rh(111) [444]. Much like benzene on Rh(111) [392], the molecular plane is parallel with the surface and the Csv symmetry of the molecule dominating the photoemission, although there is some reduction symmetry toward Cs [444]. Consistent with this result, cyclopentadienyl tings have been imaged by scanning tunneling microscopy on Ag(100) and exhibit high mobility across the Ag(100) surface (like benzene) providing every indication that the molecular plane is parallel with the surface [445]. If ever investigated in future studies, we would expect the nido-cage carborane ligands (similar to the closo-carboranes discussed in the next section), because of their similar electronic structure to cyclopentadienyl, to bond in a similar fashion to the surface. The intermolecular interaction of adsorbed benzene is strongly evident in the dispersion of the 2alg (etCH) band for N i ( l l l ) [415], Ni(ll0) [384, 387, 388], R h ( l l l ) [392], and Os(0001) [423] as seen in Figure 32 for benzene on Ni(ll0). As with the simpler CO overlayers, the benzene molecular orbital bandwidth (the extent of dispersion) can be related to the nearest neighbor lattice constant, as seen in Figure 33. The exception seems to be Pd(110) [364], where the lattice spacing might lead one to conclude that the bandwidth should be about 1/2 eV but in fact is about 0.23 eV, perhaps because the benzene is adsorbed in a tilted configuration.

BAND STRUCTURE OF MOLECULAR ADSORBATES 19. CARBORANES

o Ni (110) Substrate o c ( 4 x 2 ) Adsorbote

[~fo]

~':~

[]

Two different main group cage molecules have been studied by angle-resolved photoemission, in an effort to determine a preferential bonding orientation [446, 447]. Both carboranes C2B4H6 [446] and CaBIoH12 [447] exhibit preferential bonding orientations that not only resemble each other, but also resemble the smaller molecular adsorbates like CO as well as larger molecules like methoxy and benzotriazole. Valence band angle resolved photoemission provides very clear evidence that the initial adsorption of the small borane molecule, nido-2,3-diethyl-2,3-dicarbahexaborane, (C2H5)2 C2B4H6, on S i ( l l l ) occurs with partial dissociation of the cluster molecule [446, 448]. The dissociation results in the loss of the ethyl groups [446, 448]. Schematically, the parent molecule and fragment are shown along with their respective molecular orbitals in Figure 34. The carborane cage fragment, C2B4H6, adsorbs molecularly with the molecular axis and the basal, C2B3, plane of the cage parallel with the surface normal [446]. As with many molecular adsorbates, bonding of the carboranes to the metal surface perturbs the molecular orbitals, and some to a greater extent than others. From a comparison of the observed binding energies of the molecular orbitals of the adsorbed species with simple model calculations [446, 448], it is possible to determine that the molecule bonds to the surface through the carbon(s), C2 and C3 in Figure 34. This is clearly similar to the "uptight" bonding configuration of CO on many metal surfaces in that the molecular axis is along the surface normal and the dipole is pointed toward the surface. Subsequent adsorption of nido-2,3-diethyl-2,3-dicarbahexaborane on the oriented dicarbahexaborane is molecular but with no preferred bonding orientation that could be ascertained from angleresolved photoemission.

[oo0

20 Ig

IO.Ov

~105t,..

"

(~

q) C

A

LLI E~

XXX Z~

AX

~

~0

c I10-

X,~X~

Z~

t~

~Z~

Oo~ ~o %~~ dOO

._

x

"0 . _C :

~c)

xo

Go

03

s I

I

3

x

A' s I

i

(zC>X IBX

X

11.5

A'

I,,,

OOOKX X~00t

D'

I

I

2

B'A'B' P'

I

I

I

I

0

I

I

,

I

'

I

B' b I

I

I

2

k,,(s

[iTo] 4-

5

---[ooi]

Fig. 32. The Brillouin zone formed for the benzene c(4 x 2) overlayer structure on Ni(110) is shown at the top (a). The experimental two-dimensional band structure for the benzene 2alg molecular orbital (b) along the high symmetry directions as indicated at the top. Reprinted with permission from [384], copyright 1991, Elsevier Science.

'

'

'

'

I

'

'

'

'

I

'"i

'

'

'

I

'

0.8 - D ~,, ~ M

> v

0.7

87

'

'

"

I

'

'

'

'

I

'

'

'

'

I Hex. structures (I"A)

"-~

,

9 ~ 9

c} o O_ U3

I

12.

/ / / / / / / / / / t/'}

rn

t--

/

/

.

/ / / / / / / / / / / / / / / / 3,... (:3

n n n o

0 n 0

08 300 |

0

0.5

,

J

I

i

20 t/') r

n

,

.. 'c}

.- .I,,

t

J

t

t

I0

0

.o

9

e.k ,~-t.

,r

i" 99

t

{D m

c}

J

20

o

1.0

Fig. 37. The dispersion of the orthocarborane, on Cu(100), induced 6.5 and 12.5 eV molecular orbital bands for one monolayer (o) and two monolayers ([3). Reprinted with permission from [451], copyright 1995, American Institute of Physics.

I 0

~,. , . ~

r t-...4

,

,

I

I0

~'~ ~.

3

~ 9 "r " : ' 5"...'e. z'V lit.

s.

0_ I

\

s

in spite of the absence of long range order in the molecular adsorbate layer. This "band" dispersion is indicative of lateral interactions [451]. In this respect, this cage molecule is similar to many of the molecular adsorbates discussed, although the dispersion is quite small (~200 meV), as seen in Figure 37. In some sense, the carborane cage molecule closo-l,2dicarbadodecaborane (C2B10H12) could be thought of as a small version of the fullerenes, the buckyball C60, and related species discussed at the end of this review.

20. METALLOCENES Metallocene (i.e., MCp2, where Cp is C5H5 in the r/5 configuration with the metal center, and M is a transition metal) adsorption on surfaces has been an area of increasing interest, in part because of the utility of metallocenes for the selective area chemical vapor deposition of metals [452--456]. Of primary interest are the mechanisms for dissociation and fragmentation, but bonding orientation has also been explored. The substrate has a surprisingly strong influence on the bonding orientation of metallocenes. The adsorption of molecular ferrocene (Fe(CsH5)2) on Ag(100) [457], Cu(100) [457], and Mo(112) [458] has been recently studied by angle-resolved photoemission. As seen in Figure 38, there is a polarization dependence of the molecular orbitals and this polarization dependence differs from Cu(100) to Ag(100). There is a strong enhancement of the 4e2g, 6elu, and 4elg orbitals in p-polarized light for ferrocene on Cu(100). This does not occur on Ag(100). This is interpreted as demonstrating that the ferrocene molecular axis is parallel to the surface for molecular ferrocene ad-

I

20

,

,

I

I0

,

I

I

0

20

,

I

I0

,

I

0

Binding Energy (eV) Fig. 38. The incident light polarization dependence of molecular ferrocene adsorbed on Cu(100) and Ag(100). The photoelectrons were collected normal to the surface, s-Polarized light is with an incidence angle of 34 ~ , while p-polarized light is with an incidence angle of 70 ~ . Adapted from [457].

sorption on Cu(100), while the molecular axis is normal to the surface for ferrocene adsorption on Ag(100). These postulated differences in bonding orientation have been confirmed by independent measurements. Scanning tunneling microscopy images, as shown in Figure 39, show that ferrocene does indeed adsorb with a bonding orientation that places the molecular axis parallel to the Cu(100) surface [457]. HREELS measurements show strong dipolar a2u vibrational modes in specular scattering but not in off-specular scattering for ferrocene molecularly adsorbed on Ag(100) [457,459,460]. In particular, the two dipole active modes Vas(M(Cp)2) and 7r(CH), at 60.4 and 93.2 meV, respectively, are observed with great intensity only in the dipole scattering geometry (specular scattering) as seen in Figure 40. This observation is consistent with the bonding orientation in which the ferrocene molecule adsorbs with its molecular axis normal to the Ag(100) surface [457,459, 460], as indicated in the inset to Figure 38. While angle-resolved photoemission places the ferrocene Cp-Fe-Cp molecular axis parallel with the surface on Cu(100) [457] and Mo(112) [458], with a very strong azimuthal often-

90

DOWBEN ET AL. results were initially taken to suggest that the nickelocene was tilted away from the surface normal [465], like cobaltocene on Cu(111) [466] and nickelocene on Si(111) [467]. More detailed studies suggest that there are two adsorption states [468] for nickelocene on Ag(100)ma low coverage state consistent with HREELS and a high coverage state consistent with the angleresolved photoemission. The initial adsorption of nickelocene on Ni(100) [463], NiO(100)/Ni(100) [463], and initial cobaltocene adsorption on Cu(111) [466] appears to be dissociative, thus complicating assignment of the molecular bonding configuration of metallocenes on these surfaces.

21. PHTHALOCYANINES AND PORPHYRINS

Fig. 39. A constant-current STM image (4 nm by 4 nm) of ferrocene molecules adsorbed on Cu(100) following adsorption at room temperature. The relative orientation of the molecule on the Cu(100) surface is along the (110) direction. Adapted from [457]. ' " "

b~Iz

. . . .

'

. . . .

' . . . .

'

. . . .

' . . . .

'

. . . .

"

I / 60.4 _d

"E

0

50

I00

150 200 250 .'.'500 550 Loss Energy (meV)

400

Fig. 40. HREELS for ferrocene adsorbed on Ag(100) at 110 K. The spectra were taken following 2 langmuirs exposure. Both the specular (A) and offspecular (B, A0 = 9 ~ spectra are shown with the same scale but magnified by 150 as compared to the specular elastic peak. The inset shows the features in the range from 100 to 250 meV. The intensities of the two dipole active modes Vas(M(Cp)2) and zr(CH), at 60.4 and 93.2 meV, respectively, are greatly suppressed in the off-specular geometry while the peaks at 364.5 and 378.7 meV are not. Adapted from [457, 459].

tation for ferrocene on Mo(112) [458], the general bonding orientation for metallocenes is with the molecular axis along the surface normal. This "uptight" orientation has been observed for ferrocene on graphite [461 ] by HREELS, as well as for ferrocene on Ag(100) [457,459,460], though the preferential "upfight" orientation is lost in very thick ferrocene films [457,460]. Similarly, nickelocene is also seen, by HREELS, to adopt the "uptight" orientation with the molecular axis along the surface normal on Ag(100) [462-464]. Angle-resolved photoemission

A quantitative approach to determine molecule orientation from angle-resolved photoemission has been examined, first, for simple molecules adsorbed on crystal surfaces, as indicated by the earlier sections of this review and early reviews [1, 4, 294]. As far as large organic molecules are concerned, the first effort was undertaken by Koch and co-workers [469] in 1983 in determining the molecular orientation of lead-phthalocyanine (Pb-C32H16N8). The angular distribution of the photoelectrons from the uppermost zr band was theoretically analyzed. Although Richardson [470] later reanalyzed the data of Koch and co-workers, both results nonetheless indicated a bonding orientation with fiat configuration on the crystal surface. In the model calculation by Koch and co-workers [469], the initial and final states of the photoemission process were approximated by a single Pz atomic orbital (point emitter model) and a free-electron plane-wave, respectively. Although the challenge was the quantitative analysis of angle-resolved photoemission intensities for a large molecule, the analysis of Permien et al. (Koch and co=workers) [469] was criticized due to the use of a plane-wave for the final state. Richardson [470] later reanalyzed their data by employing a spherical-harmonic expansion for the final state and found better agreement with the experimental results. This theoretical method has been applied to analyze the molecular orientation of absorbed benzene on a Pd(100) surface [394] and pyridine on a Cu(110) surface [439]. In those theoretical approaches, the molecule was treated as a single-point emitter and interference between coherent photoelectron waves emitted from the atoms constituting the molecule was completely neglected. These calculations are too simplified to apply into large and complex organic molecules. As a result, the intensity of the molecular orbitals derived from ARUPS has continually been discussed qualitatively in terms of symmetry analysis because of the difficulties in calculating accurate quantitative descriptions of the photoelectron intensity. The next theoretical development in emission-dependent photoemission intensities from large molecules was realized in the molecular orientation study of thin films of bis(1,2,5thiadiazolo)-p-quinobis(1,3-dithiole) on graphite performed by Hasegawa and co-workers [471] in 1993. Briefly, they applied

BAND STRUCTURE OF MOLECULAR ADSORBATES the independent-atomic-center (IAC) approximation, formulated by Grobman [472], in conjunction with molecular orbital calculations to calculate angular dependent photoemission intensities. The photoelectron intensity In (R) from the nth molecular orbital at the detector position R is expressed as

/n(R) o( IAtnt(R)l 2

91

a)

b) --: ---,8:6 ~

o o

~_~o], [~o] ,8:o

.

~

(15)

where A~ot(R) is the photoelectron wave function at R represented by

IA~'ot(R)l ~ ~ -

Oa CnX a e-iknRa

a Xa

ZY;(R)MLXa L

-[- Z Z Z obCnXae-iknRb ~ Z Y;'(R) a bCa Xa L Lt l!

x t b ( k n ) G u L (Rb

-

Ra)MLXa

(16)

where Da is the phenomenological damping factor for the photoelectron wave along R from atom a to the surface due to inelastic processes, C Xa n is the nth molecular orbital coefficient

Intensity (normolized)

9

90 ~

qbs=37~ ~=0 ~

Fig. 41. The observed(opencircles) and calculated photoelectronangulardistributions for the HOMO band of Cu-phthalocyanine. (a) The tilt angle (/3)dependencies calculated by the SS/MOapproximationare shownfor/3 = 0~ (m), /3 = 6~ (. . . . ), and/3 = 15~ (m- ~). (b) Comparisonbetween the calculated azimuthal angle (q~)dependence for/3 = 0~ and the observed one. Reprinted with permission from [476], copyright 1999,American Institute of Physics.

^

of the Slater-type atomic orbital Xa, Kn (= knR) is the wave vector of a photoelectron, Ra is the position of atom a, R is the unit vector along R, and MLXa represents the matrix element including the phase shift and the radial integral. The l I terms t b (kn) and GL,L ( R b - R a ) are the single-scattering vertex and the free electron propagator, respectively. The first term of Eq. (16) is defined as the independent-atomic-center/molecular orbital (IAC/MO) approximation, where the initial state is expressed by using molecular orbital calculation, the photoelectron wave function is approximated by a coherent sum of the waves emitted from atomic orbitals that build up the molecular orbital (IAC approximation), and the self-scattering due to the residual hole upon the photoemission is taken into account for the final state. Although the independent-atomiccenter/molecular orbital calculations only explain the photoelectron angular distribution reasonably well for large organic molecules [473, 474], an appropriate choice of experimental conditions, such as light polarization and analyzer position, is essential to minimize contributions due to the single/multiple scattering of photoelectrons by surrounding atoms which are completely ignored in the IAC/MO calculation. When the kinetic energy of photoelectrons is relatively low, as in the case of ultraviolet photoemission, the scattering due to surrounding atoms is substantial and cannot be ignored. The second term of Eq. (16) describes the scattering in which the photoelectron waves scattered singly by the atoms surrounding the independent-atomic-center atoms are included in the calculation for the final states. Eq. (16) corresponds to the singlescattering approximation combined with the molecular orbital calculation (SS/MO). Ueno et al. [475] studied the orientation of the metal-free phthalocyanine (H2-C32H16Ns) on the cleaved MoS2 surface by analyzing the photoelectron angular distribution quantitatively with the IAC approximation [471 ]. They found that the observed photoelectron take-off-angle dependence could be explained well by an angular distribution calculated for the "flat"

orientation, i.e., with the molecular plane parallel with the surface. Later, a more detailed investigation was performed by employing LEED in addition to the ARUPS technique in order to determine a full structure of the copper-phthalocyanine (CuC32H16Ns) and the Ha-phthalocyanine monolayer films [476]. The electron take-off angle as well as the azimuthal angle dependencies of the top Jr band intensity (as shown in Figure 41), within the context of the single-scattering approximation/molecular orbital calculation (SS/MO) [471 ], confirmed again that the phthalocyanine molecule lay fiat on the MoS2 surface. Moreover, the azimuthal orientation of the molecules (angle between molecular axis and surface crystal axis of MoS2) was found to be about - 7 ~, - 3 7 ~, and - 6 7 ~ with respect to the three equivalent surface crystal axes of the MoS2, as indicated in Figure 42. From the LEED measurements, it was determined that the molecules form a square lattice with the lattice constant of 13.7 /k [476], again as indicated in Figure 42. These results for copper-phthalocyanine are consistent with scanning tunneling microscopy studies which have imaged copper-phthalocyanine on Cu(100) and Si(111) [477], in a packing arrangement much like that shown in Figure 42a. Both copper-phthalocyanine and cobalt-phthalocyanine have been imaged on Au(111) as well [478]. The orientation of molecules in ultrathin films (0.5 to 5 monolayers) of chloroaluminum phthalocyanine (C1A1Pc) on MoS2 has been studied by ARUPS and LEED together with Penning ionization electron spectroscopy or metastable quenching spectroscopy (MQS) [479]. In Penning ionization electron spectroscopy, or MQS, the kinetic energy of electrons (like photoelectrons) ejected from the target molecule as a result of collisions with helium metastable atoms is analyzed. Since the metastable atoms do not penetrate into inner molecular layers, only the outermost surface layer or electron orbital can be distinctively probed. For the C1A1Pc molecule, the C1 atom bonded to the center A1 atom of the phthalocyanine ring pro-

92

DOWBEN ET AL.

(o) --70

[ll~_o], ,B~lo],

(b) Bl~O], _37o, ,[~lol

1

}.21,.o]

9

9

oOo

9

9

9,

(c)

-6r,!.... "1.

I

I-e-

9

9

-le

Dl~o], A[l~lo],

9

ol

9

9

13.r~,

9 -..:

9

13.7A

Fig. 42. The experimentally determined three possibilities for the surface structures of Cu-phthalocyanine and H2-phthalocyanine monolayers on MoS2. The molecular structures are shown with molecular van der Waals radii. The arrows indicate the surface crystal axes of MoS2 and the black points indicate surface sulfur atoms. Azimuthal orientations of the molecule are - 7 ~ , - 3 7 ~, and - 6 7 ~ for (a), (b), and (c), respectively. The overlap of van der Waals radius between neighboring molecules is indicated by shaded area. The structure (a) gives the smallest van der Waals overlap. Adapted from [476].

trudes from the phthalocyanine ring. A change in the molecular orientation due to thermal annealing was observed. At 1 monolayer equivalence of the C1A1Pc deposited at room temperature, islands are formed on the substrate surface with the C1 atoms in an "up and down" mixed configuration. Upon annealing the overlayer film up to 100~ a uniform monolayer of the C1A1Pc is formed where the molecules are oriented flat to the substrate with the majority of the C1 atoms protruding outside the monolayer film surface. Moreover, the structure of the film depends upon the film thickness [479]. At 5 monolayers equivalent, the A1C1Pc molecules are tilted with an inclination angle of about 10 ~ with respect to the substrate. These molecular orientation changes in the C1A1Pc thin films were further characterized by low-energy electron transmission spectroscopy [480]. The C1A1Pc deposited on HOPG (highly oriented pyrolytic graphite) surfaces was studied by high-resolution electron energy loss spectroscopy [481]. The C1A1Pc molecules in the as-grown monolayer were found to lie flat on the HOPG surface. The shape of titanyl phthalocyanine (OTiPc) is similar to that of the C1A1Pc, but instead an oxygen atom projects from the phthalocyanine ring. The dependence of film thickness and temperature on the molecular orientation in OTiPc ultrathin films (0.2-3 monolayer equivalents) on graphite was studied by Penning ionization electron spectroscopy/MQS and ultraviolet photoemission [482]. In the submonolayers, the majority of the molecules are oriented fiat on the substrate surface with the oxygen atoms protruding outside the film. When coverage ap-

proaches one monolayer, the number of molecules having the oxygen atom directed toward the substrate increases. By annealing the films, a uniformly oriented monolayer is created in which the OTiPc molecules are oriented with the oxygen atoms directing upward (away from the surface). Different molecular orientations in a monolayer film on two substrate surfaces (graphite and MoS2) were also realized in the investigation performed by Penning ionization electron spectroscopy/MQS [483]. At room temperature, C1A1Pc molecules aggregate and form islands on the MoS2 surface, whereas the molecules spread out over the surface, wetting and almost covering the graphite surface. ARUPS measurements were used to investigate the molecular orientation of Langmuir-Blodgett (LB) grown films (eight layers) of copper-tetrakis(n-butoxylcarbonyl) phthalocyanine [484]. The photoelectron emission-angle measurements suggested that the phthalocyanine molecules are oriented with the phthalocyanine rings perpendicular to the substrate surface-much different from the results for most phthalocyanines. This conclusion is consistent with the results obtained by polarized UV-visible absorption measurements on the LB grown films [485,486]. The phthalocyanine molecules generally lie flat, with the molecular plane parallel with the surface, on a substrate surface until monolayer coverage is established. A center metal atom is of little influence in determining bonding orientation; the geometrical shape of the molecule largely influences the molecular orientation. In this regard, porphyrins may differ slightly from the phthalocyanines. Evaporated films of zinc 5,10,15,20-tetraphenylporphyrin (ZnTPP) and 5,10,15,20-tetraphenylporphyrin (H2-TPP) on Ag substrates were investigated by polarized NEXAFS/XANES spectroscopy [487,488]. The analysis of the polarization dependence of NEXAFS/XANES peak intensities (the transition from the N Is core level to the zr* LUMO) revealed that ZnTPP molecules in the film deposited on Ag substrates at 367 K have a high degree of orientation with the central macrocylic plane inclined by28 ~ 4- 10 ~ On the other hand, ZnTPP films evaporated on room-temperature substrates and H2-TPP films evaporated on Ag substrates at both room temperature and 367 K showed little polarization dependence which suggests that the molecules in these films are oriented rather more randomly. On the other hand, the porphyrin based Cutetra-3,5-di-tertiary-butyl-phenyl porphyrin seems to lie with the molecular plane parallel with the Cu(100) surface and the Au(110) surface, with a strong azimuthal orientation along the (010) direction of the Cu(100) surface in scanning tunneling microscopy images [489].

22. LARGE AROMATIC HYDROCARBONS AND ORGANIC SPECIES

In many respects the large aromatic compounds behave much like their pyridene and benzene building blocks. It is common for the planar molecules to lie "flat" with the molecular plane

BAND STRUCTURE OF MOLECULAR ADSORBATES parallel with the surface. The long chain organics are frequently dominated by the end groups. The large organics like 17,19hexatriacondieyne [490] as well as smaller species like phenylactyelene [435] and cyclopentadiene [491] are building blocks for larger polymers and in some cases will polymerize on a surface [490, 491 ]. Such molecules are of interest not only for their own sake but also because of the interest in polymers, as discussed later. The bonding orientations of naphthalene and some other aromatic hydrocarbons on Ag(111) and/or Cu(100) substrates were investigated by NEXAFS using synchrotron radiation [492]. By measuring the polarization dependence of the Cls -+ Jr* transition, naphthalene molecules were found to be oriented with an almost flat configuration (a tilt angle of 0 ~ 4- 30 ~ with respect to the Ag(111) substrate surface. Naphthalene-dicarboxylicacid-anhydride (NDCA), which is essentially half a perylene-tetracarboxylicacid-dianhydride (PTCDA) molecule (discussed later), was investigated on clean and oxygen p(2 x 2) precovered Ni(111) surfaces by NEXAFS [493, 494]. On clean Ni(111), NDCA lies flat on the surface and bonds via the naphthalene zr system, whereas on the Oprecovered substrate an upright orientation with bonding via the anhydride group is observed. The orientation and chemical bonding of big organic adsorbates depend strongly on the properties of the surface. A preferential orientation of anthracene on a metal crystal surface was investigated by both NEXAFS [492] and ARUPS [495]. By measuring the polarization dependence of the Cls --+ Jr* transition in the NEXAFS spectra, flat molecular configurations of anthracene on Ag(111) (a tilt angle of 10 4- 10 ~ and on Cu(100) were concluded. With one more ring, naphthacene (tetracene) exhibits a slightly altered bonding configuration. NEXAFS [492], with a dipole symmetry analysis, concluded that naphthacene molecules orient with a slightly canted (27 4-10 ~ configuration on the Ag( 111 ) surface, but with an upright configuration (87 • 10 ~ on Cu(100). The upright orientation of naphthalene on Cu(100) was also determined by angle-resolved photoemission [496]. Theoretical simulations of the valence band spectrum have been undertaken for oriented thin films of naphthacene [474, 497] and have been compared with the observed data on cleaved HOPG, as seen in Figure 43. The quantitative analysis of the photoelectron take-off angle dependence of the full valence band spectra were simulated completely with not only the experimental peak binding energies but also photoemission intensities in agreement with theory. It was determined that the molecular orientation in the thin films (thickness about 24/k) is quite similar to that in the single crystal, when the a - b plane of the naphthacene single crystal is placed parallel to the substrate, hence corresponding to an upright molecular configuration for the overlayer. Almost flat bonding configurations (19 + 10 ~ and 20 4- 10 ~ in perylene thin films were suggested by NEXAFS for Ag(111) and Cu(100) surfaces, respectively [492]. Most recently, the insulating ot-perylene single crystal was studied using NEXAFS and ARUPS techniques [498]. Some compensation techniques

93 '''1

....

I ....

b

I ....

I''

Calculated

~

""N 21 -

o

~ A ~ _ 52.5 ~

.M"

z

.

j ~ # ~ , , ~ # ~ . _ 67.5o

llll

15

I0

5

0

so,'

....

15

1,00,1,,,,I,,

I0

5

0

Binding Energy/eV (Evoc:O) Fig. 43. The comparison between the measured and calculated photoelectron take-off-angle dependencies of the valence band spectra for the naphthacene thin films. (a) The measured spectra after background subtraction. (b) The calculated spectra by the SS/MO approximation. The mean free path of the photoelectron 5.0 ~ was used in the calculation. Adapted from [497].

were used to overcome the influence of sample charging. The spectra, so obtained for ot-perylene single crystals, display several sharp peaks whose intensities strongly depend on the polarization angle of the incident synchrotron radiation. From the angular dependence, an average angle of inclination of the molecular planes relative to the (001) cleavage plane of 85 4- 5 ~ was derived. The PTCDA molecule is "built" around perylene but is different from the perylene molecule in that it contains reactive groups. Since PTCDA was found to form excellent ordered multilayers with high stability [499, 500], it has gained increasing interest as a promising material for organic devices. Ordered adsorbate layers of perylene and PTCDA on various single crystal surfaces, such as A g ( l l l ) , N i ( l l l ) , and Si(111), were studied using NEXAFS [501,502]. The angular dependence of the NEXAFS data reveals that the interaction between the substrate and the adsorbed molecule again plays an important role in determining the molecule orientation. For weak chemisorption or perhaps physisorption, such as PTCDA/Ag(111) and perylene/Si(111), a coplanar adsorption geometry at the interface is achieved through bonding via the molecular 7r-system. This weak interaction of perylene and PTCDA on Si(111) and the planar configuration have been confirmed by angle-resolved photoemission [503]. The planar geometry of PTCDA on Ag(111) is consistent with the STM images and LEED of monolayers on Ag(111) and Ag(110) which also confirm a strong azimuthal orientation dependence [504]. If the bonding at the interface is too strong and involves the reactive group(s), a tilted or bent adsorption geometry may occur, such as for PTCDA on Ni(111) and Si(111). Angleresolved photoemission was carried out for determining molecular orientation of PTCDA thin films on MoS2 [505]. The take-

94

DOWBEN ET AL.

off angle dependence of the photoelectron intensity from the highest Jr band was analyzed with the theoretical SS/MO calculation method (discussed in the section on phthalocyanines and porphyrins), and a flat configuration was concluded for the molecular orientation. Furthermore, new bandgap states due to reaction at the organic/metal interface were observed. The reaction between the molecule and metal atoms was considered to occur at the C=O groups in the molecule [506, 507]. On the Si(111) 7 x 7 surface, both NEXAF and angleresolved photoemission suggest that PTCDA has the molecular plane tilted slightly (perhaps some 20-30 ~) away from the surface [502]. The molecular orientation of naphthalene-tetracarboxylicacid-dianhydride (NTCDA) was also investigated by NEXAFS [508-510]. Some details of the interaction between NTCDA and the substrate can be derived from NEXAFS data. Whereas for Ag substrates the 7r*-resonances attributed to the naphthalene cores are mainly affected by the substrate interaction, the anhydride groups are more involved in the molecular bonding to Cu substrates and even more for Ni substrates. NTCDA monolayers bond strongly to Ag(ll 1) and Cu(100) surfaces via the conjugated zr-system of the naphthalene "molecular core," which leads to a orientation of the molecular plane parallel with respect to the substrate. For larger coverages, however, the interaction between molecule and substrate is negligible, leading to possible misorientation at the higher coverages. The molecular orientation can be altered by varying the substrate temperature during overlayer film preparation: the molecule is observed to be parallel to the substrate at low substrate temperature and perpendicular at higher temperature [509]. The bonding orientation of coronene on Ag(111) is also quite similar to that of perylenema fiat configuration with a tilt of 16 4- 10 ~ [492]. In addition, the core-hole effects in NEXAFS for many of these large aromatic hydrocarbons have been discussed in terms of ab initio molecular calculations [511, 512]. NEXAFS spectra of chrysene, perylene, and coronene were measured and the results were analyzed in detail using ab initio MO calculations. The observed spectra showed a large deviation from the calculated density of unoccupied states, indicating the presence of a large core-hole effect. The observed spectra were simulated well by theoretical calculations that took this effect into account by the improved "virtual orbital" method. ARUPS, infrared reflection absorption (IR-RAS), and X-ray diffraction were applied to p-sexiphenyl to investigate its valence band structure and molecular bonding orientation [513, 514]. It was found by ARUPS, using dipole selection rules to the light incidence angle as indicated in Figure 44, that the molecules in the films evaporated on a heated Ag substrate are highly oriented with the molecular axis/benzene plane parallel to the surface normal. The technique of measuring band structure, as a result of intramolecular periodicity, can be undertaken easily by changing the photon energy. This approach requires long molecules with many repeating units and with the molecular axis oriented along the surface normal [5]. Photoemission from the oriented films

I

!

I

'

I

6P/Ag/Cu hv- 36 eV

(1) (]I)

a)

a:8oo 8:o ~

or) C ::D

d v

0 >,,

b)

or) r(D .4,,,-c I---I

I

20

,

I

I0

,

I

O-E F

Binding Energy (eV) Fig. 44. Photon incidence angle (c~) dependence of normal-emission ARUPS spectra of vacuum-evaporated p-sexiphenyl film on a heated Ag/Cu substrate at 423 K for hv = 36 eV. Each spectrum is normalized by the intensity of secondary electrons. In the insert, molecular orbital patterns of the two HOMOs of benzene are shown [514].

of p-sexiphenyl appear to exhibit wave number (k) conservation (intramolecular energy band dispersion) [514], implying that the wave number k_L along the molecular axis serves as a reasonably good quantum number even in a system of only six repeating units, as indicated in Figure 45. Similar studies of intramolecule energy band mapping were performed for the 7r-band of a urethane-derived polydiacetylene [515]. Ultrathin films of oriented p-sexiphenyl on a GaAs(001) wafer were also studied by angle-resolved photoemission with the intent of obtaining the intramolecular band structure [516], using photons in the energy range between 20 and 60 eV. The thickness of the deposited films played a very important role in the orientation of p-sexiphenyl molecules. For layers having a thickness of about 35 ,~, the molecules were oriented perpendicular to the substrate surface, but for films of about 300 ]k thickness the molecules lost their "uptight" orientation. From the experimental photoelectron spectra, the full one-dimensional valence band structure of oriented p-sexiphenyl layers was determined. While valence states between 2 and 5 eV show only weak dispersion, the bands between 5 and 11 eV show a clear momentum dispersion, which indicates the high degree of order in the investigated sexiphenyl layers. ot-Sexithienyl (6T), also a six-repeating-unit molecule similar to p-sexiphenyl, is a model molecule (an oligomer) of polythiophene, which has potential device applications, for exam-

BAND STRUCTURE OF MOLECULAR ADSORBATES

95

)

% 0

% c) End-on

a=4.3A

%

60

k

/--

50 4O

blEd e-on/

Fig. 46. Schematic view of the three typical orientation models for n-alkane: (a) flat-on orientation, (b) edge-on orientation, and (c) end-on orientation. The zigzag indicates the alkyl-chain axes. Adapted from [526].

> 3O (1)

c

LLI

I, 20

C

0

-~- I0 (~ W

0

I II II

-I0

F-O

I

D

X :0.73 0-I

Wove Number k(A ) Fig. 45. The energy-band dispersion relation E = E(k) in the Brillouin zone along the molecular axis (F-X) for p-sexiphenyl and poly(p-phenylene) with a D2h symmetry (unit-cell constant a = 4.3 ,~). The solid line and filled circles A - G below the vacuum level (E = 0) show the occupied Jr orbitals delocalized over the molecule of poly(p-phenylene) and p-sexiphenyl, respectively, derived from one of the HOMOs of benzene. The broken line (D) shows localized levels derived from the other HOMOs of benzene. Above the vacuum level, free-electron-like final-state bands with a free-electron-like energy dispersion are shown with an inner potential of 5.5 eV [514].

pie, in field-effect transistors [517]. The molecular orientation of evaporated ot-sexithienyl (6T) films on Au, Ag, and Cu were studied by polarized NEXAFS and IR-RAS [518]. It was found that the ot-sexithienyl (6T) molecules on Ag and Cu substrates are highly oriented, with their molecular axis inclined by about 70 ~ with respect to the substrate surface. By way of contrast, the ot-sexithienyl (6T) molecules on Au exhibited only a little polarization dependence, indicating that the molecules are oriented nearly randomly. The orientation of quaterthiophene (4T) molecules, deposited on the Ag(111) surface, was investigated for different film thicknesses [519]. NEXAFS data taken at the S 2p absorption edge for a 4T film show the molecular planes must preferentially be oriented parallel to the substrate surface with

a high degree of orientation for thin layers (3 ML), this orientation order gradually decreases. This is consistent with the Fourier transform IR-RAS results on Ag(111) [520]. A series of end-capped oligothiophene (ECnT) monolayers with different chain lengths n (n = 3-6) were vapor deposited onto the Ag(111) surface and found to form highly ordered superstructures with flat-lying molecules [521,522] by using LEED and STM. However, the absence of angle-resolved photoemission and NEXAFS work on such systems leaves many issues open for future research. Molecular orientation changes upon a thin film solid-liquid transition were investigated by polarized NEXAFS in pentacontane (n-CH3(CH2)48CH3) film evaporated on Cu substrate [523,524]. The low vapor pressure of the long-chain n-alkane, in the liquid phase, permits such measurements to be performed under UHV conditions. At room temperature (as deposited), the pentacontane molecules appear to be placed in an almost fiat configuration with respect to the substrate surface. With increasing temperature, the molecules gradually reorient upright, and, at an elevated temperature just below the bulk melting point of pentacontane, the molecular axis is oriented almost perpendicular to the substrate surface. At the bulk melting point, this ordered structure is still preserved. However, at temperatures well above the bulk melting point (in the liquid phase), the molecular orientation becomes quite random. Upon cooling, the film surface is first crystallized and then bulk crystallization followed. In the (re)crystallized film, the molecules remain oriented in the upright configuration and this is maintained down to room temperature. The long-chain alkane tetratetracontane (n-C44H90) has been studied by LEED combined with ARUPS on Cu(100) [525-527] and Au(111) [527]. The observed LEED patterns indicated that the molecules lie with its zigzag chain axis parallel to the (110) direction for both substrates. Two additional possible orientations (schematically indicated in Figure 46) having the - C - C - C plane of the molecule parallel (flat-on) or perpendicular (edge-on) to the substrate surface were examined. These flat-on and edge-on orientations have been realized in n-alkanes investigated by Firment et al. [528] on Pt(111), in nC44H90 on Cu(111) by Dudde et al. [529], and on Au, Ag, and

96

DOWBEN ET AL.

TTC/Cu(IO0) hz/=40 ~ a-70 ~ f"

or)

-I-I

t'"

hu E ! A # " ~ , , ~ ,d.J

e-

0 68" 65 ~ 600

.m

C =3

v

0

50 ~

or) C (D

40 ~

,..II---

c

I---4

C

o

30 ~

or) . U) ,.,._

E

W

20 ~

I0 ~

OO

25 20 15 I0 5 Binding Energy (vs. E v o c ) ( e V ) Fig. 47. Take-off-angle0 dependence of the ARUPS spectra for an ultrathin film of tetratetrapentacontane on Cu (100). Adapted from [526].

Pb substrates by Seki et al. [530]. By comparing the measured take-off-angle dependence of the photoemission spectra (Figure 47) with theoretical calculations (Figure 48), it was concluded that the tetratetrapentacontane molecules are oriented in the flat-on configuration with respect to the substrate surface. Intramolecular energy band dispersion was also observed in tetratetracontane, as observed by angle-resolved photoemission, from the emission angle dependence of the binding energies in angle-resolved photoemission, as indicated in Figure 47. The dispersion is substantial in these long alkyl chain compounds [531-533], as indicated in Figure 49. The observation of such dispersion from the emission dependence is also consistent with orientation of the molecules in the flat-on configuration. The linear hexatriaconate and Cd-arachidate, like the long chain 1-octanethiol, are oriented normal to the surface of Ag(111) [532]. Intramolecular band structure down the chain of hexatriaconate on Ag(111) (as shown in Figure 50) as well as that for mercaptan-22 (22-alkane thiol) on A g ( l l l ) and Au(111) have been (again) obtained from the dispersion with changing photon energy (k• at normal emission [532], which

is made possible by the upright configuration of the adsorbed molecules. The shift in the critical points of the band structure suggests that the alkane thiol is tilted about 15 ~ off the surface normal [532]. The long chain 1-octanethiol, on the other hand, is seen by standing wave X-ray scattering and NEXAFS to be oriented along the Cu(111) [534] normal like the smaller thiolates. Bis(1, 2, 5-thiadiazole)-p-quinbis(1,3-dithiole)(C4 H4 $6 N4) (BTQBT) is another planar organic molecule, as schematically shown in Figure 51. This planar molecule is a novel singlecomponent organic semiconductor [535], and thus its electronic structure of such molecules is of great importance (particularly since a transistor based on a thiophene oligomer has been fabricated [536]). The resistivity of a single crystal is remarkably low (1.2 x 103 f2 cm) and also shows a Hall effect, which is rarely observable in organic semiconductors [537]. Photoemission studies [538] of the electronic structure of BTQBT indicated that there is only a small energy difference of 0.3 eV between the Fermi level and the top of the valence band, and this is considered to be part of the origin of the high conductivity in BTQBT. The strong intermolecular interaction of BTQBT has been investigated by ARUPS [539], by probing the photon energy dependence, as seen in Figure 52. Intermolecular energy band dispersion (as opposed to the intramolecular band dispersion just discussed) in a single-component organic molecular crystal was observed for the highest occupied molecular orbital (HOMO) and the next highest occupied molecular orbital (NHOMO) 7r bands [539], as indicated in Figure 53. The total HOMO bandwidth of 0.4 eV was obtained for the dispersion along the perpendicular direction from one plane of molecules to the next (as indicated in Figure 51). In the context of all the previous discussion, this is extraordinarily large for organic solids and explains the large hole mobility of 4 cm2/V s observed in this material. This extramolecular band structure should be compared with the extensive band structure observed for the one-dimensional organic conductor tetrathiafuvalene-tetracyanoquinodimethane discussed in the next section. The photoemission angular dependence of BTQBT thin films was measured by Hasegawa et al. [471] to investigate the molecular orientation on a HOPG substrate surface. The photoemission angular distribution was analyzed [471] with the IAC/MO approximation (discussed in the previous section on phthalocyanines and porphyrins). From this comparison of experiment with theory, it is concluded that the BTQBT molecules in the thin film ('~30 A thickness) lie nearly flat (inclination angle ~ 101~ cm -2 [164, 165] (BEN). Typically, for comparison, manual abrasion can achieve a nucleation density of ,~107 cm -2 [165]. The bias applied to the substrate is usually negative DC of --~200 V magnitude, with respect to an anode (which in many cases is the grounded CVD chamber walls). The advantage of the process is that it allows the user to nucleate diamond without mechanically damaging the substrate, as is the case for manual abrasion, for example. In principle, conventional methods described in earlier sections can be used to grow textured or oriented diamond films. Among them the MPCVD technique [ 166-168] is generally used because of the presence of ions and the ability to control the bias between the substrate and the plasma at relatively high pressure. The HFCVD technique is also used by several researchers for bias enhanced nucleation and growth of oriented diamond films on different substrates [ 169-173]. BEN is generally carried out under similar conditions to diamond CVD, but prior to the deposition. Typically, an enriched carbon feed is used, often ,~2-5% CH4/H2 [164, 165, 174, 175], but sometimes as high as 15% [176, 177]. Other studies found it beneficial to instead use a prebias carburization step, where a short period (~ 1 hour) of CVD diamond growth was carried out on the otherwise untreated wafer under comparatively CH4 rich conditions (2-5%), before application of the bias voltage [ 178, 179]. The diamond crystallites nucleated during BEN are sometimes oriented with the texture of the SiC layer, and hence the Si wafer underneath [178-180]. This causes diamond crystals formed during BEN to align with the crystallographic planes of the Si substrate, allowing growth of oriented diamond particles and films. Oriented, polycrystalline diamond films have one particular crystal facet parallel to the substrate surface and hence can be made very smooth. This would be beneficial for many applications of CVD diamond technology as it allows growth of smooth diamond surfaces (optics applications), or heteroepitaxial single crystal growth (microelectronics applications).

2.2.4.6. Nanocrystalline Diamond Deposition In general surface scratching or substrate biasing are applied for nucleation of diamond on nondiamond substrates. The first method produces normally randomly oriented diamond films with high surface roughness. The second method though could produce oriented smooth diamond films, but in both cases the

films are comprised of micron-sized crystallites and sizes increase with the increase of the thickness of the coatings. A thick diamond films therefore has a low density of grain boundary and a rough surface. This is because of the columnar nature of growth by the CVD method. If it is possible to interrupt the grain growth process by a continuous secondary nucleation process, diamond films with decreased grain size should be formed [181]. It is well known that the grain size of a film strongly affects its properties; this can be attributed to the grain boundary density [ 182]. Nanocrystalline diamond films with high grain boundary density have attracted enormous interest due their to fascinating mechanical, electrical, and optical properties [ 183]. Due to the negative electron affinity diamond is an optimum candidate for field electron emission (FEE), which has potential applications in areas such as flat panel displays and microelectronic devices [184]. Reduction in grain size may increase the conducting pathways; it is possible to improve diamond FEE by depositing size controlled diamond films. Several articles relating growth and characterization of nanodiamond have been published [ 185], but control growth for specific applications needs more careful research on this important material. Gruen et al. reported the nucleation and growth of nanocrystalline diamond film on scratched Si (100) from Ha/Ar plasma using fullerenes as carbon precursors [ 186, 187]. With the addition of N2 in the precursor gases a nanocrystalline phase of diamond can be produced [188]. Schaller et al. described the surface properties of nanodiamond films deposited by electrophoresis on flat Si (001) using nanometersized diamond particles. Gu and Jiang [181] developed a new method to synthesize nanocrystalline diamond films. In their MPCVD reactor a negative bias is applied for initial nucleation and films are grown with bombardment of H + ion of different energies. Scanning electron microscopy (SEM) and Raman spectroscopy reveal the signature of nanophase diamond in their growth technique. Field emission properties of nanocrystalline diamond have been studied by many authors who observed a threshold as low as ,

Observed Raman Bands in CVD Diamond Films

~e

Position (cm- 1)

eigN

v.-

(a) r 0 4 ,-,-~ (N O4r

FWHM (cm- 1)

Assignments

Modes

1130-1160

30-60

a-diamond

1180-1250

70-130

Diamond polytypes

1330-1340

4-15

Cubic diamond

T2g

1340-1380

120-200

Graphitic band D

Eg

1430-1540

70-130

Mixed phase

1550-1600

130-200

Graphite band G

O

c

m

o~162162 B

==

(b)

9I~i-

~.-

_

.

.

i

,

4Q

.

.

.

I

.

.....

o

~.~_

~

........

65

=

i A k t

,

1

90

_

!

_

115

I

_,

140

Fig. 18. Typical XRD patterns for diamond films with (a) {100} facets; and (b) {111 } facets on the surface. Reproduced with permission from [238], Noyes Publishing.

120 ~

'

'

"--"

'

'

"

'

'

'

r

9

I

80

4O

~ 2

" J

41

42

,,,

,

I

I

43

44

,

I

45

=

I

46

20 ( d e g r e e s )

Fig. 19. High resolution XRD pattern in the region of the (111) reflection of diamond phase. Note that the width of the diffraction peak for the 100 Torr sample (b) is more than that of the 20 Torr sample (a) grown in the HFCVD chamber. Reproduced with permission from [84].

spectrum of diamond is distinct from that of graphite, which appears at 1581 cm -1, known as the graphitic G-band (Raman active mode is Ezg). The value of the Raman scattering coefficient for diamond (6 • 10 -7 cm -1 sr -1) is "--50 times less than that for graphite (307 x 10 -7 cm -1 sr -1) [240]. Thus even a very small concentration of the sp 2 phase can be easily detected using Raman spectroscopy.

The presence of disorder or small crystallite size gives rise to a Raman peak at 1355 cm -1, known as the graphitic Dband. In CVD diamond the position of the graphitic G-band appears at slightly lower wave numbers than the actual position (1581 cm -1 ) observed for highly oriented pyrolytic graphite. In highly disordered graphitic carbons, which may contain tetrahedrally as well as trigonally bound C (sp 3 and sp 2 hybridization, respectively), the width, position, and relative position of the Dand G-bands can vary significantly. It has been established that the particle size of microcrystalline graphite can be calculated from the intensity ratio of the D-band and G-band [241 ]. In many diamond films, one observes not only a sharp diamond peak at 1332 cm -1 but also a broad band centered at 1500 cm -1, commonly known as the band due to nondiamond carbon. The broad band is a superposition of the G-band, D-band, and mixed band (M-band). The position and intensity of this band depends on the deposition conditions and the wavelength of the exciting photon [247]. Though origin of the M-band is not clearly understood, the most commonly accepted assignment is that it is due to the highly disordered C phase (diamond like carbon), consisting of sp 3 and sp 2 hybridized carbon. Nanocrystalline (crystallite sizes of 1-100 nm) diamond samples show additional features including a broad peak centered at 1133 cm -1. The peak arises from the effects of small size or disorder in the tetrahedral carbon network similar to the explanation suggested for the microcrystalline graphitic peak at 1355 cm -1. Raman active bands for various diamond polytypes have also been predicted theoretically and their presence has been confirmed in CVD diamond [242]. Laser Raman spectroscopy is also useful in determining the presence of sp 3 bonded clusters in the presence of an amorphous carbon background. This is particularly important for so-called amorphic diamond films. These are hard carbon films which contain a high proportion of sp3-bonded carbon and may be said to exhibit short-range order but no long-range order. Compared to diamondlike films, which can contain up to 30% hydrogen, amorphic diamond films contain very little, or no, hydrogen. Raman spectra of laser ablated amorphic diamond films generally show a broad band centered at ~1500 cm -1 with a large tail towards lower wave numbers. This should be contrasted with the Raman spectrum from DLC, which typically displays a band peaking at around 1555 cm -1.

SUPERHARD COATINGS I

J

.....

(

......

'

'

l

....... ,

'

"]

'

I. 20 Torr 2. 40 Torr ~.

"~.

|

~

6.140

I

J

Torr

.1~ I,.

i

.

I Ci

X

Jr'

!

I

tl

I I

--

rtl

" I~ I~

"

I

....

I

,

1 .......

1400 Raman

I

,

1600 shift

t e"

'1

,

A

-oo

1200

,

il

3. 60 T o r r [ 4. 80 T o r r J 5.120 Torr

| ~

135

"

I

1800

( c r n -~)

Fig. 20. Typical Raman spectra recorded on the sheets grown at different pressures with 0.8% CH4 in balance H 2 and Ts = 890~ All the spectra show the characteristic Raman line at 1332 cm-1 corresponding to crystalline diamond. Spectra also show a broad band around 1500 cm-1 assigned to the nondiamond phase of carbon. Reproduced with permission from [84].

Broadening of the 1332 cm -1 diamond Raman line has been reported by many authors [243-245], which was earlier assigned to strains. Ager et al. [246] have carried out detailed Raman investigations of CVD diamond films and found a symmetric broadening and blue shift of the 1332 cm - i line which could not be accounted for using the Gaussian confinement model [246]. Hence scattering from defects and compressive strains were invoked to explain the observed behavior. Although there have been some studies on nanocrystalline diamond, lineshape analysis of the Raman spectrum of nanocrystalline diamond coexisting with a-C has not been carried out. Laser Raman spectra are normally recorded in the range 1000-1700 cm -1 with a step size of 2 cm -1. To resolve the fine structure of the Raman diamond line, in the range 12801380 cm -1, a step size of 0.5 cm -1 can be used. An Ar + laser (7~ = 488 nm) with 50 mW power was used for recording the spectra shown in Figure 20 [84]. A sharp Raman line at 1332.5 cm -1 is observed in all the sheets grown at different Pd in HFCVD chamber [84]. This implies that all the sheets contain crystalline diamond [241,245]. A broad band corresponding to the nondiamond impurities [246] also appears at around 1500 cm-1 in the sheets. The nondiamond carbon components in the sheets increase systematically with the increase in Pd in the HFCVD chamber. Fitting of the spectra can be done with three Gaussian peaks and one Lorentzian peak in order to identify the different phases of carbon that exist in the sheets. Two typical fitted Raman spectra are shown in Figure 21 and they consist of D (crystalline diamond), graphitic D-band, M (mixed phase of sp 3 and sp 2 hybridized carbon), and graphitic G-band phases [84]. An increase of nondiamond carbon in the

1200

I

I

t

m

i

'

,, '

A--,,;

1400

: I

1600

I")

I

1800

Raman shift ( crrr i ) Fig. 21. Typical deconvoluted Raman spectra; (a) sheet grown at 20 Torr and (b) sheet grown at 120 Torr. Reproduced with permission from [84].

sheets with P d can be explained with the rate of etching and growth of sp 2 and sp 3 bonded carbon in the CVD environment. Atomic H is known to desorp H from the growing surface and stabilize a s p 3 precursor for further growth. Therefore, a continuous and sufficient supply of impingement flux density of atomic hydrogen (IFDH) on the growing surface is required in the CVD process for depositing diamond. Insufficient IFDH will leave a few C--H bonds intact and hence hydrogen may get incorporated in the diamond lattice. Inside the diamond lattice, the termination of the sp 3 carbon bond with H may give rise to the sp 2 bonding in the surrounding environment. This implies that the bonded H in the diamond films, which is a result of insufficient IFDH, will give rise to more hydrogenated carbon impurities. In the HFCVD process the dissociation of H2 into H atoms takes place in the vicinity of the hot filament. The recombination of H atoms occurs during their movement toward the substrate. The recombination rate will increase as the mean free path of H atoms decreases with increase in Pd. This will result in lower IFDH at higher Pd and higher nondiamond carbon as well as higher H concentrations in the sheets. This hypothesis, although a simplified picture of a complex situation, can be used to explain the well-observed correlation between the H content and the nondiamond carbon impurities reported by several groups [199, 248,249]. Wagner et al. [247] used resonant Raman scattering to study the incorporation of sp 2 bonded carbon in polycrystalline diamond films. They found that the broad band at 1500 cm -1 corresponding to the a-C phase is shifted to a higher wave number side with the increase of incident photon energy. This shift was interpreted in terms of scattering from Jr bonded carbon clusters which is resonantly enhanced for photon energies approaching the Jr* resonance of sp 2 bonded carbon. At the same time no shift was observed in the Raman diamond line. Robertson and O'Reilly [250] have shown that the most stable

136

SIKDER AND KUMAR

configuration of sp2 sites is in the form of clusters of fused sixfold rings. It is likely that in the HFCVD chamber at high P d deposited films graphitic inclusions are present in large concentrations as proposed by Robertson and O'Reilly. Knight and White [241] also pointed out that the graphitic carbon in the diamond films has the smallest particle size and is the most disordered form of carbon in diamond flms. Figure 22 shows that the linewidth of the diamond Raman line is high in the sheets grown at higher Pd in HFCVD chamber. Further it can be seen from Figure 22 that the diamond line is symmetric for low pressure grown samples, while for high pressure samples it has marked asymmetry on the low frequency side. As expected the FWHM values of diamond lines of low pressure deposited sheets are higher than those of natural diamond. This may be related to the scattering of phonons at defects, impurities, and grain boundaries in CVD diamond. It is well established that Raman lines associated with an optical phonon in a small particle can exhibit asymmetric broadening [251, 252] similar to that found in the high Pd deposited sheets. The asymmetry arises because of the contribution of phonons away from the Brillouin-zone center to the Raman scattering process. This happens because of the relaxation of the q = 0 selection rule in the case of a small particle. Richter [251 ] proposed a Gaussian confinement model for the calculation of confined-phonon lineshape and evaluated the effect of particle size on the linewidth of nanocrystalline Si. A Gaussian confinement model alone could not define the asymmetry of the Raman line observed by Arora et al. [239]. An alternative discrete phonon confinement model by Arora et al. has also been proposed to explain the observed asymmetry of the diamond Raman line [239].

z

I

'l'"

i

'

I

t

t

I

I

I

i

t

J

i

Oq

10 Torr .~

20 Torr ~ ' ~ ~ . / ~

.~

60

~

~

I I

80

J 140 Torr ~ ~ ~ ~ /

I

I

, I

1280

~

~ I

I

~ I

1330 Raman

I

I

.]

1380

s h i f t (Cm -l)

Fig. 22. Raman spectra in the region of 1300-1365 cm-1, recorded with a step size of 0.5 cm -1 of the diamond sheets grown at different P d in the HFCVD chamber. Reproduced with permission from [84].

2.3.6. Fourier Transform Infrared Spectroscopy (FTIR) IR spectroscopy is based on inelastic molecular light-scattering arising from the interaction of photons with lattice vibrations or phonons. The selection rule for IR active vibration modes is that the vibration produces a finite change in the existing dipole moment, as opposed to the change of polarizability for Raman active vibration modes. An IR spectrum can be measured either by dispersive or interferometric methods [253, 254]. The dispersive method involves dispersing radiation from an incoherent source via a prism or grating, which requires monochromator entrance and exit slits. FTIR samples all the frequencies of radiation from the source using an interferometric method resulting in improved signal-to-noise ratios. Measurements of the concentration of H atoms in diamond films have been carried out by various groups [255-257] and elastic recoil detection analysis (ERDA), nuclear reaction analysis (NRA), nuclear magnetic resonance (NMR), and infrared spectroscopy (IR) techniques have been used for this purpose. However, the concentrations obtained by various techniques do not show good agreement. Hydrogen concentration as measured using NMR is generally much lower than that obtained in IR techniques [257]. ERDA and NRA measurements of H concentration also show similar results, i.e., higher concentration than from NMR studies. Recent ERDA experiments [256] have indicated that the H content near the substrate/film, interface may be significantly higher than the front surface of the films. ERDA is a nondestructive analytical nuclear technique widely used for the identification and depth profiling of light elements in thin films [258]. Highly transparent diamond films with smooth surfaces are extremely desirable for optical applications due to their excellent optical transmission from the far IR to UV region of the electromagnetic spectrum. This property makes it an ideal material for IR windows and optical coatings. Polycrystalline diamond, however, contains grain boundaries and defects which are not present in single crystal stones. The defects usually occur due to the impurities present which can cause absorption in the regions of interest. The impurities include hydrogen, oxygen, nitrogen, etc. FTIR is an extremely powerful analytical technique for both qualitative and quantitative analysis. It is a nondestructive, simple, and quicker technique for analyzing hydrogen in CVD diamond. FTIR can also be used to identify specific hydrocarbon groups responsible for absorption. CVD diamond, for IR window applications, requires low absorption in the range 2-12/zm. Increased absorption in this region is associated with a similar increase in absorption in the CH-stretch region which indicates an increase in hydrogen concentration in the films. Even a small concentration of H ( 5.5 eV ( 3000 A, thick delaminate after some period of time in air, while films > 5000 A thick delaminate during deposition [516]. Delamination of the films from substrates occurs more severely in the presence of a high-humidity environment. It has been suggested that water may react with BN at the interfacial soft BN layer and change the volume while making the end product (B203)2(OH) at the interface [499]. This plays a major role in the poor adhesion along with the large compressive stress. This problem of delamination is also normally substrate independent [470, 520], except diamond substrate [470].

I

1 O0

,

I 120

,

0 140

Displacement (rim) Fig. 49. Nanoindentation loading/unloading curve for (a) 700 nm thick cBN film and (b) bulk cBN. Reproduced with permission from [517], copyright 1997, American Institute of Physics.

The adhesion problems come due to the interfacial soft layer and the high compressive stress in the films. Using an intermediate layer (buffer layer) in between film and substrate has been proven to enhance the adhesion manyfold. Using a boron layer and a graded BNx layer prior to the cBN layer can improve the film's adhesion with the substrate [441]. Inagawa et al. [516] investigated a number of graded layers consisting of BxNxZl-x-y (where Z = C, Si, Ge, A1, Fe, Ti, and Cr) toward the improvement of adhesion. They could deposit cBN films of 1.5/zm using Bx Nx Sil_x_y interlayers. Several other buffer layers have been used to improve the adhesion and quality of the films [421,521-523]. 3. 7. 4. Ion Energy in Growth

essential to grow a phase pure cBN layer both homo- and heteroepitaxially.

In order to stabilize the cubic phase over other competitive phases, the importance of ion bombardment of the substrate sur-

SUPERHARD COATINGS face during the deposition has been proven. Though it helps to stabilize the cBN phase, but it also incorporates a large amount of compressive stress, which is the limiting factor for growing a thick cBN layer. In CVD processes using additional gas with the conventional precursors it may be possible to stabilize the cBN phase at lower ion energies. The formation of a cBN phase in the CVD method is via a chemical route [524]. The role of hydrogen, cholorine, and florine in the gas phase is not well studied. Usually substrate biasing guides the species (ions) on the substrate surface and this effectively acts as an ion bombardment. Biasing is found to be related to the H/F ratio in the gas phase. Zhang and Matsumoto [525] found that a critical bias voltage is needed for the formation of cBN in their DC jet plasma CVD method using a gas mixture of Ar--N2--BF3--H2. They also found that fluorine acts as an effective etchant, which can preferentially etch hBN phase, and hydrogen addition is necessary for the formation of solid BN from the gas phase. A critical bias voltage has also been observed for cBN formation and its value decreased as the H/F ratio decreased. Adverse effects of ion bombardment may be avoided by using chemical methods to grow thick cBN films.

3.8. Conclusions Cubic boron nitride can now be deposited by number of physical or chemical vapor deposition techniques. Success in growing cBN films in most of the techniques is dependent on the ion bombardment on the growing surface. Films grown by different techniques contain more than 90% cBN. However, growing cBN at larger areas, thicknesses, and larger grain sizes has not yet been perfected. Deposition of cBN at low pressure and temperature is very much process dependent and has a narrow window in the variation of process parameters. High ion energy, which is being proved to be necessary for the formation of cBN films, is the cause of high intrinsic stress in the films. This again restricts the deposition of thicker films. The following issues need to be discussed in order to improve the growth of cBN films with better perfection: 9 growth of cBN with low energy ion bombardment, 9 relation with substrate temperature and ion bombardment, 9 conversion of graphitic BN into cBN, which might open the window of post-treatments effects, 9 addition of buffer layers suitable to both substrate and cBN, 9 CVD of cBN with the use of catalytic gas in the conventional precursor gases. Lot of different growth mechanisms are being discussed but none of them could describe the deposition of cBN completely. Among them the cylindrical thermal spike model and the nanoarc model may help to explain the growth mechanism completely. Large numbers of characterization tools have been used to investigate the cBN films and the most important of them are the FTIR and TEM analysis. One has to take enough care to avoid the artifacts which may be produced during the measurements. Though few companies are producing the cBN coatings on the tool materials, there are several issues that need

159

to be solved in order to utilize this novel superhard material in thin film form.

4. CARBON NITRIDE THIN FILMS 4.1. Introduction A considerable amount of interest has been generated on producing crystalline carbon nitride since Liu and Cohen [6, 7] predicted a carbon nitride, /3-C3N4, with a structure similar to /3-Si3N4. Study of C3N4 was motivated by an empirical model [8] for the bulk modulus of tetrahedral solids which indicates that short bond lengths and low ionicity are favorable for achieving large bulk moduli. Since the C - N bond satisfies these conditions, tetrahedral C--N solids were suggested by as candidates for new low compressibility solids [7]. According to their calculations it was predicted that zinc-blende C--N compounds would be unstable but/3-C3N4 can have bulk moduli comparable to that of diamond, which has the largest known bulk modulus [7]. Due to a shorter bond, /3-C3N4 may possess extremely high hardness comparable to or greater than that of diamond. These interesting properties attract researchers to synthesize this hypothetical material by means of a variety of techniques. Carbon nitrides with crystalline as well as amorphous microstructures are also of great engineering interest [526, 527] as a potential material for microelectronic devices and for optical, magnetic, and tribological applications [526, 528-533]. The computer hard-disk industry is currently working on achieving an areal density of 100 Gbits/in 2 [534]. To achieve such a density the magnetic spacing (spacing between the magnetic read/write head and and the magnetic recording layer on the disk) has to be less than 10 nm. This only leaves ~ 2 nm for the protective overcoat. Diamondlike carbon or CNx coatings (5-10 nm thick) may be used to improve the tribological performance with improved corrosion resistance (Fig. 50) [535].

Underlayer: CrV (50 nm)

Substrate: NiP/AIMg (10/800 Ilm) 9.s Glass (640 ~tm)

Fig. 50. Schematicof the different hard disk components and their layer thickness. Reproduced with permission from [535], copyright 1999, Institute of Physics.

160

SIKDER AND KUMAR Table XXIII.

Space Group, Lattice Parameters (a and c), Mass Densities p and Bulk Moduli B of the Theoretically Predicted a- and fl-C3N4 Phases

Space group fl-C3N4 Space group a(~)

6.44

6.41

6.37

6.47

6.35

6.40

c (A)

2.47

2.40

2.40

2.45

2.46

2.40

P63/m

P3

P (g cm -3) B (GPa)

P63/m 6.42

6.39 2.40

3.56 427

437

421

450

250

451

557

6.46

a-C3N 4 Space group

P31 c

a (A)

6.35

6.47

c(A)

4.46

4.71

P (g cm -3)

3.78

B (GPa)

189

6.45 4.70 3.61

425

567

Reproduced with permission from [539], copyright 2000, Elsevier Science.

The hardest material known at present is diamond, with a hardness of about 100 GPa, while the second hardest material, cBN, has a hardness of only 50 GPa. Liu and Cohen calculated [536, 537] the properties of the hypothetical compound fl-C3N4 (space group P3), which has a structure similar to tetrahedral fl-Si3N4 (space group P63/m). Because the spZ-sp 3 hybridized bonds between the tetrahedrally bonded C--N are shorter than the bond length of C--C in diamond, it is predicted that the bulk modulus will be larger than diamond. The three-dimensional tetrahedrally bonded structure would thus have a high isotropic hardness. They indicated that the material would have mechanical and thermal properties similar to diamond. On top of that, the strength, hardness, and high corrosion and wear resistance of Si3N4 (which the fl-C3N4 structure has been based on) suggest that the hypothetical C3N4 compound could have improved structural properties. Further calculations have also predicted that C3N4 can exist in two other types of structures, a zinc-blend-like cubic structure (space group P -- 43m) and a graphitelike phase with rhombohedral stacking (space group R3m) [538]. Both the zinc-blend-like and fl-C3N4 phases have similar structures, with each C atom having four N neighbors and each N atom bonded to three C atoms. The angles between the C - N - C bonds, however, are different for both the structures. The bond angle for the zinc-blend structure is close to 109.47 ~ and for flC3N4, 120 ~ The local coordination for this structure is similar to that in the hexagonal phase, except that the N atoms form sp 3 bonds rather than sp 2 bonds. The graphitelike phase consists of holey graphitelike sheets with rhombohedral stacking order (ABCABC...). Each of the C atoms has three N atoms as neighbors (threefold coordinated), as does one of the four N atoms in each unit cell. The other three N atoms are only twofold coordinated, having only two C neighbors with one C atom missing. The interlayer bonding for the sheet structures is expected then to be weak. Tables XXIII and XXIV sum-

marize the structural parameters for different phases of carbon nitride [539]. From the enthalapy-pressure ( H - P ) data it was found that the Willemite and alpha C3N4 phases are the only stable phases. The alpha phase is stable from low pressures up to 81 GPa and the Willemite phase was found to be stable between 81 GPa and the highest simulated pressure (~300 GPa). The transition between the lower pressure alpha phase and the Willemite phase occurs as the pressure-volume term in the enthalpy becomes increasingly important at higher pressures. Since the Willemite structure has a lower volume configuration, at higher pressures the pressure-volume term will be less significant compared to that of the alpha, and above 81 GPa, the enthalpy of Willemite is smaller. The beta and defect zinc-blende phases were found not to be the stable phases throughout the entire pressure range. At higher pressures the Willemite structure is preferred over the defect zinc-blende structure because of the higher energy configuration of the lone pair electrons occuring in defect zinc blende. Since hardness depends on shear modulus, it would need the shear for the alpha phase to make further conclusions about its hardness. The Willemite structure has a bulk modulus higher than the one for diamond but its shear modulus is much lower than that of diamond and therefore its hardness is expected to be much lower. 4.2. Phases of Carbon Nitride There is considerable discussion as to which of the four is the most stable, as well as to the precise values of their bulk moduli. The most recent values are 448, 496, 425, and 437 GPa for the defect zinc blende, cubic, or, and fl forms of C3N4, respectively [540]. These values are similar to, or greater than, that for diamond at 443 GPa. Similarly, the velocity of sound in flC3N4 has been estimated to be high, -~106 cm s -1, meaning that the material should have a high thermal conductivity. The bandgaps of all of the high density C3N4 materials are expected

SUPERHARD COATINGS Table XXIV.

161

Structural Parameters (Space Group, Formula Units/Cell Z, Lattice Constants a, b, c), Mass Densities, and Bulk Moduli of the Theoretically Predicted Cubic, Pseudocubic, and Graphitic C3N 4 Phases

Face centered cubic C3N4 Space group

I43d

I43d

Z

4

4

a(A)

4.67

p (g cm -3)

5.40

B (GPa)

496

3.89

Pseudocubic C3N 4 Space group

P43m

P42m

a (,~,)

3.43

3.42

3.41

425

448

556

P43m

P (g cm -3) B (GPa)

3.42 3.82

c-C3N 4

Space group a(A)

6.87

P (g cm -3)

3.77

B (GPa)

396

Graphitic C3N4 a Space group Lattice

P2mm

Rhombohedral

Z

3

a (/~,)

4.11

b(]k)

2

3

2&l b

4.09

4.37 & 4.11

4.74

c (~,) c~ (o)

P6m2 & R3m

P6m2 P3ml

6.72

P (g cm -3)

410 4.70

6.69 & 4.11 70.5

Orthorhombic 2&l c

3.2 & 6.4

90 & 70.38 2.35 & 2.56

a Stacking orders: AA, AB, or ABC.

bDepends on the space group. CAA and AB stacking.

Reproduced with permission from [539], copyright 2000, Elsevier Science.

to be in the range 3-4 eV. The cohesive energy calculated for all of the C 3 N 4 compounds indicates that they should be, at least, metastable. Furthermore, it is clear that the low-bulk-modulus graphitelike structures are the most stable, and that the other high density forms have similar but lower stabilities.

4.2.1. Alpha Structure According to the data collected, the alpha structure is the most stable of the structures investigated. In theory, this is supported by examining the lone pair interactions present in the structure. It is a trend that less of these interactions serve to lower the energy of the structure, thus increasing the stability. The decrease in these interactions is due to fewer nonplanar NC3 groups present in the alpha structure, hence the lower energy. When examining the hardness of the alpha phase, the modulii approach, but are not greater than, that of diamond. Figure 51 shows the crystal structure of different phases of carbon nitride.

4.2.2. Beta Structure Calculations for the beta structure compare very well with experimental data. fl-Si3N4 is softer than fi-C3N4 because the N - - N bond is longer and therefore there is not so much resistance to compression due to lone pairs (N--N bond changes 18% as opossed to 11% change for C3N4). The coordination tetrahedra are highly deformed at high pressures.

4.2.3. Willemite Structure C3N4 in the Willemite structure has a very high bulk modulus (474 GPa). The structure does not move around too much under hydrostatic compression. This can be seen from the graphs that are included. The bond lengths linearly decrease, and the C - C and N - N atomic distances do as well. The C - C atomic distance, however, decreases faster than the N - N atomic distance. This is probably due to lone pair repulsion. This conclusion can be reached with the aid of the bond angle plot for hydrostatic compression. The C--N--C angles stay the same, but the N-C-N angles decrease with increasing pressure. The two

162

SIKDER AND KUMAR

Fig. 51.

(Continued).

Willemite structure is relatively low (266 GPa). The N - C - N bond angle changes quite a lot compared to the C - N - C bond angle. This suggests that the lone pairs act to help the nitrogen atoms glide over one another, lowering resistance to shear. 4.2.4. Defect Zinc-Blende Structure

Fig. 51. Crystal structure of different phases of carbon nitride: (a) ot-C3N4, (b)/~-C3N 4, (c) cubic-C3N4, (d) pseudocubic C3N4, and (e) graphitic C3N4.

nitrogens are trying to get away from each other due to lone pair repulsion. Keep in mind that this effect is slight and only noticeable at very high pressures. Si3N4 in the Willemite structure has a much lower bulk modulus (266 GPa). The C - C atomic distance decreases under hydrostatic pressure but the N - N distance decreases only slightly and then actually increases, allowing the nitrogen atoms to slide over one another. This has the effect of decreasing the C - N - C bond angle while the N - - C - N bond angle stays constant. Under hydrostatic compression of Si3N4, the C - N - - C bond angle change does not allow as much energy. The shear modulus of C3N4 in the

The C3N4 zinc-blende structure was found to have a bulk modulus of 425.8 GPa and other calculations have determined a value of around 448 GPa. With this variation, the true value is somewhere in the range of diamond (443 GPa). The high bulk modulus of the defect zinc-blende structure is primarily due to strong interactions of the lone pair electrons which are all directed toward one another and strongly resist compression. The shear modulus for the defect zinc-blende structure was significantly lower (159.6 GPa) compared to that of diamond (534.7 GPa). The low shear resistance difference is again due to the presence of the lone pair electrons which move away from each other under a shearing motion, thus reducing their interaction. The deformation of the C3N4 defect zincblende structure is depicted by the bond length and bond angles vs strain/pressure graphs in the various deformation regimes. Since the shear modulus has been found to more accurately represent hardness properties, the defect zinc blende does not appear to have a hardness on the same level as diamond. Furthermore, from the H - P curves, the C3N4 defect zinc blende was shown not to be stable at any pressure; this could prevent the material from being a realistic consideration, unless a processing technique is developed which is capable of capturing the structure in a metastable state.

4.3. Carbon Nitride Synthesis Another sp 3 structure that is of current interest is C3N4. The main attraction to this elusive material is its hardness which was predicted to be comparable to that of diamond. Many methods have been used to synthesize this material and it is found that

SUPERHARD COATINGS carbon nitride is metastable and can exist in various structures. Therefore, carbon in sp 3 and sp 2 form can be found simultaneously in the films. The common observation is that the deposited CNx films are spatially inhomogeneous. Evidence of such structures can only be found on average at a micron scale. Predicted to have mechanical properties similar to diamond, carbon nitride compound has captured the attention of many researchers since 1989. So far, however, there is a little evidence of successful growth of crystalline single phase C3N4. Here we discuss some of the deposition techniques used by many researchers.

4.3.1. High Pressure Pyrolysis and Explosive Shock Attempts have been made [541 ] to synthesize CNx by a combustion of various organic precursors, such as mixtures of tetrazole and its sodium salt, or pyrolysis of polymeric precursors. Similar to diamond synthesis, the resultant materials have been subjected to explosive shock compression to synthesize the required structure. Also a-CN, produced by PECVD, has also been treated with a similar method and triple bonded carbon clusters joined by nitrogen bridging atoms were found. The other starting materials gave a-C, well-ordered diamond crystallites, or, at best, carbon structures with bridging nitrogen bonds [542]. This indicates that a considerable amount of nitrogen loss occurred during the compression stage. In the work of Wixom [543], using shock wave compression technology with nitrogen containing precursor and typical conditions of diamond and boron nitride synthesis, material was produced with low overall nitrogen content which contains some wellordered diamond. In another work [544], synthesis of a new crystalline phase was reported from a mixture of carbon and nitrogen heated to 2000-2500 K at 30 4- 5 GPa. The phase obtained in this work has an X-ray diffraction pattern compatible with cubic symmetry but does not match with theoretically expected patterns for CNx phase [545]. In their work Dymont et al. [546] prepared bulk crystalline CNx phase from a precursor containing carbon, nitrogen, and hydrogen. Precursor was synthesized from a electrochemical process. Syntheses of the CNx phase in block powder form from this precursor were performed at pressures up to 7 GPa and the temperature was varied between 300 and 600 K. X-ray diffraction spectra showed that the precursor is successively changed from completely amorphous carbon-nitride to crystalline carbon-nitride.

4.3.2. Carbon Source with Nitrogen Bombardment Basically this involved the implantation of nitrogen (incident energies of 3-60 eV) into graphite at temperature of 800~ Properties of the films are not very sensitive with the nitrogen arrival or the bias. Evaporation of carbon with nitrogen ion bombardment is another technique to grow CNx [554]. This is a high vacuum technique while substrate temperatures are kept at room temperature. The N/C impingement rate on the substrate surface appeared to be very sensitive for film properties but ion energy has less effect. However, high energy ion bombardment deteriorates the film's mechanical and optical properties. Freeman sources have also been used to generate alternating C and N beams where both ion energies (from 5 to 100 eV) and the relative arrival rates were controlled [548]. Mostly crystallite graphite is observed. The spa C content was measured as a function of the incident ion energy, and two maxima at "-~30 and < 1 eV were seen. Chemical sputtering of the carbon and CN by nitrogen was found to be of great importance. Significantly, bombardment by nitrogen ions with energies greater than "~30 eV was seen to restrain the amount of this element in the deposit. Specifically, nitrogen bombardment was seen to remove deposited material through the formation of CN, with an etch rate of "~0.5 carbon atoms per incident N~- ion. This process was estimated to limit the maximum nitrogen content to N/C ~ 1.86; however, experimental evidence indicates that

164

SIKDER AND KUMAR

the maximum may be closer to 0.67 [555]. Todorov et al. suggested that an additional mechanism involving the promotion of the formation of either molecular nitrogen or the low-boilingpoint compound C2N2 (-26~ may also take place at high nitrogen contents [556]. Kohzaki et al. used electron-beam evaporation of carbon but at a fixed low nitrogen-ion energy of 200 eV and substrate temperatures of 25 %. As nitrogen is increasing in the films, a band located at ,~4-7 eV appears, due to C 2p and N 2p electrons associated to zr bonds in aromatic tings and probably N lone-pair electrons. A band also emerges at 8-12 eV, which is normally associated with C - N and C - C a-states. No structure can be seen in the interval 0-4 eV, which is normally associated with C - C zr bonds due to 2p electrons. 4.4.5. Rutherford Backscattering Spectroscopy

RBS is commonly used to identify elements in thin films or surface layers, to measure the concentrations of the constituents,

and also to estimate the density distribution in depth. This technique involves a sample or target being bombarded with very energetic (in the MeV range) particles and detecting the scattered particles. Due to the high energy of the incident particles, the scattering would involve the nuclei of both the incident ion and the target atom. The energy of the scattered ions or particles carries the compositional, scattering depth, and structural information of the target material, thus identifying the elements present. Some of the high energy incident ions are capable of traveling a certain depth into the target material undergoing inelastic collisions before being scattered. These ions would carry the depth information required for a depth profile determination of any given constituent of the sample. The quantitation of the RBS spectra requires a standard for energy calibration. Using the fitting program RUMP, the calibrated parameters of the standard sample can then be used to quantify the unknown CNx films. Although RBS is capable of 1/zm in lateral resolution, it has poorer depth resolution compared with AES.

4.5. Mechanical and Tribological Properties Although pure crystalline phases of carbon nitride are hardly found so far, mechanical and tribological behaviors of CNx films were studied by many researchers using nanoindentation and friction and wear testing [535, 641-651 ]. Amorphous CNx films show attractive mechanical properties, and they are characterized by high hardness (up to 65 GPa) [652], high eleastic recovery (up to 85%) [652, 653], good adhesion to substrates [654], and low friction coefficient and wear [655]. High hardness, good adhesion, and low friction and wear make this material very important in industrial applications [656]. The magnetic recording industry may switch from hard amorphous carbon films to hard amorphous CNx films simply by substituting argon for nitrogen sputtering gas. Wei et al. [649] deposited fl-C3N4 films on Si and WC cermet substrates by unbalanced magnetron sputtering using a graphite target in an Ar/N2 plasma. Structural analysis was performed using FTIR, XPS, and TEM analytical techniques. The dry friction and wear characteristics at room temperature were determined using a ball-on-disk tribometer. The friction coefficient decreases with higher N/C ratio films. For the films with a N/C ratio of 0.4, the coefficient of friction increased from an initially low value to a higher stable value of about 0.075 (after 1000 rev, i.e., 62.8 m). The friction coefficient of CNx films can be decreased during dry sliding conditions [642]. This is due to the fact that sliding-induced heat may be accumulated on local contact areas and cause a gradual destabilization of C - N bonds in the sp 3 tetrahedral structure. Now removal of N atoms can trigger the transformation of sp 3 structure into a graphitelike sp 2 structure and hence the decrease in friction coefficient. The wear rate of the films decreases with the increase of N/C ratio due to the lower friction coefficient. The nanoindentation technique is also being used to determine the hardness and modulus of the films [657-659]. It is a depth sensing measurement of hardness and modulus of the films. Typical loading/unloading curves obtained for different

SUPERHARD COATINGS 6

5.5: 5: 4.51 z

4

:

:

CNx films (400 W, 1"10 .2 mbar) ----v--0%N2 ' 30%N2 50%N 2 _= .... 100%N 2

,

173

3.5

+, 2.5

E 3.5 O. 31 "o

m 2.51

~ T

o

o .~

1.5

2 1.5 0.5 [3

0.5

0

5.5

~

CN x films (400 W, 1 "10 -2 mbar) .

'l'l' .

.

.

.

'

.

'l'

, . m al-

..

.t

N2/Ar ratio (%)

I .... -175

I .... -150

I .... -125

I .... -100

4 .... -75

I ....

-50

I ....

-25

0

Substrate bias (V)

Fig. 56. Typical load-displacement curves observed in CNx films. Comparison shows that the hardness is reduced with increasing N2 partial pressure applied during films deposition. Reproduced with permission from [657], copyright 1999, American Institute of Physics. Table XXVI.

....

-200

Hardness and Modulus Values of CNx Films Grown at Different Nitrogen Concentrations at.% N 2

p (g/cm 3)

H (GPa)

E (Gpa)

0

0

1.4

16.0

175

30

26

1.2

12.5

130

50

26

1.1

10.0

110

100

33

1.0

9.5

90

Reproduced with permission from [657], copyright 1999, Materials Research Society.

CNx films grown with different N2/Ar concentrations in the gas phase in a magnetron sputtering chamber are shown in Figure 56 [657]. The penetration depth of less than 200 nm out of a film thickness of 800 nm is a good approximation of avoiding the substrate effects. Hardness and modulus values obtained from the analysis of loading/unloading curves are shown in Table XXVI along with other data [657]. Hardness and modulus values are very low in these films due to the low density of the films. 4.6. S o m e Interesting Results on C a r b o n Nitride

Extensive studies on growth and characterization of carbon nitride films were accomplished by Cameron et al. [640, 660663]. In this section we review their work a little elaborately. Films were grown using DC magnetron sputtering using an opposite target Penning-type geometry [657] (discussed in the sputtering section). Graphite of 99.95% purity was used as a target while an Ar/N2 mixture of 99.999% purity with variable mixture was used as sputtering gas. Pressure during deposition was 1 x 10 -3 mbar. Partial pressure was varied from 0 to 100%, keeping the total pressure constant. Films were grown mostly on polished Si substrates. Adhesion of films on tool steel sub-

Fig. 57. Deposition rate of films as a function of substrate bias. Reproduced with permission from [660], copyright 1999, Elsevier Science.

strates was also studied [643]. It was seen that substrate bias and nitrogen partial pressure during the deposition are the two most parameters affecting the film's structural and physical properties [660, 661 ]. The proportion of sp 3 bonding in the deposited CNx films, which is important in the growth of crystalline CN films, can be influenced by controlling the energy of the ions which bombard the substrate during the growth. The mechanisms involved in this ion induced growth process are described by the densification model of Robertson [664] and the induced stress models of Davis [665] and McKenzie et al. [666]. Again sp 3 fraction is normally found maximum in a small window of ion energies (typically 50-250 eV) [660]. Outside this range the sp 3 fraction is reduced due to either the ion energy being too low to cause significant change to the structure or being too high such that the desired bond type is disrupted. Chowdhury et al. investigated the deposition rate, film composition, and structural properties by varying the ion energies by controlling the substrate bias during deposition in sputtering [660]. The most obvious effect of the substrate bias changes was a monotonic decrease in deposition rate as the bias became more negative (Fig. 57). Growth rate declines by approximately a factor of three between 0 and - 2 0 0 V bias. Four different mechanism can cause of this decline: (i) preferential sputtering and a change in the film stoichiometry, (ii) a densification of the film, (iii) reduced target sputtering and (iv) chemical sputtering of the films. RBS measurements on the films do not show significant change in the nitrogen content in the films (Fig. 58). Therefore the first option may not be correct. Although they did not measure the density of the films, it is not not credible that a variation of the scale necessary to account for the thickness changes could occur without a major effect on the other properties, in particular the hardness (Fig. 59). Hence the second option is also not valid. Substrate bias does not change significantly the target potential and hence the sputtering rate would not have changed, which can change the deposition rate. The

174

SIKDER AND KUMAR

50

45

40

35

1

'~

20

10 -200

-150

-100

-50

0

Substrate bias (t/)

Fig. 58. Nitrogen content of films as a function of substrate bias. Reproduced with permission from [660], copyright 1999, Elsevier Science.

11

10

9

8

7

6

,

-200

.

,

,

,!

-150

,

,,

,

,,,

|

,

,

.

-100

,

9

|

-50

0

Substrate bias 0/)

Fig. 59. Hardness of films as a function of substrate bias. Reproduced with permission from [660], copyright 1999, Elsevier Science.

most likely explanation is that the increased nitrogen ion energy at the substrate stimulated a desorption of carbon and nitrogen in the ratio in which they were present in the film [667]. Valence band XPS results on these films at different substrate

biases indicate t h a t sp 3 bonding is increasing in the films during biasing in the range - 7 5 to 150 V [660]. This is might be the reason for the higher hardness values obtained in this range (Figure 59). It might be necessary to study further this biasing range with changing substrate temperatures which they did not change during their experiments (,-325~ It was found from RBS measurements that while the nitrogen content of the sputtering gas is varied from 0 to 100%, the atomic concentration of nitrogen in the films does not vary much once the N2 partial is above 25% (Fig. 60). Structural properties due to the nitrogen partial pressure are being investigated using XPS, ultraviolet photoelectron spectroscopy (UPS), EELS, and EPR studies. Deconvoluted XPS and UPS spectra of the CNx films are shown in Figures 61 and 62. In XPS data, in comparison to the structures of diamond, the large peaks at ,-19 eV binding energy are due to mixed s - p electronic states and the peak at ,-~14 eV to p states. The lower energy peaks are usually due to the cr and zr bonding electrons [668, 669]. Both UPS and XPS showed similar trends as the N2 partial pressure increased from 0 to 100%. At 0% the UPS spectrum shows a main peak at 9.7 eV (tr bonding electron) and three other states due to zr electron states. The larger peak, called 7/'1, at ~8.0 eV is due to the C = C Jr bond in aromatic rings. Others are due to sp bonded carbon atoms (zr2 = 5.5 eV) and lone pair electrons from some residual nitrogen in the films (zr3 = 2.6 eV). XPS also shows similar results in the films with 0% N2. Interesting results were observed in their films with higher N2 partial pressure. In both XPS and UPS results on their 25% N2 spectra show larger zr peaks than cr peaks. This is certainly because of nitrogen induced increase of sp 2 bonding at the expense of the sp 3 bonding [670]. Clearly resolved zr3 peaks, in both UPS and XPS are assigned to lone pair electrons on N atoms which are bonded to C atoms in a nondoping configuration such as C = N [670, 671 ]. A major change in the bonding occurs in the films with 100% N2 in the gas phase, although there has been little change in the total N concentration in the films. Both XPS and UPS spectra indicate the reduction of sp 2 bonding and hence an increase in the sp 3 fraction. This is an important indication of the possible formation of crystalline/5-C3N4 [672]. EELS (Fig. 63) of their same samples confirms the similarity between the 0 and 100% films and the difference of the 25% films which show both a broader Jr-zr* and a much larger zr-tr peak which would indicate a higher density of zr states. Electron paramagnetic resonance (also known as EPR) resuits on a range of CNx films (with different N2 partial pressures) are shown in Figure 64. Spin concentration is initially decreased up to 50% for N2 films and is then increased again. The g-factor also starts decreasing at the 50% level. This result is consistent with the idea [662] of the N bonding to C in a C=N nondoping configuration which has the effect of reducing the unpaired electrons because of the termination of the carbon dangling bonds with nitrogen atoms. An increase in the spin density with higher N2 partial pressure is a indication of changing bonding structure.

SUPERHARD COATINGS

175

0.9 .................

0.8

0.7

0.6 _o o

0.5

E o

0.4

0.3

0.2

0.1

0 v

0

I

I'

10

20

'1

30

I'

I

40

50

........

I

I

I

60

70

80

.......

I

90

'

'

1O0

I~trogen partial pressure (%) Fig. 60. The nitrogen/carbon ratio of carbon nitride films as a function of the nitrogen partial pressure during deposition. Reproduced with permission from [662], copyright 2000, Elsevier Science.

The activation energy calculated for the temperature dependent resistivity measurements on the films grown at different N2 pressures showed that it is increasing with nitrogen content (Fig. 65) [661]. The temperature-dependent resistivity of the highly conducting films (0 at.% of N, p ~ 1 x 10 -2 f2 cm) exhibits only a small variation resistivity in the temperature range. The relatively high conductivity and low gap of the carbon nitride films suggest an electronic structure having a large number of n-type band tail states with a structure which consists mostly of sp 2 hybridized aromatic rings. The increased activation energy and resistivity for nitrogen containing films suggest a reduction of density of states in the mobility gap and perhaps removal of defect states near the conduction band edge [661 ]. In another study [662] structural studies were performed on the CNx films containing different nitrogen at.% percent calculated from the RBS measurement. Figure 66 presents the Raman (a) and IR (b) spectra of CNx films containing different N concentrations. Spectra show several features due to vibrations of bonds between C and N or the same element. The out-of-plane vibrations of C - C at 700 cm -1 are becoming more intense as the nitrogen incorporation in the films increases. This is a indication of nitrogen induced stabilization of C - C bonding [17, 125]. The Raman active D- and G-bands (region 1350-1650 cm -1) are becoming very prominent with increasing nitrogen in the films. Kaufman et al. [673] concluded that nitrogen substitution is responsible for the symmetry breaking of the Ezg mode and intensity of D- and Gbands corresponding to sp 2 hybridization. The band at ,~2200 cm-1 is due to the stretching vibration of C - N bonding, while

at higher wave numbers (,~2900 cm -1) C - H stretching band is observed. The presence of this stretching band is due to residual water vapor in the chamber during deposition [663]. The E2g symmetry mode become IR active due to nitrogen incorporation. Unlike Raman spectra D- and G-band overlaps in IR spectra, the C = N stretching band at ~2200 cm -1 in IR spectra is much stronger than Raman. The N2 molecule is not IR or Raman active as it has neither net dipole moment nor a change in polarizability during the vibration. But it can be Raman/IR active while it replaces carbon atoms from the six-fold carbon ring. The formation of a N--N stretching band is unlikely here, as there is no evidence of absorption at 1150-1030 cm -1. As nitrogen incorporation increases in CN compounds, the E2g symmetry mode becomes more and more IR and Raman active. Increase in intensity of the 1350-1650 cm -1 band region is caused by the Raman active in-plane or out-of-plane N = N stretching vibration due to excess nitrogen incorporation. This N = N band overlaps with the C = N stretching band. It was also shown that over the range 25-44 at.% N there is no systematic variation of the IR absorption coefficient. This is an indication of bonding of N with N instead of C. A close looking of the Raman spectra in the region 1100-1800 cm -1 indicate a new feature in between D- and G-bands. This new peak is being assigned by N band (1400-1500 cm-1). Weich et al. [674] also derived the possibility of the formation of nitrogen-nitrogen bonding within the CN compound. This was also supported by the fact that the growth continues to increase for films with higher nitrogen content.

176

SIKDER AND KUMAR

3O

J3.0 a ~ a m e W

c

I.O

)

(a)

l

. . . .

)D.D

I 24.0

I

l

UI.O a~sdi~

I

1.2 .D

6. o

~tn'glr C~)

(b)

I

I

I

30.0

21.D

J.II.:

-

I

k2.D

I

-

" - ' ' ~

6. D

Xmerqly t ~ )

(c) Fig. 61. Valence band XPS spectra resolved into Gaussian peaks: (a) 0%, (b) 25%, and (c) 100% N2 partial pressure. Reproduced with permission from [662], copyright 2000, Elsevier Science.

SUPERHARD COATINGS

1.6.O

t2. O

e.O aLnd~.nq nn~rgV, C ~ ,

6.0

177

D.D

,-4.0

(a)

'

9

l.so

1.2o

,

8.o

40 c

I

'

o.o

'

t .

)

(b)

I

,

L6. D

L2. O

, o .o nLmJL~j

I r .o ~ r w

cry)

(c) Fig. 62. UPS spectra resolved into Gaussian peaks: (a) 0%, (b) 25%, and (c) 100% N2 partial pressure. Reproduced with permission from [662], copyright 2000, Elsevier Science.

178

SIKDER AND KUMAR 0% Npp '

100% Npp

/I; - ( Y

25%

&

25% Npp

24 eV

i

/ .,ll r,~

100% i

/

| ! !

0%

! I

,

I

50

,

I

40

30

,

I

20

,

I

, ,

10

0

Electron e n e r g y loss (eV)

Fig. 63. EELSdata on films grown with 0%, 25%, and 100% N2 partial pressure. Reproduced with permission from [662], copyright2000, ElsevierScience.

3.0

.

'

i

'

i

'

i

,

,

I

,

I

20

,oT-, E =o 1C) ,--

1.0

Z

o 0.0 2.006

I

I

-cir" {D

-~

,

I

Z006

I

.

I

(~

I

z~

-#

IZD 2.OO(3 2.0(32

-rrr I

0

,

I

25

,

I

50

,

I

75

,

I 100

~ N2pp

Fig. 64. ESR measurementson filmswith varyingN2 partialpressure. Reproduced with permissionfrom [662], copyright2000, ElsevierScience.

Annealing behavior of the sample containing 33 at.% nitrogen is being investigated by Raman and IR and valence band XPS spectroscopes. Annealing is important in order to study the phase stability with respect to temperature. Raman spectra of as-grown and annealed samples (Fig. 67a) show the increase of D-band intensity. This is due to the fact that as annealing progresses the microdomains grow in size or number, making a large contribution to the D-band. Due to annealing, outdiffusion of nitrogen and disruption of bonds occur. This disruption does not affect the N = N bond as much it affects C - C and C = N bonds. This indicates that sp 2 bonding in the CN compound is the most stable phase. These results were backed by the valence band XPS results, where the sp hybridized feature remains un-

affected after annealing but the 2s state is severely affected. IR absorbance of the same samples (Fig. 67b) shows broadly the same results except that the sp 2 band becomes more IR active. This is due to the fact that annealing favors the symmetry breaking mechanism. After annealing, the D- and G-bands are shifted due to the change in sp 2 domain size. The N = N band also shifts because the annealing process allows the bonded nitrogen atoms to be repositioned within the ring, giving rise to a wide range of shifting of the N = N stretching band. Thin CNx films were deposited on crystalline silicon substrates by e-beam evaporation of graphite and simultaneous nitrogen ion bombardment. The films were deposited at an ebeam power of 0.5-1.5 kW and N + ion energies of 300--400 eV while substrate temperature was varied from 800 to 1150~ Films were characterized by Raman and XPS spectroscopy. In the Raman spectrum D- and G-bands were seen in all the films. Two additional peaks at 1230 and 1466 cm -1 were also seen in the films grown at lower temperatures and low ion energies. These peaks are sensitive to nitrogenization changes and are identified as being due to nanocrystalline diamond species dispersed in the amorphous carbon layer [675, 676]. Decrease of this phase with higher nitrogen energy and deposition temperature is due to the formation of CNx phase by substituting carbon atoms with nitrogen atoms [677]. XPS analysis of the deposited films shows during the growth process that the ratio of sp 2 to sp 3 bonds changes and the number of C - N bonds increases with increasing deposition energy and substrate temperature. Ni substrate has been studied extensively for deposition of diamond due to its close matching of lattice constants with diamond and chemical affinity of Ni and carbon. Single crystal Ni substrates have also been studied to grow carbon nitride on it. Yan et al. [678] reported the synthesis of crystalline c~- and/~phase of C3N4 on Ni (100) substrate using a HFCVD method with nitrogen and methane. In another studies crystalline car-

SUPERHARD COATINGS

179

4

&

9

9

9

&&&

&A& 9 A 9 3

&

2 A

E o

1

9

>F x

xxx

A

= m

.>

X

X

0

,,

t" 1

n

n

= m

v)

(I) '- -1 s m

-2

-3

-4

- 5

nnUn~nnn

~

,

O.OE+O

,~-, ......

9

,

-

!

'

2.0E-3

,

,

; . . . .

~

| ......

4.0E-3

i |

,.

. . . . . .

,

.... ,

9 [] I

",

....

i

,

,

,

,

n

"!

....

8.0E-3

6.0E-3

II

,

''

,"

',

III

.....

,

~

'

1.0E-2

,

,'

'

,'

','

i

, .....

1.2E-2

,'

,'

, ......

1.4E-2

1/'1" (K "1) Fig. 65. In(resistivity) as a function of 1/T for films deposited at different nitrogen partial pressures: (mm)0%, (~I~) 25%, (• 100%. Reproduced with permission from [661], copyright 1999, Elsevier Science.

bon nitride films were grown on polycrystalline Ni substrate using a RF bias assisted HFCVD technique [679]. Large cystallites (~10/zm) are seen in the SEM picture and XRD reveals the formation of a crystalline phase of carbon nitride, but no Raman signal is found. Much literature has come out recent days regarding the formation of crystalline or amorphous carbon nitride. Here we mention the brief description of the deposition technique and obtained results. CN thin films were synthesized on Si substrate using electron beam evaporation of carbon and simultaneous nitrogen ion bombardment [680]. Clusters of Cx Ny phase with x > y are formed along with the sp 3 phase consisting fl-C3N4, as indicated by XPS, Raman, and FTIR analysis. Formation of fl-C3N4 has been reported on the Si, Ta, Mo, and Pt substrates using the MPCVD method with a methane and N2 gas mixture [681]. Extensive XRD results are shown in support of their results. Graphitic-C3N4 films were grown on Si and a highly pyrolytic grahite substrate by a MPCVD system using a methane and N2 gas mixture [682]. Films were characterized by scanning tunneling microscopy and suggested the formation of graphitic-C3N4. Hexagonal beta carbon nanocrystals were observed in the CNx films deposited on Si substrates by the RF

50%, and (A)

PECVD technique using ammonia and ethylene gas mixture followed by rapid thermal annealing to 1000~ [683]. Amorphous carbon nitride nanotips were synthesized on silicon to be used as a electron emitters by the ECR-CVD method in which a negative bias was applied to the graphite substrate holder and a mixture of C2H2, N2, and Ar was used as precursor [684]. An onset emission field as low as 1.5 V/zm and a current density of up to 0.1 mA cm 2 at 2.6 V/zm were observed. Crystallization behavior of amorphous carbon nitride films has been studied by Xiao et al. [685]. CNx films were first prepared by DC reactive magnetron sputtering and then films were heat treated under protective nitrogen. Results showed that heat treatment above 1100~ could induce the transition from an amorphous to a crystalline state of carbon nitride films. Carbon nitride thin films and nanopowders were produced by CO2 laser pyrolysis of sensitized N H 3 - N 2 0 - C 2 H 2 reactant gas mixtures [686]. Data obtained by XRD, XPS, and TEM analysis on power suggested the presence of CN bonded phases and are taken as an indication of the formation of c~- and fl-C3N4. Several other studies also reported the formation of either crystalline or amorphous carbon nitride films on different substrates [687-689, 700].

180

SIKDER AND KUMAR

20ol

......

!

D

~,

..

/AI ![

i

II

I

..

150

e 80

CuN~

/

, 100

/~C /

50 f "

40

/~

"

,

'

800

1200

0 400

800

1200 1600 2000 2400 2800 3200 3600 4000

400

Raman Shift, (cm") 100 .

.

.

.

.

.

.

.

.

.

. . . . As grown

200

120~-

,

G

16

.

.

.

.

.

I 1600

! Annealed. . . . , J 2000

',,I , ! 2400 2800

Raman Shift, (cm '') . . . . . .

I 3200

.

80 12 =

70

06

60

o~

50

~

C-It

~" 10

Annealed C=N

8

Vw

40

~

30

ao

]/.j '" 0550

600

1000 1400 1800 2200 2600 3000 3400 3800

Wavenumber, (cm "l) Fig. 66. (a) Raman spectra as a function of relative nitrogen concentration. Data were translated but not rescaled (a = 43.3 at.%, b -- 37.6 at.%, c = 33.7 at.%, d = 25.2 at.%, e = 0at.% N). (b) IR spectra as a function of relative nitrogen concentration. Data were translated but not rescaled (a = 43.3 at.%, b = 37.6 at.%, c = 33.7 at.%, d = 25.2 at.% nitrogen). Reproduced with permission from [663], copyright 1999, Elsevier Science.

I

I

I

I '

~ ' I

Wavenumber, (cm")

4.7. Conclusions

9 Substrate temperatures > 800~ may be used for the process with gaseous precursors. Such temperatures should

I

1350 1750 2150 2550 2950 3350 3750

Fig. 67. (a) Raman spectra, (b) IR spectra of the as-grown sample containing 33.2 at.% N before and after annealing at 600~ (23.2 at.% N). Reproduced with permission from [663], copyright 1999, Elsevier Science.

9

It is seen form the literature that very little definite evidence for the existence of crystalline carbon nitride is being shown. XRD and TEM analyses suggest the probability of the formation of disordered polytypic diamond in the presence of nitrogen, which might be interesting in connection to diamond synthesis [618]. In some cases crystalline phases are being identified in their films but that is in a small area or in a mixture of an amorphous carbon-nitrogen mixture. The following important comments are made by Muhl and M6ndez [562] in their recent review on the formation and characterization of carbon nitride films:

9;0

9

9

9

help inhibit the formation of polymeric and inorganic CNx compounds. Atomic nitrogen and CN are probably preferable as precursors rather than molecular nitrogen and hydrocarbon ions and radicals. The use of a CN precursor is likely to help prevent the formation of stable carbon-ring structures. Ion energies below 10 eV are necessary at low pressure synthesis to avoid chemical sputtering and the concurrent reduction in nitrogen content. For gas phase processes, the use of medium to high pressures helps to ensure that the kinetic energy of the incident neutrals is kept below 10 eV. Use of high to ultrahigh predeposition vacuums is recommendable to minimize the residual contamination. Substrate effects are complex but important; reasonable adhesion between the carbon nitride and the substrate is needed but without compound formation as in the case of silicon. There are indications that there are advantages in using nickel, titanium, or Si3N4 coated substrates. Different

SUPERHARD COATINGS

9 9 9

9

buffer layers may be used in order to promote crystalline formation of carbon nitride. Various characterization techniques should be employed in parallel in order to identify phases correctly. Measured nonoptimum N/C ratios do not mean necessarily that crystalline C3N4 does not exist within the deposit. Low s p 1 bonding cannot be assumed only by the presence of small peaks in the 2000 to 2200 cm-1 region of FTIR spectra. Effects of the chemical environment cannot be ignored in XPS or other techniques that are sensitive to the energies of valence electrons.

Further efforts are imperative for synthesizing materials that can unambiguously be identified as crystalline carbon nitride.

Acknowledgments Work leading to this chapter was partially funded by a grant under the NSF Career Award 9983535 and NSF DMI grant 0096255. The authors thank the Center for Microelectronics Research, College of Engineering at the University of South Florida, and its Director, Dr. M. Anthony, for the support and the internal release time, which made this chapter possible. The help received from Jean-Paul Deeb, F. Giglio, Ismail Irfan, P. Zantye, and T. Vestagaarden in the preparation of this manuscript is also greatly acknowledged. One of the authors (A.K.S.) would like to thank his doctoral supervisor (Professor D. S. Misra, liT Bombay, India) for his kind help and affection during his thesis work; a part of the thesis work has been presented in this chapter.

REFERENCES 1. "Hard Coatings Based on Borides, Carbides and Nitrides: Synthesis, Characterization and Applications" (A. Kumar, Y.-W. Chung, and R. W. Chia, Eds.). TMS, 1998. 2. "Surface Engineering: Science and Technology I" (A. Kumar, Y.-W. Chung, J. J. Moore, and J. E. Smugeresky, Eds.). TMS, 1999. 3. "Magnetic Recording Technology" (C. D. Mee and E. D. Daniel, Eds.). McGraw-Hill, New York, 1996. 4. "Phase diagram of Ternary Boron Nitride and Silicon Nitride Systems" (P. Rogl and J. C. Schuster, Eds.). ASM International, Metals Park, OH, 1992. 5. S. Veprek, J. Vac. Sci. Technol. A17, 2401 (1999). 6. A.Y. Liy and M. L. Cohen, Science 245, 841 (1989). 7. A.Y. Liy, M. L. Cohen, Phys. Rev, 41(15), 10727 (1990). 8. M.L. Cohen, Phys. Rev 32(12), 7988 (1985). 9. E P. Bundy, H. T. Hall, H. M. Strong, and R. H. Wentorf, Nature 176, 51 (1955). 10. P.W. Bridgman, Sci. Am. 193, 42 (1955). 11. W.G. Eversole, U.S. Patent 3,630,677, 1961. 12. S. Matsumoto, Y. S. M. Kamo, and N. Setaka, Jpn. J. Appl. Phys. 21, L183 (1982). 13. M. Kamo, Y. Sato, S. Matsumoto, and N. Setaka, J. Crystal Growth 62, 642 (1983). 14. A. Badzian, T. Badzian, R. Roy, R. Meisser, and K. E. Spear, Mater Res. Bull. 23, 531 (1988).

181

15. S. Matsumoto, Y. Sato, M. Tsutsumi, and N. Setaka, J. Mater Sci. 17, 3106 (1982). 16. K. Okano, N. Naruki, Y. Akiba, T. Kurosu, M. Ida, and Y. Hirose, Jpn. J. Appl. Phys. 27, L 153 (1988). 17. R. S. YaJamanchi and K. S. Harshavardhan, J. AppL Phys. 68, 5941 (1990). 18. Y. Tzeng, R. Phillips, C. Cutshaw, and Srivinyunon, App. Phys. Lett. 58, 2645 (1991). 19. K. Suzuki, A. Sawabe, H. Yasuda, and T. Inuzuka, AppL Phys. Lett. 50, 728 (1987). 20. E Akatsuka, Y. Hirose, and K. Komaki, Jpn. J. Appl. Phys. 27, L1600 (1988). 21. E Zhang, Y. Zhang, Y. Yang, G. Chen, and X. Jiang, Appl. Phys. Lett. 57, 1467 (1990). 22. K. Kurihara, K. Sasaki, M. Kararada, and N. Koshimo, Appl. Phys. Lett. 52, 437 (1988). 23. P. XiLing and G. ZhaoPing, Thin Solid Films 239, 47 (1994). 24. J. Karner, M. Pedrazzini, I. Reineck, M. E. Sjostrand, and E. Bergmann, Mater Sci. Eng. A 209, 405 (1996). 25. T. Leyendecker, O. Lemmer, A. Jurgens, S. Esser, and J. Ebberink, Surf. Coatings Technol. 48, 261 (1991). 26. N. W. Ashcroft and N. D. Mermin, "Solid State Physics." Saunders, Philadelphia, 1976. 27. C. Kittel, "Introduction to Solid State Physics." Wiley Eastern Ltd., New Delhi, 1986. 28. K.E. Spear, A. W. Phelps, and W. B. White, J. Mater Res. 5, 2277 (1990). 29. J.C. Angus, Thin Solid Films 216, 126 (1992). 30. R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl, "Diamond and Diamond-like Films and Coatings." Plenum, New York, 1991. 31. W.A. Yarbrough and R. Messier, Science 247, 688 (1990). 32. J.C. Angus, H. A. Will, and W. S. Stanko, J. Appl. Phys. 39, 2915 (1968). 33. T.R. Anthony, Vacuum 41, 1356 (1990). 34. B.V. Spitzyn, L. L. Bouilov, and B. V. Derjaguin, J. Crystal Growth 52, 219 (1981); B. V. Spitzyn and B. V. Derjaguin, In "Problems of Physics and Technology of Wide-Gap Semiconductors," pp. 22-34. Akad. Nauk SSSR, Leningrad, 1979. 35. S. Matsumoto, Y. Sato, M. Kamo, and N. Setaka, Jpn. J. Appl. Phys. 21, L183 (1982). 36. S.J. Harris, J. Appl. Phys. 56, 2298 (1990). 37. W. Banholzer, Surf. Coat. Technol. 53, 1 (1992). 38. R. Haubner and B. Lux, Diamond Relat. Mater 2(9), 1277 (1993). 39. P. K. Bachmann, W. Drawe, D. Knight, R. Weimer, and R. Messier, "Spring MRS Meeting Extended Abstracts, Symposium D" (M. W. Geis, G. H. Johnson, and A. R. Badzian, Eds.), pp. 99-102. MRS, Pittsburgh, PA, 1988. 40. H. Liu and D. S. Dandy, "Diamond Chemical Vapor Deposition, Nucleation and Early Growth Stages," p. 40. Noyes, Park Ridge, NJ. 41. T.P. Ong, E Xiong, R. P. H. Chang, and C. W. White, J. Mater 7, 2429 (1992). 42. J. Narayan, V. P. Godbole, O. Matcra, and R. K. Singh, J. AppL Phys. 71, 966 (1992). 43. S. D. Wolter, B. R. Stoner, J. T. Glass, P. J. Ellis, D. S. Buhaenko, C. E. Jenkins, and P. Southworth, Appl. Phys. Lett. 62,1215 (1993). e 44. D. Michau, B.Tanguy, G. Demazeau, M. Couzi, and R. Cavagnat, Diamond Relat. Mater 2, 19 (1993). 45. K. Kobayashi, T. Nakano, N. Mutsukura, and Y. Machi, Vacuum, 44, 1 (1993). 46. U. Yoshikawa, Y. Kaneko, C. F. Yang, H. Tokura, and M. Kamo, J. Jpn. Soc. Precision Eng. 54, 1703 (1988); M, Yoshikawa, Y. Kaneko, C. E Yang, and H. Tokura, J. Jpn. Soc. Precision Eng. 55, 155 (1989). 47. G.E Zhang, X. Zheng, and Z. T. Liu, J. Cryst, Growth 133, 117 (1993). 48. R.A. Bauer, N. U Sbrockey, and W. E. Brower, Jr., J. Mater Res. 8, 2858 (1993). 49. K. Kobayashi, N. Mutsukura, and Y. Machi, Mater Manufacturing Processes 7, 395 (1992). 50. P.A. Dennig, R Shiomi, D. A. Stevenson, and N. M. Johnson, Thin Solid films 212, 63 (1992).

182

SIKDER AND KUMAR

51. P.A. Dennig, and D., A. Stevenson, AppL Phys. Lett. 59, 1562 (1991). 52. B. Lux, and R. Haubner, "Diamond and Diamond-like Filmds and Coatings." In (R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl, Eds.), Plenum Press, New York, 1991, pp. 579-609. 53. J. C. Angus, Y. Wang, and M. Sunkara, Ann. Rev. Mater. Sci. 21, 221 (1991). 54. H. Liu and D. S. Dandy, "Diamond Chemical Vapor Deposition, Nucleation and Early Growth Stages," p. 97. Noyes, Park Ridge, NJ. 55. P. Ascarelli, and S. Fontana, Appl. Surf. Sci. 64, 307 (1993). 56. W.A. Yarbrough, Appl. Diamond Relat. Mater. 25 (1991). 57. P.C. Yang, W. Zhu, and J. T. Glass, J. Mater. Res. 8, 1773 (1993). 58. M.W. Geis, A. Argoitia, J. C. Angus, G. H. M. Ma, J. T. Glass, J. Butler, C. J. Robinson, and R. Pryor, Appl. Phys. Lett. 58, 2485 (1991). 59. M. W. Geis, AppL Phys. Lett. 55, 550 (1989). 60. H. Liu and D. S. Dandy, "Diamond Chemical Vapor Deposition, Nucleation and Early Growth Stages," p. 100. Noyes, Park Ridge, NJ. 61. H. Liu and D. S. Dandy, "Diamond Chemical Vapor Deposition, Nucleation and Early Growth Stages," p. 15. Noyes, Park Ridge, NJ. 62. M. Kamo, Y. Sato, S. Matsumoto, and N. Setaka, J. Cryst, Growth 62, 642 (1983). 63. T. Sharda, D. S. Misra, D. K. Avasthi, and G. K. Mehta, Solid State Commun. 98, 879 (1996). 64. R. E Davis, "Diamond Film And Coatings Development, Properties and Applications," p. 162. Noyes Publishing, Park Ridge, NJ. 65. H. Kawarada, K. S. Mar, and A. Hiraki, Jap. J. Appl. Phys. 26, L 1 (1987). 66. J. Wei, H. Kawarada, J. Suzuki, K. Yanagihara, K. Numata, and A. Hiraki, Electrochem. Soc. Proc. 393, 89 (1989). 67. P.K. Bachmann, and R. Messier, C&EN 67, 24 (1989). 68. J.C. Angus, and C. C. Hayman, Science 241, 4868, 913 (1988). 69. K. Kudhara, K. Sasaid, M. Kawarada, and N. Koshino, Appl. Phys. Lett. 52, 437 (1988); K. Kudhara, K. Sasaid, M. Kawarada, A. Teshima, and K. Koshino, SPIE Proc. 1146, 28 (1990). 70. N. Fujimori, A. lkegaya, T. Imal, K. Fukushima, and N. Ota, Electrochem. Soc. Proc. 465, 89 (1989). 71. Y. H. Lee, P. D. Richard, K. J. Bachmann, J. T. Glass, Appl. Phys. Lett. 56, 620 (1990). 72. N. Ohtake and M. Yoshikawa, J. Electrochem. Soc. 137, 717 (1990); N. Ohtake and M. Yoshikawa, Thin Solid Films 212, 112 (1992). 73. S. Matsumoto, Y. Manabe, and Y. Hibino, J. Mater. Sci. 27, 5905 (1992). 74. S. Matsumoto, J. Mater. Sci. Lett. 4, 600 (1985). 75. H.O. Pierson, "Graphite." Noyes, Park Ridge, NJ, 1993. 76. S. Matsumoto, M. Hino, and T. Kobayashi, Appl. Phys. Lett. 51, 737 (1987). 77. S. Matsumoto and K. Okada, Oyo Buturi 61,726 (1992). 78. X. Chen and J. Narayan, J. Appl. Phys. 74, 4168 (1993). 79. Z.P. Lu, J. Heberlein, and E. Pfender, Plasma Proc. 12, 55 (1992). 80. A. Hirata, and M. Yoshikawa, Diamond Relat. Mater. 2, 1402 (1993). 81. K. Eguchi, S. Yata, and T. Yoshida, Appl. Phy. Lett. 64, 58(1994). 82. Watanabe, T. Matsushita, and K. Sasahara, Jpn. J. AppL Phys. 31, 1428 (1992). 83. M. Kohzaki, K. Uchida, K. Higuchi, and S. Noda, Jpn. J. Appl. Phys. 32, L438 (1993). 84. A. K. Sikder, "Electrical and Structural Characterization of Diamond Films and Growth of Diamond Films on Stainless Steel for Tool Applications." Doctoral Thesis, IIT Bombay, India, 1999. 85. C.M. Marks, H. R. Burris, J. Grun and K. A. Snail, J. Appl. Phys. 73, 755 (1993). 86. X. H. Wang, W. Zhu, J. von Windheirn, and J. T. Glass. Cryst. Growth 129, 45 (1993). 87. I. Y. Hirose, and N. Kondo, "Japan Applied Physics Spring Meeting," 1988. 88. L. M. Hanssen, W. A. Carrington, J. E. Buffer, and K. A. Snail, Mater. Len. 7, 289 (1988). 89. P.G. Kosky, and D. S. McAtee, Mater. Lett. 8, 369 (1989). 90. M.A. Cappelli, and P. H. Paul, J. Appl. Phys. 67, 2596 (1990). 91. K.V. Ravi, and C. A. Koch, AppL Phys. Lett. 57, 348 (1990).

92. Y. Tseng, C. Cutshaw, R. Phillips, and T. Srivinyunon, Appl. Phys. Lett. 56, 134 (1990). 93. D.B. Oakes, and J. E. Buffer, J. Appl. Phys. 69, 2602 (1991). 94. Y. Matsui, A. Yuuki, M. Sahara, and Y. Hirose, Jpn. J. Appl. Phys. 28, 1718 (1989). 95. Y. Matsui, H. Yabe, and Y. Hirose, Jpn. J. AppL Phys. 29, 1552 (1990). 96. Y. Matsui, H. Yabe, T. Sigimoto, and Y. Hirose, Diamond Relat. Mater 1, 19(1991). 97. R. E Davis, "Diamond Film And Coatings Development, Properties and Applications," p. 182. Noyes, Park Ridge, NL. 98. R. Kapil, B. R. Mehta, V. D. Vankar, Thin Solid Films 312, 106 (1998). 99. P.K. Bachman, W. Drawe, D. Knight, R. Weimer and R. Meisser, In "Diamond and Diamond-like Materials Synthesis" (M.W. Geis, G. H. Johnson and A. R. Badzian, Eds.), pp. 99-102. MRS, Pittsburgh, 1988. 100. B.V. Spitsyn and B. V. Deryagin, USSR Patent 399134, 1980. 101. R. A. Rudder, G. C. Hudson, J. B. Posthill, R. E. Thomas, and R. J. Markunas, Appl. Phys. Lett. 59, 791 (1991). 102. B. J. Bai, C. J. Chu, D. E. Patterson, R. H. Hauge, and J. L. Margrave, J. Mater Res. 8, 233 (1993). 103. N.J. Komplin, B. J. Bai, C. J. Chu, J. L. Margrave, and R. H. Hauge, In "Third International Symposium on Diamond Materials" (J. P. Dismukes and K. V. Ravi, Eds.), p. 385. The Electrochemical Society Processing Series, 1993. 104. J.-J. Wu and E C.-N. Hong, J. Appl. Phys. 81, 3647 (1997) 105. E C-N. Hong, G. T. Lang, D. Chang, and S. C. Yu, In "Applications of Diamond Films and Related Materials" (Y. Tzeng, M.Yoshikawa, M. Murakawa, and A. Feldman, Eds.), pp. 577-82. Elsevier, Amsterdam, 1991. 106. E C. Hong, G. T. Lang, J. J. Wu, D. Chang, and J. C. Hsieh, Appl. Phys. Lett. 63, 3149 (1993). 107. C.A. Rego, R. S. Tsang, P. W. May, M. N. R. Ashfold, and K. N. Rosser, J. Appl. Phys. 79, 7264 (1996). 108. R. S. Tsang, C. A. Rego, P. W. May, J. Thumin, M. N. R. Ashfold, K. N. Rosser, C. M. Younes, and M. J. Holt, Diamond ReL Mater. 5, 359 (1996). 109. E. J. Corat, V. J. Trava-Airoldi, N. E Leite, A. E V. Pena, and V. Baranauskas, Mater. Res. Soc. Symp. Proc. 349, 439 (1994). 110. E.J. Corat, R. C. Mendes de Barros, V. J. Trava-Airoldi, N. G. Ferreira, N. E Leite, and K. lha, Diamond and Relat. Mater. 6, 1172 (1997). 111. V.J. Trava-Airoldi, B. N. Nobrega, E. J. Corat, E. Delbosco, N. E Leite, and V. Baranauskas, Vacuum 46, 5 (1995). 112. I. Schmidt, E Hentschel, and C. Benndorf, Diamond Rel. Mater. 5, 1318 (1996). 113. M. Kadono, T. Inoue, A. Midyadera, and S. Yamazaki, Appl. Phys. Lett. 61,772 (1992). 114. H. Maeda, M. hie, T. Hino, K. Kusakabe, and S. Morooka, Diamond Rel. Mater 3, 1072 (1994). 115. R. Ramesharm, R. E Askew, and B. H. Loo, In "Third International Symposium on Diamond Materials" (J. P. Dismukes and K. V. Ravi, Eds.), p. 394. The Electrochemical Society Processing Series, 1993. 116. K.J. Grannen and R. P. H. Chang, J. Mater. Res. 9, 2154 (1994). 117. K.J. Grannen, D. V. Tsu, R. J. Meflunas, and R. P. H. Chang, AppL Phys. Lett. 59, 745 (1991). 118. C. A. Fox, M. C. McMaster, W. L. Hsu, M. A. I Kelly, and S. B. Hagstrom, Appl. Phys. Lett. 67, 2379 (1995). 119. T. Kotaki, Y. Amada, K. Harada, and O. Matsumoto, Diamond ReL Mater. 342 (1993). 120. T. Kotaki, N. Horii, H. Isono, and O. Matsumoto, J. Electrochern. Soc. 143, 2003 (1996). 121. T. Suntola, Mater. Sci. Rep. 4, 261 (1989). 122. T.I. Hukka, R. E. Rawles and M. P. D'Evelyn, Thin Solid Films 225, 212 (1993) 123. R., Gat, T. I. Hukka, R. E. Rawles, and M. P. D'Evelyn, Ann. Tech. Conf. Soc. Vac. Coat. 353, (1993). 124. B.B. Pate, et al., Physica B 117/118, 783 (1983). 125. B.B. Pate, Su~ Sci. 165, 83 (1986). 126. T. 1. Hukka, R. E. Rawles and M. P. D'Evelyn, Thin Solid Films 225,212 (1996).

SUPERHARD 127. R. Gat, T. I. Hukka and M. E D'Evelyn, In "Diamond Materials" (H. E Dismukes, K. V. Ravi, K. E. Spear, B. Lux, and N. Setaka, Eds.). The Electrochemical Society, 1993. 128. D.V. Fedoseev, I. G. Varshavskaya, A. V. lavent'ev, and B. V. Deryagin, Powder Technol. 44, 125 (1985). 129. D. V. Fedoseev, and B. V. Deryagin, Mater Res. Soc. Syrup. Proc. 439 (1989). 130. E A. Molian and A. Waschek, J. Mater Sci. 28, 1733 (1993). 131. K. Kitahama, K. Hirata, H. Nakamatsu, S. Kawai, N. Fujimori, T. Imai, H. Yoshino, and A. Doi, Appl. Phys. Lett. 49, 634 (1986). 132. K. Kitaharna, K. Hirata, H, Nakamatsu, S. Kawai, N. Fujimori, and T. Imai, Mater Res. Soc. Syrup. Proc. 75, (1987). 133. K. Kitahama, Appl. Phys. Lett. 53, 1812 (1988). 134. E Mistry, M. C. Turchan, S. Liu, G. O. Granse, T. Baurmann, and M. G. Shara, Innov. Mater Res. 1, 193 (1996). 135. D.L. Pappas, K. L. Saenger, J. Bruley, Y. V. Kra,kow, J. J. Cuomo, T. Gu, and R. W. Collins, J. Appl. Phys. 71, 5675 (1992). 136. M. B. Guseva, V. G. Babaev, V. V. Khvostov, Z. K. Valioullova, A. Yu. Bregadze, A. N. Obraztsov, and A. E. Alexenko, Diamond Rel. Mater 3,328 (1994). 137. J. Seth, R. Padiyath, D. H. Rasmussen, and S. V. Babu, Appl. Phys. Lett. 63,473 (1993). 138. M. C. Polo, J. Cifre, G. Sanchez, R. Aguiar, M. Varela, and J. Esteve, Appl. Phys. Lett. 67,485 (1995) 139. M. C. Polo, 1. Cifre, G. Sanchez, R. Aguiar, M. Yarela, and J. Esteve, Diamond Rel. Mater 4, 780 (1995) 140. E A. Molian, B. Janvrin, and A. M. Molian, J. Mater Sci. 30, 4751 (1995). 141. M.E. Kozlov, E Fons, H.-A. Durand, K. Nozaki, M. Tokumoto, K. Yase, and N. Minami, J. Appl. Phys. 80, 1182 (1996). 142. J. Wagner, C. Wild, and E Koidl, Appl. Phys. Lett. 59, 779 (1991). 143. S. Ltsch and H. Hiraoka, J. Min. Met. Mater Soc. 46, 64 (1994). 144. B. V. Spitzyn, L. L. Bouilov, and B. V. Derjaguin, J. Crystal Growth 52, 219 (1981); B. V. Spitzyn and B. V. Derjaguin, Akad. Nauk SSSR, Leningrad 22 (1979). 145. R. J. Graham, J. B. Posthill, R. A. Rudder, and R. I. Markunas, Appl. Phys. Lett. 59, 2463 (1991). 146. W.A. Yarbrough, J. Vacuum Sci. Technol. A 9, 1145 (1991). 147. D.N. Belton, and S. J. Schmieg, Thin Solid Films, 212, 68 (1992). 148. A.-R. Badzian and T. Badzian, In "Proc. MRS Fall Meeting" (T. M. Besmann, B. M. Gallois, and J. Warren, Eds.), Vol. 250B, 339-349. Boston, MA, 1991. 149. Y. Sato, I. Yashima, H. Fujita, T. Ando, and M. Kamo, In "New Diamond Science and Technology" (R. Messier, J. T. Glass, I. E. Butler, and R. Roy, Eds.), pp. 371-376. MRS, Pittsburgh, PA, 1991. 150. S. Yugo, T. Kanai, T. Kimura, and T. Muto, Appl. Phys. Lett., 58, 1036 (1991). 151. B.R. Stoner, G.-H. M. Ma, D. S. Wolter, and J. T. Glass, Phys. Rev. B 45, 11067 (1992). 152. A. van der Drift, Phillips Res. Rep. 22, 267 (1967). 153. C. Wild, P. Koidl, W. MOller-Sebert, H. Walcher, R. Kohl. N. Herres, R. Locher, R. Samlenski and R. Brenn, Diamond Relat. Mater 2, 158 (1993). 154. R. E. Clausing, L. Heatherly, E. D. Specht and K. L. More, In "New Diamond Science and Technology, R. Messier" (J. T. Glass, J. E. Butler and R. Roy, Eds.), p. 575. Materials Research Society, 1991. 155. H.J. Fiffler, M. Rosier, M. Hartweg, R. Zachai, X. Jiang, and C. P. Klages, (1993). 156. J.E. Butler and R. L. Woodin, Philos. Trans. Roy Soc. London Set A 342, 209 (1993). 157. K. Kobashi, K. Nishimura, K. Miyata, K. Kumagai and A. Nakaue, J. Mater Res. 5, 2469 (1990). 158. E G. Celii, J. White D. and A. J. Purdes, Thin Solid Films 212, 140 (1992). 159. L. Chow, A. Homer, and H. Sakoui, J. Mater Res. 7, 1606 (1992). 160. C. Wild, P. Koidl, W. Muller-Sebert, H. Walcher, R. Kohl, N. Herres, R. Locher, R. Samlenski, and R. Brenn, Diamond Rel. Mater 2, 158 (1993).

COATINGS

183

161. T. Suesada, N. Nakamura, H. Nagasawa, and H. Kawarada, Jpn. J. Appl. Phys. 34, 4898 (1995). 162. E. Burton, Diamond London (1978). 163. J.C. Angus, Thin Solid Films 216, 126 (1992). 164. S.P. McGinnis, M. A. Kelly, and S. B. Hagstrom, Appl. Phys. Lett., 66 3117 (1995). 165. J. E. Field, "The Properties of Natural and Synthetic Diamond." Academic Press, London, 1992. 166. X. Jiang, C.-P. Klages, R. Zachai, M. Hartweg, and H.-J. Fosser, Appl. Phys. Lett. 62, 26 (1993). 167. H.Yagi, K. Hosina, A. Hatta, T. Ito, T. Sasaki, and A. Hirald, J. Jpn. Appl. Phys. 36, L507 (1997). 168. X. Jiang, K. Shiffmann, C.-P. Klages, D. Wittorf, C. L. Jia, and K. Urban, J. Appl. Phys. 83, 5 (1998). 169. G. Popovici, C. H. Chao, M. A. Prelas, E. J. Charlson and J. M. Meese, J. Mater Res. 10, 8 (1995). 170. O. Chena and Z. Lin, J. Appl. Phys. 80, (1996). 171. W. Zhu, E R. Sivazlian, B. R. Stoner and J. T. Glass J. Mater Res. 10, 2 (1995). 172. E Stubhan, M. Ferguson, and H.-J. Fusser, R. J. Behm, Appl. Phys. Lett. 66, 15 (1995). 173. X. Li, Y. Hayashi, and S. Nishino, Jpn. J. Appl. Phys. 36, 5197 (1997). 174. W. Kulisch, L. Ackermann, and B. Sobisch, Phys. Stat. SoL (a) 154, 155 (1996). 175. H.P. Lorenz, W. Schilling, Diamond Relat. Mater 6, 6 (1997). 176. J. Robertson, J. Gerber, S. Sattel, M. Weiler, K. Jung, and H. Ehrhardt, AppL Phys. Lett. 66, 3287 (1995). 177. S. Sattel, J. Gerber, and H. Ehrhardt, Phys. Stat. Sol. (a) 154, 141 (1996). 178. S. D. Wolter, B. R. Stoner, I T. Glass, P. J. Ellis, D. S. Buhhaenko, C. E. Jenkins, and P. Southworth, Appl. Phys. Lett. 62, 1215 (1993). 179. B. X. Wang, W. Zhu, J, Ahn, and H. S. Tan, J. Cryst. Growth 151, 319 (1995). 180. P. John, D. K. Milne, P. G. Roberts, M G. Jubber, M. Liehr, and J. I. B. Wilson, J. Mater Res. 9, 3083 (1994). 181. C.Z. Gu and X. Jiang, J. Appl. Phys. 88, 4 (2000). 182. S. Chattopadhyay, P. Ayyub, V. R. Palkar, and M. Multani, Phys. Rev. B 52, 177 (1995). 183. D. A Gruen, MRS Bull. 9, 32 (1998). 184. Kehui Wu, E. G. Wang, and Z. X. Cao, J. Appl. Phys. 88, 5 (2000). 185. B. Hong, J. Lee, R. W. Collins, Y. Kuang, W. Drawl, R. Messier, T. T. Tsong, and Y. E. Strausser, Diamond Relat. Mater 6, 55 (1997). 186. D.M. Gruen, S. Liu, A. R. Krauss, J. Luo, and X. Pan, Appl. Phys. Lett. 64, 1502 (1994). 187. D. Zhou, D. M. Gruen, L. C. Qin, T. G. McCauley, and A. R. Krauss, J. AppL Phys. 84, 1981 (1998). 188. S.A. Catledge and Y. K. Vohra, J. Appl. Phys. 86, 698 (1999). 189. 0. Groning, M. Kuttel, P. Groning, and L. Schlapbach, J. Vac. Sci. Technol. B 17, 5 (1999). 190. W. Zhu, G. P. Kochanski, and S. Jin, Science 282, 1471 (1998). 191. Zhou, A. R. Krauss, L. C. Qin, T. G. McCauley, D. M. Gruen, T. D. Corrigan, R. P. H. Chang, and H. Gnaser, J. Appl. Phys. 82, 4546 (1997). 192. http://www.techtransfer.anl.gov/techtour/diamondmems.html. 193. T. Sharda, D. S. Misra, D. K. Avasthi, and G. K. Metha, Solid State Commun. 98, 879 (1996). 194. Y.N.K. Tamaki, Y. Watanabe, and S. Hirayama, J. Mater Res. 10, 431 (1995). 195. W. Howard, D. Huang, J. Yuan, M. Frenklach, K. E. Spear, R. Koba, and A. W. Phelps, J. Appl. Phys. 68, 1247 (1990). 196. M. Frenklach, W. Howard, D. Huang, J. Yuan, K. E. Spear, and R. Koba, Appl. Phys. Lett. 59, 546 (1991). 197. J. Singh, J. Mater Sci. 29, 2761 (1993). 198. A.R. Badzian, and T. Badzian, Surf. Coat. Technol. 36, 283 (1991). 199. K. M. McNamara, B. E. Williams, K. K. Gleason, and B. E. Scruggs, J. Appl. Phys. 76, 2466 (1994). 200. T. Sharda, A. K. Sikder, D. S. Misra, A. T. Collins, S. Bhargava, H. D. Bist, P. Veluchamy, H. Minoura, D. Kabiraj, D. K. Avasthi, and P. Selvam, Diamond Relat. Mater 7, 250 (1998).

184

SIKDER AND KUMAR

201. E K. Bachmann, A. T. Collins, and M. Seal, "Diamond 1992." Elsevier Sequoia, S.A., 1993. 202. J. Ruan, W. J. Choyke, and W. D. Paxtlow, J. Appl. Phys. 69, 6632 (1991). 203. J. Ruan, K. Kobashi, and W. J. Choyke, AppL Phys. Lett. 60, 1884 (1992). 204. L.H. Robins, L. P. Cook, E. N. Farabaugh, and A. Feldman, Phys. Rev. B 39, 13367 (1989). 205. A.T. Collins, M. Kamo, and Y. Sato, J. Phys. D 22, 1402 (1989). 206. A.T. Collins, M. Kamo, and Y. Sato, J. Mater. Res. 5, 2507 (1990). 207. R.J. Graham, T. D. Moustakas, and M. M. Disko, J. Appl. Phys. 69, 3212 (1991). 208. A.T. Collins, Diamond Relat. Mater 1,457 (1992). 209. A.T. Collins, L. Allers, C. J. H. Wort, and G. A. Scarsbrook, Diamond Relat. Mater 3, 932 (1994). 210. Y.L. Khong, A. T. Collins, and L. Allers, Diamond Relat. Mater. 3, 1023 (1994). 211. J. Ruan, W.J. Choyke, and K. Kobashi, Appl. Phys. Lett. 62, 1379 (1993). 212. Y.H. Singh, D. H. Rich, and E S. Pool, J. Appl. Phys. 71, 6036 (1992). 213. X. Yang, A. V. Barnes, M. M. Albert, R. G. Albridge, J. T. McKinley, N. H. Tolk, and J. L. Davidson, J. AppL Phys. 77, 1758 (1995). 214. Z. Zhang, K. Liao, and W. Wang, Thin Solid Films 269, 108 (1995). 215. G.Z. Cao, J. J. Schermer, W. J. P. van Enckevort, W. A. L. M. Elst, and L. J. Giling, J. Appl. Phys. 79, 1357 (1996). 216. T. Feng and B. D. Schwartz, J. Appl. Phys., 73 1415 (1993). 217. X. Jiang and C. P. Klages, Phys. Star. Sol. 154, 175 (1996). 218. H. Jia, J. Shinar, D. P. Lang, and M. Pruski, Phys. Rev. B 48, 17595 (1993). 219. R. E Davis, "Diamond Film And Coatings Development, Properties and Applications," p. 246. Noyes, Park Ridge, NJ. 220. B.V. Spitsyn, L. L. Bouilov, and B. V. Deryagin, J. Cryst. Growth 52, 219 (1981). 221. K. Kobashi, K. Nishimura, Y. Kawate, and T. Horiuchi, Phys. Rev. B 38, 4067 (1988). 222. R. Haubner, and B. Lux, Int. J. Refract. Hard Metals 6, 210 (1987). 223. W. Zhu, A. R. Badzian, and R. Messier, Proc. SPIE 1325, 187 (1990). 224. G. Sanchez, J. Servat, P. Gorostiza, M. C. Polo, W. L. Wang, and J. Esteve, Diamond Relat. Mater. 5, 592 (1996). 225. X. Jiang, K Schiffmann, A. Westphal, and C.-P. Klages, Diamond Relat. Mater. 4, 155 (1995). 226. E. Johansson and J.-O. Carlsson, Diamond Relat. Mater. 4, 155 (1995). 227. B.E. Williams and J. T. Glass, J. Mater. Res. 4, 373 (1989). 228. H. Kawarada, K. S. Mar, J. Suzuki, Y. Ito, H. Moil, H. Fujita, and A. Hiraid, Jpn. J. AppL. Phys. 26, 1903 (1987). 229. W. Zhu, A. R. Badzian, and R. Messier, J. Mater. Res. 4, 659 (1989). 230. R.E. Clausing, L. Heatherly, and K. L. More, Surf. Coat. Technol. 39140, 199 (1989). 231. J.L. Kaae, P. K. Gantzel, J. Chin, and W. P. West, J. Mater. Res. 5, 1480 (1990). 232. A. V. Hetherington, C. J. H. Wort, and P. Southworth, J. Mater. Res. 5, 1591 (1990). 233. J. Narayan, J. Mater. Res. 5, 2414 (1990). 234. W.L. Bragg, In "The Crystalline State" (W. H. Bragg and W. L. Bragg, Eds.), Vol. I, pp. 12-21. Bell, London, 1933. 235. C. Wild, N. Herres, and P. Koidl, J. Appl. Phys. 68, 973 (1990). 236. E. D. Specht, R. E. Clausing, and L. Heatherly, J. Mater. Res. 5, 2351 (1990). 237. R. E. Clausing, L. Heatherly, E. D. Specht, and K. L. More, In "New Diamond Science and Technology" (R. Messier, J. T. Glass, J. E. Buffer and R. Roy, Eds.), pp. 575-580. Materials Research Society, Pittsburgh, PA, 1991. 238. R.F. Davis, "Diamond Film And Coatings Development, Properties and Applications," p. 300. Noyes, Park Ridge, NJ. 239. A. K. Arora, T. R. Ravindran and G. L. N. Reddy, A. K. Sikder and D. S. Misra, Diamond Relat. Mater. 10, 1477 (2001). 240. N. Wada and S. A. Solin, Physica 105B, 353 (1981). 241. D.S. Knight and W. B. White, J. Mater. Res. 4, 385 (1989). 242. K.E. Spear, A. W. Phelps, and W. B. White, J. Mater. Res. 5, 2277 (1990).

243. L. Abello, G. Lucazeau, B. Andre, and T. Priem, Diamond Relat. Mater. 1,512 (1992). 244. P. V. Huong, Mater. Sci. Eng. B 11,235 (1992). 245. M. Yoshikawa, G. Katagiri, H. Ishida, A. Ishitani, M. Ono, and K. Matsumura, Appl. Phys. Lett. 55, 2608 (1989). 246. J.W. Ager III, D. K. Veirs, and G. M. Rosenblatt, Phys. Rev. B 43, 6491 (1991). 247. J. Wagner, M. Ramsteiner, C. Wild, and P. Koidl, Phys. Rev. B 40, 1817 (1989). 248. H. Windischmann, G. E Epps, Y. Cong, and R. W. Collins, J. Appl. Phys. 69, 2231 (1991). 249. W. Wanlu, L. Kejun, G. Jinying, and L. Aimin, Thin Solid Films 215, 174 (1992). 250. J. Robertson, Adv. Phys. 35, 317 (1986). 251. H. Ricter, Z. P. Wang, and L. Ley, Solid State Commun. 39, 625 (1981). 252. I.H. Campbell and P. Fauchet, Solid State Commun. 58, 739 (1986). 253. N. B. Colthup, L. H. Daly, and S. E. Wiberley, "Introduction to Infrared & Raman Spectroscopy." Academic Press, New York, 1975. 254. P.R. Griffiths, "Chemical Infrared Fourier Transform Spectroscopy." Wiley, New York, 1975. 255. T. Sharda, D. S. Misra, and D. K. Avasthi, Vacuum 47, 1259 (1996). 256. G. Dollinger, A. Bergmaier, C. M. Frey, M. Roesler, and H. Verhoeven, Diamond Relat. Mater. 4, 591 (1995). 257. K.M. McNamara, K. K. Gleason, and C. J. Robinson, J. Vac. Sci. TechnoL A 10, 3143 (1992). 258. D.K. Avasthi, Vacuum 48, 1011 (1997). 259. M.I. Landstrass and K. V. Ravi, Appl. Phys. Lett. 55, 1391 (1989). 260. K. Baba, Y. Aikawa, and N. Shohata, J. Appl. Phys. 69, 7313 (1991). 261. K.M. McNamara, D. H. Levy, K. K. Gleason, and C. J. Robinson, Appl. Phys. Lett. 60, 580 (1992). 262. G. T. Mearini, I. L. Krainsky, J. J. A. Dayton, Y. Wang, C. A. Zorman, J. C. Angus, and R. W. Hoffman, Appl. Phys. Lett. 65, 2702 (1994). 263. E G. Celli and J. E. Buffer, Appl. Phys. Lett. 54, 1031 (1989). 264. J.E. Butler and R. L. Woodwin, Trans. Roy Soc. London A Sect. 342, 209 (1993). 265. T.R. Anthony, Vacuum 41, 1356 (1990). 266. E G. Celli and J. E. Butler, Annu. Rev. Chem. 42, 643 (1991). 267. K.E. Spear, J. Am. Ceram. Soc. 72, 171 (1989). 268. M. Page and D. W. Brenner, J. Am. Chem. Soc. 96, 3270 (1991). 269. D. Huang and M. Frenklavh, Phys. Chem. 96, 1868 (1992). 270. B. B. Pate, M. H. Hecht, C. Binns, I. Lindau, and W. E. Spicer, J. Vac. Sci. TechnoL 21,364 (1982). 271. J.C. Angus, H. A. Will, and W. S. Stanko, J. Appl. Phys. 39, 2915 (1968). 272. W.A. Yarbrough and R. Messier, Science 247, 688 (1990). 273. B. Dischler, A. Bubenzer, and P. Koidl, Solid State Commun. 48, 105 (1983). 274. A H. Brodsky, M. Cardona, and J. J. Cuomo, Phys. Rev. B 162, 3556 (1977). 275. D.M. Bibby and P. A. Thrower, Dekker, New York, 1982. 276. J. Ruan, W. J. Choyke, and W. D. Partlow, Appl. Phys. Lett. 58, 295 (1991). 277. Y. Moil, N. Eimori, H. Kozuka, Y. Yokota, J. Moon, J. S. Ma, T. Ito, and A. Hirald, Appl. Phys. Lett. 60, 47 (1992). 278. G. Davies, Dekker, New York, 1977. 279. C.D. Clark, A. T. Collins, and G. S. Woods, "The Properties of Natural and Synthetic Diamond," Academic Press, London, 1992. 280. L. S. Pan and D. R. Kania, "Diamond Electronic Properties and Applications," p. 201. Kluwer Academic, Dordrecht/Norwell, MA, 1995. 281. A.R. Badzian and R. DeVries, Mater. Res. Bull. 23,385 (1988). 282. M. Tsuda, M. Nakajima, and S. Oikawa, J. Am. Chem. Soc. 108, 5780 (1986). 283. M. Frenklach and K. Spear, J. Mater. Res. 3, 133 (1988). 284. Y.B. Yam and T. D. Moustakas, Nature 342, 786 (1989). 285. M. Fanciulli, S. Jin, and T. D. Moustakas, Physica B 229, 27 (1996). 286. M. H. Nazare, P. W. Mason, G. D. Watldns, and H. Kanda, Phys. Rev. B 51, 16741 (1995).

SUPERHARD 287. E. Rohrer, C. E O. Graeff, R. Janssen, C. E. Nebel, and M. Stutzmann, Phys. Rev. B 54, 7874 (1996). 288. E.A. Faulkner and J. N. Lomer, Philos. Mag. B 7, 1995 (1962). 289. M. Fanciulli and T. D. Moustakas, Phys. Rev. B 48, 14982 (1993). 290. Y. von Kaenel, J. Stiegler, E. Blank, O. Chauvet, C. Hellwig, and K. Plamann, Phys. Stat. Sol. 154, 219 (1996). 291. Y. Show, T. Izumi, M. Deguchi, M. Kitabatake, T. Hirao, Y. Morid, A. Hatta, T. Ito, and A. Hiraki, Nucl. Instrum. Methods B 127-128, 217 (1997). 292. S. L. Holder, L. G. Rowan, and J. J. Krebs, Appl. Phys. Lett. 64, 1091 (1994). 293. D.J. Keeble and B. Ramakrishnan, Appl. Phys. Lett. 69, 3836 (1996). 294. D. E Talbot-Ponsonby, M. E. Newton, J. M. Baker, G. A. Scarsbrook, R. S. Sussmann, and C. J. H. Wort, J. Phys. Condensed Mater. 8, 837 (1996). 295. S. Dannefaer, T. Bretagnon, and D. Kerr, Diamond Relat. Mater. 2, 1479 (1993). 296. S. Dannefaer, W. Zhu, T. Bretagnon, and D. Kerr, Phys. Rev. B 53, 1979 (1996). 297. R. N. West, Adv. Phys. 22, 263 (1973). 298. N. Amrane, B. Soudini, N. Amrane, and H. Aourag, Mater. Sci. Eng. B 40, 119 (1996). 299. T.H. Huang, C.T. Kuo, C.S. Chang, C.T. Kao, and H.Y. Wen, Diamond Relat. Mater. 1,594 (1992). 300. K. Shibuki, M. Yagi, K. Saijo, and S. Takatsu, Surf. Coat. Technol. 36, 295 (1988). 301. A. K. Mehlmann, S. E Dimfeld, and Y. Avigal, Diamond Rel. Mater. 1, 600 (1992). 302. M.G. Peters and R.H. Cummings, European Patent 0519 587 A1, 1992. 303. X.X Pan, Doctoral Thesis, Vienna University of Technology, 1989. 304. X. Chen and J. Narayan, J. Appl. Phys. 74, 4168 (1993). 305. A.K. Sikder, T. Sharda, D. S. Misra, D. Chandrasekaram, and P. Selvam, Diamond Relat. Mater 7, 1010 (1998). 306. T. Yashiki, T. Nakamura, N. Fujimori, and T. Nakai, Int. Conf. On Metallurgical Coatings and Thin Films (ICMCTF), San Diego, California April 22-26. 307. S. Kubelka, R. Haubner, B. Lux, R. Steiner, G. Stingeder, and M. Grasserbauer, Diamond Relat. Mater. 3, 1360 (1994). 308. C.T. Kuo, T. Y. Yen, and T. H. Huang, J. Mater. Res. 5, 2515 (1990). 309. B. Lux and R. Haubner, Int. J. Refractory, Met. Hard Mater 8, 158 (1989). 310. M. Murakawa, S. Takeuchi, H. Miyazawa, and Y. Hirose, Surf. Coat. Technol. 36, 303 (1988). 311. S. Soderberg, Vacuum 41, 1317 (1990). 312. R.C. McCune, R. E. Chase, and W. R. Drawl, Surf. Coat. Technol. 39/40, 223 (1999). 313. S. Soderberg, A. Gerendas, and M. Sjostrand, Vacuum 41, 2515 (1990). 314. B. S. Park, Y. J. Baik, K. R. Lee, K. Y. Eun, and D. H. Kim, Diamond Relat. Mater 2, 910 (1993). 315. H. Suzuki, H. Matsubara, and N. Horie. J. Jpn. Soc. Powder Metallurgy 33, 262 (1986). 316. Y. Saito. K. Sato, S. Matsuda, and H. Koinuma. J. Water. Sci. B 2937 (1991). 317. M.I. Nesladek, J. Spinnewyn, C. Asinari, R. Lebout, and R. Lorent, Diamond Relat. Mater. 3, 98 (1993). 318. K. Saijo, M. Yagi, K. Shibiki, and S. Takatsu, Surf. Coat. Technol. 43/44, 30 (1990). 319. T. Isozaki, Y. Saito, A. Masuda, K. Fukumoto, M. Chosa, T. Ito, E. J. Oles, A. Inspektor, and C. E. Bauer, Diamond Relat. Mater. 2, 1156 (1993). 320. S. Kubelka, R. Haubner, B. Lux, R. Steiner, G. Stingeder, and M. Grasserbauer, Diamond Relat. Mater. 3, 1360 (1994). 321. M. Nesladek, K. Vandierendonck, C. Quaeyhaegens, M. Kerkhofs, and L. M. StalS, Thin Solid Films 270, 184 (1995). 322. S. Kubelka, R. Haubner, B. Lux, R. Steiner, G. Stingeder, and M. Grasserbauer, Diamond Rel. Mater 3, 1360 (1994). 323. W.G. Moffatt, New York.

COATINGS

185

324. J. Kamer, E. Bergmann, M. Pedrazzini, I. Reineck, and M. Sjostrand, Int. Patent. WO 95/12009, 1995. 325. Volker Weihnacht, W. D. Fan, K. Jagannadham, and J. Narayan, J. Mater. Res. 11, 9 (1996). 326. E. J. Oles, A. Inspektor, and C. E. Bauer, "The New Diamond-Coated Carbide Cutting Tools." Corp. Technol. Center. PA. 327. C. Tsai, J. Nelson, W. W. Gerberich, J. Heberlein, and E. Pfender, J. Mater. Res. 7, 1967 (1992). 328. A. Fayer and O. G. A. Hoffman, AppL Phys. Lett. 67, 2299 (1995). 329. J. Narayan, V. P. Godbole, G. Matera, and R. K. Singh, J. Appl. Phys. 71, 966 (1992). 330. E. Heidarpour and Y. Namba, J. Mater. Res. 8, 2840 (1993). 331. C. Tsai, J. C. Nelson, W. W. Gerberich, D. Z. Liu, J. Heberiein, and E. Pfender, Thin Solid Films 237, 181 (1994). 332. A.K. Sikder, D. S. Misra, D. Singhbal, S. Chakravorty, Surface Coatings Technol. 114, 230 (1999). 333. H. Yang and J. L. Whitten, J. Chem. Phys. 91,126 (1989). 334. E. Johansson, P. Skytt, J. O. Carlsson, N. Wassdahl, and J. Nordgren, J. Appl. Phys. 79, 7248 (1996). 335. M. Yudasaka, K. Tasaka, R. Kikuchi, Y. Ohki, and S. Yoshimura, J. Appl. Phys. 81, 7623 (1997). 336. W. Zhu, P. C. Yang, J. T. Glass, and E Arezzo, J. Mater. Res. 10, 1455 (1995). 337. D.N. Belton and S. J. Schmieg, J. Appl. Phys. 66, 4223 (1989). 338. P.C. Yang, W. Zhu, and J. T. Glass, Mater. Res. 9, 1063 (1994). 339. W. Zhu, P. C. Yang, and J. T. Glass, Appl. Phys. Lett. 63, 1640 (1993). 340. Y. Sato, H. Fujita, T. Ando, T. Tanaka, and M. Kamo, Philos. Trans. Roy Soc. London A 342, 225 (1993). 341. B.D. Cullity, "Elements of X-Ray Diffraction." Addison-Wesley, Reading, MA, 1956. 342. A.K. Sikder, T. Sharda, D. S. Misra, D. Chandrasekaram, P. Veluchamy, H. Minoura, and P. Selvam, J. Mater. Res. 14, 1148 (1999). 343. D.N. Belton and S. J. Schmieg, Thin Solid Films 212, 68 (1992). 344. P.C. Yang, W. Zhu, and J. T. Glass, J. Mater. Res. 8, 1773 (1993) 345. H. Holleck, J. Vac. Sci. Technol. A 4, 2661 (1986). 346. L. Vel, G. Demazeau, and J. Etourneau, Mater. Sci. Eng. B 10, 149 (1991). 347. R.H. Wentorf Jr., J. Chem. Phys. 36, 1990 (1962). 348. O. Mishima, In "Synthesis and Properties of Boron Nitride, (J. J. Pouch and S. A. Alterovitz, Eds.), Vol. 54/55, pp. 313-328. Trans Tech. Publications LTD, Brookfield, 1990. 349. O. Mishima, J. Tanaka, and O. Funkunaga, Science 238, 181 (1987). 350. L. Vel, G. Demazeau, and J. Etourneau, Mater. Sci. Eng. B 10, 149 (1991). 351. L.B. Hackenberger, L. J. Pilione, and R. Messier, In "Science and Technology of Thin Films" (F. Matacotta and G. Ottaviani, Eds.). World Scientific, Singapore, 1996. 352. P. Widmayer, P. Ziemann, S. Ulrich and H. Ehrhardt, Diamond Relat. Mater. 6, 621 (1997). 353. D. R. McKenzie, W. G.Sainty, and D. Green, Mater. Sci. Forum 54/55, 193 (1990). 354. D. R. McKenzie, D. J. H. Cockayne, D. A. Muller, M. Murakawa, S. Miyake, and P. Fallon, J. Appl. Phys. 70, 3007 (1991). 355. D.J. Kester, K. S. Ailey, R. E Davis, and K. L. More, J. Mater. Res. 8, 1213 (1993). 356. D. L. Medlin, T. A. Friedman, P. B. Mirkarimi, M. J. Mills, and K. E McCarty, Phys. Rev. B 50, 7884 (1994). 357. D.L. Medlin, T. A. Friedman, P. B. Mirkarimi, P. Rez, M. J. Mills, and K. E McCarty, J. Appl. Phys. 76, 295 (1994). 358. D.J. Kester, K. S. Ailey, R. E Davis, and D. J. Lichtenwalner, J. Vac. Sci. Technol. 12, 3074 (1994). 359. S. Watanabe, S. Mayake, W. Zhou, Y. Ikuhara, T. Suzuki, and M. Murakawa, Appl. Phys. Lett. 66 2490 (1995). 360. W.L. Zhou, Y. Ikuhara, M. Murakawa, S. Watanabe, and T. Suzuki, Appl. Phys. Lett. 66, 2490 (1995). 361. P.B. Mirkarimi, D. L. Medlin, K. E McCarty, D. C. Dibble, W. M. Clift, J. A. Knapp, and J. C. Barbour, J. Appl. Phys. 82, 1617 (1997). 362. Y. Yamada-Takamura, O. Tsuda, H. Ichinose, and T. Yoskida, Phys. Rev. B 59, 352 (1999).

186

SIKDER AND KUMAR

363. D. Zhang, D. M. Davalle, W. L. O'Brien, and D. N. Mcllroy, Surface Sci. 461, 16 (2000). 364. W.L. Wang, K. J. Liao, S. X. Wang, and Y. W. Sun, Thin Solid Films 368, 283 (2000). 365. D. R. McKenzie, W. D. McFall, W. G. Sainty, C. A. Davis, and R. E. Collins, Diamond Relat. Mater 2, 970 (1993). 366. G. E Cardinale, D. L. Medlin, P. B. Mirkarimi, K. E McCarty, and D. G. Howitt, J. Vac. Sci. Technol. 15, 196 (1997). 367. M. Zeitler, S. Seinz, and B. Rauschenbach, J. Vac. Sci. Technol. 17, 597 (1999). 368. D.J. Kester and R. Messier, J. Appl. Phys. 72, 504 (1992). 369. P.B. Mirkarimi, D. L. Medlin, K. E McCarty, T. A. Friedman, G. E Cardinale, D. G. Howitt, E. J. Klaus, and W. G. Wolfer, J. Mater Res. 9, 2925 (1994). 370. E B. Mirkarimi, D. L. Medlin, K. E McCarty, and J. C. Barbour, Appl. Phys. Lett. 66, 2813 (1995). 371. E B. Mirkarimi, D. L. Medlin, K. E McCarty, G. E Cardinaie, D. K. Ottensen, and H. A. Johnsen, J. Vac. Sci. Technol. 14, 251 (1996). 372. Z. E Zhou, I. Bello, V. Kremnican, M. K. Fung, K. H. Lai, K. Y. Li, C. S. Lee, and S. T. Lee. Thin Solid Films 368, 292 (2000). 373. T. Ichiki, S. Amagi, and T. Yoshida, J. Appl. Phys. 79, 4381 (1996). 374. T. Takami, I. Kusunoki, K. Suzuki, K.P. Loh, I. Sakaguchi, M. NishitaniGamo, T. Taniguchi, and T. Ando, Appl. Phys. Lett. 73, 2733 (1998). 375. R.A. Roy, P. Catania, K. L. Saenger, J. J. Cuomo, and R. L. Lossy, J. Vac. Sci. Technol. B 11, 1921 (1993). 376. Y. Lfshitz, S. R. Kasi, and J. W. Rabaiais, Phys. Rev. B 41, 10468 (1990). 377. W. Dworkschak, K. Jung, and H. Ehrhardt, Thin Solid Films 254, 65 (1995). 378. J. Robertson, J. Gerber, S. Sattel, M. Weiler, K. Jung, and H. Ehrhardt, Appl. Phys. Lett. 66, 3287 (1995). 379. S. Uhlmann, T. Frauenheim, and U. Stephan, Phys. Rev. B 51, 4541 (1995). 380. S. Reinke, M. Kuhr, W. Kulisch, and R. Kassing, Diamond Relat. Mater. 4, 272 (1995). 381. L. Jiang, A. G. Fitzgerald, M. J. Rose, A. Lousa, and S. Gimeno, Appl. Surface Sci. 167, 89 (2000). 382. C. Hu, S. Kotake, Y. Suzuki, and M. Senoo, Vacuum 59, 748 (2000). 383. K. ELoh, I. Sakaguchi, M. Nishitani-Gamo, T. Taniguchi, and T. Ando, Phys. Rev. B 57, 7266 (1998). 384. J. Deng, B. Wang, L. Tan, H. Yan, and G. Chen, Thin Solid Films 368, 312 (2000). 385. X. Zhang, H. Yan, B. Wang, G. Chen, and S. P. Wong, Mater Lett. 43, 148 (2000). 386. J. Vilcarromero, M. N. E Carreno, and I. Pereyra, Thin Solid Films 373, 273 (2000). 387. K.P. Loh, I. Sakaguchi, M. Nishitani-Gamo, S. Tagawa, T. Sugino, and T. Ando, Appl. Phys. Lett. 74, 28 (1999). 388. K.P. L0h, I. Sakaguchi, M. Nishitani-Gamo, T. Taniguchi, and T. Ando, Appl. Phys. Lett. 72, 3023(1998). 389. X.W. Zhang, Y. J. Zou, H. Yan, B. Wang, G. H. Chen, and S. P. Wong, Mater Lett. 45, 111 (2000). 390. S.P.S. Arya, and A. D'Amico, Thin Solid Films 157, 267 (1988). 391. L.B. Hackenberger, L. J. Pilione, and R. Messier, In "Science and Technology of Thin Films" (E Matacotta and G. Ottaviani, Eds.). World Scientific, Singapore, 1996. 392. W. Kulisch and S. Reinke, Diamond Films Technol. 7, 105 (1997). 393. E Richter, In "Diamond Materials IV Electrochemical Society Proc." (K. V. Ravi, K. E. Spear, J. L. Davidson, R. H. Hadge, and J. P. Dismukes, Eds.), Vol. 94/95. The Electrochemical Society, Pennington, NJ, 1995. 394. T. Yoshida, Diamond Relat. Mater 5, 501 (1996). 395. C. Ronning, H. Feldermann, and H. Hofsass, Diamond Relat. Mater 9, 1767 (2000) 396. F.P. Bundy and R. H. Wentorf, J. Chem. Phys. 38, 1144 (1963). 397. E R. Corrigan and E P. Bundy, J. Chem. Phys. 63, 3812 (1975). 398. V.L. Solozhenko, Thermochimica Acta 218, 221 (1993). 399. S. Nakano, O. Funkunaga, Diamond Relat. Mater 2, 1409 (1993).

400. S. Bohr, R. Haubner, and B. Lux, Diamond Relat. Mater. 4, 714 (1995). 401. T. Sato, T. Ishii, and N. Setaka, Commun. Am. Ceram. Soc. 65, C162 (1982). 402. E B. Mirkarimi et al.,Mater Sci. Eng. R21, 47 (1997). 403. JCPDS 34-421. 404. JCPDS 41-1487. 405. T. Sato, Proc. Japan Acad. Set B 61,459 (1985). 406. JCPDS 26-1079. 407. J. Thomas Jr., N. E. Weston, and T. E. O'Connor, J. Amen Chem. Soc. 84, 4619 (1963). 408. J.A. Van Vechten, Phys. Rev. 187, 1007 (1969). 409. JCPDS 26-773. 410. JCPDS 19-268. 411. K. Inagawa, K. Watanabe, H. Ohsone, K. Saitoh, and A. Itoh, J. Vac. Sci. Technol. A 5, 2696 (1987). 412. D.J. Kester, K. S. Ailey, R. E Davis, and K. L. More, J. Mater Res. 8, 1213 (1993). 413. L.B. Hackenberger, L. J. Pilione, R. Messier, and G. P. Lamaze, J. Vac. Sci. Technol. A 12, 1569 (1994). 414. D.J. Kester and R. Messier, J. AppL Phys. 72, 504 (1992). 415. D. Bouchier, G. Sene, M. A. Djouadi, and P. Moiler, NucL Instum. Methods B 89, 369 (1994). 416. M. Sueda, T. Kobayashi, H. Tsukamoto, T. Rokkaku, S. Morimoto, Y. Fukaya, N. Yamashita, and T. Wada, Thin Solid Films 228, 97 (1993). 417. T. Wada and N. Yamashita, J. Vac. Sci. Technol. A 10, 515 (1992). 418. T. Ikeda, T. Satou, and H. Satoh, Surf. Coat. Technol. 50, 33 (1991). 419. S. Watanabe, S. Miyake, and M. Murakawa, Surf. Coat. Technol. 49, 406 (1991). 420. D. R. McKenzie, W. D. McFall, W. G. Sainty, C. A. Davis, and R. E. Collins, Diamond Relat. Mater 2, 970 (1993). 421. T. Ikeda, Y. Kawate, and Y. Hirai, J. Vac. Sci. TechnoL A 8, 3168 (1990). 422. M. Murakawa and S. Watanabe, Surf. Coat. TechnoL 43/44, 128 (1990). 423. M. Lu, A. Bousetta, R. Sukach, A. Bensaoula, K. Waiters, K. EipersSmith, and A. Schultz, AppL Phys. Lett. 64, 1514 (1994). 424. S. Mineta, M. Kolrata, N. Yasunaga, and Y. Kikuta, Thin Solid Films 189, 125 (1990). 425. T. A. Friedmann, P. B. Mirkarimi, D. L. Medlin, K. E McCarty, E. J. Klaus, D. Boehme, H. A. Johnsen, M. J. Mills, and D. K. Ottesen, J. Appl. Phys. 76, 3088 (1994). 426. S. Turan and K. M. Knowles, Phys. Status Solidi 150, 227 (1995). 427. A.K. Ballal, L. Salamanca-Riba, G. L. Doll, C. A. Taylor II, and R. Clarke, J. Mater Res. 7, 1618 (1992). 428. C. R. Aita, In "Synthesis and Properties of Boron Nitride" (J. J. Pouch, S. A. Alterovitz, Eds.), Materials Science Forum, Vol. 54/55. Trans Tech, Brookfield, 1990. 429. R. Ganzetti and W. Gissler, Mater Manuf Processes 9, 507 (1994). 430. J. Hahn, M. Friedrich, R. Pintaske, M. SchaUer, N. Kahl, D. R. T. Zahn, and E Richter, Diamond Relat. Mater 5, 1103 (1996). 431. M. Friedrich, J. Hahn, S. Laufer, E Richter, H. J. Hinneberg, and D. R. T. Zahn, In "Diamond Materials IV Electrochemical Society Proc." (K. V. Ravi, K. E. Spear, J. L. Davidson, R. H. Hauge, and J. P. Dismukes, Eds.), Vol. 94/95. The Electrochemical Society, Pennington, NJ, 1995. 432. V. Y. Kulikovsky, L. R. Shaginyan, V. M. Vereschaka, and N. G. Hatyenko, Diamond Relat. Mater 4, 113 (1995). 433. M. Mieno and T. Yoshida, Surf. Coat. Technol. 52, 87 (1992). 434. S. Kidner, C. A. Taylor II, and R. Clarke, AppL Phys. Lett. 64, 1859 (1994). 435. L. E Allard, A. K. Datye, T. A. Nolan, S. L. Mahan, and R. T. Paine, Ultramicroscopy 37, 153 (1991). 436. S. Nishiyama, N. Kuratani, A. Ebe, and K. Ogata, Nucl. Instrum. Meth. B 80/81, 1485 (1993). 437. T. Ichiki, T. Momose, and T. Yoshida, J. Appl. Phys. 75, 1330 (1994). 438. M. Okamoto, Y. Utsumi, and Y. Osaka, Plasma Sources Sci. TechnoL 2, 1 (1993). 439. W. Dworschak, K. Jung, and H. Ehrhardt, Thin Solid Films 245, 65 (1995).

SUPERHARD COATINGS 440. A. Chayahara, H. Yokoyama, T. Imura, and Y. Osaka, Appl. Surf. Sci. 33/34, 561 (1988). 441. M. Okamato, H. Yokoyama, and Y. Osaka, Jpn. J. Appl. Phys. 29, 930 (1990). 442. K.J. Lao and W. L. Wang, Phys. Stat. Sol. 147, K9 (1995). 443. H. Saitoh, T. Hirose, H. Matsui, Y. Hirotsu, and Y. Ichinose, Surf. Coat. Technol. 39/40, 265 (1989). 444. H. Saitoh and W. A. Yarbrough, Appl. Phys. Lett. 58, 2230 (1991). 445. S. Reinke, M. Kuhr and W. Kulisch, Surf. Coat. Technol. 74/75, 806 (1995). 446. A. Weber, U. Bringmann, R. Nikulski, and C. P. Klages, Diamond. Relat. Mater. 2, 201 (1993). 447. H. Hofsass, H. Feldermann, M. Sebastian, and C. Ronning, Phys. Rev. B 55, 13230 (1997). 448. H. Hofsass, C. Ronning, U. Griesmeier, M. Gross, S. Reinke, and M. Kuhr, Appl. Phys. Lett. 67, 46 (1995). 449. T. Ichiki, S. Amagi, and T. Yoshida, J. Appl. Phys. 79, 4381(1996). 450. M. F. Plass, W. Fukarek, A. Kolitsch, M. Mader, and W. Moiler, Phys. Stat. SoL A 155, K1 (1996). 451. D.H. Berns and M. A. Capelli, Appl. Phys. Lett. 68, 2711 (1996). 452. G. Krannich, E Richter, J. Hahn, R. Pintaske, V. B. Filippov, and Y. Paderno, Diamond Relat. Mater 6, 1005 (1997). 453. G. Krannich, E Richter, J. Hahn, R. Pintaske, M. Friedrich, S. Schmidbauer, and D. R. T. Zahn, Surf. Coat. Technol. 90, 178 (1996). 454. S. Manorama, G. N. Chaudhari, and V. J. Rao, J. Phys. D 26, 1793 (1993). 455. A.R. Phani, S. Roy, and V. J. Rao, Thin Solid Films 258, 21 (1995). 456. P. B. Mirkarimi, D. L. Medlin, T. E Friedmann, M. J. Mills, and K. E McCarty, Phys. Rev. B 50, 7884 (1994). 457. P. B. Mirkarimi, D. L. Medlin, T. E Friedmann, M. J. Mills, and K. E McCarty, Phys. Rev. B 50, 8907 (1994). 458. C.A. Davis, K. M. Knowles, and G. A. J. Araratunga, Surf. Coat. Technol. 76, 316 (1995). 459. D.A. Muller, Y. Tzou, R. Rah, and J. Silcox, Nature 366, 725 (1993). 460. H. Yokoyama, M. Okamoto, and Y. Osaka, Jpn. J. Appl. Phys. 30, 344 (1991). 461. T. Ikeda, Appl. Phys. Lett. 61,786 (1992). 462. N. Tanabe, T. Hayashi, and M. Iwaki, Diamond Relat. Mater. 1, 151 (1992). 463. P.B. Mirkarimi, D. L. Medlin, T. E Friedmann, W. G. Wolfer, E. J. Klaus, G. E Cardinale, D. G. Howitt, and K. E McCarty, J. Mater. Res. 9, 2925 (1994). 464. S. Reinke, M. Kuhr, and W. Kulisch, Surf. Coat. Technol. 74/75, 723 (1995). 465. G. Rene, D. Bouchier, S. Ilias, M. A. Djouadi, J. Pascallon, V. Stambouli, P. Moiler, and G. Hug, Diamond Relat. Mater 5, 530 (1996). 466. D. Litvinov, C. A. Taylor II, and R. Clarke, Diamond Relat. Mater 7, 360 (1998). 467. D. R. McKenzie, W. D. McFall, H. Smith, B. Higgins, R. W. Boswell, A. Durandet, B. W. James, and L. S. Falconer, Nucl. Instrum. Meth. B 106, 90 (1995). 468. J. Hahn, E Richter, R. Pintaske, M. Roder, E. Schneider, and T. Welzel, Surf. Coat. Technol. 92, 129 (1996). 469. P. B. Mirkarimi, D. L. Medlin, J. C. Barbour, andK. E McCarty, Appl. Phys. Lett. 66, 2813 (1995). 470. D.J. Kester, K. S. Ailey, D. J. Lichtenwaler, and R. E Davis, J. Vac. Sci. Technol. A 12, 3074 (1994). 471. P.X. Yan, S. Z. Yang, B. Li, and X. S. Chen, J. Cryst. Growth 148, 232 (1995). 472. W. L. Lin, Z. Xia, Y. L. Liu, and Y .C. Fen, Mater Sci Eng. B 7, 107 (1990). 473. J.J. Cuomo, J. P. Doyle, J. Bruley, and J. C. Liu, Appl. Phys. Lett. 58, 466 (1991). 474. K. E McCarty, P. B. Mirkarimi, D. L. Medlin, and T. E Friedmann, Diamond Relat. Mater 5, 1519 (1996). 475. S. Reinke, M. Kuhr, and W. Kulisch, Diamond Relat. Mater 3, 341 (1994).

187

476. S. Reinke, M. Kuhr, W. Kulisch, and R. Kassing, Diamond Relat. Mater. 4, 272 (1995). 477. J. Robertson, Diamond Relat. Mater 5,519 (1996). 478. J. Malherbe, Crit. Rev. SoL State 19, 55 (1994). 479. C. Weissmantel, K. Bewilogua, D. Dietrich, H. J. Hinneberg, S. Klose, W. Nowick, and G. Reisse, Thin Solid Films 72, 19 (1980). 480. S. Reinke, M. Kuhr, and W. Kulisch, Diamond Relat. Mater. 5, 508 (1996). 481. D. R. McKenzie, D. J. H. Cockayne, D. A. Muller, M. Murakawa, S. Miyake, S. Wantanabe, and P. Fallon, J. Appl. Phys. 70, 3007 (1991). 482. P.B. Mirkarimi, K. E McCarty, G. E Cardinale, D. L. Medlin, D. K. Ottensen, and H. A. Johnsen, J. Vac. Sci. Technol. A 14, 251 (1996). 483. Y. Lifshitz, S. R. Kasi, and J. W. Rabelais, Phys. Rev. Lett. 62, 1290 (1987). 484. J. Robertson, Diamond Relat. Mater 3,984 (1993). 485. C.A. Davis, Thin Solid Films 226, 30 (1993). 486. M. Nastasi and J. W. Mayer, Mater. Sci. Rep. 6, 1 (1991). 487. C. Collazo-Davila, E. Bengu, L. D. Marks, and M. Kirk, Diamond Relat. Mater 8, 1091 (1999). 488. D.R. McKenzie, W. G. Sainty, and D. Green, In "Synthesis and Properties of Boron Nitride" (J. J. Pouch and S. A. Alterovitz, Eds.), Materials Science Forum, Vol. 54/55. Trans Tech Publications, Brookfield, 1990. 489. D.M. Back, In "Physics of Thin Films," Vol. 15, p. 287. Academic Press, Boston, 1991. 490. S. Jager, K. Bewilogua, and C. P. Klages, Thin Solid Films 245, 50 (1994). 491. S. Fahy, Phys. Rev B 51, 12873 (1995). 492. S. Fahy, C. A. Taylor II, and R. Clarke, Phys. Rev B (1997). 493. M. Terauchi, M. Tanaka, K. Suzuki, A. Ogino, and K. Kimura, Chem. Phys. Lett. 324, 359 (2000). 494. D.J. Smith, W. O. Saxton, M. A. O'Keefe, G. J. Wood, and W. M. Stobbs, Ultramicroscopy 11,263 (1983). 495. P.B. Mirkarimi, D. L. Medlin, P. Rez, T. E Friedmann, M. J. Mills, and K. E McCarty, J. Appl. Phys. 76, 295 (1994). 496. M. P. Johansson, L. Hultman, S. Daaud, K. Bewilogua, H. Luthje, A. Schutze, S. Kouptsidas, and G. S. A. M. Theunissen, Thin Solid Films 287, 193 (1996). 497. D.J. Kester, K. S. Ailey, and R. F. Davis, Diamond Relat. Mater. 3, 332 (1994). 498. H. Hofsass, C. Ronning, U. Griesmeier, M. Gross, S. Reinke, M. Kuhr, J. Zweck, and R. Fischer, Nucl. Instrum. Meth. B 106, 153 (1990). 499. D.G. Howitt, P. B. Mirkarimi, D. L. Medlin, K. E McCarty, E. J. Klaus, G. E Cardinale, and W. M. Clift, Thin Solid Films 253, 130 (1994). 500. A. K. Ballal, L. Salamanca-Riba, C. A. Taylor II, and G. L. Doll, Thin Solid Films 224, 46 (1993). 501. D.G. Rickerby, P. N. Gibson, W. Gissler, and J. Haupt, Thin Solid Films 209, 155 (1992). 502. W.L. Zhou, Y. Ikuhara, and T. Suzuki, Appl. Phys. Lett. 67, 3551 (1995). 503. H.K. Schmid, Microsc. Microanal. Microstruct. 6, 99 (1995). 504. Y. Bando, K. Kurashima, and S. Nakano, J. European Ceramic Soc. 16, 379 (1996). 505. M.R. McGurk and T. E Page, J. Mater Res. 14, 2283 (1999). 506. W.C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992). 507. P.M. Sargent, In "Microindentation Techniques in Science and Engineering" (P. Blau and B. Lawn, Eds.), p. 160. ASTM, Ann Arbor, 1995. 508. D.J. Kester, K. S. Ailey, R. E Davis, and K. L. More, J. Mater. Res. 8, 1213 (1993). 509. D. L. Medlin, T. A. Friedmann, P. B. Mirkarimi, P. Rez, K. E McCarty, and M. J. Mills, J. Appl. Phys. 76, 295 (1994). 510. D. R. McKenzie, W. D. McFall, W. G. Sainty, C. A. Davis, and R. E. Collins, Diamond Relat. Mater. 2, 970 (1993) 511. G. ECardinale, D. G. Howitt, K. E McCarty, D. L. Medlin, P. B. Mirkarimi, and N. R. Moody, Diamond Relat. Mater 5, 1295 (1996) 512. Y. Andoh, S. Nishiyama, H. Kirimura, T. Mikami, K.Ogata, and E Fujimoto, Nucl. Instrum. Methods B 59/60, 276 (1991). 513. S. Nishiyama, N. Kuratani, A. Ebe, and K. Ogata, Nucl. lnstrum. Methods B 80/81, 1485 (1993).

188

SIKDER AND KUMAR

514. W. L. Lin, Z. Xia, Y. L. Liu and Y. C. Fen, Mater Sci Eng. B 7, 107 (1990). 515. T. Wada and N. Yamashita, J. Vac. Sci. Technol. A 10, 515 (1992). 516. K. Inagawa, K. Watanabe, K. Saitoh, Y. Yuchi, and A. Itoh, Surf. Coat. Technol. 39/40, 253 (1989). 517. P. B. Mirkarimi, D. L. Medlin, K. E McCarty, D. C. Dibble, and W. M. Clift, J. Appl. Phys. 82, 1617 (1997). 518. H. Luthje, K. Bewilogua, S. Daaud, M. Johansson, and L. Hultman, Thin Solid Films 257, 40 (1995). 519. M.P. Johansson, H. Sjostrom, and L. Hultman, Vacuum 53, 441 (1999). 520. M. Murakawa, S. Watanabe, W. L. Zhou, Y. Ikuhara, and T. Suzuki, Appl. Phys. Lett. 66, 2490 (1995). 521. M. Murakawa and S. Watanabe, Surf. Coat. Technol. 43/44, 145 (1990). 522. H. Kohzuki, Y. Okuno, and M. Motoyama, Diamond Films Technol. 5, 95 (1995). 523. P.B. Mirkarimi, unpublished work, (1996). 524. I. Konyashin, J. Bill, and E Aldinger, Chem. Vapor Deposition 3, 239 (1997). 525. W.J. Zhang and S. Matsumoto, Chem. Phys. Lett. 330, 243 (2000). 526. T.W. Scharf, R. D Ott, D. Yang, and J. A. Baranard, J. Appl. Phys. 85, 3142 (1999). 527. E.C. Cutiongco, D. Li, Y. C. Chung, and C. S. Bhatia, J. Tribol. 118,543 (1996). 528. G. Jungnickel, P. K. Stich, and T. Frauenheim, Phys. Rev. B 57, R661 (1998). 529. K. Ogata, J. E D. Chubaci, and E Fujimoto, J. Appl. Phys. 76, 3791 (1994). 530. J. Robertson and C. A. Davis, Diamond Relat. 4, 441 (1995). 531. Z.J. Zang, J. Hung, S. Fan, and C. M. Lieber, Mater Sci. Eng. A 209 5 (1996). 532. Z.J. Zang, J. Hung, S. Fan, and C. M. Lieber, Appl. Phys. Lett. 68, 2639 (1996). 533. V. Hajek, K. Rusnaka, J. Vlacek, L. Martinu, and H. M. Hawthorne, Wear 213, 80 (1997). 534. E. Murdock, R. Simmons, and R. Davidson, IEEE Trans. Magn. 28, 3078 (1992). 535. T.W. Scharf, R. D. Ott, D. Yang, and J. A. Baranard, J. Appl. Phys. 85, 3142 (1999). 536. A.M. Liu and M. L. Cohen, Science 245, 841 (1989). 537. A.M. Liu and M. L. Cohen, Phys. Rev. B 41, 10727 (1990). 538. A.M. Liu and R. M. Wentzcovitch, Phys. Rev. B 50, 10362 (1990). 539. T. Malkow, Mater Sci. Eng. A 292, 112 (2000). 540. D.M. Teter, MRS Bull 23, 22 (1998). 541. M.R. Wixom, J. Am. Ceram. 73, 1973 (1990). 542. M.B. Guseva et al., Diamond Relat. Mater 6, 640 (1997). 543. M.R. Wixom, J. Am. Ceram. Soc 73,1973 (1990). 544. J.H. Nguyen and R. Jeanolz, Mater Sci. Eng. A 209, 23 (1996). 545. D.M. Teter, and R. J. Hemley, Science 271, 53 (1996). 546. V. P. Dymont, E. M. Nekrashevich, and I. M. Starchenko, Solid State Commun. 111,443 (1999). 547. A. Hoffman et al. Surf. Coat. Technol. 68/69, 616 (1995). 548. K.J. Boyd et al. J. Vas. Sci. Technol. A 13, 2110 (1995). 549. S. Veprek, J, Weidmann and E Glatz, J. Vas. Sci. Technol. A 13, 2914 (1995). 550. Tyan-Ywan Yen and Chang-Pin Chou, Appl. Phys. Lett. 67, 2801 (1995). 551. T.-Y. Yen and C.-P. Chou, Appl. Phys. Lett. 67, 2801 (1995). 552. C. Spaeth, M. Kuhn, U. Kreissig, and E Richter, Diamond Relat. Mater 6, 626 (1997). 553. D. G. McCulloch and A. R. Merchant, Thin Solid Films 290-291, 99 (1996). 554. K. Ogata, J. E Diniz Chubaci and E Fujimoto, J. Appl. Phys. 76, 3791 (1994). 555. P. Hammer, W. Gissler, Diamond Relat. Mater 5, 1152 (1996). 556. S.S. Todorov et al., J. Vac. Sci. Technol. A 12, 3192 (1994). 557. M. Kohzaki et al., Jpn. J. Appl. Phys. 362313 (1997). 558. M. Kohzaki et al., Thin Solid Films 308/309, 239 (1997). 559. H.W. Lu, X. R. Zou, J. Q. Xie, and J. Y. Feng, J. Phys. D 31,363 (1998).

560. S. Veprek, J. Weidmann, and E Glatz, J. Vac. Sci. Technol. A 13, 2914 (1995). 561. S.A. Korenev et al., Thin Solid Films 308/309, 233 (1997). 562. S. Muhl andJ. M. Mendez, Diamond Relat. Mater 8, 1809 (1999) 563. J. Bulir et al., Thin Solid Films 292, 318 (1997). 564. R. Gonzalez et al.,Appl. Surf. Sci. 109/110, 380 (1997) 565. X.-A. Zhao et al.,Appl. Phys. Lett. 66, 2652 (1995) 566. C.W. Ong et al., Thin Solid Films 280, 1 (1996). 567. Z. J. Zhang, S. Fan, J. Huang, and C. M. Lieber, Appl. Phys. Lett. 68, 3582 (1995) 568. E. Aldea et al., Jpn. J. Appl. Phys. 36, 4686 (1997). 569. S. Acquaviva et al., Appl. Surf. Sci. 109/110, 408 (1997). 570. Z.M. Ren et al., Phys. Rev. B 51, 5274 (1995). 571. D.J. Johnson, Y. Chen, Y. He, and R. H. Prince, Diamond Relat Mater 6, 1799 (1997). 572. A.A. Voevodin and M. S. Donley, Surf. Coat. Technol. 82, 199 (1996). 573. P. Merel et al.,Appl. Phys. Lett. 71, 3814 (1997). 574. J. Hu, P. Yang, and C. M. Lieber, Phys. Rev. B 57, 3185 (1998). 575. A.K. Sharma et al.,Appl. Phys. Lett. 69, 3489 (1996). 576. S. A. Uglov, V. E. Shub, A. A. Beloglazov, and V. I. Konov, Appl. Surf. Sci. 92, 656(1996). 577. Y. Chen, L. Guo, E Chen, and E. G. Wang, J. Phys. Condens. Matter 8, L685 (1996). 578. (a) C. Niu, Y. Z. Lu, and C. M. Lieber, Science 261,334 (1993). (b) N. Xu et al., J. Phys. D 30, 1370 (1997). (c) A. Kumar, U. Ekanayake, and J. S. Kapat, Surf. Coat. Technol. 102, 113 (1998). (d) L. Wan and R. E Egerton, Thin Solid Films 279, 34 (1996). (e) H. Sjostrom et al., J. Mater Res. 11, 981 (1996). 579. R. Kurt, R. Sanjines, A. Karimi, and E Levy, Diamond Relat. Mater 9, 566 (2000). 580. B.C. Holloway et al., Thin Solid Films 290-291, 94 (1996). 581. Kin Man Yu et al., Phys. Rev. B 49, 5034 (1994). 582. H. Sjostrom et al., J. Mater Res. 11, 981 (1996) 583. P. Hammer and W. Gissler, Diamond Relat. Mat er 5, 1152 (1996) 584. N. Axen et al., Surf and Coat. Tech. 81,262 (1996) 585. P. Wood, T. Wydeven and O. Tsuji, Thin Solid Films 258, 151 (1995) 586. E Lfreire Jr, and D. E Franceschini, Thin Solid Films 293, 236 (1997) 587. M.M. Lacerda et al., Diamond Relat. Mater 6, 631 (1997) 588. Y. Zhang, Z. Zhou, and H. Li, AppL Phys. Lett. 68, 634 (1996) 589. H.K. Woo et al., Diamond Relat. Mater 6, 635 (1997) 590. P.H. Fang, Appl. Phys. Lett. 69, 136 (1996). 591. J. Sun, Y. Zhang, X. He, W. Liu, C. S. Lee, and S. T. Lee, Mater Lett. 38, 98 (1999). 592. V.P. Novikov and V. P. Dymont, AppL Phys. Lett. 70, 200 (1997). 593. Qiang Fu, Chuan-Bao Cao, and He-Sun Zhu, Chem. Phys. Lett. 314, 223 (1999). 594. K.H. Park, B. C. Kim, and H. Kang, J. Chem. Phys. 97, 2742 (1992). 595. A.R. Merchant, D. G. McCulloch, D. R. McKenzie, Y. Yin, L. Hall, and E. G. Gerstner, J. AppL Phys. 79, 6914 (1996). 596. E Link, H. Baumann, A. Markwitz, E. E Krimmel, and K. Bethge, Nucl. Instrum. Methods B 113, 235 (1996). 597. D. M. Bhusari, C. K. Chen, K. H. Chen, T. J. Chuang, L. C. Chen, and M. C. Lin, J. Mater Res. 12, 322 (1997). 598. K. Takahiro, H. Habazaki, S. Nagata, M. Kishimoto, S. Yamaguchi, E Nishiyama, and S. Nimori, Nucl. Instrum. Methods B 152, 301 (1999). 599. J. Martin-Gi, M. Sarikaya, M. Jose-Yacaman, and A. Rubio, J. Appl. Phys. 81, 2555 (1997). 600. X.R. Zou, H. W. Lu, J. Q. Xie, and J. Y. Feng, Thin Solid Films 345, 208 (1999). 601. D. Marton, K. J. Boyd, A. H. A1-Bayati, S. S. Todorov, and J. W. Rabalais, Phys. Rev. Lett. 73, 118 (1994). 602. I. Bertoti, M. Mohai, A. Toth, and B. Zelei, Nucl. Instrum. Methods B 148, 645 (1999). 603. J. Wang, S. E Durrant, and M. A. B. Moraes, J. Non-Crytst. Solids 262, 216 (2000).

SUPERHARD 604. M. Balaceanu, E. Grigore, E Truica-Marasescu, D. Pantelica, E Negoita, G. Pavelescu, and E Ionescu, Nucl. Instrum. Methods B 161-163, 1002 (2000). 605. M. Bai, K. Kato, N. Umehara, Y. Miyake, J. Xu, and H. Tokisue, This Solid Films 376, 170 (2000). 606. N. Tajima, H. Saze, H. Sugimura, and O. Taki, Vacuum 59 567 (2000). 607. K. Suenaga, M. Yudasaka, C. Colliex, S. Iijima, Chem. Phys. Lett. 316, 365 (2000). 608. E-R. Weber and H. Oechsner, Thin Solid Films 355-356, 73 (1999). 609. C. Popov, M. E Plass, R. Kassing, W. Kulisch, Thin Solid Films 355-356, 406 (1999). 610. D.Y. Lee, Y. H. Kim, I. K. Kim, and H. K. Buik, Thin Solid Films 355356, 239 (1999). 611. C. Niu, Y. z. Lu and C. M. Lierber, Science 261, 334 (1993). 612. K. M. Yu, M. L. Cohen, E. E. Hailer, W. L. Hansen, A. Y. Liy and I. C. Wu, Phys. Rev. B 49, 5034 (1994). 613. M. Y. Chen, X. Lin, V. P. Dravid, Y. W. Chung, M. S. Wong, and W. D. Sproul, Surf. Coat. Tech. 54/55, 360 (1992). 614. C. Sandorfy, In "The Chemistry of Functional Groups" (S. Patai, Ed.). The Chemistry of the Carbon-Nitrogen Double Bonds, Interscience Publishers, London, 1970. 615. L.J. Bellamy, "The Infrared Spectra of Complex Molecules." Chapman and Hall, London, 1975. 616. J. H. Kauffman, S. Metin, and D. D. Saperstein, Phys. Rev. B 39, 3053 (1989). 617. J. Widany et al., Diamond Relat. Mater 5, 1031 (1996). 618. S. Matsumoto, E.-Qxie, and E Izumi, Diamond Relat. Mater 8, 1175 (1999). 619. E Izumi, Rietveld analysis programs RIETAN and PREMOS and special applications, In "The Rietveld Method" (R. Y. Young, Ed.), Chapter 13. Oxford University Press, Oxford, 1995. 620. D.M. Teter, and R. J. Hemley, Science 271, 53 (1996). 621. Z.M. Ren, Y. C. Du, Z. E Ying, E M. Li, J. Lin, Y. Z. Ren, and X. E Zong, Nucl. Instrum. Methods Pkys. Res. B 117, 249 (1996). 622. L. A. Bursil, J. L. Peng, V. N. Gurarie, A. N. Orlov, and S. Prawer, J. Mater Res. 10, 2277 (1995). 623. D. Li, XW. Lin, S. C. Cheng, V. E Dravid, Y. W. Chung, M. S. Wong, and W. D. Sproul, Appl. Phys. Lett. 68, 1211 (1996). 624. A. Badzian and T. Badzian, Diamond Relat. Mater 5, 1051 (1996). 625. J.H. Nguyen and R. Jeanloz, Mater Sci. Eng. A 209, 23 (1996). 626. T. Werninghaus, D. R. T. Zahn, E. G. Wang, and Y. Chen, Diamond Relat. Mater 7, 52 (1998). 627. M. Kawaguchi, Y. Tokimatsu, K. Nozaki, Y. Kaburagi, and Y. Hishiyama, Chem. Lett. 1997, 1003 (1997). 628. Y. S. Jin, Y. Matsuda, and H. Fujiyama, Jpn J. Appl. Phys. 37, 4544 (1998). 629. M. L. De Giorgi, G. Leggieri, A. Luches, M. Martino, A. Perrone, A. Zocco, G. Barucca, G. Majni, E. Gyorgy, I. N. Mihailescu, and M. Popescu, Appl. Surf. Sci. 27, 481 (1998). 630. C. Niu, Y. Z. Lu, and C. M. Lieber, Science 261,334 (1993) 631. K. M. Yu, M. L. Cohen, E. E. Hailer, W. L. Hansen, A. L. Hansen, A. Y. Liu, and I. C. Wu, Phys. Rev. B 49, 5034 (1994). 632. J. Narayan, J. Reddy, N. Biunno, S. M. Kanetkar, E Tiwari, and N. Parikh, Mater. Sci. Eng. B 26, 49 (1994). 633. J. Szmidt, A. Werbowy, K. Zdunek, A. Sokolowska, J. KonwerskaHrabowska, and S. Mitura, Diamond Relat. Mater 5,564 (1996). 634. X.W. Su, H. W. Song, E Z. Cui, and W. Z. Li, J. Phys. Condens. Matter 7, L517 (1995). 635. T.Y. Yen and C. E Chou, Appl. Phys. Lett. 67, 2801 (1995). 636. T.Y. Yen, and C. P. Chou, Solid State Commun. 95, 281 (1995) 637. S. Muhl, A. Gaona-Couto, J. M. Me'ndeza, S. Rodil, G. Gonzalez, A. Merkulov, and R. Asomoza, Thin Solid Films 308-309, 228 (1997). 638. Y.A. Li, S. Xu, H.S. Li, andW. Y. Luo, J. Mater Sci. Lett. 17,31 (1998) 639. S. Xu, H. S. Li, Y. A. Li, S. Lee, and C. H. A. Huan, Chem. Phys. Lett. 287, 731 (1998). 640. M.A. Monclus, D. C. Cameron, A. K. M. S. Chowdhury, R. Barkley, and M. Collins, Thin Solid Films 355-356, 79 (1999).

COATINGS

189

641. V. Hajek, K. Rusank, J. Vlcek, L. Martinu, and H. M. Hawthome, Wear 213, 80 (1997). 642. Y. Fu, N. L. Loh, J. Wei, B. Yan, and P. Hing, Wear 237, 12 (2000). 643. A.K.M.S. Chowdhury, D. C. Cameron, and M. S. J. Hashmi, Surf. Coat. Technol. 118-119, 46 (1999). 644. H.Q. Lou, N. Axen, R. E. Somekh, and I. M. Hutchings, Diamond Relat. Mater 5, 1202 (1996). 645. Dong E Wang, Koji Kato, J. Tribo. 33, 115 (2000). 646. K. Kato, H. Koide, and N. Umehara, Wear 238, 40 (2000). 647. T. Hayashi, A. Matsumuro, M. Muramatsu, M. Kohzaki, and K. Yamaguchi, Thin Solid Films 376, 152 (2000). 648. W. Precht, M. Pancielejko, and A. Czyzniewski, Vacuum 53, 109 (1999). 649. J. Wei, P. Hing, and Z. Q. Mo, Wear 225-229, 1141 (1999). 650. M. Y. Chen, X. Lin, V. P. Dravid, Y. W. Chung, M. C. Wong, and W. D. Sproul, Tribol. Trans. 36, 491 (1993). 651. V. Haek, K. Rusnak, J. Vlcek, L. Martinu, and H. M. Hawthorne, Wear 213, 80 (1997). 652. H. Sjbstr6m, S. Stafstr6ni, M. Bohman, and J.-E. Sundgren, Phys. Rev. Lett. 75, 1336 (1995). 653. H. Sjbstr6m, L. Hultman, J.-E. Sundgren, S. V. Hainsworth, T. E Page, and G. S. A. M. Theunissen, J. Vac. Sci. Technol. A 14, 56 (1996). 654. V. Hajek, K. Rusnak, J. Vlcek. L. Martinu, and H. M. Hawthorne, Wear 213, 80 (1997). 655. A. Khurshudov, K. Kato, and S. Daisuke, J. Vac. Sci. Technol. A 14, 2935 (1996). 656. W.D. Sproul from BIRL Industrial Research Laboratory, Northwestern University, Evanston, Illinois, private communication. 657. M. J. Murphy, J. Monaghan, M. Tyrrel, R. Walsh, D. C. Cameron, A. K. M. S. Chowdhury, M. Monclus, and S. J. Hashmi, J. Vac. Sci. Technol. A 17, 62 (1999). 658. W.-C. Chan, M.-K. Fung, K.-H. Lai, I. Bello, S.-T. Lee, and C.-S. Lee, J. Non. Crys. Solids 254, 180 (1999). 659. M. Gioti, S. Logothetidis, C. Charitidis, and H. Lefakis, Vacuum 53, 53 (1999). 660. A. K. M. S. Chowdhury, D. C. Cameron, and M. A. Moclus, Thin Solid Films 355-356, 85 (1999). 661. A. K. M. S. Chowdhury, D. C. Cameron, and M. A. Moclus, Thin Solid Films 341,94 (1999). 662. A. K. M. S. Chowdhury, D. C. Cameron, M. A. Moclus, and R. Barklie, Surf. Coat. Technol. 131,488 (2000). 663. A.K.M.S. Chowdhury, D. C. Cameron, and M. S. J. Hashmi, Thin Solid Films 332, 62 (1999). 664. J. Robertson, Diamond Relat. Mater 2, 984 (1993). 665. C.A. Davis, Thin Solid Films 226, 30 (1993). 666. D.R. McKenzie, D. Muller, and B. A. Pailthorpe, Phys. Rev. Lett. 67, 773 (1991). 667. H. Sjbstr6m, M. Johansson, T. E Page, L. R. Wallenberg, S. V. Hainsworth, L. Hultman, J. E. Sundgren, and L. Ivanov, Thin Solid Films 246, 103 (1994). 668. V. G. Aleshin, and Yu. N. Kucherenko, J. Electron Spectrosc. 8, 411 (1976). 669. V.V. Nemoshkalenko, V. G. Aleshin, and Yu. N. Kucherenko, Sol. State. Commun. 20, 1155 (1976). 670. S.R.P. Silva, J. Robertson, G. A. J. Amaratunga et al., J. Appl. Phys. 81, 2626 (1997). 671. M.C. dos Santos, and E Alvarez, Phys. Rev. B 58, 13918 (1998). 672. A. K. M. S. Chowdhury, D. C. Cameron, M. S. J. Hashmi, and J. M. Gregg, J. Mater Res. 14, 2359 (1999). 673. J. H. Kaufman, S. Metin, and D. D. Saperstein, Phys. Rev. B 39, 13053 (1989). 674. E Weich, J. Widany, and Th. Frauenheim, Phys. Rev. Lett. 78, 3326 (1997). 675. M. Zarrabian, N. Fourches-Coulon, G. Turban, M. Lancin, C. Marhic, and M. Lancin, Appl. Phys. Lett. 70, 2535 (1997). 676. M. Zarrabian, N. Fourches-Coulon, G. Turban, M. Lancin, C. Marhic, and M. Lancin, Diamond. Relat. Mater 6, 542 (1997).

190

SIKDER AND KUMAR

677. S. Battacharyya, C. Cardinaud, and G. Turban, J. Appl. Phys. 83. 4491 (1998). 678. Y. Chen, L. Guo, and G. Wang, Philos. Maga. Lett. 75, 155 (1997). 679. Y. Zhang, Z. Zhou, and H. Li, Appl. Phys. Lett. 68, 634 (1996). 680. P. Petrov, D. Dimitrov, G. Beshkov, V. Krastev, S. Nemska, and Ch. Georgiev, Vacuum 52, 501 (1999). 681. Y. S. Gu, Y. P. Zhang, Z. J. Duan, X. R. Chang, Z. Z. Tian, D. X. Shi, L. P. Ma, X. E Zhang, and L. Yuan, Mat. Sci. Eng. A 271,206 (1999). 682. L.P. Ma, Y. S. Gu, Z. J. Duan, L. Yuan, and S. J. Pang, Thin Solid Films 349, 10 (1999). 683. S. E Lim, A. T. S. Wee, J. Lin, D. H. C. Chua, and C. H. A. Huan, Chem. Phys. Len. 306, 53 (1999). 684. X. W. Liu, C. H. Lin, L. T. Chao, and H. C. Shih, Mater Lett. 44, 304 (2000). 685. X.-C. Xiao, W.-H. jiang, L.-X. Song, J.-E Tian, and X.-E Hu, Chem. Phys. Lett. 310, 240 (1999). 686. R. Alexandrescu, R. Cireasa, C. S. Cojocaru, A. Crunteanu, I. Morjan, E Vasiliu, and A. Kumar, Surf. Eng. 15, 230 (1999). 687. Z. Zhang, H. Guo, G. Zhong, E Yu, Q. Xiong, and X. Fan, Thin Solid Films 346, 96 (1999). 688. D. X. shi, X. E Zhang, L. Yuan, Y. S. Gu, Y. P. Zhang. Z. J. Duan, X. R. Chang, Z. Z. Tian, and N. X. Chen, Appl. Surf. Sci. 148, 50 (1999). 689. S. Acquaviva, E. D. Anna, M. L. De Giorgi, M. Fernandez, G. Leggieri, A. Luches, A. Zocco, and G. Majni, Appl. Surf. Sci. 154-155, 369 (2000).

690. E Gonzalez, R. Soto, B. Leon, M. Perez-Amor, and T. Szorenyi, Appl. Surf. Sci. 154-155, 454 (2000). 691. I. Alexandrou, I. Zergioti, G. A. J. Amaratunga, M. J. E Healy, C. J. Kiely, P. Hatto, M. Velegrakis, and C. Fotakis, Mater. Lett. 39, 97 (1999). 692. X. C. Xiao, Y. W. Li, W. H. Jiang, L. X. Song, and X. E Hu, J. Chem Phys. Solids 61,915 (2000). 693. S. Acquaviva, A. Perrone, A. Zocco, A. Klini, and C. Fotakis, Thin Solid Films 373, 266 (2000). 694. Y. E Zhang, Y. S. Gu, X. R. Chang, Z. Z. Tian, D. X. Shi, and X. E Zhang, Mater. Sci. Eng. B 78, 11 (2000). 695. L.Y. Feng, R. Z. Min, N. H. Qiao, H. Zi. Feng, D. S. H. Chan, L. T. Seng, C. S. Yin, K. Gamini, C. Geng, and L. Kun, Appl. Surf. Sci. 138-139, 494 (2000). 696. K. Yamamoto, Y. Koga, S. Fujiwara, E Kokai, J. I. Kleiman, and K. K. KJm, Thin Solid Films 339, 38 (1999).. 697. S. L. Sung, C. H. Tseng, E K. Chiang, X. J. Guo, X. W. Liu. and H. C. Shih, Thin Solid Films 340, 169 (1999). 698. Y.K. Yap, Y. Mori, S. Kida, T. Aoyama, and T. Sasaki, J. Cryst. Growth 198/199, 1028 (1999). 699. Y. Kusano, C. Christou, Z. H. Barber, J. E. Evetts. and I. M. Hutchings, Thin Solid Films 355-356, 117 (1999). 700. M.E. Ramsey, E. Poindexter, J. S. Pelt, J. Marin, and S. M. Durbin, Thin Solid Films 360, 82 (2000).

Chapter 4

ATR SPECTROSCOPY OF THIN FILMS Urs Peter Fringeli, Dieter Baurecht, Monira Siam, Gerald Reiter, Michael Schwarzott Institute of Physical Chemistry, University of Vienna, Althanstrasse 14/UZA II, A-1090 Vienna, Austria

Thomas Btirgi Laboratory of Technical Chemistry, Swiss Federal Institute of Technology, ETH Zentrum, CH-8092 Ziirich, Switzerland

Peter Brtiesch ABB Management Ltd., Corporate Research (CRB), CH-5405 Baden-DattwiL Switzerland and Departement de Physique, Ecole Polytechnique, Federale de Lausanne (EPFL), PH-Ecublens, CH-1015 Lausanne, Switzerland

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Fundamental Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Plane Electromagnetic Wave in an Absorbing Medium . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Total Reflection and Attenuated Total Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Orientation Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Uniaxial Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Special Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Single-Beam-Sample-Reference Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Modulated Excitation Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Model Biomembranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Heterogeneous Catalysis by Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Temperature Modulated Excitation of a Hydrated Poly-L-Lysine Film . . . . . . . . . . . . . . . 5.4. Aqueous Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: Weak-Absorption Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. I N T R O D U C T I O N

191 192 192 195 197 205 205 211 211 212 216 216 219 224 225 226 227 227

Ref. [5]. F u r t h e r b o o k s should be m e n t i o n e d a m o n g the literature. A p p l i c a t i o n of internal reflection s p e c t r o s c o p y in a variety of fields has b e e n r e v i e w e d in the b o o k by M i r a b e l l a [6], while

Since the invention of internal reflection as a spectroscopic tool by H a r r i c k [ 1] and F a h r e n f o r t [2], m a n y applications have b e e n

the b o o k by U r b a n [7] treats internal reflection s p e c t r o s c o p y ap-

r e p o r t e d in the m e a n t i m e . T h e first g e n e r a l review was given by

plied to p o l y m e r s . Finally, attention should be d r a w n to Ref. [8]

Harrick in his f a m o u s b o o k [3] w h i c h was f o l l o w e d by a sup-

and for readers interested in biological s y s t e m s attention should

p l e m e n t [4]. Infrared surface t e c h n i q u e s are also discussed in

be d r a w n to the b o o k by G r e m l i c h and Yan [9]. In this chapter,

Handbook of Thin FilmMaterials, edited by H.S. Nalwa Volume2: Characterization and Spectroscopy of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512910-6/$35.00 191

192

FRINGELI ET AL.

we aim to give a comprehensive introduction to basic theory of attenuated total reflection (ATR) spectroscopy paralleled by experimental examples to enable the reader to choose an adequate approximation for quantitative analysis of the ATR spectra. It is of general interest to use Harrick's thin film approximation and the concept of effective thickness as long as possible, since working with exact mathematical expressions turns out to be a lavish expenditure. However, it is even so important to be able to check for the limits of approximate analytical methods. The introduction into basic ATR theory is followed by a discussion of orientation measurements which also results in the means of the calculation of surface concentrations of oriented samples. Two techniques for enhanced background compensation are presented, too. The single-beam-sample-reference (SBSR) technique renders a Fourier transform infrared (FTIR) single-beam spectrometer into a pseudodouble-beam instrument, enabling the measurement of sample and reference data with only little time delay. The second technique deals with modulated excitation (ME) spectroscopy. Each sample that enables periodic external stimulation by a variation of a parameter such as temperature, pressure, concentration, electric field, light flux, etc. can be investigated by ME spectroscopy. Periodic stimulation will result in a periodic response in the infrared from only that part of the system that has been affected by ME. Phase sensitive detection enables a narrow band detection of modulated responses which leads to a high selectivity and a low noise level, i.e., a high signal-to-noise ratio which is 1 or 2 magnitudes better than achieved by conventional difference spectroscopy. Moreover, if the frequency of ME is adapted to the kinetic response of the stimulated system, phase shifts with respect to the stimulation and the amplitude damping give valuable information with respect to relaxation times and reaction schemes. Heterogeneous catalysis on distinct metal surfaces is shown to be accessible by ATR spectroscopy, too, despite relatively high reflection losses due to high absorption indices of metals. The latter fact, however, requires the application of the exact ATR theory for quantitative analysis.

2. FUNDAMENTAL THEORY In this section a review and a discussion of the theory for attenuated total reflection (ATR) is given. The starting points are Maxwell's equations and the materials equations for isotropic absorbing media. Electromagnetic waves, refractive index, dielectric constant, and the intensity of plane waves are introduced. A short discussion of the Kramers-Kronig relation is also given. We then consider in detail reflection and refraction in isotropic transparent and absorbing media and we derive the appropriate Fresnel equations and reflectivities for s- and p-polarized light. Finally, we discuss ATR for two bulk media as well as for stratified media. The formalism is illustrated by considering the system Ge/H20 and the fictitious singlelayer system Ge/HC1/H20. Approximate relations for relatively weakly absorbing systems are worked out which express the

normalized reflectivities in terms of effective thicknesses and absorption coefficients. For general references, the reader is referred to the literature [3, 10-20].

2.1. Plane Electromagnetic Wave in an Absorbing Medium

2.1.1. Maxwell's Equations and Material Relations Maxwell's equations in an isotropic medium are aB

curl E =

0t 0D curl H = ~ + j 0t divD= p div B = 0

(1) (2)

(3) (4)

E and D are the electric field and the electric displacement, while H and B are the magnetic field and the magnetic induction, respectively, p is the charge density and j is the current density. Equation (1) is Faraday's law of induction. Equation (2) expresses the dependence of the magnetic field on the displacement current density OD/Ot, or rate-of-change of the electric field, and on the conduction current density j, or rate of motion of charge. Equation (3) is the equivalent of Coulomb's law and Eq. (4) states that there are no sources of magnetic fields except currents [ 13]. The materials equations are relations linking the Maxwell fields E and H with the induced dielectric polarization P, magnetization M, and current density j, thereby also defining D and B. For the time being, we disregard nonlinear optical effects observed in strong electric and magnetic fields. For sufficiently small field strengths, the material equations are linear and in isotropic media these are D = s E = SoerE = soE + P B = txH = lZnlZr H = / z n ( H + M)

j -- crE

(5) (6) (7)

The parameters describing the material properties are the real part of the dielectric constant Err (relative permittivity), the magnetic susceptibility/Z r (relative permeability), and the electric conductivity or. In anisotropic media, Eqs. (5)-(7) become more complicated with Err, lZr and cr being tensors rather than scalar quantities. The international system of units (SI) is used throughout this Chapter. Table I shows the definitions of the quantities in the equations together with the appropriate SI units. To the preceding equations, we can add the relations, e =

eOer

(8)

/Z =

/Z0/Zr

(9)

so -

1 /z0 c2

(10)

where e0 and/z0 are the permittivity and the permeability of free space, respectively, and c is the velocity of light in vacuum (Table II).

ATR SPECTROSCOPY OF THIN FILMS Table I. Symbol

193

Definitions and SI Units of Important Quantities

Physical Quantity

SI Unit

Symbol for SI Unit

E

Electric field

Volts per meter

D

Electric displacement

Coulombs per square meter

C m -2

H

Magnetic field

Amperes per meter

A m-1 T

V m-1

B

Magnetic induction

Tesla

j

Electric current density

Amperes per square meter

A m -2

p

Electric charge density

Coulomb per cubic meter

C m -3

a

Electric conductivity

Siemens per meter

S m-1

e

Permittivity

Farads per meter

F m-1 H m-1

#

Permeability

Henries per meter

P

Polarization

Coulombs per square meter

C m -2

M

Magnetization

Amperes per meter

A m-1

Table II. Symbol

Fundamental Constants c, e0, and/z 0

Physical Quantity

the x axis with velocity v, we write

Value

E = Eoe ic~

c

Speed of light in vacuum

2.997925 9108 m s-1

e0

Permittivity of vacuum

8.8541853 9 10-12 F m - 1

/z0

Permeability of vacuum

4zr 9 10 - 7 H m -1

divD = 0

(12)

From Eqs. (1) and (2), it is possible to eliminate E or H. Forming the curl of Eq. (1), differentiating Eq. (2) with respect to t, using the vector identity, curl curl E = grad div E - V2E

(13)

as well as Eqs. (5) and (6) yields 02E OE V 2 E - 8#-0--~- + / z a O---t-

O2H OH e#--5~- + # a 0--~

This equation shows that in a conducting medium (a ~ 0), the velocity v is a complex quantity. In a vacuum, we have a = 0, 8 = 8o, # =/zo, and v = c, resulting in C = (/Z080) - 1 / 2

(18)

which is identical to Eq. (10). Multiplying Eq. (17) with c 2 = 1/80/xo and dividing through by 092, one obtains C2 /Zrt7 v2 - - e r l Z r + i ~ 0980

(19)

where c / v is clearly a dimensionless parameter of the medium, which we denote by h, ~2 = 8r#r + i ~#rt7

(20)

This implies that h is of the form, (14)

In a similar way, one obtains V2H-

(17)

(ll)

In addition, for isotropic media, there is no spatial variation in 8r. Thus, div E = 0

Substituting Eq. (16) into Eq. (14) gives o92/l) 2 = 0928# -~- i091za

In the following, we assume that there is no charge density in the medium, i.e., p = 0, and from Eq. (3) it follows,

(16)

c fi - - - - - n + i k 1)

(15)

2.1.2. Plane Waves, Complex Refractive Index, and Dielectric Constant We look for a solution of Eq. (14) in the form of a planepolarized, plane harmonic wave, and we choose the complex form of this wave, the physical meaning being associated with the real part of the expression. For a wave propagating along

(21)

-

There are two possible values of fi from Eq. (20), but for physical reasons we choose that which gives a positive value of n. h is known as the complex refractive index, n as the real part of the refractive index (or often simply as the refractive index, because h is real in an ideal dielectric material) and k is known as the extinction coefficient. In the literature, the so-called attenuation index x is often used which is related to k by k = n x or h - n(1 + iK). In the latter equation, the minus sign is often used which corresponds to the choice of i 0 9 ( t - x / v ) in the exponent of Eq. (16) for the electric field.

194

FRINGELI ET AL.

At this point, we introduce the complex dielectric constant k, defined by

From Eqs. (2), (5), (7), (10), and (28), together with Eq. (20) it follows,

fi2

t~2

= e' + i t " = ~

curlH = (or - iweoer)E = - i w

(22)

/Zr

E

(34)

C2 ~O Id,r

On the other hand, using a plane-wave representation for H analogous to Eq. (28)one finds

From Eqs. (20) and (21), it follows n2 _ k2

ex

(23)

8t = 8 r - "

curl H = ~r

e" =

=

0)80

For nonmagnetic materials ~ r and (24) for n and k gives

2nk

(24)

/Lr :

O/Ox

O/Oy

nx

By

1 ~(lel

k =

1 ---~(lel + vz

ez

^

n

O/Oz = i w - ( s • H) n z

(35)

c

Comparison of Eqs. (34) and (35) gives

1 and solving Eqs. (23) - ~ E c l,l, 0 ld,r

s•

n =

+ d) e')

1/2

(25)

1/2

(27)

(8'2 -+-8"2)1/2

~ ( s

(28)

where we have introduced the wavelength ~. in free space, )~ = 2zgc/w. An analogous expression holds for H. From Eq. (28), the significance of k emerges as being a measure of the absorption in the medium: the distance )~/2~rk is that in which the amplitude of the wave falls to 1/e of its initial value. Equation (28) represents a plane-polarized wave propagating along the x axis. For a similar wave propargating in a direction given by the direction cosines (c~,/3, y), the expression becomes E = E0 e i[(2rr/~)h(~x+~y+Yz)-wt]

• E) = H

(37)

C~Ols

For this type of wave, therefore, E, H, and s are mutually perpendicular and form a right-handed set. The quantity h/(ctxotXr) has the dimension of an admittance and is known as the characteristic optical admittance of the medium, written Y:

is the modulus of e. Using Eq. (21), the electric field given by Eq. (16) can now be written in the form, E = E0 e -(27rk/x) e i[(27rn/x)x-wtl

(36)

and from Eq. (36) it follows,

(26)

where

lel :

ey

Y =

h

(38)

CIZOI~r

For a vacuum, we have h = n = 1,/Zr "-- 1 and from Eq. (10) it follows that its admittance is given by Yv = (e0//x0) 1 / 2 = 2.6544.10 -3 S

(39)

At optical frequencies ~r - - 1, and we can write Y = f i " Yv

(40)

and q• H = Y(s x E) = f i Y v ( s • E) = h Y v ~ q

(41)

(29) 2.1.3. Intensity o f Electromagnetic Waves

where c~ = cos(s, ex), 15 = cos(s, ey), y -- cos(s, ez) and s -- otex + fley + Yez -- (~, fl,

Y)

(30)

is a unit vector in the direction of propagation, and ex, ey, ez are unit vectors along the x, y, and z axes, respectively. Defining the vector r = (x, y, z) and the complex wave vector, q = ~2zr fis = q' + iq"

(31)

where 2~r q ' = Iq'l = ~ n ~.

oo = --n, c

q.

= Iq"l =

2Jr

w k = --k (32) ~. c

and ~. is the vacuum wavelength, the electric field can be written in the form, E = Eoe i[qr-~~

(33)

Electromagnetic waves transport energy and it is this energy which is observed. The instantaneous rate of flow of energy across the unit area is given by the Pointing vector, P = E x H

(42)

Since E is perpendicular to H, the magnitude of P is P = E 9 H, where E and H are the complex and time-dependent field strengths. The intensity of the electromagnetic wave is defined as the time average of the real part of E and H" I = (Re(E) 9 Re(H))t. It can be shown [12] that this average can be written in the form (1/2) R e ( E . tH*), where H* is the complex conjugate of H. Hence, the intensity of the electromagnetic wave is given by I = 1 Re(E-n*) where E and H are complex scalar quantities.

(43)

ATR SPECTROSCOPY OF THIN FILMS It is important to note that the electric and magnetic vectors in Eq. (42) should be the total resultant field due to all waves which are involved. From Eq. (41), it follows that H = h Yv E and we obtain I -- (1/2) Re(Efi*YvE*) -- (1/2) Re(Y*)EE*. Using Eqs. (21) and (40), one obtains I = (1/2)n Yv E E*. The product E E * is obtained from Eq. (29) and the final expression for the intensity is given by

I-

lnYvE2e-(4zr/z)k(~x+13Y+YZ)

(44)

The unit of I is W m -2. The expression (ax +fly +g z) is simply the distance traveled along the direction of propagation, and thus the intensity drops to 1/e of its initial value in a distance given by )~/4zrk. The inverse of the distance is defined as the absorption coefficient or, that is

ot = 4zrk/)~ = 4:r~k

(45)

where ~ is the frequency in wave numbers (in units of cm-1).

195

tronic frequencies, we can neglect co in the second integral. The second term is therefore constant and can approximately be replaced by ec~ - 1 where too is the "high frequency" optical dielectric constant associated with electronic transitions. The Kramers-Kronig relation modified for vibrational transitions is therefore, 2 [~Oc co,e- (co') e'(co) - e ~ -- -- P dco' Jo cot 2 _ o92

(49)

The inverse relation corresponding to Eq. (49) is e" (co) = _~2~ P f0 ~~ e' (co) - e ~ 7f cot2 _ 0)2 dco'

(50)

The static dielectric constant est can be obtained from Eq. (49) by setting co = 0 resulting in

fo ~~ e"(co) do) co

zr 2 (est- e~)

(51)

Relation (51) constitutes a sum rule which provides further information and checks for experimental data.

2.1.4. Kramers-Kronig Relation The real and imaginary parts of the complex dielectric constant -- e I + i E" or the complex refractive index fi = n + ik are not quite independent of one another. They are linked by dispersion relations, also called the Kramers-Kronig relations [15]. Equation (5) shows that the dielectric displacement D is linearly related to the electric field E: D = eE. When a linear relation of this kind is considered as a function of frequency, that is, as a function of time, it must satisfy the requirements of causality: there must be no displacement until after the application of the field E. It is well known that this condition requires that the real and imaginary parts of e(co) or h(co) should satisfy the Kramers-Kronig relation. For e'(co) and e" (co), these relations are

2 [ c ~ co,e,,(co,) e'(co) = 1 + - - P dco' Yf Jo cot2 _ o92

(46)

e'(co) = - ~2o9 P fo ~ e(co')- 1 dco'

(47)

7g

cot 2 _ 0)2

where P stands for the Cauchy principle value [ 15]. We are interested in the Kramers-Kronig relations modified for the analysis of vibrational transitions in solids and liquids. The resonance absorptions for light by vibrational transitions are then generally well separated in frequency from the optical processes associated with electronic transitions which take place at much higher frequencies (in the visible or UV part of the spectrum). The integration in Eq. (46) can therefore be divided in two parts, namely,

f~

co'e"(co')

L

~dco'

c cot2_o92

2.2.1. Isotropic, Nonabsorbing Media In this section, we consider the reflection and the refraction of electromagnetic waves at a plane interface between dielectrics, characterized by the refractive indices n l and n2 [ 11 ]. The coordinate system and symbols, appropriate to the problem are shown in Figure 1. The media above and below the plane z = 0 have permeabilities and refractive indices/Xrl, n l and/Zr2, n2, respectively. From Eqs. (23) and (32), we have nl = (c/w)qi - - ~ / l Z r l F , r l and n2 - (c/co)qt : ~ / ~ r 2 E r 2 , where qi -- qil and qt : qt for nonabsorbing media. A plane wave with wave vector qi and frequency co is incident from medium/Zr 1, n I at an angle of incidence Oi. The refracted and reflected waves have wave vectors qt and qr, respectively, and ez is a unit vector directed

qr [lr1'F11

~/

,X iU r2' n 2

~

ez

e'(co) - 1 = 2 P f0 )c w'e" (w') dco' 7r cot 2 _ o92 2 +--P 7r

2.2. Reflection and Refraction

~? 0 t (48)

Since we are evaluating e'(co) for co n2. According to Snell's law, sin Ot = n12 sin0i (n12 = n l / n 2 ) and if nl > n2 then Ot > 0i. The critical incident angle 0ic is defined by the condition 0t = 7r/2 or by sin0ic -- n21 = n 2 / n l

(71)

For waves incident at angles Oi = 0ic, the refracted wave is propagated parallel to the surface (0t -- zr/2). There can be no energy flow across the surface. Hence, at that angle of incidence there must be total reflection. What happens if Oi > 0ic? In this case, according to Snell's law sin0t > 1, hence sin0i > n21 or n21 - sin20i < 0 and the square root occurring in the Fresnel coefficients (62) and (65) becomes purely imaginary, i.e., (n21 - sin20i) 1/2 = i (sin20i - n21) 1/2. We then obtain COS0i -- i(sin20i -- n21 )1/2

Ps =

COS0i -at- i(sin20i -- n 2 1 ) l / 2

(72)

198

FRINGELI ET AL. a

and n21 cos0i --

i(sin20i

--

n221)1/2

--

n2---1)1/2

1.5

(73)

1.4

From these equations, it follows that IPsl = IPpl = 1, indicating that the reflection is total when n21 is real. For angles larger than 0ic, it follows that

1.35

PP

= n21 cos/9/ -k-i(sin20i

cosOt = v / 1 - sin2Ot = inl2V/sin2Oi - n21

"-

I

1.3 1.25

(74)

1.2

that is, cos Ot is purely imaginary while sin Ot = n 12 sin Oi is real. Ot is therefore a complex angle with a real sine and a purely imaginary cosine. T h e meaning of these complex quantities becomes clear when we consider the wave Et as defined by Eq. (53). We have qtr = qt(sinOt, O, cosOt)(x, y, z) = qt(x sin0t + z cos 0t). Using Eq. (74) and sin 0t -- n 12 sin Oi, the propagation factor for the refracted wave becomes

1.15

eiqtr = e-q, nlzx/slnZOi-nZl'z . eiqtn12 sinOi.x

ii

1.1 4000

3 5 0 0 3 0 0 0 2 5 0 0 2 0 0 0 1 5 0 0 1000 Wavenumber

b

0.35

'

'

'

/ cm 1

i

'

'

(75) 0.3

This shows explicitly that for Oi > 0ic, the refracted wave is propagated only parallel to the surface (second factor in Eq. (75)), but is attenuated exponentially beyond the interface (first factor in Eq. (75)). The attenuation occurs within a fraction of the wavelength ~., except at Oi -- 0ic. This becomes clear if in Eq. (75) we replace qt by its value given by Eq. (55), namely, qt = (w/c)n2 -- (2zr/~,)n2. The exponentially decaying factor in Eq. (75) can then be written as e x p ( - z / d p ) , where Z

dp

0.25 "~

0.2

~

" 0.15


0ic. This can be verified by calculating the time-averaged normal component, (ezP)t of the complex Pointing vector P. Referring to Figure 2 we have for the transmitted wave, (ezPt)t =

1

R e i n . (Et x I-It) ]

(77)

Now, Et • I-I~ -- Et H~st, where st is a unit vector in the direction of the transmitted wave. According to Eq. (41), l-It = Yt (st x El) -- Yt Ete where e is a unit vector in the direction of I-It and Yt = n2Yv is real for a transparent rarer medium. Therefore, Ht* = Yt E~ and using ezSt = cos Ot we obtain

(ezPt)t = ln2Yv Re[cosOtlEtol 2]

(78)

However, since lEt012 is real and since according to Eq. (74) cos Ot is purely imaginary for Oi > 0ic it follows that (ezPt)t = 0. This is clearly not true if the rarer medium is absorbing, since in this case, both, Yt = h2 Yv and cos Ot are complex quantities

Fig. 3. (a) and (b) Refractive index n2 (a) and extinction coefficient k2(b) of liquid water at 300 K, as a function of wave number ~.

and Re[cosOtY~lEtol 2] r 0. Part of the incident wave is then absorbed by the rarer medium and we are dealing with attenuated total reflection (ATR).

2.3.1.2. Absorbing Rarer Medium If the rarer medium is absorbing, the reflectivities can still be calculated from Eqs. (72) and (73) by replacing n2 with the complex refraction index fie = n2 + ik2. The resulting expressions are identical with those given by Eqs. (67) and (68) which are valid both for Oi < 0ic and for Oi > 0ic. It turns out that for Oi well above 0ic, measured and calculated reflectivities resemble transmission measurements, i.e., they exhibit a behavior described by ke(w). On the other hand, if Oi < 0ic, the spectra resemble the mirror image of the dispersion of nz(w) (see [3, pp. 69-75 and 243-250]). As an example, Figure 4 contains the calculated ATR spectra of water for a single total reflection using a Ge-ATR element with refractive index n l = 4.0 and an angle of incidence Oi = 45~ the calculation is based on the relations Rs = IPs I2

ATR SPECTROSCOPY OF THIN FILMS 1

!--~.%

:: :

0.95

~

': , - ~ _ - . j ~ . .

,~/ tli

:

:

~

~, ,.--. .

i

!

..... .

.

i 0.9

I~tl!

!

l\s,,,'/i i i li ::

i,,

": ...............

:. . . . . . . . . . . . . . .

: ............

i

.............

0.85

0.8

.

: ' ............. . . . ............................... . . . . . . . . . . . . . . . . . . i ........ t;'t i ............. t\' ~:. . . . . . .j//i :: i

..~~

if"

!

,~, ~

"

"

.............................

199

some physical insight into the coupling of the evanescent wave with the rarer absorbing medium. The calculation is based again on Eqs. (72), (73) (with n21 replaced by h2/nl = (n2 + i k2)/n 1) and retaining only terms linear in k2. We are therefore dealing with the "low absorption" approximation. Terms such as (k2/nl) 2 are therefore neglected which is usually a good approximation for Ge and Si in contact with a weak or moderately weak absorber (see later). A straightforward but lengthy calculation gives the following result for the approximate reflectivities Ras and Rap: des 9 ot

(79)

Rap - - 1 - dep 9 ot

(80)

Ras - -

1-

0.75 4000

3500

3000

2500

Wavenumber

2000

1500

1000

/ c m -1

Fig. 4. Calculated ATR spectra of liquid water at 300 K in contact with a GeATR element (nl = 4.0) for s-polarized (dashed line) and p-polarized (solid line) light (single total reflection at an angle of incident of Oi = 45~

where ot = (2w/c)k2 is the absorption coefficient of the rarer medium (see Eq. (45)), while des and dep a r e the effective thicknesses for isotropic media for perpendicular and parallel polarization, respectively, (~,/rt 1)rt21 c o s 0 i

0.7

des - -

e-

0.6

.................................................................................................

l::::

0.5

................................................................................. ~ .......

7r(1 - n21)(sin20i - n21)l/2

(81)

i

(~./nl)n21 cosOi(2sin20i - n21 ) ..c: ,,i,,,,a

o,)

0.4

!

!

!

i

i

:~'

i

i

i

!

i

5-."

i

d

i

i

dep - -

(82)

"0

e-

0.3

-~ " t-

0.2

._o_

o_

',

!

................................. ~ ~.... '" . . .~. . . . '. . . . .~. . . . . . . . . .;;---dp. id ......................... ~iL L L J " -................. ............

;;-'-'.--.-.-.-.-.-.....-....-..'...'-.....i

O

0

li-ii 4000

3500

3000

.... des".... ....

2500

Wavenumber

2000

..............

1500

7r(1 -- n21)[(1 + n21)sin20i -- n21](sin20i -- n21 )1/2

1 1000

/ cm 1

Fig. 5. Calculated depth of penetration dp (short dashed line), effective thicknesses des (long dashed line), and dep (solid line) for s- and p-polarizations, respectively, for the G e / H 2 0 system described in Figure 4. The weak structure is due to the dispersion of n2 as shown in Figure 3a.

and R p = Ippl 2 where Ps and pp are given by Eqs. (72), (73). The experimentally determined input spectra of water, nz(v) and kz(v), as a function of fi (~ = 1/)~ = v/c = co/2rcc) are shown in Figure 3a and 3b, respectively. The absorption peaks of kz(fi) near fi -- 3300 and 1650 cm -1 are due to the symmetric and asymmetric stretching and H - - O - - H bending modes, respectively. The depth of penetration dp is shown in Figure 5; it is calculated using Eq. (76) with nl - 4.0 and n2 -- n2(v); the weak structures are due to the dispersion of n2. An identical curve is obtained if absorption is included in the calculation of dp(v); this is due to the fact that (k2/nl) 2 >> 1. It should also be noted that the depth of penetration is independent of the state of polarization of the infrared light. While the expressions Rs = ],Os]2 and R p -- ],Op]2 with Ps and pp defined by Eqs. (72), (73) give an exact expression for the reflectivities as illustrated in Figure 4, it is desirable to establish approximate expressions for Rs and Rp which give

A detailed discussion of these effective thicknesses is given in the excellent book by Harrick [3] (note that there is an error in sign in Harrick's formula (27) at p. 43, which has been corrected in our Eq. (82)). The relations (81) and (82) are valid for a single reflection and for sufficiently low absorptions, i.e., for otd < 0.1 in transmission experiments of thin films of thickness d with transmissions T -- I/Io = exp(-c~d) ~ 1 - o t d . The effective thicknesses des and dep represent a measure for the strength of interaction of the evanescent field with the rarer medium. It should be noted that according to Eqs. (81), (82) des = 1/2dep for Oi = 45 ~ Figure 5 shows des and dep for the system Ge/H20 for Oi -- 45 ~ nl = 4, and n2(~) according to Figure 3a, along with the depth of penetration dp. We have performed calculations of the approximate reflectivities Ras and Rap defined by Eqs. (79), (80) and compared them with the exact reflectivities Rs = Ipsl 2 and Rp = Ippl 2 shown in Figure 4 which have been obtained from the generalized Fresnel coefficients given by Eqs. (72), (73) (in which n2 is replaced by fi2 = n2 + i k2). Calculations have been done for the systems Ge/H20, Si/H20, and ZnSe/H20. For the relatively weak H - O - H bending absorption near 1640 cm -1, the relative errors of the peak heights are 3, 4.7, and 16% for s polarization, and 6, 9, and 30% for p polarization. On the other hand, for the strong O - H absorption near 3300 cm -1 the corresponding errors are 9, 12, and 47% for s polarization, and 14, 23, and 87% for p polarization. This illustrates the fact that for absolute reflectivities as defined by Eqs. (79), (80) the "weak absorption approximation" is good for Ge/H20, acceptable for Si/H20, but completely breaks down for ZnSePrI20. However, as discussed later, the weak absorption approximation is much better for suitably normalized reflectivities.

200

FRINGELI ET AL. by window reflections, ambient absorption, diffuse scattering, etc. However, since these loss factors tend to be constant, the reflectance ratio, Rnu, can be measured accurately. By definition, Rnu may be smaller or larger than 1, depending on whether Ru (1, 2 . . . . . N § 2) is smaller or larger than Ru (1, N § 2). If all layers 2, 3 . . . . . N § 1 are identical and equal to the bulk-phase N + 2, then Ru (1, 2 . . . . . N + 2) = Ru (1, N + 2) and Rnu = 1. The general expressions for dl + E2<m~'z>

(Ak,p)iso (de,p)iso = (Ak,s)iso (de,s)iso (de,x)iso + (de,z)iso E 2 -'t- E 2 = (de,y)iso E2

For the isotropic case, (Ex2 -(Rk)iso" -(Rk,)isoEy 2 2Ez2) = 1/3, thus fulfilling the condition (de,k,p)iso = (de,k,x)iso + (de,k,z)iso and (de,k,s)iso = (de,k,y)iso. The final step leading from effective thicknesses to concentrations and surface concentrations is easily done by applying Lambert-Beer's law, resulting in the volume concentration of a given species as de-

e y /(e x

(144)

E2(m2,y) In the isotropic case, the probability to absorb light by interaction of the transition dipole moment with the electric fields in

ATR SPECTROSCOPY OF THIN FILMS

211

termined by the kth molecular vibration. So,

c=

fbandk (Ak,u)d~ nN(de,k,u) fbandk 8k(V) d~

(150)

fbandk (Ak,u)d~ is the integrated absorbance where u stands again for (p,//)- and (s, &)-polarized incident light, n is the number of equal functional groups per molecule and N denotes the number of active internal reflections. (de,k,u) is the effective thickness relevant for the kth vibration measured with (p,//)and (s, &)-polarized incident light. Note that in our notation (de,k,u) depends on the orientation of the transition moment of the kth vibration. Only (de,u)iso is independent of the vibrational mode considered. Finally, fbandk ek(~)d~ denotes the integrated molar absorption coefficient of the kth vibration. It should be noted that Eq. (150) also holds for wave numberspecific spectroscopic data, such as peak absorbance and peak molar absorption coefficient according to c --

(Ak,u) nN(de,k,u)ek(v)

(151)

In the case of thin layers (d < dp), it is often adequate to quantify in terms of surface concentration F instead of volume concentration c. The relation is given by

F = cd

(152)

d denotes the geometrical thickness of the sample. Thus, F indicates the number of particles in the unit volume projected to the unit area.

4. SPECIAL EXPERIMENTAL TECHNIQUES In the following two sections, we describe two experimental techniques which have turned out to considerably enhance the quality of background compensation and in the case of modulated excitation (ME) spectroscopy to enable time-resolved measurements. In the latter case, the measurement of phase lags of the system response with respect to the external stimulation, as well as the frequency depends of the amplitude, is the principal means for kinetic analysis and for the evaluation of the underlying reaction scheme.

4.1. Single-Beam-Sample-Reference Technique Most FTIR spectrometers are working in the single-beam (SB) mode. As a consequence, a single channel reference spectrum has to be stored for later conversion of single channel sample spectra into transmittance and absorbance spectra. This technique favors inaccuracy due to drifts resulting from the instrument or from the sample as well as disturbance by atmospheric absorptions. To eliminate these unwanted effects to a great extent, a new type of ATR attachment has been constructed, converting a single beam instrument into a pseudodouble beam instrument. The principal features of this attachment are depicted in Figure 13. As usual, a convergent IR beam enters the

Fig. 13. Single-beam-sample-reference (SBSR) ATR attachment. (A) The focus in the sample compartment is displaced to the position F by the planar mirrors M1 and M2. The off-axis parabolic mirror M3 produces a parallel beam with a diameter of one centimeter, i.e., half of the height of the IRE. The cylindrical mirror M4 focuses the light to the entrance face of the IRE. M5 which has the same shape as M4 reconverts to parallel light passing via the planar mirror M6 through the polarizer POL and being focused to the detector DET by the off-axis parabolic mirror M7. (B) Alternative change from sample to reference and vice versa is performed by computer-controlled lifting and lowering of the ATR cell body. Reproduced from [41 ] by permission of the American Institute of Physics, 9 1998.

sample compartment with a focal point in the middle. This focal point is now displaced by the planar mirrors M1 and M2 to the new position F, whereas the off-axis parabolic mirror M3 performs a conversion of the divergent beam into a parallel beam with fourfold reduced cross section. This beam is focused to the entrance face of a trapezoidal internal reflection elemen (IRE) by a cylindrical mirror M4. Therefore, the ray propagation in the IRE is still parallel to the direction of light propagation (x axis), enabling a subdivision of the large IRE surfaces (x, y plane) in perpendicular direction (y axis) to the light propagation. One half of the IRE is then used for the sample (S) and the other one for the reference (R). Both, S and R, were encapsulated by flow-through cuvettes, independently accessible by liquid or gaseous flow through. This principle is referred to as the single-beam-sample-reference (SBSR) technique. A computer-controlled lift moves the cell platform alternatively up and down aligning the sample and reference cuvettes with the IR beam, respectively. Thus, SBSR absorbance spectra are calculated from sample and reference single channel spectra which have been measured with very short mutual time delay. Figure 14 shows the results of a series of hydrogen deuterium (HD) exchange measurements performed in the

212

FRINGELI ET AL.

i

.-.o, .................i---!---!

. . . . . . . . .

< ~

:i

i

ii i

. . . . . . . . . .

0.4

t~ 0.3 ..................*....................................... *...............~-........-=...... ~176 -ii ili!ii " o SB ~-

" '

iii

0.2

< 0

.

0 4000

1

~

350~) 300~ T i o

,

2500

2000

"-----

= ~

-E

0 z

1560

r

|

1000 0

To

{

,-.~ Z)

i

0.5 ...................:...~.............z~...................................~..................................... ii i

< 0.4 I1) 0 t~ 0 . 3 t~

o r ..Q

0.2


... 090.6

n" 2 0 0 0

133 11"

1000

~\,

0.4

- -o--100K

0.2

~

u-200K

150

200

250

300

350

400

450

Channel

Fig. 45. The 1.5-MeV 4He+ ions RBS random and the (lll)-channeling spectra from the same superlattice as in Figure 44. The Xmin is higher than that in the (100) direction but is less than 10%. Reprinted with permission from [108], copyright 1997, Elsevier Science.

this smooth and nearly linear dependence could be the indication of an abnormal structural change. The sample studied by Ruders et al. was a (100)-oriented [Fe(1.4 nm)/Cr(6.2 nm)] superlattice (14 periods) grown on a single crystal MgO with a 10-nm Cr buffer layer. The sample was cooled by a closed-cycle refrigeration system. A 1.5-MeV well-collimated (angular divergence o

.............+l

= -

-t--~'--ik

.

Lii ! ~. 0.090

.

.

.

;Li;i ?:71-;

L :,.-i:: ::L :: ::::l:::f:::L:l:-:i=.i.:

i...-.2.

-

.

-

.

~

;

:

_~_...i.._'_.. 2...?..i.-_~....]._. : .. : _ : ............... L T . ]

i

..............~.....~ ....... t

E "E 0 . 0 6 0

,.

,

9

I

.I" l

::t ...i.-.;-.-:-.:--.:.:-:..--. i--.. L§ ' " ' .

' : -i i :. ::...: :.--:.... :.-.:......i--:.~

:::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::.:.=,:.. t t !- i .......... '

"

'.

.

~

~. . . . . . . . . . . . . .

:

=

.....

0.030

'

'

'

:

:

l

"

'

9

-

"

i

"

."

'

--'

. . . .

-

:

-,

-1..

-

:--.

-.--t--

'---i,---I-

-4~-

;'"

. . . . . . . . . . .

,

-}---i-.

" i

-:::::::::::::::::::::::::: i-.:t._4__r ....................... t._..t...+_...-.-~....-.-..:- .- :. ::[-zi:=V-. -T i-. ........... i-...-.:----,---i-.-..-,--.--- .......... 1---T----r ..................... , , " rr- .... " .............. 9 -. .... i........... : i.i...... '..... il ! 'i"l-'t-4.i i i ............................ I i ........ r-4-.i........ i ......., , ' /'............... . ..~" i-..'-~ ..... _L_,.i..4.._.~t!il ,-,-', !............. r:,~ ~ - .il _ .....Hi-:t~ i , ' ......... : - ' ,r-i , ......... i tl---t,i.-,' i ' ~' !

0.000 50

100

150

200 Temperature

250 /

300

350

K

Fig. 49. Minimum yields, Xmin, for the (100) and (111) scans (Figs. 46 and 47) from the 14-period (100)-oriented [Fe(1.4 nm)/Cr(6.2 nm)] superlattice as a function of temperature. Reprinted with permission from [108], copyright 1997, Elsevier Science.

temperature varied from 100 to 300 K. Although no abnormal structural changes that can be linked to the lattice strain or the distortion were observed, the ion channeling study carried out by Ruders et al. provides an excellent example about the characterization of the structural change in the superlattice using the RBS-channeling technique.

4.3. Characterization of Superlattice Containing Sb It-Layers by Medium Energy RBS The semiconductor n-i-p-i superlattice with thin doped 8-layers is a promising material for novel device applications due to its quantum size effects and the two-dimensional cartier gas [ 134, 135]. Generally speaking, integral properties of such a superlattice depend on the following parameters: (1) the thickness of the ti-layers, (2) the dopant activation (dopant lattice location), and (3) the dopant redistribution during the growth process and

the following thermal treatments [107]. Therefore, characterization of those parameters is crucial for growing and processing such types of the superlattices. Obviously, for characterization of the superlattices containing impurity doped 8-layers, a technique with high depth resolution is required. Secondary ion mass spectrometry (SIMS) is a good tool for depth profiling that requires high depth resolution. However, it is a destructive method and is not capable of providing the information about the crystalline quality of the superlattices and the lattice locations of the dopant. The RBS technique combined with the ion channeling effect not only can provide high depth resolution comparable with that of SIMS but also can provide the information about the crystalline quality of the superlattices and the lattice locations of the dopant. In addition, RBS and channeling techniques are nondestructive methods. Lenkeit et al. have successfully applied RBS and channeling techniques to the characterization of the Si superlattices with Sb doped 8layers [107]. To achieve high depth resolution, Lenkeit et al. used medium-energy 4He+ ions (305 keV) as the probing particles and a cylindrical electrostatic analyzer as the detector. Depth resolution as high as 0.8 nm has been achieved in the near-surface region. The samples investigated are five-period Si superlattices with Sb doped 8-layers [Fig. 50], grown either on (100) Si or on (111) Si substrates. The superlattices were grown by MBE at low temperature (200~ and then annealed at 600-800~ for amorphous layers to recrystallize into crystals. The concentration of the Sb in the 6-1ayers ranges from 0.4 x 1014 cm -2 to 1.4 x 1014 cm -2. To achieve high depth resolution in the RBS measurement, 4He+ ions with energy as low as 305 keV (to obtain higher energy loss) were used as probing particles. To further improve the depth resolution, a cylindrical electrostatic analyzer was used to record the backscattered 4He+ ions, which has an energy resolution of ~E/E0 = 7.6 x 10 -3, 20 times smaller than that of the Si detector ( r E / E o =

ION-BEAM CHARACTERIZATION IN SUPERLATTICES 12 keV/305 keV = 3.9 • 10"2). That allows a very high depth resolution of 0.8 nm in the near-surface region of Si. In the RBS-channeling measurement for checking the crystalline quality, 1.7-MeV 4He+ ions were used as the probing particles. Figure 50 shows a typical experimental (solid circles) and simulated (dashed line) random RBS spectra of 305-keV 4He+ ions on a five-period Sb 7i-doped superlattice [107]. Six Sb peaks are clearly resolved. The first Sb peak located near channel 272 is from the Sb that segregated to the surface. The other five Sb peaks correspond to the five Sb doped 7i-layers. To determine the thickness of the ~-layers and the concentration of the Sb from the RBS spectra, computer simulation has to be performed. Lenkeit et al. developed a computer program that is capable of simulating RBS spectra for 1H+ or 4He+ ions in the energy range from 100 keV to 2 MeV and for sam-

!

I

1 .......

I

"

'

1

263

pies consisting of 30 layers and containing a maximum of 10 elements. The following important information were obtained by RBS-channeling measurement: (1) the thickness of the 7ilayer, the concentration of Sb, and the depth of the 7i-layers, which were determined by the comparison between the measured RBS spectrum and the simulated one (see Fig. 50); (2) the channeling analysis done with 1.7-MeV 4He+ ions showed that the superlattices had Xmin as low as 3.2% near-surface region, indicating that Sb 7i-doped Si superlattices have very high crystalline quality (see Figure 51 [107]); (3)the superlattices investigated were thermally stable as no broadening of the Sb profiles in the ~-layers were observed after 700~ (60 min) annealing (Fig. 52 [107]); (4) although Sb diffusion in the superlattice did not take place during the annealing process from 600 to 800~ segregation of Sb towards the surface did occur as revealed in Figure 53 [ 107], indicating enhanced diffusion near the surface.

'

o

randnnl

'': I

He + Eo - Z7 MeV

o, - ~m ~

~4

....

i

r..-.-

I

'.

/

,'p

4

.

.

.

'

_s-3o , v ,1

9 /

0

i!

9

il

--

I

'

I

-I ! ! ! d !

2

I!

I

.. I'',"

d #

7.0

7.7

,,~

I-',

.,i

,,

,,

II

,

!,

It

:"

''

'~'

b~ I.~

,40

~! i

.1_

..

"'20' m

o>_

'

4o

1

' [8.

20

l,

I o

I

l

I

I

1

l

-2.00 -I.50 -I.00-0.50 0 0.50 1.00 TILT ANGLE { d e g }

, I 1.50 2.00

269

ing with depth (low part of Fig. 60b [69, 160]). The top part in Figure 60b shows the structure of the SLS. The observed difference between the best channeling direction for the first two layers, 0.17 • 0.'03 ~ gives a lower limit for the strain. This measurement also can be compared with the Monte Carlo simulation and the real strain value can be obtained from the best agreement between the experiment and the simulation. However, care needs to be taken with the beam steering effect by the surface layer. The steering effect could significantly distort the shape of the angular scan of the strained layer, making the interpretation of the angular scan difficult. Planar channeling angular scan also can be used to measure the strains. Due to the tetragonal distortion along the growth direction, for an SLS grown along the (100) direction, the atomic planes are not straight when looking along the inclined planar direction such as the { 110} planar direction. There is a small-angle change from layer to layer at each interface. Hence, similar to the axial case, an angular scan across the inclined planar direction also can provide information about the strain. Davies et al. gives the details of the strain measurement by planar angular scan in Ref. [73, 74]. The influence of the steering effect is more serious in planar channeling than axial channeling. Detailed discussion on steering effect is given at the end of this section. This angular scan technique can measure the strain from a large value down to about 0.03 ~ or ~0.06% misfit.

(a) 5.4. Strain Measurement by Planar Dechanneling Analysis

9 "~st

,,'e,,a

The third and most sensitive method of analysis of the strain in SLS is to use the resonance match between the superlattice period and the planar channeling trajectory wavelength of the probing ions [146-148, 151,153, 155, 156]. When an ion beam is channeled along a planar channel direction, it will be steered back and forth between the planes giving rise to a focusing effect. The focusing effect of the planar channel on the probing ions was first observed through the oscillation character of the planar aligned energy spectra by Abel et al. [ 159]. Figure 61 shows the planar RBS-channeling spectrum with an oscillation for 1.2-MeV He ions entering GaP { 110 } planes [69, 160]. The interpretation of the measured oscillation is very simple based on a harmonic planar potential. The wavelength of the ion-beam can be expressed as [ 160],

,,'J,.~ , , ~ in ,

0" 45 09 }.~,aye,," ,(Layer (" Layec Layer r"

-45:o8~ ok [

;

,,,o,

"

i !F:

\!

! :

3Onto 3Onto 30nm ~ 3Onto ',

/o

- ~""-

'; /

'~o

-- 2zr (2E/c01/2

/92 44 92

i I

SURFACE

g'

' 2

1

4 5 NUMBER OF INTERFACES 3

DEPTH

(b) Fig. 60. (a) Angular scan by setting an energy window from the first to the fourth layer from 52 spectra run at different angles on a GaSb/A1Sb superlattice across the inclined {110} direction. (b) The top portion shows the sample schematics of the GaSb/A1Sb superlattice. The lower portion shows the angular position of the dips in (a). Reprinted with permission from C. K. Pan et al. [ 149], copyright 1983, American Physical Society. Reprinted with permission from W. K. Chu et al. [69], copyright 1983, American Physical Society.

(72)

where E is the energy of the projectile and ot is the force constant of the harmonic potential U(x) = 1/2otx 2 with x = 0 at the center between two neighboring atomic planes. The steering potential in a real crystal is anharmonic, so the real focus will be blurred and only an effective wavelength or a mean wavelength can be defined. In practice, the effective wavelength can be measured from the energy shifts between the oscillating peaks or the valleys, and then convert this energy shift in to depth by the energy loss of the ions in the materials. For example, in Figure 61, the effective wavelength of a 1.2-MeV He ion in [110] planes of a GaP crystal is defined as )~/2 = 48 nm.

270

ZHANG, LIU, AND CHU

@

a) PLANAR FOCUSING GaP II10} PLANES

@

SURFACE V

- ~ ~ : ~ = ~ : , . , . - ~ ~ : : : ~ , . . . . . . . . . . ~

- ~

2

1.2 . . v 4..

~

2qJp. In this case, the He + ions that are channeled in underlying strained layer must be in random direction S

S

l

- 1.2 ~

-.8 ~

-.4 ~

0~

.4 ~

.8 ~

ANGLE FROM BULK (110)

Fig. 70. Off-normal axial (110) angular scan of the indium scattering yields (InGaAs strained layer) using 2 MeV He + ions. (a) Sample #108: surface layer (GaAs)-25 nm; strained layer (In0.17Ga0.83As)-25 nm. (b) Sample #192: surface layer (GaAs)-36 nm; strained layer (In0.1Ga0.9As)-22 nm. Reprinted with permission from [73], copyright 1989, American Vacuum Society.

when they are traversing the surface layer and vice versa. Therefore, the scattering of the He + ions in the surface layer will not interfere with their channeling behavior in the strained layer. Thus the mid-point of the angular scan of the strained layer gives the correct value of the kink angle (Fig. 69).

5.5.2. Axial Channeling The steering effect is less serious in axial channeling as compared with that in planar channeling. Axial scan about the off-normal axis of the InGaAs strained layer (SL-layer) from two significantly different samples are shown in Fig. 70 [73]. In each case, the correct (110) orientations of the SL layer and the surface layer (S) are indicated by arrows. For sample #108, the path length Lp in the surface layer (35 nm) is smaller than the characteristic interaction distance d/We (40 nm for 2 MeV He + in GaAs) between the channeled ions and the (110) atomic rows, the mid point (dashed line) of the measured axial scan gives the correct SL orientation

274

ZHANG, LIU, AND CHU

(Fig. 70a), indicating that most of the He + ions do not suffer significant steering in traversing the surface layer. In other words, most channeled ions do not have reflection in traversing the surface layer. But for sample #192, the path length Lp in the surface layer (54 nm) is much larger than d/~Pc. A major fraction ofthe channeled ions undergo at least one reflection off the atomic rows in traversing the surface layer and thus have been shifted from their incident direction before entering the strained layer (SL). The resulting angular scan is now much more asymmetric than that in sample #108 (Fig. 70a) and the mid-point of the scan deviates significantly from the correct orientation of the strained layer (Fig. 70b). From these two examples, Davies et al. [73] concluded that (1) the steering on the channeled ions in traversing the surface layer can cause significant distortion of the shape of axial angular scan of the underlying strained layer if the thickness of the surface layer is larger than the d/q%. In this case, the accurate value of the kink angle can not be obtained by the axial channeling angular scan; (2) to reduce the influence of the steering effect on the kink angle measurement, it is necessary to tune the energy of the ions in such way that the characteristic interaction distance d/~Pc is never less than the thickness of the surface layer or to make the thickness of the surface layer less than d~ ~Pc.

REFERENCES 1. W.K. Chu, J. W. Mayer, and M.-A. Nicolet, "Rutherford B ackscattering Spectrometry," Academic Press, Orlando, FL, 1978. 2. M. Dobeli, A. Lombao, D. Vetterli, and M. Suter, NucL Instrum. Methods B 89, 174 (1994). 3. J. P. Thomas, M. Fallavier, and A. Ziani, Nucl. Instrum. Methods B 15, 443 (1986). 4. T.M. Stanescu, J. D. Meyer, H. Baumann, and K. Bethge, Nucl. Instrum. Methods B 50, 167 (1990). 5. R. A. Weller, K. McDonald, D. Pedersen, and J. A. Keenan, Nucl. Instrum. Methods B 118, 556 (1996). 6. D. Hunter, O. Meyer, J. Reiner, and G. Linker, Nucl. Instrum. Methods B 118, 578 (1996). 7. R.G. Smeenk, R. M. Tromp, H. H. Kersten, A. J. H. Boerboom, and E W. Saris, Nucl. Instrum. Methods 195,581 (1982). 8. H.D. Carstanjen, NucL Instrum. Methods B 136-138, 1183 (1998). 9. K. Kimura, K. Ohshima, K. Nakajima, Y. Fujii, M. Mannami, and H.-J. Gossmann, Nucl. Instrum. Methods B 99, 472 (1995). 10. K. Kimura, K. Nakajima, and H. Imura, Nucl. lnstrum. Methods B 140, 397 (1998). 11. J.W. Mayer and E. Rimini, "Ion Beam Handbook for Material Analysis" Academic Press, New York, 1977. 12. J.R. Tesmer, M. Nastasi, J. C. Barbour, C. J. Maggiore, and J. W. Mayer, "Handbook of Modem Ion Beam Materials Analysis," Materials Research Soc., Pittsburgh, 1995. 13. L. C. Feldman, J. W. Mayer, and S. T. Picraux, "Materials Analysis by Ion Channeling," Academic Press, New York, 1982. 14. N. Bohr, Philos. Mag. 25, 10 (1913). 15. N. Bohr, Philos. Mag. 30, 581 (1915). 16. H. A. Bethe, Z. Phys. 76, 293 (1932); H. A. Bethe, Ann. Phys. 5, 325 (1930); H. A. Bethe and W. Heitler, Proc. R. Soc. London A 146, 83 (1934). 17. E Bloch, Ann. Phys. 16, 287 (1933); Z. Phys. 81,363 (1933).

18. J. Lindhard and M. Scharff, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 27, (1953). 19. J . Lindhard, M. Scharff, and H. E. Schiott, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 34, (1963). 20. O.B. Firsov, Zh. Eksp. Teor. Fiz. 36, 1517 (1959); Zh. Eksp. Teor. Fiz. 32, 1464 (1957); Zh. Eksp. Teor. Fiz. 33, 696 (1957); Zh. Eksp. Teor. Fiz. 34, 447 (1958). 21. W.K. Chu and D. Powers, Phys. Rev. A 13, 2057 (1976). 22. W. K. Chu and D. Powers, Phys. Lett. 40A, 23 (1972); W. K. Chu and D. Powers, Phys. Lett. 38A, 267 (1972). 23. J. Lindhard, V. Nielsen, and M. Scharff, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 36, (1968). 24. K.B. Winterbon, P. Sigmund, and J. B. Sanders, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 37, (1970); K. B. Winterbon, Radiat. Eft. 13, 215 (1972). 25. J. E Ziegler, J. P. Biersack, and U. Littmark, "The Stopping and Range of Ions inSolids," Pergamon, New York, 1985. 26. J. E Ziegler, "Helium: Stopping Powers and Ranges in All Elemental Matters," Pergamon, New York, 1978. 27. J. P. Biersack and L. G. Haggmark, Nucl. Instrum. Methods 174, 257 (1980). 28. N. P. Barradas, C. Jeynes, O. A. Mironov, P. J. Phillips, and E. H. C. Parker, Nucl. Instrum. Methods B 139, 239 (1998). 29. N. Bohr, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 18, (1948). 30. J. Lindhard and M. Scharff, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 27, (1953). 31. W. H. Bragg and R. Kleeman, Philos. Mag. 10, $318 (1905); 10, 5318 (1905). 32. D.J. Thwaites, Nucl. Instrum. Methods B 12, 84 (1985). 33. D.J. Thwaites, Nucl. Instrum. Methods B 27, 293 (1985). 34. E Bauer, Nucl. Instrum. Methods B 45, 673 (1985). 35. J. Herault, R. Bimbot, H. Ganvin, B. Kubico, R. Anne, G. Bastin, and E Hubert, Nucl. Instrum. Methods B 61,156 (1985). 36. J. E Ziegler and J. M. Manoyan, Nucl. Instrum. Methods B 35, 215 (1988). 37. Feng et al. private communications to R. E Cox, J. A. Leavit, and L. C. McIntyre, Jr., Appendix 7 in [12]. 38. J.A. Davies and G. A. Sims, Can. J. Chem. 39, 601 (1961); J. A. Davies, J. Friensen, and J. D. McIntyre, Can. J. Chem. 38, 1526 (1960). 39. M. T. Robinson and O. S. Oen, Appl. Phys. Lett. 2, 30 (1963); M. T. Robinson and O. S. Oen, Phys. Rev. 132, 2385 (1963). 40. J. Lindhard, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 34, (1965). 41. J.H. Barrett, Phys. Rev. B 3, 1527 (1971). 42. J. U. Andersen, "Lecture Notes on Channeling" Institute of Physics, Aarhus University, Denmark, 1980. 43. D. V. Morgan, Ed., "Channeling: Theory, Observations and Applications," Wiley-Interscience, New York, 1973. 44. O.B. Firsov, Soy. Phys. JETP 6, 534 (1958). 45. G. Moli6r6, Z. Naturforschung A 2, 133 (1947). 46. W.D. Wilson, L. G. Haggmark, and J. E Biersack, Phys. Rev. 15, 2458 (1977). 47. J. E Biersack and J. E Zirgler, Nucl. Instrum. Methods 194, 93 (1982). 48. I. M. Terrens, "Interatomic Potentials," Academic Press, San Diego, 1972. 49. M. Nastasi, J. Mayer, and J. Hirvonen, "Ion-Solid Interactions: Fundamentals and Applications," Cambridge Univ. Press, Cambridge, U.K., 1996. 50. J.U. Andersen and L. C. Feldman, Phys. Rev. B 1, 2063 (1970). 51. J.U. Andersen, N. G. Chechenin, Yu. A. Timoshnikov, and Z. H. Zhang, Radiat. Eft. 83, 91 (1984). 52. J.U. Andersen, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 36, (1967). 53. S. T. Picraux, W. L. Brown, and W. M. Gibson, Phys. Rev. B 6, 1382 (1972). 54. J.U. Andersen, O. Andreasen, J. A. Davies, and E. Uggerhcj, Radiat. Eft. 7, 25 (1971). 55. B.A. Davidson, L. C. Feldman, J. Bevk, and J. E Mannaerts, Appl. Phys. Lett. 50, 135 (1986). 56. R.W. Fearick, Nucl. Instrum. Methods B 164, 88 (2000).

ION-BEAM

CHARACTERIZATION

57. M. Abramowitz and I. A. Segun, Eds., in "Handbook of Mathematics Functions," p. 998. Dover, New York, 1965. 58. D.S. Gemmel, Rev. Mod. Phys. 46, 129 (1974). 59. J.E. Westmoreland, J. W. Mayer, E H. Eisen, and B. Welch, Radiat. Eft. 6, 161 (1970). 60. Y. Qu~r~, Phys. Status Solidi A 30, 713 (1968); 61. Y. Qu~rb, Ann. Phys. 5, 105 (1968). 62. S.T. Picraux, E. Remini, G. Foti, and S. U. Camisano, Phys. Rev. B 18, 2078 (1978). 63. K. Yasuda, M. Nastasi, K. E. Sickafus, C. J. Maggiore, and N. Yu, Nucl. Instrum. Methods B 136-138, 499 (1998). 64. Z. Atzmon, M. Eizenberg, Y. Shacham-Diamand, and J. W. Mayer, J. Appl. Phys. 75, 3936 (1994). 65. Z. Zhang, I. Rusakova, and W. K. Chu, Nucl. Instrum. Methods B 136138, 404 (1998). 66. N. Yu, T. W. Simpson, P. C. Mclntyre, M. Nastasi, and I. U. Mitchell, Appl. Phys. Lett. 67, 924 (1995). 67. E W. Saris, W. K. Chu, C. A. Chang, R. Ludeke, and L. Esald, Appl. Phys. Lett. 37, 931 (1980). 68. W.K. Chu, J. A. Ellison, S. T. Picraux, R. M. Biefeld, and G. C. Osboun, Nucl. Instrum. Methods 218, 81 (1983). 69. W.K. Chu, C. K. Pan, and C.-A. Chang, Phys. Rev. B 28, 4033 (1983). 70. S. T. Picraux, L. R. Dawson, G. C. Osboun, R. M. Biefeld, and W. K. Chu, Appl. Phys. Lett. 43, 1020 (1983). 71. D.W. Hetherington, P. E Hinrichsen, R. A. Masut, D. Morris, and A. P. Roth, Can. J. Phys. 69, 378 (1991). 72. G. W. Fleming, R. Brenn, E. C. Larkins, S. Burkner, G. Bender, M. Baeumler, and J. D. Ralston, J. Cryst. Growth 143, 29 (1994). 73. J. A. Davies, B. J. Robinson, J. L. E. Stevens, D. A. Thompson, and J. Zhao, Vacuum 39, 73 (1989). 74. J.L.E. Stevens, B. J. Robinson, J. A. Davies, D. A. Thompson, and T. E. Jackman, J. Appl. Phys. 65, 1510 (1989). 75. E. BCgh, Can. J. Phys. 46, 653 (1968). 76. K. L. Merkel, P. P. Pronko, D. S. Gemmell, R. C. Mikkelson, and J. R. Wrobel, Phys. Rev. B 8, 1002 (1973). 77. E H. Eison, in "Channeling: Theory, Observation and Applications" (D. V. Morhan, Ed.), Chap. 14, p. 415. Wiley-Interscience, New York, 1973. 78. L. Meyer, Phys. Status Solidi B 44, 253 (1971). 79. P. Sigmund and W. K. Winterbon, Nucl. Instrum. Methods 119, 541 (1974); NucL Instrum. Methods 121,491 (1975). 80. E. Lugujjo and J. W. Mayer, Phys. Rev. B 7, 1782 (1973). 81. M. D. Thompson and G. J. Galvin, private communication to Feldman et al., Chap. 6. 82. S. T. Picraux, D. M. Follstaedt, P. Baeri, S. U. Camisano, G. Foti, and E. Remini, Radiat. Eft. 49, 75 (1980). 83. S.T. Picraux and D. M. Follstaedt (1982), in "Material Analysis by Ion Channeling" by L. C. Feldman, J. W. Mayer, and S. T. Picraux, Academic Press, New York, 1982, p. 103. 84. H. Kudo, J. Phys. Soc. Jpn. 40, 1645 (1945). 85. H. Kudo, Phys. Rev. B 18, 5995(1978). 86. H. Kudo, Nucl. Instrum. Methods 170, 129 (1970). 87. L. Z. Merz, L. C. Feldman, D. W. Mingay, and W. M. Augustyniak, in "Ion Implantation in Semiconductors" (L. Ruge and J. Graul, Eds.), p. 182. Springer-Verlag, Berlin, 1971. 88. J.W. Petersen, J. U. Andersen, S. Damgaard, E G. Lu, I. Stensgaard, J. T. Tang, G. Weyer, and Z. H. Zhang, Hyperfine Interact. 10, 989 (1981). 89. E. Alves, M. E da Silva, K. R. Evans, C. R. Jones, A. A. Melo, and J. C. Soares, Nucl. Instrum. Methods B, 80-81, 180 (1993). 90. L.M. Howe, M. L. Swanson, and J. A. Davies, "Methods of Experimental Physics," Vol. 21, p. 275. Academic Press, New York. 91. R. G. Elliman, J. S. Williams, W. L. Brown, A. Leiberich, D. M. Maher, and R. V. Knoell, Nucl. Instrum. Methods B 19-20, 423 (1987). 92. A. Kinomura, A. Chayahara, N. Tsubouchi, Y. Horino, and J. S. Williams, Nucl. Instrum. Methods B 148, 370 (1999). 93. S. T. Johnson, J. S. Williams, E. Nygreen, and R. G. Elliman, J. Appl. Phys. 64, 6567 (1988).

IN SUPERLATTICES

275

94. M. C. Ridgway, S. T. Johnson, and R. G. Elliman, Nucl. Instrum. Methods B 59-60, 353 (1991). 95. N. Kobayashi, Thin Solid Films 270, 307 (1995). 96. R.G. Elliman, M. C. Ridgway, J. S. Williams, and J. C. Bean, Appl. Phys. Lett. 55, 843 (1989). 97. A.J. Yu, J. W. Mayer, D. J. Eaglesham, and J. M. Poate, Appl. Phys. Lett. 54, 2342 (1989). 98. M. C. Ridgway, R. G. Elliman, and J. S. Williams, Appl. Phys. Lett. 56, 2117 (1990). 99. N. Kobayashi, D. H. Zhu, M. Hasegawa, H. Katsumata, Y. Tanaka, N. Hayashi, Y. Makita, H. Shibata, and S. Uekusa, Nucl. Instrum. Methods B 127-128, 350 (1997). 100. N. Yu and M. Nastasi, Nucl. Instrum. Methods B 106, 579 (1995). 101. S.C. Jain, "Germanium, Silicon Strained Layers and Heterostructures," pp. 69-93. Academic Press, New York, 1994. 102. C.C. Van d Walle and R. M. Martin, Phys. Rev. B 8, 5621 (1986). 103. T. Akane, M. Sano, H. Okumura, Y. Tubo, T. Ishikawa, and S. Matsumoto, J. Cryst. Growth 203, 80 (1999). 104. B. Hollander, R. Butz, and S. Mantl, Phys. Rev. B 46, 6975 (1992). 105. B. Hollander, S. Mantl, B. Stritzker, and R. Butz, Superlattices Microstruct. 9, 415 (1991). 106. B. Hollander, S. Mantl, B. Stritzker, and R. Butz, Nucl. Instrum. Methods B 59-60, 994 (1991). 107. K. Lenkeit, A. Pirrwitz, A. I. Nikiforov, B. Z. Kanter, S. I. Stenin, and V. P. Popov, Phys. Status Solidi A 121,523 (1990). 108. E Ruders, L. E. Rehn, P. M. B aldo, E. E. Fullterton, and S. D. B ader, Nucl. Instrum. Methods B 121, 30 (1997). 109. K. Lenkeit, R. Flagmeyer, and R. Grotzschel, Nucl. Instrum. Methods B 66, 453 (1992). 110. K. Lenkeit and A. Pirwitz, Nucl. Instrum. Methods B 68, 253 (1992). 111. K. Lenkeit, Superlattices Microstruct. 9, 203 (1991). 112. G.W. Flemig, R. Brenn, E. C. Larkins, S. Btirkner, G. Bender, M. Baeumler, and J. D. Ralston, J. Cryst. Growth 143, 29 (1994). 113. S. Sugden, C. J. Sofield, T. C. Q. Noakes, R. A. A. Kubiak, and C. F. McConville, Appl. Phys. Lett. 65, 2849 (1995). 114. C. E McConville, T. C. Q. Noakes, S. Sugden, P. K. Hucknell, and C. J. Sofield, Nucl. Instrum. Methods B, 118, 573 (1996). 115. D. Love, D. Endisch, T. W. Simpson, T. D. Lowes, I. V. Mitchel, and J.-M. Baribeau, Mater. Res. Soc. Symp. Proc. 379, 461 (1995). 116. T. Laursen, D. Chandrasekhar, D. J. Smith, J. W. Mayer, E. T. Croke, and A. T. Hunter, Thin Solid Films 308-309, 358 (1997). 117. O.A. Mironov, P. J. Phillips, E. H. C. Parker, M. G. Dowsett, N. P. Barradas, C. Jeynes, M. Mironov, V. P. Gnezdilov, V. Ushakov, and V. V. Eremenko, Thin Solid Films 306, 307 (1997). 118. C. Lin, P. L. F Hemment, C. W. M. Chen, J. Li, W. Zhu, R. Ni, G. Zhou, and S. C. Zou, Phys. Status Solidi A 132, 419 (1992). 119. G.Q. Zhao, Y. H. Ren, Z. Y. Zhou, X. J. Zhang, G. L. Zhou, and C. Sheng, Solid State Commun. 67, 661 (1988). 120. J.G. Beery, B. K. Laurich, C. J. Maggiore, D. L. Smith, K. Elcess, C. G. Fonstad, and C. Mailhiot, Appl. Phys. Lett. 54, 233 (1989). 121. A. Pathak, S. V. S. Nageshwara Rao, and A. M. Siddiqui, Nucl. Instrum. Methods B 161-163,487 (2000). 122. T. Xu, P. Zhu, J. Zhou, D. Li, B. Gong, Y. Wan, and S. Mu, Nucl. Instrum. Methods B 90 392 (1994). 123. E. A. Dobisz, M. Fatemi, H. B. Dietrich, A. W. McCormick, and J. P. Harbison, Appl. Phys. Lett. 59, 1338 (1991). 124. R. Flagmeyer, Superlattices Microstruct. 9, 181 (1991). 125. L.V. Melo, I. Trindade, M. From, P. P. Freitas, N. Teixeira, M. E da Silva, and J. C. Soares, J. Appl. Phys. 70, 7370 (1991). 126. T. Taguchi, Y. Kawakami, and Y. Yamada, Physica B 191, 23 (1993). 127. K. Roll and W. Reill, Thin Solid Films 89, 221 (1982). 128. M. Murakami, CRC Crit. Rev. Solid State Mater Sci. 11,317 (1983). 129. M.N. Baibich, J. M. Broto, A. Fert, E Nguyen Van Dau, E Petroff, P. Etienne, B. Greuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61,2471 (1988). 130. E. E. Fullerton, M. J. Conover, J. E. Mattson, C. H. Sowers, and S. D. Bader, Phys. Rev. B 48, 15755 (1993).

276

ZHANG, LIU, AND CHU

131. S. S. P. Parkin, N. More, and K. E Roche, Phys. Rev. Lett. 64, 2304 (1990). 132. R.P. Sharma, T. Venkatesan, Z. H. Zhang, J. R. Liu, R. Chu, and W. K. Chu, Phys. Rev. Lett. B 77, 4624 (1996). 133. W. K. Chu, "Laser and Electron Beam Processing of Electronic Materials" (C. L. Anderson, G. C. Heller, and G. A. Rozgonyi, Eds.), p. 361. Electrochemical Soc., Pennington, NJ, 1980. 134. G.H. Dohler, IEEE J. Quantum Electron. 22, 1682 (1986). 135. L.H. Yang, R. E Gallup, and C. Y. Fong, Phys. Rev. B 39, 3795 (1989). 136. J. P. Thomas, M. Fallavier, and A. Ziani, Nucl. Instrum. Methods B 15, 443 (1986). 137. T.M. Stanescu, J. D. Meyer, H. Baumann, and K. Bethge, Nucl. Instrum. Methods B 50, 167 (1990). 138. R. A. Weller, K. McDonald, D. Pedersen, and J. A. Keenan, Nucl. Instrum. Methods B 118, 556 (1996). 139. S.T. Picraux, G. W. Arnold, D. R. Myers, L. R. Dawson, R. M. Biefeld, I. J. Fritz, and T. E. Zipperian, Nucl. Instrum. Methods B 7-8, 453 (1985). 140. J. Li, Q. Z. Hong, G. Vizkelethy, J. W. Mayer, C. Cozzolino, W. Xia, B. Zhu, S. N. Hsu, S. S. Lau, B. Hollander, R. Butz, and S. Mantl, Nucl. Instrum. Methods B 59-60, 989 (1991). 141. D.R. Myers, S. T. Picraux, B. L. Doyle, G. W. Arnold, L. R. Dawson, and R. M. Biefeld, J. Appl. Phys. 60, 3631 (1986). 142. D.R. Myers, G. W. Arnold, T. E. Zipperian, L. R. Dawson, R. M. Biefeld, I. J. Fritz, and C. E. Barnes, J. Appl. Phys. 60, 1131 (1986). 143. L. Esaki, and R. Tsu, IBM J. Res. Develop. 14, 61(1970). 144. W.K. Chu, Phys. Rev. A 13, 2057 (1976). 145. W. K. Chu, E W. Saris, C.-A. Chang, R. Ludeke, and L. Esaki, Phys. Rev. B 26, 1999 (1982). 146. W.K. Chu, J. A. Ellison, S. T. Picraux, R. M. Biefeld, and G. C. Osbourn, Phys. Rev. Lett. 52, 125 (1984). 147. W. K. Chu, W. R. Allen, J. A. Ellison, and S.T. Picraux, Nucl. Instrum. Methods B 13, 39 (1986).

148. W.K. Chu, W. R. Allen, S. T. Picraux, and J. A. Ellison, Phys. Rev. B 42, 5932 (1990). 149. C. K. Pan, D. C. Zheng, T. G. Finstad, W. K. Chu, V. S. Speriosu, and M.-A. Nicolet, Phys. Rev. B 31, 1270 (1983). 150. S.T. Picraux, W. K. Chu, W. R. Allen, and J. A. Ellison, Nucl. Instrum. Methods B 15, 57 (1986). 151. S.T. Picraux, W. K. Chu, W. R. Allen, and J. A. Ellison, Nucl. Instrum. Methods B 15, 306 (1986). 152. S.T. Picraux, W. R. Allen, R. M. Biefeld, J. A. Ellison, and W. K. Chu, Phys. Rev. Lett. 54, 2355 (1985). 153. S.T. Picraux, R. M. Biefeld, W. R. Allen, W. K. Chu, and J. A. Ellison, Phys. Rev. B 38, 11086 (1988). 154. J.A. Ellison, S. T. Picraux, W. R. Allen, and W. K. Chu, Phys. Rev. B 37, 7295 (1988). 155. J. H. Barret, AppL Phys. Lett. 49, 482 (1982). 156. J.H. Barret, Phys. Rev. B 28, 2328 (1983). 157. D.Y. Han, W. R. Allen, W. K. Chu, J. H. Barret, and S. T. Picraux, Phys. Rev. B 35, 4159 (1987). 158. W. K. Chu, in "Nuclear Physics Applications on Materials Science" (E. Recknagel and J. C. Soares, Eds.), pp. 117-132. Kluwer Academic, Dordrecht/Norwell, MA, 1988. 159. E Abel, G. Amsel, M. Bruneaux, and C. Cohen, Phys. Lett. 42A, 165 (1972). 160. S. Hashimoto, Y.-Q. Peng, W. M. Gibson, L. J. Schowalter, and B. D. Hunt, Nucl. Instrum. Methods B 13, 45 (1986). 161. C. Wu, S. Yin, J. Zhang, G. Xiao, J. Liu, and P. Zhu, J. AppL Phys. 68, 2100 (1990). 162. K. Lenkeit and A. Pirrwitz, Nucl. Instrum. Methods B 67, 217 (1992). 163. A. Kozancecki, J. Kaczanowski, B.J. Sealy, and W.P. Gillin, Nucl. Instrum. Methods B 118, 640 (1996).

Chapter 6

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES: CARBON BASED AND METALLIC TiNx THIN FILMS GROWTH S. Logothetidis Aristotle University of Thessaloniki, Physics Department, Solid State Physics Section, GR-54006, Thessaloniki, Greece

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Theoretical Background of Ellipsometry for Study of the Properties of Materials . . . . . . . . . . . . . 279 2.1. Ellipsometry in Bulk Materials and Macroscopic Dielectric Function . . . . . . . . . . . . . . . . 279 2.2. Ellipsometry in Thin Film Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 3. Macroscopic Dielectric Function, Effective-Medium Theory, and Microscopic Surface Roughness . . . 283 4. Ellipsometric Techniques and Extension of Ellipsometry from the IR to the Deep UV Range . . . . . . 285 4.1. Rotating Analyzer Spectroscopic Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 4.2. Phase-Modulated Spectroscopic Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 4.3. Ellipsometry in the IR and Deep UV Energy Regions . . . . . . . . . . . . . . . . . . . . . . . . 287 5. Ellipsometric Studies of Carbon-Based Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 5.1. The Dielectric Function of a-C:H Films in the Energy Region 1.5 to 10 eV . . . . . . . . . . . . 291 5.2. Graphitization of a-C:H Films during Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 5.3. Dielectric Function of Amorphous Carbon Materials with Various Bonding . . . . . . . . . . . . 293 5.4. Real-Time Ellipsometry to Optimize the Growth of Sputtered a-C Films . . . . . . . . . . . . . . 294 5.5. In Situ Spectroscopic Ellipsometry to Study the Optical Properties and Bonding of a-C Films . . 298 5.6. Multiwavelength Real-Time Ellipsometry to Study the Kinetics of the Growth of CarbonBased Films Deposited with Sputtering Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 303 5.7. Study of Carbon Nitride Films with FTIR Spectroscopic Ellipsometry . . . . . . . . . . . . . . . 307 6. Optical Characterization and Real-Time Monitoring of the Growth of Metallic TiNx Films . . . . . . . 312 6.1. The Dielectric Function of TiNx Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 6.2. Optical Response of TiNx Films and Correlation with Stoichiometry . . . . . . . . . . . . . . . . 313 6.3. Study of the Stoichiometry of TiNx Films by Spectroscopic Ellipsometry . . . . . . . . . . . . . 316 6.4. Electronic and Microstructural Features of TiNx Films . . . . . . . . . . . . . . . . . . . . . . . 317 6.5. Multiavelength Real-Time Ellipsometry of TiNx Films Prepared by Unbalanced Magnetron Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 6.6. Oxidation Study of TiNx Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 7. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

1.

INTRODUCTION

t h a t c a n m o n i t o r - - i n situ a n d , m o r e i m p o r t a n t l y , in r e a l t i m e - thin film p r o p e r t i e s a n d p r o c e s s i n g . H o w e v e r , f o r c o n t r o l p r o -

The increasing d e m a n d s of p e r f o r m a n c e specifications and the

c e s s a p p l i c a t i o n s , a n y in situ a n d r e a l - t i m e p r o b e m u s t s a t i s f y

related sophistication of manufacturing processes have pro-

s e v e r e r e q u i r e m e n t s , s u c h as to b e n o n i n v a s i v e , n o n p e r t u r b i n g ,

v i d e d a s t r o n g i n c e n t i v e to d e v e l o p h i g h l y s e n s i t i v e d i a g n o s t i c s

c o n t a c t l e s s , a n d fast e n o u g h . D i f f r a c t i o n t e c h n i q u e s like r e f l e c -

Handbook of Thin FilmMaterials, edited by H.S. Nalwa Volume 2: Characterizationand Spectroscopy of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512910-6/$35.00 277

278

LOGOTHETIDIS

tion high-energy electron diffraction have been used widely to monitor growth of materials under ultrahigh-vacuum conditions by molecular beam epitaxy. Traditional surface probes based on either electrons or ions, however, cannot be extended to the high pressures and reactive environments associated with the chemical vapor deposition and the physical vapor deposition techniques, which are extensively used in thin film and material processing. Optical techniques based on specular reflection can satisfy the previously mentioned requirements. Among them, ellipsometry measures the change in polarization of a polarized beam of light after nonnormal reflection from a material to be studied. The polarization state of the polarized light can be characterized by two parameters (e.g., the relative amplitude and the relative phase) of the electric field. This provides ellipsometry an advantage over other optical techniques, since from it one can directly calculate two quantities, e.g., the complex dielectric function [~(co) = el + ie2] of a bulk absorbing material at a given photon energy co (which is related to the electronic, vibrational, structural, and morphological characteristics of the material) or the film thickness d and the real part of dielectric function el (= n 2, the refractive index) in transparent films. In contrast, reflectance, for example, provides only one parameter: the ratio of the reflected to the incident intensity of the electric field. As a consequence, spectroscopic ellipsometry (SE) has extensively been used for thin film growth monitoring [1-3]. SE can provide a lot of information about thin films, such as the optical gap, electronic structure, physical structure (crystalline and amorphous phases), composition, and stoichiometry, as well as their density and thickness. Moreover, SE analysis can be extended to multilayer systems, can be used in situ to identify the various stages of the film growth (nucleation, coalescence, and surface roughness evolution [2, 3]), and is very sensitive to the surface and bulk properties of the materials [4-6]. Since over all types of materials the absorption coefficient varies from 1 to 2 x 106 cm-1, the penetration depth of light from the infrared (IR) to the deep ultraviolet (UV) range varies from ~ 108 to 0.5 x 102 A, a fact that enables SE to be used as a probe for screening not only bulk, but also surface material properties. In metals with a penetration depth in the IR-to-UV range below about 200 A, SE can be used as a probe to screen the bulk and surface properties with high sensitivity. In semiconductors, SE can probe different depths of the material from the near infrared (NIR) to the visible (Vis) energy region. In particular, in the UV range the penetration depth is reduced to the order of 100 A or below, and then ellipsometry can provide their surface electronic properties and characterize their surfaces and interfaces. Whatever the configuration or approach used, SE has generally been applied in the last fifteen years in the near-UV-Vis range. However, the optical response in the UV-Vis range is sensitive neither to the vibrational properties of materials nor to the electronic properties of the wide-bandgap semiconductors (e.g. GaN [4, 5], SiC [6]) and the insulating materials (e.g. SiNx [7], SiO2). The former can be a strong limitation when dealing with complex compounds, such as thin films of hydrogenated

amorphous carbon (a-C:H) [2, 8] and carbon-related materials such as carbon nitride (CNx) [9] and boron nitride (BN). A detailed understanding, for example, of hydrogen and nitrogen incorporation from the gas phase into the film and the dependence of the vibrational properties upon the local environment and the CNx and BN film bonding configuration and composition requires the extension of the spectroscopic measurements into the IR, and this has been done the last few years [2, 8-15]. Finally, the availability of the synchrotron radiation sources has given SE the ability to overcome the limitation of conventional light sources to energies below 6.5 eV, and (together with the development of the new polarized devices) to be extended in the deep UV energy region, where the strong absorption of widebandgap and insulating materials takes place [4-7, 16-18]. Moreover, as a consequence of recent advances in optical instrumentation, fast real-time SE monitoring (in the UV-Vis range) is becoming compatible with most of the kinetics involved in thin film processing techniques [2, 3]. Thus, this fast and sensitive optical technique makes possible feedback control of the thickness and the refractive index of transparent films [ 19-21 ] or the thickness and the composition in absorbing films [22, 23]. Various applications of SE are presented here, with particular emphasis on in situ and real-time studies of thin film processing. More precisely, this review is organized as follows. The fundamentals of ellipsometry in bulk and thin films and the application of SE to the most-studied material, silicon (which is also used widely as a substrate for thin films) are briefly described in Section 2. Section 3 provides an overview of the effective-medium theory and microscopic surface roughness in an attempt to understand and quantify the information about the properties and growth stages of thin films during and after preparation. Among the various ellipsometric techniques available, rotating analyzer ellipsometry (RAE) at low frequency (~20 Hz) and phase-modulated spectroscopic ellipsometry (PMSE) at high frequency (50 kHz) are the most important. These techniques, together with the extension of ellipsometry to IR and deep UV energy are presented in Section 4. Then selected examples of applications of both techniques to thin film processing are described in two sections. In particular, Section 5 is devoted first to a detailed in situ spectroscopic study of the optical and electronic properties of a-C:H films in the energy region 1.5 to 10 eV, combining Vis-UV and synchrotron radiation ellipsometry. After that are described real-time ellipsometry and spectroscopic ellipsometry studies in the UV-Vis energy range on hydrogen-free amorphous carbon (a-C) films during deposition by magnetron sputtering techniques. The resuits obtained by these studies are discussed and reviewed as a case study in optimizing the deposition parameters and in producing films with desired properties for specific applications. Moreover, a very fast PMSE technique at certain wavelengths is introduced, which has been applied to investigate the initial stages of growth of carbon-based (a-C and CNx) materials and their differences in growth when they are produced by various magnetron sputtering techniques. Finally, recent applications of IR ellipsometry are reviewed, where the high sensitivity of this

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES technique to film properties such as vibrational modes, bonding configuration, and composition of carbon nitride films is underlined. Section 6 describes the in situ and real-time monitoring of metallic TiN thin films by PMSE in the UV-Vis range, from which information about the electronic structure, stoichiometry, oxidation, and structural and morphological characteristics of the films are obtained. The procedure to mesure the TiNx film's stoichiometry and its thickness during deposition is described analytically; it has been applied in real-time monitoring of TiNx film deposition by a very fast deposition technique-unbalanced magnetron sputteringmin an attempt to test the acquisition speed and software analysis limits of the current SE technology. It is shown that real-time ellipsometry, with fast recording capability, is a promising technique to provide feedback control of the growth of absorbing thin films.

2. THEORETICAL BACKGROUND OF ELLIPSOMETRY FOR STUDY OF THE PROPERTIES OF MATERIALS 2.1. Ellipsometry in Bulk Materials and Macroscopic Dielectric Function

The interaction between a material and a polarized light beam, incident at an angle 0 and reflected from the material's surface, modifies the polarization of the beam. Ellipsometry is conducted in order to obtain information about a system that modifies the state of polarization of the specular reflection. This

279

is achieved by measuring the initial (incident) and final (reflected) states of polarization of the beam. An ellipsometric arrangement is shown in Figure 1. A wellcollimated monochromatic beam from a suitable light source is passed through a polarizer to produce light of known controlled linear polarization. This is reflected by the surface of the sample under investigation, and is passed through the second polarizer (the analyzer) of the ellipsometer, to be analyzed with respect to the new polarization state established by the reflection, and finally the intensity of the linearly polarized light is detected and transformed to raw data through the electronics and computing devices. This last part of the ellipsometric arrangement determines the accuracy and the speed of acquisition of the information obtained about the investigated sample. In order to understand how ellipsometry works, the differences between it and other optical techniques, and the differences among various ellipsometric techniques, we are going to outline some results of the electromagnetic theory. Consider first the propagation of an electromagnetic plane wave through a nonmagnetic medium, which can be described by the electric field vector E; in the simplest case this is a plane wave given by the following expression: -- Eie i(kz-wt)

(1)

For oblique incidence, plane waves are typically referred to a local coordinate system (x, y, z), where z is the direction of propagation of light with wave number k, and x and y define the plane where the transverse electromagnetic wave oscillates. That is, the latter are the directions (see Fig. 1) parallel (p) and perpendicular (s) to the plane of incidence, respectively (these

Fig. 1. Schematic diagram of an ellipsometer with the incident monochromatic beam linearly polarized. Here p and s denote polarization parallel and perpendicular to the plane of incidence (defined by the normal to the sample and the incident beam), respectively. The detector, electronics, and computing devices collect the information about the sample and transform it to raw data.

280

LOGOTHETIDIS nel reflection coefficients ?p and ?s. These reflection coefficients describe the influence of the material on the p and s electric field components referred to the plane of incidence, and characterize the interface between two media---e.g., the ambient (medium 0), and the material studied (medium 1)--and are given by the expressions

~ rp -

E"'r,p ~i,p

Ir,Pl

lEr, p l ' e iOr'p IE~',pl" eiOi'p = ~

ei(Or, p--Oi,p )

"

--lTplei~p

Fig. 2. Oblique reflection and transmission of a plane electromagnetic wave at the sharp interface between two media 0 and 1 with refractive indexes n o and fi 1, respectively. The electric field components Ep and Es, parallel (p) and perpendicular (s) to the plane of incidence, and the wave vector for the incident (i), reflected (r), and transmitted (t) waves are shown. 0 and 01 are the angles of incidence and refraction.

two directions are the two optical eigenaxes of the material under study). The complex electric field amplitudes Ep and Es represent the projectionsof the plane wave E along x and y. Therefore, the quantity Ei in Eq. (1) does not only carry information about the amplitude of the plane wave E when it is propagated in vacuum, but also carries information about its polarization as well. Namely,

Fs : ~ r ' s : Ei,s

(7)

[F-'r,s[ " ei~ _ IEi,sl- e iOi,s

(2)

In addition, the amplitude k of the wave vector during the propagation of the wave in matter is in general a complex number given by the dispersion expression k - fiw/c. Here h(w) is the refractive index, which is in general a complex quantity, and it is related to dispersion and absorption of the radiation by the medium: fi(w) = n + ix

(3)

The complex dielectric function 5(w) (-- el + ie2) is the quantity directly related to the material properties, and is connected to the refractive index through the following equation: ~(co) = el + i t 2 =- fi2(o9) = (n + itc) 2

::~ el = n 2 -- K2,

e2 = 2ntc

(4)

Equation (1) for an electromagnetic wave transmitted in a dispersive and absorbing material can be rewritten as follows:

Ei - (Eix~ + Eiyy)eiwnz/ce-WXZ/Ce -iwt

(5)

with the absorption coefficient ot - 2 w z / c (= 4zrx/~.) representing the depth of the wave in the material, and ~. being the wavelength in vacuum. When the electromagnetic wave is reflected by the smooth surface of the material (see Fig. 2), the polarization of the outgoing wave can be represented as /~r = (FpE0x.~ + 7sE0y~)

(6)

In this approximation, the interaction of the electromagnetic wave with the material is described by the two complex Fres-

~i,s

= lTsleiSs

(8)

The Fresnel reflection coefficients on the interface between two media i and j, e.g., medium 0 and medium 1 in Fig. 2, with refractive indices/~i and fij, respectively, are given by the following expressions: r'ij,p --

/~j COS Oi -- rti COS Oj ~ nj cos0i +t~i cos0j

(9)

r'ij,s =

/~i COS Oi -- rtj cos Oj ~ n i COS Oi + 7lj COS Oj

(10)

...r

Ei = E i x x + E i y Y

[Er ~l . ei Ei >_30eV and 230 > Ei > 130 eV, respectively. In order to extract the bulk dielectric function e(w) of the a-C films from the measured (e(w)) we used an inverse fitting procedure [24, 74]. In this mathematical inversion fitting procedure all the quantities that are involved in the three-phase (air-a-Cfilm-Si-substrate) system are known except the bulk dielectric function [e(w) - E1 "+- ie2] of the a-C film, which is deduced with a Newton method. More specifically, the pseudo-dielectric function (e(w)) of the a-C-film-Si-substrate system and the dielectric function e(w) of the Si substrate (after ion etching) are

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES '

I

'

'

I

'

I

'

- - -u +10 V, Type I Vb : -40 V, Type II . . . . Vb --160 V, Type III N

"QI

,D I I

E1

~b

"t,b 441Q

\

\ 2

"

l

%%

9

,

I

1

,

2

I

,

I

,

I

,

3 4 5 Photon Energy (eV)

6

Fig. 40. The real part e 1(o9) for three representative a-C films of type I, II, and III deposited by magnetron sputtering at different bias voltages Vb applied to the substrate during growth.

'

I

'

I

'

I

'

I

"s. .= ..= =,. ==

9 *=

S

9 =., 9

=.

%

,

1

...

9 9 II

E2

0

9

%%

.o

I

2

,

I

,

I

%

II

iiI

%

,

I

3 4 5 Photon Energy (eV)

in agreement with those found with the Lorentz oscillator description [74]. Films of type I exhibit high absolute e2-values in the range 1.5-4.0 eV, an optical gap below 0.5 eV, and a fast reduction in e2(co) above 4.5 eV, the characteristic behavior of graphite as discussed in Sections 5.1-5.3. The low absolute values in e2 (co) over the whole energy range 1.5-5.5 eV in films of type II, and the appearance of an optical band gap ~ 1.5 eV, are in agreement with the fact that these films contain larger percentages of sp 3 sites. On the other hand, e(co) in films of type III exhibits high absorption over the whole spectral range and an interband transition at ~ 1.4 eV [74, 83]. The optical response of these films is rather unexpected if we assume that the C-C bonding configurations in the material are only the well-known sp 2 and sp 3 ones. Additional studies on the films by XRR and stress measurements showed that these films are denser with lower stress and sp 3 content than the ones of type II [73]. Nevertheless, a complete analysis of the amorphous carbon films, with regard to their the electronic and optical properties versus their different bonding configurations in the energy region from IR to deep UV, will be presented in a forthcoming publication [84].

5.6. Multiwavelength Real-Time Ellipsometry to Study the Kinetics of the Growth of Carbon-Based Films Deposited with Sputtering Techniques

'

- - - V b= +10V, TypeI ~ V b -- -40 V, Type II . . . . Vb --160 V, Type III

~d,.

303

,

6

Fig. 41. The imaginary part e2(09) of three representative a-C films of type I, II, and III deposited by magnetron sputtering at different bias voltages Vb.

measured (known) quantities, and the film thickness d is known (for example, calculated by SE, XRR, and XTEM) with high accuracy too. Then Eq. (18) is solved at each photon energy for the two unknown quantities el and e2 of the film. In Figures 40 and 41, the real and imaginary parts, respectively, of the bulk dielectric functions obtained through the inverse fitting procedure for the films of types I and II are presented. The bulk e(co), for a-C films of type III, is measured directly from an a-C film ~ 180 nm thick, where no contribution of the Si substrate occurs, since these films are very absorbing in the energy region 1.5-5.5 eV. The results of this analysis are

Real-time monitoring is essential for the production of modem engineering materials. Particularly, nondestructive optical access to a surface in vacuum is important for real-time monitoring, control, and characterization during film development, providing reduction in production time and increase of production yield. If the data collected in real time can be also interpreted in real time, then it becomes possible to control materials' characteristics through a closed-loop adjustment of process variables, such as an external bias voltage applied to the substrate during deposition, which controls the bonding and composition of the carbon-based materials. From a technological point of view, this means that one can assess process reproducibility and quickly attain the desired process variables. Even if the real-time interpretation is not possible and only one characteristic of the thin film is obtained, the information deduced in a postprocess analysis of the real-time measurements can be applied to a better understanding of the process. In situ spectroscopic ellipsometry (SE) is a surface-sensitive optical technique used to monitor deposition rates and composition of films during deposition and can be used in a complementary manner with other postdeposition techniques such as Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) [98]. In this subsection we will present a real-time SE monitoring process by multiwavelength ellipsometry (MWE) of a-C film deposition by closed field unbalanced magnetron sputtering (CFUBMS) [22, 23], which is a technique achieving high deposition rates and is applied on an industrial scale. The high deposition rate of a-C by CFUBMS is used to test the acquisition speed and software analysis limits of the currently available SE MWE technology.

304

LOGOTHETIDIS

Fig. 42. A schematic representation of the high-vacuum closed field unbalanced magnetron sputtering (CFUBMS) system, the magnetrons (MAG 1, MAG 2) and the sample holder, and the attached multiwavelength ellipsometer, with the excitation and detection heads, the light sources, the 16-wavelength unit, and the monochromator. The monochromator allows the whole ellipsometric unit to be used as a spectroscopic ellipsometer in the energy region 1.5-5.5 eV as well. A fiber optic in front MAG 1 is used for optical emission spectroscopy (OEM).

The deposition experiments were performed in a highvacuum system with base pressure better than 10 -5 Torr by using the CFUBMS technique. The deposition system and the ellipsometers used for these experiments as well as their integration are shown in Figure 42. The high-vacuum deposition system consists of two or four high-field-strength magnetrons with graphite targets, mounted on the vertical walls of the cylindrical chamber. Plasma etching of c-Si and pre-sputtering were performed prior to carbon and carbon nitride thin film deposition. The partial pressures of working gas (Ar) and reactive gas (N2) were 3 and 1.6 mTorr, respectively. The real-time measurements were performed with a 16-wavelength phasemodulated ellipsometer, which was attached to the CFUBMS vacuum chamber. The ellipsometer provides also the possibility of SE measurements in the energy region 1.5-5.5 eV. With the 16wavelength ellipsometer are obtained simultaneously the ellipsometric angles q~ and a for the 16 different wavelengths of the film-substrate system in continuous, distinct, timed steps. The 16 wavelengths are distributed in the Vis-UV energy region from 1.52 to 4.19 eV. The dielectric function e(w) of the system is calculated directly from qJ and A through the complex reflection ratio/5 (= tan qJ eiA). In the case of thin films the measured quantity is the pseudo-dielectric function (e(co)) that includes the effect of the substrate. The speed of the real-time measurements depended on the integration time (IT) used for the simultaneous acquisition of the 16 wavelengths. The smaller the IT value, the closer the monitoring of the phenomena. In order to monitor the CFUBMS processes, 10 < IT < 125 ms must be used, and subsequently the sampling time (ST) for ev-

Fig. 43. Real-time 16-wavelength spectra of (e2(w)) during a-C film growth on a c-Si substrate for 150-s total deposition time. The MWE spectra of the substrate before and after etching are also plotted.

ery step measurement must be at least slightly longer than 10 and 125 ms, respectively. The IT = 10 ms is set by the accuracy and the reproducibility of the MWE measurements. The results presented in this work were obtained with IT = 62.5 ms, providing a total time of 1 s for each 16-wavelength spectrum. In Figure 42 is shown the use of the 16-wavelength ellipsometer with the high-vacuum CFUBMS deposition chamber, which is used for real-time MWE and in situ SE measurements. The ellipsometers have the same excitation and detection head, and the angle of incidence is 70.05 ~ [22, 23].

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES The real-time monitoring of thin film optical properties is achieved with the spectral response of dielectric function at 16 wavelengths in the energy region 1.52-4.19 eV. Figure 43 presents the evolution of the imaginary part (e2(co)) versus photon energy during the deposition of an a-C film grown by unbalanced magnetron sputtering for 150-s total deposition time. Figure 44 presents (e2(co)) measured by the same procedure during deposition of CNx films grown with the same technique. The multiwavelength spectra were collected with IT -- 0.25 s and ST = 0.50 s for the first 30 s of deposition. After the first 30 s, in order to reduce the number of spectra, the IT and ST were set at 0.25 and 1 s, respectively. In continuing the discussion on the modeling of the initial stages of growth in Section 5.5, we should mention here that at these stages of a-C and CNx film growth on a Si

Fig. 44. Real-time16-wavelengthspectra of (82(o9)) during CNx film growth on a c-Si substrate for 150-s total deposition time. The MWE spectra of the substrate before and after etching are also plotted.

305

substrate, phenomena such as interdiffusion, chemical reactions, and SiC formation [95, 96] also take place, depending on the deposition conditions. On the other hand, the volume and the rate of data collection by real-time MWE are very high and yield more or less enough information about these phenomena. The problem is how to handle the SE data and how to model them. For example, the simplified one-layer model we used in the data analysis in Section 5.5 may not be able to provide all the details, but at least provides reliable information on whether or not in homogeneous film growth takes place. A more sophisticated model of analysis is required to describe quantitatively the a-C-film-Si and the CNx-Si substrate systems. However, a more sophisticated model increases the free parameters, a fact that affects its accuracy and reliability. That is beyond of the scope of this work; instead (i) describe the phenomena at the a-C-Si interface qualitatively, leaving details about the a-C-Si interface phenomena under ion bombardment during deposition and layer-by-layer growth to [95-99], and (ii) discuss and compare the a-C film growth mechanisms in different magnetron sputtering techniques and the differences between a-C and CNx films prepared by CFUBMS, in an attempt to optimize the techniques and to tailor the films' properties for specific applications. Thus, for the analysis of measured (e(co)) spectra we applied the BEMT in combination with the three-phase (air-compositefilm-c-Si substrate) model [27, 62], assuming that the composite film, of thickness d, consists of sp 2 and sp 3 phases (see for example the discussion in Section 5.3) and voids. Two representative examples of this analysis are shown in Figure 45, where are plotted two experimental MWE (e(co)) spectra, among those collected during deposition, at times t -- 15 and 150 s of Figure 43, together with the corresponding fitted spectra (solid lines). By the described analysis of the measured (e(co)) we calculated the thickness, deposition rate, and composition

Fig. 45. The measured real [(81 (w)), closed diamonds] and imaginary [(82(o9)) , closed circles] parts of the pseudo-dielectric function during growth of an a-C film at deposition times t = 15 and 150 s, and the fitted results (solid lines) based on the analysis with one-layer model in combination with BEMT.

306

LOGOTHETIDIS

Fig. 46. Evolution of thickness of a-C and CNx films, grown by closed field unbalanced magnetron sputtering (CFUBMS) under identical conditions, obtained from real-time MWE data analysis, based on the one-layer model (see inset) and assuming that the grown films, with an average thickness d, consist of sp 2 and sp 3 carbon phases and voids.

(not presented here) of representative (i) a-C and CNx films deposited by CFUBMS and (ii) a-C films deposited by planar dc MS with dc bias voltage pulses applied to the substrate (for more details see [23]). The a-C and CNx films were deposited by CFUBMS using identical deposition conditions [23]. The only difference between them is the introduction of nitrogen gas (partial pressure PN2 = 3 x 10 -3 Torr) and the equivalent reduction of the argon partial pressure in the chamber when depositing the CNx film. The results for the best-fit evolution of the thickness d of the a-C and CNx films are given in Figures 46 and 47. In Figure 47, the scale is magnified to show the details at the very initial stages of growth. The results of Figure 47 provide quantitative signatures of the nucleation processes of a-C and CNx materials. In a-C the nuclei increase in size to ~ 10 .& in the first 7 s and then make contact until 20 s, and for t > 20 s the bulk layer thickness increases linearly with time. In CNx the nuclei initially increase more abruptly in size, to ~ 2 5 / ~ in the first 35 s. The coalescence stage lasts until 60 s, and for t > 60 s we obtain the linear time dependence of film thickness that signifies bulk homogeneous CNx layer deposition. The differences deduced in the deposition rates between the two CFUBMS materials deposited under identical conditions are due to the presence of nitrogen in the growth of CNx films. In the stage of homogeneous film growth presence of the nitrogen leads to reduction of the deposition rate, mainly due to the preferential sputtering under the ion bombardment at the growing film surface. At the initial stages of growth the main differences are due to the chemical reactions of the nitrogen species with the Si substrate and their mobility at the growing film surface, which dissociate the sputtered carbon clusters and

Fig. 47. Evolution of thickness of a-C and CNx films, as in Figure 46, but at the very initial stages of growth.

affect the bonding structure and bonding configuration. More details about the formation and bonding structure and configurations of CNx films will be presented in Section 5.7. A floating bias and a pulsed negative dc bias voltage (Vb = --50 V) were applied to the Si substrate for the deposition of a-C films by dc MS. The results for the best-fit evolution of thickness are presented in Figure 48a, whereas in Figure 48b they are magnified to show the details at the initial stages of growth. The nucleation and coalescence stages are not completely different in the two a-C films [23] as in the case of rf-magnetron-sputtered films presented in Section 5.5, because the applied negative dc bias here is low. Even so, when a negative dc bias Vb = --50 V is applied, the nucleus size is smaller and the duration of nucleus contact is shorter than with floating bias. This is more or less expected, due to the contribution of Ar + ion bombardment to the growth process when the negative bias is applied. Consequently, the stage of homogeneous film growth, identified by the linear time dependence of thickness (Fig. 48a), is characterized by a lower deposition rate. In analyzing the MWE data [99] the process of the film evolution can be better described by the ideas of the two-layer model shown in Figure 49. Accordingly, we performed a linear regression of the thickness (according to one-layer model) calculated by MWE versus time deposition rate during homogeneous film growth, that is, while there is a clear steady state and a linear dependence of thickness on time (e.g., for the films of Fig. 48a for time beyond 250 s). The linear regression provides a deposition rate of a homogeneous layer (Fig. 49) that has the same properties during growth; only its thickness varies. On the other hand, a thin nucleation layer (or surface layer), where the C adatoms are sticking on the Si or a-C surface, is formed on top of the homogeneous layer. The thickness of this layer is determined by subtracting from the curve of total thickness versus time the contribution of the homogeneous layer. This analysis discriminates between nucleation and the

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES

307

Fig. 49. (a) Evolution of thicknesses (ds and db) of an a-C film deposited on a c-Si substrate with dc magnetron sputtering and pulsed dc biasing of the substrate, obtained by fitting the two-layer model. The three stages of growthm the nucleation (1), the coalescence (2), and homogeneous film growth (3)--are shown. (b) A schematic representation of the two-layer model with the nucleation layer (surface layer) ds and the homogeneous bulk layer db, both consisting of the same carbon phases.

Fig. 48. Evolution of thickness of a-C films, grown by dc magnetron sputtering at different bias voltages Vb applied to the substrate, obtained from multiwavelength ellipsometry data analysis (a) at different stages of growth, and (b) at the initial stages of growth.

homogeneous layer, as shown in Figure 49a. At the very initial stages of growth (region 1), there is only the development of the nucleation layer and corresponding growth of a-C nuclei before they make contact with each other and cover the whole Si substrate. As the size of the carbon islands increases, the thickness ds of this nucleation layer gradually increases to a maximum ds ,~ 36 ~ at about 150 s. At the second stage of film growth (Fig. 49a, region 2), the Si substrate has been completely covered by the a-C film, there is no interaction of the deposited C species with the Si, and the homogeneous layer starts to form. At this stage the thickness ds of the nucleation layer decreases to a final value ~10 ,~ as the deposited C species fill the free

space between the a-C islands. In the steady state (region 3), the development of the homogeneous layer dominates the film growth. The open space between islands has been filled, and a very thin nucleation (surface roughness) layer exists due to the formation of smaller islands by the deposited species, which act as nucleation sites during deposition. These islands are formed continuously, contributing to the development of the homogeneous layer. By this type of analysis, based on the one-layer model and using the ideas of the two-layer model [99], we can find the differences (in the nucleation, coalescence, and homogeneous growth stages) between the a-C films grown by dc MS and those grown with pulsed dc bias, and between a-C and CNx films deposited by CFUBMS.

5.7. Study of Carbon Nitride Films with FTIR Spectroscopic Ellipsometry Continuous technological progress creates an increasing demand on the properties and functionality of materials. Im-

308

LOGOTHETIDIS

provements of the mechanical, optical, thermal, chemical, and electrical features of thin films, especially hard coatings, are highly desirable in modern industry. Carbon nitride (CNx) thin films are among the good candidates for several technological applications. The theoretical prediction of the fl-C3N4 phase [ 100, 101 ] and its interesting properties initiated vast efforts by several groups for its synthesis. Carbon nitride is now considered as an outstanding material, characterized by high hardness, low friction coefficient, chemical inertness, and variable optical bandgap. Its use is spreading to a wide variety of applications such as wear-resistant coatings, hard coatings, protective optical coatings, protective coatings on magnetic disk drives, cutting tools, and hard barriers against corrosion, and as a novel semiconductor material. This wide range of valuable application has led to an intensive investigation of CNx films using several techniques, such as magnetron sputtering, ion-beam deposition, laser ablation, and plasma-enhanced chemical vapor deposition CVD [ 102]. However, there has been no clear evidence of the formation of crystalline stoichiometric fl-C3N4 except for the existence of small crystallites of this phase, embedded in an amorphous carbon matrix [103-105]. The difficulty in its production arises from the large amount of N (57 at. %) that must be incorporated in the films. Nevertheless, nitrogen-deficient (~20-40 at. %) carbon nitride films are found to exhibit interesting properties, comparable to other carbon-based materials. These properties have been attributed to the bending and cross-linking of the graphite planes through sp3-coordinated bonds, leading to the formation of a fullerenelike microstructure through the formation of three-dimensional molecular structures [ 106-109]. Fourier transform IR spectroscopic ellipsometry (FTPME) can be used for the study of carbon nitride materials, since the analysis of the characteristic bands in the infrared can give a great deal of both qualitative and quantitative information about their bonding structure. This can significantly contribute to the understanding of the mechanisms that take place during the formation of the different bonding structures between carbon and nitrogen atoms. The excellent diamond-like properties that these materials exhibit are due to the sp 3 bonding fraction, which varies considerably with the synthesis parameters. Furthermore, during the growth of CNx thin films by sputtering, there exists an intense positive ion bombardment on the growing film surface [110]. The energy Ei of the bombarding ions is controlled by the negative bias voltage Vb applied to the substrate through the relation Ei = Ep + elVb], where Ep is the discharge energy. The use of FTPME can help to establish a definite correlation between the growth conditions (Vb) and the films' bonding structure, which straightforwardly reflects their optical, mechanical, and electrical properties as well as their thermal stability [9]. The role of nitrogen atoms in determining the degree of diamond-like character is complicated, because N has the ability to form several bonding configurations with C [9]. These include the sp3-hybridized (tetrahedral, C - N ) , sp2-hybridized (trigonal, C=N), and chain-terminating spl-hybridized (linear, - C - N and - N = C ) bonds. The vibration frequency of each

bonding structure depends on the atom species and the bonding configuration, but also on its neighboring environment. Although the identification of bonding structures of different hybridization is possible, that is not the case for different bonding structures with the same hybridization state, which contribute to the FTPME spectra in overlapping vibration bands that are difficult to distinguish. Particularly, the existence of sp3-hybridized C - N bonds in the films gives rise to an characteristic band in the wave-number region 1212-1270 cm -1, while the existence of sp2-hybridized C=N bonds is evidenced by a vibration mode appeared at ~ 1530 cm -1 [9, 111-113]. The sp 2 C=C bonds are normally IR-inactive, since the C=C bond is a nonpolar bond. However, the contribution of this bond to the FTPME spectra is the result of N incorporation in the graphific rings, which tends to destabilize the rings' planar geometry [ 114], rendering the sp 2 C=C bonds IR-active [ 115]. Furthermore, the existence of sp 2 C = N bonds in linear chains is evidenced by a characteristic band appearing in the wave-number region between 1650 and 1680 cm -1 [112]. The spl-hybridized bonding structures between carbon and nitrogen atoms are characterized by low IR responses. The vibration frequencies of the terminating C - N stretching modes associated with both nitrile ( - C - N ) and isonitrile ( - - N - C ) structures greatly depend on the type of component bonded to these structures. The contributions of the above structures to the FTPME spectra corresponds to ~2250 and ~2150 cm -1, respectively [9, 111-113]. In the context of this discussion, the optical response of CNx thin films deposited by reactive rf magnetron sputtering (see for example Figs. 24 and 25) on c-Si (100) substrates was studied [9, 116]. The films were deposited using a graphite target in a deposition chamber with a base pressure better than 1 x 10 -7 mbar at room temperature (RT), by applying different Vb's on the substrate, film #A (Vb = --20 V), and film #B (Vb = --250 V). The substrates were located 65 mm above the target and coated using a sputtering power of 100 W. The partial pressure of the sputtering gas was 4 x 10 -3 mbar. Both films have thicknesses ~4500 ,~. The FTPME measurements were performed in the wave-number range 900-3500 cm -1 at a resolution of 8 cm -1, using the FTIR phase-modulated-ellipsometer, which has been described in Section 4.3. Figure 50 shows the imaginary part (E2(O))) of the pseudo-dielectric function for the two CNx films measured, together with the characteristic bands corresponding to the various carbon-nitrogen bonding structures. From Figure 50 it can be seen that the contribution of the various carbon-nitrogen bonding structures is different in the measured pseudo-dielectric functions of the two films. For example, the contribution of the spZ-hybridized C=C bonds and spZ-hybridized C = N bonds contained in linear chains is greater in film #A than in film #B. These differences in the IR response of the CNx films are a result of the nitrogen distribution in the films and among the possible bonding configurations with carbon atoms. The mechanisms governing N incorporation in the a-C network are affected by the energy Ei, controlled by the applied Vb, of the positive ions (N +, N 2+, Cn+, (CN) +, etc.) that bombard the growing film surface during the films' growth

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES

9 i,_

l

'

I

'

I

'

I

'

cillator strength is analogous to the concentration Ni (number of oscillators per unit volume) of the specific bond:

,

'

8

1

i ::

7

=

sp

,2

-

C-N N-C

:

309

" --

f i 0)2 i =

4zr Ni e

The quantity s ~ , described by the relation

6

0)p2

e~ = 1 + ~

4

~s A 4

1t

CTN (chain'i ~~0.~ ,,

I

1000

I

,

I

'

,

I

1500 2000 2500 Wavenumber (cm 1)

I

!.~ /

3000

Fig. 50. Imaginary parts (82) of the pseudo-dielectric function for two carbon nitride (CNx) films deposited by rf magnetron sputtering onto c-Si substrates by applying different bias voltages (film #A: Vb = --20 V; film #B: Vb = --250 V). The various sp 3, sp2, and sp 1 hybridized carbon-nitrogen and C=C bonds are shown. The vertical dotted lines denote the positions of the characteristic band frequencies of the various carbon-nitrogen bonding structures.

[ 110]. The high-energy ion bombardment during deposition enhances the chemical reactions between the different species as well as their mobility at the growing film surface. As a resuit, the high-energy gas ions dissociate the sputtered carbon clusters, affecting the nitrogen distribution among the possible bonding configurations with carbon atoms, and thus the films' bonding structure. The optical response of the CNx films measured in the infrared spectral region is a direct result of the distribution of nitrogen atoms among the mentioned bonding configurations with carbon atoms. The bonding vibrations that are excited by the electric field of the IR beam are modeled, to a first approximation, using a damped harmonic oscillator (Lorentz model). The contribution of each oscillator to the measured pseudodielectric function is evidenced by a maximum in the imaginary part (s2) together by an inflection in the real part (El). The study of the imaginary part is preferable, since the contribution of the vibrational modes is more pronounced in this representation. The effect of the several vibration modes on the complex dielectric function is described by the expression

8(0)) -- ~ex~ +

t~. f/0)2i . 0_)2i --0) 2 +

iF/o)

(50)

is the static dielectric constant and represents the contribution to the dielectric function of the electronic transition that occurs at an energy 0)0 in the NIR-Vis-UV energy region. The plasma energy 0)p is given by

i

2

0

(49)

m

(48)

where 0) is the energy of the light and 0)0i is the absorption energy of the ith vibration mode. The constants f / a n d Fi are the oscillator strength and the damping (broadening) of the specific vibration mode, respectively. Considering a specific bond between certain atoms where the effective charge e*, the reduced mass m, and the absorption energy 0)0 have fixed values, the os-

2

4zoNee2

0)P --

m*

(51)

where e and m* are the electron charge and effective mass, respectively. Ne is the density of electrons [ 117, 118], which is associated with the existence of voids and structural imperfections and is a measure of the density of the film. Figure 51 shows the real ((el)) and imaginary ((e2)) parts of the pseudo-dielectric function for two CNx films #A and #B and the best-fit simulations resulting from the fitting analysis of the experimental data, represented by solid lines [9]. For the fitting analysis we assumed a layer of thickness d on top of a Si substrate (bulk), while the optical response of the layer was modeled by three oscillators. It is evident from the above discussion that the overlapping of the characteristic bands corresponding to the different carbon-nitrogen bonding structures has to be overcome in order to enhance the contribution of each bonding structure to the spectra. This can be performed by calculating the first derivative d (s(0)))/do) of the pseudo-dielectric function (s(0))), which allows the enhancement of the contribution of each bonding structure around the absorption bands [9]. The expressions for the real and imaginary parts of the first derivative of s(0)) can be calculated through Eq. (48) and are given by d(sl(0))) __ _ ~ do)

2f/0)_2i0)~ [ r ii02) o2 _ ( 0 ) 2 i - 0)2)2]

z,,,,,a i

d(s2(0))) = _ X-~ fiFi0)2i[(0)2i_ do)

l_~ i

(52)

[ ( 0 ) 2 i _ 0)2)2 _}_ r20)212

0)2)(0)2i + 3092)_

[ ( 0 ) 2 i _ 0)2)2_.t_ r20)212

(53) Thus, in order to obtain quantitative information about the vibrational as well as the electronic properties from the measured IR spectra, two types of analysis can be performed [9]. In the first analysis the experimental (e(0))) data were analyzed based on Eq. (48) and assuming a CNx layer of thickness d on top of a bulk substrate (c-Si) (see for example the results in Fig. 51), providing information about the film's bonding structure and its electronic properties as well as its thickness. In the second analysis, by calculating the first derivative and analyzing the experimental data by using Eqs. (52) and (53), assuming a bulk CNx material around the region of the absorption bands,

3 10

LOGOTHETIDIS

5

~

I

'

.

.

I

'

I

'

I

sp2 <e2(co)> C=N

'

I

~

I

Film#A Vbias='220V-5.0

Results of Fitting the First Derivative of the Pseudo-dielectric Function (e(w)) for Films #A and #B

Table II.

Film @

Vb

e~

Bond

F

(V)

~n ~:~

- 4.5

#A

-20

4.2

N3 "~

4.0

=. 2 -

C-N

-

~ D

C-N

#B

(a) 1 ll00

~

I

1200

,

I

1300

~

I

,

I

1400 1500 Wavenumber (cm "l)

,

I

1600

,

I

1700

10

]3.5

6.8

y

(cm -1) 750

C-N

1.66

1338

C=N

0.03

1524

177

C=C

0.28

1693

322

--C-N

0.003

2233

104

--N-C

0.027

2161

193

C-N

2.6

1330

709

C=N

0.123

1540

233

C=C

0.11

1645

274

--C-N

0.008

2210

153

--N-C

0.021

2145

201

6.5

i

6.0

~

5.5

~

5.0

4.5

1100

-250

a~0

(cm -1)

1200

1300

1400 1500 Wavenumber(cm1)

1600

1700

Fig. 51. Real ((el)) and imaginary ((e2)) parts of the pseudo-dielectric function for two carbon nitride (CNx) films deposited by rf magnetron sputtering onto c-Si substrates by applying different bias voltages (film #A: Vb = - 2 0 V; film #B; Vb -- - 2 5 0 V). The solid lines represent the best-fit simulations resulting from the fitting analysis of the experimental data based on the theoretical model of e(w) described by Eq. (48) and assuming a CNx film of thickness d on top of a c-Si substrate.

one can obtain information about the vibrational properties of the films. Combining the results from the above types of analyses with those of the dielectric function in the NIR-Vis-UV spectral region a detailed study of the bonding mechanisms, the electronic properties, and the microstructure of the films is completed. In Figure 52 the first derivative of the real parts (el) of the pseudo-dielectric functions for films #A and #B are shown along with the simulated spectra. Chemical bonds, for example, for the sp 3 C--N, sp 2 C=N, and sp 2 C = N bonds can be identified by extrema in d(el (oJ))/dw much better than in the case of the direct (e(w)) spectra as in Figures 50 and 51. The observed differences in d(e)/dco spectra between the CNx films #A and #B prove that the bonding structure of the films is significantly affected by the energy of the ion bombardment during deposition. The characteristic band around 1300 cm -1 is attributed to the C - N bonds, while the one around 1530 cm -1 is assigned to the stretching vibration of

the sp2-hybridized C = N bonds contained in aromatic rings [9, 111-113]. Since the stretching vibration frequencies of the spZ-hybridized C = N bonds contained in linear chains and of the C = C bonds are reported in the region 1650-1680 cm -1 and at 1680 cm -1, respectively [112], their contributions overlap the characteristic band at around 1680 cm -1, making its separation difficult. The C = C vibration mode is normally IRforbidden, since the C = C bond is a nonpolar bond. However, the contribution of this bond to the FTPME spectra is the result of nitrogen atom incorporation into the amorphous carbon network, where the excess of electrons coming from the nitrogen atoms induces charge variations in the C = C neighborhood and renders these bonds IR-active [ 115]. Also, the appearance of a small amount of the chain-terminating nitrile ( - C - N ) and isonitrile ( - N = C ) groups is obvious in all spectra as a broad peak centered at around 2200 cm -1. The results of the fitting analysis on the experimental data concerning films #A and #B are summarized in Table II. It is clear, based on the strength of the oscillators f/, that in film #B, which is characterized by high-energy ion bombardment during deposition, the formation of sp 3 C--N as well as sp 2 C = N bonds is favored, even though the IR response of the latter is variable and very dependent on the local symmetry of the graphite rings. The reduction of the sp 2 C = C bonds in film #B could be the result of the existence of graphitic tings with more than one N atom because otherwise the distribution of N to a large number of rings would induce a large-scale distortion in the graphite planar symmetry. Furthermore, as far as spl-hybridized - C - N bonds are concerned, their formation is gradually suppressed in film #B [9]. The variation of the N concentration in the films, as measured by X-ray photoelectron spectroscopy (XPS), cannot explain the observed differences in the bonding structure between films #A and #B [9, 119]. Therefore, these differences must be the result of the N bonding and distribution in the films as affected by the applied Vb, which controls the energy of the ion bombardment during deposition. Particularly, low-energy

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES -0.01

'

I

'

I

'

I

'

I

'

I

'

sP 3

0.00

'

sP 2

-0.02

i

'

Z2:c

-0.02

C=N

C-N

-0.03

.,.~ -0.o4

sp 2

= =

I

311

sp a

o

C=N

-0.04 a~ -0.06 -0.05

3

-0.08

o0 -0.06

-0.10

-0.07

Vb,~ =_250

-0.08 1100

,

I

1200

,

I

1300

,

I

1400

~

I

~

1500

I

1600

,

I

1700

-0.12 1100

,

1800

I

~

I

1200

~

I

1300

~

I

1400

Wavenumber(cm1)

i

I

1500

,

V

I

1600

,

1800

1700

Wavenumber(cm-')

Fig. 52. First derivative of the real part (e I ) of the pseudo-dielectric function for two CNx films deposited by rf magnetron sputtering onto c-Si substrates by applying different bias voltages (film #A: Vb = - - 2 0 V; film # B ; Vb = - - 2 5 0 V) in the IR energy region 1100-1800 cm -1, where the C - - N , C = N , and C=C bonds are active. The solid lines represent the best-fit simulations resulting from the fitting analysis of the experimental data.

ion bombardment during deposition (film #A) promotes the homogeneous N distribution in a large number of graphitic tings and results in a large-scale distortion of the graphite plane symmetry. These distortions explain the enhanced contribution of the sp2-hybridized C--C bond-stretching vibration in film #A's FTPME spectra. In contrast, high-energy ion bombardment during deposition (film #B) promotes nonhomogeneous N distribution in local regions in which the nitrogen concentration is higher than that measured in the film. In these regions of increased N concentration, where a large number of graphitic rings contain more than one N atom, intense local distortions are induced, since the lengths of the C--N (1.47 ,~,) and C = N (1.22 ~,) bonds are shorter than the lengths of C - C (1.54/k) and C=C (1.33/k) bonds. Relaxation of these distortions arises through the formation of pentagonal rings, which lead to local reduction of the distance between graphite planes and cross-linking with sp3-coordinated bonds [106-109]. Thus, the formation of fullerene-like or C3N4 structures is expected. These threedimensional bonding structures are capable of a high degree of bond angle deformation, resulting in highly elastic behavior, significantly improving the films' mechanical properties [119]. Additional support for the above discussion arises from the study of the static dielectric constants es and eoo as determined by analysis of the pseudo-dielectric function (e(co)). Here es describes the losses in the material in the whole electromagnetic region [9]. Figure 53 shows the evolution of es and e ~ for a series of CNx films of the same thickness (~4500 A) that were deposited by applying Vb in the range between + 16 and - 2 5 0 V [9]. From Figure 53 a clear trend is observed. In films grown with high negative Vb (high energy of the bombarding ions during deposition) the contribution of the IR-active bonds is enhanced. This is followed by an increase of e ~ . According to Eq. (50), the increase of e ~ suggests that either the kth electronic transition energy co0~ decreases, or the plasma energy copk, which is proportional to the density, increases. This

I0

I

'

I

'

I

'

I

'

I

'

I

'

I

'

~176 o

9 ~ oo

ra~

8

~~

= ra~

=

9

9~

9 oO 9176176176

9 .. o

o

E

6

9176

s

O

...11 .... II

Oo .-

o~

.o~149 ..~176149

....~149

I

oo 9176 ~

9~

oo.O~176176

o

o o 9~ ~ ~ 99

o

9

.oO 9176

~

7

o-'~

5

~149

...... .O .... O ...........

ii

.~

~'oo 3

I

-20

,

I

i

I

20

,

60

I

i

100

I

140

,

I

180

i

I

220

i

260

Negative Bias Voltage (V) Fig. 53. Dependence of the static dielectric constants es and ec~ of IR-active bond and electronic contributions as a function of applied Vb for a series of CNx films of the same thickness ( ~ 4 5 0 0 / ~ ) , calculated through analysis of the pseudo-dielectric function (e(w)) spectra. The dotted lines are guides for the eye.

is also demonstrated by considering the Kramers-Kronig integral s1 ( c o -

0) -

6oo -- 1 + ~

1 f0 ~ 62(coco't) dog'

(54)

where the static dielectric constant e ~ is inversely proportional to co and proportional to e2(co) (the density of states of electronic transitions), which is in turn proportional to the film's density. The correlation between the variation of e ~ and the bonding structure of the films can be examined by studying their electronic properties by SE measurements in the NIR-Vis-UV spectral region (1.5 to 5.5 eV) [9]. The analysis of the pseudodielectric function (e(co)) of the films in this energy region

312

LOGOTHETIDIS

provides further insight through the study of the :r-Tr* (attributed to sp 2 bonds) and tr-cr* (attributed to both sp 2 and sp 3 bonds) electronic transitions [9]. In particular, this analysis reveals that the energy of both :r-~r* and or-or* electronic transitions decreases in films grown with high-energy ion bombardment during deposition. This decrease is followed by an increase of their strength [higher e2(w) values] as well as by an additional oscillator, at ~ 1.5 eV, needed for describing the measured pseudo-dielectric function. This structure has been correlated, in the amorphous carbon films, with the formation of a dense carbon phase [74, 120], however, in the case of CNx films it is not clear yet whether it is correlated with carboncarbon and/on carbon-nitrogen bonds too. Finally, the ability of FTPME to perform a precise determination of thin film bonding structure has just been illustrated. FTPME is well adapted for the study of carbon-based materials, and by combining it with SE in the NIR-Vis-UV spectral region it can provide important information about the vibrational and electronic properties [9] of the materials under study. This capability constitutes a crucial advantage for studies in which information about the type as well as the amount of chemical bonds is needed. Furthermore, this technique can also probe the local structural order of thin films. Thus, taking into consideration its high sensitivity and capability for real-time measurements, it is anticipated that FTPME will be used extensively in the future for process monitoring as well as for probing the growth mechanisms of a wide variety of thin film materials.

6. OPTICAL CHARACTERIZATION AND REAL-TIME M O N I T O R I N G OF THE GROWTH OF METALLIC TiNx FILMS

6 -

4 2

14

12

0 10

-2 r

-4

8 ~

-6 -8

~

o~ . ~

6

(a)

_,o

-12

1.5

2.0

2,5

3.0

3.5

4.0

4.5

4

5.0

5.5

Photon Energy (eV) 20 TiN

16

~x

....

Ti

\\\

12 8

4 0

~ I

,

I

,

I

,

i

,

i

4

,

I

9

,

I

,

I

,

.

c- "4

6.1. The Dielectric Function of TiNx Films -12

One of the most interesting and important categories of engineering materials are the metal nitrides, used mainly as hard, protective coatings. Especially, titanium nitride (TiNx) thin films ([N]/[Ti] close to 1) with the NaC1 crystalline structure are known to exhibit a unique combination of high hardness with excellent wear and corrosion resistance [121] and are widely used as coatings for cutting tools and wear parts [ 122]. Moreover, TiNx has lately gained much interest in different areas of Si device technology as a diffusion barrier in metallization schemes, in rectifying and ohmic contacts [123], and in Schottky barrier contacts [124]. TiNx exhibits a typical metallic optical response due to the intersection of the Ti 3d valence electron band by the Fermi energy level [125]. In addition to that response, which is due to intraband absorption by the Ti 3d electrons, interband absorption takes place in the visible energy region [ 126]. This behavior is strikingly similar to that of the noble metals, where the electronic interband transition is responsible for the characteristic color. In partiuclar, in stoichiometric TiN an interband transition occurs in the same energy region as in gold, and it therefore exhibits a gold like color. Figure 54a shows the dielectric function of a pure, stoichiometric polycrystalline TiN film of thickness about 1000 ,~, in the

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Photon Energy (eV) Fig. 54. The dielectric function (real part e I and imaginary part e2) of: (a) A pure, stoichiometric polycrystalline TiN film of about 1000 ]k. The characteristic features in the dielectric function of TiN are the screened plasma energy in el (w) and the energies of the interband absorption in e2(w), all denoted by arrows. (b) TiN and pure Ti films, in the energy region 1.5-5.5 eV, measured by spectroscopic ellipsometry in vacuum after deposition. The high energy of the interband transitions of TiN distinguishes clearly the intraband (up to ~2.5 eV) and interband (above ~2.5 eV) absorption regimes. In pure Ti the intraband regime is not clear, due to the shift of the interband transitions to lower photon energy.

energy region 1.5 to 5.5 eV. Figure 54b shows for comparison the dielectric functions e(w) (= S1 + iS2) of bulk TiN and pure polycrystalline Ti films, both deposited by dc MS, in the same energy region. In situ SE and MWE have been used to study and characterize TiNx films, and a detailed monitoring procedure by MWE has been developed in order to determine the film thickness and stoichiometry as well as other microstructural details during deposition [22, 126].

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES ~ V b = 0

Intraband

......

i

C

o

V

V b =-40 V

...:,.:.......................... '~;~.

......... V b =-120 V /" / ! |

o C

8

Interband 1 -

i

,/

9, ~.: : ! : !

L_ .4...*

'.. :~.

0

'._\~

",

4--

o

lnterband 2

......... V b = - 8 0 V

+..,

u_

6

_

,

~l

o 0_

\,,

"

/l //

"~"~,

".,.

/

of

.r"

j/" ,,,,f9 .+.

,,/ ,," -

/tI

I

/

:'

OI)ps

/ i

:" i / ./ _

_

E

-

_

,.

",

/ /

:

/

4

~

/

9

t~ t'-I:~ t~

313

/

.

9 ,: ~Vb= 0 V i ,. . . . . . . Vb= -40 V i

o,~

-

!i

......... Vb= -80 V

f

......... Vb= -120 V

/ ,i

1

2

3

4

5

Photon Energy (eV)

(a)

6

1

I 2

,

I 3

,

I

,

4

I 5

6

Photon Energy (eV)

(b)

Fig. 55. The dielectric function of representative TiNx films deposited with different Vb: (a) imaginary e2, and (b) real part el. Arrows in (a) denote the intraband contribution and the position of interband transitions, whereas in (b) the arrow denotes the position of Wps. The deposition conditions strongly influence both the intraband and interband absorption due to stoichiometry and microstructure variations. (After [129].)

Two sets of TiNx thin films were deposited on (001) Si wafers by dc reactive magnetron sputtering (conventional and unbalanced) from a Ti target (99.999% purity) up to a thickness of 1000/k. The experimental deposition chambers were already described and are shown in Figures 24 and 42 (see the discussion of a-C in Section 5). The main difference between the sputter deposition of TiN and the deposition of a-C is in the reactive process, viz., for TiN the sputtering is done by using a mixture of working inert gas (Ar) and reactive gas (N) to promote the Ti--N chemical reaction. The reactive sputtering process is very sensitive and requires careful selection of process parameters as well as extreme stability of gas flows and pressures. It was found that there is a very narrow window of process parameters to produce stoichiometric TiN by reactive sputtering [127-129]. Here we briefly discuss the most important conditions and parameters affecting the properties and quality of the deposited films. The Si substrates were cleaned by standard surface cleaning procedures before entering the deposition chamber and then by a dry ion etching process, with very low-energy Ar + to remove the native SiO2 and avoid substrate damage. In the conventional MS a gas mixture of Ar and N2 was used at a flow rate of 15 sccm and 2.2 sccm, respectively, producing a total pressure of 8.3 x 10 -3 mbar. The discharge power on the Ti target was 450 W, and the substrate-to-target distance 65 mm. The final structure, stoichiometry, and properties of TiNx thin films mainly depend on the N2 flow and the bias voltage Vb applied to the substrate [ 127-129]. As an example, we report here on the latter dependence. In order to develop films with different stoichiometries, deposition was carried out at various values of bias voltage Vb applied to the substrate be-

tween 0 and - 2 2 0 V and substrate temperatures from RT to 650 ~ with fixed N2 flow. In situ SE spectra of the dielectric function were obtained with a phase-modulated spectroscopic ellipsometer mounted on the deposition system (see Fig. 24) and operated in the energy region from 1.5 to 5.5 eV with a step of 20 meV. SE measures directly the complex dielectric function e(co) of the materials and enables the investigation of their electronic structure [e.g., e2(w) is related directly to the joint density of states for interband absorption] and their structural and morphological characteristics. Figure 55 shows the real and the imaginary parts of e(w) obtained from a number of fcc TiNx films deposited at four different bias voltages. It is clearly seen that e(co) is strongly dependent on the applied bias voltage. Of special interest, however, is the plasma energy O)p, of the TiNx, which depends strongly on the stoichiometry of the material [127-129]. FTPME measurements in the energy region 900-3500 cm -1 were performed using a Jobin-Yvon FTIR phase-modulated ellipsometer. The incident beam was initiated by an IR spectrometer including a glow bar source and a Michelson interferometer (see Section 4.3). The spectral resolution of the FTPME measurements was 16 cm -1, and the average total number of measurements per spectrum was 600.

6.2. Optical Re s po ns e of TiNx Films and Correlation with Stoichiometry

TiN, like all real metals, exhibits a dielectric function that can be analyzed by the Drude and Lorentz models. The Drude model, which was proposed for ideal metals, describes phenomenologically very well the intraband transitions that cor-

314

LOGOTHETIDIS 18

!

16

~

12

-L'

10

EF 8

X5 ~ X2, and L3 ~ L 3 of the Brillouin zone, which correspond to strong interband absorption at ,~2.8, 3.9, and 6.5 eV [126]. There is also a weak transition at ~2.2 eV assigned to ! F25 --+ F12, which is hardly seen in the current SE data, due the Drude term and the F15 --+ F12 transition. This transition can only be discriminated from the Drude and the other interband contributions in the second-derivative spectra of the dielectric function and for TiNx films with large crystalline grains and low defect density [ 126]. In any case, this first interband transition should be responsible for the characteristic color of the TiNx films. The optical properties depend strongly on the stoichiometry and the structural characteristics of the TiNx films as in all real metals. Assuming such an ideal metal (only free electrons contribute to its properties and the energy loss mechanisms due to scattering are very low), obtain 2

~(0))- 1-

2

~ 1-

0)2 + i 0) F D

/ L

0)pu

0)pu

(55a)

0)2 nt_ [,2

2 ~, 0)2, so that, when F2

--

/f

-

lo ~.

-3 6

13~ 9x10~ 8x101

7x10 ~ 6x10 ~ 5x10 ~

4

4x10 ~

,

,

,

5

6

7

Unscreened %

2 1

oO."

......

0 1.5

2.0

"'"

)-..-"~" .. ~

2.5

3.0

3.5

Energy

8

(eV)

Fig. 58. Electrical resistivity versus (.Opu. The two quantities are correlated through an inverse square law similar to the one described by the Drude theory of a free electron gas. The inverse square law is clear evidence that all TiNx films are in general good metals following the free electron model and only quantitative differences exist regarding their metallic behavior.

ooO'~

%%

Plasma

\ t l

4.0

4.5

5.0

5.5

Photon Energy (eV) Fig. 57. The real (el) and the imaginary (e2) part of the dielectric function of a 1000-/~-thick TiNx film deposited with Vb = - 4 0 V and Td = RT. The experimental dielectric function (solid lines with asterisks) has been fitted with three terms: the Drude term (dotted lines) describing the optical response of free electrons, and two Lorentz oscillators located at 3.3 eV (dashed-dotted lines) and 5.2 eV (dashed lines) and corresponding to the TiNx interband transitions. Arrows on the graph of e I denote the screened (Ogps) and unscreened (Wpu) plasma energies. The characteristics of the Drude term (Wpu and FD) and the energy position of the Lorentz oscillators are the fingerprints of the stoichiometry and microstructure differences of the TiNx films.

other hand, O)ps depends on both the free and the bound electrons in the material and is related with a more complicated manner with the TiNx film metallic character and stoichiometry [129]. However, this quantity is directly obtained from SE measurements without the need for analysis. For example, Figure 57 shows the S1 (O9) of a TiNx film ~1000 ,~ thick, deposited with Vb -- --40 V at RT in the energy region 1.5-5.5 eV; here COps (denoted by an arrow) is a directly measured quantity and is about 1.8 eV. In Figure 57 are also shown strong interband transitions in TiNx (with x ~ 1.1) that occur at about 3.0 and 4.5 eV. These energies differ from the 2.8-, 3.8-, and 6.5-eV enI ergy differences in the F15 --+ F12, X5 --+ X2, and L3 ~ L 3 directions in the Brillouin zone, where the interband transitions take place in pure stoichiometric TiN films. These differences may be due to the difference in stoichiometry of this film which exhibits a cell size a = 0.424 (instead of 0.430 nm of the stoichiometric TIN), and to a different density of defects (vacancies at Ti lattice sites) [126, 133].

In order to calculate O)pu, we used a model that describes the dielectric response including both the Drude and the interband absorption (Lorentz oscillator) contributions [132]" 2

2

O)pu S(O)) -- S ~ -- 092 Jri FDO) + j .~ l O)2j _ 092 _ i y j o )

(58)

Here e ~ is a background constant, larger than unity (varying from 2.1 to 2.3, depending on the deposition conditions) due to the contribution of the higher-energy interband transitions not taken into account. The Drude term is characterized by the unscreened plasma energy O)pu, as discussed previously, and the damping Up. In turn, 1-'D is due to scattering of electrons and, according to the free-electron theory, is the reciprocal of the relaxation time To . The quantifies F D and rD are closely related to the electrical resistivity p of the metal and are influenced by the existence of grain boundaries, defects, phonons, and electron-electron interactions not taken into account in the free electron model. Each of the Lorentz oscillators is located at an energy position woj, with strength fj and damping (broadening) factor yj. The energy position, strength, and broadening of each individual oscillator depend on the deposition conditions, since the latter affect the stoichiometry and the microstructural characteristics of the deposited films. Figure 57 describes the above procedure for a representative TiNx film. The fitting of both real and imaginary parts of the measured e(o)) spectra with Eq. (58) is very precise. The contribution of the free electrons to the total dielectric function is described by the Drude term (dotted curve), from which we calculate COpu = 5 eV (denoted with an arrow in Fig. 57) and FD = 1.3 eV. In addition to the Drude contribution, we see

316

LOGOTHETIDIS

in Figure 57 the two strong interband transitions in the VisUV spectral region, which are described by the corresponding Lorentz oscillators (dashed curves). The first oscillator, which is located at co01 = 3.1 eV, is well defined (low values of the broadening Yi) with less strength j5 than the second one, in all cases. Although the broad second oscillator at co0e = 5 eV is acting as a smooth background in the e(co) in the Vis-UV region, it has a considerable effect on the cops because of its high strength. In general, the two TiNx Lorentz oscillators, in all examined films, are located in the ranges 3.1-3.9 and 5.06.5 eV, respectively. The experimental value of COps (= 2 eV), denoted by an arrow in Figure 57, is far away from COpu = 5 eV because it is strongly affected by the existence of interband transitions (Lorentz contributions) and thus in a way describes the response of all electrons (bound and free). Although COps is affected by several factorsmfree electron density, interband absorption, grain size, etc.mexhibits an almost linear dependence on the film stoichiometry, as was found by combined SE and XPS-AES analysis; this will be discussed subsequently. On the other hand, changes of COpumay be attributed, according to Eq. (57), either to changes in free electron density or to changes of the electron effective mass [134]. In any case, the increase of COpu is strongly correlated with the enhancement of TiNx metallic character expressed in terms of electrical resistivity. Indeed, experiment has confirmed the explicit relation between COpu,calculated by the above analysis, and the ex situ measured resistivity [134]. The resistivity follows an inverse square law, p ~ 20.500/CO2u, in COpu. The inverse square law is illustrated on a semilog scale in Figure 58 and is clear evidence that all TiNx films, though of different stoichiometry and microstructure, are in general good metals following the free electron model, and only quantitative differences exist regarding their metallic behavior. This inverse square law is an intrinsic property of fcc TiNx films: it was observed for films deposited with various Td and Vb, and thus describes the combined effect of these two deposition parameters on the electrical resistivity. In order to explain the inverse square law we should consider all the possible effects contributing to the resistivity decrease in terms of the free electron model, according to which COpu is closely related to electrical resistivity p. The relaxation time is associated with the film resistivity p through the relation (in cgs units) [135] "CO

--

m * / p N e 2 -- 4Jr/pCO2u

(59)

From the fitting of the experimental points (Fig. 58) with a relation of the form p - ot/CO2u we can roughly estimate the mean relaxation time for all TiNx films deposited under different conditions and exhibiting different resistivity values. According to this analysis ro = 0.1 x 10 -14 s, which is a typical value for heavy transition metals with high resistivity (above 40 laf2 cm). The above analysis is useful in the case of TiNx films for applications in microelectronics, since it can provide a realistic estimation of the TiNx resistivity during deposition, through its dependence on COpu.TiNx films have been found to make very good rectifying or ohmic contacts on Si, depending on the deposition conditions. High Td and Vb result in ohmic contacts

with very low resistivity, while low Td and Vb result in rectifying contacts (Schottky type) with barrier height V = 0.5 V and ideality factor close to 1 [124].

6.3. Study of the Stoichiometry of TiNx Films by Spectroscopic Ellipsometry Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) have been used in the past for the characterization of this type of films [121,136, 137]. However, the above and other analytical techniques used for compositional analysis suffer from the inherent difficulties that (1) they usually require the exposure of the TiNx films to air, leading to absorption and reaction with oxygen, and (2) even worse, they are destructive. Optical nondestructive access to a surface in vacuum is important for real-time information, control, and characterization during film development. Techniques such as SE and MWE are already used to monitor deposition rates and composition of films during deposition [22, 23] and can be used in a complementary manner with other postdeposition techniques. Here we present an approach [127, 129] to study the stoichiometry and characterize TiNx thin films by using either in situ or ex situ SE in combination with XPS and AES. The electronic and optical properties of TiNx films, as already discussed, depend on their actual nitrogen content and microstructure, and they are strongly affected by the deposition conditions (e.g. the bias voltage applied to the substrate during deposition). The real and imaginary parts of the dielectric functions of representative TiNx films deposited with different Vb have been shown in Figure 55a and b. As we have already mentioned, of special interest is the adjustable screened plasma energy Wps of TiNx, which depends strongly on the stoichiometry of the material [ 129]. The value of the plasma energy COps based on the XPS results has been used as a criterion to determine in situ the stoichiometry of TiNx films during deposition. That value was found to be about 2.6 eV when x = 1, and less than 2.6 eV for x > 1. Figure 59 presents the values of the screened plasma energy COps for TiNx thin films that were deposited at various values of Vb. The COps-values were extracted from the real part of the measured dielectric function spectra, as shown in Figs. 55b and 57, obtained from the TiNx films. The results show that films prepared with Vb between - 1 0 0 and - 1 4 0 V are stoichiometric (region II in Fig. 59). Films deposited at IVbl values lower than 100 V (region I) deviate from stoichiometry and more than likely are overstoichiometric, as they exhibit a bronze color. The screened plasma energy exhibits strong, almost linear dependence on IVbl in the region from 0 to 100 V, with a slope dwps/d Vb = 5 meV/V. In the same region the stoichiometry changes from 1.1 to 1 (see Fig. 60), indicating that the COps is a very sensitive probe of the TiNx film stoichiometry. Finally, the slight decrease in COpsobserved beyond - 140 V (region III) may be attributed to the expected substantial increase in Ti sputtering in that range ( - 100 to - 2 4 0 V) under the higher energy of the sputtering plasma ions [ 138].

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES 2.8

1600

"

l

I

I

317 '

I

'

Vb=-40 V, T~=230 ~ 1

I

I

~

m

1400

2.6 1200

....

Vb=-40 V, Td=400 ~

......

Vb=-80 V, Td=400 ~

%

>

ID

2.4

-

I

I

I

!

1000

-.

TiNx films

I

~. 800

t. r

t~ 2.2

,-:.. 600

%,., ,.

E

o~

./ 2.0,

o

E_

400 ~149176 O-Oooo

200 1.8---

'

L

0

,

50

l__

J

I

100

.._1

150

Negative

!

i

200

B;cs Voitc=je

I 1000

250

1.20

TiN x Films

=

"..,~ - .

9 n

!-. 1.1o -

AES XPS

% % % %

1.o5

1.00

0.95

, 1.8

I 2.0

,

I 2.2

Plasma

,

I 2.4

I 2000

,

I 2500

3000

,

I

2.6

W a v e n u m b e r (cm ~) Fig. 61. The IR absorption of representative TiNx films. With increasing bias and substrate temperature the intraband absorption (measured in the IR region) becomes stronger, indicating the increase of conduction electron density and mobility. The conduction electron density and mobility increase as the TiNx films approach the stoichiometric TiN (x = 1), which can be consider similar to ideal metals.

IVbl values showed only sharper Ti 2p3/2 peaks situated at Eb = 455.2 eV. The XPS results suggest that oxidation (more than likely with formation of TiO2) takes place in films developed at low IVbl, whereas no oxidation occurs in films deposited at higher IVb I, as we will discuss in Section 6.4. Figure 60 shows the dependence of [N]/[Ti] ratios, estimated by XPS and AES, on the screened plasma energy COps. The data presented in Figure 60 exhibit an almost linear relationship between [N]/[Ti] and COps. The differences in [N]/[Ti] between the two techniques, especially in TiNx films developed with Vb below 60 V, are mainly due to the inherent difficulties of AES rather than to the calibration procedure used in analyzing the XPS measurements [ 139].

%

z

,

{V)

Fig. 59. The variation of the screened plasma energy COpswith the bias voltage Vb on the substrate during deposition. At 100 V a saturation value is reached, indicating that by applying higher bias the material does not change significandy with regard to stoichiometry and microstructure. (After [ 129].)

1.15 -

I 1500

-,...

I

2.8

Energy (eV)

Fig. 60. The [N]/[Ti] ratios of TiNx films obtained by XPS (open squares) and AES (solid squares) versus the screened plasma energy COps. The direct correlation of COpswith the film stoichiometry [N]/[Ti] enables the use of this feature of TiNx films for real-time ellipsometry monitoring of TiNx stoichiometry during deposition. (After [129]).

High-resolution XPS spectra from films deposited at low IVb I, viz. Vb = - 2 5 V, showed broad Ti 2p3/2 peaks with peak heights at binding energies Eb -- 455.4 eV and about 458 eV. The former value corresponds to overstoichometric TiNx (for example, for Vb = - 2 5 V it was found that x = 1.1), and the latter is close to TiO2 (the maximum position reported for TiO2 is 458.5 eV) [139]. Spectra from films deposited at higher

6.4. Electronic and Microstructural Features of TiNx Films Having made a detailed discussion of the correlation of COps and COpu with the intrinsic properties of the TiNx films, let us now consider the actual effect of the substrate temperature (Ta) and IWbl on the optical response of the TiNx films. FTPME was used to study the intraband absorption within the conduction band in the IR region9 Figure 61 shows representative FTPME e2(CO) spectra of TiNx films in the range 950-3000 cm -1 . The IR intraband absorption gradually increases with both Vb and Td. The maximum absorption, or the most intense metallic optical response, was observed in films deposited at high IWbl > 1O0 V and Ta = 400 ~ (dotted curve). Several causes, such as TiNx stoichiometry, vacancies at Ti lattice sites, grain size, and void

318

LOGOTHETIDIS 6.2

'

I

'

I

'

I

'

1.2

I

'

I

'

I

'

I

'

I

'

I

'

> ~'

6.0

>o

.o

1.0

v

rll

~

5.8

9t=-

0.8

O "0 0 t~

5.6

rn 0.6 0 "o

O

L_

5.4

a

O

0.4

5.2 0.2 I

20

,

I

40

,

I

60

,

I

80

,

I

100

Negative Bias Voltage (V) Fig. 62. The energy position of the second interband transition of TiNx films versus Vb. The energy position of this absorption is an indication either of stoichiometry variation changing the structure of the Brillouin zone, or of the changes of the lattice parameter with the bias voltage.

content, are contributing to this behavior. In general, increase of negative bias Vb and of the substrate temperature Td affects the adatom mobility, promotes the formation of larger grains, and leads to the elimination of voids and the growth of stoichiometric (x = 1) TiNx. In particular, the film stoichiometry and crystal structure may affect the TiNx band structure, as has already been mentioned and will be discussed in detail in the following. The effect of the deposition conditions on the band structure can be mainly described by the variations of the interband absorption characteristics (in a classical way by the Lorentz oscillators), viz. the energy position co0j, strength f j , and damping (broadening) factor yj. All the Drude and Lorentz parameters are strongly affected by the electronic and microstructural features of TiNx films and therefore may be used to probe and study the TiNx microstructure With respect to the deposition conditions and film stoichiometry. In all cases, the first Lorentz oscillator is well defined (low broadening values }I/), with less strength 3~ than the second one, and is located between 3.0 and 3.8 eV; its location is considerably affected by the deposition conditions such as Vb and Td. On the other hand, the second one is very sensitive to structural and compositional changes caused by changing the deposition conditions. Figure 62 shows the variation of the energy position of the second strong interband absorption of TiNx versus Vb. For high IVbl, approaching 100 V, the grown TiNx approaches the stoichiometric TiN [ 129], suggesting that the second interband absorption of TiN is located at ~6.5 eV. The lower energy of interband absorption that was detected for films deposited with low IVbl is an indication of the band-structure modifications of overstoichiometric (x > 1) TiNx films with respect to TiN. The modification of the band structure is attributed to changes of the crystal cell size of TiNx

I

0

20

40

60

80

100

120

Negative Bias Voltage (V) Fig. 63. The variation of FD versus Vb. The linear behavior is not followed for IVbl > 100 V; from that point a saturation value of ~0.3 eV is reached, indicating that in this bias regime there is no further change in film stoichiometry and microstructure, in accordance with the behavior of the plasma energy.

and to the Ti vacancy density, as we have already discussed, and therefore is directly related to the film microstructure and stoichiometry. Intraband absorption is also affected by the film microstructure (grain size and void content) and composition. In addition to the unscreened plasma energy Ogpu, the intraband absorption is also described by the Drude broadening FD, which is caused by the scattering of free electrons and is the reciprocal of the relaxation time ro [ 140, 141], according to the freeelectron theory. FD and rD are closely related to the electrical resistivity of the metal, as we have already discussed, and are influenced by the existence of grain boundaries, defects, phonons, and electron-electron interactions. Elevated deposition temperatures promote the adatom mobility and result in elimination of microvoids and dissociation of the weakly bonded excess nitrogen atoms. The negative Vb applied to the substrate induces Ar + ion bombardment of the film surface during deposition. This ion bombardment results in compositional (sputtering of the nitrogen excess) [129] and structural (larger grain size) modifications in the films. The energy transferred to the film from the bombarding ions is considerably higher than the thermal energy for deposition at Td < 650 ~ Thus, IVbl has similar but stronger effect than Td on the optical properties, structure, and composition of TiNx films. Figure 63 shows the variation of Fo versus Vb. The decrease in FD is attributed to the higher free electron mobility, due mainly to the stoichiometry changes from overstoichiometric to stoichiometric TiNx, and to a lesser extent to the increase of the TiNx grain size. For IVbl > 100 v a saturation value of ,~0.3 eV is reached, as shown in Figure 63, and remains almost constant up to 200 V, similar to what we have found for the dependence of stoichiometry on Vb.

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES 8.5

I

'

I

'

I

'

I

'

I

'

- - 0 - - RT > v

(L) >~

8.0

--O-- 400 ~

7.5

So ~

o

E

7.0

(o t~ 12.

6.5

9

6.0

E (1)

,dL

9

f~

UJ

0 .- .... 0 ...... 0 ,dh V

i._

o

5.5

E: Z:) 5.0

,

4.5

I

0

,

I

50

,

I

100

,

I

150

250

200

Negative Bias Voltage (V) Fig. 64. The effect of Vb on OOpu.There is an increase of Wpu with IVbl until a saturation value is reached. Deposition at high Td shifts the COpuvalues to higher energy.

'

I

'

I

'

I

'

I

'

I

'

I

'

6

> >' (!) liii

5

both O)pu and O.)ps. In addition, both quantities exhibit a linear dependence on Td on keeping the other deposition conditions constant. However, the two lines in Figure 65 are not parallel, and COpuis strongly affected by Td. By raising Td from RT to 650 ~ a 15% and a 35% increase in COpsand COpu,respectively, are observed. The parameters of the Drude term, Wpu and FD, may be used to calculate the mean free path of free electrons in TiNx. The mean free path of electrons is governed by the type of scattering sites in TiN, so it can be limited by the grain boundaries of crystallites [ 140-142] or by defects (mainly vacancies in Ti lattice sites) [ 126]. Combined SE and XRD studies have shown that for thin, stoichiometric films the grain boundaries play the dominant role in determining the mean free path, whereas in substoichiometric films the Ti vacancies also play a significant role. The mean free path of electrons in stoichiometric TiN corresponds to the mean crystalline grain size and thus is directly related to the film's microstructure [126]. In the case of substoichiometric TiNx (x > 1) the calculated mean free path of electrons can be smaller than the grain size, due to the existence of Ti vacancies in the crystallites that act as scattering centers. Nevertheless, the mean free path of electrons is expected to be close to the grain size and thus can be used as an estimate of grain size [ 126]. The mean free path L g of the free electrons in TiNx can be calculated from the relaxation time. It be expressed [ 140, 141 ], in first approximation (assuming that the relaxation time associated with the bulk crystalline TiN is very small) [ 126], in terms of the relaxation time and the mean electron velocity as follows:

rl

E (/)

Unscreened i Screened

a. 3

9 . . . . 0 " -0 . . . . . 9 . . . . . 9 . . . . . O 9 0

(60)

Lg -- TDVF

n 9

Or,

319

"1

100

,

n

200

,

,

300

,

,

400

,

I

500

,

,

600

,

700

S u b s t r a t e T e m p e r a t u r e (~ Fig. 65. The effect of deposition temperature on Ogpu and Ogps. It is seen that COpuis more affected by Td.

In Figure 64 the variation of COpuwith IWbl is presented for substrate temperature Td at RT and 400 ~ We see that COpu increases with IVbl from 4.5 eW to a saturation value of ~7.5 eV for IVbl > 100 w. Deposition of TiNx films at Td = 400 ~ results in a similar curve, but shifted to higher Wpu values (up to 7.8 eV). The differences between the two curves (Fig. 64) are larger for low IVb I, This happens because for higher IVbl the bombarding Ar + ion energy is much higher than the thermal energy and thus IVbl plays the dominant role in the deposition process. When the TiNx films are deposited at higher T~, then relatively small changes with Vb are observed (see Fig. 65) in

where VF is the velocity of electrons at the Fermi surface (ground state energy of electrons at T - 0 K). The velocity of electrons due to thermal energy is neglected, since it is two orders of magnitude smaller than the velocity at the Fermi surface. A detailed calculation of ro for each particular case may be performed using the damping factor 1-'o through the relation (the units are shown in brackets): 1 r D [S] - -

FD [l/s]

0.66 • 10 -15 --

(61)

FD [eV]

The velocity at Fermi surface is calculated according to the free electron model through the following relations [ 131 ] in cgs units: OF -- "~h (3zr2N) 1/3 __ ~ , ( 0 " 7 5 h 3 r r w 2

)1/3

(62)

From Eqs. (60)-(62) it is evident that the mean free path Lg may be calculated in terms of the quantities 1-'o and O)pu obtained by SE data analysis. Figure 66 shows the calculated mean free path versus Vb and Td. The void content in the bulk TiNx films was estimated by BEMT, assuming that each of the deposited TiNx films consisted of stoichiometric TiN and voids. According to BEMT the dielectric function e(co) of a layer consisting of n different

320

LOGOTHETIDIS lated density and void content by XRR. We briefly describe here how one can calculate the density of the TiNx films from XRR measurements; more information can be found in [ 143, 144]. Information on the density, thickness, and surface roughness is deduced from XRR through the dependence of the reflection coefficient on the angle of incidence. XRR is based on the same principles as SE regarding the optical response of materials. The dielectric function of all materials in the X-ray region has the form [see Eqs. (55a) and (58] [126]

35 3O

,~= 25 ~.~ 20

~

15

t2

81 (09) -- 1

C~

t2 t 62 ~,~ o9puFD ~ 0

and

092

for

5

) i

I

0

,

I

40

,

I

80

t

I

120

,

160

I

,

200

240

N e g a t i v e B i a s V o l t a g e (V)

o93

o9 >> Wpu

t2

t2 COpu>> F D

and

where CO,pu and F o, are the effective plasma energy and broadening and take into account all free and bound electrons. Therefore, the refractive index n for X-rays, which is associated with el (co) through the relation

18

t2

Vb=-40 V

/'/(CO)

II

8~/2(O9) ~'~

~D

i / i

cos Oc - 1

8

(b) ,

0

I

,

I

100

,

200

I

,

300

I

,

400

I

500

,

I

600

700

phases can be described by

i=1 8i -+- 2e "~

-

0

02 = n 2

(66)

,

Fig. 66. The effect of (a) the bias voltage Vb applied to TiNx films deposited at Td = 400 ~ and (b) deposition temperature Td of TiNx films deposited with Vb = --40 V, on the mean free path L g of the free electrons. There is an increase of L g with IVbl until a saturation value is reached. Deposition at high Td results in large L g.

8i--8

(65)

o9pu

From Eqs. (57) and (64)-(66) the mass density Pm of the material is correlated with the critical angle for total reflection:

Deposition Temperature (~

n

1

will be less than 1 (not taking into account the negligible absorption term associated with e2). Total reflection of the X-ray beam occurs at the film surface. Its refractive index is smaller than that of the ambient air, which is closer to 1. The critical angle of total reflection, which is between 0.2 and 0.6 ~ for most materials, can be expressed in terms of the refractive index n of the material:

II

10

--

2o92

16

o

(64)

(63)

where 6i and j5 are the dielecric function and volume fraction of constituent i (TiN or voids). This analysis suffers from the fact that TiNx films show differences in their second interband absorption when the films are deposited at various Vb. This is due to the fact that we use the same TiN reference dielectric function, which corresponds to stoichiometric TiN film. Therefore, we expect the accuracy in determining the void content to decrease when examining films deposited at low IVb I. In order to estimate the accuracy of BEMT analysis, we have also calcu-

e2

02 -- 2 N o ( 2 J r m c 2 ) ( f - - ~ ) ) ~

2

(67)

where No is Avogadro's number, A the atomic mass, )~ the X-ray wavelength, and Z the number of free electrons per atom. The measured intensity in a specular reflectivity scan that is obtained from a thin film at incidence angles larger than the critical angle Oc exhibits interference fringes that originate from the multiple reflection of X-rays at the film-substrate interface. These fringes, beyond the region for total reflection, are related to the thickness of the film and are very sensitive to the surface and interface roughness, which causes an overall reduction in the reflected intensity by scattering into nonspecular directions [ 145, 146]. The distribution of roughness is usually assumed to be a Gaussian one. The rms roughness, in each interface, is incorporated as a damping effect on the specular reflectivity R0" R0 exp(-qZa2), with qz the perpendicular component of the momentum transfer vector. R0 is calculated through the Fresnel diffraction theory [147] or equivalently the Ewald-von Laue dynamical diffraction theory. The XRR measurements were analyzed using a Monte Carlo algorithm assuming a single-layer model of stoichiometric TiN on an atomically smooth c-Si(001) substrate. The maximum measured density was 5.7 g/cm 3 for a film deposited at 400 ~

IN SITU AND REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES 10~ ..r#~

...... ......

F 9~

Experimental Simulation

321

25

10z

20

o,,.~ 0

o--v,

vwA^_

1 0 -4

g,

v

n,' 15 n,' X >, ..Q 10

I

;~ 10-6

t~ "0 ,m 0 I

10-8 0.0

~

I

0.5

~

I

1.0

,

I

1.5

,

I

2.0

~

I

2.5

>

O 5

3.0

Scattering Angle 20 (deg) '

5.8

I

'

---~--density

I

I

I

" 0"" Voicls by SE' --1 rs = - - = E st no cos 4'0 -t- n 1 cos q~l

(5)

t

tp -Fig. 1. Illustration of incident, reflected, and transmitted electric vectors for the p and s states of polarization at a single interface between two semi-infinite m e d i a characterized by no and n 1-

(4)

Ep _ 2no cos q~o i -Ep n 1 cos 4>0 + no cos q~l

Est ts - -

(6)

2n0 cos ~b0

i "-Es n o COS ~b0 + n 1 COS ~bl

(7)

GROWTH ELLIPSOMETRY Two assumptions have been made in the derivation of the Fresnel coefficients. The first assumption is that the electromagnetic waves are assumed to be plane waves. The second assumption is that the media are isotropic such that the refractive indices are the same in all directions. It should be remembered that the refractive indices in the Fresnel coefficients (4)-(7) are complex numbers, with the form n - ik, for the case of a semiconductor or a metal.

1.2. Reflection of Light by a Single Film The reflections and the transmissions of light by a single film are shown in Figure 2. Figure 2a illustrates the method of summation while Figure 2b illustrates the method of resultant waves in the derivation of the reflection coefficients. The final expression for the reflection coefficients will be valid for either p or s polarization, and thus the subscripts p and s will be omitted during the derivation. Another assumption made here is that the film is nonabsorbing such that the refractive index is real. Even with this assumption, there is no loss in generality in the final expression of the reflection coefficients. For the case of an absorbing film, the same expression for the reflection coefficients for a nonabsorbing film can be used except that the complex number, n - ik, for the refractive index is used for this case instead of a real number, n, for the case of a nonabsorbing film.

1.3. Method of Summation The multiple reflections and transmissions by interfaces of a single film are shown in Figure 2. The total reflected ampli-

333

tudes are obtained by adding up the contributions to the reflected amplitude due to each of the multiple rays within the film while taking into account the phase differences associated with the various rays. Appendix A goes through this method of summation in detail and shows that the total reflected amplitudes for s and p polarization of light can be written rls 4- r2s e-2i81

Rs = 1 4- rlsrzse -i2~1 rlp 4- r2pe -2i~ Rp -- 1 4- rlpr2pe -i2~1

(9)

where rl (r2) is the Fresnel reflection coefficient at the no-n 1 (n l-n2) interface, respectively, and e -i2~1 is the phase factor associated with one complete traversal of the film and the phase difference, 4yg

281 : - : - n l d l COSr

(10)

1.4. Method of Resultant Waves The method of summation becomes very awkward when one gets to a more complicated situation than a single layer on a substrate, whereas the method of resultant waves proves to be much more versatile. This method uses the vector sums of the reflected and transmitted waves and applies the appropriate boundary conditions at the interfaces to derive the reflection coefficients. Appendix B shows how the method of resultant waves is applied first to a single layer and then to a multilayer structure. Each layer in a multilayer structure can be represented by a characteristic matrix which links components of the electric and magnetic vectors in one layer to the preceding layer. We consider the case of m layers each of thickness dm sandwiched in between two semi-infinite media no and nm+l. The theory is developed in terms of the tangential components of the electric and magnetic fields at each interface, so that E j, H j are these components at the interface between the j th and j 4- l th layers. The characteristic matrix of the j th layer is denoted by Mj (d j). Appendix B shows that the tangential components E0, H0 in the semiinfinite medium no at the interface with the first layer may be expressed in terms of the tangential components Em+l, Hm+l in the semi-infinite medium nm+l at the interface with the mth layer, as

[E0 H0]--M[~m+l]-Hm+l

Fig. 2. (a) The multiple reflections and transmissions of light in a single film are shown (method of summation) and (b) the incoming and outgoing electric wave vectors are shown (method of resultant waves).

(8)

(11)

where M = Ml(dl) 9 M 2 ( d 2 ) . . . M j ( d j ) . . . Mm(dm). Of course, it is necessary to differentiate the state of polarization and this is accomplished by adding the superscript p or s to the matrix variable M and the subscript p or s to the other appropriate variables. Appendix B shows that Eq. (1 l) can be rewritten in terms of the reflection coefficients, and thus one can derive that the

334

LESLIE ET AL.

reflection coefficient, rp, for TM (Transverse Magnetic) waves (p polarization) can be written as rp --

Cp-1 cp+l

(12)

where Cp is an expression involving the components of M p. Similarly, one can derive that the reflection coefficient, rs, for TE (Transverse Electric) waves (s polarization)can be written as

rs --

Cs- 1 cs+l

(13)

where Cs is an expression involving the components of M s. The key fact is that the reflection coefficients can be calculated from Eqs. (12) and (13) by a computer program once the optical characteristics of the system being studied are input. Once the reflection coefficients are known, the ellipsometric parameters can be determined. The relation between the reflection coefficients and the ellipsometric parameters are discussed in the next section.

1.5. Principles of Ellipsometry and Null Ellipsometry In general, a reflection of a light beam at the interface between two media will cause the state of polarization of the light beam to change. The change in the state of polarization can be described by the fundamental equation of ellipsometry, defined as p =

rp rs

= tan ~eiA

(14)

where A = A 1 - A2 and tan ~r = Irpl/Ir~l. A1 is defined as the phase difference between the perpendicular component and the parallel component of the incoming wave while A2 is defined as the phase difference between the perpendicular component and the parallel component of the outgoing wave. Equation (14) is the basis of defining ellipsometric data as the pair of values ~f and A, and the use of this data to obtain the refractive indices and layer thicknesses of the sample being studied. The most accurate way of measuring ~ and A employs null ellipsometry. Usually, when linearly polarized light is incident on the surface of a sample, the sample substrate plus any layers on the substrate will cause the reflected light to become elliptically polarized as shown in Figure 3a. In null ellipsometry, the earlier process is reversed. Instead of having linearly polarized incident light, elliptically polarized light it used. The ellipticity of the incident light is selected so that it will cancel the ellipticity introduced by the surface. As a result, the light reflected off the sample is linearly polarized as shown in Figure 3b. The orientation of the resulting linearly polarized light can be determined by passing it through a polarizer (henceforth called the analyzer) and rotating the analyzer until a detector indicates no light is being received. In this condition, the detector indicates a null, hence the name "null ellipsometry." The orientation of the linearly polarized light is perpendicular to the direction of the polarization axis of the analyzer.

Fig. 3. (a) Illustrates that in general linearly polarized light incident on a sample will produce elliptically polarized reflected light, while (b) illustrates that if we select the correct elliptically polarized light incident on a surface, the ellipticity caused by the reflection can be canceled and we obtain linearly polarized light.

1.6. Operation of the EXACTA 2000 Faraday-Modulated Single-Wavelength Ellipsometer The EXACTA 2000, whose schematic diagram is shown in Figure 4, normally operates in the following way: A linearly polarized laser (L) and the first quarterwave plate (Q 1 ) produce circularly polarized light. The polarizer prism (PP) and the second quarterwave plate (Q2) produce elliptically polarized light, whose A value is set by the polarizer angle P, to produce a linearly polarized reflected beam. The analyzer prism (AP), when rotated to the appropriate angle A, produces a null at the photodetector (D). The action of the Faraday rods and drive coils are described later. (Appendix C shows that the relation between the ellipsometric parameters A and ~ and the null ellipsometer variables P and A is just A -- 2P + 90 ~ and 7t - A. Here, P and A are angles of rotation of the axis of the polarizing direction of the polarizer and the analyzer from the plane of incidence, respectively, and the expressions assume that the fast axis of the second quarterwave plate is at - 4 5 ~ and we are in the first zone.) The polarizer (PP) and analyzer (AP) prisms are each mounted on precision rotary positioners which can be posi-

GROWTH ELLIPSOMETRY

335

Fig. 4. Schematic of the EXACTA 2000 Faraday-modulated self-nulling single-wavelength ellipsometer.

tioned with a resolution of 0.000625 ~ under the control of stepping motors with their controllers. A Faraday rod in a Faraday drive coil (F) is in series optically with each of the polarizer and analyzer prisms. The Faraday rods and drive coils are used to slightly rotate the polarization of the light passing through the polarizer and the analyzer using quadrature modulation, and the detector signal is analyzed by a two-phase lock-in amplifier to provide feedback to the stepping motors rotating the polarizer and analyzer prisms to keep them at null. With this combination of Faraday modulation and mechanical rotation of the polarizer and analyzer prisms, we can obtain up to 10 polarizer and analyzer null readings per second over a very large range of polarizer and analyzer angles. With this approach, we can measure the polarizer (P) and analyzer (A) angles at null with a precision of better than i 0 . 0 1 ~ at 10 readings per second andbetter than +0.003 ~ if we average the 10 readings over 1 s. Figures 5 and 6 show some drift measurements of P, A for a single crystal silicon wafer that shows that with good surfaces one can get even less scatter than is implied by the previous precision specifications. Figure 5 shows that the P value is drifting slightly over the 1159 s of the measurement, but that when averaged over 1 s the P value can be measured to better than +0.001 ~ Figure 6 shows that the A value when averaged over 1 s can be measured to better than +0.001 ~ One can also operate the ellipsometer in an all-Faraday drive mode in which one can improve the precision of the polarizer and analyzer null angle determinations to better than 4-0.001 ~1 at one reading per second when P and A vary within a range of -t-0.25 ~ The self-nulling mode via the motor control modules is switched off. Now, the polarization rotation function that was provided by the motor control modules, stepping motor drivers, rotary stages, and polarizing prisms is replaced by time integrating the lock-in amplifier signals and feeding them to the summing points in the Faraday rod coil driver amplifiers. Now, the voltage at the output of the integrator or the dc current in the Faraday rod coils represents the amount that the null angles 1With a good surface such as a single crystal silicon substrate, the precision can be 4-0.0003 ~ .

Fig. 5. Plot of the EXACTA 2000 ellipsometer polarizer null readings versus time from an air-exposed single crystal silicon surface where each data point is the average value per second of the 10 readings per second, and data were taken for a total of 1159 s.

Fig. 6. Plot of the EXACTA 2000 ellipsometer analyzer null readings versus time from an air-exposed single crystal silicon surface where each data point is the average value per second of the 10 readings per second, and data were taken for a total of 1159 s.

have rotated from the intial null positions. The conversion factor between angular and electrical variables, i.e., degrees per volt or degrees per ampere, is determined by measuring the P, A reading of a known surface, then backing P and A off by a set amount such as 0.25 ~ from the values measured and determining the voltage at the output of the integrator or the dc current in the Faraday rod coils to bring the detector signal back to null.

1.7. What a Single-Wavelength Nulling Ellipsometer Can Measure A single measurement of a single-wavelength nulling ellipsometer can yield only two pieces of information, i.e., the values of P and A that yield a null at the detector, which henceforth we will call just the P, A values. We will see that this has

336

LESLIE ET AL.

a very significant effect on what ellipsometry can tell about a system consisting of a substrate with a sequence of layers on it. It will also be important to differentiate between ex situ and in situ measurements. E x situ measurements are where the sample exists in completed form before the ellipsometric measurements are made. In situ measurements are where the ellipsometric measurements are being made while the sample is being fabricated, so that the ellipsometer can follow the time evolution of the fabrication of the sample. Of course, for a singleWavelength ellipsometer the index of refraction for the substrate or any layer is the value at the wavelength of the measurement, which in the present case is always 633 nm. For the case of an optically thick substrate, a single ellipsometric measurement is sufficient to determine the index of refaction of the substrate. (By an optically thick substrate, we mean that no light reflected from the back surface of the substrate reaches the spot on the front surface where the light is being reflected. This could be due to the substrate being sufficiently thick that the light being reflected from the back surface is shifted laterally sufficiently to avoid being directed into the detector, or the back surface being sufficiently rough that no specular reflection occurs, or the layer is so absorbing that no reflected energy reaches the front surface.) For this case, the substrate is either characterized by n if it is nonabsorbing or by n - i k if it is absorbing. The two values (P and A) obtained from a single ellipsometric measurement are sufficient to determine the unknown values (n or n - i k) for this case and thus we have sufficient information from a single ellipsometric measurement to characterize an optically thick substrate. For the case of a single layer on top of an optically thick substrate (assuming the index of refraction of the substrate is known), a single ellipsometric measurement is or is not sufficient to characterize the layer depending on whether the layer is nonabsorbing or absorbing, respectively. A nonabsorbing layer is characterized by the index of refraction n and layer thickness d. Since the number of unknowns (2) for this case is the same as the number of data values (two--one for P and one for A), a single ellipsometric measurement can determine the value of n and d, assuming that the index of refraction of the substrate is known. If the layer is absorbing, then it will be characterized by three unknowns, n - ik and d, then a single ellipsometric measurement does not have enough information to characterize this layer. Since this is an ex situ measurement, the only way to characterize an absorbing layer with a singlewavelength ellipsometer is to measure the P and A values at another angle of incidence or on another sample with a different thickness (assuming that the layer has the same n - i k and the same substrate, then one has enough information to uniquely fit the data to a uniform layer model). However, the best way for a single-wavelength ellipsometer to determine the index of refraction and thickness of such an absorbing layer would be to monitor the growth in situ of the absorbing layer on the optically thick substrate. By monitoring the growth, a number of different values of P and A can be measured as the thickness of the layer increases to its final value. The plot of A versus P traces out a trajectory which is

characterized by the index of refraction and thickness of the layer. This trajectory is referred to throughout this chapter as a P - A trajectory. The curvature of the P - A trajectory depends on the value of the index of refraction and the displacement along the trajectory depends on the layer thickness. By doing the best fit of this P - A trajectory based on the fundamental ellipsometric equation defined in Eq. (14), the index of refraction and the thickness of the layer can be determined. We have shown earlier that P and A are linearly related to the ellipsometric parameters A and ap. We plot P and A in the P - A trajectory, rather than convert over to A and ap for the following reasons. First, since we measure P and A directly, the plot of P and A show the actual experimental error that is being encountered in the measurement of P and A. If we convert P over into A and A into ~p, we make the error in A appear bigger than the error in ~ because the factor of 2 in the relation converting P into A. Second, since the operation of the EXIIC'I'II 2 0 0 0 ellipsometer involves measuring values of P and A, it is easier to think in terms of P and A rather than always to be converting P and A values into A and ap values.

1.8. Advantages-Disadvantages of Using a Spectral Ellipsometer for In Situ Measurements Spectral ellipsometers are often used in ex situ measurements, because one can use the ellipsometric information, A and ~, obtained at different wavelengths to characterize the sample in terms of layers on a substrate. Such characterization is always somewhat model dependent, in that the user has to define the number of layers that are going to be used in the fit, and the user has to assume dispersion relations for the different layers, i.e., how the index of refraction of each layer is assumed to vary with wavelength. However, obviously, spectral ellipsometers provide more information for fitting than is available from varying the angle of incidence on a single-wavelength ellipsometer. Spectral ellipsometers have less utility in doing in situ measurements. First, spectral ellipsometers tend to have a severe tradeoff on accuracy versus speed: the shorter the time spent in acquiring the ellipsometric parameters at each wavelength, the lower the accuracy in each measurement. In ex situ measurements, one can take additional time to obtain more accurate measurements. However, with an in situ measurement, the film growth is occurring at a rate determined by what is optimum for the deposition of the film, and cannot be slowed down to make it easier to get more accurate measurements. The only possible advantage that a spectral ellipsometer might have would be to operate it at only one wavelength that has been selected to give the maximum difference in index of refraction between adjacent layers to get a larger structure in the P - A trajectory. However, usually the technique used to measure the ellipsometric parameters in a spectral ellipsometer is sufficiently inaccurate that a Faraday-modulated fast-nulling ellipsometer can outperform it, even if the difference in index of refraction between adjacent layers is small.

GROWTH ELLIPSOMETRY

337 OAPU = Optical Axis of Polarizer Unit OAAU = Optical Axis of Analyzer Unit

1.9. Practical Considerations for In Situ Ellipsometry In doing in situ ellipsometry, one normally has the sample inside some sample growth chamber, e.g., a magnetron sputtering (MS) system, a molecular beam epitaxy (MBE) system, a metal organic chemical vapor deposition (MOCVD) system, or even an electrolytic cell if the film growth involves anodic oxidation or electrodeposition. In all cases, the laser beam from the polarizer unit has to enter the growth chamber via an entrance window, strike the sample at the angle of incidence, reflect off the sample at the same angle as the angle of incidence and in the plane of incidence, exit the growth chamber via an exit window and enter the analyzer unit and strike the detector. The EXACTA 2000 uses on-axis optics, so the alignment procedure is very simple, i.e., one uses a pinhole at the entrance to the analyzer and a pinhole at the detector to line up the laser beam when the polarizer unit is facing the analyzer unit. (Essentially, one is lining up the optical axis of the polarizer unit with the optical axis of the analyzer unit. The laser beam exiting the polarizer unit defines the optical axis of the polarizer unit. The pinholes at the entrance to the analyzer and at the detector define the optical axis of the analyzer unit.) In the operation of the ellipsometer, one needs a clear view of the sample from both the entrance window and the exit window, because unfortunately we cannot use any mirrors to redirect the beam, because such a mirror would change the state of polarization of the beam and of course this change would be different for different states of polarization of the beam hitting the mirror. So, we have some practical considerations to address regarding how we mount the polarizer and analyzer units and how we handle the entrance and exit windows. 1.9.1. External Beam Mount

If the sample can be moved and rotated in a measurable way from outside the growth chamber, then the process of aligning the sample relative to the ellipsometer is relatively straightforward. One adjusts the orientation of the sample until the incident beam is reflected directly back along the incident beam. The orientation of the sample then defines the direction of the incident beam. Then, one changes the orientation of the sample until the light beam incident on the sample is reflected through the exit window and into the entrance pinhole on the analyzer unit and strikes the center of the detector. Then, from the change in orientation of the sample, one can determine what the angle of incidence is. However, usually the sample cannot be moved and rotated in a measurable way from outside the growth chamber. In such cases, we have found an external beam mount to be the easiest way to align the ellipsometer on a sample. Figure 7 shows a schematic of an external beam mount and shows that it consists of an external beam on which are two parallel shafts, that can be rotated through measurable amounts by the use of protactors on each shaft. The polarizer unit is mounted transverse to one shaft and the analyzer unit is mounted transverse to the other shaft. By rotating the polarizer and analyzer units until

cz : 90 ~ - ~

~ = a n g l e of i n c i d e n c e

I Polarizer Unit 7 Protractor.

_[ v

!

OAPU~~/c, f

sample

OAAU r N~

Analyzer unit

|

Protractor

Shtfl a

htaflable

can be translated, rotated and tilted while keeping angle of incidence constant. Rotatable Shafts are perpendicular to External Beam Mount. Protractors are attached to Rotatable Shafts to measure angle of rotation. Polarizer and Analyzer units are rigidly attached to shafts so they rotate in the plane perpendicular to the shafts. Fig. 7.

Schematic of an external beam mount.

they face each other by using the pinhole at the front of the analyzer unit and a pinhole in the detector location, one can put the ellipsometer into the straight-through aligned position. (Essentially, we are aligning the optical axis of the polarizer unit with the optical axis of the analyzer unit.) If one cannot do this, then the polarizer and analyzer units are not perpendicular to the shafts and at the same distance from the beam, or the two shafts are not parallel to each other. After aligning for the first two conditions, one can check for parallel shafts by rotating the polarizer unit and the analyzer unit to the same angle with respect to the external beam mount and demonstrating that one can find a position of a mirror so that the laser beam from the polarizer unit is reflected through the pinhole in the analyzer unit into the pinhole at the detector. Once the shafts have been aligned perpendicular to the beam and the polarizer unit and analyzer unit are perpendicular to the shafts, then the angle of incidence can be set by rotating each unit through 90 ~ -4~ from the straight-through aligned position. At this point, the incident laser beam and the reflected laser beam are in the same plane of incidence with an angle of incidence of 4). Figure 7 has been drawn assuming ~b = 45 ~ Now, by moving and tilting the external beam mount one can ensure that the incident laser beam will hit the sample at the desired location and the reflected laser beam will pass out through the exit window and through the pinhole in the analyzer unit and will strike the center of the detector, while knowing that the external beam is maintaining the angle of incidence at ~b, and keeping the incident laser beam and the reflected laser beam in the plane of incidence.

1.9.2. Effect of Windows If the incident laser beam and the reflected laser beam pass through the windows normally, i.e., an angle of incidence of zero, then Eqs. (6) and (7) show that the Fresnel coefficients for both the p and s orientations are the same, and the windows

338

LESLIE ET AL.

have no effect on the polarization of the light passing through. Even if there are layers of deposits on the windows, as long as the angle of incidence is zero, the layers on the windows will have no effect on the polarization of the incident and reflected laser beams. If one is using an external beam mount, it is much easier to adjust the orientation of the windows so that the beams go through the windows at an angle of incidence of zero. With the windows properly aligned so that the angle of incidence on the window is zero, the polarization states do not change for the incident and reflected laser beams that pass through the windows. However, the intensity of the incident and reflected beams will be lowered. This can affect the accuracy of ellipsometers that use the variation of intensity with angle of rotation (e.g., a rotating polarizer or a rotating analyzer ellipsometer), since as the deposited layers get thicker, the variation of intensity with rotation gets smaller. This is one of the advantages of a nulling ellipsometer such as the EXACTA 2000. In a nulling ellipsometer, as long as one can still detect a null, a drop in intensity has no affect onthe accuracy. We have made m e a surements on growth chambers where the deposits on the windows were so thick that the intensity was cut to 1% of its initial value without any effect on the accuracy of the measurements. Birefringence in the entrance and exit windows is another matter for concern, because such birefringence shifts and rotates the P - A trajectory from its ideal behavior and makes it harder to fit. There are essentially two approaches to this problem. First, one can employ windows that have low birefringence, such as the Bomco window. Second, one can use a software-based correction that removes the birefringence from the P, A data as it is being collected. The EXACTA 2 0 0 0 has software to make such a correction in real time. However, to do this one needs to know the amount of the birefringence of each window and the orientation of the fast axis in each window. One of the problems that we and others have encountered is that if one measures the birefringence of a window and the orientation of the fast axis, the process of bolting the window back onto the growth chamber changes the birefringence due to stress on the window. However, we finally discovered a simple solution to this problem, i.e., bolt the window to be measured onto a bellows-equipped port-aligner before measuring the birefringence in the ellipsometer. Then, do not tighten or loosen or otherwise adjust the bolts holding the window to the portaligner. Then the port-aligner, with the window already attached and measured, can be bolted to the growth chamber without affecting the magnitude of the birefringence of the window. In addition, if the direction of the fast axis has been marked on the window, one can easily determine (or even set) the orientation of the fast axis with respect to the plane of incidence. The birefringence of a window acts like a compensator, i.e., there is a fast axis and a slow axis, and the refractive index of the window is not isotropic. If the birefringence is small then it will only translate the P - A trajectory. However, if the birefringence is large, it not only causes the whole P - A trajectory to shift but will also cause it to tilt, which will make the P - A trajectory more difficult to fit. A Bomco window is a special type of window with a much smaller birefringence, such that the trans-

lation of the P - A trajectory is small, and the tilt is small enough not to be readily observable in the P - A trajectory. It should be remembered that birefringence of the windows causes an error in the ellipsometric data but if the effect of the birefringence is small, then it will not affect the accuracy of fitting the ellipsometric data to determine the thickness of layers on samples inside the chamber. In theory [5], the error caused by birefringence of the windows can be determined. The ellipsometric data can be corrected by taking this error into account in the ellipsometric equation. In calculating the error, the window is treated as a compensator which is characterized by a retardation, t, and an angle Of the fast axis, W, relative to the plane of incidence. If the retardation and angle of the fast axis relative to the plane of incidence for the entrance window are tp and Wp, and for the exit window are ta and Wa, then the errors in P and A can be predicted by the followings [5],

1 1 A P = --~tp cos 2Wp - -~ cos 2Wa 1

+ -~ta sin 2Wa cot2A A A = --~tp sin2Wp sin 2P + ~

(15) sin2A

(16)

Hence, to calculate the errors, the retardations and the angles of the fast axis relative to the plane of incidence of the windows have to be determined. The two birefringence parameters, the retardation and the angle of the fast axis relative to the plane of incidence, can be determined by using the ellipsometer in a straight-through mode. The positions of the plane of incidence of the windows when they are mounted on the growth chamber should be marked on the windows before they are taken off the growth chamber. Each window is placed between the polarizer and the analyzer unit of the ellipsometer such that the laser beam is incident at the center of the window. When the window is rotated at a constant rate, the plot of P versus time or A versus time will trace out a sinusoidal plot. The amplitude of this plot is the retardation and the position of the window where this maximum amplitude occurs should be marked on the window, because this is the position of the fast axis of the window. The angle of the fast axis relative to the plane of incidence is the angle between the mark of the plane of incidence and the mark of the fast axis on the window.

1.10. Simulations of P - A Trajectories Let us examine the P - A trajectories that we can expect if we were doing in situ monitoring of the growth of a dielectric, semiconductor, or metal layer on a semiconductor substrate. The P - A trajectories that we will show are based on the simulation of the changes in ellipsometric parameters that would be taking place as the layer is being deposited. These simulations are obtained in a computer program as follows: The layer is divided into N sublayers of equal thickness, and the matrix M from Eq. (11) associated with each sublayer is generated for each polarization. By multiplying the matrices M associated

G R O W T H ELLIPSOMETRY

339

26-

9 .~149 . . . . . . . . . . . . ~

ooOO~176176176 oo~ oo

~ 9

60.

~, C~

20.

50-

v L_

18"

40-

N >, -~ t-

16.

O~ "O "~ N -~ t'-

~149 .9 9

99


0 for n-type SCs; see Fig. 4a) when a space-charge region, having width Xsc, is formed inside the semiconductor. In the case of p-type material a space-charge layer develops inside the SC for A ~sc < 0.

Csc(:r A(I) s c , ~[

* e,(-~)

i

............

1 -X H

Fig. 3.

0

377

X sc

Potential profile across the semiconductor-electrolyte interface.

2.2. Determination of the Space-Charge Width in Crystalline SCs and the Mott-Schottky Equation

Energy

E red F .......

In order to calculate the dependence of Xsc on A ~sc, we need to solve the Poisson equation, which relates the Galvani potential drop at a point x of the space-charge region, ~ (x) - 4~sc(x) 4~sc(c~), to the charge density inside the semiconductor, p(x)"

Ec sc

EF

J

d2~ dx 2

p(x) = - ~ 880

(2.2.1)

Ev

I

I

"X H

0

I

x

Xsc

(a) Energy -e U fb E red F .......

i i | 1 ! i i I 1 i ! Ev I

-X H

x

0

(b) Fig. 4. Electron energy levels in the SC/E1 junction (a) under depletion conditions and (b) at the flat-band potential. ~ (x) represents the potential drop at a point x of the SC space-charge region. E SC and E~ed are the Fermi levels of the SC and the redox couple in solution, respectevely. Ufb is the fiat-band potential.

(see Section 2.2) under the same conditions used for an ideal metal-semiconductor (M/SC) Schottky barrier and by taking into account that the potential drop within the semiconductor is only a part of the total potential difference measured with respect to a reference electrode. Moreover, by taking into account that in the presence of a sufficiently concentrated (>0.1 M) electrolytic solution the potential drop in the GouT layer is negligible, the equivalent electrical circuit of the interface in electrochemical equilibrium can be represented again by two capacitors in series: Csc for the SC space-charge layer, and CH, for the Helmholtz layer [28-30]. The value of Csc changes with the width of the space-charge region within the semiconductor, Xsc, and it is a function of the total potential drop A ~sc within the SC.

where p is the total density of charge (mobile and fixed) inside the space-charge region, e is the dielectric constant of the SC, and e0 is the vacuum permittivity. The usual boundary conditions of zero electric field and zero Galvani potential in the bulk of the semiconductor [dC,/dx(oo) - 0 and ~sc(CXz) - 0] can be assumed. This choice implies that ~sc(X) - 4~sc(X)-4~sc(C~) has opposite sign to the electrochemical scale of potential. The width of the space-charge region, Xsc, as well as the potential distribution inside the semiconductor under reverse polarization of the SC/E1 junction can be easily found by using the Schottky barrier model of the junction and by solving the Poisson equation (2.2.1) under the depletion approximation and the hypothesis of a homogeneously doped semiconductor with fully ionized donors Nd (for n-type SCs) or acceptors Na (for p-type SCs) [28-30, 46]. The depletion approximation implies that the net charge density varies from the zero value of the bulk to the value +eNd (or -eNa for a p-type SC) at the depletion edge. As a consequence of such a charge distribution, a linear variation of the electric field is obtained according to Gauss's law, which relates the electric field intensity at the surface of the SC, Fs, to the charge density: Fs --

eNdXsc

(2.2.2)

880

For an electric field varying linearly inside the space-charge region, the potential drop inside the SC can be calculated as A~sc =

FsXsc

2

=

eeoF2 2eNd

(2.2.3)

from which a dependence of Fs on (A~sc) 1/2 is derived. By relaxing the depletion approximation and taking into account the more gradual drop of the electron density at the

378

DI QUARTO ET AL.

depletion edge, we get for Fs the expression [46]

Fs

=

(2eNd)l~2(

EEO

kT) 1/2

A~sc - ~

e

using the following equation: (2.2.4)

showing that the depletion approximation differs from the exact one by the thermal voltage contribution kT/e. The dependence of the width of the space-charge region on the potential drop A ~sc can be obtained by using Eqs. (2.2.2) and (2.2.4) [46]"

kZ) 1,2

(2EE0) 1/2( Xsc=

-~d

A~sc

e

(2.2.5)

This expression can be used for deriving also the dependence of the space-charge capacitance on A ~sc [29, 33]"

Csc

Ee0

(eeoeNd)l/2(

= Xsc -

2

kT) -1/2 A~sc

e

(2.2.6)

This is the well-known Mott-Schottky (MS) equation, which can be employed to derive the fiat-band potential Ufb of the SC/E1 junction. For this aim we need to relate the Galvani potential drop within the semiconductor to the measured electrode potential Ue. By defining the fiat-band potential of the SC/E1 junction as the electrode potential at which A~sc = 0 (Fig. 4b), in the absence of surface states we can write at any other electrode potential

A (I)sc -- Ue - Ufb

(2.2.7)

where Ue and Ufb are measured with respect to the same reference electrode. By substituting Eq. (2.2.7) in Eq. (2.2.6) we get the final form of the MS equation, usually employed for obtaining the fiat-band potential and the energetics of the n-SC/E1 junction [29, 33]:

= eeoeNa Ue -- Ufb

e

(2.2.8)

An analogous equation holds for a p-type material, with a minus sign in front of fight-hand side and Na instead of Nd. From the electrical equivalent circuit of the interface (see Section 2.1), it is obvious that the following relation holds in a concentrated electrolyte" 1

Csc

=

1

Cm

-

1

CH

(2.2.9)

where Crn is the capacitance of the interface measured experimentally, and a constant value of CH -- 30/zF/cm 2 is frequently used for aqueous solutions. The determination of the fiat-band potential is the first step in the location of the energy levels at the SC/E1 interface. Once Ufb is known, it is possible to locate the Fermi level of the SC with respect to the electrochemical scale by means of the relationship: E~

--

--eUfb

(2.2.10)

It is also possible to relate the Fermi level of the SC to the electron potential energy in the vacuum)

physical scale (zero

E~

= --eUfb(ref) + eUref(vac)

(2.2.11)

where the first term on the right is the fiat-band potential, measured with respect to a standard reference electrode, and the second one is the potential of the reference electrode with respect to the vacuum scale [33, 45]. In the case of a standard hydrogen reference electrode (SHE), the most commonly accepted value of e USHE(Vac) is --4.50 eV. Slightly different values have been reported by different authors, so that an uncertainty on the order of 0.2 eV remains when the energy levels are referred to the vacuum scale [35]. The location of the remaining energy levels of the junction is easily obtained by means of the usual relationships for n- and p-type semiconductors:

Ec= EO+kTln(N ) E g - E c - Ev

for n-type SC

(2.2.12a)

for p-type SC

(2.2.12b) (2.2.13)

where Nc and Nv are the effective densities of states at the bottom of the SC conduction band and at the top of the SC valence band, Na and Na are the donor and acceptor concentrations in the SC, Ec and Ev are the conduction and valence band edges, respectively, and Eg is the bandgap of the SC. The rather simple MS method for locating the energy levels at the SC/E1 interface is very popular among electrochemists. However, we have to mention that, although the validity of Eq. (2.2.8) has been tested rigorously for several SC/E1 interfaces [47-56], since the seminal work of Dewald on singlecrystal ZnO electrodes [47, 48], in many cases a misuse has been made of this equation, neglecting the limits under which it was derived. This is particularly true in the case of passive films, which are usually amorphous or strongly disordered and display a frequency dependence of the measured capacitance not in agreement with the hypotheses underlying Eq. (2.2.8). A more detailed discussion of the inadequacy of the MS analysis for interpreting the Capacitance data of the amorphous SC/E1 interface can be found in Section 3. Here we summarize the main assumptions used for deriving Eq. (2.2.8) [54]: (1) a crystalline SC electrode homogeneously doped in the depletion regime; (2) a fully ionized single donor (or acceptor, for p-type SC) level; (3) absence of deep-lying donor (acceptor) levels in the forbidden gap of the SC; (4) negligible contribution of surface states and minority carriers to the measured capacitance; (5) absence of electrochemical faradaic processes at the SC/E1 interface. In the case of passive films it is rather improbable that the first four points are satisfied simultaneously. In our opinion, any

PHOTOCURRENT SPECTROSCOPY OF THIN PASSIVE FILMS model of the space-charge capacitance of passive films that assumes the existence of discrete donor (acceptor) levels in the forbidden gap without taking into account the dependence of the response of localized gap states to the frequency of the modulating ac signal, fails to provide the correct analysis of experimental data.

379

[::c $c

EF

h'v

red

F

\

2.3. Photocurrent-vs-Potential Curves for Crystalline SC/EI Junctions: The G~irtner-Butler Model The first attempt to model the photocurrent behavior of a SC/E1 junction under illumination can be ascribed to M. A. Butler [57], who adapted a previous model developed by G~rtner for the M/SC Schottky barrier [58] to the case of a SC/E1 interface. A close similarity between the Schottky barrier junction and the semiconductor-liquid interface was assumed in the model. The quantitative fitting of the experimental photocurrent-vs-potential curves for an n-type single-crystal WO3-electrolyte junction under monochromatic irradiation, performed through the Butler-G~_rtner model, attracted the attention of many electrochemists, who recognized in the ButlerG~rtner mathematical treatment an alternative way to get the fiat-band potential of the junction, circumventing some of the difficulties related to the MS analysis. In this subsection we will derive the theoretical expressions for the photocurrent in a crystalline SC/E1 junction as a function of the electrode potential in the frame of the G~irtner-Butler model. The results will also be used for getting the relationship between bandgap of photoelectrodes and the quantum efficiency of the junction at constant potential. The limits of the G~irtner-Butler model will be discussed briefly, and the new features of photoelectrochemical behavior of the passive-film-electrolyte junction will be discussed in Section 3.2. In Figure 5 we report a schematic picture for a crystalline n-type SC/E1 interface under illumination. In the figure, ~0 (in cm -2 s -1) is the photon flux entering the semiconductor (corrected for the reflection losses at the SC/E1 interface), which is absorbed following the Lambert-Beer law. According to this, the number of electron-hole pairs generated per second and unit volume at any distance from the SC surface, g(x), is given by g ( x ) -- ~Poote-~x

|

fly

|

(a)

Light intensity

o

x

xsc

0

(b) Fig. 5. Schematic representation of a crystalline n-type SC/E1 interface under illumination, showing (a) the electron-hole pair generation and (b) the change of light intensity due to absorption within the semiconductor.

Moreover, in the model it is assumed that minority carriers generated in the space-charge region of the SC do not recombine at all, owing to the presence of an electric field which separates efficiently the photogenerated carriers. The same assumption is made for the minority carriers arriving at the depletion edge from the bulk region of the SC. In order to calculate Idiff, G~irtner solved the transport equation, which for a n-type SC is dp(x) d2p(x) dt = Dp d x 2

p-

po t

~- g ( x )

(2.3.2)

(2.3.1)

where or, the light absorption coefficient of the semiconductor, is a function of the irradiating wavelength. It is assumed that each absorbed photon (having energy, h v, higher than the optical bandgap of the semiconductor photoelectrode, Eg) originates a free electron-hole pair. In the G~irtner model the total photocurrent collected in the external circuit is calculated as the sum of two terms: a migration term/drift, which takes into account the contribution of the minority carriers generated in the space-charge region, and a diffusion term ldiff, arising from the minority carriers entering the edge of the space-charge region from the field-free region (x > Xsc). No reflections of light at the rear interface is assumed, so that all the entering light is absorbed within the SC.

with the boundary conditions p = p0 for x --+ c~ and p = 0 for x = Xsc. Here p is the hole concentration under illumination, P0 the equilibrium concentration of holes in the bulk of the (not illuminated) SC, and Dp the diffusion coefficient for holes. The zero value of p at the boundary of the depletion region follows from the previous assumption that all the holes generated into the space-charge region are swept away without recombining. According to GLrtner, for the total photocurrent we can write lph -- /drift d-/diff

-- e

f sc ao

(2.3.3)

g ( x ) d x + eDp \

dx

X "- Xsc

380

DI QUARTO ET AL.

where e is the absolute value of the electronic charge. By solving Eq. (2.3.2) in the steady-state approximation to obtain the distribution of holes in the field-free region, and by substituting Eq. (2.3.1) for g(x) in the integral of the drift term, we get finally the G~irtner equation for n-type semiconductor [58]: Iph -- e~0

1 - exp(-otXsc) + 1 -q- otLp

Dp epo~

(2.3.4)

Lp

where Lp is the hole diffusion length. The same equation holds for p-type SCs, with Dn and Ln (the electron diffusion coefficient and diffusion length, respectively) instead of Dp and Lp, and no (the electron equilibrium concentration) instead of p0. Equation (2.3.4) was further simplified by Butler for the case of wide-bandgap SCs (e.g., n-type WO3), where the concentration of minority carriers in the bulk, p0, is very small. In this case, by using Eq. (2.2.5) for Xsc, he derived the G~irtnerButler equation for the photocharacteristics of a crystalline SC/E1 junction [57]: Iph -- e~0

1-

exp(-otX~

-

kT/e)]

1 +otLp

(2.3.5)

In this equation, X~ represents the space-charge width at the SC electrode at 1 V of band bending, and A~sc = Ue - Ufb. It is easy to show [57] that if otXsc Xc) where all electronic states fully respond to the ac signal, and the second (for x < Xc) where no states respond at all. The band bending at Xc is given by 9 c = ~(Xc) = - k T ln(oor0) - AEF

(3.1.4)

where AEF = (Ec - EF)bulk: It was shown in [83, 94-96] that by assuming the model of an a-SC Schottky barrier to be valid also for the a-SC/E1 junction, the equivalent electrical circuit of the junction reported in Figure 11 can be obtained for concentrated electrolytic solutions. Once again, the main differences with respect to the equivalent electrical circuit of the junction for crystalline materials occur on the electrode side, which is now represented by a frequency-dependent resistance, R(A~sc, w), in parallel with two capacitors in series, the first of which, C(~c, 0), is quite insensitive to both frequency and bias, whilst the second, C(Xc) = eeo/Xc(A~sc, w), is frequency- as well as biasdependent. In the simplified case of a constant DOS within the mobility gap of the a-SC [N(E) = N; see Fig. 10], the analytical solutions for the admittance components of the junction can be derived for A~sc > ~c and at not too high band bending (A~sc < Eg/2 [83, 85, 94, 104]). The total parallel capacitance is given by

(eeoe2N)l/2 c(ZX~sc, oJ) =

1 + ln(A~sc/~c)

(3.1.5)

whilst the parallel conductance of the junction is given by G(A~sc, w) =

wyr kT

(eeoe2N) 1/2

2 e~c [1 + ln(A~sc/~c)] 2

(3.1.6)

It has been shown that G(A~sc, CO) has a spectroscopic character with respect to the distribution of electronic states, whilst variations in DOS cause only minor changes in the

V

3.8

(she)

Fig. 12. Measured parallel capacitance Cm vs electrode potential at different frequencies in 0.5 M H2SO4 solution for an a-WO 3 film grown in the same solution up to 54 nm. (a) f = 3 Hz; (b) f = 10 Hz; (c) f -- 100 Hz; (d) f = 3 kHz. [AIChE J. 38(2), 219-226 (1992); reprinted with permission from the American Institute of Chemical Engineering.]

C(A ~sc, co)-vs-potential plots [94-96]. With respect to the MS analysis, which allows one to get both the doping density of the SC and the fiat-band potential of the junction from the same plot [see Eq. (2.2.8)], in the case of a-SC a longer fitting procedure is required in order to get the fiat-band potential and to locate the mobility band edges. As reported in [94-96], the fitting must be carried out on both components of the admittance of the junction, after the correction of the measured quantifies for the equivalent circuit shown in Figure 11, by imposing the condition that at all the frequencies employed for the ac signal both the 1/ Csc-vs-A ~sc and the 1/ Gsc-vs-A ~sc plots give the same Ueo-value, within an assigned uncertainty (in our case, 0.05 V). Moreover, an additional constraint arises from Eq. (3.1.4), which predicts for ~c a variation of 59 mV over a decade of frequency at room temperature. Figures 12-14 display the experimental capacitance and conductance curves recorded for a-WO3 and a-Nb205 anodic films at various frequencies, whilst a fitting of the admittance components according to Eqs. (3.1.5) and (3.1.6) is shown in Figure 15 for an a-TiO2 film; the results of the fitting procedure are reported in Table II. Despite the simplifying assumption of constant DOS, the very good agreement with the experimental data supports the theoretical analysis outlined. The fact that the theory of a-SC Schottky junctions predicts a parabolic potential distribution inside the a-SC in the highdepletion regime [94-104] explains why different authors have observed experimentally linear MS plots for many disordered passive film-electrolyte junctions. However, the extrapolation of such MS plots to the potential axis gives fiat-band potential values that are completely wrong, as can be easily inferred from the study of the a-TiO2/E1 junction reported in [85, 96, 104]. More importantly, the theory of a-SC Schottky barrier allows us: (a) to explain, without any further assumption, the experimentally well-known frequency dependence of

PHOTOCURRENT SPECTROSCOPY OF THIN PASSIVE FILMS the capacitance values reported for amorphous semiconducting passive films; (b) to locate correctly the CB mobility edge, Ec, through Eq. (3.1.4) [and not by means of the Eq. (2.2.8), which is valid for crystalline SCs but misleading when used for a-SCs]; (c) to calculate the DOS distribution around the Fermi

1

j

'

|

!

level by means of the relationship [94, 96, 102] Gp

N [ E F - e~c(CO)] = c o n s t ~

(3.1.7)

o)

where Gp is the parallel conductance and the constant is independent of the ac frequency. Further support for the model for the impedance of the a-SC/E1 junction, outlined above, derives from new features

J

Hz

'7,

385

10-3

....

,

6 ol

E

10-4

U

3

E 0

2I ~ kHz

~

0~,,,

I

....

0 UE

/

.,.

J

1 V (MSE)

1o

i|l|. i

i

!

ii

-5 100

10

1o

--~

I

-.5

!

1.0

,_~j~

"

%

m~

m

a~PdPa~ ,~oo

n

~"

.

U e = 1.Z

0.125

V(MSE

O

1

100 ',9.

,// U e = -0.3 V(MSE)

50

,,d'~p

B 0.075 ~

.~,~

U e = -0.24 V(MSE)

0 -3

i -2

.5

/ V(MSE)

ill

!

U e = 0 . 4 4 V(MSE)

r~

Hz

I_,

.5

0.0

Hz

Fig. 14. Parallel conductance vs electrode potential at different frequencies for the same film as in Figure 13. [Electrochim. Acta 35(1), 99-107 (1990); reprinted with permission from Elsevier Science.]

ii

150

I

....

UE

Fig. 13. Measured parallel capacitance vs electrode potential at different frequencies in 0.5 M H2SO4 solution for an a-Nb20 5 film grown in the same solution up to 84 nm. [Electrochim. Acta 35(1), 99-107 (1990); reprinted with permission from Elsevier Science.]

,_

! kHz

1

~

kHz

, -1

i 0

.

0.025 1

In (U~-UFB) Fig. 15. Fitting, according to Eqs. (3.1.5) and (3.1.6), of the impedance data recorded at f = 3 Hz for an a-TiO2 film grown at 2 V/s in 0.5 M H2SO 4 solution up to 20 V. Flat-band potential: - 0 . 4 7 V (MSE). [Ber. Bunsenges. Phys. Chem. 101(6), 932-942 (1997); reprinted with permission from VCH Verlagsgesellschaft mbH.]

386 Table II.

DI QUARTO ET AL. Physical Parameters Derived for Three Anodic Oxide Films a Thickness

Ufb (SHE)

~c ( f = 3 Hz)

AEF

N(EF)

Oxide

(nm)

(V)

(mY)

(eV)

(cm -3 eV -1) 2.0 x 1019

a-WO 3

54

0.51 4-0.04

174

0.44

a-Nb20 5

84

0.06 4-0.04

186

0.43

1.5 • 1019

a-TiO 2

83

0.10 4- 0.05

162

0.45

2.3 • 1020

aFrom the fitting, according to Eqs. (3.1.5) and (3.1.6), of the impedance data in 0.5 M H2SO 4. Raw data were corrected for the electrical equivalent circuit of Figure 11; a value of 30 ~tF/cm2 has been used for CH. [AIChE J. 38(2), 219-226 (1992); reprinted with permission from the American Institute of Chemical Engineering.]

observed in the photoelectrochemical behavior of amorphous passive films, which are strictly related to the electronic structure of the films.

3.2. Optical Absorption and Photoelectrochemical Response of the Metal-Passive-Film-Electrolyte Junction Like the electronic properties, the optical properties of materials, are considerably affected by their amorphous nature. The main differences in the photocurrent response of disordered thin films with respect to the case of bulk crystalline semiconductors arise from the following facts: (a) The optical bandgap of an amorphous material may coincide or not with that of the crystalline counterpart, depending on the presence of different types of defects that can modify the DOS distribution. (b) In contrast with crystalline materials, the generation of free carriers by the absorption of photons having energy equal to or higher than the optical bandgap of the film may depend on the electric field, owing to the presence of an initial (geminate) recombination. (c) The presence of reflecting metal-film and film-electrolyte interfaces makes possible the occurence of multiple reflections, even for photons having energy higher than the optical absorption threshold; this fact causes interference effects in the curves of photocurrent vs film thickness. (d) The small thickness of the film makes possible optical excitation at the inner metal-film interface, which can inject photocan'iers from the underlying metal into the VB or CB of the passive film (internal photoemission), or directly into the electrolyte (external photoemission) in the case of very thin films (1-2 nm thick). In the following sub-subsections we will analyze the foregoing points in detail by comparing the theoretical expectations with the experimental results pertaining to different metalpassive film-electrolyte junctions.

3.2.1. Optical Gap in Amorphous SCs As to the first point, we recall the relationship between the optical absorption coefficient and the opticalband gap Eg of a material, valid near the optical absorption threshold [33, 105]:

~hv = A ( h v - Eg) n/2

(2.3.7)

where, for crystalline materials, n can assume different values depending on the nature of the optical transitions between occupied electronic states of the VB and vacant states of the CB. The optical transitions at energies near the bandgap of a crystalline material may be direct or indirect. In the first case no intervention of other particles is required, apart the incident photon and the electron of the VB; in the second case the optical transition is assisted by lattice vibrations. Assuming a parabolic DOS distribution [N(E) (x E 1/2] near the band edges, in the case of direct transitions n assumes values equal to 1 or 3, depending on whether the optical transitions are allowed or forbidden in the quantum-mechanical sense [33]. In the case of indirect optical transitions the value of n in Eq. (2.3.7) is equal to 4 [33]. In the case of amorphous materials, owing to the relaxation of the k-conservation selection rule, "no intervention of phonons is invoked to conserve momentum and all energy required is provided by the incident photons" [105]. By assuming again a parabolic DOS distribution in the vicinity of the mobility edges of both the conduction and the valence band (above Ec and below Ev, with reference to Fig. 9), it has been shown [91] that the following relationship holds:

~hv = const(hv - Eg) 2

(3.2.1)

where Egm _ E c - E v is the mobility gap of the a-SC. The exponent 2 is reminiscent of the indirect optical transitions in crystalline material, but now photons interact with the solid as a whole; this type of transition in amorphous materials is termed nondirect. Because some tailing of states is theoretically foreseen for a-SC by every proposed model of DOS, Egm represents an extrapolated rather then a real zero in the density of states. In the presence of a DOS distribution varying linearly with energy in the ranges Ec - EA and EB -- Ev of Figure 9b, it is still possible to get a similar expression for the absorption coefficient [90]:

~hv = const(hv b-,opt

-

Egpt) 2

(3.2.2)

where ,_,g now represents the difference of energy EA -- Ev or E c - EB in Figure 9b, whichever is the smaller, and the constant assumes values close to 105 eV -1 cm -1. The range of energy over which Eq. (3.2.2) should be valid is on the order of 0.3 eV or less [ 105]. In order to distinguish between these two different models of optical transitions, both giving the same dependence of the absorption coefficient on the photon energy, we will refer to the first one as the Tauc approximation for the calculation of the SC mobility gap and to the second one as the Mott-Davis approximation for the SC optical gap. When the plots of (c~hv)~ vs hv

PHOTOCURRENT SPECTROSCOPY OF THIN PASSIVE FILMS

.010

9 i Iilmwi

\

|

~k

|

387

i

J OZ

i

\

0

\

j

,,

,

m

\

l.O

/ o/

r

\

..C

Q.

\

.5

-

/

0

/0

I,I

..

n,,. 0 0 5 -

0.0~ 0/0

O.O--~'orv" 3.g

b

nr

/_l 3.5

,

\

0 "r" fl_

|

.........

| ......

4.0

\

L) 0

.2

0/~

h~

4.5

5

o

.1

/oV

\

\\ \

0.0

0. 0 0 0

250

300

350 NRVELENGTH

400

/

450

nm

Fig. 16. Photocurrent action spectra for films grown anodically on Nb in 0.5 M H2SO 4 electrolyte up to (a) 0 V and (b) +0.5 V (MSE). The spectra were recorded polarizing the electrode at the final formation voltage. Inset: determination of the optical bandgap from spectrum b. [J. Electroanal. Chem. 293, 69-84 (1990); reprinted with permission from Elsevier Science.]

display a linear region larger than 0.3 eV, it seems more correct to interpret the data on the basis of the Tauc model of optical transitions. In Figure 16 we report an interesting case of coexistence of both types of transitions for thin anodic films grown anodically on niobium [ 106], where the presence of a mobility gap on the order of 3.5 eV is observed in the high photon energy range, extending around 1 eV, followed by an optical gap (in the Mott sense) of around 3.05 eV over an energy interval of about 0.3 eV. In the case of anodic films on valve metals, the so-called Urbach tail for the absorption coefficient is frequently observed for photon energies lower than the mobility gap; it follows the law oe = o~0exp - y

k------~

(3.2.3)

with y and oe0 constant. Such a relationship, which has been found to hold for crystalline materials too, has been rationalized in the case of amorphous SCs by assuming an exponential distribution of localized states in the band edge tails [ 107]. In this situation the value of E0 obtained from the In ~-vs-h v (Urbach) plot should coincide with the mobility gap determined according to Eq. (3.2.1). A typical example is reported in Figure 17 for an a-MoO3 film [108]" the value of E~n, equal to about 3.10 eV, is in good agreement with the value of E0 (~3.15 eV) derived form the Urbach plot. Other explanations have been suggested

by different authors for such behavior in the case of crystalline materials [ 105]. In interpreting the information provided by the optical gap values, it is important to recall the statement in Mott and Davis's book [105]: "A general rule appears to be that, if the local atomic order is not appreciably altered in the amorphous phase, the gaps in the two states (amorphous and crystalline) are not appreciably different." This rule works better for materials whose band structure is mainly determined by the nearestneighbor overlap integral (tight-binding materials). In Table III we report the optical gap values determined by photocurrent spectroscopy for different passive films: for the amorphous anodic oxides on valve metals they are systematically larger than those of their crystalline counterparts. The difference ~amor _ ~g Ecryst g

is in the range of 0.1-0.35 eV, in agreement with the extension of the localized state regions near the band edges due to the lattice disorder. Moreover, by taking into account that a value of E0 nearly coincident with the mobility gap has been frequently derived from the Urbach plot, it seems quite reasonable to suggest for this a class of amorphous materials a band model similar to that shown in Figure 9b, with an exponentially decreasing DOS in the mobility gap of the films at energies lying below Ec and above Ev. A mobility gap of the passive film lower than the bandgap of the crystalline counterpart must be interpreted as an indication

388

DI QUARTO ET AL. I

I

I

3

!2 a) i

,

,

I

300

I

350

i

400

450

wavelength / nm

|

150

.

i I

I

000000

_

0

_

"3

100

oo

-

that there are differences in short-range order between the two phases. A different short-range order can lead to the formation of a defective structure, with a high density of localized states within the mobility gap as well as changes in the density of the passive film, which is known to affect also the value of the optical gap in amorphous materials [86, 87, 90, 91]. The experimental findings on passive anodic films and corrosion layers suggest that large differences in the bandgap values between the amorphous and crystalline counterparts must be due to a different chemical environment around the metallic cation or to the presence of large amount of defects within the passive films, which produce electronic states within the mobility gap. We will come back to these aspects in Section 4, where the use of the PCS technique in a more quantitative way will be discussed. In order to derive the optical gap of passive films from the photocurrent spectra (see Figs. 16, 17), we need to relate the optical absorption coefficient ot to the photocurrent measured experimentally. This goal will be accomplished in Section 3.3.

2

3.2.2. Geminate Recombination in Amorphous Films

50

./ ,,,~no.

b)

/

c)

1 [

0

3

4

2.5

hv / eV

3

,

3.5

4

hv / eV

Fig. 17. (a) Photocurrent action spectrum recorded at +2 V (SCE) for a film grown up to 40 V on sputtered Mo in 0.1 M sodium acetate in a 2% v/v aqueous acetic acid solution. Lower part: determination of the optical bandgap, (b) assuming indirect transitions, and (c) from the Urbach tail. [J. Electrochem. Soc. 147, 1366-1375 (2000); reprinted with permission from The Electrochemical Society, Inc.]

Table III. Measured Optical Gap Egm for Passive Films on Pure Metals Compared with the Bandgap Eg of the Crystalline Counterpart

E~

Eg

AEam a

Phase

(eV)

(eV)

(eV)

ZrO 2

4.70-4.80

4.50

0.20-0.30

Ta205

3.95-4.05

3.85

0.10-0.20

Nb205

3.30-3.40

3.15

0.15-0.25

TiO2

3.20-3.35

3.05b-3.20 c

0.15-0.20

WO3

2.95-3.05

2.75

0.20-0.30

MoO3

2.95-3.10

2.90

0.05-0.20

Cr203

0.0-0.25

3.30-3.55

3.30

NiO

3.43

3.45-3.55

0

Cu20

1.86

1.86

0

Fe203

1.95

1.90

0.05

aDifference between Egm and Eg (see text). bRutile phase. CAnatase phase.

A major aspect to take into account in the formulation of the transport equations of the photocarriers is related to the possible presence of geminate recombination effects in the generation of mobile photocarriers. This phenomenon occurrs generally in any material where the photogenerated carriers display very low mobility. In the case of amorphous materials, localized states are present below the CB and above the VB mobility edges as a consequence of lattice disorder. The mobility of carriers in these states is much lower than that in the extended states, so that the existence of initial recombination effects in amorphous materials is quite probable. In fact, during the thermalization time the electron-hole pairs do not cover a distance long enough to prevent recombination due to their mutual coulombic attraction. Owing to this insufficient separation, a certain fraction of the photogenerated carriers recombine before the transport process can separate them permanently. As a consequence, the efficiency of free photocarrier generation must be taken into account when dealing with amorphous materials, and it acts to lower the quantum yield in comparison with crystalline materials. The clearest evidence for the presence of geminate recombination effects in passive films comes from the photocurrentvs-potential curves (photocharacteristics) at constant film thickness recorded under suprabandgap illumination with light of different wavelengths. In the absence of initial recombination effects, no influence of the photon energy on the shape of the Iph-VS-Ue plots is expected according to the simple G~_rtnerButler model valid for crystalline SCs. Moreover, the model predicts a linear dependence of Ip2h on the electrode potential [see Eq. (2.3.6)] as long as the surface and space-charge recombination rates are negligible, which has been confirmed experimentally at high electrode potentials. Even more complicated models for the photocurrent in crystalline SC/E1 junctions

PHOTOCURRENT SPECTROSCOPY OF THIN PASSIVE FILMS !

58

i

o 48

!

i

!

~,,-30enm n-O.B25

a~ _l~-

+

X-25~nm n-l. 333

_ J

/

!

!

r

~I,=370nm n--0.700

X

389

0.1

/

/

a) %=230 nm

n=0.80

b) L=270 nm

n=0.75

c) %=300 nm

n=0.67

J

i 1

I 2

b

38

%

\ =~- 2 8

0.05

18

0 -I

0 0

I POTENTIRL

2 /

V

3

4

(mse) 0

Fig. 18. Fitting, according to different power laws, of experimental curves of photocurrent vs potential for an anodic film grown on Ti at 2 V/s in 0.5 M H2SO 4 electrolyte, recorded at different wavelengths. [Electrochim. Acta 38(1), 29-35 (1993); reprinted with permission from Elsevier Science.]

t 0

-1

3

Potential / V(HgO) Fig. 19.

Ipnhvs electrode potential at different wavelengths for a Ta205 film

grown at 8 mA/cm -2 in 0.1 M NaOH solution up to 10 V (MSE).

do not predict any change of the shape of the photocharacteristics with the wavelength. In fact, however, the energy of incident photons affects the shape of the photocharacteristics, recorded experimentally for different passive-film-electrolyte junctions, in such a way that the curves are fitted as power laws, Ipnh vs Ue with n increasing for decreasing wavelength. Such behavior, depicted in Figure 18 for a thin anodic oxide on titanium, has been observed in amorphous semiconducting films on valve metals (a-WO3, a-Nb205, a-TiO2) [84, 85, 109-111 ]. In the case of insulating crystalline materials, one expects the photocurrent to depend linearity on the electrode potential, and the shape of the photocharacteristics to be independent of the photon energy, in the absence of trapping phenomena which could modify the electric field distribution [ 112]. In presence of trapping, phenomena sublinear behavior of the photocurrent has been predicted [ 113]. On the other hand, if trap-limited mobility of the photocarriers is taken into account, supralinear photocurrent behavior is expected only at very high electric fields--once again, independent of the photon energy [114]. The different behavior of amorphous materials is evidenced in Figure 19, displaying the photocharacteristics at various wavelengths for an insulating Ta205 anodic film [115]: a clear change of the supralinear shape with the wavelength is reflected in the different exponent n of the fitted power laws, all giving the same zerophotocurrent potential (about - 1.3 V with respect to HgO). A model for the initial recombination effects in amorphous materials, based on the treatment originally developed by Onsager for electrolytic solutions [116], has been proposed by Pai and Enck [117]. The model takes into account the threedimensional aspect of the generation of photocarriers and yields a mathematical expression for the efficiency of free carrier generation, Og, as a function of the electric field F and of the thermalization distance r0. The latter quantity is the distance traveled by a photogenerated electron-hole pair during the thermalization time. According to these authors the efficiency of

generation is given by the following expression:

kT (eFro) exp(-A) exp eFro kT

r/g(ro, F) = ~

x ~ - - ~ . ~'~ m=0

Z

n=0 l=m+n+l

eFr~ l x 1 kT J (3.2.4)

where k is the Boltzmann constant, T the absolute temperature, e the electronic charge (in absolute value), and A = e 2/4zr eeorok T. In Eq. (3.2.4) the only parameter the varies with the photon energy is the thermalization distance r0, which is a function of the excess energy h v - Eg, representing the difference between the energy of incident photons and the optical gap of the material. This excess energy is dissipated by collisions with the constituents of the material during the thermalization time. It has been suggested that in Eq. (3.2.4) an average dielectric constant between the static and the high-frequency values should be used. Anyway, the value of e affects the absolute value of r/g, but it does not change its functional dependences. This fact is evident in Figures 20 and 21, where the theoretical curves of rig as a function of the electric field and the thermalization distance are plotted for two different values of the dielectric constant. From the figures it is clear that both r0 and e act in the same direction, because an increase in either tends to lower the coulombic attraction between the photogenerated electron-hole pair (Poole-Frenkel effect). The mathematical structure of the Pai-Enck expression for /78 [Eq. (3.2.4)] is in agreement with a series of experimental results on passive films, showing the influence of electric field and photon energy on the shape of the photocurrent potential curves [84, 85, 109-111, 115]. According to these findings, we will use Eq. (3.2.4) for Og, both for insulating (constant electric field) and for semiconducting amorphous films. In this last case

390

DI QUARTO ET AL. 10 0

4

0

~

" " " ~""

10 "1

an average value of the electric field within the space-charge region will be used in Eq. (3.2.4) for calculating the generation efficiency to be used in the expressions for the photocurrent vs electrode potential (see Section 3.3).

lOA

3.2.3. Interference Effects during the Growth of Passive Films

10"

~"

10"

10"'

10 "s

1 0 . ,

. . . . . .

10 s

..,

. . . . . . . .

10'

,

. . . . . . . .

10'

,

101

. . . . . . . .

10'

F [V/cm] Fig. 20. Theoretical dependence of the efficiency of free carriers generation on the electric field, calculated from Eq. (3.2.4) for a material having e = 15. Different curves correspond to different values of the thermalization length. [Electrochim. Acta 38(1), 29-35 (1993); reprinted with permission from Elsevier Science.] 10 0 4O A

t,oA

10LA,

10"

,

SA

10" .................................... 10 s 10 ~ 10 i 10 e

10'

F [V/cm] Fig. 21. Theoretical dependence of the efficiency of free carriers generation on the electric field, calculated from Eq. (3.2.4) for a material having e = 48. Different curves correspond to different values of the thermalization length. [Electrochim. Acta 38(1), 29-35 (1993); reprinted with permission from Elsevier Science.]

In our opinion, one of the most interesting findings about the photoelectrochemical behavior of thin films in comparison with bulk materials is the appearance of interference effects in the photocurrent measured as a function of the film thickness. The phenomenon of multiple reflections of unabsorbed light in thin films is very well known, and it has been used in the past for obtaining information on the change of thickness of passive films during anodization [118-120]. In this case the light reflected from the metal-film-electrolyte function is monitored as a function of the film thickness. Less frequently has been reported the presence of interference effects on the measured photocurrent when photoconducting films are illuminated with photons having energy higher than their optical bandgap. Figure 22 shows the interference effects on the photocurrent measured during the anodic growth of an oxide film on tantalum metal under illumination with light having energy higher than the mobility gap of a-Ta205 (about 4.05 eV). Maxima and minima in the measured photocurrent as a function of the formation voltage (proportional to the film thickness) are very evident as long as the film thickness is much smaller than the light absorption length c~-1, so that the phenomenon is well observable for incident photons having energy slightly higher than the bandgap of the film. With increasing photon energy the interference effects disappear at progressively lower thicknesses, as expected for strongly absorbed light. Analogous findings have been observed with semiconducting oxide films both during the growth (variable thickness and nearly constant anodizing electric field) and with electrodes anodized up to different thicknesses and investigated at lower electrode potentials [ 121,122]. In the latter case, the photocurrent values recorded at constant wavelength and electrode potential on passive films grown on niobium up to different formation potentials have been plotted against the film thickness: the nonmonotonic behavior of these curves was analogous to previous findings on anodic TiO2 films [ 123]. The theoretical fitting of this phenomenon will be performed in the next section by taking into account multiple interference effects caused by the reflections of the light at the solution-oxide and oxide-metal interfaces (see Fig. 23), once the analytical expressions are known for the photocurrent in insulating or semiconducting amorphous films. It is worth mentioning here that the film thicknesses at which maxima and minima occur in the photocurrent intensity are essentially governed by the anodization ratio (expressed in angstroms per volt), which is the reciprocal of the anodizing electric field. In turn, the fitting of the curves reported in Figure 22 allows one to derive the kinetic parameters for the film growth. The possibility of obtaining the growth parameters of the films by simply recording the photocurrent during their growth opens a new

PHOTOCURRENT SPECTROSCOPY OF THIN PASSIVE FILMS

391

1.5 wavelength = 300 nm a) 100 mV/s b) 200 mV/s

l,t

0.5

0

80

160

Cell voltage / V

Fig. 22. Photocurrentintensity vs formation voltage for passive films growingtensiodynamically on Ta at different growth rates in 0.5 M H2SO4 solution, under monochromatic irradiation with )~= 300 nm.

in organic-anion-containing solutions under illumination with photons having energy much lower than the bandgap of A1203 (-~6.3 eV). The intriguing aspect of such experiments is the occurrence of the interference effects only in the presence of selected organic electrolytes, which favor the incorporation into the anodic oxide of species originating a band of defects within the forbidden gap of the a-A1203 film. Support for this interpretation comes from both the anodic photocurrent spectra and experiments performed successively in different electrolytic solutions containing or not containing the organic anions [ 125].

3.2.4. Photoemission Phenomena at the Metal-Passive-Film Interface

Fig. 23. Opticalmodel for multiple internal reflections at the metal-passivefilm--electrolyte junction. The light flux is partially transmitted and partially reflected at both the interfaces.

prospect for investigating the influence of the absorbed light on the kinetics of growth of passive films as well as on their solid state properties during growth [120, 121,124]. Another interesting finding, reported in Figure 24, is the presence of interference effects in the recorded photocurrent during the anodization of electropolished aluminum electrodes

In this sub-subsection we discuss the role of the inner metalfilm interface in the generation processes under illumination for thin passive films. In this case, regardless of the wavelength of the incident light, a large fraction of photons impinging the oxide-solution interface arrive at the metal-film interface, where the electrons in the metal surface can be excited to higher energy levels, leaving vacant states below the Fermi level of the metal. The fate of the excited states in the metal depends on the occurrence of different physical deactivation processes at that interface. Besides thermal deactivation by scattering of excited electrons by lattice vibrations, photoemission of excited photocarriers of the metal can be observed. In the case of very thin passive films (dox < 2 nm), external photoemission processes become possible, by tunneling of the electrons or holes excited at the metal surface through the film. Although a hole photoemission process was suggested years ago in the case of a gold electrode covered with a very

392

DI QUARTO ET AL. 100 growth rate=200 mV/s ...... growth rate = 20 mV/s .
5 nm), where the external photemission processes are forbidden owing to a very low probability of tunneling through the film, the possibility of internal photoemission due to the injection of photoexcited electrons (or holes) from the metal into the CB (or VB) of the passive film must be considered. In such a situation the internal photocurrent emission varies with the photon energy according to the so-called Fowler law [ 130, 131 ]: lph -- const(hv - Eth) 2

(3.2.7)

where Eth is the internal photoemission threshold energy, which can be obtained from a plot of ip0h5 vs the photon energy. This threshold is a measure of the distance in energy between the Fermi level of the metal and the edge of the film CB (electron

PHOTOCURRENT SPECTROSCOPY OF THIN PASSIVE FILMS photoemission) or VB (hole photoemission). The occurrence of electron or hole internal photemission in the case of insulating films is established by the direction of the electric field, and in turn by the electrode potential value with respect to the inversion photocurrent potential. In the absence of trapping effects, the inversion photocurrent potential can be used to determine the flat-band potential of insulating passive films.

...ou:.o v.,,,v,.,E, .) u =-1.8 vms~>

u

o o

//

/So

u=-,,

Obviously, Eqs. (3.2.5) and (3.2.7) can be referred also to the photoemission yield (Iph/e~o). In the case of insulating anodic films on valve metals, internal electron photemission processes are usually observed under cathodic polarization and under illumination with photons having energy lower than the optical bandgap of the film [127, 129]. In Figure 27 we report the determination of the internal photoemission threshold for an anodic oxide film grown on electropolished aluminum metal. It is interesting to note that, for anodic oxide films grown on A1 irradiated with photons having energy lower than the bandgap of A1203 (Eg ~ 6.3 eV), the cathodic photoemission process is always observed, regardless of the anodizing conditions and the metal surface treatment, whilst an anodic photocurrent spectrum is recorded only for films anodized in solutions containing organic species [125] or when a hydrated layer is formed on the surface of the films [132]. Moreover, we mention that in the intermediate range of film thickness, between the very thin (__5 nm) anodic films grown on aluminum, the presence of a variable cathodic photoemission threshold, due to the quantum size effects, has been hypothesized [ 127]. In Table IV we report the cathodic internal photoemission thresholds for a series of insulating oxide films grown on different valve metals; these allow one to locate the energy level of the conduction band of the oxide films with respect to the Fermi level of the underlying metal, once the work function of the metal is known. In the case of semiconducting films no internal photoemission is expected, owing to the absence of any electric field at the metal-film interface.

/o .) /

Z ~

/=7

4
> 1 and otXsc 1 and afortiori otdf >> 1) Eq. (3.3.8) gives the same saturation limit as the Crandall equation (3.3.7), but there are appreciable differences in the photocharacteristics before the saturation. In this last case the more rigorous Crandall equation will be used. For values of film thickness and absorption coefficient obeying the relationship c~df > r' is satisfied everywhere. Then p l r - r'l - pr~/1 + (r'/r) 2 - 2(f. r')/r ,~ pr - p'. r' (13)

~ exp(-iept)

f (2jr)3/2 "q e x p ( - i p 9 A q t ) x ( q ) e x p ( i q . r)

-- exp(iept) f (2Jr)3/2 dq exp[iq- ( r - Vpt)]x(q)

(20)

t /

where Vp = p is the group velocity of the wave packet. By comparing the first and final expressions of Eq. (20), we can see that ~0 is simply represented by 9 0(r, t) ~ exp(iept)~o(r- Vpt, 0)

(21)

This demonstrates that the packet indeed moves with velocity Vp along the classical trajectory without distortion.

418

FUJIKAWA

We now tum to the term ~]k (r, t) in ~ + involving the spherical wave part of Eq. (12), 9 l:k(r, t) =

lfdqfdr, eXp(+iqlr-r'l) Ir - r'l

If (2:r)3/2 dq x ( q ) e x p [ i ( q r - E q t ) ] f ( p '

9 ~(r,t) ~ r

2zr

x V(r')4~(r') exp(-iEqt)X(q)

and we have the asymptotic form of ~ - from Eq. (22) by using the symbol defined by p~ - p f at the infinite future,

(22)

We shall refer to ~1:k as the scattered packet. The q-integration in (22) will give a negligible contribution unless we are at the point of the stationary phase, which is determined by 0 0q [u (q) -- Eq t 4- q Ir -- r'[ 4- ~.q+ (r')]p - - 0

q) (26)

We shall now make the additional assumption that f(p~, q) varies sufficiently slowly in the interval Aq to permit its replacement by f(p~, p). As before, Eq ,~ --Ep 4. q " Vp, and qr is approximately replaced by ( q . ~)r; then ~ + ( r , t) becomes 9 +(r, t) ~ f ( p l , p) e x p ( i e p t ) d P o ( p r _ Vpt, 0)

(t ~

cx~)

F

where u is the phase of X (q) and ~.ff (r') is the phase of ~b~ (r'). Because of the presence of V (F) in the integrand in Eq. (22), the variable r ~ is confined to the region specified by r ~ < a, where a is the range of the potential. In analyzing Eq. (22), we must therefore bear in mind that r I < a. Since ~ l ( r , 0) is assumed to have its maximum at - z 0 p (z0 is macroscopic), we require the stationary phase point of the integrand of (18) to be 0u = zoo 0q

(23)

The stationary phase point of ~]L is therefore determined from 0 ~ : (r') (ZO -- Vpt 4- [r -- r'l)O 4-

0q

p

-- 0

(24)

If r in the defining equation for 4 ~ ( r ) is microscopic, there are simply no macroscopic lengths in Eq. (12), and all lengths characterizing 4~ (r) for such values of r must themselves be microscopic. In particular, the length 10)~/0ql should be microscopic. At time to the wave packet will actually hit the target. For t to, zo - Vpt is a macroscopic negative value, and I r - F [ (r ~ < a) must be macroscopic if Eq. (24) is to be satisfied. Thus for t >> to, ~ + is nonvanishing in a shell of radius vet - zo - Vp(t - to). In the same way, if we use the incoming wave in Eq. (24), we find that ~ 1 vanishes for t >> to, and ~ - ( r , t) ~ ~0(r, t) for such later times. We now study the behavior of ~ + for r >> a and t >> to. In this case Opt is macroscopic, and Eq. (24) is satisfied for macroscopic r. Since r >> r ~ everywhere, I r - r'[ ~ r - ~. r'

(25)

(27) In the same way we obtain the asymptotic behavior of ~ 1 at the infinite past, 0 1 ( r , t ) ,~

f - (p', p)

exp(iEpt)4Po(-Or - Vpt, 0)

F

(t ~ - c ~ )

(28)

The propagation of the wave packets ~ + is schematically shown in Figure 2. From the above discussion we see that we can select the proper boundary condition for each experimental method. For example, we have to use the boundary condition for photoelectrons because we measure their momenta at t >> 0. In the case of EELS, the incident wave with momentum p is described by ~+, and the scattered wave with momentum pl is described by ~ . For practical purposes we use the time-independent stationary states ~b~:instead of the wave packets 9 ff.

2.1.2. P a r t i a l W a v e Expansion

When the potential V(r) is spherically symmetric, it is convenient to use an angular momentum representation of the scattering functions Cpp a:. We can write the plane wave ~po as dp~ =

2~~ ~

iljl (pr)YL (r)Y~ (P)

(29)

L

The total wave function 4~- can also be written as a superposition of partial waves, dp+ =

2s/~ Z

iIRl(pr)YL(~)Y;(o)

(30)

L

From Eq. (5) Rt should satisfy the integral equation Rl(pr) = j l ( p r ) 4.

f

gqp)(r, r t ) V ( r t ) R l ( p r t ) r '2 dr'

(31)

where gp(l) (r, rt)'S are expansion coefficients of the free propagator go given by Eq. (9), g0(r - r') -- Z L

g(p/)(r, r') YL(r) Y~ (r')

(32)

ELECTRON ENERGY LOSS SPECTROSCOPY define the phase shifts

III

419

61(p) as

exp[2irt(p)] -- 1 - 4ip

Ill

f jl(pr)V(r)Rl(pr)r 2 dr

The asymptotic form of the radial solution from Eq. (31),

Before the Collision

(34)

Rl(pr) is written

i-l-1

Rl(pr) .~ 2pr {exp[ipr + 2irl(p)] - ( - 1 ) / exp[-ipr]} -- exp[iSl(P)l sinlp r

lyr

--

2

pr

} + 6l(p)

(35)

exp(ipr)/r represents the outgoing spherical wave and exp(-ipr)/r the incoming spherical wave, we obtain a con-

As

dition for the probability conservation,

lexp(2irl)l- [ ( - 1 ) / I - 1 that is, the phase shifts 8t should be real. It is important to relate the phase shifts to the scattering amplitude defined by Eq. (3). For this purpose we calculate the asymptotic form of ~b+ - q~o at r >> a with the use of Eqs. (29), (30), and (35),

After the Collision

(a) r

~ _ ~o .~ (2yr)-3/zexp(ipr______~)f (p,, p) F

= (2yr)-3/2 exp(ipr_______~)4y r F

exp(2i 6t) - 1

After the Collision

x Z

2ip

L

YL(~) Y~ (P)

(36)

Therefore we can write the scattering amplitude in terms of the phase shifts, f (p', p)

= -47r Z 0 (P) YL (P') Y~ (P) L cx)

= - Z(2/+

1)tl(p)Pl(cosO)

(37)

/=0

0 = -

Before the Collision

(b) Fig. 2. The wave packets (a) ~ + and (b) ~ - before and after they arrive at the scattering center.

exp(2irl)- 1

2ip

Here 0 is the angle between ~ and ~ , and 0 (p) is closely related to the T matrix discussed later. We can demonstrate the optical theorem where the total scattering cross section a(p) is related to the forward scattering amplitude [5, 19-21 ], 4Jr a (p) = ~ Im f (p, p) P

This is written in integral representation and in terms of the spherical Hankel function ht and the spherical Bessel function jl,

(38)

(39)

2.2. Formal Scattering Theory

2.2.1. T Matrix g(lp)(r, r') = --1 f_~ dq Jl(qr)jl(qr')qZp2 2 yr ~ - q +i~ = --2iphl(pr>)jl(pr = max(r, r ~) and r< - min(r, r'). When r is outside the potential region, the condition r > r ~ is satisfied. We now

We now follow Gottfried's treatment for the time-dependent approach to general scattering theory [19]. Let It) be a solution of the complete Schr6dinger equation, i~-~ - H

It) - 0

(40)

420

FUJIKAWA

The Hamiltonian H -- H0 + V is assumed to be time independent. For early times It) tends to It)0, where i~-~ - H0 It)0 -- 0

where G + ( E ) = 1 / ( E - H + io). Let consider the transition a --+ b (a ~ b). Because of the orthogonality condition, we have, from Eq. (47),

(41)

Although It)0 coincides with It) for - t >> 0, the former is not a solution of Eq. (40) once V comes into play. We may now construct an integral equation that incorporates Eq. (40) and the initial condition. As usual, we write

(b[a(+)) -

From this we can calculate the transition rate Wa-+b, in the limit 1/--+0, Wa--+b --

i ~-~ - H0 It) - g l t )

(42)

and introduce a Green's function (Green's operator) that satisfies i - ~ - Ho G(t - t') = ~(t - t')

(43)

T(b, a) -

a(+)(t -t')vlt1(+))dt '

(45)

The notation It(+) ) is intended to emphasize that the solution of Eq. (45) will tend to the free wave packet It)0 as t --+ - c ~ . We shall require these special states that are actually eigenstates of H. These states shall be denoted by la (+), t) la (+)) e x p ( - i Eat). The symbol a incorporates all of the quantum numbers necessary for the specification of the state. The corresponding stationary state belonging to H0 is written as la, t) -- la) e x p ( - i Eat). Because we are concerned with states belonging to the continuous rspectrum we have to assign the same energy eigenvalue Ea to both la) and la(+)). Retuming to Eq. (45), we have exp[i(H0 - E a ) t ] V [ a ( + ) ) d t

(46)

o> 1, we obtain the simple expression W(RI, fl)r ---->i/pr 2, so that we get al -- -2ip. Finally we obtain the explicit formula of gl as

gl(r, r') = --2ipRl(r)

(97)

Next we derive the formula to shift the origin around which angular momentum expansion is applied. From now on we use k instead of p. First we calculate the following integral representation for the free propagator (see Eq. (9)), 2 g0(r + R - r') - (2Jr)3

f

exp[q. (r + R - r')] dq k 2 _ q2 + it/

(98)

i I1+12-13

L1L2L3

fo ~176 Jll(qR)Jl2(qr)Jl3(qr')q2 dq k2 _ q2 + i77 (99) , (2)

Noting that j t ( - r ) = (-1)l jr(r), jl(r) = [hi(r) + n 1 (r)]/2, and that the Gaunt integral G(L1LzIL3) defined by f YL,YL2Y~3d~ does not vanish only for 11 + 12 -+- 13 -- even, we can replace the integral f o dq with 89f _ ~ dq in Eq. (99). As we can assume that R > r + r', the integral in Eq. (99) now becomes

_if_ 4

"~

~

--+ i - 1 - 1

[hq (q R) + tttl (q R)]Jl2 (qr)Jl3 (qr')q 2 k 2 - q2 + irl

exp(ix)/x,

h}2)(x) --+ i l+l e x p ( - i x ) / x

(100) From these relations hll(qR)Jl2(qr)Jl3(qr') behaves like exp[iq(R 4- r 4- r')] on the very large semicircle in the upper half complex plane, and the counter-integration on the semicircle completely vanishes. The residue analyses give us the result of the integration,

1 4

• YL1 (R)YL2ff)Y~3ff')G(L1L2IL3) (102) Substituting r = 0 in Eq. (102) and using the relations jl(0)YL(f) = 3 L , 0 0 / ~ , G(LIOOIL3) = 3L1,L3/V~-~, weobtain the formula shown by Eq. (33). We can see that IR+rl > r' if R > r + r t. From Eq. (33) we thus have g0(r + R -

r')

= - 2 i k ~ hl(klr + RI)j,(kr')YL(r-'~-R)Y[(~')

(103)

L

Comparison of Eq. (102) with Eq. (103) yields an important relation,

= 47r Z

il'+12-tht, (kR)jt2(kr)YL1 (fi) YL2(~)G(L1L2[L) (104)

ElL2

GLu(kR) - -4zrik ~

il'hll(kR)YL1 (R)G(LILIL') (105)

L1

dq hl~ (q R)jl2 (qr)Jl3 (qr')q 2 ~ k 2 _ q2 + i~ rri k - - - - - - - ~ h l l (kR)jt2(kr)jl3(kr')

g0(r+R-r')

il-I'GLL'(kR)jl(kr)YL (~)jl,(kr')Y~,(f')

= 2Z LL t

(106) From Eqs. (104) and (105) we have a useful relation for shifting the origin,

-ikhl(klr + RI)YL (r-'~R) = Z il'-1GL'L (kR)jl,(kr)Yc,(f) L~

(107) When we put r = 0 in Eq. (98) and in Eq. (102), we obtain an integral representation,

. (2)

The asymptotic forms of the first and second kinds of Hankel functions are

hi(x)

it~+t2-13hll(kR)jt2(kr)Jl3 (kr')

L1L2L3

then g0(r + R - r t) is written in terms of GLL,(kR),

• YL~ (R)YLzff)Y*L3 ff')G(LILzlL3)

dq

go(r + R - r') - -gyrik Z

Now we define GLL,(kR) as

r')

-- 16 ~

Noting that h~2)(-x) -- (-1)thl(x) and using the parity of spherical Bessel functions mentioned above, we find that the integral including the function h~2) is the same as Eq. (101). Then we obtain the result,

ht (klr + RI)YL ( r - ~ R )

By use of the angular momentum representation of each plane wave shown by Eq. (29) we find that g0(r + R - r') is also written as g0(r + R -

423

- 2 i k Z hl(kR)j,(kr)YL(R)Y~(f) L

_ 2 [ -- (2yr)3 j

exp[iq. ( R - r)] dq k 2_q2_+_i~

(108)

We now multiply both sides of Eq. (108) by jl,(ktr)YL,(f) and integrate over r, and then we obtain

-2ikhl,(kR)YL,(R)

~(k - k') k2

8yri -1' f exp(iq- R) 6(k' - q) = (2yr)3 ~ k 2 _ q2 + i 0 q~ YL'(q) dq

(109)

where we have used the orthogonality relation, (101)

jl(kr)Y[(~)jl,(k'r)Yu(~)dr - -~6LL'6(k -- k')/k 2 (110)

424

FUJIKAWA

Again we integrate Eq. (109) over U, and we find that i-t f

exp(iq- R)

-2ikhl(kR)YL(R) -- --~ ., k 2 _ q2 + ioYL(~t)dq

(111)

In the above equation the sum over 14 is restricted to ll 4- 1 and 12 4- 1, so that we have a simple relation between those Gaunt integrals. From Eq. (105) we can obtain the recurrence relation between GLL, conserving m and m t with the aid of Eq. (118),

The substitution of Eq. (111) into Eq. (105) yields an integral representation of GLL,(kR), GLL,(kR) = 2 f

exp(iq-R)

-~

k 2 _ q2 ~ io Y~(r162

al+l,mGl+l,m;U -t- al,mGl-l,m;U -- al,+l,m~GL;l,+l,m, at- al,,m, GL;F_I, m,

(112)

(119)

where

In the above derivation we have utilized the identity

~ (l + m)(l - m) Z YLI (r

LIL')

alm -

(120)

( 2 / + 1 ) ( 2 / - 1)

L1

For the special case where I = 0, we obtain the relation L1 L1

= S dO~(~i - O)Y~(O)YL'(O) = Y~(q)YL'(q) (113) By use of the integral representation (112) and the parity of the spherical harmonics YL( - r ) = ( - 1)IyL (f), we have a symmetry relation of GLt., (kR), GLL,(-kR) = (-1)l+rGi~i..,(kR)

(114)

almGlm;U -- (al'+l,m'GOo;l'+l,m' + al'm'GOo;l'-l,m')~m,O (121) From Eq. (121), we can obtain the expressions for GlO;U in terms of Goo;l,+l.m~, and from Eq. (119) Gz0;L, in terms of Glo;Y+l,m ~and G00;u, and so on. To obtain the matrix elements such as Gl,+l;U from Glo;u's, we have to derive a recurrence relation to change m. We now use the relation between the Gaunt integrals,

Furthermore, we obtain another symmetric relation by use of the property YL(r) = ( - 1)m y~ (~), where L = (l, - m ) ,

GLL,(kR) = (-1)m+m'G[.,[_.(kR)

f YI,+I (r)YL3 (r) YL1(r) YZ2(~) df = ~ G(Lll, •

(115)

4- llLe)

14 Combining Eq. (114) and Eq. (115), we obtain the following useful relation:

GLL,(-kR) = (-1)I+I'+m+m'GL,L(kR)

(116)

These symmetric relations reduce the number of matrix elements to be calculated and save storage memory in XANES and ELNES analyses [24, 25, 144]. To reduce the computation time further, some recurrence relations between GLL,(kR)'s are useful, which are discussed in [25]. The direct calculation of GLL, (kR) requires much computation time, but the simplest elements, such as G00,L (kR), are easily calculated from Eq. (105), G00,L (kR)

--

-~4-~Cl

b+Gl+l,m+l;L ' + bL G l - l , m + l . U

---- -b+l',-m' GL;I'+I,m'-I - b~7,_m,GL;I'-I,m'-I b l,-m + a t + l ,m- 1;U + bl,- m G l - l , m - 1 ; U : -b+,GL;l,+l,m,+l - buGL;l,_l,m,+l

b+ (117)

To obtain other elements of GLL,(kR) conserving m and rn t, we apply the relation

f YIO(~)YL3(~)YL1 (~) Y/~2(f) d~ = ~_, G(L1 lO]I4)G(L314mllL2) 14

14

From Eq. (105) we obtain the recurrence relations changing m and m t by 4-1,

(123)

/

where z = i/(2kR) and Cl(Z) is defined by the relation

= Z G(L21OI14)G(L3LI]14)

(122)

14

where

(z) YL(R) exp(i kR) / R

hl(kR) = i -l-1 exp(ikR)cl(z) kR

G(L21, q:lll4)G(L3Llll4)

= - ~

(118)

b~

[ ( l + m + 1 ) ( / + rn + 2)

V

2 ( 2 / + 1)(21 + 3)

_ / (l

V

-

m)(l

-

m

-

1)

2(21 + 1)(21- 1)

(124)

From these recurrence relations and symmetric relations we can calculate all of the matrix elements of GLL,. The Green's function gA for the full potential VA at site A is expanded in angular momentum representation as in Eq. (88). Now let us consider the situation where r is in the region at site R, and r t is in the region A. In this case Ir + RI > r t is satisfied, and 36 is simply replaced by hi. We can thus apply the origin

ELECTRON ENERGY LOSS SPECTROSCOPY shift formula (104) and have an origin shift formula of gA,

gA (r + R, r') = ga (r t, r + R)

= :2E il-l'exp(iS~')GLL'(kR)jl(kr)YL(r)Rl'(r')Y; '(~') LL' (125) where Rl (r') is written as Rl (r') = exp(i 8A)/~t (r'). The radial function R is real for the real potential VA (see Eq. (95)). Of course, Eq. (125) is reduced to Eq. (106) when the potential VA is switched off. This formula is very important for the study of EELFS spectra as discussed later.

2.3.3. Site T Matrix Expansion for No noverlapping Potential

T = V + VgoV + VgoVgoV + . . . + E v•176

+""

= E ( v a + v~gova + vagovagova + " ") Ol

+ Z ( v 3 + v3g~

+'")g~

= E t ~ + E t3g~ + E

3.1. B a s i c T h e o r y o f E l e c t r o n S c a t t e r i n g

At a high enough energy of the scattering electron, its identity with the electrons in the target may be neglected. We can then use a product space for the total state vector, with the scattering electron in one space and the electrons in the target in another. Exchange effects between scattered and target electrons are thus neglected. We use the following Hamiltonian: H -- Te + Hs + Ves

(129)

Te is the kinetic energy operator for the scattering electron. Hs is the many-body Hamiltonian for the target. Ves is the total Coulomb potential between the scattering electron and the target,

Ves- E E C?klCk2[(kllllvlk212)C?llCl2-+-(kllVenlk2)] (130) klk2 lll2

When the potential is given as a sum of nonoverlapping atomic potentials V - )--~c~v~, we have an expression for the total T matrix expanded in terms of site T matrix from Eq. (54),

: E v~ + E v3g~

425

+ v~gov~ + . . . ) + . . . t•176176

+""

(126)

where Ven is the Coulomb interaction between the scattering electron and the positive nuclei, and (... Ivl..-) is the usual two-electron matrix element of the Coulomb potential 1/r12. The one-electron states of the scattering electron are denoted by k, and those of electrons in the target by 1. The indices k specify both momentum and spin. The indices l correspond to whatever quantum numbers are pertinent for the electrons in the target, such as crystal momentum, band index, and spin. It is convenient to introduce some subsidiary quantities defined by

H = Ho+V H0 = Te + (~0lVesl~0) + Hs = h0 + Hs

V = Ves- (O0lVesIO0) h0 = Te + VH

Here we define the site T matrix at site c~,

(131) (132) (133)

Wn = (O01VeslO0) to~ :

va + va go va + va go va go vu + 999

= va + vagota

= E (127)

By use of the site T matrix expansion of T, we have a useful expression for the Green's function g from Eq. (53),

g -- E g~

+ E t3 + E

t•176 + ' " ) g ~

(128)

where ga - go + got~go is the full Green's function under the influence of the potential v,~ at site or. These formulas are extensively used in the EELFS analyses discussed in Section 5.

3. M A N Y - B O D Y

ELECTRON

SCATTERING

THEORY

In this section we discuss some rather general formulas for electron scattering from solids [9], which describe the effects of losses. The results are given in terms of one-electron expressions involving dumped one-electron functions and optical potentials, which are important for explaining why EELS spectra are surface sensitive.

E C t k , Ck2 (kl/llvlk2/2)(~01c;lc/21~0)

klk2 lll2 + (kllVenlk2)

(134)

where 1~0) is the ground state of Hs. The states with index k in Eqs. (130) and (134) are scattering states of h0 with outgoingwave boundary conditions

h01~-) - "p 1~-)

(135)

and ~p -- p2/2. The transition matrix for scattering 0p ~ np t can now be written from Eq. (50) as

Z(np t, 0p) --(np'l Ves]~P~p)

(136)

where Inp') is an eigenstate of Te + Hs, Inp') -- I~n)lr ~ (where [~n) is an eigenstate of Hs, nslaPn) = EnlaPn), and ]~P~,) is a plane-wave state) and I~P~p) is an eigenstate (outgoing-wave solution) of H. We write this latter state, using the Lippman-Schwinger equation (48), as

I ~ p ) - [1 +

a(E)V]lO+p)

(137)

where G(E) = (E - H + it/) -1, 0 is a positive infinitesimal, and I~-p) is an eigenstate of H0. IO+p), like Inp'), is a direct

426

FUJIKAWA

product I~+p) - I~0)1~ ), and I~o)(= 10)) is the ground state of Hs. The energy E is the total energy, E - Eo + e p = En +

Ep:.

Collecting our results, we obtain (1 +

av)10>lN) -

We now have for the transition matrix,

x (,p - ho +

T(np'; 0p) - (nP'lVes[1 + G ( E ) V ] I r

= (~b0,l(nIVes[1-+-G(E)V]IO)Iqb

+)

(138)

T (np'; 0p) is thus given as a matrix element of a one-electron operator (nl Ves[ 1 + G ( E ) V] 10). This operator in turn is a matrix element involving correlated target wave functions ~n and ~o. To evaluate this complicated operator we make an expansion of G ( E ) in terms of diagonal operators of the Van Hove type. Such an expansion can be done by projection operator techniques. We introduce the projection operators, P -10)(0l,

Q = 1- P

(139)

We then define a new unperturbed Hamiltonian and its corresponding perturbation, 171o - Ho + Q V Q,

f/=PVQ-4-QVP

(140)

Because P V P = 0 [cf. Eq. (132)], we have H -- Ho + V Ho -4- V. From our definitions in Eq. (140) it trivially follows that

~1o)-

(1 q- GoV)I0)[Ep - h0 - E ( E ) q-it/] -1

rio)

Hol0) --= Hol0) -- (Eo + ho)10)

(141)

The Green's function related to Ho, Go = (E - Ho + i~)-1

(142)

has the properties QCJoP = P ( 7 o a = O, P G o P = P G o P = P ( E - Ho + irl) -1

(143)

as easily follows from the identities Go - Go + G o Q V Q G o - Go + G o Q V Q G o

i~)1%+)

(148)

We can now define a one-electron function for a dumped outgoing wave by

[~;)

-- [•p -- h0 - ]E ( E ) -+- i t/]

-1 (,p -- ho + i0)1~-)

-- io[6-p - ho - E ( E ) -1- /O] -1

+)

= (1 + [ep - h0 - E ( E ) + i r / ] - I E ( E ) ) [ r +) (149) Clearly from Eq. (48) I!/r+ ) satisfies the equation [,p - ho - E ( E ) + it/] [!P~-)-- 0

(150)

We now have a formally exact expression (within our basic approximations, stated at the beginning of this section) for the scattering amplitude T(np'; 0p) = (r176

+ (~o(E)V]10)lgr+)

(151)

This expression is valid for inelastic as well as elastic scattering. If we compare Eqs. (151) and (138), the only differences are that Ir +) is replaced by a dumped wave Igr+) and that G is replaced by (~0. We obtained our new expression for T by rearranging the perturbation expansion in V in such a way that the state 10) never appears as an intermediate state. Thus the effects of coherent scattering are summed exactly and taken into account by the dumped wave function lgr+). The quantity E is an optical potential, which will be discussed in detail later. To the lowest approximation E is an imaginary constant inside the solid and zero outside; hence the solutions of Eq. (149) are dumped states. We note that T is still given by a one-electron formula and that the one-electron operator (hiVes(1 + GoV)I0) is still defined from a matrix element involving correlated target wave functions.

(144) 3.2. Elastic Scattering

We want to rewrite (1 + GV)I0) in Eq. (138), which by Eq. (141) equals (1 + G I7')10). Expanding G in powers of I), G = (~0 + (~of'O0 + (~0Q(~oVOo + (~0PO0f'(~of'50 + ' " (145) and collecting even and odd powers of V in the expansion of 1 + G V, we have 1 + GI) -

Before turning to inelastic scattering in the next subsection, we give a short discussion of elastic scattering, showing how our results in the previous subsection relate to the exact formula obtained by Bell and Squires [26]. From Eq. (151) we have T(0p'; 0p) = (r176I(0[Ves(1 -4- 50v)10>1% +) and from Eqs. (141) and (147),

(1 + (~oV)(1 - (~oV(~ol)) -1

(0lEes(1 -q-(~oV)[0) -- (01V~sl0)+

- (1 + ( ~ o V ) ( E - H o - V(~oV + it/) -1 x (E - / t o + it/)

(147)

(01f'Gof'10)

: VH + E ( E )

(146)

By Eqs. (141) and (143) we can replace (E - / ~ o + ir/)10) with (ep - ho + ir/)lO) and (E -/-)o - I?C, ol? + ir/)lO) with [ep ho - E ( E ) + i~][0), where we define the non-hermitian optical potential for the state [0), E ( E ) = (0lg(~0(E)f'10)

(152)

(153)

Thus T(0p'; 0 p ) = (r176 [VH + E ( E ) ] [!k+)

(154)

which is the same expression as obtained by Bell and Squires [26], except that E ( E ) as defined in Eq. (147) lacks the first-order (unscreened) exchange term and the second-order

ELECTRON ENERGY LOSS SPECTROSCOPY exchange terms. It contains, however, the very important dynamical polarization (cf. next subsection). The lack of the exchange terms is clearly due to the fact that we have regarded the scattering electron as distinguishable from the electrons in l the target. We will find later that we can easily recapture exchange (cf. Section 3.4). From Watson's theorem for two potential scattering (see Section 2.2.3, particularly Eq. (78)), we can rewrite Eq. (154)

as T(0p'; 0p) =

lp+>

(155)

3.3. Inelastic Scattering

In the last subsection we specialized our general expression for electron scattering to the case of elastic scattering. In this subsection we will take up the main topic, inelastic scattering. The general expression for electron scattering is given in Eq. (151). Go given by Eq. (142) contains the interaction potential V = Ves - (01Vesl0). We will do a perturbation expansion in V in such a way that all "coherent" contributions are eliminated. By a "coherent contribution" we mean a term in which two intermediate states are equal, or one intermediate state coincides with the initial 0 or the final n state of the target (which are different for inelastic scattering). Such an expansion can be made with projection-operator techniques. We use a slightly different definition of H0 and V; H0 now includes the diagonal part of Ves, and V has zero diagonal elements, (nlVIn) - O,

Ho - Te + Hs + ~

T(np'; 0p) --(q~~ (nlVes + VesGr(E)Ves[O)[~ )

n H -- H0 + V

(156)

Qon projects away the states 0 and n, Qon - 1 - P o - Pn

(157)

where as before, Pn = In) (nl. We now put a prime on the quantities used in Sections 3.1 and 3.2; H~ = Te + Hs + (0lVesl0) and V' = Ves - (0[Vesl0). H -- Te + Hs + Ves is unchanged. The projection operators in (140) refer to eigenstates of Hs. The full space of eigenstates to H0 is given by the product space of eigenstates of Hs and of hn -- Te + (nlVes In), {In), q~+}. In Eq. (151) we have the term GoQ - Q ( E - H ~ - Q V ' Q + i o )

-1.

Here Q is the same as that in Eq. (139). Furthermore, (~0Q G 6 since H~ + QV'Q - re + Hs + (0lVesl0)-+- Q ( V e s - (01Vesl0))Q

= Te + Hs + eVesP + QVesQ -- Ho + Q v a

(n # 0) (160)

First we will rewrite this equation so that G 6 is replaced by Goa, where Grh = Q~176

= Q o n ( E - H O - QonVQon -Jr-it/)-1 (161)

We insert 1 - Pn + Qn to the right of G 6 in Eq. (160). The contribution with Pn is (nlVes + VesGoPnVeslO) = (1 + (nlVesGoln))(nlVeslO). The remaining contribution is (nlVesGoQnVeslO). Since Qon = QoQn and Qo - Qon + Pn, we have G OQn = G OQon -- Grh -k- Gr(Qon V Pn -+- Pn V QOn)Grh = G6~ + GrPn VGr~ - Gra + GrPn VesG6~ (162) which gives (nlVesGrQn Ves 10) = (nlVes(GOr, + GrPn VesGrn)VeslO) = (1 + (nlVesGrln))(nlVesGrr, VeslO)

(163)

Combining this with our first term of Eq. (160) gives r (npt; Op)

--(~b0, l(1 q-(n[VesGoIn))(n[Ves--I-

VesGOfiVeslO)llP;)

(164)

Pn Yes Pn

Yes - ~

Equation (151) now becomes

enVesPn

n v -

427

(158)

The first step, replacing G O with Gr,~, is now completed. It remains to rewrite (4~~ + (nlWesGoIn)) as a dumped wave function. For that purpose we use expansion in diagonal Green's functions developed by Hedin [27]. We note that V -- Q V Q = V0n + f'0n, where Vo,, = Qo,, V Qon, f'0n = PnVQOn + QonVPn, and Goln ) - (Pn + Qon)GOPnln). We now introduce an unperturbed Green's function, Gr~ = (E - Ho - Von -I- i 0 ) - I

(165)

Expanding G O in powers of Von, we obtain the result P n a r P n -- Pn(ar--h 1 -- Vonarh Von)-l pn

= Pn[E - HO - EOn(E)]-lPn

(166)

where the optical potential EOn(E) is defined by E0n(E) = (nIVGraVIn)

(167)

the properties of which are discussed later in detail. For convenience we introduce a diagonal Green's function Gdn (E), adn(E) - aoen(E

- n o - TOn(E) + ir]) -1

(168)

where G 6 is defined by (Q - Q0) G O -- Qo(E - Ho - QoVQo + it/) -1

(159)

Equation (166) is thus written as Pn GO Pn - Pn Gdn en. In the same way we have the relation QonGoP n - Gr~VPnGdnPn.

428

FUJIKAWA

With the use of this identity and Eq. (166), we can get an expansion in terms of the diagonal Green's function [9, 27], Goln ) -- (1 + GonV)G~nln ) __ ( a d n . 4 _ ~

All of this may look rather abstract and useless. However for extended excitations, as discussed later (Section 4.3), EOnt El. Furthermore, as discussed in Section 4.3, El (E) -- E0 (E E1 + Eo) and ho ,~ hi. We then have

~p,On-- ~ ~p,

d k V Gdn Gon k

+ Z dGOnklVGOnkVGdn d ) "'" In)

Z,Onl(E) "~ E 0 ( E -

(169)

k#l Taking a particular term in this expansion, the same intermediate state can never appear more than once. The expansion describes "coherent" propagation, described by the diagonal operators, interrupted by inelastic scattering events. The optical potential provides a shift in energy and some damping in the coherent propagation. From Eq. (169) we have Grin ) = (1 + G o ~ V ) Q o ( E - Ho - ~On "[- i~7)-lln) = (1 + GOnVes)Qo[n)(~. p, - hn - E0n + i0) -1 (170) with h n - Te "4- (n[ Ves In) -- Te -+ Vn , and thus 1 + (n[VesGo[n)

El + EO)

hl ~ h0

(178)

Adopting Eq. (178), we can write Eq. (175), T(np'; Op) = (~[(nlVes[O) + Z (nlVesll)go(% + E o l#O,n

Et)(llVeslO)

+ . . . [~+)

(179)

where g0(w) = [w - h0 - E0(w + E0) + ir/] -1 is the oneelectron damping Green's function. In the case of very high energy excitation, the wave functions for the scattering electron ~p,0n-- and ~ + can be taken as plane waves, and only the lowest order term in Ves is important. We can then Fourier transform the Coulomb interaction in Ves to obtain a well-known Bethe approximation [5],

= 1 + (nlVes(1 + GOh Ves)[n)(E p, - h n - EOn 4-it/) -1 = 1 + (Vn + ]~On)(~Sp'- T e - Vn - XOn + it/) -1 (171)

T(np'; 0p) - (n[ Z

where AP = p' - p is the momentum transfer of the scattering electron. In the second quantized form, this is written as

+ (nlVesGrln))

- ( , ~ I[1 + (Vn + = (~pOn- [

ZOn)('p'-

Ze-

Vn - ZOn -4-/0) -1]

(~On- ](~?p, _

T(npl;

(172)

The dumped wave function ~ppC,n- satisfies the equation Te -- Vn - EOn + i ri) = 0

(173)

= (~p0n- [(nlVes+ VesGrhVes]O)[~;),

n # 0 (174) The Green's function Gr~ can be expanded in powers of V with the use of Eq. (169); to second order we have

0p) =

f

e x p ( - i A P , r) (n lp (r)10) d r / ( A P ) 2 (181)

where p (r) = ~ t (r) ~ (r) is the density operator. Eventually one obtains the differential scattering cross section for the energy loss with E = ~p - Ep,,

Combining Eqs. (172) and (164), we have now derived the general expression for inelastic scattering amplitude, T(np'; 0p)

(180)

J

We now have (~~

exp(-iAP, rj)[O)/(AP) 2

dE da

(Ap)2

v S(AP' E)

(182)

where S(AP, E) = E f e x p [ i A P "

( r ' - r)] (0lp(rt) ln)

n x (nlp(r)10) dr dr' 8(En - EO - E)

T(np'; 0p) = (~p~

V,esaon d I Ves + " "

+ Z

[0)[ l/r;),

1 n ~ 0

(175)

= / exp[iAP. (r' - r)](0l@(r', t)Sp(r)[O) dt x exp(i Et) ~ dr dr'

(183)

where Gdnl is diagonal with respect to the target Hamiltonian

Hs, Gdnl = Q O n e l ( E - H O - ~Onl-[-it/) -1 = QonPI(E - El - hl - EOnl + i0) -1

(176)

where EOnl is an excited-state optical potential and hi is a Hamiltonian for a scattering electron, ]~Ont = (llVesGr~fVesll)

(177)

where 8p(r) = p(r) - (018p (r)10) is the density fluctuation operator. The Heisenberg representation 8p(r', t) is defined as usual as $p(r', t) = exp(i Ht)Sp(r') e x p ( - i Ht). The correlation function (018p(r', t)Sp(r)lO) is just the reducible polarization propagator i FI > (r't, r). The dynamic scattering factor S is written in terms of the reducible polarization propagator. It is not easy to handle the reducible polarization I7, so we relate it to the irreducible polarization propagator P and the screening

ELECTRON ENERGY LOSS SPECTROSCOPY Coulomb interaction W [28] with the notation 1 = (rl, Oil, tl),

rI(1, 2 ) - P(1, 2) +

fd3d4P(1,3)W(3,4)P(4,2)

Here Inp') -- In)lqb~ as defined in Section 3.1, and IqJ~) is an eigenstate of H. Again we write H as H = H0 + V, with

(184)

Note that we need only the greater part of the second term of the fight-hand side of Eq. (184). For that purpose we can use a skeleton diagram expansion in the Keldysh formulation [28, 29]. Some useful properties of S for electron gas have been discussed in various excellent textbooks [2, 30] and are not repeated here. It is important to note, however, that the simple expression in Eq. (180) is valid only under very special conditions, where both lpp, and ~ - are replaced by the plane waves 4)o, and 4)o . This condition is satisfied when both the incident and the scattered electrons, that is, the probe electron, have high enough energy compared with the electron-target interaction energy. This problem is studied in Section 5 in detail.

H0

1

(186)

and a part that is bilinear in both k and 1,

Ves- Wen- Z (klllllk21e)ctklckectllCl: klkzlll2

(187)

t V - Ves- E V(kl'k2)CklCk2 kl ,k2

--

Z (klllllk212)CtklCk2(C:lCl2 - (OlCtllC1210)) (191) klk2lll2

where V (kl, k2) - Z I k l I111k212)(0lc/t1Cl210) nt- (kl IVenlk2) (192)

1112 For Iq J ; ) we now have

r ( n p ' ; 0p) = (np'[Ves(1 + GV)[q~-p)

What is left in Vc then are terms with one, three, or four k indices, plus terms of type ctkctk2cl1% and their Hermitian conjugates. A term with one k index can destroy the scattering electron and couple to a resonant quasi bound state. We will discuss such processes in the next subsection. The terms in Vc that we have included with Hs and Ves are expected to be the most important, except close to the threshold or to a resonance. Unlike in Section 3.1 we now fully account for the identity of the electrons. The full Hamiltonian is formally the same as before, but now Ves is defined by Eq. (187). The T matrix is

T(np'; O p ) - (np'l Vesl*~p)

(189)

(194)

Here G as usual is given by ( E - H + i r/) -1, and Cp t corresponds to an eigenstate of Te + ~kl,k2 V (kl, k2) with outgoing-wave boundary conditions. Despite that we now allow for the identity of electrons, we can follow the development in Section 3.1 closely. This is due to the fact that V only contains the operators Ck as c~1Ck2. Thus when we expand G in powers of V, each term with its product of V operators will, when it operates on I*+p), only create states of the type I.+p) - ctoln), i.e., with only one scattering electron present. The expression for T thus becomes a sum of matrix products with the matrices labeled by k and n. These same matrix-element products, however, are also reproduced if we use a product space In)Iq~+ ). This shows that we can work with direct product states, despite the fact that we consider the electrons as identical. Hence we can take over all results from Sections 3.2-3.3, only by replacing the Coulomb matrix element (klll lvlk212) with the antisymmetrized matrix element (k11111k212). For elastic scattering we obtain .L

T(0p'; 0p) -- (0p'IVHF + (188)

(193)

with Iq~+p) -- c;10) and thus

Here (l I) stands for the antisymmetrized matrix element

(pqllrs) = (pqJvlrs) -(pqlv[sr)

(190)

and

(185)

As in Section 3.1 we divide the one-electron states into one set {l} to be used for the electrons in the solid, and another set {k} for the scattering electrons. The dividing line is taken at some energy e0, chosen so that the electrons in the solid can be well correlated. To be more specific, we calculate the ground state of the solid in Hartree-Fock theory and choose as {l} the groundstate orbitals plus the virtual orbitals up to the energy e0, which may be, say, some 50 eV. We now pick from the full Coulomb interaction Vs the part that describes the interaction between the electrons in the solid,

Ws-- ~ Z (/11211314)c/t1Cf2Cl4Cl3 11121314

V(kl, k2)CktlCk2 + Hs

[ q / ; ) - (1 -+-GV)[*ffp)

The full Coulomb interaction between all of the electrons is

1

Te + Z

kl ,k2

3.4. Inclusion of the Direct Exchange Effects

Vc -- -~ E (pq Irs)ctpCtqCsCr pqrs

429

(195)

Here VHF is the Hartree-Fock potential, and E is given by the same expression as in Section 3.1, except for the replacement with matrix elements (klll llk212). The explicit expression for inelastic scattering is the same as in Section 3.2, except for the replacement with matrix elements. As a very simple explicit example of the use of Eq. (174), we write down the expression for spin flip scattering of an electron from a hydrogen atom. To lowest order in Ves we have from Eqs. (155), (174), and (187),

T (np'; 0p)

(~o, i l 1 frr r> d c (rl)rl drl

d c(rl)r121 drl

(270)

where R~ is the radius of the atomic region oe. In addition to this intraatomic contribution to the first term of Eq. (259) we have the interatomic term, where r and F are still in region oe, whereas rl (= r2) is in region fl (fl -r a). This term is given by l~(r, r') (

4~

21 + 1

]FI~I"(R/~)]Z(rr')lyu(r)Y~'(f'){r21)/~

FL(r, r'; Rt~,~)YL(f)Y{(F )

(271)

L where in terms of Gaunt's integral G(LL'IL")

=

f r~(~)•

r~, (f) r~,, (f)df , F~, (R~.) =

4 ~ r ( - 1 ) l ( 2 / + 2 1 ' - 1)!! ( 2 / - 1)~(2/' + 1)fIR ~+~'+1

• G(l + l ~, m - m', L']L) • Y~+~f,m,_m(R~) FL(r,r'; Rr

i

(276)

j

where dij(x) = dpi(x)dpj(x), and we assume that the core orbital j is localized on site or. We take both r l and r2 to be in the same region oe. For the occupied states we will not use B loch functions but instead take a simplified approach and use localized functions Rn~ YLn" This is well motivated for rare gas solids, but a more serious approximation is needed for, say, metals. By spherically averaging d/j (r) at each site or, we can get a simple representation for Eq. (276) as p(rl, r2)pC(r2, rl) core

) 2

LL I

= Z

occ core P(Xl, x2)pC(x2, Xl) -- Z Z dij(xl)di; (x2)

(269)


.

~. o.4

Rg(~

A (r, r')l YL (r) Y~ (r')

,

o.6 0.$

Cross terms such a s dflmngive no contribution to J,~ because of the orthogonality between mth and nth shell functions. Therefore A (r, It) can be written as a (r, r') = ~

--

.~ o.a "-

O.2

~""~ ....

O,f

(282)

I

0

" ~'~.~ ..... .7~"~'~'--.~--.-.._.-__~

~

I

. . . .

2

3

4

L

$ T

'

6

~

9

a

9

,

..... I _

7

4

9

.......

10

(O~.IL.)

where A is a sum of one- and two-center terms,

A(r,

rt)l =

A~(r,

rt)l + E

A~(r,

rt)l

(283) O. t O - - -

,

,'

0.14

a~(r, r')0 = (4zr)z[I~(r, r')0 - 47r Ja(r, r')0]

(284)

A~(F,F')I -- ( 4~r ) 2 21 + 1 I~ (r, r')l

(285)

Afa (r, r~)l = (42r)2( 1 + 1 ) (r2)/~ ( r r ' ) l + . . . \/2l + 1

(286)

/721+4

We find a good convergence for the two-center sum, the second term in Eq. (283), when we include the surrounding atoms up to the third shell for the systems considered here. The optical potential can be given by Eq. (287) after the spherical averaging of the potential over ~ and ~ in the same atomic region, Vp~

r'; E0 + ep) = E

V/p~

~ ' ! ! o t

0.12

'

r'; ep)YL(~)Y~(f')

~""

II i.

0

--

3

el o i

0.1

(l > 1)

L=2

,

0.00

,

.

o.oa o, o4

"

: ~

"..

,, .~ ..aC-

o k.E': / " - I - - - 0

I

i 2

"".,-:':':~,,.,-,_._--._..._ . . . . . . . . . . . . . . . . . 3

4

$

6

10

7" (~.~.)

,-o_ , (,.~.) ,.o.n. /.,.~.) r. !...o..(.~.~.)r-a.o_r Fig. 3. Al(r, r t) (l = 0, 1, 2) for a h y d r o g e n atom. r is fixed at 0.1, 0.5, 1.0, and 2.0 a.u. [41].

(287)

L

where V/p~ is expressed in terms of Al,, gl", and ClebshGordan coefficients, vp.

(2l' + 211)(2/" Ol(r, rt ; (~p ) -- - ~1 S-" ~ + 1 + 1)(l'Ol"Oll'

+/"0)

2

Fl"

x Al,(r, r')g~,,(r, r'; ~)

(288)

Figure3 shows the At(r, r t) (1 -- 0, 1, 2) for hydrogen atoms where r is fixed at 0.1, 0.5, 1.0, and 2.0 a.u. [41]. Both A]

and A2 vanish at r t = 0, which can be easily verified from Eqs. (268)-(270), and have a maximum whose position shifts to larger r t with r. In contrast, A0 is a smoothly and rapidly decreasing function of r and r ~. We see that A0 is much larger than A 1 and A2 inside the atomic region. At small r, A0 is dominant, and the relative importance decreases with I. At large r (> Rc~), A0 becomes small faster than Al (l > 1), as shown in those figures, and A 1 becomes the most important. Calculated results for Ne atom also show quite similar behavior.

ELECTRON ENERGY LOSS SPECTROSCOPY

439

(a)

Ei,e = 200eV

Ein~ = e-

200eV

He

2.5 2.5

2

5" d r

O

~"1.5

1.5 1

...,,. 9 . . . . . r4

0-

. . . .

.

.

.

.

--0

.

.

.

.

.

9

.

.

.

.

.

"0 .

.

.

.

.

0.5

~'

""

'"" ;;:":":,.....

_ . ~. ~'~'~'~: .............................

I

0.5

0

0

5

10

15

20

I 25

I 30

35

O(deg) 0 | 0

I 5

I 10

I 15

I 20

I 25

I 30

I 35

4{I 0.25

Fig. 4. Forward differential cross section in a.u. 2 for electron elastic scattering from He at 200 eV (a) and 500 eV (b) [42]. The convergence is investigated in partial wave expansion; the solid line (dashed line) is the result for the HF + optical (HF only) potential with A = 20 eV.

\

0.2

o.15 c~

As demonstrated above it is enough only to include A0 and A1 in the expansion in Eq. (288). We thus obtained an explicit expression for Vp~

0.1

0.05

V/p~ (r, r'; ep) 1

I

~ [Ao(r, r')gl(r, r'; p) + Al(r, r')~l(r, r';/3)] (289) 4zr where

gl

is defined by l

l+l

gl(r,r'; p) -- 21-+- 1 gt-l(r'r'; ~) + 21-F 1 gl+l(r'r' ~) (290) Each gl,, includes the radial solution for the potential El,,(Ep) to be determined, so that our optical potential Zt can be solved self-consistently. Note that Vp~ depends on gt and gl+l, so that we have to solve coupled self-consistent equations. 4.4.3. Results and Discussion Figure 4 shows the forward differential cross section (in atomic units) for electron elastic scattering by He at 200 eV [42]. The convergence is investigated in partial wave expansion; the solid line (dashed line) is the result for the Hartree-Fock+the optical potential (only the Hartree-Fock potential). We see that good convergence is obtained for Imax = 10 for the HartreeFock potential, whereas many partial waves are necessary to obtain good convergence for the Hartree-Fock + the optical potential discussed above, converged at lmax = 35. Here lmax

40

60

80

100

120

140

160

:

:) 180

0(deg) Fig. 5. Differential cross section in arbitrary units for electron elastic scattering by He at 200 eV (a) and 500 eV (b) [42]. The solid (dash-dotted) line shows the SCF (non-SCF) result for the HF + optical potential with A = 20 eV. The dotted (dashed) line shows the result for the Hartree-Fock (Hartree) potential.

corresponds to the impact parameter in the classical collision theory, the long-range polarization part is mainly responsible for this large impact parameter. Figure 5 shows the importance of the self-consistency in the optical potential calculations [42]. Nonself-consistant field (SCF) means the results for the first iteration calculation, including both the exchange and the optical potential when we use the Hartree solution as input data. In the small-angle region (0 < 30~ SCF iteration, which is a nonlinear effect, plays an important role at 200 eV, and in the region 0 < 15 ~ at 500 eV. The results for the Hartree-Fock and Hartree solutions are shown for comparison. These two approximations give quite poor results in the small-angle scatterings. Figure 6 also shows the forward differential cross section in a.u. 2 for e-Ne (a) and -Ar(b) at 200 eV [43]. The con-

440

FUJIKAWA

Fig. 5. (Continued).

vergence of the partial wave expansion is studied here. We see that good convergence is found for Imax - 3 (Ne) and lmax =- 8 (Ar) for the Hartree-Fock potential, whereas more partial waves are necessary to get good convergence for the Hartree-Fock + the optical potential. The calculated result converges for lmax - 15 (Ne) and lmax - 18 (Ar). In comparison with the result for e-He scatterings, we find rather rapid convergence in the partial wave expansion for the e-Ne and -Ar scatterings. Figure 7 shows the importance of the self-consistency in the optical potential calculations [43]. In the small-angle region 0 < 5 ~ the SCF iteration has some effect at 200 eV, whereas it is not important at 700 eV. The results for the Hartree-Fock and Hartree are shown for comparison; quite large differences are found at the small-angle scatterings. Figure 8 shows the differential cross section in a.u. 2 as a function of scattering angle for electron elastic scattering scattering by Ne at 200 and 400 eV for different values of A [43].

Fig. 6. Forwarddifferential cross section in a.u.2 for electron elastic scattering from (a) Ne and (b) Ar at 200 eV [43]. The convergence is investigated in partial wave expansion; the solid line (dashed line) is the result for the HF + optical (HF only) potential with A = 0 eV.

The solid line shows the result for the parameter A = 0 eV, the dashed line the result for A = 20 eV, and the dotted line the result for A -- 40 eV. Some experimental results and the result from the Hartree-Fock calculation are also shown for comparison. Only in the small-angle region (0 < 20 ~ do the calculated results depend on the parameter A, though the dependence is weak. For A = 20 eV, good agreement with experiment is obtained. Figure 9 shows the calculated scattering cross sections from Ar at 200 and 400 eV for the same three A values [43]. For comparison, some available experimental results and the result from the Hartree-Fock calculation are also shown. Satisfactory agreement is found for both Figure 9a and Figure 9b; however, the Hartree-Fock calculation gives a poor result in the smallangle region, as observed in e-He and -Ne scatterings. The calculated results are not so sensitive to this parameter compared with the results for e-He and -Ne scatterings.

E L E C T R O N E N E R G Y LOSS S P E C T R O S C O P Y

Fig. 7. Differential cross section (DCS) in a.u.2 as a function of scattering angle for electron elastic scattering from Ne at (a) 200 eV and (b) 700 eV [43]. The solid (dashed) line shows the SCF (non-SCF) result for the HF + optical potential with A -- 0 eV. The dotted (three-dot-dashed) line shows the result for the Hartree-Fock (Hartree) potential.

The H e d i n - L u n d q v i s t potential has been compared with the present theoretical approach [ 143]: the H e d i n - L u n d q v i s t potential overestimates the small-angle scattering intensity. For the valence electron optical potential we can safely use a local density approximation because the charge density changes fairly slowly. For these electrons plasmon-pole approximation can also be applied, whereas these two approximations present serious problems for core electrons. This is why the H e d i n Lundqvist potential for all electrons (including core electrons) does not give such good results.

5. THEORY OF DEEP CORE EXCITATION EELS In this section we now apply the general electron scattering theory developed in the previous sections to deep core excitation EELS; in particular, EELFS is studied [10, 11]. In this case,

441

Fig. 8. Differential cross section (DCS) in a.u.2 as a function of scattering angle for electron elastic scattering from Ne at (a) 200 eV and (b) 400 eV [43]. The solid line shows the result for the parameter, A = 0 eV; the dashed line, 20 eV; and the dotted line, 40 eV. Some experimental results are also shown for comparison. The calculated result for the Hartree-Fock approximation is also shown.

the three different damping wave functions are considered for a secondary excited electron from a deep core and a probe electron before and after the core excitation. Correspondingly, we have to calculate three different optical potentials, even if we apply the energy shift theorem for the optical potentials with different energy arguments. We apply site T matrix expansion for these wave functions to explicitly discuss the EELFS and the intensity oscillation due to the elastic scatterings of probe electrons.

5.1. Basic Formulas of Deep Core Excitation EELS We consider the amplitude of inelastic scattering in the transition Op --+ n p t, where the target is excited from the ground state I0) to an excited state In) (n ~ 0) and the probe electron

442

FUJIKAWA analyze X-ray absorption spectra, I(p', p) = - 2 Im(01U(p', p)t(E - H + ir/)-lU(p ', p)10) ( r / ~ c~)

(294)

where E = E0 + A E and H is the full many-body Hamiltonian. The difference between EELFS and XAFS only comes from the difference between U (p', p) and Hep (electron-photon interaction Hamiltonian). Hedin has developed a very useful EXAFS expression, starting from Eq. (294) and using quasi-boson approximation [39]. An alternative approach has been developed by Fujikawa [57] with the use of many-body scattering theory. Here we follow the discussion in [28]. Above the core threshold U (pt, p) can be written as U(p', p) = ~ ( k l u ( p ' , p)lc>ctk b + h.c. k

(295)

b(Ctk) is the annihilation (creation) operator of the core state ~bc (photoelectron state), and h.c. means the hermitian conjugate of the first term. To specify the problem we introduce the Hamiltonian widely used to study deep core processes [22], H = Hv + h + V + Vcbb t + e.cbtb

(296)

Here Hv is the full many-electron Hamiltonian for valence electrons, Vc is the interaction between the core hole and valence electrons, and Ec is the core electron energy. From the interaction operator Ves (see Eq. (130)) between the photoelectron and the other particles in the solid, the diagonal (elastic) interaction Va and the off-diagonal (inelastic) interaction V can be constructed by use of the projection operator Pn ('- Inv*)(nv*I), Vd = Z

en VesPn,

V = V e s - Vd

(297)

n

Fig. 9.

The projection operator Pn is now defined for the hole state Inv*) that satisfies the eigenvalue equation

As in Figure 8, but for e-Ar scatterings [43].

Hv*ln*) = EV*lnv), is scattered from p to p~, which is given by Eq. (179) in Section 3.3. When we consider the high-energy excitation where e.p, e p, >> Ves is satisfied, we can neglect the second term of Eq. (179) and change the order of integration as in Eq. (180); then we have T(np'; 0p) ~ (nlU(p',

p)10)

(291)

U(p', p) - ~ ( l l u ( p ' , p)ll')CtlCl ,, (llu(p', p)II') lF

-(p'lllpl')

H* = Hv + Vc

The effective one-electron Hamiltonian h for a photoelectron is now given by h -- Te q- Vd

Within the present approximation shown by Eq. (296), the initial state 10) is written by the product 10) = 10v)Ic), where 10v) is the ground state of Hv" Hvl0v) - E~10v). The loss intensity is then I(ff, p) -- - 2 Im(0vlTt(E - H * - h -

(292)

The loss intensity I (p~, p) from the ground state 10) is now given by

(298)

V +ir/)-lTl0v) (299)

where T is an operator that creates photoelectrons:

Z = ff-~(klulc)ctk

(300)

k

I(p', p) = 2:r Z [ ( n l U ( p ' , p)lO)128(En - EO - AE) (293) n

where A E -- Ep - Ep, is the loss energy. One way to treat the loss intensity utilizes a standard expression frequently used to

This operator, if used on a photoelectron vacuum state, is then replaced by ulc) by use of the approximate closure relation Ik) (kl ,~ 1 k

ELECTRON ENERGY LOSS SPECTROSCOPY This approximation can be good well above the threshold. By use of these simplifications, a compact formula first derived by Hedin is obtained [39] for XAFS and EELFS analyses,

I (p', p) = - 2 Im(clu(p', p)* (~(E)u(p', p)lc) G(E) -

(0vl(E - nv* - h - V + ir/)-ll0v)

By inserting the closure written as

relation

Zn

Inv*)(n*l -

(301)

1, (~ can be

G.(E) -- ISol 2(OvlG(E)IO* ) 4- Z(S*So(n*vIG(E)]O*) 4- SnS~)(0*lG(E)lnv*))

443

where Vnm -- (nv*lVeslmv*) is the extrinsic loss amplitude for the transition, m v* ~ n v. * The first term of Eq. (305) describes the normal EELS intensity without extrinsic and intrinsic losses of the photoelectrons. This term is the most important. The second term describes the interference between the intrinsic and the extrinsic losses, the third term describes the intrinsic losses, and the last term describes the higher order terms, which includes both the intrinsic and the extrinsic losses at least in third order. Equation (305) is useful for practical purposes, because this formula can properly describe the damping of photoelectrons during propagation in solids.

n>0

4-~

ISnl2(n*vla(E)ln*v)

5.2. Suppression of Loss Structures

n>0

4-

(302)

Z S* S n ( m * I G ( E ) I n * ) n~:m>O

where G ( E ) = (E - Hv* - h - V + it/) -1, and the intrinsic loss amplitude Sn is given by Sn - ( n v * 1 0 v ) -

(nv*lbl0)

With the use of the technique discussed in Section 3.3, the diagonal part of G ( E ) is simply written as (n*lG(E)ln*) =

gC(E - -

(.On) - -

[E - - o) n - - h -

~(E

-

(_On) 4 -

it/] -1 (303)

where O)n - - E v* - E 0Vr162 is the excitation energy of the target and E - E - E~ is the kinetic energy of photoelectrons in the normal ionization process 10)lc) ~ 10v*). The optical potential is responsible for the damping of photoelectrons during the propagation in solids. The off-diagonal part of G ( E ) is systematically calculated by use of the diagonal Green's function expansion as shown by Eq. (169), which yields

EELFS spectra are usually analyzed without considering the interference term (the second term of Eq. (305)). In this approximation we can expect an abrupt jump of the EELS intensity of the additional excitation of outer electrons [59]. However, such structures have not been observed in EELFS and XAFS spectra. In the case of XPS spectra the destructive interference between the intrinsic and the extrinsic losses has been well established from experimental results for plasmon losses [60, 61 ]. For excitation by low-energy photons, the loss spectra are featureless and are lost in the background; the two losses are canceled at the threshold because of the strong quantum interference. A similar situation can be expected for EELFS and XAFS: for XAFS the subtle cancellation of these losses has been explained based on many-body scattering theory [39,57,62]. To study this problem in detail, Eq. (305) is not convenient because the imaginary part of the optical potential Im has some characteristic features around the loss threshold [37]. The effective one-electron operator G for photoelectrons in Eq. (302) can be written in terms of the core hole excitation operator Xc defined by Xc = y ~ In*)(Sn/So)(O*[

4-

~ gC(r162 j(#,O,n)

(306)

n>0

(O~,IG(E)In*) = gC(e)(OlVln)gC(r - (.On) as

- wj)

x (jlVln)gC(r

--ISol2(O*IG(E) 4- XtcG(E) 4- G ( E ) X c 4- Xtca(E)Xc]O *) 4 - . . . (304)

Finally we obtain a useful formula for the study of EELFS and ELNES spectra,

(307) By noting that PXc -

l ( p ' , p) - - 2 Im(clu*gC(•)ulc)lSol 2

PVP

- 2 Z I m [ ( c l u * g C ( E - wn)VnogC(~:)ulc)S*So

XcQ - 0

- O(P = P o -

10v*)(0v*l, O = 1 - P)

and

n>0

4- (clu* gC(~)VongC(E -- Ogn)UlC)SnS~]

X c P -- Q X c -

- 2 Z I m ( c l u * g C ( ~ : - Wn)Ulc)lSn] 2

Xc

the relation

n>0

PGP - PGoP + PGoVGVGoP

- 2 Z Im[ (clu*gc(e - O)n) n~m>O x gnmgC(E - COm)UIC)SmS*] . . . .

(305)

(308)

is obtained, where Go( E ) -- (E - Hv* - h + it/) -1. Finally a simple formula to describe the cancellation of loss structures

444

FUJIKAWA

is obtained, G(E) -- IS012(0*[G0 + (GoV + X*c)G(VGo + Xc)[0*}

(309)

As demonstrated in several papers on XPS theory, the interference term (VGo + Xc)10v*)AIc) is responsible for the suppression of the loss structures when the kinetic energy of a photoelectron is comparable to the loss excitation energy, 6k ~'~ O)n [32, 38, 63, 63a, 64, 64a]. Therefore we can expect that the suppression of the loss structures at threshold is also found in EELFS and XAFS spectra. This result does not mean that unknown peaks, which cannot be analyzed within a oneelectron approximation, can be safely interpreted in terms of shake effects as shake-up or shake-off processes. From the above discussion, in the ELNES region (6 < 50 eV), the loss intensity is approximated by I(p', p) ~ -2Im(clu*~C(6)ulc)

(311)

n

5.3. Multiple Scattering Expansion of a Secondary Excited Electron We first consider the multiple scatterings of photoelectrons, which cause oscillations in the EELS intensity compared with XAFS. In Section 5.4 we also consider the multiple scatterings of probe electrons.

l<e, YLlulc>l2

i0(p,, p) = 4k

(316)

L

The single scatterings loss intensity with regard to photoelectrons is given with the use of Eq. (311) and the second term of Eq. (313) as I 1 (p,, p) -- - 8 E

(clu*gCA(e - C~

ISnl2 Im E

(6 -- Wn)UlC) (317)

oe(-~a)

In contrast to I ~ calculation, each channel gives EXAFS-like rapid oscillation, and we have to explicitly keep the energy difference in g~. For the spherically symmetric potential at each site, I 1 is explicitly written in terms of phase shifts at A and or, ii(p,,p) _ _4EiSnl2im{~Li n

EZil3-11(clu,

iRl3YL3)

L2 L3

A X e x p [ i (~lA @ ~ll)]

x E GL3L2(Kn;--I~)ti2GL2L1 (Kn; ROe) ol

5.3.1. E E L F S Spectra Now we separate the core hole optical potential E0, into a real part Re E0, and an imaginary part - i F0,. For the very high energy case (6p > 200 eV), 1-'0, can be constant; F0, = 0 outside the solid and 1-'0, > 0 inside. We also separate the effective oneelectron real potential (0*lVesl0*) + Re E0, into each atomic scattering potential

+ Re Eo, - Z v~

(312)

where v~ is a one-electron effective potential centered on site or. It is Hermitian, nonlocal, and approximately spherically symmetric, and depends parametrically on energy. The core orbital q~c is strongly localized at site A, and it is sufficient to pick up the following expansion of gC,

Z gCatugCa+ E ot# A

(315)

which can be written in terms of partial waves RI (kr)YL (r) at site A (6 = k2/2),

n

In the above equation gC describes the damping.

gC _ g aC +

iO(p,, p) _ - 2 Im[(clu*gCA (6)ulc)]

(310)

where ~c(6) is also a core hole one-electron Green's function without optical potential, that is, without damping. On the other hand, in the EXELFS region (6 > 50 eV) the loss intensity is approximated by neglecting the interference terms in Eq. (305) I(p', p) ~ - 2 I m ~ ( c l u * gC(6 - Wn)ulc)lSnl 2

The free propagator gO now includes the imaginary part of the potential g~ = (6 - Te + i1-'0,) -1, which can describe the damping of the electron propagation. First we consider the EXELFS spectra. The direct loss intensity I ~ where a photoelectron suffers no elastic scattering is calculated by use of Eq. (310) or (311). We can neglect the energy difference between gac (6) and gac (6 - (.On) in Eq. (311) because it contributes to the atomic excitation cross section which shows smooth variation in energy. We thus have the atomic loss intensity by noting that ~ , ISn 12 -- 1,

gCat ~ g o t~ g Ca+ ' ' "

lulc) [/

(318)

where Kn is the principal value of ~/2(e - (-On @ iF) and kn : ~/2(6 - COn), Rl = Rl(knr). The T matrix t~ is given in terms of phase shifts as Eq. (87). Here GLU denotes the damping outgoing propagator in an angular momentum representation as shown in Eq. (105). Higher order scattering terms such as double scattering can easily be calculated in the same way; here the double scattering term is shown by

,2(p,,p) = _4EISnl2 E n

E EIm{

(cIu*IRI4YL4)

L1L2 L3L4 ot:/:fl

x e x p [ i (8lA -~- ~lA)]i 14-11

(313) • GL4L3(Kn', --R~)ti3GL3L2(K n ", R~ - Ra)t ~12

~ #ot # A

where t~ = v~ + vagot~ is the site T matrix st ot (Section 2.3.1, Eq. (127)), and the core Green's function at site A is given by

gCa -- go -+- gotago -- (e -- Te

X (Rll YL1

--

va

-+-

i~7)-1

(314)

X GL2L1 (Kn; I ~ ) ( e l l EL 1 lulc>}

(319)

In Eqs. (318) and (319) we have to include a lot of partial waves in the EXELFS region. The direct calculation of I 1 and

ELECTRON ENERGY LOSS SPECTROSCOPY 12 with the use of these formulas is not practical. In the next subsection we discuss a separable formula that is useful in the high-energy region kR >> 1.

445

(2x - x 2 ) m p l m ( 1 - x ) and b(x) -- l~Fm(1 - x ) ,

lfo~

I(z) --- -

exp(-x/z)a(x)b(x)

z

dx

(326)

When we define the Laplace transform of a and b,

5.3.2. z Axis Propagator

The angular momentum representation of the propagator GLL' in Eq. (105) has characteristic features if R is on the z axis, as pointed out by Fritsche [65] and Rehr and Albers [66]. First we note that from Eq. (105),

A(Z) -

lf0~ lfo

-

Z

B(z) -- -

z

exp(-x/z)a(x)

dx (327)

e x p ( - x / z ) b ( x ) dx

m

gtv(k, R) :_ G L u ( k R ~ ) = -~4-~k Z

ill+lhll(kR)v/211 § 1G(IIOLIL')

(320)

a and b are given by the inverse Laplace transform with the use of some appropriate closed contour F,

11

(328)

m m glv -- gll- )m = gl'l

(321)

and from these relations we can restrict our discussion to the case l ~ > 1 _> m _> 0. With the aid of the recurrence relations (119) and (123), we have

1 g~v(k R) -- i kR '

The substitution of Eq. (328) into Eq. (326) yields the integral representation

l(z) --

(322)

Rehr and Albers have derived a very useful separable formula starting from Eq. (320) [66]. The spherical Hankel function is written as the integral formula

1 f r mdz B(z) exp(x/z) 27ri z

b (x ) -

~1+1

21 + 2 gl+l,l,(k, R) ~ + 3 x/(l' - l)(l' + l + 1)

hi(z) -- - i -I

1 f r --dzA(z) exp(x/z) 2rc i z

a (x ) --

We can show the symmetric relations

f F dZl dz2 A(Zl)B(z2) 27ri 2:ri ZlZ2 - ZlZ - z2z

_ f m

L

dzl A ( z l ) B ( z + z 2 / ( z l 2rci Zl - z

z))

(329)

From Eq. (322) we can relate g~r to g~r

exp(izt)Pl(t) dt g~l' -- z l ~ (21 + 1)!!(/+ l')!gOv (2/)11(/' - l)!

By analytical continuation of the interval Itl _< 1 to all complex planes, we have from Eq. (320)

(330)

and gOt, is simply - e x p ( i p ) x / 2 1 ~ + lcl,(z)/R, where the /th m

gll,(k, R) -- 4rcik

fioo

exp(ikRt)Yl* (O, dp)Yl,m(O, ~) dt

= 47rikNlmNl'mJll m

JHm --

(323)

exp(ikRt)(1 -- r

(324)

where t -- cos 0. As m -- m ~, the above integral does not depend on 4~. The factor Nlm is given by

Nlm

i

(_l)m/(21

V

+ 1 ) ( / - m)! 47r(/+ m)!

(m > 0)

and/Stm (t) is a polynomial defined by Plm (t) - d m/dt m Pl (t). The Cauchy theorem can change the line integral dl f i ~ to fl -~176 Thus we rewrite Eq. (324) as a Laplace transform,

jllm = _ exp(ip______~)I (z) ip

lfo

I (z) -- -

polynomial cl(z) is defined by Eq. (117). Noting that fill(x) -(2/-- 1)!!, we can relate it to A(z) from Eq. (325), / i

g~l,

exp(ip) /(21 + 1)(2Y + 1 ) ( F - 1 ) ! - ~ V (21)!(F + 1)! (21 - 1)!!ka(z)

(l' > l)

(331)

The comparison of these two different expressions (330) and (331) gives an explicit formula of A (z) in terms of cr, after we interpret I as m, and l ~ as l,

A(z)-

(332)

We can calculate B(z) directly from the definition (327)" l

B ( z ) -- ( - 1 ) m Z

Pl,rZ r - m

r=m

e x p ( - x / z ) (2x - x 2) m

(--1)r(/+

Z

P l ~r

• ?lm(1 -- x)l~l,m(1 -- x ) d x

(1 + m ) ! zmcl(z)~ (1-m)!

2rr!(l - r ) !

(325)

where p - kR and z - 1/ip. The function I(z) is considered as a Laplace transform of a(x)b(x), where a(x) -

r)!

l

(333)

We note that ct(z) - - ~r--0 e l , r zr" Substituting Eqs. (332) and (333) into Eq. (329), we obtain a closed expression of I (z) in

446

FUJIKAWA

terms of CI(Z)'S and their derivatives [66],

l(z)

(-1) m

(1 + m)!

c~r)

(I - m)!

(mwr)

(Z)CI,

(Z) zm+2 r

r!(m + r)~

r=0

(334)

m where )~ = min[l, l t - m]. The z axis propagator gllt is thus separable as

m exp(ikR) Z z~ l It gllt = Ymr (Z) Ymr (Z)

R

~l

Ymr (Z) :

r:0 21 + 1 c~r)(z) Zr Nlm r!

I1 (335)

D ms (l) (~"2)Umts~,.~,,j r~(/t) [r1766ll,(k, R) R

4~--~lSnlZlm ~

exp(2iKnRa) R2

c~

• ~

till

Y~ (clu t IL2)exp[i (~lA "1- ~A

X rL2*( - ~ ) i l~-l~cl2 (z~)F(ao~a; K.)cI~ (Za) • YL1 (~)(Lllulc)

}

(340)

12 = 4 Z ]Snl2 Y~ Im{ exp[ixn(R# + R#a + Ra)] n otS~~ R~R~Rot ll)]i 12-11 x Z (clutIL2) exp[i (~iA -~- ~A L1L2

S

exp(ikR)

-

L1 L2

The integral representation (112) helps us to write GLL, in terms of the z axis propagator by use of the Euler rotation f2 and the rotation matrix D (Wigner D function), which rotates the z axis to the R direction,

=

-

n

-(m+r)(z ) It 1)m+1 Clt zm+r Ymr (Z) -- Nl'm (-(m + r)!

GLu(kR) = ~

where 0• is the scattering angle at site/3 in the scattering process. When ct(z) is replaced by 1, it is reduced to the ordinary plane wave scattering amplitude. Typically we find rapid convergence of the (s, r) expansion in the EXELFS region [66, 67]. The damping effect is introduced through Xn. For simplicity only I 1 and 12 are explicitly shown here in the lowest order Rehr-Albers expansion. With these approximations we have

L,

X YZ2(-R~)cl2(Z~)Cll (z~)F(Aflt~; tcn)F(flotA; Kn)

ZFLr(Z)I"sr(Z) rs

x YLI(~)(LlluIc)}

FLr(Z ) = o(l~ (~'2)~lls[,r(Z ) rsL; (Z) -- ~.mts l~(l') (~"2)*y[s[,r(Z) it

(r > O)

(336)

Each of the (s, r) terms is in the order of Z Isl+2r. As an example, we calculate the amplitude G(R• -Rt~)tt~ • G(Rt~ - Ra) with the use of the separable formula (336),

GL1L'(Re -- RI3)t~ GLtL (Rt3 - I~) Lt

exp[ik(R• • y~ Z St"

+ Rr F~lr , (Zgfl) F/~ s,rt,sr(Zyfl, Zflt~) r~r (zt~a)(337)

Stt" t

where

Fs'r',sr ~ (z• '

Z !

: ZFs,r,(Z• Lt

~L' (Z~ot) I"sr

(338)

is the spherical wave scattering amplitude at site/3 in the ot 13 ~ F scattering process. Here we define Rat~ = IR• - Rt~ l, zr~ = 1/(ikR• The lowest order (the most important) term is (s, r) = (0, 0), and the next order terms are (s, r) = (+1, 0) under the condition k R >> 1. For example, Foo,oo(Z~, t~ ~, z#a) is the most important and is quite similar to the plane wave scattering amplitude shown by Eq. (37),

E00,00 ~ (z•

z#a) = F(yflot; k) =

Z(2/+ 1)4 (k)Pl(cosO~,/3a) l X Cl(Zy~)Cl(Zfl~) (339)

(341)

where ]L2) = ]RI2YL2) and Ic) = I~bc). Rehr and his coworkers have developed a standard computer code called FEFF for XAFS analyses based on Rehr-Albers expansion [ 147, 148]. They used efficient path-by-path multiple scattering calculations. In principle we can apply this code to EXELFS analyses; however, as discussed in Section 5.4, probe electrons suffer elastic scatterings in addition to core excitation loss, which raises a problem with regard to or0.

5.3.3. ELNES Spectra Rehr-Albers expansion is very useful for the study of EXELFS spectra where excited EXAFS electrons have quite high energy (kR >> 1). On the other hand, in the ELNES region (kR .~ 1), the convergence of the Rehr-Albers expansion shows slow convergence. In this energy region, the number of partial waves to be taken into account is also small. Scatterings from surrounding atoms are strong enough that the multiple scattering renormalization is crucial. From Eqs. (318) and (319), the full multiple scattering resummation ELNES formula is obtained in the closed form as a typical XANES formula [24, 25, 57], I cr (p', p) - i 0(p,, p) + I 1(p', p) + I 2(p', p) + . . . = - 4 Im Z { ill-I (t~) -1 exp[i (8lA --[-8A)] LL1 • (clutltl)[(1_

x (tlulc)}

X)_IjL1.L.aA

(342)

ELECTRON ENERGY LOSS SPECTROSCOPY where the matrix X c~t~is defined by

XL~IL2--tU(k)GL,L2(kR~ll

-

-

5.4. Multiple Scattering Expansion of a Probe Electron

(343)

kR~) (1 - 8u~)

This matrix element describes a physical process where a photoelectron propagates from site fl with angular momentum L2 to site ot and is scattered with angular momentum L1. In the EXELFS region core electrons play an important role in backscattering, whereas outer electrons play an important role in the multiple scatterings in the ELNES region (see also Section 4.4). The T matrix reflects the electronic structure, whereas G reflects the geometric structure. Thus ELNES spectra can give us useful information on electronic and geometric structures around the excited atom. As discussed in Section 5.2, the loss effects of ELNES electrons are not so important. It is thus sufficient to consider only the main channel. The inverse matrix (1 - X) -1 includes infinite-order full multiple scatterings inside a cluster. In some cases this direct calculation is formidable, because the dimension of the matrix X amounts to 1000 for a cluster composed of 40 atoms and for a partial wave sum up to g wave. Equation (342) shows that we need only a small part of the large matrix (1 - X)-1 to calculate ELNES spectra. We now separate the atoms in the cluster into two groups, a near region including the core excited atom A (group 1) and a far region (group 2). For example, group 1 has only the atom A, or in the other cases it includes the atom A and its nearest neighbors. We can divide the matrix 1 - X according to the above partitioning as

l - X - - (All \

A21

447

A12

5.4.1. Basic Formulas Both Eqs. (310) and (311) can be used for all excitation operators u; for example, we can consider the X-ray absorption processes. Hereafter we will specify the operator u for highenergy electron impact excitation. The basic ingredients needed to calculate u are the damping wave functions gr+ and grp-; for probe electrons in the solid; they are calculated by use of the site T matrix expansion as discussed in Section 2.3.3. From Eq. (126)both ~ + and ~p--; are expanded,

~r; -- E ~r(i) ,

the principal value of v/2(~p + iF). ~(1) includes single elastic scattering of the incident electron, 7t(2) double elastic scatterings, and so on. The lowest order Rehr-Albers expansion for G LL' can express ~pp(1)as ~P(1)(r) = p

'7" (~ ~.Aup(r)F(Aap;

E

(346) where F(Ac~p; ~) is also the scattering amplitude with spherical wave correction, however, it includes only linear terms of Cl in comparison with F(Vfl~) given by Eq. (339),

where Oaotp is the angle between p and - l ~ and z,~ is defined by i/(~R~). The damping PW with spherical wave correction ~(0) A~p propagates toward - R a with kinetic energy ep, which is represented by

as

~(o)

iljl(pr)cl(z~)Y;(r)YL(-~a)

(348)

L

From the above relation we have an expression for the submatrix All, I(1

,

AaP (r) -- ~ Z

Higher order terms, such as the double scattering term, are given in the same way by

A l l - ( a l l - A12A21A21) -1

xl

1)Cl(Z~)tff(fi)Pl(cosOa~p) (347)

l

The submatrix that we have to calculate is only A 11, and it is written in terms of the submatrix Aij's,

_ ([(1 -

~) exp{ i(~R~+O 9Ra)} /R~

ot(:/:A)

F(a~p;/3) = - E ( 2 / +

(1--x)-l-- ( ~llA21 A22A12t

[(1 - X)-I]AA

(345)

i=0

where gfio) is the damping plane wave (PW), whose wave vector p is given by P(pl + ip2) = ~/3 in simple PW q~o; t5 is

A22 :

Correspondingly we can write the matrix (1 - X)-1

~P-/-- E V-p: dr(i)

i=0

~.a~,p(r)F(aot'ot, /3)F(o/c~p; /3)

ar162

-

• exp{i/3(Rce

+ R~,~) + iO. Ra }/(RaRa,~)

(344)

(349)

We can expand [(1 - X) -1 ]22 in the power series of X; we should note that the power series is already in the inverse [ . . . ] - l , so that the low order expansion still includes a infinite partial sum of the multiple scatterings [24, 25]. Numerical calculations demonstrated the efficiency; for example, the computation time is only about 5% of that for the full multiple scattering calculation for a cluster with 27 Fe atoms [25].

We can also explicitly write down the single scattering function after the loss ~ ) and the double scattering function ~p~2) and so on in the same approximation, l-

~(~) (r) =

Z

It"

't'(~ exp{ --i (/3'Rg + ~'. Rt~)} Wp,flA(r)

fl(r

• V(p'fla; ff)*/R~

(350)

448 r

FUJIKAWA Z

(r) =

~,(o) v"p,E,E (r)

i

/

E#E'(#A)

x exp{-i/Y(R E 4- R~E,) 4- iP'. R E, }

x F(p'i6'fl;/Y)*F(/3'/3A; ~')*/(REREE, ) (351)

/

A

where ~' is defined by ~' = ~'/5' and/5' is the principal value of V/2(ep,- iI'f). Substituting Eq. (345) into Eq. (292), we can express u in the form OO

u(p'; p) -- ~ A(p'; p) j=l

(352)

A2

(llA(p'; P)llm) = (P'(~176 (llA(p'; P)2lm) = (P'(1)llp(~ (/Ia(p'; P)31m) = (P'(~ (/Ia(p'; p)4lm) = (P'(Z)/lp(~

(353)

(IIA(p'; P)51m) = (P'(~ (IIA(p'; P)61m) = (P'(1)llp(1)m) where p(2) is the abbreviation of 7z(2), and so on. The A1 term describes the direct deep core excitation inelastic scattering, whereas A2 and A3 describe the inelastic scattering at site A accompanied by single elastic scatterings after (A2) or before (A3) the inelastic scattering. A4, A5, and A6 describe the second-order processes with regard to elastic scattering of the probe electrons. In the above expressions we neglect the bare exchange effect, which becomes negligibly small in the high energy excitation. Schematic representation of these terms is given in Figure 10. We now have the explicit formula for the excitation operator A(p'; P)I, A(p'; P)I --

exp(--iApl ~~pl)~

9 r)

, ,) exp{--(lAP2 4-lAP 2 }

(354)

where Apl is the real part of the momentum transfer, Apl = P] - Pl, and IA and 1~ are the distance between site A and the solid surface measured in the directions Pl and p~. In Eqs. (345), (348), (349), and (350), if we replace ~(0) with ~ (0) in the core region and use the same approximation to derive Eq. (353), we obtain the explicit formulas for A2 and A3, A (p'; P)2 1

exp{iRE(/Y - p~ COSOp,flA -- iApl 9RA)}

R IP A -- P'i1

E(#A)

x F(p'flA; if) ' ') x exp{--(laP2 4-1Ep 2 - i(pE a - Pl)" ( r - RA)}

AL

5

A6 Fig. 10. The inelastic scattering amplitudes are schematically shown. The hatched (empty) circles stand for the atomic site at which the inelastic (elastic) scattering occurs. The arrows indicate the propagation of the electron waves. A 1 shows the direct inelastic scattering amplitude accompanied by no elastic scattering. A 2 (A 3) shows the one accompanied by a single elastic scattering after (before) the inelastic scattering. In the same way, A4, A 5, and A 6 describe the second-order contributions; A4, for example, shows the inelastic scattering amplitude with double elastic scattering after the deep core excitation.

where PEA t and Paa are defined by PEA ' -- [IE Pl' and PAc~ = - R a p 1 . The higher order terms such as A4, A5, etc., can easily be obtained in the same way. By use of the expansion shown by Eq. (351), the intensity I ~ (see Eq. (316)) is represented by the sum o f Aij's, which are defined by A

,0_ Za~ ij

(355) ~o _ 2k ZRe{(g)clA~IRIYL)(R, YLIAjlc~c) } (356)

A (p'; P)3

Jr

1 2Jr2 Z

exp{iRa(/5 - Pl cosOAotp -- iApl 9RA)}

c~(#A)

Ra IPAa - Pl 12

x F(A~p; fi) x exp{-(lap2 + l'aP2') --i(P] -- PAa) ( r - RA)}

It is easy to show that .~o : /~i" For simplicity we will consider the excitation from the core orbital 4u = Rlc (r)YLc (r) with angular momentum quantum number Lc = (0, 0), that is, the excitation from K and L1 edges and so on. In this simple

ELECTRON ENERGY LOSS SPECTROSCOPY

DIAMOND (111) 0

o

0

0

o

X

X

X

X

X

X

0

0

o

0

o

o

x

x

0

0

X

0

0

X

X

o

X

o

e

x

~

X

X

o

x/~

0

x

~

.515 j~

x

0 X

o

DI AMOND (111 ) C K - e d g e Ei=3OOOeV ek=20OeV e i = e t = 3* 19x2 atoms

o

X

X

o

o

0 0

K

At (111)

449

X

.ut)J

o

X

X

X

O

O

O

%-2 o-4

o 1st layer

;,,,

x 2nd layer

1

Fig. 11. The surface structures of diamond (l 11) and AI (111) surfaces. The arrows indicate the directions of the incident electrons.

"1o

b

1

-

'

I

....

:

........

I

-

"~'-~-

t

) dipole

0

0

r

case

o ,..=,

AO1 is given by

-1

,4~1 - rh(0, k; Apl, Apl)

exp{--2(IAP2 + l~APP2)}

(357)

;

4

where rh (0, k; p, q) is defined by rh(0, k; p, q) =

32zrk

p2q2 Z ( 2 / +

1)p(k,

p)tp(k q)lPl(COSOpq)

l

(358) In the above formula, Opq is the angle between p and q, and p(k, q)l is the radial integral defined by

p(k, q)l = f Rl(kr)jl(qr)Ro(r)r 2 dr

(359)

We can also obtain the explicit formulas for ,412, ,413, etc., which include the effects of elastic scattering of a probe electron. Here only those for ,412 and ,~ 13 are shown: /~01 = 2 Z

Re[exp{-iRc~(ff-

pt1COSOp,flA)}

.....

; ....

(c) error

."

.......

-4

~~~"

%2 171

o

0

- - - - - direct inelastic scattering 0

30

60

90 120 q:lf.( d e g r e e )

" i80

Fig. 12. The calculated carbon ls EELS intensity from a diamond (111) surface as a function of ~bf [68]. In (b) we show the EELS intensity calculated in the dipole approximation, and in (a) we include the effects from the multipole excitation. In (c) the relative error of the dipole approximation is shown for the direct EELS and the EELS with single scatterings of probe electrons.

j3(:/:A)

F*(p'flA"/3')]th(lc ' -- P, Apl) , , k", P[3A • exp[--{ZlAP2 + (l~a + l~)p~2}]/R E •

(360) /]~ 1 = 2 ~

Re[exp{-iRa(fi

- Pl cosOAotp)}

ot(-CA)

• F*(aotp;/5)]rh(lc, k; p ' - Paot, Apl) • e x p [ - { 2 / ~ p i + (1A -Jr-l~)pz}]/R~ The explicit formulas of rh for lc = 1 and 2 are given in [ 10]. In Eqs. (357) and (360), the damping effects of probe electrons are explicitly included as the exponential damping factors, which are important for the study of the surface sensitivity of EELFS spectra in a variety of modes (see Fig. 1). 5.4.2. Calculated Results

We discuss here the effects of elastic scatterings of probe electrons on EELS. First we discuss the grazing incidence and small takeoff angle EELS from diamond (111) and AI(111)

surfaces (see Fig. l c). Their surface structures and the direction of incident electrons are shown in Figure 11. We use the cluster approximation to describe the processes of scattering from the surfaces. For small incident (0i) and takeoff angles (Of), 0i = Of = 3 ~ the two-layer cluster model is sufficient; that is, this mode is very surface sensitive. Figure 12 shows the calculated C Is EELS intensity A~1 + 2(,402 + ,403) from the diamond (111) surface as a function of ~bf under the conditions 0i = Of = 3 ~ Ep -- 3 keV, and Ek = 200 eV [68]. In Figure 12b the intensity of the dipole approximation, where we use only one term l = 1 in the sum (358), is shown, whereas in Figure 12a we include the effects from the multipole excitation processes in Eq. (358). In Figure 12c we show the relative error 6or, defined by 6er -- [I ~(dipole) - I ~ (multipole)] / I ~ (multipole) The solid lines show the calculated results including the elastic scatterings of probe e l e c t r o n s AI01 -]- 2(,402 + ,403) , and the dashed lines show the results without the elastic scatterings ,~~1

450

FUJIKAWA

A1(111) A I K - e d g e Ei=3000eV r eV el=Of=3" 13 x2 atoms (a) multipole

(a) DIAMOND(Ill) C K-edge .:.:.'_:_:,"::4.. "~':,:,: : < < . Ei:3OOOeV ei:ef:3* -

---O--- ~12

2

"'-... " ~ .

~''-'~22

...., L

"

........ s i n g l e

~.......'7"~-~

~23

4-,

...... "'..~..

: • : 14 ~ ~15

~

"'--.

--'--;~'~6

~

~....

...... ~ ~ " .

0

,

,

.

.

.

.

~,

-

~,

.

.~,.".'-..2'

.

.

.

0

.-

"

O .

.

.

.

.

1

I

i

2

3

'

''

I

"'

4

5

r (~1

so '

'

~oo : ; 0i . . . . .200 . . . . ~. . 25o . . . . secondary electron energy (eV)

:

3 oo

(b) ,,.-,.,

E, ,,,..,

8

(b)

v ......

...

6

1.66

AL(111) AI K-edge Ei=3000eV .oi=ef=90 ~ 13x 5 atoms

- ~ ~

>. ,.w,,, o~ I/1

i,,,,

E

E

~., 4 l:

.~

> o~

-.-, 2 11} ll/

~176

- - - - - - ~11 ----13--- ~'12 ~~'23

""

"-'~

-"

~22

I

;~14 ~15 ~16

single ,double ........ s i n g l e

9

0

"!

1

'

I

!

t'

2

3

4

,

5

r(~,) 50

100 150 200 secondary eledron energy

250 (eV)

300

Fig. 15. As in Figure 14, but for the backscattering.

the case of EELS from diamond, none of these terms show oscillatory behavior, for the reason given above. Several workers have made use of a backscattering experimental setup (see Fig. l b) [4, 69]. The EXELFS spectra observed in this mode have also been analyzed with the use of conventional EXAFS analyses; however, we have had no sound theoretical background for the analyses. Figure 15 shows the energy scan mode of (a) carbon and (b) aluminum K-edge EELS from diamond and A1 (111) surfaces under backward reflection conditions ( 0 i - - O f - " 90~ where Ep is fixed at 3 keV but ~p, is scanned [12]. We use five layers to obtain good convergence with regard to the cluster size. This setup is less surface sensitive than the mode in Figure 1c and discussed above. All of A~i's are much smaller than the corresponding terms in Figure 14 because of the small atomic excitation matrix elements rh in Eq. (358) in the large-angle scatterings. In Eq. (359) p(k, Ap)t should be small enough for large Ap in the spherical Bessel function jt (Ap). Although the large-angle scattering EELS are expected to give oscillation (see Eq. (360)), we do not find such oscillation for the C 1s EELS from diamond

Fig. 16. Fourier transform of the spectra in Figure 15b after the subtraction of the monotonic part [ 12]. Only the single elastic scattering effects are included in (a), and the single and the double elastic scatterings are included in (b). The transform is performed in the range 50 < Ek < 300 eV. The phase correction is applied in the transform.

(111) surfaces. This unexpected result is explained by the fact that the carbon atom is a very weak scatterer for fast electrons (Ep, > 2.5 keV). On the other hand, we find prominent oscillations in A~2 and A~4, and small oscillations in A~2 and A~3 for the backscattering EELS from A1 (111) because the elastic scattering is not so weak. In the EXELFS analyses, the Fourier transform is usually used to obtain the distance from an excited atom to surrounding atoms [4]. The EELFS oscillation is caused by the interference of the electron waves ejected from a deep core orbital, which is described by Eq. (318). However, as we have observed in Figure 15b, the interference between elastically scattered electron waves of probe electrons can show the other kind of oscillation, similar to XPD oscillation, particularly under the large-angle scattering condition [70]. We now apply the Fourier analyses to the EELS spectra shown in Figure 15b. If we misunderstand the oscillation as the EXELFS and apply the conventional Fourier transform technique to such an EELS spectrum, we may obtain incorrect information about the bond length. Figure 16a shows the result for the single scattering approximation, and

452

FUJI KAWA

0 K-edge

Ei= 2000 eV

m

(a)

" " ' , . . , o ,,,,

o

e i=ef=3* ",,

... -.o

~

..

D

" ,,.

~4

",.,. ~ -~

v

o. ~176176 ,,,,. ~ ...,,.

" ~

~

ol r"

*~

,,

,..

r ~ ,,,.,.,,

O-

'

50

-~

--:

100

"',

150

=of=

0

i lb>

,.,

-'

'-

200

250

300

9o* """

......................

"'--

2

--!

8?..

..

5

~

"-.

"-

6="

2~

9"

I 0-

-"

50

100

secondary

.... '

150

"-

200

electron

0 ~

-~. . . . . . . . . .

250 energy

300 (eV)

Fig. 17. As in Figure 14, but for p(2 x 2)O/Ni(001) (solid line), c(2 x 2)O/Ni(001) (dashed line), and Ni(001) (dotted line) surfaces in two detection modes: (a) 0i = Of = 3 ~ (b) 90 ~ The EELS intensifies are normalized to those in (a) [12].

tions of e~. The EELS intensity reflects the density of oxygen atoms in the surfaces. Under this very small-angle scattering condition, the observed EELS is very sensitive to the first layer, and then EELS intensities for the adsorbed systems are not so small compared with that from the oxide surface. However, the EELS spectrum for the NiO surface shown in Figure 17b is quite different from those for c(2• and p(2• surfaces, and the spectra for the adsorbed systems are nearly the same. The EELS intensity for the oxide surface is about 100 times larger than those for the adsorbed surfaces. In the case of adsorbed systems, if the elastic scatterings from the surrounding oxygen atoms, which are in the first layer, mainly contribute to the EELS spectra, we would observe different behaviors between them because of different atomic arrangements around excited oxygen atoms. Therefore the elastic scattering not from O atoms but from Ni atoms in the substrate plays an important role in the backward reflection because Ni is a stronger scatterer than O. The relative atomic configurations between excited O and the nearby Ni atoms are the same in these adsorbed systems, and we find the same EELS spectra for the adsorbed systems. The plural oscillation is stronger than that found for A1 surfaces because Ni is a much stronger scatterer than A1. Other approaches to the elastic scatterings of probe electrons are also found in some of the literature; they are based on the long-range order theory in terms of Bloch waves [71-73]. Of course, this technique can be applied only to well-ordered surfaces. Mila and Noguerra also proposed a short-range order theory that takes the single elastic scattering of fast electrons only after the core excitation [74]. Furthermore, they simplified the EELS formulas by averaging over 4zr. Because of the presence of the surface, 4zr averaging is impossible in practice and is an oversimplification.

5.4.3. EXELFS Formulas Figure 16b shows the result for the single + double scattering approximation [12]. In Figure 16a we find a strong peak at 1.61/~, and in Figure 16b we find a strong peak at 1.66/~. If the oscillation is true EXELFS due to excited electrons from a deep core, we can obtain a true bond length of 2.01 ~. If the plural oscillation happens to give a realistic length, we could be led to an incorrect conclusion. Calculated results for more complicated surfaces help to reveal the surface sensitivity of the grazing incidence and smalltakeoff-angle EELS. Here we illustrate the calculated results for adsorbed systems p(2• and c(2• O/Ni(001) and a single crystalline NiO(001) surface [ 12]. Adsorbed oxygen atoms are on hollow sites with the shortest O-Ni distance (1.96 ~) for both systems. The calculated EELS spectra for probe electrons of 2 keV are shown in Figure 17, where (a) and (b) are spectra at 0i = Of = 3 ~ and 90 ~ In the forward scattering shown in Figure 17a, the three spectra are smoothly decreasing func-

The single elastic scattering intensity I 1 with regard to the photoelectron is also represented by the sum of each contribution of elastic scattering within the intrinsic approximation (see Section 5.2), / I ( E ) -" Z

ISnl2 Z / ~ ] j

n

(E -- (,On)

(361)

ij

where each ,41j is given in the same way as defined by Eq. (356). Here we have to calculate ,4~j for different channels of core hole states. For the excitation from a deep s orbital we obtain the explicit formula of/]~1 from Eqs. (339) and (340), ~1

32at

11--(Apl)4

Z n

ISn

12

Z

Im[exp(ZiKnRy)F(AyA;xn)

y (=~a)

x F~,(Apl; tCn)Fy(-Apl; Kn)]

t t) }/R•2 x exp{--Z(lAP2 + iAP2

(362)

ELECTRON ENERGY LOSS SPECTROSCOPY 1.4

where l"y (Apl" Ifn) is given by F•

Kn) -- Z ( 2 / + l x

1)i-lPl(cosO•

1.2

Ap)t

c/(z•

_ 0

K) ~ 3i - l c o s 0 •

(a)

~

(363)

where 0• is the angle between the momentum transfer Ap and R e. F• ( - A p l ; Xn) can be obtained, if we replace cos 0• with - c o s 0 y in Eq. (363). In the very small Ap limit, we can show that the ratio A^111/A^011 is reduced to an ordinary EXAFS formula, which will be checked below. In this limit, jl(Apr) is approximately given by jl(Apr) ~ (Apr)//(21 + 1)!!, and p(k, Ap)0 vanishes because of orthogonality between the s wave radial part Ro(kr) and the core radial part R~ (r). Then the main contribution arises from p(k, Ap)I; 1-'~, is approximated by

r•

453

Ap)lcl(z•

A)

n" 0.6 0.4

0.2

0

50

L:4.

0.8

(364)

After we substitute the approximate expression shown by Eq. (364) into Eq. (362), we obtain the ordinary EXAFS formula for the ratio .4 ~1///~01'

0.8

,l=..~.

1O0

)Z.6.

150

~

j

(b)

o

0.6

0 CO rr" 0.4

0.2

-3 Z ~'~ n

Isnl2 Kn Z

cOS2 0y Im[exp{2/(Xn R e

+ ~A)}

y(=/=A) 0

• F(AFA; Kn)C1(Z•215

2

(365)

The oscillating term Z• in EXELFS, which is given by the argument of Im in Eq. (362), is quite similar to the corresponding term Z~, in EXAFS, which is given by

Z• = -9exp(2ikR• + 2i6~)F(AyA;

50

1O0

150

0scat (de0.) Fig. 18. The ratio 1(21 + 1)p(l)/3p(1)l as a function of the scattering angle for ek = 50 eV (a) and 350 eV (b) [58].

K n ) p ( 1 ) 2 COS2 0V

(366) In the very small Ap limit, we have shown that Zy is reduced to Z• because of the orthogonality between R~(r) and Ro(kr). When they use high-energy (ep > 100 keV) EELFS in transmission mode, this condition is satisfied, and they obtain the EELFS spectra equivalent to the corresponding XAFS spectra [3]. When we study EELFS spectra in the reflection mode, we should carefully investigate the energy and angular dependence of Z• [58]. Figure 18 shows the absolute value of the ratio of ( 2 / + 1)p (l) to 3p (1) as a function of a scattering angle for I = 0-6, where the fast probe electron (2400 eV) excites an oxygen ls electron. The photoelectron kinetic energy ek is 50 eV in Figure 18a and 350 eV in Figure 18b; EELFS measurements are usually carried out for the energy range ek = 50-350 eV. Because the relative contribution of the s-wave Ip(O)/3p(1)l at forward scattering is about 10% for e~ - 50 eV and about 5% for 350 eV, transition to the s-wave cannot be neglected, even in the forward scattering in these energy ranges. As the binding energy of an oxygen ls orbital is 532 eV, Apl is about 3-5/~-1, corresponding to ek = 50-350 eV. The wave vector of X-ray plays the same role as Apl in the X-ray absorption,

whereas it is small (only 0 . 3 - 0 . 5 ~ - 1 ) in the EXAFS energy region. In contrast to the forward scattering, the s-wave plays a more dominant role in the backscattering. A similar result has been obtained by Tomellini and Ascarelli [70]. Furthermore, we can see that p(0) happens to vanish at a scattering angle of l0 ~ In the low-energy region (~50 eV), the excitation amplitude of the partial waves of 1 -- 2, 3 . . . . becomes negligibly small, and the amplitude of the s-wave disappears at this angle, so that the dipole approximation in the sense of the irreducible tensorial expansion works well (see Eq. (363)). Thus we can expect that the electron ELNES would be equivalent to the corresponding XANES under this condition. Here we have only studied "4~1; however, the r" dependence is nearly the same in the multiple scattering ELNES formula (342) as in "4~1" An experimental proof for the above theoretical consideration is also shown later. We are very familiar with the polarization-dependent anisotropy of EXAFS cos 2 0• as shown by Eq. (365). This simple anisotropic behavior is due to the electric dipole transition approximation. In EELFS, however, several partial waves have nonnegligible contributions to 1-'• as described above, so that the phase function of EELFS, arg Z• in Eq. (362) is different from that of EXAFS, arg Z• Furthermore, this phase func-

454

FUJIKAWA

,.2 ~ p

l

O /

O

Oout

.. ..

9

9..

....

..

..

...-

~' '~ .,~

_

/ . ' . ~ ' " ~ ' " ' - . ' . " "'-...

,"

L

"...

E ..........

,,';.," . . :: ::. ................... ::.::....... .:: .: ::_._:: :: :: ...-.....

o.e F

.,?.,=

J

ff~t"~

[ "" .~

.......-" ...

1 ~"

Ni

\

(a)

/ - ,"]./-

I

"

"'-.b.. "-, ' " - , ""..

,',.'>-"

/// o.e LF/..'>" I,'./: /

"-,.

,

-.l

I

"'-C'"-

I

-,. "'~. '-vJ

F ,.:;'

0.4

" ..

"..

" - . '-..

'/


s +

q~i = 2nzr

n e Z

(26)

Introducing 4) = 4>s + 4~i, one arrives at the condition In the basic theory discussed previously, we assumed a symmetric quantum well, V(Q, z) = V ( Q , - z ) , thus ignoring any effects of the substrate that would affect the potential of the film at the film-substrate interface. It is straightforward to enhance the model to a different barrier height at the film-substrate boundary with respect to that at the vacuum-film boundary. Further, one can introduce additional potential steps in order to mimic polarization effects due to the substrate.

2.2.2. EnvelopePicture of Quantum-Well States In the preceding section, we employed a description of quantum-well states based on plane waves; for example, we assumed free electrons in the three regions of the system and neglected any "internal structure" of the potential in the film region. Now we take into account the crystal potential in an approximation, which was originally introduced for semiconductor superlatrices [ 18, 19]. We start with the Schrrdinger equation (8) for the infinitely extended system, the so-called bulk system, where V (r) is now the potential of the bulk. The latter can be written as a sum over site, potentials V(r) = ~ i V ( r Ri), where the vectors Ri form a lattice; that is they can be expressed in terms of basic translation vectors aj, j = 1, 2, 3: Ri --- ~ = 1 nijaj, nij E Z (cf. Section 2.1.1). Therefore, the crystal potential is translationally invariant with respect to lattice vectors R, V (r) = V (r4-R). Following the argumentation in Section 2.2.1 [Floquet's theorem; cf. also Eq. (7)], the wave functions fulfill the Bloch condition qJ(r + R; k) = exp(ik. R)qJ(r; k)

(24)

Because the wave functions have to be square integrable, the wave vector k has to be real. These wave functions are called Bloch states and can be classified with respect to k. Their energy eigenvalues, the bulk-band structure, are denoted E (k). The electrons have to be confined to the film, which is again considered as infinitely extended in the xy plane. We therefore

k• =

2n~r - 4)

2Nd

n e Z

(27)

In conclusion, the boundary conditions at the interface restrict the allowed values of k• to those compatible with the "roundtrip" criterion. The energies of the QWSs are therefore given by E(k• with k• from Eq. (27). For a rectangular well with infinitely high barriers, the phase shift 4) is either 0 (odd parity, 4~s = ~bi = 0) or 27r (even parity, 4>s = ~bi --- ~ ) , which immediately yields Eq. (22). The preceding k• quantization allows for an accurate determination of the bulk-band structure E (k• by ARPES [20-22]. For fixed kll, one measures photoemission intensities for films with different numbers of layers N and thus determines E (k• For semi-infinite systems, this method does not work because there is no restriction for k• that is, it is not conserved in the photoemission process and therefore remains unknown. Now consider a Bloch state with energy E (k• in the range of a bulk band. Its wave function can be written as qJ(z; k•

= exp(ik•

(28)

where u(z) is periodic with the interlayer distance, u(z + d) = u(d), which follows immediately, from Eq. (24). We now assume that k• takes a value hedge ,,• close to a band edge; for example, hedge ,,• = 0 or Jr/d. A wave function at another energy than the bulk-band edge but within the bulk-band range, and therefore k• ~ hedge ,~• , can be approximated by qJ(z; k•

~ F(z)~P(z; k~_dge)

(29)

where F (z) is slowly varying: The wave function qJ is given by qJ (k~_dge) but modulated by the envelope F (z). According to the previous consideration on interference within a film, the envelope is given by exp(ik~nVz). Thus, the total wave number k• reads k• -- k~_nv + hedge ~• . Note that, a Bloch state with hedge ,~• can occur as QWS if it fulfills the boundary conditions, that is, hedge ,~• - k• In this case, F(z) = 1. Further, the envelope

486

HENK

accounts for the correct boundary condition at the interfaces and obviously, according to Eq. (27), k~_nv depends on the phase hedge

shift 4~. If~•

(a) Ev

Ev

Ev

T

1i

E V

is given by zr/d, we have

k ~nv =

2(n - N)zr - r

n E Z

(30)

2Nd It is worth noting again that the microscopic details at the interfaces are "smeared out" in the preceding envelope approximation. Therefore, it should be applied only in cases of thick films in which there is a bulklike potential of considerable spatial extent. In very thin films, for example, those in which the interfaces are very close, the previous approximation becomes questionable.

2.2.3. Tight-Binding Description of Quantum-Well States: Rare-Gas Films on a Metallic Substrate We now address a description of quantum-well states based on the envelope theory. This model has been introduced by Grtine and co-workers in order to describe photoemission experiments of rare-gas films on metallic substrates [22]. Due to the inert behavior of the rare gases, bulk- as well as surface-band structures can be described very well within tight-binding theory. For example, the Xe 5p states are split due to spin-orbit coupling (SOC) into 5pj=l/2 and 5pj=3/2 states, j denoting the total angular momentum. In layered structures (as well as in the bulk of fcc-Xe), the 5pj=3/2 states are further split due to lateral interactions, for example, the overlap of orbitals located at different Xe sites [23-25]. Tight-binding models have proven to reproduce the experimentally determined energy dispersions very well [26, 27]. The main problem in describing the energy dispersion of Xe states on a metal substrate measured by means of ARPES is to account for the change in the Xe binding energy in dependence on the amount of adsorbed Xe. In particular, the binding energies of states located at the Xe-metal interface are substantially smaller than those of states in the other Xe layers. This behavior can be attributed either to a change in the work function, 9 which is due to the adsorption of Xe, or to the image force acting on the hole, which has been created in the photoemission process (cf. Section 4). The first effect is a so-called initial-state effect because it is present in the ground state of the system. The second is a final-state effect because it occurs in the excited system, that is, in the state with the photoelectron missing. To account for these effects, the simple rectangular well has to be extended as shown in Figure 8. Instead of three regions (I, II, and III), we now have four (A, B, C, and D). In the initialstate model, the change of the work function is VB, which is known from experiment. The Fermi energy EF is fixed by the substrate. The binding energies are E = VD + VB -- ~M - - EF and E = VD + ~ M - - EF in the initial-state and the final-state model, respectively. 9The work function is the energy difference between the vacuum level and the Fermi level.

B!

C t E

E

1 '

I

,!....

!

o

C

.-|--i

1

X

! ' i

O it

~X

Fig. 8. Quantum-well models for rare-gas films on a metallic substrate (left, initial-state model; right, final-state model). E is the electron energy and ~M the work function of the substrate (no film present). The four regions A, B, C, and D are the substrate, the rare-gas layer next to the substrate, the remaining rare-gas layers, and the vacuum, respectively. Reprinted with permission from M. Grtine, T. Pelzer, K. Wandelt, and I. T. Steinberger, J. E l e c t r o n Spectrosc. Relat. P h e n o m . 98-99, 121 (1999). Copyright 1999, by Elsevier Science.

Due to the confinement of the electrons to the Xe film, one assumes exponentially decaying plane waves in regions A (substrate) and D (vacuum) with constants lr a and too [cf. Eq. (16)]. The latter are given by KA = V/2(VD + VB -- di)M -- E )

(31a)

KD -- V / 2 ( V D -

(31b)

E)

in the initial-state model, which we focus on in the following discussion. In region C, the Xe film, one writes the wave function according to the envelope theory as

~ c ( z ) = C sin(kcz + @)u(z)

(32)

where sin(kcz + 8c) is the envelope and u(z) is periodic with respect to the interlayer spacing d: u(z) = u(z + d). One further assumes that u is symmetric with respect to the Xe layers, OzU(Z) = 0 at z = n d , n = 0 . . . . . N, where N is the number of Xe layers. In region B, the wave function takes the same form as in Eq. (32) but with labels B. Note that u(z) need not be explicitly specified. The band structure E(k) of bulk Xe is approximated by

E(kB) = --yB[1 -t-cos(kBd)] -+- VB -- 2(yB -- YC)(33a) E(kc) = - y c [ 1 + cos(kcd)]

(33b)

that is, one uses the energy dispersion of a simple tight-binding model. Note that YB and Yc are allowed to differ. As in the case of a rectangular quantum well, the dispersion relation is obtained via matching the wave functions at the interfaces. This yields the transcendental equation

kc tan[kBd + arctan(kB/xa)] = --kB tan[(N - 1)kcd + arctan(kc/xo)]

(34)

which is used to determine the energies of the QWSs. After eliminating xa, xO, and k . , one eventually obtains an equation in kc with adjustable parameters y . , Yc, and Vo that have to be determined by comparing the experimental QWS energies with

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY 9

I

"

I

"

I

'

I

"

'I'"'

'

I

'

I

" Xe/Cu(100)

Xe/Cu(lO0)

"

I

'

I

'

I

I I I @ @ID -

-

He I, normal emission 45 K

487

14' 4~ I, I o o l 4 , ~.4 # I @ al l~z~ I @ @ ~ e # '11" ~ 4~ ell ~ ~I" e ollo ~ Io = al I~ 9

n

,

I

,

I

,

I

n

9

.

I

.

I

n

n

,

I

-

n

I

7 - Xe/Ru(0001)

6 -

el el

E: :3

u.I

L9 < rr LU > O O (1.) X

.6 L_

1_.__..

,--..,

03 Z iii I-Z

4 3 -

II

r I

6.5

7.0

7.5

8.0

8.5

Fig. 9. Experimental photoelectron spectroscopy from Xe films on Cu(100) in normal emission (kll - 0) and unpolarized light with 21.22 eV photon energy He(l). The Xe dose in langmuirs (L) is denoted on the right of each spectrum. Arrows indicate intensity maxima attributed to spin-orbit split 5pj=l/2 and 5p j=3~ 2 quantum-well states. Reprinted with permission from M. Grtine, T. Pelzer, K. Wandelt, and I. T. Steinberger, J. Electron Spectrosc. Relat. Phenom. 98-99, 121 (1999). Copyright 1999, by Elsevier Science.

that obtained by theory for all film thicknesses. Note that the adjustable parameters do not depend on the number of layers N. The experimental photoelectron spectra for Xe films on Cu(100) are shown in Figure 9. For very low Xe coverage (cf. the lowest spectrum), one observes two Xe-derived maxima with binding energies that differ considerably from those at higher coverages. This can be attributed to the different potentials in regions B and C. At higher Xe coverages, the number of QWSs increases, as can be seen in Figure 10. For all three substrates, the pattern of energy positions is similar except for the specific binding energies. Each pattern can be divided into two groups, one for the 5pj=l/2 states, the other for the 5pj=3/2 states. This separation accomplishes the fitting procedure because each group can be fitted separately. For film thicknesses N > 2, each pattern is almost symmetric in energy, which can be attributed to the underlying tight-binding band-structure of Xe, Eq. (33) (see also Section 4.2.4). However, distinct deviations from the symmetry occur: Open circles

.II 4, oll 9 i 0). Inserting Eq. (130) into Eq. (133) and introducing the nonlocal spectral density

G+(E) - 27ri Z n

In)(nlr(E - En)

(135)

508

HENK

one eventually obtains K G+ R2(j(R)) - -32zr2c2(~*(E+co)[AIm (E)At I~ .

(E+og))

(136) K -- ~/2(E + co) is the momentum of the photoelectron. The time-reversed final state lO) fulfills G+(E)

9 (r, E + co) -- exp(iK 9r) + f dr'G r (r, r'; E + 09)V(F) G r(E+w)

x exp(iK. F)

(137)

A+ ~"which establishes the connection of photoemission with LEED. First, I~) is a superposition of an incoming plane wave, the first term in Eq. (137), and outgoing waves. The latter are represented by the integral in Eq. (137), which gives nonzero contributions only inside the crystal, in particular, where V (F) # 0. The retarded Green function propagates electrons from the interior of the solid (F) to the vacuum region (r). Therefore, the integral can be regarded as giving rise to reflected beams in vacuum. In short, I~) is a state suitable for the description of a LEED experiment. I~*) is known as a time-reversed LEED state. As a last step, we observe that the final state can be written as 1~*) = Gr(E -1- o9)1~) where I ~ ) is the plane wave at the detector position. The expression for the photocurrent then eventually reads

j ~ - ( ~ [ a a ( E + c o ) A I m G + ( E ) A t G r ( E + o9)1~) (138) Equation (138) can be represented by the Feynman diagram shown in Figure 30. Its interpretation is straightforward if Eq. (138) is read from the right. First, the photoelectron state I ~ ) with energy E + co is propagated by the retarded Green f u n c t i o n G r from the detector to the interior of the solid. Subsequently, the dipole operator At mediates a deexcitation to initial states with energy E, which are described by the nonlocal density of states, Im G +. These are excited into the outgoing photoelectron state ( ~ [ G a by the dipole operator A. The diagram in Figure 30 is that of lowest order. Higher order diagrams include, for example, the (screened) Coulomb interaction between the final and the initial states, that is, scattering between the photoelectron and the remaining hole. These terms are, for instance, essential for the description of the resonant behavior of photoemission intensities from Pd [158]. Usually, one neglects higher order terms; that is, one assumes the sudden approximation [ 159-161 ]. Applying the Dirac identity,

1

lim = 7) ~--,o+ x 4- i rl

(1)x

TiS(x)

~l12~(gm

the photocurrent can be expressed in golden-rule form, j ,~ ~ [ ( ~ * ( E

(140)

(141)

The main difference between the golden-rule and the Green function expression, Eq. (138), is that the former holds only for real energies, whereas the latter can also be applied for complex energies. In other words, the golden rule is only valid for infinite lifetimes, whereas the Green function takes into account finite lifetimes of both photoelectrons and holes. The description of electron scattering in a many-body theory leads to quasi-particle states and to the self-energy E, sometimes denoted optical potential [162]. In the lowest order approximation, the self-energy is local and homogeneous. Its real part gives rise to shifts of the quasi-particle energies. For example, fundamental bandgaps obtained from densityfunctional calculations for zinc-blende semiconductors are too small with respect to the experimental values; inclusion of E in the GW approximation [ 163] increases the bandgaps considerably. Another example is Ni where the experimental energy shift between spin-split bands is about 0.3 eV, in comparison to 0.6 eV from density-functional calculations [ 164]. The imaginary part of E accounts for the lifetime of the quasi-particles; that is, an increase of Im E leads to broader photoemission spectra [ 165, 166]. This can be attributed to the spectral function A(E) = - ImTr G(r, r; E)/Jr,

A(E)

Em)

+ ~o)lAIm>12~(E + co- E m )

m

(139)

which establishes for any state IE> the relation [cf. Eq. (134); 7) stands for principal value] Im(EIG(E + ir/)lF~)- -Jr

Fig. 30. Feynman diagram of photoemission according to Eq. (138). The double line represents the detected state I ~ ) with energy E + 09 and surfaceparallel momentum kll. Green functions G a, G r, and G + are represented by arrow-decorated lines, photons by wavy lines.

_=_

S

TM

m

3 ( E - Em) real energies F 1 Jr ( E - E m ) 2 -Jr- r 2 complex energies Im E(Em) (E - Em - Re ]E(Em)) 2 q- (Im E(Em)) 2 general case (142)

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY

4.2.3. Formulation within Multiple-Scattering Theory

509

solutions [V(r) = 0] read [76]

As we have seen in Section 3, multiple-scattering theory provides an excellent description of the LEED process. In the previous, we have further established a close connection between LEED and photoemission; in particular, the final state in photoemission is a time-reversed LEED state. Guided by these findings, photoemission should also nicely be described in terms of multiple-scattering theory. Instead of sketching Pendry's formulation [136, 167], which provides a very fast algorithm (in terms of computational time) but a rather technical theoretical description, we present a formulation in terms of Green functions. Of course, both methods give identical results. In the formulation of the LKKR method for LEED, we have obtained the scattering properties of the entire semi-infinite system by consecutively treating the scattering of smaller entities: the single-site t matrix for scattering from atoms, the M and Q matrices for layers, and from these eventually the reflection matrix of the semi-infinite solid. This idea appears again in the calculation of the Green function. We shall start with the Green function of free space, then treat an empty layer embedded in the otherwise occupied system, and eventually treat a full layer. Before turning to the investigation of the Green function, we sketch the very basis of multiple-scattering theory, the Lippmann-Schwinger equation and the Dyson equation.

(r[ f~r ) --

2c 2

co'. k E + c 2Xr

exp(ik, r)

(145)

and (fkL [r) -

~E+c2( 2c 2

(X

r)r

r r co''k)exp(_ik.r ,(X) /~c 2

) (146)

In angular-momentum representation, they are given by

(rlz~}

--

ickSx

2c 2

E+c

z-f(kr) ( r l x x )

(147)

2

and

(z~lr)_~E+c2( 2c 2

zl(kr)(XAI ~f) '

-ickSK E+c

2

z~(kr)(xxl~f)

)

(148) with z = j for regular or z = h for irregular solutions. The wave number k is x/E 2 - c4/c. Each representation can be transformed into the other by

(riftRk:}--

Z_.,\r[ jA/aAr ~_,

(149)

A i

with aAr(k) from Eq. (98).

Lippmann-Schwinger and Dyson Equations.

Consider an eigenstate [~0) of a reference Hamiltonian H ~ H ~ ~ E[~~ The associated Green function G o fulfills ( z - H ~ • G O = 1, with z -- E + i r/, 77 -- 0 +. The eigenfunction 1~) of the Hamiltonian H -- H ~ + V, V being the perturbation, fulfills H I~) -- E I~) and can be obtained via the LippmannSchwinger equation I~) - I ~~ + G~

(143)

Solving for I~) yields formally I~) = (1 - G ~ 1 7 6 Introducing the transition operator T = V(1 - G~ -1 gives VI~) -- TI~~ and I~) = (1 + G~176 The Dyson equation for the Green function G With ( z - H) • G = 1 can be obtained from (z - H~ = 1 -t- VG,

G = G O + G~

= G O+ G V G ~

The retarded Green function of free space obeys the Dirac equation

( E - H ) G - ~ ( r , r "1E ) -,- (

0 10) 6 ( r - r ' ) |

(150)

with the Hamiltonian H = cot . p + c2fl and V(r) = 0. 6spin denotes the Kronecker 6 in spin space, ~spin -- ~ r = 4 - X r (X r) T. For given energy E and wave vector kll, G~- is given in plane wave representation by 1

z'

1

G + (r, r') - i FA g ~ :

{ (rl fkir)(fki r R /-' [r')

We recall briefly basic properties of the solutions of the free-space Dirac equation for a given complex energy E. Because in this case the Hamiltonian is no longer hermitian, one has to deal with left-hand side (superscript L) and right-hand side (superscript R) wave functions [168]. The former obey (~LIH = E(~LI, the latter H I ~ R) = EI~R). In general, the 1.h.s. solutions are not the hermitian conjugate of the r.h.s, solutions. In plane wave representation, the free-space

z < z'

(151)

(144)

Or, in terms of T, G - G o + GOT G ~ which immediately gives V G - T G ~ This result can also be used for the wave function I~), I~) - I ~~ + GVl~~ 9

Free-Space Solutions.

Free-Electron Green Function.

kgi is taken from Eq. (94) and the + ( - ) sign refers to the case z > z' (z < z'). FA is the area of the two-dimensional layer unit cell. In angular-momentum representation, G + (r, r') reads G~-(r, r') = - i k Z

{ (rlj~}(h~lr') a (rlhRA}(jL]r' )

r < r'

(152)

r>r'

With r> (r) A

- k 2 E ( r < Ih~ (k, E))tAA, AA p

(156)

X

and obtains with the regular solutions after integration over angles in reciprocal space

dk (rl jR (k, E))(JL (k, E)Ir') E + i o _ k2 (157) Because the integrand is even in k, the integration can be extended to the interval [-oo, +oo], allowing the integral to be treated as a contour integral. Defining a = p + irl/(2p), p = ~/-E, and noticing that 0 = 0 +, one has c~2 - E + i r/. Thus, the preceding integral contains the factor G + (r, r') = 2 S-' Jr z ~

k2 oe2 + k 2

-- - -

/0

1 ( 2k 2 k-a

q

k k +c~

k ) k-c~

(158)

It'L(+)(k E)lr>) \,~A ~

(161)

Empty-Layer Green Function. Now consider a solid buildup by layers from which one layer of scatterers is removed (cf. Fig. 31). We will denote this layer with index i as "empty". For semi-infinite solids, one side belongs to the surface region, the other to the bulk region. Note that the following method can treat any kind of embedded layers, the embedding regions may consist of vacuum, films, or semiinfinite solids, respectively. For the Green function of the empty layer, one makes the ansatz + GEL(re , rl)

t = a + ( r i , ri)--1- ~ ( r /

.R ii .L Ire) t IJA)DAA,(JA

(162)

AA t

~r

(k 2 in the numerator on the 1.h.s. is due to the path element). The underbraced term is odd in k and thus gives no contribution to the integral. Therefore, one is left with

with arguments E and kll dropped. The coordinates are taken with respect to layer i, ri -- r - Re. G~ is the retarded Green ii have to function of free space, Eq. (152). The coefficients DAA, be determined by the boundary conditions: the Bloch condition parallel to the layers,

k - t~ (k' G+(r' r ' ) = - - J r l ~ f _ ~ ~ dk (rlJ#(k E))k(jLA GE+L(ri + R, r~) -- exp(ikll. R) GE+L(ri, rl) (159) Replacing (JL(k, E)IF) by thesum of (HZ'(+)(k, E)IF) and (HL(-)(k, E)IF), the integral can be performed. Taking the limit lim~0+ eventually yields G+(r, r ~) - - i k Z ( r < l J g ( k , E))(HL(+)(k, E)lr>)

(160)

A

Alternative representations of the single-site Green function follow immediately from operator equations for G. For example, G - G O + G ~ ~ yields [72]

(163)

(R is a vector of the layer lattice) and correct reflection at both the surface and the bulk side. Thus, OAA,ii is decomposed into ii ii ii ii DAA, -- AAA, + BAA,. AAA, is the structure constant of layer i, which obeys

ii E +c 2 AAA, --- - ik C2 ~

ii GAA,(-R) exp(ikll. R)

(164)

R#0

Further, one has h~- (kit - RI) (r~"RI XA)jt,(kr) (~f lxA, ).

- Y]~A' a

iiAA,(--R) x

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY To determine the coefficients B~A,, it is convenient to switch from angular-momentum (x/z) to plane wave representation (gr), which yields B ii AA'-

* ~ Z oA r (kSg)u:sst ,, gr,gCrt (aAtr,(kgtt)) s,s/=-t- gr g:r t ~

(165)

Thus, the matrix B ii is completely determined by the matrices W ++. Considering the reflection at the boundaries of the empty layer, one obtains the following matrix equation:

, 1

where the upper (lower) signs are for the case z > z' (z < z'). According to this decomposition, the Green function can be interpreted as a propagator: From r 'i there are outgoing plane waves into the +z direction (v + and ~,+) and into the - z direction (v- and ~-) that are collected at ri via fR. This interpretation is quite helpful in obtaining the interlayer part of the Green function.

Full-Layer Green Function.

For the layer-diagonal Green function for the full layer i, we make the ansatz 15 l

-R -+

W -+

G ( r i , r e) -- G + ( r i ,

W--

'iA(""0)( 0 0

166,

R + - and R - + are the reflection matrices at the surface side and the bulk side, respectively, which can easily be computed from the scattering matrices of the layers forming the surface and the bulk side stacks. Further, Kgr,gtrt : (~gr,gtr,/kg_L. Eventually, one obtains W ++ = R + - W - +

(167a)

511

t

IjiALItre)

liR\l[ii

ri) + Z ( r i I ~ A /'-'AA'\ AAt

(171)

with the single-site Green function G + for a site at layer i, Eq. (160). The regular solutions of the single-site problem fulfill the Lippmann-Schwinger equation for the site potential Vi (r), (rilJ~ R) = (ri lj~) + ff~ G+ (ri , rl ) Vi (rl )(rl lJiAlC)dr:3(172) i

Thus, the single-site t matrix is given by

tiARA, -- - i k s (j~lri)Vi(ri)(rilJiAR, }dr3i

(173)

i

W + - = 1-~--(1 - R+-R-+) - 1 R + - K

(167b)

~ 1 R_+( 1 - R + - R - + ) - I K

(167c)

iFA

W_+=

iFA

W - - = R -+ W+-

(167d)

Note that for a standalone layer, that is, a layer without vacuum embedding on both sides, R + - = R - + = 0, which leads to W ++ -- 0, and the matrix D is given by the structure constant A alone. It is illustrative to write the empty-layer Green function in terms of outgoing and incoming plane waves. With the definitions

I

(Vg~lr:) -- i FAkg_L

(f~g•

+ Z Z w+st ,,gr,gtrt( fli~ r t I rti }

(168a)

st==l=girt

(Og~lr~) = Z Z w+S" Lst, Ir~) st=-t- g,r t gr'gtr'(fkg, rt

(168b)

one has in matrix form

v-

(-)~-

=

=

11 w++ ) (f,+) W- +

W-+ W--

~

1 K+W-iFA

1( )

fL-

fL-

(169a)

(169b)

and the empty-layer Green function is given by G+L(ri, r I) -- ~(rilfk:+r)(Vg~lrl)-t- ~(rilf~g~:r)(f):~rlrti) gr gr (170)

Further, tat AiL _ tAA,ilr The single-site solutions show the asympii are determined by totics as in Eq. (88). The coefficients UAAt the Dyson equation for G, G(r, r') = GEL(r, r') + f.. GEL(r, r")V(r")G(r", r')dr ''3 dhg

(174) Using the asymptotics for the single-site solutions, one obtains ii , which in matrix after some manipulation an equation for UAA, form reads U ii--

(

1---s i

Di i ti R

)1

Dii

(175)

where the indices of g ii , O ii , and t i R run over all A. Now we turn to the calculation of the non-layer-diagonal parts of the Green function, that is, the matrices g ij for i r j. As we have seen, the empty-layer Green function can be interpreted in terms of outgoing and incoming plane waves, Eq. (170). Now the incoming waves do not belong to the empty layer (with index j ) but to the full layer (with index i); see Figure 32. The first task is to find the transfer matrix from layer j +to layer i. Therefore, the reflection matrix Rsurf at the surface side, the scattering matrix Mslab of the layers sandwiched be-+ tween layers j and i, and the reflection matrix Rbulk at the bulk side have to be computed according to the methods presented in Section 3. Then the matrix g ij c a n be computed according to the following scheme: (i) The wave fields outgoing from layer j in the +z direction are given by v j+ in the plane wave representation, Eq. (169). These have to be 15Note that the ansatz showsthe same structure as in Eq. (162).

512

HENK Table III.

Properties of Single-Site Solutions

Function

Behavior for r --+ 0

Asymptotics for r --+ cx~

[J)

Regular

IH)

Irregular

[j) -+-[h)t Ih)

IZ)

Regular

Ij)t -1 + Ih)

lJ)

Irregular

lj)

function is given by

G(ri, r~) -- G + (ri, rl)Sij + Z ( r i ]JiAR)UiJAw(JJALIrj) AA'

(178)

Scattering-Path Operator and Scattering Solutions.

Fig. 32. Arrangement in the calculation of the interlayer part of the emptylayer Green function in the cases i > j (top) and i < j (bottom). The empty layer is labeled j (white), the full layer i (dark gray). Left (right) the surface (bulk) side is displayed. The stack is shown in between layers j and i. Arrows represent outgoing (u j++ l ' U f _ l ) and incoming (u/i) wave functions.

propagated to the boundaries of the layer stack and give rise to tlj++ 1 = P + 'v+j and u j-_ 1 -- P - v j -. (ii) The wave field impinging on layer i, which is due to the wave field outgoing from layer j, has to be calculated. For the case i > j, that is, the empty layer on the surface side (cf. lower part of Fig. 32), one has u+ U i-

= --

(1

--

+ - Rbulk) -+ Mslab

-1M++. + slab u j +

1

(176a)

Rb+ ( 1 __ Mslab + - R b + ) - 1 .IV/slabUj+l -++ +

-+ + - - RbulkU i

(176b)

For the case i < j, that is, the empty layer on the bulk side (cf. upper part of Fig. 32), analogously U i- - -

u?

(1 -- MslabRsurf) -+ + - - 1 MS~uj_ 1 +-+ + - -1

- - e s u r f ( 1 - Mslab Rsurf)

(177a)

M~abUj-1

-- es+ u r-f U i+

U mn -- ( t m R ) - l ( r mn -- tmR~mn)(tnL)-I

(179)

Consider, for example, the Green function that propagates an electron from a site Rn to a site Rm, m ~ n. Taking rn and rm outside the muffin-tin sphere and using the asymptotic behavior of IJ ne) and (JmZ l, cf. Eq. (88), one arrives at G(rn , r m ) -- (rnljR(tmR) -1 -+- hR },cmn(j L (t n L ) - 1 -+- hL ]rm} (180) The preceding equation establishes the regular scattering solutions [ 169]. Within the muffin-fin sphere, they are given by IZ~) - Z

-1

IJ~ ')(tR)A'A

(181a)

(tL)~xl'(Jk '1

(181b)

At

(Z~I - Z Af

Analogously, the Green function at site Rn can be written as (177b)

(iii) To express the incoming wave field in terms of regular solutions of layer i, one has to multiply u/i by (1 - iAiiti/k) -1, where A ii and t i are the structure constant and the single-site t matrix of layer i, respectively. (iv) To obtain the "full layer" j, one has to solve the Dyson equation. Applying the similar considerations as for the layer-diagonal part, v + j has to be multiplied by - i ( 1 + itJuJJ/k). In summary, the Green

Certain equations of multiple-scattering theory become nicer when they are not formulated in terms of regular and irregular solutions of the single-site problem but in terms of scattering solutions; for example, the matrices U mn are replaced by the scattering-path operators (SPOs) 75mn . The latter are the on-the-energy-shell matrices of the transition operator T. Because the derivation of .gmn can be found in several textbooks (see, e.g., [70-72]), we just recall some basic properties. The SPO .gmn from site n to site m obeys 75mn ----- t mR~mn -4tmR ~ k C m Gmkrkn, where G mk is the structure constant. The matrices U and r are closely related,

G(rn, rtn) - ( r n [ Z n R ) 7 : n n ( Z n L l r t n } -

ik(rnlZnR)(jnLlrtn) (182) where ]]) is an irregular scattering solution. The main properties of the single-site solutions are given in Table III.

Screened-KKR Methods.

The Green function G of a system can be obtained from the Dyson equation with respect to the free-space Green function Go, G - Go + GotG, where t is the single-scattering matrix. The S P O r is implicitly defined by G - Go + GorGo, which leads to r - (t -1 - Go) -1 or G - t - l r t -1 - t -1.

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY The preceding formalism is based on free space as a reference system but can, in fact, rely on any other reference system [ 170]. The Green function Gr of the reference system is given by Gr - G0(1 - trGo) -1. Now G can be expressed in terms of Gr as G - Gr(1 - At Gr) -1 with At -- t - tr. For the SPO, one obtains r/x - [(At) -1 - Gr] -1. Now, one can ask for a reference system that (i) can easily be computed and (ii) allows for a rapid computation of the Green function G by means of G - (At)-lz'A(At) -1 - (At) -1. One answer is the screened-KKR method, that is, the transformation of the KKR equations into a tight-binding (TB) form. 16 In TB calculations, one exploits that the interaction integrals, which describe the hopping of the electron from one site to another, decay rapidly in configuration space, so that only a few nearest neighbor shells have to be taken into account. This approximation allows for the use of a variety of computational methods to obtain the Green function. Of practical interest is the renormalization scheme or, in the case of disordered systems, the recursion method [ 171 ]. Within the screened-KKR method, one uses a reference system that allows a fast computation of rA. Because At is site diagonal, a perfectly suited Gr should also be site diagonal. This, however, cannot be the case in real solid systems. Thus, one tries to construct a reference Green function, that decays as fast as possible in, configuration space. One way is to follow Anderson who invented the screening method and to exploit the scaling properties of the preceding equations in order to construct a "most screened" set of basis functions [172]. Another, more practical way builds the reference system by repulsive (V0 > 0) well-shaped and spherically symmetric potentials of muffin-tin form [ 173],

using the plane wave representation, we turn again to angularmomentum representation. With Eqs. (147) and (149) for regular solutions (z - j), the LEED state at site Rn is given by ~LEED(rn. E k) = exp(/k. R n ) Z ( r n l j R ) a A r ~ ) A

+

d rmG(rn, r m

exp(ik- Rm) m

A

• v (r'm)(r'm

m

&

/ V0 r < rmt

/ 0 otherwise

(rnlJ~')U~x'ma''

exp(ik. Rm) Z m

AAIA n f~

x

t t t t d 3 rm(JL,,lrm)V(rm)(rmljR)aAr(k) m

=tLnA/(--ik) i

= k Z

exp(ik. R m )

m

Z (rnlJRl) AAtA n

U~k'mA'tL''AOAr~)

Photoemission Final State.

The final state in photoemission, the time-reversed LEED state, can be computed either directly via the reflection and transmission matrices of the layers [ 136] or within the Green function formalism presented here. The LEED state (b (r; E k) at energy E, wave vector k, and A LEED T spin r fulfills the Lippmann-Schwinger equation cI)LEED(r; E, k) - - ( r l f ~ ) +

[ d3r'G(r, r'; E)V(r')(r'lf(~) t/

(184) that is, the relativistic version of Eq. (137), with the freespace solution If ~ ) and the potential in the solid V. Instead of 16Therefore, screened methods are sometimes loosely denoted as TB methods (TB-KKR, TB-LMTO, where LMTO is short for linearized muffin-tin orbital).

(186)

For the evaluation of the remaining single-site terms, one exploits the Lippmann-Schwinger equation (172) for the regular solutions. Thus, these terms reduce to IJ~xR). In summary, the LEED state at site Rn is given by I)LEED-

r

trn ; E, k)

= exp(ik. R n ) Z ( r n l J ~ ) a A r ( k )

x

(183)

the t matrix of which can easily be calculated analytically. The screening, that is, the exponential decay of the SPO in real space, can be tuned by the height of the potential wells. Further, in order to compute the reference Green function, one can employ the translational properties of the reference system, in particular, the Bloch property.

(185)

with G from Eq. (171). Inserting the interlayer contribution to the Green function, one arrives at a term

i

+ -k ~

A

V(r)-

513

~

exp(ik. Rm)

m

(rnlJ~,)U~x,mA,,t~,,AaAr(k)

(187)

AAtA n

A slightly more compact form is obtained using the SPO, I)LEE D . T

trn; E, k ) -

i

~ Z m

nm

exp(ik. R m ) ~ ( r n l Z R ) r A A , aAr(k) AA t

(188) It is worth mentioning that a construction of the final state in terms of Bloch states has been given by Bross [174] (see also [69]).

Transition-Matrix Elements and Photocurrent. A photoemission theory is incomplete as long as the transition-matrix elements are not taken into account. The interaction of an electron with incoming monochromatic light of frequency w and with wave vector q is relativistically described by the Hamiltonian H'(r, t) = or. A(r, t) = or. A0 exp(iq 9r - c o t )

(189)

Upper and lower components of the Dirac spinors are coupled via or, Eq. (79). Usually, one decomposes A = (Ax, Ay, Az) into (A+, A_, Az) with A+ = Ax + iAy, that is, into contribution from left- and right-handed circularly polarized light as well as linearly polarized light.

514

HENK

The transition-matrix elements between the Dirac spinors at a particular site are integrals over the muffin-tin sphere. Integration over angles, that is, matrix elements of c~ 9A of the central-field spinors IXA), yield the well-known "atomic" selection rules [ 175]: The angular momentum 1 has to differ by 1, Al = -t-1, and its z projection m is conserved for linearly polarized light, Am = 0, or for circularly polarized light it is changed by 1, Am = 4-1. The integration over the radial part has to be computed numerically. The Green function of the initial state consists of both regular and irregular solutions, the time-reversed LEED state of regular solutions only. Therefore, one has to consider two general types of matrix elements. For those between regular solutions, one has 1) iAtA

M(

f Rmt

-- J0 I

(JA, l r ) ~ i A i ( r I J A ) d r

i = 4-, z

(190)

The single-site term of the Green function gives rise to a double integral, Mi(~!A, due to the selection of regular and irregular wave functions with respect to r; see Eq. (160). In the preceding definition, we have suppressed the indices L and R, which are due to the occurrence of left and right wave functions. Eventually, the spin-density matrix p of the photoelectron is given by [cf. Eq. (138)] Prr' ~" (~0rlGa( E + w ) A I m G + ( E ) A t G r ( r, r ' =

E + w)l~0r,)

4-

(191)

which, besides the computation of the photocurrent I = tr(p), allows for computation of the spin polarization of the photoelectrons P = tr(rrp)/tr(p). Note that due to SOC the spin polarization can be nonzero even from nonmagnetic solids (see, e.g., [150]). Because the final state is a time-reversed LEED state, it shows the same symmetry properties as a LEED state; cf. Section 3.2.2. This, together with knowledge of the light polarization, allows for a detailed group-theoretical analysis of photoemission from (ferromagnetic) surfaces [58, 176]. In particular, it reveals the initial states for which dipole transitions are allowed or forbidden (see also [97]). A popular approximation for analyzing experimental spectra is the direct-transition model. If the initial states are taken as Bloch states, for example, by neglecting the surface of the sample, the normal component k• of the wave vector is conserved in the transition process. This allows for a mapping of the intensity maxima to the band structure k• (E, kll). Before turning to applications of the multiple-scattering theory of photoemission, basic properties of photoemission from ultra-thin films should be addressed. 4.2.4. Simple Theory o f Photoemission f r o m Ultra-Thin Films In recent experimental work on photoemission from films with thicknesses of a few layers, the photoemission intensity maxima show dispersion, as in the bulk case, and can be well described within the direct-transition model using bulk-band structures.

t

t

9 ~ =0

t 9

t 9

t 9

t 9

9

t

t

t

t

9

9

9

9

Fig. 33. Linear chain along the z axis with n = 11 equidistant sites with intersite distance a. The tight-binding parameters, cf. Eq. (192), are the on-site energy E and the next nearest neighbor hopping energy t, visualized by dashed lines.

This led to the conclusion that even ultra-thin films "show a (bulk) band structure" [177, 178]. This behavior can be understood within a simple theory of photoemission from linear chains [179], which will be presented in the following (for an approach based on Green functions, see [ 180]). There are two limits in which valence electrons in a film can be described (see Section 2 and, e.g., [21,181-184]): (i) In a plane wave representation, free electrons can be confined to a quantum well. (ii) In a fight-binding description, electrons are allowed to hop only within a finite number of layers. The prototypical realization of the latter model is rare-gas layers on a (metal) substrate (cf. Section 2.2.3). The film is represented by a linear chain oriented along the z axis, that is, perpendicular to the surface, with n equidistant sites i, i = 1 . . . . . n, with one orbital I~i) per site. The latter is located at iaez, a denoting the intersite distance (Fig. 33) [ 185-188]. Further, the overlap between the normalized orbitals located on different sites is assumed to be 0, (Oi[Oj) -- r~ij. Neglecting the substrate completely, the elements of the Hamiltonian matrix H (n) read

HiT)

i, j = 1 . . . . . n

-- Er~ij q- tr~li-j[,1

(192)

with on-site energies E = (Oi In(n)lOi) and next nearest neighbor hopping energies t = ( O i l H ( n ) [ o i + l ) . The eigenvalues of n (n) can be written as ~'i(n) = E + 2 t

Cos(k} n ) a )

i = 1. . . . . n

(193)

with k} n) -- rri/[a(n + 1)]. In the case of a single site where there is obviously no hopping, X~l) -- E. For an infinite chain (i.e., in the limit n --, e~), k}n)a is dense in [0, zr] and, thus, the eigenvalues represent the bulk-band structure E(k) = E + 2t cos(ka); cf. Figure 34. An eigenfunction Iq~}n) ) of H (n) with energy X}n) can be written as n

]qJ}n') = ~ c}~'l~j)

i = 1. . . . . n

(194)

j=l

the coefficients c}~) of which can be calculated iteratively by (n) 1 _ c }; ) = 2co S ( k( ni ) a)ci,j_

c!n) t,j-2

j = 2 ..... n

(195)

with c~g) = 0 and C~l) --- 1. The additional relation 2 cos(k} n)a) ci, _(n) _(n) 1 ensures that k}n) has to be chosen n -- Ci,n_ properly. It can easily be shown that c}~) ~ sin(Trij / a (n + 1)). Strictly speaking, k} n) is not a wave number as it is in the case

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY 9 i

9

1 ~I 0 9

y-

9 i 9 i 9 i . ._ o 0 0 9 0 ~ 0 9 0 0 ~ ~ 9

9

9

9

i

i

~

9

2

Fig. 34.

i

9 .

l

4

9999 .

t

n

" ,

6

i i

8

t

. i]

I

.

0

1

I

0

DOS (states)

7r/2

7r

ka

4

~

X , / j J

~

//I

0-8

0.1

0

~r/2

' Ir

31r/2

21r 0

7r/2

Ir

3rr/2

0.0 21r

Re(ka)

Fig. 35. The "k-conservation" function IA(n)12, as defined in Eq. (198). (a) Dependence on the number of sites n in the linear chain, n ranges from 2 to 32, as indicated, Im(ka) = 0. (b) Dependence on Im(ka). Im(ka) ranges from 0.0 to 1.0, n = 8.

Tight-binding electronic structures of linear chains. The tight-binding

parameters are e and t; cf. Eq. (192). (a) Eigenenergies )~i(n) [dots; cf. Eq. (193)] of chains with n = 1. . . . . 10 sites. (b) Density of states (DOS) of the infinite chain. (c) Band structure E(k) = E + 2t cos(ka) of the infinite chain. Reprinted with permission from J. Henk and B. Johansson, J. Electron Spectrosc. Relat. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

of Bloch states because there is no translational symmetry and therefore no periodicity. Due to the inversion symmetry, the eigenstates kI/}n) s h o w the expected even-odd alternation [cf. Eq. (19)], and the number of nodes in the wave function increases with Ik}n) I. The photoelectron state IqJf) can crudely be approximated by a single plane wave, (rlqJf) = exp(ikf 9r), as is often done in the interpretation of experimental data. This way, quantumsize effects in the upper band structure that show up, for example, in LEED (cf. Section 3.3) are ignored. The wave vector k f is determined by both the position of the detector and the energy of the photoelectron, E f

"~

k~. The photocurrent Ii n) at

photon energy co from the initial state I~{ n)) is given by Fermi's golden rule, Eq. (141). Inserting the previous expressions for the wave functions and defining the Fourier-transformed atomic wave function F(k) by F(k) = f ~*(r) exp(ik.r) d3r, one obtains eventually

Ii n) (X

.

Re(ka)

n

(b) n - 8

,-0 0.5

0 0.0

(a)

Im(ka) =

-

-1

9

~

=

-

9

4, 8, 16, 32; Im(

0.8

515

IE.kfl21F(kf )121Ai(n)(kf•

-co

(n)

--)~i ) ( 1 9 6 )

The function A~n) (k), which is defined by

A~n)(k) -- ~ c~;)exp(ikja)

(197)

j=l

determines considerably the dependence of the photocurrent on the photon energy and, thus, should be discussed in more de(n) tail. Obviously, A i is periodic with period 27r/a. In the case of a single site, n = 1, IA(1)(k)l - 1 and the photon energy dependence of the photocurrent is determined solely by F (kf). In the case of an infinite chain, n --+ cx~, strict wave vector conservation, A(eC)(kf• -- (~(kf• - k), is obtained; that is, the direct-transition model is recovered. Setting all c}~) = 1 leads to a geometrical series for A (n), n

A(n) (k) =

fork - 0

(qn _ 1)/(q - 1) otherwise

q -- exp(ika) (198)

Obviously, A(n) shows n - 1 zeros in [0, 2Jr] at ka = 2zr i/n with i = 1 . . . . . n - 1. Its absolute value increases with n in the vicinity of k = 0, whereas it decreases in the interior of the interval [0, 2zr]. In short, A (n) is an approximation of Dirac's function [ 189] (cf. Fig. 35). The main photoemission intensity comes from the region around k - 0 (i.e., kf_L -- k~n)), but additional intensity maxima, which are due to the oscillatory behavior of A (n), should occur. So far, we have considered only the case of infinite lifetime of the photoelectron. Introducing a finite lifetime leads to a complex wave number [53], which results in an additional weakening of the k conservation, as is also shown in Figure 35. A (n) decreases rapidly around k = 0 with increasing Im(ka) (as is evident from the geometrical series), but the oscillatory behavior is still visible, except for very strong damping, for example, Im(ka) = 0.5 in Figure 35b. Photoemission from chains with length of 5 and 10 sites is compared in Figure 36. The intensities were obtained from (n) Eq. (196) with IE" kfl21F(kf)J 2 set to 1, but A i calculated with the coefficients c}n) obtained from Eq. (195). At the bottom of each box, the initial-state band structure E(kf• is shown (note that kf• is related to the photon energy co by (n) k} ~ )~i -+-co). The individual photoemission intensities show (n) main maxima a t k~n), that is, E ( k f • - - )'i 9 In other words, one obtains approximate k• conservation. However, the intensities show oscillatory behavior (cf. Fig. 35). Further, the main maxima for n = 5 (Fig. 36b) are much broader than those for n = 10 (Fig. 36a) due to the weakening of the k conservation for shorter chains. The finite photoelectron lifetime can be modeled using complex energies [53], which leads to complex kf• Its effect is addressed for a 10-site chain in Figure 37. For a rather large lifetime [Im(kf• = 0.2, in Fig. 37b], there are still oscillations with kf_L in the photoemission intensities from the individual initial states. These become smeared out for decreasing lifetime [e.g., Im(kf• = 0.5 in Fig. 37a]. However, the intensities follow the bulk-band structure in both cases. At a fixed photon energy or a fixed Re(kf• for example, Re(kf• = 0, the EDC becomes broader with increasing Im(kf• which is due to the smearing out of the individual maxima and not to the uncertainty in k f / .

516

HENK

Fig. 36. Photoemission from linear chains with lengths 10 (a) and 5 sites (b), respectively. The intensity I is shown for each initial state at energy ~.!n) ! [cf. Eq. (193)] for final-state wave numbers kf• ranging from 0 to 2:r/a and Im(kf• = 0. The initial-state band structure E(k) = E+ 2t cos(ka) (dashed) is shown at the bottom of each box. Intensities are scaled to the same maximum in each box. Reprinted with permission from J. Henk and B. Johansson, J. Electron Spectrosc. Relat. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

In summary, photoemission from ultra-short chains shows the following properties: (i) The confinement of the valence electrons to the chain leads to a weakening of the wave number conservation: the shorter the chain, the broader the photoemission maxima in kf_l_. (ii) Besides the periodicity with 2:r/a, individual photoemission intensities show oscillations with kf_t_, the number of which is proportional to the chain length. These oscillations become smaller in intensity with decreasing photoelectron lifetime [increasing I m ( k f x ) ] . (iii) Even for very small lengths, the main maxima in the photoemission intensity follow the initial-state bulk-band structure, despite the fact that the initial-state energies are discrete (quantum-well states).

4.3. Applications In the following, we focus on theoretical photoemission results for metallic films on metal substrates, which were obtained by multiple-scattering methods. Further, representative experimental data that show fingerprints of QWSs are presented.

Fig. 37. Sameas Figure 36, but for photoemission from chains with 10 sites = 0.5 (a) and Im(kfza) = 0.2 (b), respectively. Reprinted for Im(kf• with permission from J. Henk and B. Johansson, J. Electron. Spectrosc. Relat. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

4.3.1. Ultra-Thin Cu Films on fcc Co(lO0) Hansen et al. performed photoemission experiments for ultrathin Cu films on fcc Co with an identical number of Cu layers but different crystallographic orientation of the substrate [ 190]. For 14 layers of Cu on fcc Co(111), they found a bulklike dispersion in the C u s p states but three quantized states with fixed energy for fcc Co(100) and fcc Co(110) substrates (see Fig. 38). These findings were explained by the bulk-band structure of Co: Only in the latter two cases do bandgaps lead to confinement of the valence electrons to the Cu films and thus to QWSs. Further, it was observed that for the (100) and (110) films the photoemission intensities from the QWSs behave similarly to those of semi-infinite Cu(100) or Cu(110), respectively, which can also be understood by means of photoemission from linear chains (Section 4.2.4). A closer look at the intensity variations, however, gives hints that the maxima show more structure in their dependence on both the binding energy and the photon energy. Ultra-thin Cu films on fcc Co(001) lend themselves support as prototypical systems because of extensive experimental and theoretical work. However, experimental [183, 191-194] and theoretical [195] investigations dealing with Cu/Co have focused mainly on the properties of QWSs as a function of the film thickness (e.g., binding energy and spin polarization). Usu-

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY

517

t~

J ~

t~ O

.m

J

2

1

0

2

I

0

2

1

0

Binding Energy (eV)

Fig. 38. Experimentalnormal-emissionphotoelectron spectrafor single-crystalCu surfaces and for Cu films 14 layers in thickness on Co substrates for (100) (left), (110) (middle), and (111) (right) orientation. Photon energies are evenly spaced between the lower and upper bounds indicated in each graph. The vertical dashed lines for Cu/Co(100) and Cu/Co(110) indicate the position of intensity maximarelated to quantum-well states, while the dashed line for Cu/Co(111) indicates the dispersion of a peak related to emission from a Cu bulk band. Reprinted with permission from E. D. Hansen, T. Miller, and T.-C. Chiang, J. Phys.: Condens. Matter 9, L435 (1997). Copyright 1997, by the Institute of Physics.

ally, such analyses were performed at a fixed photon energy. In the following, we focus on a few film thicknesses but extend the analysis to variable photon energy in order to work out the manifestation of quantum-size effects in photoemission. Photoemission from Cu/Co(001) is analyzed by means of calculations within the one-step model of photoemission based on multiple-scattering theory (SPRLKKR), as presented in Section 4.2.3. Quantum-Well States in Cu Films on fcc Co(O01). Typical photoemission spectra from Cu/Co(001) for various thicknesses of the Cu films are shown in Figure 39. The intensity maxima are labeled by numbers that refer to the QWSs in the film (cf. Fig. 7). With increasing thickness, the maxima disperse to higher energies. At a fixed binding energy, for example, at the Fermi level EF, the intensity is higher if a QWS crosses this energy than if there is no QWS at that particular energy. This gives rise to oscillations in the photoemission intensity at a fixed binding energy, as shown in the top panel of Figure 39 (and discussed later). Before turning to the photoemission results, the electronic structure of Cu films on fcc Co(001) at F, which is relevant for normal emission, kll - 0, is briefly analyzed. The perpendicular component k• of the wave vector takes values from the direction 1-'-A-X in the bulk Brillouin zone. The C u s p band belongs to the double-group representation A6; the related

wave functions show a prominent A 1 single-group (spatial) contribution (for applications of group theory in solid-state physics, see [59, 196]). To confine these electrons completely within the Cu film, the Co substrate has to have a gap in the A 1 bands. This is the case for minority electrons below - 0 . 6 5 eV (light-gray area in Fig. 40), for majority electrons below - 2 . 0 9 eV (dark-gray area in Fig. 40). To distinguish among surface states, interface states, and QWSs, one calculates the layer-resolved Bloch spectral function (LDOS) for the whole Cu film and the subsequent Co layers. Surface and interface states, the energies of which may also lie in a bandgap of Co, are localized at the respective boundary (e.g., vacuum/Cu or Cu/Co). This means that the corresponding maxima in the LDOS decrease with distance from the boundary. Quantum-well states, however, show maxima in the whole Cu film but decreasing maxima in the Co substrate. The latter can be attributed to the gap in the bulk-band structure of Co because the QWSs cannot couple to Bloch states but to evanescent states in the Co substrate. Further, the energetic position of surface and interface states is expected not to depend significantly on the number of Cu layers, whereas QWSs should show the typical dispersion with film thickness (see Section 2 and Fig. 39). The Bloch spectral function for a 14-ML Cu film shows two sharp maxima of minority spin character with energies - 1 . 5 2 and - 0 . 8 0 eV, respectively, which are denoted as QWSs A

518

HENK

Fig. 39. Experimentalphotoemission from Cu films on fcc Co(100) for kll -0 and 83 eV photon energy. The lower panel shows intensity versus Cu film thickness (as indicated on the right of each spectrum). Intensity maxima related to quantum-well states are labeled by numbers (cf. also Fig. 7). The upper panel depicts intensity modulation at the Fermi level (0 eV) versus film thickness. Reprinted with permission from P. Segovia, E. G. Michel, and J. E. Ortega, Phys. Rev. Lett. 77, 3455 (1996). Copyright 1996, by the American Physical Society.

and B in Figure 40b. The latter agree reasonably well with those obtained experimentally by Hansen and coworkers [ 190], who found QWSs at - 1 . 5 and - 0 . 9 eV (see also Fig. 39 and [191, 192]). At energies larger than - 0 . 6 5 eV, the Bloch spectral function shows weak maxima, which may also be associated with QWSs but lack the complete confinement due to the weak reflection at the Cu/Co interface at these energies [ 197]. There is no e v e n - o d d alternation of the QWSs, as found in the simple fight-binding model (Section 4.2.4), due to the lack of inversion symmetry in the Cu film. The reflectivity at the Cu/Co boundary, as obtained theoretically by Dederichs and co-workers [ 197], is shown in Figure 41. In the lowest panel, the reflectivity of the Bloch state, which is associated with the Cu sp valence band, is shown for incidence on a Co film with 20 M L thickness. At energies less than - 0 . 6 eV, there is almost complete reflection in the minority spin channel, in accordance with the band structure shown

Fig. 40. Spin-resolvedrelativistic electronic structure of 14-ML Cu on fcc Co(001) for F (kll = 0, I'-A-X in the bulk Brillouin zone). (a) Band structure of fcc Co(001) along F-A-X. The sliding gray scale of the bands indicates dominant majority (minority) spin orientation with black (light gray). (b) Density of states of 14-ML Cu on fcc Co(001) for the outermost (S) and a central (S - 6) layer with black (light gray) lines indicating minority (majority) spin orientation. (c) Same as (a), but for Cu(001). Gray areas indicate gaps in the Co band structure: dark gray for both majority and minority electrons, light gray for minority electrons with prominent A 1 spatial symmetry. The latter leads to confinement of minority electrons in the Cu film; see maxima A and B in panel (b). For C, see text. The Fermi energy is at 0 eV. Reprinted with permission from J. Henk and B. Johansson, J. Electron Spectrosc. Relat. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

in Figure 40. Above - 0 . 6 eV, there are QWSs in the Co film, which reduce the reflectivity; cf. the pronounced minima in the reflectivity. This picture corresponds nicely to that of the quantum-well resonances in LEED (see Section 3.3): Here, the incoming wave is the Cu Bloch state, whereas in LEED it is the electron beam.

Manifestation o f Quantum-Size Effects in Photoemission. As a prototypical example, normal photoemission (kll = 0) with p-polarized light that impinges with a polar angle of 45 ~ onto the surface is discussed in detail. In Figure 42, photoemission from semi-infinite Cu(001) is compared to that of 14-ML Cu on fcc Co(001). For the former (Fig. 42a), the intensity at energies below - 2 eV stems from the d-band regime. The m a x i m u m that disperses from the Fermi energy at 10 eV photon energy down to - 2 eV at 17 eV photon energy is due to emission

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY

f --

'-oo

1.OF-

:

-1.5 1.5

/

-1.0

....

I

-0.5 ~ i

4

0

0.5

-

1.0

n

T

....

1.5 -

-

'[..] /

5 ML Co ~.. 1.0

~---

O"

uS 9- 0.5

/

i

o

~ . . . . .

-'

.5

1

I

-1.0

-0.5

.

0.

i

.

.

.

.

0

0~5

1.0

!

20 ML Co

:

1.5

.

0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

E - EF[eV ] Fig. 41. Reflectivity r of a Cu Bloch wave of A1 representation (along the F-A-X direction, kll - 0) at the Cu/Co interface versus Co film thickness [from top to bottom, 1-ML, 5-ML, and 20-ML Co on Cu(001)]. Note that distinct minima occur which can directly be attributed to quantum-well states in the Co film (cf. [198]). Solid lines, minority spin; dashed lines, majority spin. Reprinted with permission from P. H. Dederichs, K. Wildberger, and R. Zeller, Physica B 237-238, 239 (1997). Copyright 1997, by Elsevier Science.

from the C u s p band (cf. Fig. 40c). The direct-transition model can be used to explain the widths of these maxima: The sp band and the final-state band are almost parallel in the band structure and, thus, there is a certain energy range where the difference in the respective k• is rather small [ 166]. The slightly weakened k• conservation results therefore in a broad maximum. For the 14-ML Cu film on fcc Co(001) (Fig. 42b), the energies of the QWSs lead to narrow maxima [199]. The two sharp peaks, A and B, correspond to those found in the LDOS (Fig. 40b). The intensity distribution of structure C, however, agrees with that found for Cu(001), which can be also explained by the LDOS: Near EF there are no strictly confined electronic

519

states in the Cu film because the reflection at the Cu/Co interface is small. This qualitative difference between A and B on the one hand and C on the other is further established in the photoelectron spin polarization. A and B show strong minority polarization (P ~ -0.75), whereas C is weakly spin polarized (P ~ -0.05), as expected from the LDOS. The intensity variation with photon energy of maxima A and B is similar to that found for semi-infinite Cu(001) at the respective binding energies, a finding that confirms nicely both the simple theory presented in Section 4.2.4 and the experiment. At this point, quantum-size effects seem to occur only in the widths of those intensity maxima that are associated with QWSs [199]. This feature should be observable with high-resolution photoemission techniques [200]. However, hints about this behavior may be seen, for example, in the work by Hansen et al. (Fig. 38). Further pronounced manifestations of quantum-size effects in photoemission are intensity oscillations with photon energy. These can be observed in the CIS mode of photoemission (Fig. 29): The initial-state energy is chosen as that of a QWS and the photon energy is varied while keeping kll fixed. The resuits for semi-infinite Cu(001) and 14 ML on fcc Co(001) are shown in Figure 43 where the initial-state energies were chosen as those of QWSs A, B, and C. For semi-infinite Cu(001), one observes for each initial-state energy a dominating maximum and a few smaller maxima and shoulders (Fig. 43a). The former directly reflects the k• conservation; the latter can be explained by the final-state band structure. Further, because the wave function of the initial state does not change rapidly with energy, as is evident from the band structure, the three CIS spectra show almost the same shape, which appears only shifted in photon energy (see the inset in Fig. 43a). In other words, the CIS spectral shapes are governed by the final states. The fine structure for the energy of state C is slightly more pronounced when compared to those for A and B because of the larger photoelectron lifetime, which decreases with kinetic energy. The most important observation, however, is the absence of significant oscillations with photon energy. For the 14-ML film, one finds similar behavior regarding the overall CIS intensity distribution (Fig. 43b). In particular, the relative heights of the main maxima for A, B, and C are close to their counterparts of semi-infinite Cu(001). The main differences are distinct intensity oscillations, which become clearly visible in the insets showing the logarithm of the intensities. In particular, maxima A and B show almost the same oscillation period, which is indicated by vertical lines in the inset of Figure 43b. The period for maximum C, however, differs significantly from those of A and B. Further, the spectral shapes of A and B are nearly identical and again differ from that of C; in particular, the double-peak structure near the maximum intensity occurs for both A and B but is missing for C. This double-peak structure is clearly due to the quantum-size induced oscillations of the CIS intensity. These findings show directly the different confinement strengths of the QWSs: strict confinement for A and B, less confinement for C.

520

HENK

Fig. 42. Photoemission for kll = 0 with p-polarized light incident at 45 ~ off-normal from Cu(001) (a) and 14-ML Cu on fcc Co(001) (b). Thephoton energy ~o ranges from 9 eV (bottom spectra) to 17 eV (top spectra), as indicated on the right. Gray areas in (b) indicate gaps in the Co band structure as in Figure 40. A, B, and C refer to quantum-well states (see text and Fig. 40). The Fermi energy is at 0 eV. Reprinted with permission from J. Henk and B. Johansson, J. Electron Spectrosc. Relat. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

Fig. 43. Constant initial-state photoemission for kll = 0 with p-polarized light incident at 45 ~ off-normal from Cu(001) (a) and 14-ML Cu on fcc Co(001) (b). The initial-state energies are chosen as those of quantum-well states A (solid lines), B (dotted lines), and C (dashed lines); see text as well as Figures 40 and 42. Insets show the logarithms of the intensities, which are normalized to 1 and shifted in energy such that the maximum intensity is at 13 eV (relative photon energy). Vertical lines in the inset of (b) indicate intensity minima of state A. Reprinted with permission from J. Henk and B. Johansson, J. Electron Spectrosc. Relat. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

Finally, the dependence of the oscillatory behavior on film thickness is addressed. According to Section 4.2.4, the oscillation period should decrease with increasing film thickness. For quantum-well state A of the 14-ML film and the corresponding states for films with thicknesses of 9 ML, 19 ML, 24 ML, and 29 ML, the energy positions are almost identical. This means that hole and photoelectron lifetimes are also almost identical, and the main differences in the CIS spectra can unambiguously be attributed to the difference in film thickness. Constant initial-state spectra for the various film thicknesses are shown in Figure 44. Both the width of the main maximum and the oscillation period decrease with film thickness. Further, the intensity at higher photon energies decreases with film thick-

ness, which is also evident from Section 4.2.4, particularly from Figure 35. The double-peak structure can clearly be attributed to the quantum-size induced oscillations: For the Cu film, the main intensity maximum is broadened with respect to the semiinfinite case due to the weakening of the k• conservation, as is evident from Figure 44. This maximum is "divided" in two due to the intensity oscillations (cf. the dashed-dotted guideline in Fig. 44). With increasing film thickness, the double-peak structure disappears. In summary, quantum-size effects in photoemission from ultra-thin films manifest themselves in the following features: (i) Strict confinement of valence electrons to the film leads to a weakening of the k• conservation: the thinner the film,

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY 15

10 9

i

20

u

9

i

25 9

u

521

30 9

A

24

a)

Cu/Co(100) EB= 0 . 3 e V

20

= 16

,

n •

,

9

T /\

/

~4 - . P

/

q\\/

~.,12

0.3 (D

c-

,,

- v

>" =

8

(\\I

I

I

I

J

Experiment

e~ 0.2

E

.

.'

0.J

I

10

15

20

25

30

Photon Energy (eV) Fig. 44. Constant initial-state photoemission for kll = 0 with p-polarized light incident at 45 ~ off-normal from Cu films on fcc Co(001). The initialstate energies are chosen as those of quantum-well state A for selected film thicknesses n from 9 ML (top spectrum) to 29 ML (bottom spectrum), as indicated on the right. Dashed and dashed-dotted lines visualize the behavior of oscillations. Short horizontal lines represent zero intensity for each respective spectrum. Reprinted with permission from J. Henk and B. Johansson, J. Electron Spectrosc. Relal. Phenom. 105, 187 (1999). Copyright 1999, by Elsevier Science.

Model

... 0.2 . v

=

,

; r--

0.6 ..

13)

Another example of investigating QWSs at a fixed binding energy is illustrated in Figure 45. Kl~isges et al. recorded experimentally the photocurrent at 0.3 eV binding energy and fixed photon energy (co = 77 eV) of Cu films on Co(100) for a variety of film thicknesses (1 ML-17 ML) [194]. Besides a global decrease of the intensity with film thickness, they found significant oscillations in the current, which, of course, can be attributed to QWSs. The period of the maxima was determined as 2.3 ML + 0.1 ML. Results of electronic-structure calculations of Cu films on Co(100) are shown in Figure 45b. Dederich's group calculated self-consistently the Bloch spectral function AB (kll, E) = - Im G(kll; E)/rc. Each maximum in AB in the sp-band range indicates a QWS (filled circles in Fig. 45b). Again, one finds the familiar dispersion with film thickness, as discussed in Section 2.2. With increasing film thickness, the QWSs disperse in energy toward the Fermi level, as visualized, by the dashed lines. The latter cross the binding energy of 0.3 eV with ape-

~

.

,"

.

,

:

;

.

.'

..'

."

6

.:

~'

9

.'"

.

"

,.

,,

o"

.O

9

,6

."

9

..'

:"

I

0.8 -

Oscillations of Photoemission Intensity with Film Thickness.

.

b)

0.4

kl.I

the broader the photoemission maxima. (ii) Photoemission intensities from individual QWSs show oscillations with photon energy, the period of which decreases with film thickness. (iii) Even for films only a few layers thick, the main maxima in the photoemission intensity follow the initial-state bulk-band structure, despite the fact that the initial-state energies are discrete.

.'~

:'

:

~'

.

I/

.'

.'"

.

,' '

..

9. '

./ ID

.o .. . O

e"

;'

"

,-

"

I

"

l

'

9

8"

~'

,9

,.

. 0"

;

.9

o.

9

1.2

0

5

10

15

Cu Thickness (ML)

Fig. 45. Photoemission intensity from Cu films on Co(100) at 0.3 eV binding energy versus Cu film thickness. The emission angle chosen is 12 ~ (kll = 0 . 9 4 / ~ - 1 ) . (a) Shows experimental data (dots) and results of a model calculation (solid line). Binding energies of quantum-well states are shown in (b). Dashed lines serve as a guide to the eye. The hatched area indicates the binding energy as chosen in the photoemission experiment. Reprinted with permission from R. Kl~isges, D. Schmitz, C. Carbone, W. Eberhardt, P. Lang, R. Zeller, and P. H. Dederichs, Phys. Rev. B. 57, R696 (1998). Copyright 1998, by the American Physical Society.

riod of 2.4 ML, which corresponds nicely to the experimentally obtained value. Because the photoemission intensity shows a maximum at the energy position of a QWS, the dispersion of the QWSs can be translated into a dispersion of the photoemission maxima. As shown in Figure 45a, a model photoemission calculation reproduces all general features found in the experimental results, in particular, the global decay and the oscillations. The model assumes that each QWS contributes to the photocurrent with a finite peak width corresponding to the experimental energy resolution. Further, this intensity is expected to be proportional to the inverse of the film thickness. The background intensity due to the Co substrate is approximated as decaying

522

HENK

exponentially with Cu thickness, in accordance with the mean free path of the photoelectron (Fig. 12). This causes the global decay of the intensity. Missing are, however, interference effects in both the initial and the final state of the photoemission process. These can, for example, lead to significant changes in the photocurrent that call into question the one-to-one correspondence between maxima in the B loch spectral function and the photocurrent maxima. These effects have been observed, for example, for Co/Cu(001) [201 ] and Au/Ag(111) [202]: Due to destructive interference in the final state at a particular kinetic energy, only one of two QWSs of the 2-ML films has been observed in both experiment and theory although the layer- and symmetry-resolved Bloch spectral function of both states shows maxima of comparable height. The effect of interference is discussed in more detail in the following Section.

(see Sections 2.2.2 and 3.3) and holds for perfectly reflecting boundaries (IRsl = IRil = 1). The more general case can be discussed in terms of an interference factor I. For each round trip, the wave function of the electron is changed by the factor P+ Rs P - R i , with P + -exp(ik + .d). For kll -- 0, the interference factor I then becomes oo

I -- ~ (P+ Rs P - Ri)J j=0 = (1 - Rexp (i(r + 2 k •

with the definitions R = IRs Ril and r = r + r Note that the mean free path )~ is taken into account. The modulus of the interference factor is given by 1 - R exp

III 2 =

4.3.2. Quantum-WeU States and Interference: Ag on Fe(O01) Particle wave duality is one of the fundamental features of quantum mechanics. We now investigate how photoemission from a thin film establishes an almost perfect analogy between a standing electromagnetic wave caught between two mirrors and an electron confined to a thin film. Consider an electron confined to a quantum well, the latter, for example, being realized by a thin film (Fig. 46). The electron is reflected at both the surface side (s) and the substrate side (interface, i) of the film with reflection coefficients es = Iesl exp(iCs) and Ri = IRil exp(ir respectively. The propagation from one side to the other is taken into account via the phase factors P + and P - . For kll - 0, these read P+ - exp(ik• where N is the number of layers of the film, d is the interlayer distance, and k• is the wave number of the electron. The Bohr-Sommerfeld quantization rule, which is well known from the theory of atomic spectra, then reads 2k• + Cs + t~i -'- 2nzr, n ~ Z. In other words, constructive interference occurs if the accumulated phase shift is an even multiple of Jr. This relation is known as the round-trip criterion

x

[ () 1+

2f

----Z

(

2 sin 2 k •

r

)]l

(200)

with f --

rr ~/-R exp ( - N d / 2 Z ) 1 - R exp ( - N d / ) O

(201)

f is the finesse (i.e., the ratio of peak separation and peak width) of a Fabry-P6rot interferometer with an absorptive medium (~. < cr Such a device was invented by Fabry and P6rot in 1899 [203]. Equation (200) establishes the close analogy between interference of electromagnetic waves and of electrons (cf., e.g., [204]). The first factor in Eq. (200), (1 - R e x p ( - N d / ~ ) ) -2, depends on both the mean free path ~. and the reflectivity R, quantities that are expected to depend rather smoothly on energy. The same holds for the finesse f and the phase shift r Therefore, the modulation of the interference factor can be mainly attributed to the wave number k• Assuming the first factor, the finesse, and the phase shift as energy independent, the interference factor becomes approximately III 2 ~

Fig. 46. Electron confined to a quantum well. Arrows P + denote propagation between the interfaces (vacuum-film and film-substrate). Ri and Rs are the reflectivities at the film boundaries.

-1 (199)

1+

sin 2 k •

+

(202)

which is shown in Figure 47. Maxima in Ill 2 occur if sin2(k• + r - 0 or, equivalently, if k• = (nzr - r n 6 Z. The relevant quantities that determine the interference can be cast into two categories. (i) The wave number k• (E) and the mean free path ~.(E) depend on the band structure of the film material. Because the electrons can be described as quasiparticles, the band structure k i ( E , kll) is, in general, complex (cf. Section 3.2.2). The imaginary part of k• is related to the mean free path by the group velocity v• - Ok• E(k• = v•177 (ii) The reflectivity R and the phase shift r depend on the quantum-well boundaries, in particular, on the reflection properties at the film-substrate interface. For thick films, R and r can be regarded as independent of the film thickness Nd. Therefore, one can expect to determine them by

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON SPECTROSCOPY 1.0

f '/! i/'\

"" .........

"/illil",\/lill', I l', \\

///i/i'/I ;I,

523

Ag/Fe(100)

)

/'N = 16 eV

Thickness (ML)

0.8

i rii/\ 0.6

2

//ii/\

t IA \~ l

/ I,, ~

I i

I

! ~ ,

.,'1~

//i ',,

i~

,,

l It I \

/

li

0.4

71 -

0.2 \.,,

0.0

,i

\

,,.,,

,,,,,,r 0

7r/2

7r

37r/2

\

57

27r

k• Fig. 47. Interference factor I (k_L) for a Fabry-P6rot-type quantum well as a function of wave number k_L for finesses 0.5, 1.0, 2.0, 4.0, 8.0, and 16.0 (from top to bottom, alternating solid and dashed lines). N and d are the number of layers and the interlayer distance of the film, respectively. The phase shift 4~ is chosen as 0; cf. Eq. (202).

e.r-"

9 E

=,,~,%

O o ARPES from films with different thicknesses Nd. For very thin films, however, the interfaces (surface side and substrate side) cannot be separated and R and ~b should differ considerably from their values for thicker films. This becomes evident by comparing reflectivities for various film thicknesses, as, for example, shown in Figure 41. The peak positions depend on k• and 4~, the peak widths on R and k. If the film were infinitely thick, the photocurrent ,Is would be expressed in the form of Fermi's golden rule, Eq. (141). However, for a finite thickness, the initial state Ii) can be seen as modulated by the interference factor I, Eq. (200), and thus is given by Ii Ii) [205]. Therefore, the photocurrent from the film with finite thickness reads

Jqw "~ Z

IIi lel(flA

9 pli)i2~(Ef

- co

-

Ei)

(203)

i

The task to determine the interference-determining quantities k• 4~, R, and )~ might be complicated by several facts. (i) The growth of the film material on the substrate should be in the layer-by-layer mode, which leads to well-defined film boundaries and minimizes film imperfections. (ii) The electronic properties of the film and the substrate should "match". In other words, they should allow for QWSs; for example, there has to be a gap in the band structure of the substrate. (iii) In general, several initial states ]i) contribute to the total photocurrent in the considered energy range and, thus, one has to deal with a set of parameters for each initial state. Fortunately, there are systems in which only a single initial state is present in the considered energy range. Paggel et al. reported on an experimental investigation of the interference properties of Ag films on Fe(001) [206], another prototypical system. In the considered initial-energy range ( - 2 eV up to 0 eV) and the chosen photon energy, the spectrum for semi-infinite Ag looks almost structureless. Therefore, the intensity modulations due to the Ag films can be easily identified (cf. Fig. 48). Further, Ag films grow in a layer-by-layer

121..

~..,/ ,

,

.

~

.,,,..,.~...,,. x,,..,....,,,/. 27.5

~ ,

2

r 7_-z,-

,

J

I

0

Binding Energy (eV) Fig. 48. Photoemission spectra for Ag films on Fe(001) for various film thicknesses in monolayers (ML), as indicated on the fight of each spectrum. The experimental data (given by dots) were recorded for normal emission (kll = 0) and 16 eV photon energy. Solid lines correspond to the fitted interference spectra and the background. Reprinted with permission from J. J. Paggel, T. Miller, and T.-C. Chiang, Science 283, 1709 (1999). Copyright 1999, by the American Association for the Advancement of Science.

mode on Fe(001), which allows for a very accurate thickness calibration via the observed intensity modulation. As an example, the spectrum for a film with thickness 27.5 ML shows simultaneously the peak structures of films with 27 and 28 ML. The modulated intensity appears as a superposition of those of the latter films (this holds, in addition, for the 42.5-ML film). To determine the reflectivity R, the phase shift 4~, and the mean free path )~, one has to know the initial-state band structure of Ag. The latter can be obtained either by the photoemission experiment itself, for instance, via band mapping using various photon energies or by a band structure calculation. The relevant band in the considered energy range is the sp valence band, which is roughly a free-electron parabola; see Figure 49a (cf., e.g., the band structure of Cu in Figure 40, which shows an sp band, too). Applying a fitting procedure, Paggel et al. obtained R(E), ~(E), and )~(E), which are assumed to be independent of the film thickness. The resulting

524

HENK

(b)

(a) >~ 2

ble to acknowledge them all. Therefore, I want to mention only four to whom I am especially grateful: Roland Feder, Samed Halilov, Thomas Sch~unemann, and Eiichi Tamura.

.-.

o

REFERENCES

w =

5

"E

-4

0.0 i . r 0.6

0.8

0

1.0

k,/h'FK

(d)

(c)

9 , i

,

1

,

,

,

i

II

2

Binding Energy (eV)

1.0

0,8 9"g

0.6

r o ,..,.,., "$ 13:

~

-1

0.4 !

0.2 0.0

i

, =, ," *

0

-2 1

1

.

i

9

I

_1

2

Binding Energy (eV)

0

1

2

Binding Energy (eV)

Fig. 49. Electronic structure of Ag films on Fe(100). Panel a shows the Ag band structure near the Fermi energy (i.e., the sp band range). The solid line corresponds to the experimentally determined dispersion of the sp band, the dashed line to one theoretically obtained. Panel b depicts the inverse lifetime as obtained from the experimental data. Panels c and d show the reflection coefficients and the phase shift at the Ag/Fe interface. Reprinted with permission from J. J. Paggel, T. Miller, and T.-C. Chiang, Science 283, 1709 (1999). Copyright 1999, by the American Association for the Advancement of Science.

theoretical modulated intensities are shown in Figure 48 and

match almost perfectly the experimental ones for all film thicknesses. Note that the peak shapes in the experimental spectra agree very well with that of the interference factor I shown in Figure 47. The determined reflectivity R was less than unity (R 6 [0.6, 0.85], Fig. 49c), indicating that the electrons are not strictly confined to the Ag film. This can be attributed to the fact that the bandgap in the Fe substrate is not an absolute one but a hybridization bandgap. In the former case, there are no states in the bandgap energy range, whereas in the latter, there are states with different spatial symmetry, which, however, are mixed by SOC. Further, the small, but not negligible lattice mismatch between Ag and Fe leads to nonspecular reflection at the boundaries. The inverse lifetime depends quadratically on the binding energy (Fig. 49b and [207]), as in Fermi liquid theory.

Acknowledgments It is a great pleasure to thank those colleagues who have made the present chapter possible. Unfortunately, it is nearly impossi-

1. L. Bennett and R. Watson, Eds., "Magnetic Multilayers." Word Scientific, Singapore, 1993. 2. J. Bland and B. Heinrich, "Ultrathin Magnetic Structures." SpringerVerlag, Berlin, 1994. 3. A. Barthflfmy, A. Fert, and F. Petroff, In "Handbook of Magnetic Materials" (K. H. J. Buschow, Ed.), Vol. 12, p. 1. Elsevier, Amsterdam, 1999. 4. J.M. Daughton, J. Magn. Magn. Mater. 192, 334 (1999). 5. U. Hartmann, Ed., "Magnetic Multilayers and Giant Magnetoresistance: Fundamentals and Industrial Applications," Springer Series in Surface Sciences, Vol. 37. Springer-Verlag, Berlin, 1999. 6. A. Zangwill, "Physics at Surfaces." Cambridge Univ. Press, Cambridge, UK, 1988. 7. N. Ashcroft and N. Mermin, "Solid State Physics." Holt-Saunders, London, 1976. 8. L. Brillouin, "Wave Propagation in Periodic Structures." McGraw-Hill, New York, 1946. 9. R.L. Park and H. H. Madden, S u ~ Sci. 11,188 (1968). 10. S. Gull, A. Lasenby, and C. Doran, Found. Phys. 23, 1175 (1993). 11. T.G. Void, Am. J. Phys. 61,491 (1993). 12. G. Ertl and J. Ktippers, "Low Energy Electrons and Surface Chemistry," Chap. 9, p. 201. VCH, Weinheim, 1985. 13. E Bloch, Z. Phys. 52, 555 (1928). 14. P. Harrison, "Quantum Wells, Wires and Dots" Wiley, Chichester, 2000. 15. E. Merzbacher, "Quantum Mechanics" 2nd ed. Wiley, New York, 1970. 16. K.R. Brownstein, Am. J. Phys. 68, 160 (2000). 17. H. A. Kramers, Koniklije Nederlandse Akademie van Wetenschapen 33, 959 (1930). 18. G. Bastard, Phys. Rev. B 24, 5693 (1981). 19. G. Bastard, Phys. Rev. B 25, 7584 (1982). 20. P.D. Loly and J. B. Pendry, J. Phys. C: Solid State Phys. 16, 423 (1983). 21. J.E. Ortega, E J. Himpsel, G. J. Mankey, and R. F. Willis, Phys. Rev. B 47, 1540 (1993). 22. M. Griine, T. Pelzer, K. Wandelt, and I. T. Steinberger, J. Electron Spectrosc. Relat. Phenom. 98-99, 121 (1999). 23. K. Horn, M. Schemer, and A. M. Bradshaw, Phys. Rev. Lett. 41, 822 (1978). 24. M. Schemer, K. Horn, A. M. Bradshaw, and K. Kambe, Surf. Sci. 80, 69 (1979). 25. K. Kambe, Surf. Sci. 105, 95 (1981). 26. P. Trischberger, H. Dr0ge, S. Gokhale, J. Henk, H.-P. Steinriick, W. Widdra, and D. Menzel, S u ~ Sci. 377-379, 155 (1996). 27. W. Widdra, P. Trischberger, and J. Henk, Phys. Rev. B 60, R5161 (1999). 28. C. Davisson and L. H. Germer, Nature 119, 558 (1927). 29. C.J. Davisson and L. H. Germer, Phys. Rev. 30, 705 (1927). 30. L. de Broglie, Comte Rendu 179, 676 (1924). 31. L. de Broglie, Comte Rendu 179, 1039 (1924). 32. L. de Broglie, Comte Rendu 180, 498 (1925). 33. J. E van Veen and M. A. van Hove, Eds., "The Structure of Surfaces II" Springer Series in Surface Sciences, Vol. 11. Springer-Verlag, Berlin, 1988. 34. S. Y. Tong, M. A. van Hove, K. Takayanagi, and X. D. Xie, Eds., "The Structure of Surfaces III" Springer Series in Surface Sciences, Vol. 24. Springer-Verlag, Berlin, 1991. 35. C. Davisson and L. H. Germer, Phys. Rev. 31,307 (1928). 36. C. Davisson and L. H. Germer, Phys. Rev. 31,155 (1928). 37. M.P. Seah and W. A. Dench, Surf. Interface Anal 1, 2 (1979). 38. Z.-J. Ding and R. Shimizu, Surf. Sci. 222, 313 (1989). 39. J. Rundgren, Phys. Rev. B 59, 5106 (1999). 40. C.J. Davisson, J. Franklin Inst. 205, 597 (1928).

LOW-ENERGY ELECTRON DIFFRACTION AND PHOTOELECTRON 41. 42. 43. 44. 45. 46.

47. 48.

49. 50. 51.

52. 53. 54.

55. 56. 57. 58. 59.

60. 61. 62. 63. 64. 65. 66.

67. 68. 69. 70.

71. 72. 73. 74. 75. 76. 77. 78. 79.

80.

K. Heinz, U. Starke, and J. Bernhardt, Prog. Surf. Sci. 64, 163 (2000). K. Kambe, Z. Naturforsch., A: Phys. Sci. 22, 322 (1967). K. Kambe, Z. Naturforsch., A: Phys. Sci. 22, 422 (1967). K. Kambe, Z. Naturforsch., A: Phys. Sci. 22, 1280 (1967). J.B. Pendry, "Low Energy Electron Diffraction." Academic Press, London, 1974. M.A. van Hove, W. H. Weinberg, and C. M. Chan, "Low-Energy Electron Diffraction." Springer-Verlag, Berlin, 1986. S.Y. Tong, In "Progress in Surface Science" (S. G. Davisson, Ed.), Vol. 7, p. 1. Pergamon, London, 1975. M. A. van Hove and S. Y. Tong, "Surface Crystallography by LEED: Theory, Computation and Structural Results," Springer Series in Chemical Physics, Vol. 2. Springer-Verlag, Berlin, 1979. R. Feder, Solid State Commun. 31,821 (1979). R. Feder and J. Kirschner, Surf. Sci. 103, 75 (1981). R. Feder, In "Polarized Electrons in Surface Physics" (R. Feder, Ed.). Advanced Series in Surface Science, Chap. 4, p. 125. World Scientific, Singapore, 1985. J. Kirschner and R. Feder, Phys. Rev. Lett. 42, 1008 (1979). J.C. Slater, Phys. Rev. 51,840 (1937). V.N. Strocov, R. Claessen, G. Nicolay, S. Htifner, A. Kimura, A. Harasawa, S. Shin, A. Kakizaki, P. O. Nilsson, H. I. Starnberg, and P. Blaha, Phys. Rev. Lett. 81, 4943 (1998). I. Barto~, Prog. Surf. Sci. 59, 197 (1998). V. Heine, Proc. Phys. Soc. 81,300 (1963). Y.-C. Chang, Phys. Rev. B 25, 605 (1982). J. Hermanson, Solid State Commun. 22, 9 (1977). T. Inui, Y. Tanabe, and Y. Onodera, "Group Theory and Its Applications in Physics," 1st ed., Springer Series in Solid State Sciences, Vol. 78. Springer-Verlag, Berlin, 1990. J.B. Pendry, J. Phys. C: Solid State Phys. 2, 1215 (1969). J.B. Pendry, J. Phys. C: Solid State Phys. 2, 2273 (1969). J.B. Pendry, J. Phys. C: Solid State Phys. 2, 2283 (1969). V.N. Strocov, H. I. Starnberg, and P. O. Nilsson, J. Phys.: Condens. Matter 8, 7539 (1996). V.N. Strocov, H. I. Starnberg, and P. O. Nilsson, J. Phys.: Condens. Matter 8, 7549 (1996). J. Henk, W. Schattke, H.-P. Barnscheidt, C. Janowitz, R. Manzke, and M. Skibowski, Phys. Rev. B 39, 13286 (1989). J. Henk, J.-V. Peetz, and W. Schattke, In "20th International Conference on the Physics of Semiconductors" (E. M. Anastassakis and J. D. Joannopoulos, Eds.), Vol. 1, pp. 175-178. World Scientific, Singapore, 1990. J. Henk, W. Schattke, H. Carstensen, R. Manzke, and M. Skibowski, Phys. Rev. B 47, 2251 (1993). S. Lorenz, C. Solterbeck, W. Schattke, J. Burmeister, and W. Hackbusch, Phys. Rev. B 55, R13432 (1997). W. Schattke, Prog. Surf. Sci. 64, 89 (2000). I. Mertig, E. Mrosan, and P. Ziesche, "Multiple Scattering Theory of Point Defects in Metals: Electronic Properties," Teubner-Texte zur Physik, Vol. 11. Teubner, Leipzig, 1987. P. Weinberger, "Electron Scattering Theory of Ordered and Disordered Matter," Clarendon, Oxford, 1990. A. Gonis, "Green Functions for Ordered and Disordered Systems," Studies in Mathematical Physics, Vol. 4. North-Holland, Amsterdam, 1992. J. Korringa, Physica 13,392 (1947). W. Kohn and N. Rostoker, Phys. Rev. 94, 1111 (1954). J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, Phys. Rev. B 40, 12164 (1989). E.M. Rose, "Relativistic Electron Theory." Wiley, New York, 1961. S. Bei der Kellen and A. J. Freeman, Phys. Rev. B 54, 11187 (1996). A. Gonis, P. Turchi, J. Kudrnovsk~, V. Drchal, and I. Turek, J. Phys." Condens. Matter 8, 7869 (1996). J. W. Krewer, "Beugung spinpolarisierter langsamer Elektronen (SPLEED) mit nicht-sph~irischen Potentialen," Ph.D. Dissertation, Universit~it Duisburg, 1990. J.W. Krewer and R. Feder, Physica B 172, 135 (1991).

SPECTROSCOPY

525

81. M. Abramowitz and I. Stegun, Eds., "Handbook of Mathematical Functions." Dover, New York, 1965. 82. E. Tamura, Phys. Rev. B 45, 3271 (1992). 83. B. Ackermann, "Relativistische Theorie der Photoemission und Streuung langsamer Elektronen von ferromagnetischen Oberfl~ichen," Ph.D. Thesis, Universit~it Duisburg, 1985. 84. D.D. Koelling and B. N. Harmon, J. Phys. C: Solid State Phys. 10, 3107 (1977). 85. H. Gollisch and L. Fritsche, Phys. Status Solidi B 86, 156 (1978). 86. T. Takeda, J. Phys. F: Met. Phys. 9, 815 (1979). 87. E. Tamura, private communication. 88. H. Ebert, H. Freyer, A. Vernes, and G. Y. Guo, Phys. Rev. B 53, 7721 (1996). 89. H. Ebert, H. Freyer, and M. Deng, Phys. Rev. B 56, 9454 (1997). 90. L.A. Mac Coil, Phys. Rev. 56, 699 (1939). 91. R. Jones, P. Jennings, and O. Jepsen, Phys. Rev. B 29, 6474 (1984). 92. E. Tamura and R. Feder, Z. Phys. B: Condens. Matter 81,425 (1990). 93. C.S. Lent and D. J. Kirkner, J. Appl. Phys. 67, 6353 (1990). 94. Y. Joly, Phys. Rev. Lett. 68, 950 (1992). 95. R. Feder, J. Phys. C: Solid State Phys. 14, 2049 (1981). 96. J. Kessler, "Polarized Electrons," 2nd ed., Springer Series on Atoms and Plasmas, Vol. 1. Springer-Veflag, Berlin, 1985. 97. R. Feder, Ed., "Polarized electrons in surface physics," Advanced Series in Surface Science. World Scientific, Singapore, 1985. 98. E. Zanazzi and E Jona, Surf. Sci. 62, 61 (1977). 99. J.B. Pendry, J. Phys. C: Solid State Phys. 13, 937 (1980). 100. E. Tamura, R. Feder, G. Waller, and U. Gradmann, Phys. Status Solidi B 157, 627 (1990). 101. O. Hjortstam, J. Trygg, J. M. Wills, B. Johansson, and O. Eriksson, Phys. Rev. B 53, 9204 (1996). 102. I. Delgadillo, H. Gollisch, and R. Feder, Phys. Rev. B 50, 15808 (1994). 103. R. Feder, B. Awe, and E. Tamura, Surf. Sci. 157, 183 (1985). 104. E. Tamura, R. Feder, J. Krewer, R. E. Kirby, E. Kisker, E. L. Garwin, and E K. King, Solid State Commun. 55, 543 (1985). 105. P. Bruno, J. Phys.: Condens. Matter 11, 9403 (1999). 106. T. Scheunemann, R. Feder, J. Henk, E. Bauer, T. Duden, H. Pinkvos, H. Poppa, and K. Wurm, Solid State Commun. 104, 787 (1997). 107. B. Johnson, P. Berlowitz, D. Goodman, and C. Bartholomew, Surf. Sci. 217, 13 (1989). 108. J.G. Ociepa, P. J. Schultz, K. Griffiths, and P. R. Norton, Surf. Sci. 225, 281 (1990). 109. M. Tikhov and E. Bauer, Surf. Sci. 232, 73 (1990). 110. H. Knoppe and E. Bauer, Phys. Rev. B 48, 1794 (1993). 111. E. Bauer, Rep. Prog. Phys. 57, 895 (1994). 112. L.M. Falicov and J. Ruvalds, Phys. Rev. 172, 498 (1968). 113. C. M. Schneider, P. Bressler, P. Schuster, J. Kirschner, J. J. de Miguel, and R. Miranda, Phys. Rev. Lett. 64, 1059 (1990). 114. H. Bonzel and C. Kleint, Prog. Surf. Sci. 49, 107 (1995). 115. H. Hertz, Ann. Phys. Chem. Neue Folge 31,983 (1887). 116. W. Hallwachs, Ann. Phys. Chem. Neue Folge 33, 301 (1888). 117. J. Elster and H. Geitel, Ann. Phys. Chem. Neue Folge 38, 40 (1889). 118. J. Elster and H. Geitel, Ann. Phys. Chem. Neue Folge 38, 497 (1889). 119. P. Lenard, Ann. Phys. 8, 149 (1902). 120. A. Einstein, Ann. Phys. 17, 132 (1905). 121. K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johanson, T. Bergmark, S.-E. Karlsson, I. Lindgren, and B. Lindberg, "ESCA-Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy." Almqvist & Wiksell, Uppsala, 1967. 122. E.O. Kane, Phys. Rev. Lett. 12, 97 (1964). 123. M. Campagna and R. Rosei, Eds., "Photoemission and Absorption Spectroscopy of Solids and Interfaces with Synchrotron Radiation." NorthHolland, Amsterdam, 1990. 124. R.Z. Bachrach, Ed., "Technique," Synchrotron Radiation Research: Advances in Surface and Interface Science, Vol. 1. Plenum, New York, 1992. 125. R.Z. Bachrach, Ed., "Issues and Technology," Synchrotron Radiation Research: Advances in Surface and Interface Science, Vol. 2. Plenum, New York, 1992.

526

HENK

126. C. Berglund and W. Spicer, Phys. Rev. 136, A1030 (1964). 127. M. Cardona and L. Ley, Eds., "Photoemission in Solids I," Topics in Applied Physics, Vol. 26. Springer-Verlag, Berlin, 1978. 128. A. Liebsch, In "Photoemission and the Electronic Properties of Surfaces" (B. Feuerbacher, B. Fitton, and R. E Willis, Eds.), p. 167. Wiley, Chichester, 1978. 129. S.V. Kevan, Ed., "Angle-Resolved Photoemission: Theory and Current Applications." Elsevier, Amsterdam, 1992. 130. I. Adawi, Phys. Rev. A 134, 788 (1964). 131. G.D. Mahan, Phys. Rev. B 2, 4334 (1970). 132. G. D. Mahan, Phys. Rev. Lett. 24, 1068 (1970). 133. W.L. Schaich and N. W. Ashcroft, Phys. Rev. B 3, 2452 (1971). 134. D.C. Langreth, Phys. Rev. B 3, 3120 (1971). 135. J.B. Pendry, J. Phys. C: Solid State Phys. 8, 2431 (1975). 136. J.B. Pendry, Surf. Sci. 57, 679 (1976). 137. J. E L. Hopkinson, J. B. Pendry, and D. J. Titterington, Comput. Phys. Commun. 19, 69 (1980). 138. G. Thtirner and G. Borstel, Phys. Status Solidi B 126, 617 (1984). 139. J. Braun, G. Th6rner, and G. Borstel, Phys. Status Solidi B 130, 643 (1985). 140. J. Braun, G. Th6rner, and G. Borstel, Phys. Status Solidi B 144, 609 (1987). 141. M. W6hlecke and G. Borstel, In "Optical Orientation" (E Meier and B. P. Zakharchenya, Eds.), North-Holland, Amsterdam, 1984. 142. E. Tamura, W. Piepke, and R. Feder, Phys. Rev. Lett. 59, 934 (1987). 143. E. Tamura and R. Feder, Europhys. Lett. 16, 695 (1991). 144. J. Henk and R. Feder, Europhys. Lett. 28, 609 (1994). 145. B. Ginatempo, P. J. Durham, B. L. Gyorffy, and W. M. Temmerman, Phys. Rev. Lett. 54, 1581 (1985). 146. B. Schmiedeskamp, B. Vogt, and U. Heinzmann, Phys. Rev. Lett. 60, 651 (1988). 147. B. Schmiedeskamp, N. Irmer, R. David, and U. Heinzmann, Appl. Phys. A 53,418 (1991). 148. N. Irmer, E Frentzen, S.-W. Yu, B. Schmiedeskamp, and U. Heinzmann, J. Electron Spectrosc. Relat. Phenom. 78, 321 (1996). 149. R. Feder, E Rosicky, and B. Ackermann, Z. Phys. B: Condens. Matter 52, 31 (1983). 150. R. Feder and J. Henk, In "Spin-Orbit Influenced Spectroscopies of Magnetic Solids" (H. Ebert and G. Scht~tz, Eds.), Lecture Notes in Physics, Vol. 466, p. 85. Springer-Verlag, Berlin, 1996. 151. W. Kuch, A. Dittschar, K. Meinel, M. Zharnikov, C. Schneider, J. Kirschner, J. Henk, and R. Feder, Phys. Rev. B 53, 11621 (1996). 152. A. Fanelsa, E. Kisker, J. Henk, and R. Feder, Phys. Rev. B 54, 2922 (1996). 153. A. Rampe, G. Gt~ntherodt, D. Hartmann, J. Henk, T. Scheunemann, and R. Feder, Phys. Rev. B 57, 14370 (1998). 154. P.J. Durham, J. Phys. F: Met. Phys. 11,2475 (1981). 155. P.J. Durham, J. Staunton, and B. L. Gyorffy, J. Magn. Magn. Mater. 45, 38 (1984). 156. P. Feibelman and D. Eastman, Phys. Rev. B 10, 4932 (1974). 157. C. Caroli, D. Lederer-Rozenblatt, B. Roulet, and D. Saint-James, Phys. Rev. B 8, 4552 (1973). 158. H. Gollisch, D. Meinert, E. Tamura, and R. Feder, Solid State Commun. 82, 197 (1992). 159. W. Schattke, Prog. Surf. Sci. 54, 211 (1997). 160. L. Hedin, J. Michiels, and J. Inglesfield, Phys. Rev. B 58, 15565 (1998). 161. L. Hedin, J. Phys.: Condens. Matter 11, R489 (1999). 162. T. Fujikawa and L. Hedin, Phys. Rev. B 40, 11507 (1989). 163. S. Lundqvist and N. H. March, Eds., "Theory of the Inhomogenous Electron Gas." Plenum, New York, 1983. 164. A. Liebsch, Phys. Rev. Lett. 43, 1431 (1979). 165. A. Goldmann, R. Matzdorf, and E Theilmann, Surf. Sci. 414, L932 (1998). 166. R. Matzdorf, Surf. ScL Rep. 30, 154 (1998). 167. J. Braun, Rep. Prog. Phys. 59, 1267 (1996). 168. P.M. Morse and H. Feshbach, "Methods of Theoretical Physics," Vol. 1. McGraw-Hill, New York, 1953.

169. 170. 171. 172. 173. 174. 175. 176.

177. 178.

179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204.

205. 206. 207.

J. S. Faulkner and G. M. Stocks, Phys. Rev. B 21, 3222 (1980). P. Braspenning and A. Lodder, Phys. Rev. B 49, 10222 (1994). G. Grosso, S. Moroni, and G. P. Parravicini, Phys. Scr., T 25, 316 (1989). L. Szunyogh, B. 10jfalussy, and P. Weinberger, Phys. Rev. B 51, 9552 (1995). K. Wildberger, R. Zeller, and P. H. Dederichs, Phys. Rev. B 55, 10074 (1997). H. Bross, Z. Phys. B: Condens. Matter 28, 173 (1977). J. Henk, A. M. N. Niklasson, and B. Johansson, Phys. Rev. B 59, 13986 (1999). J. Henk, T. Scheunemann, S. Halilov, and R. Feder, J. Phys.: Condens. Matter 8, 47 (1996). C.M. Schneider, J. J. de Miguel, P. Bressler, P. Schuster, R. Miranda, and J. Kirschner, J. Electron Spectrosc. Relat. Phenom. 51,263 (1990). W. Kuch, A. Dittschar, M. Salvietti, M.-T. Lin, M. Zharnikov, C. M. Schneider, J. Camarero, J. J. de Miguel, R. Miranda, and J. Kirschner, Phys. Rev. B 57, 5340 (1998). J. Henk and B. Johansson, J. Electron Spectrosc. Relat. Phenom. 105, 187 (1999). A. Beckmann, Surf. Sci. 349, L95 (1996). R. Paniago, R. Matzdorf, G. Meister, and A. Goldmann, Surf. Sci. 325, 336 (1995). R. Schmitz-Htibsch, K. Oster, J. Radnik, and K. Wandelt, Phys. Rev. Lett. 74, 2995 (1995). P. Segovia, E. G. Michel, and J. E. Ortega, Phys. Rev. Lett. 77, 3455 (1996). E G. Curti, A. Danese, and R. A. Bartynski, Phys. Rev. Lett. 80, 2213 (1998). H. Hoekstra, Surf. Sci. 205, 523 (1988). J. Henk and W. Schattke, Comput. Phys. Commun. 77, 69 (1993). S.V. Halilov, J. Henk, T. Scheunemann, and R. Feder, Surf. Sci. 343, 148 (1995). J. Heinrichs, J. Phys.: Condens. Matter 12, 5565 (2000). W.-H. Steeb, "Hilbert Spaces, Generalized Functions and Quantum Mechanics." B.I. Wissenschaftsverlag, Mannheim, 1991. E.D. Hansen, T. Miller, and T.-C. Chiang, J. Phys.: Condens. Matter 9, L435 (1997). K. Garrison, Y. Chang, and P. Johnson, Phys. Rev. Lett. 71, 2801 (1993). C. Carbone, E. Vescovo, O. Rader, W. Gudat, and W. Eberhardt, Phys. Rev. Lett. 71, 2805 (1993). C. Carbone, E. Vescovo, R. Kl~isges, D. Sarma, and W. Eberhardt, Solid State Commun. 100, 749 (1996). R. Kl~isges, D. Schmitz, C. Carbone, W. Eberhardt, P. Lang, R. Zeller, and P. H. Dederichs, Phys. Rev. B 57, R696 (1998). P. van Gelderen, S. Crampin, and J. Inglesfield, Phys. Rev. B 53, 9115 (1996). C. Bradley and A. Cracknell, "The Mathematical Theory of Symmetry in Solids." Clarendon, Oxford, 1972. P. H. Dederichs, K. Wildberger, and R. Zeller, Physica B 237-238, 239 (1997). P. Bruno, Phys. Rev. B 52, 411 (1995). J.J. Paggel, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 81, 5632 (1998). R. Matzdorf, A. Gerlach, R. Hennig, G. Lauff, and A. Goldmann, J. Electron Spectrosc. Relat. Phenom. 94, 279 (1998). D. Reiser, J. Henk, H. Gollisch, and R. Feder, Solid State Commun. 93, 231 (1995). E Frentzen, J. Henk, N. Irmer, R. David, B. Schmiedeskamp, U. Heinzmann, and R. Feder, Z. Phys. B: Condens. Matter 100, 575 (1996). C. Fabry and A. P6rot, Ann. Chim. Phys. 19, 115 (1899). M. Born and E. Wolf, "Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light," 3rd ed. Pergamon, Oxford, 1965. P. Voisin, G. Bastard, and M. Voos, Phys. Rev. B 29, 935 (1984). J.J. Paggel, T. Miller, and T.-C. Chiang, Science 283, 1709 (1999). A. Beckmann, Surf. Sci. 326, 335 (1995).

Chapter 11

IN SITU SYNCHROTRON STRUCTURAL STUDIES OF THE GROWTH OF OXIDES AND METALS A. Barbier, C. Mocuta, G. Renaud CEA/Grenoble, D~partement de Recherche Fondamentale sur la Matikre Condens~e SP2M/IRS, 38054 Grenoble Cedex 9, France

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Introduction: Particularities of Metal/Oxide Studies . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Refraction from Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Grazing Incidence X-Ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Grazing Incidence Small-Angle X-Ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Preparation and Structure of Clean Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. SpecificConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. MgO(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. c~-A1203(0001)-(1 • 1) and Its Reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. NiO(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. CoO(lll) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Model Metal/Oxide Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Ag/MgO(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Pd/MgO(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Ni/MgO(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Comparison between the Different Metal/MgO(001) Interfaces . . . . . . . . . . . . . . . . . . . 5. Exchange-Coupled Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. SpecificConsiderations: Magnetism Versus Metal/Oxide . . . . . . . . . . . . . . . . . . . . . . 5.2. Co/NiO(111) . . . . . . . . . . . . . . . . . . . . . . ......................... 5.3. Ni80Fe20/NiO(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Growth of Nickel Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. NiO(111)/c~-A1203 (0001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. NiO(111)/Au(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

527 529 529 530 531 537 538 538 539 541 545 549 553 553 564 568 571 572 572 574 580 585 585 589 592 592 593

1. INTRODUCTION

the layer? W h a t are the structural defects, w h i c h are k n o w n to

W h e n dealing with thin film growth, a w e a l t h o f o p e n questions

residual strain in the g r o w n film and w h a t are the m e c h a n i s m s

have i m p o r t a n t effects on the properties o f devices? W h a t is the

must be a n s w e r e d for each materials c o m b i n a t i o n . A m o n g the

a l l o w i n g the r e l a x a t i o n o f this strain? W h e r e do the a d s o r b a t e

m a j o r questions that i m m e d i a t e l y arise, we m a y cite the fol-

atoms rest on the surface? W h a t kind o f atoms (surfactants)

lowing: W h a t is the g r o w t h m o d e and w h a t is the resulting

or gases m i g h t be a d d e d to m o d i f y the g r o w t h m o d e , to ren-

m o r p h o l o g y o f the layer? Is the g r o w t h epitaxial and w h a t are

der it m o r e 2D (layer by layer) or better c o n t r o l l e d 3 D ? H o w

the epitaxial r e l a t i o n s h i p s ? W h a t is the crystalline quality o f

can we q u a n t i f y the g r o w t h laws and especially the 3D cluster

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 2: Characterization and Spectroscopy of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512910-6/$35.00 527

528

BARBIER ET AL.

growth and how do we control it to eventually obtain controlled self-organization? How can the physical properties of the heterostructures like reactivity, magnetism, electron transport, or light emission, for example, be connected to their crystalline quality? In this respect, is the morphology the dominant parameter or does the structure eventually influence the overall properties of the overlayer? How can we access buried interfaces; are they ordered or not? What is the role of the crystalline quality and cleanliness of the substrates? The situation is even more complicated when we consider that all of these questions should be addressed throughout the growth. As a matter of fact, during growth many parameters may change. This affect not only the incoming atoms. Indeed, except for 2D growth, during the elaboration of the layer the atoms impinge on an evolving surface, for instance from an initial flat and clean substrate to an assembly of clusters or, finally, a continuous overlayer. All of these situations are very different, and the relative importance of each energetic term defining the behavior of the incoming atoms may change throughout the growth process. Thus it is only once we are able to answer most of the questions underlying growth, for each thickness, throughout the growth, that we may understand the physical processes that underlie the formation of a given interface. The description of the film, as a whole, after growth, can lead to erroneous interpretations if we do not know what happened to the film throughout its growth. Within this framework, the investigation of the structure of the film, in situ, during the growth itself is mandatory for an in-depth understanding and identification of the pertinent parameters. Such a fine-tuned description should then, in turn, allow theoreticians to evaluate the importance of each parameter and to elaborate improved models and potentials to describe thin film growth more adequately. Surface and interface techniques and, in particular, synchrotron light provide a wealth of in situ and ex situ methods, allowing the investigation of almost any type of materials or physical properties. However, many of them will not be able to address all of the questions concerning the growth. Near-field techniques, although they are most helpful in providing an understanding surface structures, can provide only a top view of a surface, with or without a deposit on it. The information depth is thus extremely limited. The morphology of an overlayer can be more easily accessed, although the image will result from the convolution of the tip shape and the actual morphology that could lead to artifacts. Electrons, ions, or atom diffraction experiments undergo similar limitations, because their penetration depth is limited to a very few atomic planes, thus giving access only to the structure of the top layers. Spectroscopies are another important class of techniques. They often rely on charged particles, especially electrons. The electron mean free path in the material, which ranges roughly from 0.5 to 5 nm, thus limits the information depth. Moreover, because the inner shells of the atoms are probed and their energies are discrete, one does not generally have a choice of information depth. With such techniques the growth of a few layers is generally well described, although chemical reactions or bond formation of the atoms may transform the spectra and render a quantitative interpre-

tation difficult or impossible. Finally, electron microscopy is a powerful technique that fully enables the investigation of buried interfaces but in a destructive way, preventing any investigation of growth modes. On the one hand, increasing the information depth requires the use of particles that interact only weakly with matter. On the other hand, extracting useful information in a realistic counting time, for a number of atoms as limited as a tenth of a monolayer, will require very high fluxes to compensate for the weak interaction. This apparent contradiction has been solved with the advent of third-generation hard X-ray synchrotron sources. Of course, the number of possible techniques is reduced, but in this field, synchrotron light, especially through diffraction, gives insights into the intimate mechanisms in situ during growth. Such an approach allows an understanding of each step of the formation of an interface and avoids speculation from the observation of the final state. Because the information depth is as large as from submonolayer depositsup to micron-thick layers for hard X-rays, and because there are no limitations in experimental environment, the possible investigations represent wide and comparatively virgin fields. Indeed, X-ray experiments can be performed at almost all pressures, from ultrahigh vacuum to high-pressure conditions, with reactive gases or not, as well as at all temperatures, from a few Kelvin to thousands of degrees. When dealing with surfaces and X-ray diffraction one may observe that we have access to the Fourier transform of the object under investigation (or, more exactly, its autocorrelation function). Of course, the phase information is lost and only the intensity can be measured, but it remains that each feature in direct real space has a counterpart in the reciprocal Fourier space. Intrinsically the information exists somewhere in reciprocal space. Specific techniques and equipment were designed to allow a quantitative record of the intensity in the regions of reciprocal space that are of interest with respect to surface and growth studies. Choosing the pertinent measurement and acquisition conditions is an important task in this respect, but the quality of the resulting data is noteworthy because they are quantitative and allow the determinication of exact parameters with their error bars. Moreover, X-ray diffraction as we use it in this chapter is kinematical; the experiments will thus not be hampered by multiple scattering effects or transformations of the electronic structure. In Section 2 we describe the basics of two methods that we have used and developed for our investigations: grazing incidence X-ray diffraction (GIXD) and grazing incidence smallangle X-ray scattering (GISAXS). These techniques make it possible to quantitatively tackle all of the open questions, although not all of them will be answered for all systems. Through the examples, none of the questions enumerated above will be ignored. In some situations, complementary techniques must be used, after the growth, and in general the knowledge acquired during the growth plus the investigation after the growth will make it possible to draw a coherent and complete picture of the whole growth process. To illustrate these powerful synchrotron-based in situ techniques, we give examples of interfaces that could not be

SYNCHROTRON STUDY OF OXIDES AND METALS investigated by other tools. In all cases, at least one component, substrate, film, or even both, will be an insulator, thus preventing the investigation, in an extended thickness range, from other techniques. This applies, in particular, to the investigation of buried interfaces in situ, during growth, and to insulating surfaces. The net result is a comparatively poor understanding of the physics and overall properties of these materials. However, these materials are neither rare nor unimportant. As a matter of fact, most crystallized matter is insulating or poorly conducting, and the way in which minerals interact with the atmosphere or water determines erosion and aging mechanisms that are of growing interest, for instance, with respect to waste storage. Thus, surfaces or interfaces of ceramic materials are very common in nature. Understanding their properties is a very important issue if one wishes to understand the formation processes and the reactivity of these materials. Ceramic surfaces are increasingly studied both theoretically and experimentally, because they are also involved in many rapidly innovating industrial sectors. Until very recently they were mainly used as supports for catalysis or thin film growth. Recent advances in their synthesis have extended the range of potential new applications. Indeed, ceramics as well as semiconductors or metals provide a large diversity of intrinsic properties: they might exhibit different gap widths, and some of them are ferrimagnetic, ferromagnetic, or antiferromagnetic. Unfortunately, because of their intrinsic insulating properties, only very little is known about the crystallographic structure of oxide surfaces and of the interfaces they may form with other materials. The present chapter deals with these surfaces and growth on them. In Section 3 we examine in detail two single-crystal oxide surfaces that are routinely used in metal growth and semiconductor and superconductor thin film growth: MgO(001) and ot-A1203(0001). We show that they can be obtained with an excellent and controlled crystalline quality. Examination of the growth of metals on MgO(001), reported in Section 4, was undertaken with respect to the lattice parameter mismatch and the adhesion energy, both parameters increase from Ag to Pd and finally to Ni. Polar NiO(111) and COO(111) surfaces exhibit attractive physical properties and thus are particularly interesting. They are antiferromagnets, and only a few years ago interfacial magnetic ordering effects on NiO-based films were observed, including evidence of the interlayer exchange interaction and antiferromagnetic ordering along the (111) planes in superlattices. There are also hints of an enhanced reactivity of NiO(111) films. In contrast to MgO or ot-A1203 (0001), NiO and CoO play an active role in the heterostructures built on them. They are substrates, but they are also responsible for the magnetic exchange coupling in spin valve devices. Despite these interesting properties, single-crystal surface studies were only undertaken in very recent years. The preparation conditions for NiO(111) and COO(111) single crystals are be discussed in Section 3. Whereas the NiO(111) single crystals can be produced in a quality similar to that of the other oxide substrates, COO(111) remains stabilized by a nonstoichiometric surface layer. The growth of exchange-coupled ferromagnetic metallic layers (Co

529

and Ni80Fe20) on single-crystalline NiO(111) is the subject of Section 5. The formation of the ferromagnetic film is characterized from the very beginning, as well as a reactive interface formation in the NiFe/NiO case. For this last system, the use of other techniques (atomic force microscopy, transmission electron microscopy) was necessary to achieve a complete picture of the interface. Finally, the growth of NiO(111) itself as epitaxial films on other materials like ot-A1203 (0001) and Au(111 ) is discussed in Section 6.

2. EXPERIMENTAL TECHNIQUES 2.1. Introduction: Particularities of Metal/Oxide Studies Although many oxides are commonly used as substrates for thin film growth, their surface structures and properties are still not very well described, in contrast to metal or semiconductor surfaces. The control of the crystalline bulk structure is not the limiting issue, inasmuch as bulk A1203 or MgO may be grown in large quantities with a quality closer to that of Si than to those of many metals. From another point of view, although metals often have poorer bulk crystalline quality, because of their generally small fusion temperature, the polishing-induced polycrystalline texture can easily be removed by gentle annealing at moderate temperatures (below 1000 K). In contrast, many oxides have high fusion temperatures, and the atomic mobility in the surface region during gentle annealing is comparatively very small. The adequate preparation conditions for oxides are specific and require high temperatures, which imposes a design of specific furnaces that is often not available in standard ultrahigh vacuum (UHV) preparation chambers. Second, oxides are generally of complex structure, inasmuch as they are made of at least two elements, making their investigation more difficult than that of pure elements. However, the most stringent limitation comes from their insulating character. Indeed, many oxides are good insulators, and because most of the common surface science techniques are based on the backscattering of charged particles (electron spectroscopy and diffraction, tunnel microscopy), the charge buildup severely limits their use. For clean surfaces, the use of float guns or small densities of incident particles allows for some investigations, but as soon as metallic particles are deposited, the charge buildup becomes so large and uncontrollable that no clear conclusion can be reached. The situation is better when the incident particles have no charge, as is the case for photons. Some perturbations still occur if the analyzed scattered particles possess a charge, like electrons in X-ray photoelectron spectroscopy (XPS). Thus it is clear that the methods bestsuited for the investigation of oxide surfaces have to be based on neutral incident and neutral scattered particles. Of course, these methods also have their drawbacks and limitations. In particular, the generally small interaction cross sections of matter with X-rays require high incidence fluxes on the samples. The use of synchrotron light then becomes a necessity. Moreover, even with high fluxes, geometrical constraints and sample requirements (see Section 3.1) will apply, and, in particular, grazing

530

BARBIER ET AL.

incidence geometry will be used to enhance the surface signal with respect to the bulk contribution. We describe in the next section some grazing incidence X-ray methods. They are techniques of choice for the investigation of any type of surface (metals, semiconductors, or insulators), but are among the very unusual methods that apply as well to insulating oxide surfaces and interfaces. We describe the diffraction and diffusion of X-rays by a surface and focus on practical considerations, limitations, and orders of magnitude. For a more comprehensive description of the well-known and well-documented standard diffraction and crystallography, the reader may refer to standard textbooks and reviews [ 1-10].

When light crosses a fiat interface between two different materials, some part of the beam is reflected and some is transmitted through the interface. Depending on which material is the optically denser medium, the propagation direction in the second medium will be closer to or further from the normal of the interface. This very general phenomenon is called refraction, and it occurs for all wavelengths and all types of interfaces, crystalline or not. Mathematically, the behavior is well understood by introducing the index of refraction. For visible light, air has the smaller index of refraction, and total reflection is known to occur within materials: an evanescent wave that is damped exponentially in the material appears instead of emergent light on the other side of the interface, under internal incidence conditions given by Snell's law. In the case of a sharp interface between the vacuum and a surface of a material of wavelength-dependent index of refraction n, the geometry that applies is given in Figure 1. An incident beam made of a linearly polarized plane wave impinges on a surface at an angle Oci, with an amplitude Ei, and along a wave vector ki; the reflected beam leaves at an angle Ocf, at amplitude Ef, and along a wave vector kf; and the transmitted beam makes an angle Oct with the surface and has an amplitude Et and a wave vector kt. Applying Snell's law gives COS(OCi) and

OCf - - OCi

(1)

As long as n > 1 total reflection cannot occur when light travels from the vacuum to the material, even if OCi = O. Fortunately, unlike visible light, when hard X-rays (i.e., the energy is above several keV) are considered, the index of refraction is generally less than unity and can be written as

n=l

(2)

with )2 . e 2 . NA . p 2srmc2

9

Y~j~Cell(ZJ - f ; ) ~j~Cell A j

(2a)

and

2. e 2 " NA. p [3-

27rmc2

~ ~ ' r kf O~f

iiiiiii~!!~!i~!iiiiiiiiiiiii~iii~:!.:~iiii~iiiii~.iii~iii!!!

Niiiiiiiiiii

i iiiiiiiiii!!iii!i~ii}iiiiiiiiiiiiiiiiiiii~:::'~iii!iiiii::~iiiii~:~tii!iiiiiii

ii!!!!~}!i!iii,iiiiiiiiiiiiiii!iiii!!!il!iii!!iiiiiiiiii}iiiii~,,: .... ':~i"~!i!~i iiiiiiiiiiiii..!i!iiiiiiiiiiiiiiii!i!iilliiiiiigliiiiiiii!iiiiiiiiiiii~. "iii:

I

'i:iiiii,,,,,iiiiiiiiii i

where the summation is over all atomic species j present in the unit cell; NA, ( Z j - f a), fj', A j, p, lz, and ~. are, respectively, Avogadro's number, the scattering factor, the anomalous dispersion factor, the atomic weight of species j, the density, the photoelectric absorption coefficient, and the wavelength. Thus in the case of hard X-rays, total external reflection occurs on the vacuum side (although for very grazing angles, because a and 13 are, respectively, in the 10 -5 and 10 -6 range), leaving a critical angle for total external reflection Occ ~ ~/-2" in the 0.1-0.6 ~ range. It is important to note that the value of n < 1 is the key that allows surface investigations with hard X-rays; in turn, it also fully defines the geometry of the experiments. When Oci < OCc, the component of the transmitted wavevector normal to the surface becomes imaginary and the refracted wave is exponentially damped as a function of the distance below the surface and is an evanescent wave traveling parallel to the surface. The 1/e depth of penetration for the intensity of the X-rays becomes )v A =

Y~j eCell f j ' " Y~-jeCell

Aj

=

~.l.Z 47r

(2b)

(3) 4 . z r . Im(v/oc2 - Oc2 - 2i/3)

The reflection and the transmission coefficients of the surface are critically dependent on Oci,and their variations are given by Fresnel's formulae, If Ocisin sin ~i - v/n 2 - cos___2 2 ~i ,I2 R(oci) -- ~ -~ ~ n 2 7 COS 2 Oci T (oci)

n = 1 - a - ifl

6-

r:f

Fig. 1. Refractionand reflection of a plane wave with amplitude Ei incident upon the interface between a vacuum and a material of index n.

2.2. Refraction from Surfaces

COS(OCt)" n =

normal

Ei

It

2 sin Oci

12

~

sin Oci 7 ~ n 2 7 cos 2 Oci

I

(4)

Let us now discuss some of the important features of these formulas. Figure 2 reproduces the calculated A and T for some typical situations. For Oc < Occ, R - 1 and total external reflection occurs, and, as expected, the penetration depth is a minimum and is in the nanometer range, highlighting the great surface sensitivity that can be achieved. The departure from unity of n depends linearly on a, showing that Occincreases with the density of the material; light elements like MgO and A1203 thus have particularly small critical angles. Moreover, through

SYNCHROTRON STUDY OF OXIDES AND METALS

531

Fig. 3. Grazing incidence X-ray diffraction geometry. See text for the definitions of the notations. Fig. 2. Calculated transmission coefficients (left ordinate) as a function of the reduced grazing incidence angle, ai/Otc, for a nonabsorbing Cu surface (--), a real Cu surface (...), and a real Ta surface ( - - - ) . Penetration depths (right ordinate) versus oti/C~c for real A1 (o) and Ta ( 9 surfaces.

their small absorption coefficients they also have small/3 values, and thus larger A, making grazing incidence conditions even more desirable for such surfaces (to limit A). From another point of view, the reflectivity falls off rapidly as oC 4 when Oq ) ) O~c, enabling tunable depth analysis and in turn the investigation of buried interfaces under up to micrometer-thick capping layers; it also allows growth monitoring up to fairly thick deposits. For a crystalline surface the diffracted intensity will be proportional to the transmission coefficient because it is related to the electrical field strength at the dielectric boundary, i.e., at the surface. Although the wave does not propagate below de, the signal will be enhanced by a factor of 4 for a nonabsorbing material when Oti = Ore. Because of time microreversibility, the diffracted beam experiences exactly the same refraction effects, and a second enhancing factor can be obtained when the exit angle from the surface is equal to Ore. A comprehensive discussion of the refraction effects of the outgoing beam can be found in [ 1]. This advantage exists for all elements, although it is damped by increasing absorption, i.e., for heavier elements (Fig. 2). However, working at grazing incidence has another very useful feature: it allows a drastic reduction of the background. As a matter of fact, except for the fluorescence contribution, most of the background originates from the bulk (thermal diffuse scattering, point defect scattering, etc.) and can be removed or heavily reduced by limiting the incidence and/or the emergence angle to Ore. The only other less efficient way of overcoming the bulk background, at least the thermal diffuse scattering, is to cool down the sample to very low temperatures, thus reducing the thermal agitation of the atoms. For light elements, reducing the penetration depth and the background and the necessity to enhance the weak scattering often imposes the requirement of working at the critical angle for total external reflection. In such conditions great care must be taken to keep the incident angle strictly constant throughout the data collection. Large intensity variations are obtained for very small variations of the incidence angle, because Oti = Ore corresponds to the maximum of the T (oti) function. Working at 2Ore or 3Ore allows for more comfortable measurement conditions, if the background remains acceptable. In any event,

grazing incidence often remains the mandatory condition in investigations of surfaces with hard X-rays. This principle is used for grazing incidence X-ray diffraction (GIXD) as well as for grazing incidence small-angle X-ray scattering (GISAXS), which are the two main methods that we have used to investigate metal/oxide interfaces.

2.3. Grazing Incidence X-Ray Diffraction

2.3.1. Surface Diffraction Considering the remarks of the previous section, the general geometry of a GIXD experiment will be as depicted in Figure 3. An incident beam with wavevector ki falls on a surface under an incidence angle Oti that is kept close to Ore. If the material is a single crystal, the reflected beams will organize, for given incidence conditions with respect to the atomic planes, along well-defined directions with a wavevector kf and an exit angle otf: They are diffracted by the well organized array of atoms. It is convenient to define the momentum transfer Q = kf - ki and to decompose it into components parallel (QII) and perpendicular (Q• to the surface. For hard X-rays and small objects the kinematical approximation of single scattering is valid [6]. The intensity, I (Q), elastically scattered in a direction defined by the momentum transfer Q is proportional to the square modulus of the coherent addition of the amplitudes scattered by all electrons in the diffracting object. The field seen at large distance R from a scattering electron of charge e and mass m at r t is given by the well-known Thomson formulae. Within the Born approximation a single atom at r diffracts an amplitude obtained by integrating over its electronic distribution function p(F) about r. Defining the atomic form factor, f (Q), as the Fourier transform of p (F), a unit cell of a crystal with N atoms diffracts an amplitude

e2 ACell

-- ~

AO

= ~/'-PAo

mc2R e2

mc2R

N Z (f J(Q)

eiQrJ " e-My)

j=l

9 F(Q)

(5)

which defines the structure factor, F(Q), of the unit cell, and where P, A 2, and e-Mj are, respectively, the polarization factor, the incident intensity in photons per unit area per second,

532

BARBIER ET AL.

Fig. 4.

Free standing surface layer of atoms.

and the Debye-Waller factor [6, 11] for species j. M may be written as B sin2 0/~ 2, where B - - 87t'2(U2) is called the temperature factor and (u x2 ) is the mean square component of vibration of the atom along the direction of momentum transfer. The thermal motion can yield to a single B value for all atoms or individual B's for each atom or even components of a tensor describing the anisotropic thermal motion. For example, it has been shown that the thermal motion at the surface can be enhanced compared with its bulk [ 12] counterpart, although this is not necessarily the case. The polarization factor, P, describes the dependence of Ei on the polarization of the incoming wave. Because the direction of the electrical field determines the direction of the electron motion that will radiate the wave, the angle 20 between the incident and the exit beams will modulate the observed intensity. When Ei is normal to the scattering plane (the plane spanned by ki and kf) P is unity, and when Ei is in the scattering plane P = cos 2 20. If we now consider a two-dimensional surface built with N1 and N2 atoms along the a l and a2 directions as shown in Figure 4, we will obtain the scattered intensity by summing the amplitudes over the N1 x N2 unit cells. It is convenient to express Q - q l + q2 + q3 in the reciprocal space basis as Q = hbl + kb2 -k- s with the reciprocal bi vectors related to the direct vectors by bi - - 2rr(aj • ak)/(ai, aj, ak), where a3 can be any vector perpendicular to the (al, a2) plane. As a convention in surface diffraction, e (resp. Z) is always chosen perpendicular to the surface, and h and k (resp. X and Y) span the surface plane (Fig. 3). Defining also the S s ( x ) = sinZ(Nx/2)/sin2(x/2) function, the intensity of the total scattered signal from the surface is e4

I2D(Q) = p A 2 m2c4R 2

IF(Q)I2SN1(Q. al). SN2(Q" a2)

(6)

For large N1 and N2 values, I2D(Q) yields significant intensities only when both Laue conditions are fulfilled simultaneously: Q . al = 2zrh and Q . a2 = 2Jrk, where h and k are integers, defining a two-dimensional reciprocal lattice. Because the intensity is independent of q3, the scattering is diffuse in the direction perpendicular to the surface and the reciprocal space is made of continuous rods as shown in Figure 5. The intensity in the diffraction rods reduces to

I~2D -- PA~

e4

mZc4R2 ]Fhk

I2N2N 2 1 2

(7)

Fig. 5.

Reciprocal space of Figure 4.

The expression of lh2D is valid as long as only exactly one layer diffracts. This is the case when the surface layer has a periodicity different from that of the bulk, i.e., in the case of surface reconstruction or if a 2D film with a mismatched lattice parameter is deposited on a substrate. Both situations will be illustrated by reconstruction analysis of NiO(111) and ot-AleO3 (0001) (see Section 3) and by the structural description of a NiO(111) layer deposited on Au(111) (see Section 6). As soon as there are several layers in the perpendicular direction, the diffraction rods become modulated because the periodicity in the third direction must be taken into account and the intensity will take the usual form, e4

Ih3D = p A 2 m2c4R2 IFhkel2 x SN1 (Q" a l ) . SN2 (Q" a2). SN3 (Q" a3)

(8)

For small N3 values, the rods will modulate along Q• In contrast, for large N3 values, the intensity will concentrate along a discrete array in the third direction too, leading to a third Laue condition: Q - a3 = 2zrs where ~ is an integer. This situation corresponds to the classical 3D diffraction, where Bragg peaks correspond to the possible h, k, and s An intermediate situation is obtained when a physical surface is considered (i.e., the truncation of a bulk material, that is only semi-infinite), and Eq. (8) will no longer apply because it assumes infinite extension of the diffracting object in all three directions. Taking into account the summation from - c ~ to 0 along a3 of N1 x N2 surface unit cells, the scattered intensity for a perfectly sharp surface becomes IhCTR

ke --

pA 2

e4 m2c4R2

IFhkeleaNl(Q.al).Ss2(Q.a2).I CTR

(9)

with =

ICTR

1

2 sin 2 (Q. a3/2)

(10)

The intensity variation along a crystal truncation rod (CTR) now contains Bragg peaks for integer values of h, k and ~, not excluded by the 3D extinction rules that are still valid, and diffuse scattering in between, as shown in Figure 6. Importantly,

SYNCHROTRON STUDY OF OXIDES AND METALS

The result of a b/a3 ratio of 1.05 in the case of a Ag(001) surface is illustrated in Figure 6. The effect increases with increasing perpendicular momentum transfer. In practice, the geometry of the diffractometer and the wavelength will limit the maximum reachable s value. We have described the main features that may occur in the reciprocal space when surfaces are considered. Let us now concentrate on the way in which these intensifies can be efficiently measured and the underlying practical limitations.

iI

__1! """,,,,

....,,,'"']

10

,'" "9""

........

"'., . . . . . . .

0

i

""

i

2.3.2. Practical Considerations

3

g or 2rtQ• Fig. 6. Evolution ofthe calculated intensity along the (lle) r o d o f a A g ( 0 0 1 ) surface (face-centered cubic structure) as a function of the perpendicular momentum transfer Q_l_ (or Qz or e) for a perfectly sharp surface (m), an outside oriented relaxation of +5% of the last Ag layer ( - - - ) and a surface with a 4-A roughness (fin model with/3 = 0.6) and no relaxation (...).

this means that, insofar as the two first Laue conditions are fulfilled, s must be considered as a continuous variable for surface diffraction. Even half-way from the Bragg peaks some intensity remains, because the last term in Eq. (9) is then 1/2 unity; this remaining intensity is comparable to the intensity of a single layer, I 2D (Q). Real surfaces have roughness; i.e., the probability distribution of the atoms is less sharp than a simple step. In that case the intensity will concentrate more near the Bragg peaks and decrease in the zone center. To take this effect into account, a functional form used to fit the data has been derived [13] within the fin model for simple unit cells, and the adequate CTR term becomes ICTR _ 1+

(1 --/3) 2 . 1 2/3 cos(Q, a3) sin2(Q 9a3/2)

(11)

t2 _

with 0 < fl < 1 representing the roughness and where fl = 0 (resp. 1) corresponds to a perfectly flat (resp. infinitely rough) surface. This model gives generally good results, although it can give significant occupancies for planes fairly far away from the average surface. The sensitivity of the CTRs to roughness is well illustrated in Figure 6, where the decrease in intensity in the zone center can easily represent an order of magnitude for roughness well below a nanometer. Alternative models, in which the roughness is treated like an additional Debye-Waller factor, were also proposed [ 14]. A last important feature of the CTRs is their great sensitivity to surface relaxation. Relatively small variations in the last layer spacing are able to produce measurable asymmetries in the shape of the intensity variation along CTRs. If, for example, the last interplanar distance is b instead of a3, the intensity along the CTR will obey irrs CTR

-

e

2i sin0r s

+

ei2rr s

533

2 (12)

In practice, the reciprocal space is a space of directions; with respect to the scattering geometry from Figure 3, at least four settable angles are needed: one for the incidence angle, a rotation of the sample around its normal to bring the atomic planes into diffraction conditions, and two degrees of freedom to position the detector arm to reach all QII and Q_L positions in space. Because an extra angular degree of freedom is available (three angles are enough to define any direction of Q), one condition can be imposed. For standard four-circle diffractometers, the most popular working conditions in surface diffraction are incidence fixed, emergence fixed, or incidence equals emergence. Including one of these conditions, all (h, k, ~) positions in reciprocal space are connected in a unique manner to an angular setting. It is convenient to add two additional cradles below the sample to align the optical surface. Prevention of contamination during the study of surfaces or interfaces requires UHV conditions. From the expression of I2D(Q) it appears that the diffracted intensity is proportional to the incident flux, and, through F (Q), it is proportional to the square of the atomic number Z. A comparison of (8) and (6) shows that bulk scattering is roughly six orders of magnitude larger than surface scattering. Moreover, if A is the area of the unit cell, the intensity falls off as A 2, which strongly reduces the diffracted intensity for large unit cells occurring for reconstructed surfaces; the increased number of atoms only partially compensates for this effect. Thus, although surface diffraction experiments can be carried out with a laboratory rotating anode for very dense materials with high Z, they becomes almost impossible for lighter elements and large reconstructions that will require high flux synchrotron radiation sources like the ESRF [15] (European Synchrotron Radiation Facility, Grenoble, France). When deposited layers of only a few monolayers are considered, the flux condition becomes even more stringent. Importantly, the synchrotron beam is strongly polarized in the horizontal plane. For crystallography, vertical sample geometry is then preferred because the polarization factor will remain unity for all in-plane reflections, whereas in the horizontal sample orientation the scattering at 90 ~ would vanish. Considering all of the previous remarks, several UHV diffractometers, all dedicated to in situ surface diffraction, were recently built on various synchrotrons; they all have about the same overall characteristics [ 16-23]. The GIXD experiments of our group were mainly performed with the setups located at the ESRF [ 15] on beamlines ID03 [21 ], ID32 [22], and BM32-SUV [17]. The last

534

BARBIER ET AL.

Fig. 7. (Left)Photograph of the BM324-circle diffractometer.The UHV chamber, with a base pressure of 2 x 10-11 mbar,is equipped with a smallinput and a large exit Be window that is transparent to high-energyX-rays. (A) An Auger analyzer. (B) A reflection high-energyelectron diffraction (RHEED) facility. (C) A fast transfer system. (D) Several evaporation sources. (Right) Geometricalprinciple of the diffractometerand definition of the angles.

setup is installed on a bending magnet beamline and is represented in Figure 7. Alternatively, the bulk truncation can be understood as the multiplication of an infinite lattice by a step function. In reciprocal space, this leads to the convolution of the reciprocal space of the infinite 3D crystal with the Fourier transform of a step. The result is a smearing of the intensity of each Bragg point in the direction perpendicular to the surface. Note that in the case of a crystalline surface and where optical surfaces are not identical (because of miscuts or vicinal surfaces), the smearing is still perpendicular to the optical surface and not to the lattice, leading to partial CTRs emerging from each Bragg peak without continuity along s The intensity along the CTR is not modified by a miscut, but the correct (h, k) position, for a given s at which the rocking scan must be performed will be affected and must be refined experimentally [24]. A convenient practical criterion is to remember that the derived roughness should not depend on which rod is measured, nor should it depend on whether the rod is above or below the Bragg position [25]. Inadequate measurements when a miscut is present lead to additional asymmetry and thus to overestimated roughness and to erroneous relaxation values. The measurements must thus be carded out with great care; the observation of a diffracted beam is only quantitatively significant if all angles are perfectly defined and if the (h, k, s position has been adequately refined.

2.3.3. Data Collection, Integrated Intensities, and Corrections In contrast to bulk diffraction, the intensity cannot be recorded simply by placing a detector with a wide enough aperture at

the right (h, k, s positions, because surface diffraction is diffuse, at least in the direction perpendicular to the surface. Peak broadening may also occur in various well-defined directions, depending on its physical origin. Some of the possible features are reported in Figure 8. When the diffracting object has a finite size D (for example, an island) it means that the number of planes N1 and/or N2 in Is2D (Q) will be small and the Laue condition will be partially relaxed: the intensity is no longer strictly peaked at integers (h and k). The finite domain size leads to a constant broadening with respect to QII (Fig. 8a) and is related to the angular width Aco by O =

2zr

(13)

Qll'" Aw Relative disorientation between individual grains will lead to a constant angular broadening (in Qll) because each grain has its own reciprocal space with some angular deviation from the average reciprocal space (Fig. 8b). Finally, when a parameter distribution is present, reciprocal spaces with different basis vectors will superimpose about the average lattice, and the diffraction features will accordingly broaden (Fig. 8c and d). Measuring the angular and radial in-plane widths of several orders of diffraction (i.e., as a function of all) allows decorrelation of at least the two first effects. This approach is used and discussed in Section 5.2.2. Because all of these lineshapes may coexist at any point in the reciprocal lattice, the pertinent intensity is the integrated intensity that is obtained by scanning one or several angles through the investigated position. To put it simply, it allows collection of all of the intensity that should ideally be present at a given point in the reciprocal space. In practice this corresponds

SYNCHROTRON STUDY OF OXIDES AND METALS

535

Fig. 8. Schematic drawing of the major sources of peak broadening. (a) Finite domain size. (b) Mosaic spread. (c) In-plane parameter distribution. (d) In-plane and out-of-plane parameter distribution.

to scanning one direction while integrating along the perpendicular direction with sufficiently opened slits, i.e., an adapted resolution function. This strategy applies well for in-plane measurements and works in principle for measuring CTRs through a scan along ~, but other broadening perpendicular to the CTR is often so great that not all intensity reaches the detector. Moreover, scanning along a CTR implies a perfect stability of all angles of the diffractometer. Successive rocking scans with a constant angular speed, f2, around the surface normal (w scans with the SUV setup in Fig. 7) for discrete ~ values are thus the usual and preferred measurement strategy, although the slice of integrated intensity now depends on the aperture of the slits before the detector. The measured intensity thus depends on geometrical settings; fortunately, in grazing incidence Q• is also perpendicular to the surface plane, and the integrated momentum width A Q• is nearly constant for small s and is simply related to the exit slit size L by 27rL AQ• = ~cosfl XR

(14)

Because the integration is performed over an angular unit volume (doedfld6) and not a momentum unit volume (dql dq2 dq3), the measured intensity will depend on the relationship between the reciprocal space coordinate and the angular coordinate. The corresponding factor that divides the intensity is called the Lorentz factor, L. In particular, this means that the intensity will depend on the type of scan that is performed and that each type of scan will produce a different Lorentz factor. Finally, the measured integrated intensity will also sit on a background 13 and will be proportional to the active area of the sample defined by the slits before and after the sample because they define the number of atoms (N1 x N2) that contribute to the signal. Finally, if co is the rocking angle, the integrated intensity that is really measured during a rocking scan is iMes __ "hkg,

B -~

pA2

e4

ff_,,~ m 2 c 4 R 2

P(r)

- Z IFhkel2" e - i Q ' r

:

f

p ( r ) p ( r + r') d3r '

d

hks

= (p (r)p (0))

(16)

For in-plane measurements (i.e., s = 0), because of Friedel's law (IFh,k,OI = [F-h,-k,01), the Patterson function is real and reduces to

IFhke I2

x N1. N2 . fe+AQ1/4Jr lCTR du } d6o

measurement requires a correction of the integrated intensity for the factors that are introduced by the experiment and the geometry. The background subtraction (generally a linear regression) requires large enough scans to reach points where no scattering contributes. Generally, a beam monitor is mounted before the sample to normalize the intensity with respect to the incident photon flux and in turn permits rescaling of scans that were not performed at the same speed. Another correction comes from the integration in (15); because A Q• varies slowly and because the slope of the rod along s may vary much faster, the actual s corresponding to a measurement is shifted when the slope is large. Finally, the Lorentz, area, and polarization factors depend on the diffractometer geometry and on the beamline characteristics that include the degree of linear/elliptical/circular polarization and must be calculated for each setup. The reader may refer to the reference adapted to a given setup for these corrections [26-30]. Once the structure factors have been extracted from the measured signal, they have to be averaged with their symmetryrelated equivalents to find the right symmetry of the signal, and complementarily, to deduce the systematic error, which generally is close to 10% for GIXD experiments. In the absence of a model and because the phase information is missing, the Patterson map analysis is a convenient tool to test at least in-plane projected structures for reconstructions. The Fourier transform of the structure factor moduli does not give the electron density map in the unit cell, p(r), but the density-density correlation function (or autocorrelation function). Its planar section in the direct space is referred to as the Patterson map. It can be written as

(15)

Je.-AQ1/4Jr

The measured intensity in itself is not of direct use. The important quantity is IFhkel, although the phase is definitively lost. Deducing a quantity proportional to the structure factor from a

P(r) -- 2 ~

IFhk[2 cos(2Jr(hx +

ky))

(17)

hk

where x and y are the coordinates within the unit cell. To test the agreement between a model structure and the experimental data, two criteria can be used. The first is the

536

BARBIER ET AL.

chi-squared, X2, approach. For N measured diffraction peaks, p parameters in the model, and an experimental uncertainty O./~ks for an (h, k, s peak, one can write 1

X2 =

N-

~ P ~kl

I" hks l -- l- hke l

(18)

~163

A good agreement is obtained when X2 is close to 1, and no new parameter should then be introduced in the model. The second criterion is the reliability factor R, which is given by R :

K,exp I

K,calc I

~--~hke II- hke, -- l- hke, [

(19)

pexp I

I- hk ,

.-.exp,

when R approaches (1/N) ~-~hke(crhke/lrhk e I) the agreement is good. Both criteria are helpful in discriminating between different possible models.

2.3.4. Application to Structure Determination and Growth Mode Studies When a reconstructed surface is investigated, the accuracy of the final model will depend on the type of data that were measured. To obtain in-plane diffraction peaks for a complete structural determination, reconstruction rods and CTRs are needed. Peaks in the Patterson map allow identification of interatomic vectors and thus elaboration of projected possible 2D models. Once a convenient model is found, the perpendicular atomic positions z can be introduced, and the modulations along reconstruction rods can be reproduced, hence resolving the structure of the atomic planes contributing to the reconstruction and those that do not belong to the bulk. Finally, taking into account CTRs should allow determination of the registry of the reconstructed cell with respect to the underlying bulk. Only models that are able to simultaneously reproduce all three features (Patterson map, rods, and CTR) are acceptable. It is exactly this approach that has been used for the determination of the structure of p(2 x 2)-NiO(111) reconstructed surfaces. The resulting model, however, may not be unique and remains strongly dependent on the number of reflections that are measured. As a general rule, the level of confidence in a model increases with the number of measured reflections. If only inplane data and rods are available, only the internal structure of the reconstructed unit mesh can be obtained. This was the case for p(2 x 2)-NiO( 111 )/Au(111) layers because of the small lattice mismatch between Au and NiO. Finally, if the scattering material is too light, only the in-plane reflections may be accessible, as is the case for the ot-A1203 (0001) reconstructions. For these studies it is of practical use to note that as a general rule, the h, k, and s indexes are always expressed in reciprocal lattice units (r.l.u.). When an epitaxial thin film is deposited on a substrate surface, all of the features in reciprocal space that have previously been discussed may exist for the epilayer, plus interferences between the film and the substrate. The deposited film will exhibit its own reciprocal lattice, which will superimpose on the reciprocal space of the substrate. Because the penetration depth of

X-rays is large, attenuation of the substrate features will only occur for fairly thick oveflayers (several nanometers). If the film is fully incoherent, with a parameter different from the substrate, both reciprocal spaces will be fully resolved and can be studied separately by Fourier filtering. The peak positions during growth give a direct access to the strain relaxation of the layer and the widths of the peaks to the quality of the growing film. Such investigations were performed for the growth of Co and Ni80Fe20 on NiO(111) (see Section 5) and for the native C o 3 0 4 overlayer on COO(111) (see Section 3.5). It may happen that the overlayer adopts different possible variants because the symmetries of the film and the substrate do not match. Each variant will exhibit its own reciprocal space, and the relative intensities between the peaks allow quantification of the structural composition of the film. The Ni(110) epitaxy on MgO(001) (see Section 4.3) corresponds to such a situation. Because GIXD allows investigation of the reciprocal space in 3D, it is also easily able to discriminate and to quantify different out-of-plane stacking with the same in-plane structure, like twins and stacking faults in the face-centered cubic (FCC) structures observed for Co and Ni80Fe20 on NiO(111). Although pseudomorphic growth is quite rare (exact parameter match), it happens often that at least some of the epilayer atoms occupy positions continuing the staking of the substrate. In such a case these atoms are correlated via the substrate, and they will diffract at the same QII positions as the substrate. But because they also belong in some way to the substrate stacking, it is not the intensities that will add at these QII positions, but the amplitudes leading to constructive or destructive interferences. In practice the substrate CTRs will be modulated and become asymmetric, basically for exactly the same reason that relaxations make them asymmetric. The effect is particularly marked when the substrate is the lighter scatterer. The detailed investigation of the modulations along the CTRs during growth allows the extraction of the registry of the epitaxial atoms. This has been done for Ag, Pd, and Ni films on MgO(001) (see Section 4). Finally, not only arrangements of atoms may diffract, but also well-organized superstructures of such defects as, for example, dislocations, that may organize in networks to accommodate the lattice mismatch between two materials. Such a dislocation array will produce in-plane satellites visible between the substrate and epilayer peaks. The dislocation networks between Ag/MgO(001) and Pd/MgO(001) were investigated in detail (see Sections 4.1.3 and 4.2.2). Although GIXD is a very powerful method, it has a very poor chemical resolution, insofar as the atomic species have close atomic numbers, Z. In the case of Ni80Fe20 on NiO(111), the interface can be rendered reactive and diffusion occurs, but all metallic atoms have close Z numbers. For this situation we have used energy-filtered electron transmission microscopy (EF-TEM) and high-resolution TEM as a complementary method to determine the nature of the diffuse interface (see Section 5.3).

SYNCHROTRON STUDY OF OXIDES AND METALS

2.4. Grazing Incidence Small-Angle X-Ray Scattering Determining the morphology of islands during their growth on a substrate is a very important step in the fabrication control of nanometer-sized objects (nano-objects). For this reason, a new method, called grazing incidence small-angle X-ray scattering (GISAXS), has been developed in the last decade [31-33] and very recently applied in situ, in UHV, in real time during growth [34, 35]. We briefly describe below some useful characteristics of this new method. We have seen up to now that the periodicity at the atomic level, i.e., with typical periods of a few 0.1 nm, can be characterized by measurements of the scattered intensity in reciprocal space far from the origin. If objects of much larger dimensions, typically between a few nanometers and several tens of nanometers, are present in the sample, additional scattering will be found close to the origin of the reciprocal space. This scattering contains information on the density, the shape, and the organization of these large objects. Its use in the measurement and analysis for bulk samples is the basis of a very well-known and old method called small-angle X-ray scattering (SAXS) [36], for which measurements are usually performed in transmission. This method has recently been extended to analyze the morphology of nanometer-scale particles deposited on or embedded below the surface of a sample, by combination of the SAXS technique with grazingincidence conditions, thus making it surface sensitive [31]. This new technique of GISAXS is performed under conditions close to total external reflection conditions. It was first developed to investigate ex situ the morphology of aggregates deposited on a substrate. One of the most exciting possibilities of GISAXS is the in situ investigation, in UHV, of the evolution of the morphology of deposits growing in 3D on a substrate, when the use of imaging techniques is difficult. This is the case of many metal/oxide interfaces, because the atomic force microscope (AFM) tip is big and often moves the metal clusters, and because a scanning tunneling microscope (STM) cannot be used on an insulating substrate. Examples of such in situ investigations [34, 35] are given in this chapter.

537

The experimental geometry of GISAXS is schematically represented in Figure 9. The incident beam impinges on the sample under grazing incidence close to Otc, and a 2D detector is placed behind, thus recording the intensity in the (QII, Q• plane of the reciprocal space. This scattering contains information on the islands' shape, height, and lateral size, as well on the organization of the islands with respect to each other. Because this scattering is very small, the direct, transmitted, and reflected beams are completely stopped by a beam stop before the detector, to avoid saturation. To get accurate morphology characteristics of the islands, it is extremely important to carry out a precise, quantitative GISAXS analysis. Because the investigated distances are large compared with interatomic distances, the particles are generally treated as a continuum. For a dense system of Np identical and isotropic particles, the scattered intensity I (Q) can be expressed as I(Q) = A. Np. P ( Q ) . S(Q). T(otf)

(20)

where A is a constant, P (Q) is the form factor of one particle, S(Q) is the interference function, and T (otf) is the transmission factor that reflects the effect of refraction of the scattered wave. The form factor P(Q) is the square of the amplitude F(Q) scattered by a single island of volume V: (21)

F (Q) = f v p (r)e-iQ'r d V

where p is the electronic density within the island. The interference function S(Q) enters the expression only if the particles are correlated. S(Q) is related to the particleparticle pair correlation function g(r) by S(Q)

1 + Ps f (g(r) - 1)e -iQr dr

(22)

where ps is the surface density of the islands. This statistical g(r) function thus tells us how the particles are distributed with respect to each other. In general, the analysis is complicated by the fact that the different islands are not all identical. Assuming a constant shape, such as truncated pyramids, the islands generally exhibit height and lateral size distributions. The height and lateral size of a given island are generally correlated, and hence these distributions are not independent. To a first approximation, however, the mathematical treatment can be simplified by assuming independence. According to microscopy studies, the dimensional parameters of the islands generally follow a log-normal distribution. For the lateral size R (respectively, the height H), the maximum is denoted as/z R (resp. #/-/), and the distribution parameter is err (resp. ORB):

I -- ANp

P(Q, R, H) • S(Q)

e ( - 1/2) x ((log R-log/~R) / log erR)2 •

~/2 • zr x log err e ( - 1 / 2 ) • ((log H - l o g / z u ) / l o g CrH)2 Fig. 9.

Typical geometry for a GISAXS experiment.

x

dRdH x/2 x Jr x log O'H

(23)

538

BARBIER ET AL.

In practice, the form factor P (Q, R, H) can be analytically calculated for most simple shapes usually assumed by islands growing on a surface, such as truncated cylinders, ellipsoids, or pyramids. The resulting intensities have characteristic profiles with a series of well-defined zeros (minima when dealing with experimental data). The position of the minima as well as the profile of the intensity unambiguously allows determination of the shape, as well as estimation of the average height and lateral size. If the particles are correlated, the main resulting feature is an interference peak as a function of QII, whose position Qp directly yields a rough estimation of the average center-to-center interparticle distances D, according to D = 2rc/Qp [37-40]. However, this is a crude approximation that yields a systematic error. Finally, the distributions of dimensional parameters yield large variations in the intensity in the minima, from which the distribution parameters cr can be estimated. Going further (i.e., refining the average dimensional parameters, the inter-island distance D, and widths of the distributions) requires fitting the intensity with simple approximate analytical formula and, finally, simulations by performing the whole Fourier transform and integration over the distributions, which is computer-time consuming. In the end, it is possible to wholly reproduce the 2D pictures. Note that the above treatment implicitly used the kinematical (i.e., Born) approximation. It can be shown that this is valid when the substrate reflectivity is not too high, i.e., for light substrates as compared with the deposit [41 ]. If this is not the case, a more complicated treatment must be performed within the distorted wave born approximation (DWBA) [42]. 3. PREPARATION AND STRUCTURE OF CLEAN SURFACES

3.1. Specific Considerations Only a few oxide surfaces have been quantitatively investigated by GIXD [4]: mainly the sapphire ot-A1203 (0001) surface, the MgO(001) surface, and the rutile TiO2 (110) surface, and more recently the NiO(11 i), COO(111), and ZnO(0001) surfaces. In all cases, specific experimental considerations apply, particularly for the measurements of the CTRs, to determine the atomic relaxation of the surface. The two first systems are very light scatterers ((ZMgO) = (ZA1203) = 10). The possible intensity that can be collected depends on the material and is given by Eqs. (6), (8), or (15), depending on the type of scattering, and cannot be increased. Therefore, to get measurable CTRs, the intensity needs to be concentrated over a very narrow angular range along these CTRs. This requires two conditions: first a very good starting single crystal, with a very small mosaic spread, and, second, a very flat surface on the length scale of the coherence length of the X-ray beam, which is typically 1 #m. These conditions are not trivial, because commercially available sapphire or MgO single-crystal surfaces have rocking curve widths on the order of a few 0.01 ~ and a typical r.m.s, roughness of 1 nm. For ot-A1203 and MgO(001), both the bulk crystalline quality and the surface flatness can be improved

by annealing in air or under partial oxygen pressure at high temperature (~ 1500~ The rocking curve full width at halfmaximum then decreases from ~0.03 ~ down to 0.0025 ~ in the case of sapphire, and from '~0.01 o down to 0.001 ~ in the case of MgO, thus yielding a 10-fold enhancement of the peak intensity along the CTRs, while leading to a negligible r.m.s, roughness of less than 0.05 nm in the case of ot-AleO3 (0001) and less than 0.25 nm in the case of MgO(001). These r.m.s, roughness values were deduced from fits of the measured CTRs in both cases and confirmed by AFM measurements. However, in both cases, the high-temperature anneal has the drawback of enabling surface segregation of bulk impurities. This phenomenon can be minimized in the case of sapphire by limiting the duration of the annealing to a few hours, while Ca segregates on the MgO(001) surface. In the case of TiO2, the experiments seem to be less stringent, because titanium is a heavier scatterer, and very good single crystals with low surface roughness are readily available from the suppliers. As soon as the atomic species become heavier, as in the case of the N i O ( l l l ) surface ((ZNio) = 18), the above constraints could be expected to relax dramatically. The intensity scattered by the surface is larger, and the bulk background decreases because the X-ray absorption is larger. However, NiO(111) and CoO(111) crystals were practically ignored in the past, and commercial wafers have mosaic spreads as large as 1.7 ~ In the NiO(111) case the crystalline quality can be improved through the same method used for MgO(001) and c~-A1203 (0001): high-temperature annealing. Figure 10a shows the progressive improvement of the rocking curve of an in-plane NiO(111) Bragg peak with increased annealing temperature. GIXD has, indeed, the nice ability to allow investigations at any temperature. Direct annealing reduces the mosaicity to 0.1 ~ before the crystal melts. Further improvements need better starting crystals (i.e., crystals annealed before cutting and polishing). However, quantitative CTR measurements can be performed on samples with a 0.5 ~ mosaic spread. Such crystals are still not adequate for investigation of the p(2 x 2) reconstruction, because a unit cell that is four times larger reduces the intensity by an order of magnitude, and the surface layers of the reconstructions are incomplete, reducing the/TSurf\ down to 13 (for \'-'NiO / the Ni-terminated octopolar reconstruction, see Section 3.4). The ultimate quality for NiO(111) that we could achieve was a 0.02 ~ mosaic spread and surface morphologies like that of the AFM image reported in Figure 10b and is sufficient for investigating the reconstruction. The annealing procedure works fine when the oxide has only one stable stoichiometry; in the case of COO(111) it failed and the crystals could not be improved. Another difficulty is the large noise due to the bulk of the sample. Indeed, if we wish to atlain a high accuracy for the atomic coordinates, it is necessary to measure the CTRs over an extended range of Q_L, which requires an X-ray beam of large enough energy. The energy was fixed at 23 keV for the ot-A1203 (0001) surface, and 18 keV for the MgO(001) and NiO(111) surfaces. At this energy, as soon as the incident angle is larger or equal to the critical angle for total external reflection, a large background scattering is present, presumably arising from bulk point defects, that overcomes the surface scat-

SYNCHROTRON STUDY OF OXIDES AND METALS

539

Fig. 10. (a) Scans througha Braggpeak of NiO(111)that lies in the surfaceplane during in situ recrystallization of a NiO(111) sample from room temperature up to 2100 K. (b) AFM image of a NiO(111) single crystal after optimal preparation. The terraces are several #m2 wide, and the mosaic spread is about 0.02~ Reprinted with permission from [91], 9 1997, Elsevier Science. tering. Consequently, the experiment must be performed under very stringent conditions, with the incident angle kept below the critical angle for total external reflection for MgO(001) and ot-A1203 (0001) and close to it for NiO(111). Because in this region the amplitude of the wavefield varies very rapidly with the incident angle, the diffractometer as well as the sample alignment have to be of the topmost quality. This, of course, also requires that the sample surface be very flat and well defined. 3.2. MgO(O01) The MgO(001) surface has been the object of numerous studies because it is widely used as a substrate for the epitaxial growth of metals [43-46] and as a model support for finely dispersed catalytic particles. It is also used as a substrate to grow hightemperature superconductors because of its close lattice match to YBa2Cu307-x and its small chemical reactivity. Because the detailed structure and morphology of the surface may play a significant role in the overlayer properties, well-defined procedures for preparing MgO surfaces of very high quality are important in a number of areas of surface physics and material science. A precise knowledge of the MgO(001) surface atomic structure is also important because this surface is often chosen as a model system for testing calculations on ionic oxides [47]. In particular, the top plane relaxation and the differential relaxation between anions and cations (rumpling) have been extensively studied, both theoretically [48-55] and experimentally [56-65]. These relaxations were always found to be extremely small on this surface. As shown below, when it is performed on a surface of very high quality, GIXD is well adapted for studying such small deviations from the ideally truncated surface. The procedure for preparing surfaces of high quality necessarily involves a first step of annealing at high temperature

(1500-1600~ However, this annealing also results in a strong surface segregation of bulk impurities, mainly calcium. AFM and fluorescence scanning electron microscopy (SEM) showed that the annealed MgO(001) surface was composed of very large terraces, several 100 nm wide and running over distances of microns, separated either by monolayer high steps, or by steps that were several nanometers high. In addition, large, nearly equidistant "droplets" of hemispherical shape with diameters varying from 0.1 # m to 10 # m were found on these terraces. The droplets were found to have a rich chemical composition: Mg, P, Ca, Si, C, O and V, with ratios of 1 0 0 : 6 0 : 3 0 : 1 5 : 10:3 : 1, respectively. In between, the terraces are atomically flat. Outside the droplets, on the flat surface, only Ca, in a quantity of about one monolayer, was detected. Low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), and GIXD were performed in UHV. In addition to the main diffraction spots, which were very sharp, half-order diffuse spots were present, corresponding to a (~/-2 x ~ ) R45 ~ surface reconstruction. The atomic structure of this reconstruction was investigated by quantitative measurements and analysis of the MgO(001) CTRs [43]. On the MgO(001) surface, there are two nonequivalent CTRs: (i) "strong" ones with h and k even, the intensity of which is proportional to the square of the sum of the atomic form factors of O and Mg, and (ii) "weak" ones, with h and k odd, whose intensity is proportional to the square of the difference of the form factors. When h and k have different parities, the CTRs are forbidden by symmetry. In view of GIXD studies of the clean surface and of growing metal/MgO interfaces, a procedure was developed to remove the Ca surface contamination while keeping the MgO surface as perfect as possible. For this purpose, the surface was etched by Ar + bombardment at 1550~ which is a temperature high

540

BARBIER ET AL.

enough to allow the surface to reorder faster than it disorders, and to keep its smoothness. After this treatment, oxygen or magnesium vacancies could be expected on the surface. To restore the surface stoichiometry, a procedure suggested by several groups [62, 63, 66] was followed: the sample was annealed for 15 min at 700~ at a partial oxygen pressure of 10 -4 mbar. The surface cleanliness was checked with the use of AES, and no remaining impurities were found, to the level of 1% of a monolayer. After this preparation, the samples were never exposed to air, to avoid the well-known attack of the surface by water vapor [67]. The GIXD measurements on this clean surface were aimed at the determination of the roughness, the relaxation p, and the rumpling e, defined according to p = (1/2)(el + e2) and e = el - e2, where el and e2 are, respectively, the fractional displacements of the surface anions and cations, expressed as a percentage of the bulk interplanar distance (2.106 A) perpendicular to the surface. The "strong" (20e) CTR was mostly used to determine the r.m.s, roughness and the "weak" (11 e) one to determine the surface relaxation. On the surfaces prepared as described above, both CTRs, measured by rocking the sample, were everywhere above background, with a very small width (~0.01~ always resolution limited, whatever the experimental resolution, which was a confirmation of the high crystalline quality and a first indication of a small surface roughness. The Lorentzian shape (FWHM 0.01 o) at the in-plane anti-Bragg location (1, 1, 0.05) indicates an exponentially decaying height-height correlation function with a terrace length of ~600 nm. Figure 11 shows the (20e) and (lie) CTRs for clean MgO(001). Figure 11 illustrates the sensitivity of the ( 11 s CTR to rumpling and relaxation, which is obtained only if the roughness is small enough, and when the CTR is measured over an extended range. The two CTRs were simultaneously fitted with four parameters: an overall scale factor, the relaxation and rumpling in the top plane, and the r.m.s, roughness. The data could not be fitted by restricting the step heights to multiple values of the MgO lattice parameter, i.e., to an even number of atomic planes, which introduces a clear maximum between Bragg peaks. All step height possibilities had to be introduced, which indicates that most steps are presumably only one atomic plane high (i.e., 2.1 ,~). The Debye-Waller factor was fixed at its bulk value of 0.3 A2 [68] for all ions. The normalized chisquared agreement factor of 1.14-0.1 was very close to the ideal value of 1, which shows that no new parameter, such as atomic relaxations of deeper atoms, could be added. All substrates prepared according to our new procedure yielded the same roughness value of 2.4 4- 0.1 A, which is also the value determined on the Ca-segregated surfaces. One could suggest that further decrease of the roughness would be achieved by stopping the ion sputtering before starting to lower the annealing temperature. This is not obvious, because the time for annealing without bombardment is limited by the inevitable new segregation of impurities from the bulk. Because the relaxation and rumpling are both very small, slightly different values were found on the different substrates.

10

m

y

Bes'"'II

V

.~.,

".,~ _

+3% rumpling,

v

LL :~"

1

no rumpling

J

10 2

101

0

1

2

3

(r.l.u. of MgO) Fig. 11. Modulus of the structure factor of the (11s (a) and (20s (b) CTRs of the clean MgO(001) surface, as a function of the perpendicular momentum transfer e, in reciprocal lattice units of MgO, after 20 min of Ar + ion bombardment at 1500~ (11 with error bars). For the (lle) CTR, the.continuous line is the best result of a simultaneous fit of the (20e) and (1 le) data. Calculated curves without rumpling and with a 2% relaxation (short dashed line) and with 3% rumpling and no relaxation (long dashed line) illustrate the sensitivity of the (lie) CTR to rumpling and relaxation. The measured (20e) CTR is represented for different surface states: after 20 min of Ar + ion bombardment at 1500~ (11 linked with a thick line) and after 30 min (O) and 2 h (A) of Ar + ion bombardment at 900~ Dotted lines correspond to the best fits, which yield, respectively, r.m.s, roughness values of (a) 2.4 A, (b) 4 A, and (c) 6 ~. The (20e) CTR calculated for a perfectly flat surface is also shown (thin continuous line) for comparison. The rough surfaces are obviously not suitable for a quantitative study. Reprinted with permission from [43], 9 1998, Elsevier Science.

The average values of p = ( - 0 . 5 6 4-0.35)% and e = (1.07 -t- 0.5)% are thus given, with the error bar estimated from the uncertainties of each fit, and from the different values obtained. In the original paper [43], these values are compared with previous experimental and theoretical determinations. Thanks to the high substrate quality and the extended measurement range, the error bars are significantly smaller in the present study. Many early shell model calculations and several experiments (reflection high-energy electron diffraction (RHEED) [68], He diffraction [61], ICISS [59], and SEELFS [62]) yielded much too large rumpling values. In most cases, this can be attributed to an inadequate substrate preparation, i.e., exposure to air before introduction in the UHV chamber. Most other theoretical or experimental results are close to the present ones, especially the latest one obtained by

SYNCHROTRON STUDY OF OXIDES AND METALS

541

Fig. 12. (10s CTR or the ct-A1203(0001)-(1 x 1) surface. Experimental (solid circles with error bars) and best-fitmodels for each possible termination: singleA1layer (thick solid line), double A1layer (dashed line), and oxygen-terminated surfaces (dotted line). The logarithm of the structure factor is reported as a function of the out-of-plane momentum transfer in reciprocal lattice units of A1203. Reprinted with permission from [69], 9 1997, Elsevier Science. medium energy ion scattering [65], which yields similar values of the relaxation and rumpling with larger error bars. The precise values reported in the present work might help further refinement of the theoretical calculations. In summary, a new procedure has been developed to prepare MgO(001) surfaces of very high quality. These surfaces are ideally suited to performing GIXD measurements. This offers the opportunity to investigate the atomic structure and morphology of metal/MgO interfaces by this technique, during in situ deposition in UHV by molecular beam epitaxy, from the very early stages of submonolayer deposition up to fairly thick metallic layers. Such measurements are presented in Section 4. 3.3. e~-AIzO3(0001)-(1 x 1) and Its Reconstructions

3.3.1. Termination and Relaxation of the Unreconstructed Surface The (0001) surface of sapphire (or-alumina, corundum) is one of the most widely used substrates for the growth of metal, semiconductor, or high-temperature superconductor thin films [69, 70]. It is also used as a substrate in silicon-on-sapphire (SOS) technology. Moreover, its initial state is known to play a role on the overlayer properties [71 ]. Despite many theoretical calculations of the a-A1203 (0001) surface structure and relaxation [72-77], the nature (A1 or O) of the terminating plane of the unreconstructed surface is still an open topic because of the lack of experimental results. The single Al-terminated surface is favored by electrostatic considerations as well as surface energy calculations [72]. Indeed, for an A1 termination no dipole moment is left across the surface, and only the longer, and thus the weaker, anion-

cation bonds are broken. However, the (1 x 1) structure is also experimentally observed on alumina surfaces heated in an oxygen-rich atmosphere and could thus be suspected to be oxygen terminated. With regard to the Al-terminated surface, large relaxations have been predicted by pair-potential calculations [73]. More recently, ab initio calculations, by the density functional theory combined with pseudopotential techniques [74, 75], predicted very large relaxation of the last atomic plane ( - 8 7 % ) , whereas Hartree-Fock calculations [76] yielded smaller, although still sizable, relaxation (-40%). A fight binding, total-energy method [77] also predicted large out-of-plane relaxations of the A1 planes and in-plane displacements of the oxygen atoms. The aim of the GIXD study was to determine experimentally, for the first time, the nature of the terminating plane and the relaxations of the first few atomic planes below the surface by quantitative measurement and analysis of the CTRs. The experiments were performed on a first sample with the LURE W21 beamline and diffractometer [22] and on a second sample with the ESRF [15] ID03 surface diffraction setup. Both samples were first annealed in air for 3 h at 1500~ resulting in a surface with wide, atomically flat terraces, and a good near-surface crystalline quality. The two data sets yielded exactly the same conclusions. During the second, more precise experiment, eight CTRs were measured over an extended range of perpendicular momentum transfer from 0 up to 7.2/~-1, and corresponding to 873 nonequivalent reflections. The (10s CTR is reported in Figure 12. Bulk sapphire has rhombohedral symmetry, which is usually treated as hexagonal (space group R3c), with 30 atoms (six A1203 units) per primitive unit cell. The lattice parame-

542

BARBIER ET AL.

ters (a -- b -- 4.7570 ,~, c -- 12.9877 ,~) and the internal coordinates (x = 0.3063, z = 0.3522) are taken from [78]. The bulk unit cell consists of an alternated stacking, along the c-axis, of two A13+ Planes (12 in the unit cell) with one atom per plane, and one oxygen plane (six in the unit cell) with three 0 2- ions arranged with a threefold symmetry. From a crystallographic point of view, no two planes among the 18 of the unit cell are equivalent, under any translation. For each possible chemical termination (oxygen, single A1, or double A1) there are thus six crystallographically nonequivalent terminations. Fortunately, only two of these yield nonequivalent diffraction patterns. The (1 • 1) surface has p3 symmetry, with the threefold axis lying on the A1 atoms. Hence, only their coordinate along the c-axis can vary, whereas oxygen can also move parallel to the surface plane as long as the atoms keep their threefold symmetry around the A1 sites. Because of this symmetry, they must also remain coplanar. The surface model included displacements of three A1203 units plus those of the terminating planes (15, 16, or 17 parameters, depending on the termination). Because of the extremely high sensitivity of CTRs to atomic positions, deeper atomic displacements can enhance fit quality, even with very small values, but they are not significant for the structure. A13+ and 0 2- atomic scattering factors were used for all atoms, although theoretical arguments [76] as well as an experimental AES study [79] suggest that surface atoms may have a different charge. This should be of little importance, especially at large momentum transfer. Debye-Waller parameters were taken to be isotropic and were set to the bulk values [78] for all atoms. Least-squares fitting and visual inspection (Fig. 12) clearly allowed the oxygen and double A1 terminations to be ruled out. The surface is thus terminated with a single A1 layer, which yielded X2 - 0.92. The surface structure is schematically shown in Figure 13. The top two planes undergo large displacements from their bulk positions (0.34/k and 0.23 .&, respectively). The top A1 layer moves down toward the bulk, so that the interplanar spacing with the nearest-neighbor oxygen layer is reduced by 51%. The underlying oxygen atoms shift mainly parallel to the surface plane and are repelled from the first layer A1 sites, moving almost radially toward the second layer. This is an almost bond-length conservative motion: the bond length is only 4.5% (+2.5%) shorter than the bulk nearestneighbor value. Displacements below the first two planes are smaller: relaxations are + 16%, - 2 9 % , and +20% for the next three interplanar spacings. These results were compared with theoretical calculations. The single A1 termination was always the predicted one, because it is the only termination that is "autocompensated" (both charge neutral and chemically stable) and with no electric dipole moment across the surface. Regarding the surface relaxations, all theoretical studies agreed with the large negative relaxation of the top A1 layer. Godin and LaFemina [77] suggested a rehybridization of the top A1 atoms from the fourfold coordinated arrangement (which may be thought of as a sp 3 configuration) to a nearly perfect sp 2 configuration. More generally, all authors agree on the stronger bonding between A1 and

Fig. 13. Illustrationof the sapphire (0001) surface: truncated bulk and bestfit model obtained from CTR measurements. The two top planes are strongly shifted with respect to their bulk positions in a nearly bond length conservative displacement. Reprinted with permission from [69], 9 1997, Elsevier Science. oxygen atoms near the surface, which is the general trend of the GIXD results; bond lengths are shortened by 4.5% to 6.1% in the first four planes. The results are also in very good agreement with very recent theoretical [80] and experimental [81 ] results. To the author's knowledge, this was the first experimental determination of the relaxations of an oxide surface by GIXD and the first experimental determination of the relaxation and termination of the ot-A1203(0001) surface. Another determination was made performed very recently by combining time-of-flight scattering and recoiling spectrometry with LEED and classical ion trajectory simulations [81], with essentially the same results. 3.3.2. Projected Atomic Structure o f the ~-A1203(0001)(~ x ~)R 4-9 ~ Reconstruction

When the ot-A1203(0001) surface is heated to high temperatures in UHV, several reconstructions appear: (~/3 • ~/3)R30 ~ around 1100~ (2x/~ • 24r3)R30 ~ around 1150~ (3x/3 • 3~/3)R30 ~ around 1250~ and finally (~/3-1 • ~/31)R + 9 ~ around 1350~ [82]. Although their electronic structure and symmetry were well characterized [83-85], their atomic structure remained essentially unknown. The ( ~ ] - • 4~-1)R + 9 ~ reconstruction is of particular interest because it has been reported to help epitaxy and enhance adhesion in some cases [71] and because it is unusually stable, even after air exposure. A structural model for this reconstruction had been proposed three decades ago [85]. The LEED pattern was interpreted as the superposition of two reciprocal lattices: that of the hexagonal substrate and that of a nearly cubic overlayer with composition A120 or A10, plus the interference pattern because of double diffraction. However, this model remained controversial. In particular, this interpretation did not include a supercell formation with atomic relaxations. The aim of the GIXD study was to analyze the ot-A1203(0001)(Vr3] - • V/3]-)R-t-9 ~ recon-

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 14. Experimentaldiffraction pattern, indexed in the reciprocal space of the reconstructed unit cell (in 1/6 of the e = 0.12 reciprocal plane). The radii of the right-hand halves of the open circles are proportional to the experimental structure factors, and the left-hand open circles are calculated from the best model (X2 = 1.2). Black disks represent bulk allowed and CTR reflections. The bulk unit mesh is superposed as dotted lines. The three main diffraction peaks of the reconstruction, corresponding to the "parent" phase, are hatched. Reprinted with permission from [82], 9 1994, American Physical Society. struction to get unambiguous answers concerning the presence of a supercell, and ultimately to determine its atomic structure. Clearly, in the case of a reconstruction or of a thin layer, multiple scattering of X-rays is completely negligible. Hence, the GIXD pattern can be fully interpreted with the use of the kinematic theory of diffraction, where only the single scattering events are taken into account. The or-A129 (0001) single crystals were first annealed in air at 1500~ for 3 h, and next heated to ~ 1350~ for ~ 2 0 min in UHV to obtain the ( 4 ' ~ x x/~-i-)R+9 ~ reconstruction. Measurements were made with the LURE W21 beamline and diffractometer [22]. A large number, 366 (of which 267 were nonequivalent), of in-plane reflections arising from the reconstruction were measured. All peaks were exactly centered at the expected positions to within 0.001 ~ of azimuthal rotation, which showed that the surface reconstruction is perfectly commensurate with the underlying bulk lattice. Their width and Lorentzian shape indicated an exponential decay in correlations with a decay length of ~ 5 0 nm. Several reconstruction diffraction rods were also measured. The absence of symmetry of the rod intensity with respect to g = 0 showed that the reconstruction has the minimal hexagonal symmetry p3. The experimental diffraction pattern (Fig. 14) has sixfold symmetry. Measurable intensity was found at all reciprocal lattice points of the reconstructed unit cell, even far from bulk Bragg peaks. Because X-ray scattering by surfaces is in essence kinematical, this result contradicts previous interpretations of the LEED pattern [85] in terms of multiple electron scattering due to the coincidence of lattice sites between a rearranged surface layer with a small unit cell and the hexagonal substrate. In that case, X-ray diffraction peaks other than bulk would be found only at the reciprocal lattice points of the surface and bulk

543

Fig. 15. ExperimentalPatterson mapofthea-A1203(0001)-(~-i-x ~/~-])R9~ reconstruction in the whole reconstructed unit cell. Lines are only guides to locate the three-fold axes and the centered two-fold axis of the Patterson p6 symmetry. Bold lines delimit the asymmetric unit cell of the Patterson map. Reprinted with permission from [82], 9 1994, AmericanPhysical Society. unit cells. The X-ray diffraction intensity distribution proved that there indeed is a genuine (~/3-i- x ~/3-]-)R+9 ~ supercell formation with atomic relaxations. The diffraction pattern was shown to be qualitatively very similar to that predicted [86, 87] in the case of rotational epitaxy of an hexagonal overlayer, which is expanded and rotated with respect to an ideal overlayer R in perfect registry. The main peaks (hatched in Fig. 14) correspond to the firstorder approximation (called the "parent" phase) of the adsorbed structure. Their locations yield the expansion, 10.62%, and rotation, 2.361 ~ applied to the R phase to obtain this rigid hexagonal "parent" phase. The other diffraction peaks are satellites corresponding to the static distortions of this parent phase and possibly to additional disorder. Figure 15 shows the experimental pair-correlation (Patterson) function. Most Patterson peaks have a nearly perfect hexagonal arrangement. The positions of these peaks can be directly constructed by a rotation of ,-~1.4 ~ followed by a small expansion of the projected atomic positions of an FCC(111) stacking on top of the oxygen HCP(0001) stacking of the underlying bulk lattice. Many possible models were tested before the final one was proposed. The reconstructed structure, schematically shown in Figure 16, was interpreted as a tiling of domains bearing a close resemblance to that of two metal AI(111) planes, separated by a hexagonal network of domain walls. In the middle of domains, the overlayers are well ordered, with a lattice parameter very close to that of metallic A1 (expansion of 4% with respect to the registered state) and a small rotation ('~ 1.4 ~ with respect to the R state) with the epitaxial relationships (111)A111(0001)A1203 and [i 10]All] (R1.4~ 1120]A1203. In the domain walls, large expansion and rotation and even loss of honeycomb network topology were found. The observed structure was interpreted as due to rotational epitaxy with nonlinear distortions. The study described in the previous paragraph (Section 3.3.1) showed that the unreconstructed or-A129 (0001) surface is terminated by an A1 layer with 1/3 compact packing. Hence, starting from this surface, removing the two last O planes would

544

BARBIER ET AL.

Fig. 16. Several domains of the projected atomic structure of the ct-A120 3 (0001)-(~/~-i- x ~/~i-)R9 ~ reconstruction, where the unit cells as well as domain walls are drawn. The two constituting A1 planes are shown separately, with evidence of one being much better ordered than the other. Numerical relaxation has shown that the ordered layer could be associated with the second layer, and the more disordered one with the layer adjacent to the substrate. Reprinted with permission from [82], 9 1994, American Physical Society.

leave five A1 layers with 1/3 compact packing occupancy at the surface, which is the observed 5/3 filling ratio. It was then suggested that the reconstruction is obtained after evaporation of the two upper oxygen layers of the unreconstructed surface. The physical origin of the ~ 4 % expansion in the domains is clear, because the overlayer is very close to bulk A1 and registry. A minimum-energy numerical simulation of the two A1 planes, interacting with each other and with the substrate via a Lennard-Jones potential, was performed. The observed atomic structure was shown to be consistent with previous studies of the ( ~ - i - x x / ~ ) R + 9 ~ reconstruction [83-85, 88], which yielded an A1 enrichment, intermediate oxidation states of surface aluminum atoms, and a reduced surface band gap. It is also consistent with the observation [85, 89] of a ( ~ - • ~ / ~ ) R + 9 ~ reconstruction during the first stage of A1 deposition (between 0.4 and 2.5 AI(111) monolayer coverage) on an ct-A1203 (0001 ) surface with (1 x 1) structure, followed by AI(111) domain growth for larger coverage. Thus, a fundamental question was opened concerning the process and dynamics of this reconstruction formation by different routes: reduction or A1 deposition. This motivated a structural study of the intermediate reconstructions briefly reported in the next paragraph.

Fig. 17. In-plane radial scan along the (100) direction of the c~-A1203(0001)(2~/3 x 2~/'3)R30 ~ (a) and ( 3 ~ • 3~/3)R30 ~ (b) reconstructions, h is in reciprocal lattice units of the reconstructed unit cells. Note the very intense and narrow reconstruction peaks, indicating very large domain sizes of several microns.

3.3.3. GIXD Studies of the (2 P 4r3 x 2~t])R30 ~ and ( 3 ~ x 3~fJ)R30 ~ Reconstruction The (2~/3 • 2VC3)R30 ~ and (3~/'3 • 3~/-3)R30 ~ reconstructions were recently investigated by GIXD at the ESRF [15], on the ID03 and BM32 beamlines, under experimental conditions very similar to those of the (~/~]- • V/3-i-)R4-9~ study [90]. Both reconstructions can be prepared in a very well-defined state, with large domain sizes, and very similar data were obtained in the two cases. Figure 17, which shows in-plane radial scans along the [h00] direction for (2~/3 • 2~/3)R30 ~ and (3~/3 • 3~/3)R30 ~ reconstructions, illustrates this high structural quality. The experimental Patterson map of the (34r3 • 3~/-3)R30 ~ reconstruction is shown in Figure 18. Out-of-plane rod measurements showed that, as in the ( ~ / ~ • x / ~ ) R 4 - 9 ~ case, the thickness of the reconstruction is limited to one or two atomic planes.

Fig. 18. Experimental Patterson map of the ct-A1203(0001)-(3,v/3 x 3V%R30 ~ reconstruction in the whole reconstructed unit cell. Bold lines delimit the asymmetric unit cell of the Patterson map. Reprinted with permission from [4], 9 1998, Elsevier Science.

Although the analysis has not yet been performed, a qualitative comparison with the diffraction pattern and Patterson map of the (v/3] - • ~ / ~ ) R • ~ reconstruction shows that the structures are likely to have the same origin, except that no rotation is involved in the case of the (3x/~ x 3~/r3)R30 ~ reconstruction. More precisely, the structure of the (3~r x 3~/~)R30 ~ reconstruction is likely to consist of an overlayer with hexago-

SYNCHROTRON STUDY OF OXIDES AND METALS

545

nal symmetry, made of one or several planes close to compact planes, and with a lattice parameter slightly larger (~12%) than that of sapphire, such that, along the [110] directions of sapphire, the two lattices coincide every 9 (110) d-spacing of sapphire, and 8 (110) d-spacing of the overlayer, yielding a (3x/3 x 3~/3)R30 ~ superlattice unit cell of ~25-A periodicity. Such a rigid overlayer would yield only the strongest peaks of the diffraction pattern. All of the other, weaker peaks would correspond to harmonics in Fourier decomposition, arising from small displacements of the atomic positions with respect to the average "parent" rigid lattice. A quantitative analysis with modeling of the compact overlayer is required to get a more detailed picture of the structure. 3.4. Ni0(111) The structures of electrostatically polar (111) surfaces of the rock-salt oxides (NiO, CoO, MnO, and MgO) have been the focus of many studies in very recent years and were long considered a mystery in surface science because they are difficult to investigate both experimentally and theoretically [91-98]. Because the bulk structure has alternating cationic and anionic sheets along the [ 111 ] direction, the simple truncated surfaces have a divergent electrostatic energy, in theory making them highly unstable [99]. Thus, the polar rock-salt surfaces were long believed to be unstable, according to Tasker [100] and to early experimental evidence of (100) faceting on MgO(111) [ 101 ]. However, their technological importance is growing because their electrostatic specificity provides properties that could be particularly interesting, as in catalysis, for example [102]. Furthermore, the (111) plane of NiO is a highly interesting place to perform exchange coupling of ferromagnetic films [ 103] in the newest giant magnetoresisfive sensors [ 104]. Wolf recently predicted that such surfaces may be stabilized by a particular p(2 x 2) "octopolar" reconstruction, which cancels the divergence of the electric field in the crystal [105]. A schematic representation of this nonstoichiometric surface structure, which organizes in a p(2 x 2) surface reconstruction, is shown in Figure 19. Indeed, NiO(111) surfaces were known to naturally exist as facets on small NiO single crystals [ 106] and as thin films with a p(2 x 2) structure on gold and nickel substrates [107, 108]. Early experiments on N i O ( l l l ) also showed complex reconstructions attributed to Si segregation [ 109]. Thus the real structure of polar oxide surfaces and the importance of the electrostatic criterion were really puzzling, and the possibility of preparing NiO(111) surfaces of high crystalline quality and known structure could open new possibilities for theorists and experimentalists in the fields of highly correlated materials [ 110], magnetism [ 111-113], and catalysis [102]. The aim of our GIXD experiments was thus to establish the optimal preparation conditions, if they exist, of NiO(111), to investigate its stability and reconstruction ability, and finally to use it as a substrate for the growth of ferromagnetic and well-controlled thin films. The situation rapidly appeared to be much more complex than for MgO(001) or

Fig. 19. Schematic drawing of the Ni-terminated octopolar reconstruction of NiO(111). Small circles stand for Ni atoms and the large ones for O atoms. The first and second planes are, respectively, 75% and 25% vacant. The thick arrows indicate the basis vectors of the p(2 x 2) surface lattice mesh. The symmetryrelated radial relaxations 61S and 82S are respectively represented around apex atoms labeled 1 and 2 by dashed and dotted arrows and apply to the second oxygen and the third nickel layers. The corresponding atoms are whited out.

ot-A1203 because of a different surface chemistry, likely driven by the electrostatic properties of the surface. To elucidate this puzzeling topic of the polar NiO(111) surface, the first GIXD experiments [91] were carried out on the SUV-BM32 setup [17] at ESRF [15]. The beam energy was set at 18 keV to avoid fluorescence background from the Ni K-edge. The beamline optics were doubly focused. The beam size at the sample was 0.3 mm(H) • 1 mm (V). The incidence angle was set at the critical angle for total external reflection (0.17~ The N i O ( l l l ) sample (purity 99.9%) was provided, aligned to better than 0.1 ~ and polished by Crystal GmBH (Berlin). The surface basis vectors describe the triangular lattice that is appropriate for (111) surfaces, they are related to the bulk ones by as - [ll0]Cube/2, bs = [011]Cube/2, and es -- [ 111 ]Cube. The h and k indexes are chosen to describe the in-plane momentum transfer, Q II, and ~ of the perpendicular one, Q• All three indexes are expressed in reciprocal lattice units (r.l.u.) of NiO(111). To check the stability of the bulk lattice against decomposition and to follow the improvement of crystal quality, in-plane rocking scans of the (110) Bragg peak were performed on another sample during in situ annealing at increasing temperatures until melting (2200 K). Figure 10a shows that the near-surface crystalline quality improves drastically during the temperature treatment: the initial mosaic spread of about 2 ~ falls to 0.1 ~ without a change in the structure because the integrated intensity remains constant. Other crystals were airannealed up to 1800 K, but the surface morphology, checked by AFM, showed many steps, hexagonal shaped holes, and defects. Only below 1300 K did the direct annealing of the crystal show unchanged surface morphologies. The crystal used in the first study was thus first annealed in air at 1273 K for 3 h and introduced in the chamber just after cooling. The mosaic spread of the sample measured on in-plane and out-of-plane Bragg reflections was 0.30-0.4 ~ The detector slits were adapted to integrate the intensity over this angular width.

546

BARBIER ET AL.

Fig. 21. (11s CTR of N i O ( l l l ) for an air-annealed crystal with a mosaic spread of 0.4 ~ compared with a simple bulk truncation with relaxation (...), an O-terminated surface with C contamination (--), and a metallic surface covered by two layers of pure Ni ( - - - ) . Reprinted with permission from [92], 9 1998, American Physical Society.

Fig. 20. In-plane measurements along the (h h 0.06) (a, b, and c) and the (h 0 0.06) (d, e, and f) directions of the NiO(111) surface after air annealing (a and d), UHV annealing (b and e), and in situ postoxidation (c and f) under 2.5 x 10 - 6 mbar 02 for 45 min at 860 K. Note that the strong CTRs of NiO are present in the (h 0 0.06) direction, showing that the topmost surface planes of NiO(111) are very well defined. Ni appears in the form of islands during decomposition because only Bragg peaks and no CTRs are observed. The curves were shifted for the sake of clarity, but the relative intensities are comparable. The ordinate scale is logarithmic. Reprinted with permission from [91], 9 1997, Elsevier Science.

Without outgassing, strong crystal truncation rods (Fig. 20 and [91]) were measured perpendicular to the surface up to the highest accessible Q_L values (s = 6). At the out-of-phase conditions (between Bragg reflections) the rods were still intense and sharp, indicating a surface of very slight roughness. No oscillations were observed by X-ray specular reflectivity measurements, only an inflection at "-,1.5~ which could correspond to a very thin (less than 10 ,~) adsorbed layer on top of the surface. In-plane measurements (Fig. 20a and d) along the high-symmetry directions showed only a weak first-order p(2 x 2) reconstruction peak, leading to the idea that the surface structure could be mainly (1 x 1) at this stage. No contribution from ordered adsorbates, metallic Ni, or (100) facets could be detected. A first attempt to interpret the CTRs with a (1 x 1) surface cell showed that a simple truncation of the bulk or a metallic Ni-covered surface was not the actual structure. At least surface contamination has to be introduced to reproduce the shape of the CTRs, as shown, for example, in Figure 21 [92].

The surface was next annealed at 860 K for 30 min resulting in desorption of the typical air contaminants. This leads to a slight decrease in the CTR intensity, indicating a limited surface roughening. The in-plane measurements (Fig. 20b and e) reveal two new and strong features: extra peaks at each halfinteger value corresponding to the p(2 x 2) reconstruction, and Bragg peaks at the exact positions expected for epitaxial relaxed FCC Ni(111) (h = 1.17 and 2.24 in Fig. 20b). Out-of-plane scans confirm the 3D character of the metallic Ni. The lack of asymmetry or interference along the NiO CTRs indicates that no significant amount of Ni is pseudomorphic. Direct annealing of the surface thus leads to reduction through a loss of O atoms. In regions not covered by Ni, the surface exhibits the p(2 x 2) reconstruction, and no macroscopic faceting was observed. The Ni clusters were then removed by heating the surface at a partial pressure of oxygen of 2.5 x 10 -6 mbar at 860 K for 45 min. Only the p(2 x 2) reconstruction remains (Fig. 20c and f). Again, no macroscopic facetting was observed. A quantitative description of the surface structure requires better crystals with a higher signal-to-noise ratio, but the previously described encouraging first results showed, at least, that the NiO(111) surface is quite stable, although not that easy to manipulate. It was thus worth improving the crystal preparation. Improved crystals showed that in fact the (1 x 1) assumption was erroneous because the p(2 x 2) reconstruction structure that applies after air-annealing has small structure factors, which were below the bulk background, with samples having mosaic spreads of 0.4 ~. Optimal crystals can be produced with the following procedure. High-quality surfaces with good morphology were obtained by annealing the NiO boule at 1850 K for 24 h in air, then cutting, polishing, and re-annealing at 1300 K for 3 h, which yields a flat, shiny surface. A mosaicity of 0.054 ~ and a typical domain size of 1800 A were obtained. Such crystals have high crystalline quality up to the surface and are well suited

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 22. Structural evolution of p(2 x 2) reconstruction of NiO(111) with respect to the temperature, under 1 x 10 -5 mbar 02, from room temperature (top) to 950 K (bottom), and comparison with a model of a combination of octopolar and spinel-like reconstructions. First column: temperature, ratio of octopolar reconstruction in the model and X2 for the in-plane data. Second and third columns: experimental and calculated Patterson maps. Fourth column: experimental (right half-circles) and calculated (left half-circles) structure factors for NiO(111)-p(2 • 2) measured at the four different temperatures.

for detailed GIXD investigations. In the vacuum chamber, such surfaces were immediately p(2 x 2) reconstructed with some residual C and sometimes Ca. GIXD data were recorded after such an ex situ sample preparation because further treatments proved ineffective. Annealing under up to 10 -4 mbar 02 at 700 K removes the C contamination but drastically transforms the internal structure of the reconstruction. An 02 sputtering at 2 keV and an anneal in air at 1000 K removes the Ca contamination but leaves a large surface mosaicity, making a complete analysis also impossible. Nonetheless, because the first orders of the reconstruction retain the same relative intensities, the Ca is not responsible for the reconstruction or for its internal structure. Thus, our ex situ preparation has given the best surface. For single crystals prepared according to our optimized preparation method, the p(2 x 2) reconstruction obtained, after air annealing, can be measured quantitatively. However, the intensity remains weak and the measurements were carried out on the ID03 undulator beamline at ESRF [15] at a photon energy of 18 keV and an incidence angle of 0.17 ~ [94]. Because the single crystals are always reconstructed, it is more convenient to use the p(2 x 2) lattice to index the reciprocal space (i.e., the crystallographic basis vectors for the surface unit cell are related, for the rest of this chapter to the bulk basis by asurf = [110]Cube, bsurf "- [ 0 i 1]Cube, and Csurf = [ 111 ]Cube)For the as-prepared NiO(111) single crystal, the in-plane and out-of-plane structure factors are reported in Figures 22 (top) and 23 (right). The in-plane scattering of the p(2 x 2) patterns

547

Fig. 23. NiO(111)-p(2 x 2) crystal truncation rods measured for a non-UHVannealed sample (right) and a sample annealed at 950 K under oxygen (left). The (20s and (22s rods were measured for both situations. The straight lines represent the best fits for the octopolar model (right) and the spinel-like model (left). Reprinted with permission from [95], 9 2000, American Physical Society.

was measured quantitatively by rocking scans at all accessible positions belonging to the reconstruction. A total of 33 nonzero peaks were measured at ~ = 0.1. The symmetry of the diffraction pattern is P 6 m m , leaving 14 nonequivalent peaks with a systematic uncertainty of 12%. The measured and calculated in-plane scattering can be directly compared, using the octopolar model predicted by Wolf [105] with both Ni- and O-termination. Reproducing the crystal truncation rods (CTRs) restricted the solution to the Ni termination uniquely, plus the following symmetry-related atomic relaxations in each atomic layer p (p = 0 for the apex layer of atoms). Note that three of the four atoms in layer p of the unit cell have symmetry-related vertical displacements (pS, whereas the independent atom has a vertical displacement (p. Likewise, 6pS defines a radial displacement of symmetry-related atoms away from the in-plane position of the apex atom (Fig. 19). The Pps terms define the possible rotational displacements. Detailed fitting reveals that all 6pS and PpS terms are negligible, except 61 = 0.117 4- 0.015 A, which indicates a dilation of the threefold hollow site where the apex atom rests. The least-squares refinement converges for a 0.2 ~ r.m.s, roughness, ~'0 = 0.06 4- 0.02 ,~, (lS = - 0 . 1 7 +0.02/k, (e - 0.13 4-0.01 ~, (es - -0.0294-0.007 ,~, ~3 - 0.23 4-0.12 ,~, (3s = - 0 . 0 9 • ~, (4 - - 0.02+0.01 ,~,

548

BARBIER ET AL.

Fig. 24. Structural transformation steps needed to obtain the spinel configuration starting from the octopolar reconstruction. Large (resp. small) circles stand for O (resp. Ni) atoms. (1) O-terminated octopolar reconstruction. (2) Rotation and centrifuge motion of the Ni atoms. (3 and 4) Translation of an O atom on top of a Ni atom. (5) Global (010)/3 shift of the reconstructed layer with respect to the bulk. The final spinel-like configuration is reported in Figure 26. Reprinted with permission from [95], 9 2000, American Physical Society.

and (4s = - 0 . 0 0 5 -4- 0.003 A. For the 138 measured structure factors a global X 2 of 1.5 is obtained with nine structural parameters, the roughness, and a scale factor. The agreement is good, and further relaxations do not significantly improve the fit. The relaxations extend deeply into the crystal. The smallest bond length in the refined model is 1.9 ,~ (i.e., a 10% contraction) and is located between the last complete layer (p = 2) and the 25% vacant layer of the octopole (p - 1). The same procedure with an O-terminated surface did not converge, and the best X 2 was 30. In conclusion, the theoretically predicted octopolar reconstruction effectively applies to NiO(111) to overcome the divergence of the electrical field. The observed relaxations remain very limited with respect to the ideal structure. Let us now concentrate on the structure obtained during annealing under partial oxygen pressure to avoid the formation of Ni clusters. This was achieved by using a partial oxygen pressure of 1 x 10 -5 mbar during annealing. The in-plane scattering has been measured at several temperatures and is reported in Figure 22. The continuous evolution of the structure factors is obvious, and one may suggest that either the transformation is continuous or two different structures combine to yield the observed scattering. In any case, it is necessary to first describe the final structure, which is expected to be close to the final transformation state or the second surface structure. Fortunately, the high-temperature reconstruction yields much larger intensities than the octopolar reconstruction, and several reconstruction rods could be measured in this case. The out-of-plane CTRs are reported in Figure 23 and still resemble the octopolar reconstruction, showing that the number of planes involved remains close to that of the octopolar reconstruction. Thus we have taken this structure as a starting point to develop a model able to reproduce the observed structure factors (Fig. 24 (1)). Already in early interpretations it was obvious that a centrifuge rotation, 81, which consists of a displacement along the three equivalent (100) directions (arrows in Fig. 24 (2)), was mandatory to describe the structure after annealing under oxygen in UHV [ 114]. Further improvements of the fit could be obtained by using the O-terminated surface only (as depicted in Fig. 24).

Fig. 25. Out-of-plane configuration for NiO(111) single-crystal substrates annealed at high temperature (1000 K) under partial 02 pressure. The straight lines are calculated for the spinel configuration. (a) (2ie) reconstruction rod. (b) (01e) reconstruction rod. (c) Structural configuration for the best fit in the spinel configuration. Large (resp. small) circles stand for O (resp. Ni) atoms. Reprinted with permission from [95], 9 2000, American Physical Society.

The next determining step is not intuitive, because it consists of the positioning of the apex atom on top of one particular Ni atom, as shown by the arrow in Figure 24 (3); the resulting position corresponds to Figure 24 (4). One could argue that this might lead to nonphysical perpendicular distances. In fact, the fits of the reconstruction rods (Fig. 25a and b), which are highly sensitive to the out-of-plane stacking in the reconstructed unit cell, fortunately converge then only for a very realistic stacking (Fig. 25c). The three-symmetry nonequivalent Ni atoms of the second layer adopt a configuration in which the interatomic distances are close to the bulk values, but one of the atoms does not move, another moves upward, and a third moves downward. At the same time, the O atom moves away from the surface at the fight position to obtain the expected N i - O bond length. At that point, the proposed structure is not able to reproduce the CTRs at all. This becomes possible only after a global shift, 82 along the (010) direction, of the reconstruction with respect to the bulk, as indicated in Figure 24. The best fit of the reconstruction rods is obtained with 82 exactly equal to two-thirds of the reconstruction lattice parameter, as shown in Figure 26 (left-

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 26. Final model derived from GIXD data of the structure of hightemperature NiO(111)crystals annealed in UHV under partial oxygenpressure. Large (resp. small) circles stand for O (resp. Ni) atoms.

hand side). The final positioning allows the upward moving Ni atom to sit directly on top of an O atom, whereas the downward moving Ni atom rests at a three-fold site that offers the necessary space. The registry of the reconstruction finally seems very realistic, although the structure is now very different from the initial octopole. The best fit yields a global X2 of 1.85 over 119 structure factors with 61 - 0.84 4- 0.05 i , $ 2 - - 1.95 4- 0.09 A, ffl - - +0-+- 0.02 A, ~'3 - +0.24-4- 0.02 i , ~2 - - - 0 . 2 9 + 0.03 A, and fro - +0.76 -4- 0.05 A. The X2 over the 11 nonequivalent in-plane structure factors is 2. Combining this O-terminated structural model with the Ni-terminated octopolar reconstruction obtained after the room temperature annealing allows easy reproduction of the scattering observed at the intermediate temperature. The best fits for 300 K, 503 K, 723 K, and 950 K were obtained with 100%, 82%, 62%, and 7% of octopolar reconstruction and in-plane X2's of 1.3, 0.7, 0.6, and 1.3, respectively. The quality of the fits is very satisfactory, as can be seen in Figures 22 and 23. Note that for the 950 K situation, the in-plane X2 is strongly reduced by the addition of 7 % octopolar reconstruction, showing that the transformation is still not fulfilled. When this combination is used to fit the 950 K data, the global X2 reduces from 2 to 1.7 over the 119 structure factors. The two proposed structures are thus sufficient to completely reproduce the data at all temperatures. Although the Ni304 spinel bulk phase does not exist, the annealed crystal adopts the configuration we would expect from such a surface over the four last planes. The nonextension of Ni304 toward the bulk is likely to be the origin of the protective effect of the spinel-like surface layer. It is interesting to note that for this configuration the reconstruction unit mesh contains one atom of oxygen in the top layer and three atoms of Ni below; the crystal is thus reduced compared with the octopolar reconstruction, and the divergence of the electrostatic potential is avoided as well. The Patterson maps observed for the Ni304

549

spinel-like surface structure are identical to that of a Co304 surface spinel layer (see below), strongly supporting this structural model. Interestingly, the transformation is fully reversible by air exposure, switching the crystal back to its oxidized (octopolar reconstructed) state. Moreover, once the Ni304 spinel-like surface layer is formed, no decomposition with the appearance of Ni clusters could be observed, showing that the surface chemistry has strongly changed. Dosing the surfaces with up to 106 L at a partial H20 pressure of 10 -6 mbar in the chamber tested the eventual role of hydroxyl groups. No effect could be observed. The same conclusion applies to the adsorption of more oxidizing gazes like NO and NO2 under similar conditions. They were found to be unable to transform the spinel configuration back to the octopolar one. The stability of the reconstruction is attributed to the high quality of the NiO(111) surfaces, which contain only a very small density of defects, which are believed to be mandatory for the initiation of reaction with these gases. Apart from the fact that the NiO(111) surface is always p(2 • 2) reconstructed to cancel the diverging electrical field because of the polarity, it behaves like most oxides: it is almost insensitive to contamination or air exposure, it may decompose through UHV annealing, and it may exhibit a surface layer that prevents decomposition. The structural models, derived from GIXD measurements, for the p(2• reconstructions of NiO(111) are fully coherent with these properties. The p(2 x 2) reconstructions of NiO(111) are based on two states: the Niterminated octopolar reconstruction, which corresponds to the oxidized surface state, and the O-terminated Ni304(lll)-like spinel configuration, which stands for the reduced surface state and is more stable against decomposition. Fortunately, NiO(111) can be obtained and prepared in both pure extreme states (fully reduced and fully oxidized) in common UHV preparation conditions. This may not necessarily be the case for other polar surfaces that could perhaps exhibit combinations of structures or phases (like COO), making their analysis even more difficult, although these difficulties are not directly related to the polarity problem. From our studies on NiO(111) it clearly appears that the reconstruction scheme proposed to stabilize polar surfaces is correct. Because we have established the optimal conditions for the preparation of very high quality NiO(111) substrates and understood the chemistry of these surfaces, we can use them as substrate for metal growth, as will be detailed in Sections 4.2 and 4.3. 3.5. C o O ( l l l ) CoO, like MgO and NiO, has a very simple cubic rock-salt structure, in which pure O and pure Co(111) planes alternate along the cubic (111) direction [ 115]. Exactly as for the NiO(111) case, the (111) surface is polar, and an ideally cut surface should be (theoretically) unstable or p(2 • 2) reconstructed, at least if these assumptions are general rules. COO(111) could be expected a priori to have a behavior very similar to that of NiO. Indeed, the two share the same structure and have nearly the same lattice parameter. In addition, in CoO, as well as in

550

BARBIER ET AL.

Fig. 27. (a) The reciprocal space of COO(111) (black circles) and Co304(111) (gray circles) in CoO reciprocal lattice units (r.l.u.) indexed in a triangular unit cell. Bragg peaks in the (hOe) and (hhg.) planes are shown, for both COO(111) and Co304(111). Straight thick lines (respectively, dashed and thin lines) represent CTRs with (resp. without) in-plane Bragg peaks. (b) Schematic representation of the structure of Co304(111). The horizontal arrow points to the position of the truncation used in simulating data. Reprinted with permission from [ 115], 9 2000, Elsevier Science.

NiO, the atoms in the (111) pure Co (Ni) planes are spin uncompensated [ 116, 117]. The antiferromagnetic ordering is along the (111) direction, exchange-moderated by the pure oxygen planes. The N6el temperature of CoO ( T N - - 292 K) is lower than that for NiO (520 K), but with a higher unidirectional anisotropy. Mixed Ni and Co oxide or multilayers combine almost linearly the advantages of each of the simple antiferromagnetic oxides: high anisotropy and high working temperature [118-123]. Because both oxides are highly resistant to corrosion they are both good candidates for the building of giant magnetoresistive read heads [ 118, 124-128]. The aim of the GIXD study was thus to establish preparation conditions and to make a structural quantitative investigation of the COO(111) single crystal surface in a way similar to that of the NiO(111) study. All of the measurements on COO(111) were performed on the BM32-SUV setup [ 17] at the ESRF [ 15]. The samples were illuminated by a well-focused 18-keV X-ray beam (350 lzm (horizontal) x 500 # m (vertical) FWHM) under an incidence angle c~ on the order of the critical angle for total external reflection of CoO (Otc = 0.16 ~ at 18 keV). When information from a larger depth was required, the incidence angle was increased to higher values, up to 0.6 ~. Several samples were investigated in the UHV chamber. Polished single COO(111) crystals of purity 99.9% were provided by Crystal GmBH (Berlin). The samples were cut and aligned to better than 0.1 ~ before polishing. A triangular unit cell was chosen to describe the three-fold symmetry of the (111) surface plane. The unit vectors are related to the cubic ones by as - [[10]Cube/2, bs -- [0[1]Cube/2, Cs -- [111], with

as - bs - 3.002/k; Cs - 7.3533/~; ot = 90 ~ fl = 90 ~ and y = i20 ~ The h and k indexes describe the in-plane momentum transfer and the e index, the perpendicular one, expressed in reciprocal lattice units (r.l.u.). The (h00) and (0k0) in-plane directions are defined in such a way that a Bragg peak is found at the (1, 0, 1) position in the reciprocal space. Very surprisingly, the air annealing, which allowed efficient recrystallization of NiO(111), completely failed for COO(111). After annealing at 1300 K the crystals lost their surface polish and the stoichiometry was severely changed. Fortunately, directly after polishing, the COO(111) single-crystal surfaces exhibit acceptable (< 1~ and much better surface mosaic spreads than NiO(lll), thus allowing for a direct investigation by GIXD. The presence of contaminants was checked by AES. Carbon was the unique contaminant and an oxygen annealing at 550 K for 10 min under p(O2) = 10 -5 mbar proved to be effective at cleaning the surface. The stacking of the Co and O atoms in the unit cell gives rise to the reciprocal space shown in Figure 27 (black circles). Several directions in the reciprocal space are particularly interesting. Figure 28 presents a scan along the in-plane (h 00) direction; obviously many more peaks than expected appear. Positions corresponding to the expected COO(111) structure (integer h indexes) are marked by arrows. As can be seen, by comparison with Figure 27, scattering at the in-plane (100) and (200) positions corresponds to the intersection of (10e) and (20~) CTRs of COO(111) with the ~ = 0 plane and arises from the truncation of the surface. These features look like the ones observed for NiO(111) and correspond well to the rock-

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 28. In-plane scan along the (h00) direction. The positions of scattered signals from different structures are indicated. The most intense Bragg peak of CoO (at h -- 3) was avoided because of its large intensity. CoO CTRs appear at integer positions of h (arrows). Peaks marked by 9 and o correspond to the spinel structure and the filled circles to the (3, 0, 0) and (6, 0, 0) CoO Bragg peaks. Reprinted with permission from [ 115], 9 2000, Elsevier Science.

salt structure of COO(111). But extra peaks were systematically found (Fig. 28) at positions corresponding to another crystallographic structure that has in-plane parameters a l = bl 5.716/~ and an out-of-plane parameter Cl - 9.9 A, almost twice those of COO(111). The small width in h and k shows that the in-plane lattice parameter is very well defined. The surface mosaic spread of this structure is on the order of the CoO one, ~0.8 ~ However, it is not a surface reconstruction, inasmuch of as the out-of-plane Bragg peaks of this structure are peaked and correspond to an estimated thickness of about 50 ,~. Integrated intensities of all of the extra in-plane Bragg peaks (o in Fig. 28) were quantitatively measured at g = 0.1. The experimental data set had a P6mm symmetry, indicating an overlayer of cubic lattice, with a cubic lattice parameter of 8.083 A, which corresponds to that of the bulk spinel phase of cobalt oxide" Co304(111) (8.085/k). A set of 34 nonequivalent reflections was deduced from a total of 150 measured peaks (systematic error 17%). The experimental diffraction pattern could indeed be well simulated on the basis of the spinel Co304(111) unit cell with the epitaxial relationship Co304 (111)II COO(111) and Co304 (100)IlCoO(100), provided that the metallic surface termination shown in Figure 27b is used in the model. Other terminating planes of the spinel structure were not able to reproduce the experimental data. A comparison between the experimental and calculated Patterson maps is drawn in Figure 29 (X 2 = 1.17 and R -- 0.176). The agreement is very good. Interestingly, the extra peaks used here would correspond in the p(2 x 2) NiO(111) case to the in-plane reconstruction peaks, and in fact the Patterson maps of the reduced NiO(111) surface and the one shown in Figure 29 for COO(111) are very close.

551

Fig. 29. Comparison of the structure factors deduced from the extra peaks in the CoO(l 1l) scattering with a model based on metallic terminated Co 304 (111) in a spinel structure. Only interatomic distances and angles characteristic of the Co304 structure appear here because no scattering from the COO(11 l) lattice can exist at these locations. (Left top) Self-correlation electron density map (Patterson map) for the in-plane reflections. (Left bottom) Calculated self-correlation map for a Co-terminated Co 304 (11 l) surface. (Right) Experimental (right half-circles) and calculated (left half-circles) structure factors. For the unit cells in the maps (thick lines) the edge of the cell is 5.716/k and the real angle is 120 ~ .

We thus conclude that the COO(111) polished surface is stabilized by the presence of a thick spinel Co304(111) surface layer. The CTR scattering at the (100) and (200) positions is much weaker than for the NiO(111) surface, which seems to indicate that the interface between the Co304 (111) layer and the COO(111) crystal is rough or diffuse (i.e., an oxygen gradient). For use as a pinning antiferromagnetic layer and for an understanding of the exchange coupling phenomenon, COO(111) surfaces with a 1:1 Co:O atom ratio are mandatory. The presence of a Co304 (111) layer is expected to modify the exchange coupling. Indeed, bulk Co304(111) is known to be ferrimagnetic. However, studies of magnetic exchange phenomena at ferrimagnetic/antiferromagnetic or ferromagnetic/ferrimagnetic interfaces [ 129-131] were performed. Moreover, the magnetic properties of the spinel thin layer may be different from the bulk ones, rendering the situation even more complex. An antiferromagnetic substrate should thus not exhibit different stoichiometries near the surface. Because air annealing turned out to be unable to restore good surfaces, we have checked the possibility of removing the Co304 layer and improving the crystallographic quality of the CoO surface by the usual procedures in surface science: annealing in UHV or under O2 and Ar + etching. Annealing in UHV leads to the formation of small metallic Co clusters on the surface, which is similar to the NiO case [91 ]. The X-ray scattered signal arising from (and so characteristic of) the Co304 layer was found to be approximately constant during the whole annealing process, at 500 or 800 K (Fig. 30). While metallic Co is formed, the quantity of the spinel remains roughly constant. Distinguishing between the formation of metallic Co in the spinel or in the CoO is not possible from these data. A post-annealing at 800 K and 10 -5 mbar 02 totally oxidized the Co clusters in a few minutes, but the Co304 layer

552

BARBIER ET AL.

Co~04

Co

C%04

CocO4

Co

C%04

/

109 r~ ,m r~

:::1

'

1if'&

= =1 ,I,,,1

=

10h o

1.0

111

112 //'" h [r.l.u. CoOl

'

1.'6

1.0

,

1'.1

:

1.'2 h [r.l.u. CoO]

//

,

1.'6

Fig. 30. In-plane scans along (hhO) during UHV and oxygen annealing (open squares: as-polished sample; black line: UHV annealed at 500 K; filled squares: UHV annealed at 800 K; open circles: oxygen annealed at 800 K, 10 min; filled circles: 800 K, 02, 60 min; gray line: 800 K, 02, 10 h; open diamonds: 800 K, 02, 12 h). Quick annealing in oxygen (less than 10 min) oxidizes the metallic Co formed during the UHV annealing but increases the amount of Co3 04. The arrows indicate the evolution of the intensity between successive measurements. Reprinted with permission from [115], 9 2000, Elsevier Science.

Fig. 31. In-plane (hhO) scans during Ar + etching (bottom curves) showing the onset of metallic Co during sputtering and the decrease in the spinel thickness (open squares: reference, as polished sample; line: after 10 min of Ar + bombardment; filled triangle: 30 min of Ar + bombardment; filled circles: after 90 min of Ar + bombardment; open diamonds: 110 min of Ar + bombardment). Annealing under 02 restores the Co304 layer (top curve, filled diamonds: 10 min of 02 annealing). The arrows indicate the evolution of the intensity between successive measurements. Reprinted with permission from [ 115], 9 2000, Elsevier Science.

is still present. Moreover, its scattered intensity increases with increasing oxidation time, as can be seen in Figure 30 from the C o 3 0 4 peak, showing a development of the spinel. UHV annealing thus proved ineffective in removing the spinel layer. Another polished sample (covered by a ~50-A-thick C o 3 0 4 layer) was Ar + bombarded, first at room temperature and then at 800 K (U = 800 V, p(Ar +) = 2.6 x 10 -5 mbar, drain current ~10/zA). At high temperatures, Co in-plane Bragg peaks are observed, showing again the formation of metallic Co, presumably in the form of flat and extended islands, inasmuch as scattering is found in the surface plane, at intersections with positions of the Co CTRs, far from Co Bragg peaks. Meanwhile, the scattering from the C o 3 0 4 layer decreases (Fig. 31), proving definitively that the C o 3 0 4 layer sits on top of the COO(111) crystal. In other words, we deal with a top spinel layer, and not with a buffed interface. The crystallographic quality of the metallic Co is poor, with a measured mosaic spread of 2.6 ~ Scans along Co rods, perpendicular to the surface, make it possible to distinguish the different stacking in the Co islands, as these scans pass through Bragg peaks of FCC, twinned-FCC, and HCP Co. Co is mainly of FCC stacking (continuing that of COO(111)) with small quantities of twinned FCC (rotated by 60 ~ with respect to the FCC) and HCP. This result is similar to what was obtained for the growth of Co on the polar NiO (111) surface [ 132], indicating the strong influence of polar oxide surfaces on metallic films. The Ar + bombardment thus reduces the thickness of the C o 3 0 4 layer, but with formation of metallic Co islands. Regardless of the sputtering time, it was not possible to completely

remove the spinel surface layer. With annealing in a partial pressure of oxygen, the Co clusters rapidly oxidized and transformed again in the spinel oxide. All of these observations show that Co304(111) is likely to have a much lower surface energy than COO(111) or any possible stabilizing reconstruction. This behavior probably explains why Co crystals become almost impossible to clean once they have been oxidized [133]. In summary, whatever the preparation, the polished (111) surface of COO(111) single crystals is covered by an (111) oriented epitaxial Co304 layer (epitaxial relationship C o 3 0 4 ( 1 1 1 ) IlCoO(lll) and Co304(100)11CoO(100)), which can be prepared free of any contaminant. This may be the major reason why Nil-xCoxO compounds exhibit spinel structures when x > 0.6 [134]. Air annealing of the sample to improve the crystallographic quality of the surface does not reestablish the Co :O 1 : 1 surface stoichiometry but destroys the sample. UHV annealing or Ar + bombardment reduces the thickness of the C o 3 0 4 layer, but induces the formation of flat metallic Co(111) islands, which are reoxidized upon annealing in oxygen. With oxygen annealing, the signal coming from metallic Co clusters vanishes. Longer oxygen annealing yields the transformation of CoO into C o 3 0 4 . This shows a better stability of the spinel structure. Unlike NiO(111), which is stabilized by a p(2 x 2) reconstruction, the COO(111) surface is stabilized by a Co304 spinel structure, in which the problem of the diverging potential is also avoided. This raises questions about some of the results concerning ferromagnetic metals/CoO exchange-coupled interfaces, because the bulk Co304 is ferrimagnetic. If the Co304

SYNCHROTRON STUDY OF OXIDES AND METALS layer were always present, it would modify magnetic coupling (however, exchange-coupled interfaces were found with the use of ferrimagnetic/antiferromagnetic interfaces). A similar situation appears for the NiFe/NiO(111) single-crystal interface (Section 5.3). In defined conditions, a controlled spinellike interface can be produced, and the magnetic measurement data support a modification of the permalloy-based spin-valve sensor characteristics when the spinel interface is formed. Thorough knowledge of the surface stoichiometry and structure is thus a very important issue in the framework of magnetic coupling. Although magnetic coupling with the spinel cannot be excluded, the knowledge of the structure of the crystal on which the deposit is made is of great importance to an understanding of the magnetic properties. It is possible that preparation techniques like RF sputtering can yield an entirely stoichiometric CoO film. However, the poor crystallographic quality of such films makes a quantitative characterization very difficult or even impossible. The establishment of the correlation between the structure and the magnetic properties in exchanged-coupled systems of this type thus remains experimentally difficult.

4. MODEL METAL/OXIDE SYSTEMS Studying thin films by performing in situ GIXD measurements during metal deposition, from the very early stages up to fairly thick films, allows one to address many fundamental questions in surface science, some of which are listed here. First, is there epitaxy, and if yes, what are the orientational relationships? What is the structural quality of the growing film? What is the registry of the metal with respect to the substrate, i.e., the adsorption site and the interfacial distance between the last oxide plane and the first metal plane? For instance, in the case of a metal/MgO(001) interface, is the metal on top of the O ions or the Mg ions of the last MgO(001) plane or in between, above the octahedral site? How does this interfacial distance evolve with the thickness of the metal film? What are the growth mode and the morphology of the growing film? How is the accommodation of the lattice parameter misfit performed? When does the transition from elastic to plastic relaxation happen? Which defects are involved in the process of plastic relaxation; stacking faults or interfacial dislocations? What is the interplay between these structural relaxation processes and the morphology? Finally, can we improve the structure and morphology of thick films by UHV annealing? Can annealing studies provide kinetic information? When the film thickness is larger than a few hundred angstroms, the top of the metal film is generally close to being fully relaxed to its bulk lattice parameter. From the point of view of elasticity, the relaxation of an epitaxial film on a substrate is governed by the lattice parameter misfit f . In the case of parallel epitaxy, like that of Ag/MgO(001), f is defined by f = (af - as)/as, where af and as are, respectively, the film and substrate bulk lattice parameters. For small values

553

of f (< 10%), the lattice parameter relaxation is generally realized by localized, ordered misfit dislocations [135-137], in which case the interface is said to be "semi-coherent." When f is larger, the density of misfit dislocations becomes so large that they cannot remain localized and organized, and the proportion of the interface in "poor epitaxy" increases. In that case, the interface is said to be "incoherent." There are numerous exceptions, however. For instance, the Pd/r/-A1203(111) interface is incoherent with f = 2.7% [138] as are the Au/MgO(001) interface ( f - 3%) [139-141], the Cu/A1203 interface ( f = 10%) [142], and the Ag/CdO interface [143], whereas the Au/ZrO2 (111) interface is semicoherent, with a very large misfit of 22% [138]. The technique of choice for investigating interfacial dislocations is high-resolution transmission electron microscopy (HR-TEM) [138]. However, HR-TEM does not always provide all of the required information concerning dislocations and may in some cases lead to erroneous conclusions. In these cases, it may be useful to resort to GIXD, as will be shown in the few examples below. Three examples will be given of in situ studies during growth for the three FCC metals Ag, Pd, and Ni, with cubeon-cube epitaxy on MgO(001) (with increasing misfits of 3%, 7.6%, and 16.4%, respectively). The Ag/MgO(001)system has been chosen by most theoreticians as a model because it is one of the simplest metal/oxide interfaces: the MgO(001) surface is nonpolar, epitaxial relationships are particularly simple (square/square) with a small lattice misfit (3%), and chemical and charge transfer contributions to bonding are negligible. Many studies have been devoted to the Pd/MgO(001) interface because it is a model catalyst. The Ni/MgO(001) interfaces are also of particular interest because they are simple transition metal/oxide interfaces in which the metal is ferromagnetic. The analysis of interfacial dislocation networks by GIXD will be described in the cases of the Ag/MgO(001) and Pd/MgO(001) interfaces. 4.1. A g ~ g O ( 0 0 1 )

4.1.1. In Situ Studies of the First Stages of Formation of the Ag/MgO(O01) Interface In this model metal/oxide system, all theoretical calculations minimize the interfacial energy with respect to two structural parameters: the silver adsorption site (on top of O atoms, on top of Mg atoms, or in between, above the octahedral sites of the substrate), and the interfacial distance between the MgO(001) surface and the first Ag(001) plane [44, 144146]. However, although crucially needed by theoreticians to evaluate and refine their models [46], no accurate experimental determination of these parameters was available at the time the GIXD study was performed. The aim of the GIXD study was to determine these parameters and their evolution with the Ag thickness and to analyze the growth mode. The scattered X-ray intensity measured during radial inplane scans along (h, h, s = 0.1) and (h, 0, s = 0.1) is shown in Figure 32 around h = 2, for deposited thickness 0 ranging from 0 to 72 Ag monolayers (ML). These scans show

554

BARBIER ET AL.

11 ) ,8

2

~

(20s

6

2.2 h

h

O

.

"

1

=d

~'~.12.

I

|m

'4

s II

Z

9

MgO

--Ag ~. (hO0.1)

cr) 0 ..J

m~

j/

i1

II

_1

_

I I I

_

.1.5,

I

1.0

'

15

1.

'

!

2.0

'

[MgO r.l.u.] 1.9

2.0

2.1

2.2

h [MgO r.l.u.] Fig. 32. Radialscans at e = 0.1 along the (h 0 0.1) (a) and (h h 0.1) (b) directions, as a function of the amount of deposited Ag (0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 22, 25, 28, 32, 36, 42, and 72 monolayers (ML)), which is indicated above the corresponding curves. The curves corresponding to the different deposits have been shifted vertically for clarity. Vertical lines indicate the h = 2, h = 2.03, and h = 2.06 positions. The top figure (c) is a scan at e = 0.16 along the (h h 0.16) direction, performed at 300 ML. Reprinted with permission from [145], 9 1997, Elsevier Science.

the presence of relaxed Ag(001) in cube/cube epitaxy with the MgO(001) substrate from the very beginning of Ag deposition, as revealed by the broad peak in both directions, approximately centered at the expected position (h = 2.062) for bulk Bragg peaks of Ag in cube on cube epitaxy. The integrated intensity of this relaxed Ag component increases linearly with 0, showing that, at all deposits, most of the Ag is incorporated into this relaxed part. However, at the early stages of Ag deposition, another significant effect is present: between 0 and 2 ML, a significant decay of the MgO (2, 2, ~ = 0.1) intensity occurs. This decrease originates from a destructive interference between the waves scattered by the Ag layer and the substrate on the (2, 2, 0.1) MgO CTR. This implies that at least part of the deposited Ag is initially perfectly on site, i.e., exactly lo-

Fig. 33. Comparison between the measured (crosses) and calculated (solid lines) CTRs for various Ag thicknesses. The dashed lines correspond to the

clean MgO. The (1 l e) and (20e) CTRs have been represented on the same e-scale, although they are at different h, k values. The curves corresponding to the different amounts of deposited Ag are shifted vertically for clarity. Reprinted with permission from [4], 9 1998, Elsevier Science.

cated above atoms of the substrate. Rocking scans of the MgO (2, 2, 0.1) peak are resolution limited (0.003 ~ whether or not Ag is present and correspond to a correlation length of the registered Ag of at least 2000 nm. This indicates that the epitaxial site is perfectly well defined: the Ag atoms responsible for this destructive interference effect are correlated via the substrate. This registered part can be selected in reciprocal space, because it yields rods that are located at exactly the same integer (h, k) values as the MgO CTRs. The interference between the waves scattered by the MgO substrate and by the registered Ag film yields modulations of the intensity along the bulk CTR directions, which can be analyzed to determine the structural parameters of interest: site of epitaxy and interfacial distance. For this purpose, the (11 ~) and (20~) rods were measured as a function of 0 (Fig. 33). The sign of the interference (destructive on the high ~ side of both the (111) and (202) Bragg peaks of MgO, at least for very small amounts deposited, because for large amounts, the MgO(11 ~) CTR is rapidly overcome by the

SYNCHROTRON STUDY OF OXIDES AND METALS Ag CTR) at the first stages of deposition unambiguously allows the assignment of the epitaxial site: the Ag atoms sit on top of oxygen atoms of the substrate. The location of the Ag intensity in a small ~ range on the high ~ side of the MgO Bragg peaks indicates that the surface of the registered part is rougher than the substrate's surface. Quantitative analysis of the Ag/MgO CTRs was carried out with four parameters: (i) the total occupancy of registered Ag (i.e., the amount of Ag ML that is perfectly on site); (ii) the interfacial distance; (iii) the average out-of-plane distance between registered Ag; and (iv) the additional roughness of the registered Ag film with respect to the substrate. These parameters are reported in Figure 34 as a function of deposited thickness. The main results are that only a small fraction of the deposited Ag, amounting to 10% until 0 ~ 5 ML is perfectly on site, and that the thickness of this registered part is always larger than the equivalent thickness deposited, which shows that the growth is three-dimensional from the very beginning. Despite the fact that most of the Ag deposited is relaxed, the selection of the registered fraction on CTRs allowed a determination of the parameters of interest. The interplanar distance in Ag is very close to that in bulk silver, which is consistent with registered Ag surrounded by relaxed Ag. The interfacial distance is found to increase at the beginning of deposition and stabilize around an average value of 2.5 ,~. In the first stages of growth, the smaller interfacial distance may originate from the different local environment of Ag atoms at the interface. Indeed, all theoretical studies indicate that there is little charge transfer between Ag and O, when a bulk Ag crystal above the MgO(001) surface is considered, but this may not be the case for isolated atoms or very thin films on the surface. These results were next compared with the theoretical models of the Ag/MgO(001) interface. As far as the site of epitaxy is concemed, the image interaction model predicts that the Ag atoms are above the octahedral sites of the MgO(001) surface, but this translational state was shown to result from the hard-core repulsion used [ 147]. The most recent ab initio calculations [ 148, 149] show that the energetically favored configuration is for Ag on top of oxygen atoms of the substrate. The GIXD results experimentally demonstrate this latter conclusion for the first time. They were later confirmed by an EXAFS investigation [150]. Regarding the interfacial distance, the experimental steady-state value is very close to the most recent ab initio calculations: 2.49/k [ 149, 151 ]. This, along with the adsorption site, shows that recent ab initio calculations give a good description of the Ag/MgO(001) interface. This quantitative analysis thus demonstrated for the first time the possibility of characterizing by GIXD a small fraction of the Ag film (those Ag atoms that are perfectly on top of substrate sites) and of precisely determining the epitaxial site and interfacial distance and their evolution from the very early stages of deposition to thick deposits. The next question was, what can we learn from GIXD about the morphology and the structure of the major part of the Ag film? As far as the morphology is concemed, because the adhesion energy of Ag on Ag is larger than that of Ag on MgO (1.36 eV and 0.45 eV, respectively [152]), Ag is expected to grow in

555

J .7 .

2.4

.

.

.

.

(d) ,Bulk

2.05

',..e; 2

(C)

AStrain

1.95

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

. ~. ~.

9-6-"-*-6+~ +~+~+~

g 20 10

(b) O

.

0.5

.

,

.

-

i

-

,

.

,

:

--I

=E

:

..I 0

: 0

(a) 2

i

g

OAg (ML) Fig. 34. Evolution with the amount 0 of deposited Ag (in equivalent ML) of (a) the total amount of "on-site" Ag expressed in number of ML (solid circles with error bars), compared with the total amount deposited (dashed line); and (b) the "on-site" Ag thickness (solid squares). This is compared with the average island height deduced from two independent GISAXS measurements with the 1D detector (crosses and open triangles). The total equivalent thickness of Ag deposited is also represented (solid line). (c) The interplane distance dAgAg in Ag, perpendicular to the surface, compared with the distances ABulk '~AgAg expected for bulk Ag, and '~AgAg AStrain calculated according to isotropic elasticity for Ag strained in-plane to the MgO lattice parameter (dashed lines). (d) Interfacial distance dAg_MgO deduced from the fits of the CTRs (open circles) and average interfacial distance (dashed line).

the form of islands. The growth morphology was actually probed by performing GISAXS measurements as a function of 0 (Fig. 35). A measurable peak appears at 0 = 0.5 ML and then increases in intensity with 0, while becoming narrower and moving toward the origin of reciprocal space. This small angle pattern is typical of small correlated islands that nucleate, grow and coalesce as the film gets thicker. The deposited Ag therefore rapidly evolves toward the classical island growth regime (Volmer-Weber). The average distance between islands can easily be deduced from the location of the intensity maximum, and the average island diameter can also be deduced

556

BARBIER ET AL.

=10 s

22

e~

-101

0.1

5 (deg.)

1

Fig. 35. Intensity scattered at small angles, as a function of the in-plane scattering angle 3, for different amounts of deposited Ag. The amount of Ag in ML is indicated above the corresponding curve. The intensity measured on the clean MgO was subtracted.

by several means, assuming given shapes of the islands, for instance, hemispherical in the present case. If GISAXS can provide useful information on the morphology, GIXD (performed at wide angles) can provide very detailed information on the structure of the relaxed part of the Ag film. For that purpose, rocking scans were systematically performed on the relaxed Ag Bragg peaks as a function of 0. They were all found to be of Lorentzian lineshape, perfectly centered on the (110) direction, which shows that there is no rotation between the relaxed structure and the substrate. The lineshape corresponds to exponentially decaying correlation functions with small (~100/~) correlation lengths increasing with 0. The corresponding "domain size" and its evolution with 0 were found to be in good agreement with the island size deduced from GISAXS because of the excellent substrate and epilayer qualifies (see Section 5.2 for an example in which domain size and GISAXS island sizes do not match). Further information on the relaxation process of the lattice parameter was gained by looking in more detail at the intensity distribution along the radial scans of Figure 33. Apart from a broadening induced by the finite island size, the lineshape mainly reveals the distribution of lattice parameters in the silver film. Between 0 and 4 ML, the scattering is composed of only one component, the center of which progressively shifts from h = 2.06, corresponding to Ag fully relaxed to its bulk lattice parameter, toward an intermediate value, ~2.03 for 0 ~ 4 ML. Above ~ 4 ML, in both directions, the scattering progressively splits into two components centered respectively around h = 2.03 and h = 2.06, and whose exact positions evolve with 0. Whereas these two components remain up to large thickness along the (h h 0.1) direction, the intermediate component, around h = 2.03, progressively disappears along the (h 0 0.1) direction, for thicknesses larger than 20 ML. We will see in Section 4.13 that, for thick enough films, the satellite around (2.03 2.03 s arises from the formation of a well-ordered

network of interfacial dislocations releasing the lattice parameter misfit between Ag and MgO. This ordered network does not yield any satellite around (2.03 0 s because this is the location of an extinction for this structure. Thus, at intermediate thickness, between 0 ~ 4 and 20 ML, the scattering around h - 2.03 in both directions does not arise from a new interfacial supercell, but rather is due to an inhomogeneous distribution of lattice parameters within the Ag islands. The observed evolution was analyzed as follows. At the very beginning (below 1 ML), the relaxed Ag fraction is made of very small islands of fully relaxed Ag, with the lattice parameter of bulk Ag. At this stage, the width in radial scans is completely dominated by the finite size effect. As shown by GISAXS and by the decreasing widths of Ag scattering, both radially and transversely, the islands next become larger. At the same time, the Ag becomes more strained by the MgO substrate, with an average in-plane lattice parameter intermediate between that of MgO and Ag for 0 ~ 4 ML. This is likely connected to an increased interfacial area over Ag volume ratio, i.e., to a decrease in the aspect ratio (height/width) of the islands. Up to 4 or 5 ML, radial scans are composed of only one contribution, because the strain in Ag is homogeneous. In other words, there is continuity between net planes in the MgO substrate and in the Ag islands: the Ag islands are said to be coherent with the substrate. The elastic strain energy stored in the islands increases as the islands grow in size, up to a point, around 4-5 ML, where it becomes energetically more favorable for the islands to release part of the strain by introducing a defect, such as a stacking fault or an interfacial dislocation. At this stage, the coherency with the substrate is lost, and the misfit relaxation is said to be plastic, as opposed to elastic when the islands were still coherent. Therefore, the strain within the islands becomes inhomogeneous, leading to the two components observed along both radial directions. The component around h ~ 2.06 is due to fully relaxed Ag, in which the strain is indeed homogeneous, whereas the component around h ~ 2.03 arises from the regions surrounding the cores of the interfacial dislocations, where the strain is strongly inhomogeneous. A detailed study was performed to determine whether these structural defects were appearing in the center of islands or near their edges. The observed intensity distribution in the two directions could only be explained by locating the net plane discontinuity at the edges of the islands. This is the first experimental evidence that misfit dislocations nucleate at the edges of islands during the growth of this kind of metal/oxide system. The intensity of the shoulder around h ~ 2.03 decreases above 20-30 ML, until complete disappearance above 50 ML. This can be related to the beginning of the coalescence of the Ag islands around 20 ML, as shown, for instance, by the increase in the critical angle for total external reflection, which is due to an increase in the average density of the Ag layer. As islands coalesce, the interfacial misfit dislocations can reorganize into the energetically favored ordered interfacial network, resulting in an extinction of the intensity around (2.03 0 s and a well-defined satellite around (2.03 2.03 s

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 36. Schematic representation of the morphology and structure during the first stages of growth of Ag on MgO(001) at room temperature, as a function of the amount of Ag deposited, 0. A side view of the atomic positions within these islands is depicted. For all deposited amounts below 30 ML, the deposit consists of Ag islands with a height-to-width ratio of ~0.37 4- 0.05. The growth is decomposed into three stages: (a) For 0 < 0 < 4-6 ML, the Ag islands are coherent with the MgO. Their lateral size is smaller than 90 A. Their in-plane lattice parameter is equal to that of bulk Ag at 0.5 ML, and then becomes intermediate between that of bulk Ag and that of MgO between 0.5 and 4-6 ML. (b) Around 4-6 ML, on the average, the islands reach a critical size ('~90/~) above which disordered misfit dislocations are introduced near their edges. (c) Above 30 ML, the film becomes continuous, and the dislocations reorder to form a square network. On all figures, the arrows locate the presence of a column in Ag that is exactly "on site." The supercell used to calculate the CTRs is shown schematically.

In summary, this GIXD study provides much information concerning the growth and relaxation at the Ag/MgO interface, as summarized in Figure 36. The growth of Ag on MgO(001) was shown to be always of the 3D Volmer-Weber type. Between 0 and 4 ML, coherent Ag islands form and grow laterally, with decreasing aspect ratio. Ag is fully relaxed on the edges at the very beginning and becomes increasingly strained to the MgO in-plane lattice parameter as the islands grow laterally. Around 4 ML, the islands reach a lateral critical size of ~ 100 for which interfacial defects such as misfit dislocations and stacking faults are naturally introduced at the edges. The coalescence happens around 10-30 ML. Above 30 ML, the film is continuous, and interfacial dislocations rearrange on a regular network. The fraction of Ag that is on site is made of columns located at the center of islands before coalescence and between dislocation lines after.

4.1.2. Surfactant-Assisted Growth of Ag

on

MgO(O01)

Finding new ways to improve the adhesion of a metal on a ceramic surface is of great importance for many applications. The growth of Ag on MgO(001) is 3D because Ag does not

557

thermodynamically "wet" MgO(001), but also because of the lattice misfit. The introduction of adequate surfactants to promote 2D with respect to 3D growth has been found to be very efficient in numerous systems, in both homoepitaxy [153-155] and heteroepitaxy [153, 154]. In particular, antimony (Sb) has been shown (actually by GIXD) to be a surfactant during the homoepitaxial growth of Ag, of both (111) [153] and (100) [154] orientations. For the Ag/MgO system, Sb could be expected to induce several kinetic effects promoting a 2D growth, like an increase of the nucleation density, the concentration of lattice accommodation in Sb-rich regions, the earlier formation of the misfit dislocation network, as well as the earlier appearance of the coalescence or the suppression of stacking faults due to the dendritic shape of islands inducing connections between islands, as has been observed, for instance, in the case of the homoepitaxial growth of Cu(ll 1) [155]. A GIXD study was thus performed to investigate the effect of Sb as a surfactant during the heteroepitaxial growth of Ag(001) on top of MgO(001). The same measurements as above were performed under two conditions for Sb deposition: after deposition of 0.2 ML of Sb on the bare substrate on the one hand, and after deposition of ~ 1 ML of Ag before deposition of 0.2 ML of Sb on the other hand, followed by Ag growth. Whatever the growth conditions, only extremely small differences were observed in measurements made with and without Sb. The conclusion of this study is that Sb does not modify the structure, the morphology, or the kinetics of the growth of the Ag/MgO(001) interface. Complementary AES experiments were performed which showed that Sb indeed does not wet MgO(001), at least for alternated deposition. Nevertheless, the GIXD technique could be useful for testing other ideas to modify growth, such as the association of a wetting tensioactive element like Fe with a surfactant, or growth under partial oxygen (or CO) pressure, which is found to improve wetting in some cases.

4.1.3. Thick Ag Films on MgO(O01) For the Ag/MgO(001) interface, the misfit is f = - 2 . 9 8 % [156, 157]. Hence, a semicoherent interface would be expected. Ordered, localized interfacial misfit dislocations had actually been observed by HR-TEM [152]. The HR-TEM conclusion was that the dislocation lines are oriented along the (100) directions, with a 1/2(100) Burgers vector. This could only be explained by the coexistence of two possible epitaxial sites for silver in the regions of "good match" between the Ag film and the MgO substrate: regions where the silver atoms sit above oxygen ions of the last substrate plane, and regions where they sit above magnesium ions. This conclusion was very surprising, because all theoretical calculations of the epitaxial site performed so far arrived at only one kind of epitaxial site, above O ions, which was also our experimental conclusion from GIXD [44]. These discrepancies motivated a GIXD investigation of the interfacial dislocation network. According to the different possible epitaxial sites, different coincident site lattices (CSLs) may be considered. In "good

558

BARBIER ET AL.

Fig. 37. Schematic representation of the (hkO) interfacial plane of the reciprocal lattice of the Ag/MgO(001) interface with an interfacial networkof misfit dislocations. The MgO and Ag Bragg peaks are respectively represented by large black and gray disks. The reciprocal lattices of the two possible interfacial misfit dislocation networks are also shown, as grids, with continuous lines for the (110) CSL and a dashed line for the (100) CSL. The locations of satellites from the interfacial network are represented as gray disks for the satellites that are common to the two CSL, and as open circles for those satellites that pertain only to the (110) CSL. The experimental radial scans performed on the different samples are also indicated. A scan along the (110) reciprocaldirection, between the MgO and Ag Bragg peaks, should make it possible to distinguish unambiguouslybetween the two possible networkorientations. match" regions, because of the symmetries of the MgO(001) plane, the Ag atoms may sit either above oxygen ions of the substrate, or above magnesium ions, or in between, above the octahedral sites, with two possible variants [152]. If they sit above only one of the possible epitaxial sites, a square CSL of 97 A periodicity oriented along (110) directions is obtained. If there are two equivalent epitaxial sites, for instance, O and Mg, or two variants of the octahedral site, then a square network oriented along (100) directions is obtained, of 69 ,~ periodicity, smaller than for the (110) CSL. As illustrated in Figure 37, it is possible to distinguish between the (100) and (110) dislocation networks by performing X-ray scattering along the (h00) and (hhO) directions of the reciprocal space. Indeed, along the (hhO) direction, the satellite periodicity is double in the case of a (110) CSL with respect to the (100) case. Many different samples were studied, with different Ag thicknesses ranging from 5 to 150 nm, different substrate surface preparations, and different miscuts of the MgO(001) substrates ranging from 0 ~ to 3 ~ In all cases, as shown in Figure 38 for a miscut substrate and in Figure 39 for a flat substrate, a satellite was found between the MgO(220) and Ag(220) Bragg peaks, which unambiguously demonstrates that the dislocation network is of (110) orientation and is sufficiently ordered to yield at least a first-order satellite diffracted by this network.

In addition to the orientation, many other features were deduced from these measurements. On all substrates with a significant miscut, a large background of diffuse scattering was found in the region of the Bragg peaks. It takes the form of two shoulders, symmetric with respect to the Ag peak, with a significant diffuse scattering between. As shown in Figure 40, on large radial scans taken at different values of the perpendicular momentum transfer s (in r.l.u, of MgO), the separation between these two peaks increases with s in such a way that they are aligned on rods along the (111) and (111) directions emanating from the Ag Bragg peak located at (2.0612.061 0.04). These rods were shown to originate from stacking faults along (111) planes [158]. Another interesting feature seen in Figure 40 is the peak measured around (2.404 2.404 0.35), which was shown to arise from twin formations, corresponding to two crystals of reverse FCC stacking, with a mirror plane at the fault location. Twins no longer produce rods, but produce additional peaks at (220) + 1/3(111) and (220) + 2/3 (111), in reciprocal lattice units of Ag. Hence, these data showed that, in addition to the interfacial dislocation network, growth faults are present within the Ag thin film, mainly stacking faults and twins along (111) planes. These faults are likely to occur during coalescence of neighboring islands of different stacking. The density of stacking faults

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 38. Radial scans along the (h h 0.1) direction around the (220) Bragg peak at different temperatures during heating, followed by cooling to room temperature, for a 1500-/~-thick Ag film grown by MBE on an MgO(001) substrate with a 2~ miscut.

559

Fig. 40. Radial scans (h h s around h = 2 on a 1500-/~-thick Ag film with a 2.5 ~ miscut. A vertical translation, proportional to the e coordinate, has been introduced between the different scans. In addition to the MgO and the Ag CTRs and to the dislocation satellite rod, there are additional rods of scattering, oriented along the (111) directions, crossing the relaxed Ag peak around s 0.04. These rods are due to stacking faults in the silver film. The peak around h = 2.404 and s = 0.35 arises from twinned Ag domains. The shift in s (0.04) of the origin of the stacking fault rods is due to refraction in the Ag film.

was found to increase with the step density of the substrate, i.e., its miscut.

Fig. 39. Radial scans on a 1500-/~ Ag film on a MgO(001) substrate with a very small residual miscut ( 0. Figure 42 gives an example of the construction of (100) oriented truncated pyramids. The amount g(p) is the number of atoms at level p; thus g(Pmax)/g(h) is the coverage of the surface. The sum over g(p) represents the number of atoms in an island, and y~ g(p)/g(h) is the number of monolayers that have been deposited, | | is connected to the g function by

t 0 - - (1 - e)

/ /Mien )

g(P) g(h)

)

q

/

[Max(n h) h] +-~ + ; \ p=l (24) Because n(| and q(| define the morphology, this equation must be reversed. The analytical solution can be written if - e) and if ns, the we define s(n) - Z p g(P) and 0 -- | root of ns - s -1 (0 9g(h)), can be found. Then, n(O) and q(O)

562

BARBIER ET AL.

Fig. 42. Example of the construction of (100) oriented truncated pyramids within the GMID formalism, g(p + k) = (p + k) 2. Outer left and right columns indicate the number of atoms in each layer. To proceed from three layers to four layers, the island has to receive 25 additional atoms. The central column indicates the percentages of atoms that each layer has to receive to reach the n = 4 situation. When fawer than 25 atoms are added, they will be put on each layer according to the percentage of atoms they have to receive, and n will stay at 3 until 25 atoms are added. The number of layers depends on the generating function and must be recalculated for each thickness. In this example the first layer is truncated.

take an analytical form, n(O)

= Int(ns)[1

H(Int(ns)

-

h)]

s(h) } + . h, i . H[Int(n~ ) - h] (25a) g--~

+ [Int{0 q(O) = g(h) .

-

Frac|0"k

s[Min(Int(ns; g(h)

h))l|"

(25b)

d

In the Ag/MgO(001) case, truncated pyramids with (110) orientation apply well, the corresponding generating function is g(p, k) = 2. (p + k) 2, and all of the equations of the GMID can be solved analytically. The sum function is n

s(n, k) = ~_~ g(p, k) p=l

= 2k2n + 2kn 2 + 2kn +

2ng3

+,,2+ gn

(26)

and ns = s - 1 ( 0 . g(h)) = Int 9t A + 12----A--

2

with A =

+

+

+-~O(h+k) 2

1 + ~-~[-3 + 18213602h 4 + k(120 (h 2 + 120h 3) + k(1 + 120(3h 2 + 2h + 180h 2 + k(6(1 + 20(1 + 2(h 2 + 3h + 20h)) + k(13 + 120(4h + 3(1 + 0) + k(12(1 + 20) + 4 k ) ) ) ) ) ) ) ) / ] 1 / 2 ]

1/3

(28)

thus linking the coverage in a unique way to the morphology. From SEM it is known that, even for very thick deposits, about

10% of the surface will never be covered; thus e = 0.1 in the present case. The GMID returns nO,h,k and the way in which the remaining atoms have to be put on the pyramids. The lattice mesh of Ag is aAg -- 4.17 /~. Let us now derive the quantifies of interest in the present study. The height of a pyramid, H, is the number of layers times the height of one layer: H ( O , h, k ) - - nO,h,k 9 a A g / 2 . Because the basis layer of the island contains g(Min(nO,h,k; h), k) atoms (see Fig. 42) the lateral size, S, of the island along the (100) direction is given by S(O, h, k) = v/g(Min(no,h,k; h), k) 9 a g g / ~ / r 2 . T h e interisland distance, D, along the (100) measurement direction is D(O, h, k) = ~/g(h, k) 9 aAg/~/1 -- e. These are exactly the quantities one can extract from the GISAXS data. The formulation allowing estimation of the XPS intensity is complex and has been described in detail in [ 163]. Varying h and k permits the exploration of a huge number of possible morphologies. Intuitively, calculating the different quantifies for which data are available and drawing the confidence ratio, R, with respect to h and k should allow a determination of the actual morphology of the Ag islands. As can be seen in Figure 43, this approach leads to incoherent results. Each data set providing different best couples (h, k) and the corresponding fits remain extremely poor. Sometimes, as for the interisland distance, the minimum is not defined at all and belongs to a one-dimensional space of solutions. Thus there is no defined shape of static islands that allows reproduction of all of the data. The islands must evolve in some way during the growth. This analysis can also be quantitatively performed with the GISAXS data and the GMID formalism. It can be shown that k is connected to the experimental GISAXS data by k = ( S - 2H)/agg. The linear law k(O) = (2.36 4- 0.60) + (0.83 4- 0.06)0 reproduces the behavior well (Fig. 44d). From k and D one can extract h: h - k + D/(aAg 9 ~/2/(1 -- e)). Here again a linear law h(O) = (10.96 4- 0.40) + (0.96 4- 0.04)0 applies (Fig. 44d). At this stage the growth is completely characterized. Using these laws

SYNCHROTRON STUDY OF OXIDES AND METALS

563

Fig. 43. Confidence ratio, R, maps for constant h and k drawn for XPS data (top) and the GISAXS interisland distance (bottom left) and island size (bottom right). The Az's indicate the interval size between levels in the map. The best h and k are indicated in each map.

Fig. 44. (a, b, and c) Experimental size (11), height (V), and interisland distance (A) compared with the evolutive shape growth model (straight) and to the best (h = 13.5, k = 7) couple deduced from the XPS data alone (dashed). (d) h (El) and k (A) deduced from the GISAXS data and the best linear laws. (e) Calculated island density for the evolving shape model (straight) and for (h = 13.5, k = 7) (dashed). (f) Number of layers in the islands for the evolving shape growth (straight), the best XPS (h, k) (dashed) and a layer-by-layer growth (dotted).

and the GMID formalism, one can now calculate any quantity of interest and evaluate experimental measurements. The agreement (XPS and GISAXS; Fig. 44a-c) is always very good. Note

that there is no fitting parameter, because everything is directly calculated from the growth laws. One can also extract quantities that describe the growth more intuitively. The island density per

564

BARBIER ET AL. lands during their growth. Indeed, the present description is fully coherent with the Ag diffraction peak width evolution during growth. For the Ag/MgO(001) interface we have thus extracted precise and quantitative growth laws for growth at room temperature. 4.2. Pd/MgO(O01)

4.2.1. In Situ Studies of the First Stages of Formation of the Pd/MgO(O01) Interface

Fig. 45. Detailed evolution of the number of layers in a Ag island during growth, from the quantitative growth laws.

square centimeter is given by nAg = D2/2 = (7.864 x 10-80 + 5.855 • 10-7) -2 (Fig. 44e); the number of layers nO,h,k present in the islands with respect to 0 is reported in Figure 44f. The characterization of the growth thus remains a difficult task because for a given data set it is possible to extract an (h, k) couple that is unable to reproduce other measurements. Moreover, the different measurements are more or less sensitive to the morphology: XPS data are only poorly able to separate the different possibilities obtained from the model (compare the h = 13.5, k = 7 case with the final model), whereas other data sets, like the particle size, are highly sensitive to variations. These observations show that care must be taken when growth modes are described. The ability of a model to reproduce a given data set is obviously not enough to conclude. The present analysis shows that the growth of Ag on MgO(100) is, in essence, of an evolving nature. Snapshots at different thicknesses will not be similar in particle size, density, and shape. But the growth laws show that the overall shape is always the same (constant aspect ratio of 0.36 for 0 > 0.2 monolayers), because h is directly connected to k by h = 8.23 + 1.16k. On the other hand, the density is only governed by the thickness, and its behavior is compatible with a nucleation, growth, and coalescence behavior. To compare our present interpretation with previous ones, we have to extract the behavior in the submonolayer regime (Fig. 45). One can show that from 0 to 0.15 ML only 1-MLthick islands form; then the second layer starts its growth up to 0.3 ML, where the third layer begins its growth, and so on. Thus the interpretations of a pseudo-Stranski-Krastanov growth up to 0.1 ML or a bilayer-by-bilayer growth up to 0.4 ML are consistent with the actual growth mode, but they are inaccurate at higher coverage [ 164]. A description of the growth of islands with variable shapes and densities was not possible in simpler approaches because the shape is then generally fixed a priori. Finally, the model presented here, combined with GISAXS data and GIXD, has shown its ability to reproduce all of the available data within an evolving shape behavior of the Ag is-

Unlike the Ag/MgO(001) interface, the Pd/MgO(001) interface had been the subject of a large number of studies [165-178], mainly to investigate the kinetics of nucleation in the submonolayer regime between 400 K and 800 K. Whatever the temperature, the growth was found to be 3D (Volmer-Weber), with nucleation, growth, and coalescence of clusters. These clusters are single-crystal particles, fully relaxed and in cube/cube epitaxy, excepted for the first layer in contact with the MgO(001), which, according to HR-TEM results [ 174], would be perfectly accommodated. No twins could be detected by HR-TEM [ 174, 176], and a SEELFS study performed at the Pd N2,3 edge [ 179] concluded that the Pd atoms adsorb on top of Mg ions. In addition, an HR-TEM study of the Pd/MgO(001) interface formed by internal oxidation [ 176] concluded that the 7.6% misfit is accommodated by a network of interfacial dislocations of (110) orientation and 1/2 (110) Burgers vector, in agreement with the O-lattice theory. The GIXD experiments were aimed at studying the growth morphology at room temperature, the epitaxial site, and interfacial distance, as well as characterizing the interfacial dislocation network. They were performed during the in situ growth at room temperature of Pd on MgO(001) substrates of high quality, prepared according to the procedure described in Section 3.1 The ID32 ESRF [15] beamline and the W21 surface diffractometer setup were used. The (20s and (31 s CTRs measured on the clean MgO(001) surface and after the room temperature deposition of 0 = 1 ML of Pd are shown in Figure 46. The large modification induced by deposition shows that, as in the Ag/MgO case, a significant fraction of the Pd deposited is in perfect registry (i.e., on site or pseudomorphic), and the sign of the interference makes it possible to rule out the octahedral epitaxial site. A quantitative fit of the integrated and corrected CTR intensifies was performed, yielding with high accuracy the amount of Pd in registry (0 = 0.5 ML), the additional roughness of the pseudomorphic fraction (2.7 ,~ (r.m.s.)), and an interfacial distance of 2.216 4- 0.02 ,~ = 1.05 • dMgO ~(002)" This (20s CTR is not sensitive to the difference between O and Mg epitaxial sites, unlike the (11s or (31s rods, which are very sensitive to the actual site. This is illustrated in Figure 46b and c, which show the experimental and calculated (31s CTRs for 1 ML of Pd deposited, superimposed on the CTRs of the bare substrate. The qualitative comparison makes it possible to conclude that Pd is above the O ions and not the Mg ions. This is in contradiction to a previous SEELFS investigation, but both the epitaxial site and interfacial

SYNCHROTRON STUDY OF OXIDES AND METALS

565 9

10 2

I

"

I

"

I

"~

"

I

"

I

"

(a) 1

1 10

?, o=

1/

z/

uP 10 0 I,,.., .,!..,.I

0

1

2 [MgO r.l.u.]

3

Fig. 46. Modulus of the structure factor of the (20~) and (31~) CTRs for the bare substrate and for 1 ML of Pd deposited. (a) (20e) CTR, obtained by integration and correction of rocking scan measurements, for the bare MgO(001) substrate (open squares with the dashed line showing the best fit) and for 0 = 1 ML of Pd deposited (open circles with error bars; the continuous line is the best fit). The best fits yielded the following parameter values: dpd_MgO = 2.22 4- 0.02/~, Oon_site = 0.5 4- 0.1 ML, apd = 2.7 4- 0.3 ~, and dpd-Pd = 1.86 -4- 0.03 ]k. (b) e-scan measurements of the (3 le) CTR for the bare substrate (open squares) and after deposition of 0 = 1 ML (open circles). (c) Calculated (3 le) CTR, for the bare substrate (open squares) and for 1 ML of Pd deposited, with Pd above either Mg ions (dashed line) or O ions (thick

continuous line). distance are in very good agreement with a recent theoretical calculation [ 180] yielding 2.18 ,~. The evolution of the CTRs with 0 is very similar to that in the Ag/MgO(001)case: above 0 ~ 1 ML, only a small fraction of the Pd deposited remains on site, most of the film being relaxed. If the epitaxial site is identical to the case of the Ag/MgO interface, the interracial distance is much smaller (2.216 A as compared with 2.45 ~, in the case of the Ag/MgO interface), likely because of the much stronger bonding in the case of a transition metal like Pd, as compared with a noble one like Ag. For all deposits between 0 = 0 and 12.5 ML, the (20e) and (3 l e) CTRs measured in e-scans were simultaneously fitted over the ranges e -- 1 to 3.7 and 0.5 to 3.7, respectively, assuming the oxygen site. The best fits of the experimental data are reported in Figure 47, and the corresponding parameters, in Figure 48. For all deposits, the agreement is good, which shows that the chosen model is adequate. For 0 > 0.8 ML, all four fitting parameters are well decorrelated and can be fitted inde-

co 1 2

6 8 10 12.5 9

I

3 1 2 3 [MgO r.l.u.]

Fig. 47. Comparison of the measured (rough line) and calculated (smooth line) (20e) and (31~) CTRs during the room temperature growth of Pd on MgO(001). The modulus of the structure factor is reported as a function of the out-of-plane momentum transfer. The two CTRs have been simultaneously fitted over a large range of out-of plane momentum transfer. The amount 0 (in ML) of Pd deposited is indicated in the figure. The curves were vertically

shifted for clarity. pendently. For 0 = 0.58 and 0.2 ML, dPd-MgO and dPd-Pd w e r e found to be correlated. Oon-site (Fig. 48a) and O'pd (Fig. 48b) are found to first increase quickly with 0, and then slowly reach asymptotes around 1.3 ML and 6 ,~, respectively. The r.m.s, roughness reaches 4.7 ,~ and 6.2 * for 0 - 5 and 12.5 ML, respectively (i.e., for equivalent deposited thicknesses of 9.72 A and 24.3 ,~, respectively). It thus always remains much smaller than the equivalent deposited thickness, dPd-Pd (Fig. 48c) decreases from 1.895 ,& for 0 = 0.2 ML to 1.79 A for 0 = 4 ML, and next stays nearly constant, with only a very slight decrease down to 1.785 A for 0 = 12.5 ML. Finally, dpd-O (Fig. 48d) shows a peculiar behavior: it first decreases from ~2.23 ,& at 0 - 0.5 ML to 2.15 ,~ for 0 -- 4 ML, and then increases to reach a steady-state value of 2.22 4-0.02 ,~ above 10 ML. Note that all of these dpd-o values are very close to each other. A remarkable feature is that, although they were fitted independently, the same parameters are obtained for 0 = 1 ML after fitting of the CTRs measured in rocking scans and in e-scans, although the fits are performed over a very large range of e values. This demonstrates the adequacy of our intensity corrections for e-scans.

566

BARBIER ET AL. r.

gstz I .9o


600 K) the island size ceases growing linearly (Fig. 66). A last key remark is to understand that 0.4 ~ mosaicity represents terraces of about 20 nm on the NiO(111) surface. We can now draw a coherent picture of the morphology and of the GIXD limits. For excellent substrate mosaicities and Ts large enough to ensure good epitaxial growth (Ts > 600 K), the GIXD domain size, the GISAXS island size, and the AFM average island size are fully coherent. When the substrate has a limited mosaic spread, and thus small terraces and many defects, these defects propagate into the Co islands, and the GIXD domain size will always be limited by the initial mosaicity of the substrate, giving in turn the asymptotic behaviors reported in Figure 64. In this case the GIXD domain size is no longer a good measurement of the island size. On the other hand, the presence of the defects modifies the intrinsic growth mode; the defects are likely to pin the islands, thus preventing their growth and explaining the deviation from linear size increase in Figure 66. The last situation occurs when the crystalline quality within the Co island is so poor that the islands have defects breaking the coherence of the X-rays on a shorter length scale than the terrace size of the substrate. Then this last phenomenon will limit the observed GIXD domain size (room temperature growth in Fig. 64) and limit the growth of the islands themselves (Fig. 66, growth at 480 K). To summarize, we have fully characterized the growth of the Co islands at different temperatures and on substrates of different crystalline quality. We have also shown that one and only one of the following lengths may limit the GIXD domain size: the distance between defects in the Co islands, the terrace size on the substrate, or, finally, the size of the islands. The GIXD domain size is thus only a good measurement of the island size when the well-crystallized islands have small extensions compared with the terrace size of the substrate.

5.2.3. Magnetic Properties We have shown the possibility of building Co/NiO(111) interfaces of controlled crystalline quality. The next question is how the magnetic exchange coupling depends on this crystalline quality, especially in view of the divergent interpretations of magnetic exchange coupling. In our case the NiO grain size can be considered infinite compared with sputtered NiO films. Were the magnetic exchange coupling, for example, to be born at the grain boundaries, we would not observe this phenomenon on single crystal interfaces [132]. After the growth we measured the magnetic behavior of our Co/NiO(111) sample by MOKE and VSM. The MOKE measurements for room temperature grown and annealed and high-temperature (HT = 700 K) samples are reported and compared in Figure 67a. The annealed room temperature deposited film has a large and distorted hysteresis loop, which is characteristic for polycrystalline films, with a coercive field Hc = 200 Oe. The HT sample shows a much squarer hysteresis loop, with Hc = 410 Oe. The factor of 3 in the saturation signal obtained at the external applied field of 600-700 Oe

579

4

.~

900

(a)

800

~2

9

700 600

~

500

~0 ~

r~

i-2

150

g

,~ "~ ~.,

100

:~ , ~ ~

50 0

4

!

9

i

,

-800-400

,

0

i

9

i

400 8 0 0 0

H (Oe)

100

200

300

T (K)

Fig. 67. Magneticproperties of 20-nm Co/NiO(111) films. (a) RT measured MOKE hysteresis loops for a RT deposited and annealed sample (45 min at 970 K) (--) and a HT (703 K) deposit (r-q).(b) VSM measurementof the evolution of the coercive (Hc, D) and exchange (Hxc, I) fields with respect to the temperature.

can be well explained by the poorer reflectivity of the rougher RT sample. Obviously, the well-crystallized sample shows a much squarer hysteresis loop and acts as a harder (magnetically pinned) layer. To fully understand the exchange coupling, the magnetic properties of the 703 K deposit have been investigated by VSM with respect to the temperature (Fig. 67b). Hc increases with decreasing temperature, and below 150 K the exchange field (unidirectional shift of the hysteresis loop) appears, and it exhibits a behavior similar to that of Hc, with a maximum of 135 Oe at 50 K. These features undoubtedly confirm the onset of classical exchange coupling between the Co islands and the antiferromagnetic NiO(111) substrate at low temperatures. As a general rule the samples prepared at least at 600 K exhibit features similar to those of the HT sample: large coercive fields at room temperature and increasing exchange fields below 150 K. Measurements for different Co thicknesses, in the 14-23-nm range, for samples prepared at 800 K showed the expected Hc = A/0Co law (where A is a constant) and no hysteresis loop shift at room temperature. If we now consider the coercive field values in more detail, we observe that the Hc obtained for single-crystal substrates for 0Co = 20 nm is comparable to those obtained for spin valves prepared by sputtering [221,222, 238]. Knowing that the thickness of the pinned layer in a Co-based spin valve is typically 3 nm, and considering the 1/0Co dependence of Hc, the corresponding Hc for a 3-nm deposit on a single crystal would be as huge as 1200 Oe. Moreover, our interfacial magnetic energies (J = MsOcoHc, where Ms is the spontaneous magnetization of the Co layer, 1420 emu/cm 3 for the bulk Co) are nearly an order of magnitude larger than those obtained for sputtered systems (J = 1.27 erg/cm e compared with J = 0.11 erg/cm 2 in Co-based spin valves [238]). The coercive fields observed here are huge (at least an order of magnitude larger) compared with what could be expected

580

BARBIER ET AL.

from an equivalent freestanding layer. This phenomenon is thus connected to the magnetic exchange coupling as much as the hysteresis loop shift is. Obviously, in the single-crystal substrate case the increase in Hc is augmented and the Hxc field is reduced, leading to the idea that Hxc may be related to defects such as grain boundaries, whereas the large Hc is more intrinsically connected to the interface between a ferromagnet and an antiferromagnet. To summarize the Co/NiO(111) study, we confirmed experimentally that the p(2 x 2) reconstruction of the NiO(111) single-crystal surface vanishes through metallization, and we have shown that the structural quality of the Co islands can be tuned from polycrystalline to perfectly single crystalline and that the related magnetic properties are strongly correlated with the structure. Moreover, the interface is strongly exchangecoupled for a single-crystal substrate, but it is the coercivity increase that is the basic phenomenon rather that the hysteresis loop shift. Because the structure is tunable, the magnetic properties are also tunable. However, the 3D growth is not favorable in this system inasmuch as it shows that by itself Co does not wet NiO(111) (i.e., a Co layer deposited by sputtering is far from thermodynamic equilibrium); thus devices based on this interface may always remain fragile and may have unforeseeable aging properties. This system also allowed verification of the limits of the finite domain size interpretation of the GIXD peak lineshape analysis, which only gives the distance between two defects that break the coherence of the X-ray scattering.

5.3. NisoFezo/NiO(111) To improve our understanding of the magnetic exchange coupling phenomenon and related devices (spin valves), one needs pinned ferromagnetic layers that are continuous. An assembly of clusters like the ones observed during the growth of Co on NiO(111) are not adequate because the electron flow could avoid crossing the pinned interface. For this reason we have undertaken the study of other ferromagnetic layers based on the ferromagnetic transition metals (Fe, Ni, and Co). A similar approach to the Co case was used: in situ X-ray investigations, followed by ex situ magnetic measurements. The growth of permalloy (Py = Ni80Fe20) is a particularly interesting case, and its growth is described in this section. We focus on the growth characteristics and interface formation, which, in contrast to all of the other cases, can be rendered reactive. In addition to the GIXD study; the samples were characterized by HR-TEM and energy-filtered (EF)-TEM, which allows access to the concentration profile across the interface. For these studies we always used high-quality NiO(111) single crystals, with mosaic spreads below 0.05 ~ The substrates were always prepared to exhibit the p(2 x 2) reconstruction spinel configuration, which stabilizes the surface against decomposition (see Section 2.4). The growth was studied by GIXD, and the surface unit cell was indexed as described previously for the Co/NiO(111) interface. The Py film has been obtained by codeposition with the use of two independent remote-controlled sources with electron-bombarded rods

(Ni and Fe, 99.99% purity). Each source was calibrated with a quartz microbalance, and the composition was checked after growth by chemical dissolution in HNO3, which dissolves only the metals and not NiO, and dosing the Ni and Fe in solution. The typical deposition rate was 0.58/~ Py/min. During the growth, different thicknesses of Py (0ey) were investigated in situ, at each 0py, in-plane and out-of-plane GIXD measurements were carried out. Then, a new deposit of Py was performed. Thus, the given thickness must be understood as cumulative quantifies. The deposition was continued until a total nominal thickness of the Py film of 20 nm was achieved. Different samples were prepared in the 600-650 K temperature range. Some samples were magnetically coupled in situ by an anneal at 800 K for 20 min and left to cool to room temperature under an external static field of about 500 Oe to generate the magnetic unidirectional exchange anisotropy and to recrystallize the samples. The annealing temperature is chosen to be between the Curie temperature of the ferromagnetic layer and the Nrel temperature of the antiferromagnet, allowing for the magnetic saturation of the ferromagnet while the antiferromagnet is not ordered. During cooling down, in such a configuration, the unidirectional magnetic coupling occurs in the direction of the initial external magnetic field. After the UHV annealing, the film was capped by a protective 20-A-thick Ag or Au capping layer. 5.3.1. Structure and Growth Mode Versus Temperature Like Co/NiO(111), the Py/NiO(111) interface is 18% lattice mismatched. As can be seen in Figure 68, which presents a HR-TEM image of a room temperature Py deposit, room temperature and low-temperature deposits are fairly polycrystalline. Several grains can easily be identified on the image. Note the high quality of the NiO(111) single-crystal substrate, which shows no defect over the entire image. Moreover, the interface is chemically perfectly sharp and flat. This is quite similar to the Co/NiO(111) interface, with the exception that Py films of 10 nm are almost 2D and wet the NiO(111) substrate very well. Such situations are not well adapted for GIXD investigations, and the film quality is similar to that obtained by sputtering. Because we want to produce single crystalline interfaces, we have explored higher temperature growths. We now describe the structure of the Py film when the growth takes place at 650 K. Because Py cannot adopt HCP stacking, the reciprocal space is identical to the Co/NiO(111) case without the HCP peaks (Fig. 58). The investigation of the same reciprocal space regions permits an understanding the structure of the Py layer during its growth. Figure 69 shows the evolution of the (110)ey peak with respect to the Py thickness though a (hhO) scan with h close to 1. This Bragg peak contains all of the scattered intensity from the FCC and twinned FCC stacking (Fig. 58). The peak continuously intensifies from the very beginning of the deposition, showing that Py grows epitaxially, with a CC epitaxial relationship, from the early stages of growth. The (110)py peak immediately appears at h = 1.18; similarly to Co, the Py film is thus always fully

S Y N C H R O T R O N STUDY OF OXIDES A N D METALS

581

Fig. 68. HR-TEMimage of a polycrystalline Py film grown at RT on NiO(111). On the HR-TEM image, several Py grains with different orientations with respect to the substrate can be seen.

Fig. 69. In-plane scans along (hhO) for different thicknesses of deposited Py between 0 and 20 nm. The thickness are, from bottom to top, 0, 2, 3, 6, 8, 12, 16, 24, 34, 50, 80, 120, and 200 A (the last situation is the annealed film). The position of the NiO (110) Bragg peak (at h = 1, in the left part of the figure) has not been recorded to avoid the very high intensity of the NiO Bragg peak. The higher background for the last scans (large 0py; top curves) originates from the absorber used to avoid the saturation of the signal in the detector when it passes through the Py peak.

relaxed. Scans along other high-symmetry directions ((h00), (h 2h 0), (0k0) . . . . ) confirmed our conclusions, and no other epitaxial relationships were found. The NiO(111)-p(2 x 2) reconstruction signal has been used again to monitor the progressive surface coverage, and again the metallization effectively kills the reconstruction (Fig. 70) and heals the polarity problem. At 0py - - 3 nm, the uncovered surface signal ('-~3%) comes close to the noise. Importantly, the reconstruction signal decreases much faster than the attenuation of the beam and finally vanishes completely around the 4-nm Py deposit (Fig. 70), highlighting the good surface coverage and wetting of Py. Simultaneously, the evolution of the intensity of the (1, 1, 0)py Py peak, characteristic of the ordered part of the metallic film, has been measured quantitatively. Its behavior is reported in Figure 70. It increases from the beginning until the thickness of the Py film limits this increase because of refraction around 8 nm; above this thickness it is always the same amount of Py that contributes to the GIXD signal.

Fig. 70. Characteristic signals of growth with respect to the deposited Py thickness. II, Evolution of the normalized (3/2, 0, 0)NiO intensity sensitive to the uncovered surface fraction. O, Normalized (1, 1, 0)py Bragg peak intensity sensitive to the ordered fraction of the film. 0, FCC fraction of the film and (--) evolution of the p(2 x 2) signal that could be expected from the X-ray damping alone (absorption length in Py at 18 keV = 30.56/zm for an incidence angle of 0.17~ The absorption in the Py layer cannot explain the attenuation and disappearence of the NiO reconstruction signal.

To separate the different ways of stacking in the film, out-ofplane scans along the (10s direction, which passes successively through FCC and twinned FCC Bragg peaks (Fig. 58), were performed. Several such scans are shown in Figure 71 for different Py coverages. The existence of narrow peaks in the s direction supports a 3D growth mode. In particular, in the submonolayer regime, three layers are needed to distinguish between the two ways of stacking ( A B C A B C . . . and A C B A C B . . . ) , and a 2D layer would yield a rod of constant intensity along s (see Section 2). This shows that already for small quantities of deposited Py, islands form that have at least three atomic layers. Interestingly, the FCC part, which corresponds to the NiO(111) stacking, is dominant for all thicknesses. To accurately quantify this observation, which could also originate from different crystalline qualities, rocking scans at the exact locations of the (1, 0, 1)py and (1, 0, 2)py peaks were performed on both the FCC and twinned FCC peaks to get the integrated intensities. The widths along s were also taken into account to refine the integration. After correction the con-

582

BARBIER ET AL. 10 4

Py(lO0)

10

'

'

NiO(lO0)

-9 10 .~ t_ ~q

.~

10 0

10 2

101

ol==l

t

d-q

am

9

.-'

9

.---=,,=,

.m

o-

Py(200)

4o

r~

=

NiO(200)

g 10 -1

10 ~

-9 104 o

9~ 10 -2

E ~

10 "3

~

10-4

o

|

.

~

~,

.

~

~.~

0

1

2

3 4 s [r.l.u. N i O ]

N 10-2

Ii

z

"-

5

6

Fig. 71. Out-of plane scans along the (1, 0, s rod for different thicknesses of the Py film, 0py. From bottom to top, the Py thickness are 3, 6, 12, 24, 50, 120, and 200/~. The last situation is the annealed film and was shifted on the graph (x 40) for the sake of clarity.

centration 0FCC of the FCC part in the film can be deduced through Ae((lO1)py). I ((lO1)py) r/FCC =

As

10 .3

l((101)py) + Ag((102)py)- l((102)py) (29)

The evolution of the fraction 0FCC with respect to the thickness is reported in Figure 70. The FCC stacking is always dominant (at least 80%), and at large 01,y, the film is mostly in FCC stacking (95%). The larger error bars at low coverage are due to the smaller signal-to-noise ratio at the beginning of the growth. The residual twinned FCC stacking is here likely to occur from stacking faults rather than from an intrinsic growth mode in which FCC and twinned FCC stacking should be present in a 1 : 1 ratio. This general behavior of the Py/NiO(111) interface is similar to that observed for Co/NiO(111): polycrystalline layers at low temperature and single crystalline layers at high deposition temperatures. As for Co/NiO(111), the FCC stacking, which continues the NiO(111) stacking, is selected during growth when enough atomic mobility is available (i.e., at high enough temperature). Moreover, this happens for fairly thick layers, indicating the strong influence of the polar surface, probably through the charge image term, on the crystalline structure of the overlayer. There are, however, some important differences between the two systems. Although the initial growth mode is 3D in both cases, the Py film progressively covers the surface and coalescence occurs at about 30-40 ~. Because metal/oxide systems are likely to adopt 3D growth modes, this behavior deserved further investigation. Annealing and higher temperature growth will permit identification of the corresponding driving force.

10 .4 ,

I

1

,

h [r.l.u. NiO]

'/

2

Fig. 72. (h00) scan for a 20-nm Py/NiO(111) film deposited at 650 K and annealed at 800 K for 30 min at different incidence angles. 0, c~i = 0.05~ m , oq = C~c --- 0.17~ O, oq -- 0.35 ~ Arrows indicate the peaks that grow with the incidence angle.

5.3.2. Interface Compound After the deposition of the 20 nm at 650 K, the sample was annealed at 800 K for 30 min to improve the crystalline quality of the Py film. The crystallographic structure of the sample was then reinvestigated after cooling to room temperature under a magnetic field to exchange couple the sample and check the modifications induced by annealing. The annealing effectively completely washed out the twinned FCC Py: the characteristic peak at the (1, 0, 2)py position disappeared (Figs. 70 and 71). Although the annealing recrystallized the Py layer and improved its mosaic spread (and thus showed larger signals in radial scans), a significant loss in the integrated intensity of the (1, 1, 0)py and (1, 0, 2)py peaks is observed (last point in Fig. 70). Surprisingly, in-plane scans along the (h00), (0k0), and (hhO) directions, for instance, show the presence of new features at almost half integer indexes (expressed in NiO r.l.u.). Their widths are much larger (5-7 ~ than those of the p(2 • 2) reconstruction (0.1 ~ indicating a different origin and not a reorganization of the reconstruction or of the film, which could lead to Py islands and uncovered NiO(111). Moreover, out-of-plane scans also show peaks at almost halfinteger s values, showing that this new structure is bulk-like: it has a fairly large thickness. Some (h00) scans were performed at different incidence angles, ranging from grazing (0.05 ~) to large enough to cross the Py layer and the interface (0.35 ~ (Fig. 72). They allow the exclusion of a surface type structure. Scans at very grazing incidence do not show at all the peak located at (3/2, 0, 0), and only a small signal from the peak at (1/2, 0, 0) is observed. These features all increase faster than the signal-to-noise ratio when the incidence angle is increased. This unambiguously shows that this new phase is located at

SYNCHROTRON STUDY OF OXIDES AND METALS

583

Fig. 73. HR-TEM image of the interface of a 20-nm Py layer deposited on NiO(111) at 650 K and annealed at 800 K for 30 min.

the interface between Py and NiO(111). Moreover, it is interesting to note that the Py thick film exhibits CTRs, indicating a fiat top surface. Basing the interpretation on the lattice parameter alone indicates that a Fe2NiO4 phase is likely to occur. In any case, the interface obviously becomes reactive during annealing, and a diffuse structure with poor crystalline quality (mosaicity about 5-7 ~ appears at the interface. A quantitative characterization was not possible. Moreover, differentiating Ni and Fe positions and concentrations in the interfacial compound is not at all easy with GIXD, because all of these atoms have very close scattering cross sections. Understanding this interface in more detail required additional HR-TEM and EF-TEM investigations. Transverse cross sections of the interface were examined, with a 3010 Jeol microscope working at 300 keV with a LaB6 filament and equipped with a Gatan image filter [253]. The results confirm the data taken with X-rays, but also show some new features not accessible by GIXD. The chemical analysis was performed to get concentration profiles of the three elements (Ni, Fe, and O) along the growth direction of the film. The so-called three-windows technique was used. It consists of taking images of the interface at precise emerging electron energies (in a band A E = 20 eV) corresponding to characteristic absorption edges (ionization levels) of different elements (in our case, Ni L23, Fe L23, and O K edges, at energies O K = 532 eV, Ni L23 = 855 eV, and Fe L23 = 708 eV). For each element, two more images are recorded, at energies below the edge. They are used to deduce the background signal. Once the background is subtracted, the images obtained correspond to the chemical distribution of each of the elements. A semiquantitative analysis has been carried out, using the NiO substrate and the Py layer far from the diffuse interface as references for the chemical composition. Elemental distribution maps of Fe, Ni, and O with a lateral resolution on the order of 1 nm and chemical concentration profiles across the interface were obtained. The interfacial diffuse layer, with a double unit cell with respect to NiO identified by GIXD, has effectively been observed

Fig. 74. EF-TEM images of the sample corresponding to Figure 73. The zeroloss image (a) shows the resolution and the overall morphology. (b), (c), and (d) are the maps for which the white zones in the image correspond to O, Fe, and Ni, respectively.

on HR-TEM images (Fig. 73). The different layers are clearly separated and are easy to identify because the different structures yield different contrast. The poor crystalline quality of the diffuse region appears in TEM as well as in GIXD, and the images are compatible with a diffusion process. Note that NiO and the Py film are of excellent crystalline quality without any detectable defects. The lattice parameter of the inverse spinel structure of Fe2NiO4 (trevorit) is about twice as large as that of NiO, which leads to positions of new Bragg peaks at about half the distance between NiO peaks. Diffraction TEM images taken in the interface region confirm that the lattice parameter observed in GIXD corresponds only to the diffuse zone. A detailed observation of the HR-TEM images reveals that the Py/spinel interface becomes wavy and remains quite smooth, whereas the spinel/NiO interface is much rougher. This leads to the idea of a diffusion process at the interface into the NiO(111) substrate. In quantifying this result more precisely, EF-TEM images were most helpful (Fig. 74). As concluded from the GIXD coverage estimation (Fig. 70) and the occurrence of strong Py CTRs (Fig. 72), the film is smooth and 2D (Fig. 74a). For oxygen the interface is sharp, showing that there is an oxide region and a metallic region without oxygen (Fig. 74b, O K edge). The iron (Fig. 74c, Fe L23 edge) and nickel (Fig. 74d, Ni L23 edge) are more interesting. Between the NiO substrate and the Py film, an Fe-rich (resp. Ni-poor) region alternates with an Fe-poor (resp. Ni-rich) region. However, these images are only qualitative. A semiquantitative approach is possible here with the use of the NiO and Ni80Fe20 known compositions [253] and a refer-

584

BARBIER ET AL.

Fig. 76. VSM-measuredcoercivefield and magnetic exchange couplingfor a 10-nm Py/NiO(111) sample grown at 630 K with respect to the measurement temperature. Fig. 75. Concentrationof O, Ni, and Fe across the interface of the sample corresponding to Figure 73. The profiles were obtained by integrating across the interface slides of energy-filtered electron microscopyimages.

ence trevorit (Fe2NiO4) sample, which permits determination of the scattering cross section for each element in each compound. The resulting composition profile across the interface is reported in Figure 75. As a matter of fact, the interfacial spinel compound does not correspond to stoichiometric Fe2NiO4, but it lacks in Fe. The interfacial layer is thus rather of the Ni~Fe3_~O4 composition, where ~ varies continuously across the interface, between 1 and 2. Indeed, the lattice parameter of such a compound is not expected to significantly vary for 1 < ~ < 2, making the investigation of the composition change through the interface nonobservable for GIXD. The diffusion profile of Fe into the NiO(111) substrate across the interface is responsible for the large composition range. Moreover, the interface is strongly wavy (Fig. 73), and because the interface morphology may also extend along the other directions, the chemical images and profiles are certainly blurred because of the integration through the sample. However, the HR-TEM estimated thickness for the interface compound is in the 2.5-3 nm range and is in good agreement with the thickness deduced by GIXD from the e-widths of the spinel Bragg peaks (3.6 nm). The Ni-rich region was undetectable by GIXD because Ni and Py have close parameters. Interestingly, HR-TEM images indicated a network of dislocations 1.5 nm apart in the Py film along the [ 112]Cube direction, which is close to the 1.77-nm value expected from the triangular coincidence network for Ni (or Py) on NiO(111). This network fully explains the full relaxation of the Py film. In contrast, no network could be detected in the spinel compound, showing that the spinel/NiO interface is coherent. In this latter case the relaxation is likely to occur through the wave-shaped plastic deformation of the interface. One might now suspect the initial interface, built at 650 K, to already be diffuse. During the deposition process, as well as at

the end of the growth, plane scans, even at large incident angles ('~2Ctc), show no presence of additional peaks. From GIXD we concluded that diffusion starts to occur around ,~630-650 K. However, to observe a signal coming from the spinel structure, it must be of a minimal crystalline quality and thickness. HRTEM and EF-TEM would place the onset of diffusion at slightly smaller temperatures, because around 600 K a tiny contrast is observable on the Py/NiO interface, extending over a very few atomic planes. In the present section we have shown that annealing a Py layer at temperatures above 650 K leads to an interfacial compound. For its quantification HR-TEM and EF-TEM proved to be excellent complementary techniques to GIXD.

5.3.3. Magnetic Properties We have seen that the Py/NiO(111) system can be prepared with a controllable crystalline quality and that flat and continuous 2D films can be obtained. Py is a soft magnetic material and is only used as a soft sensing layer in sputtered spin valves. What about the magnetic properties of Py on single crystalline NiO(111)? Is it exchange coupled and is it usable? To answer these questions we have performed VSM measurements for Py films deposited in the 600-650 K temperature range. The VSM hysteresis loops were measured from 300 K down to 15 K. Figure 76 shows the evolution of the coercivity and of the exchange field with respect to the temperature. The general behavior is very similar to that observed in the Co/NiO(111) case. The coercive field increases nearly linearly with decreasing temperature, and the magnetic exchange field appears below 100 K, proving that the Py layer undergoes unidirectional magnetic exchange coupling. Interestingly, the coercive field for a 10-nm Py film is already huge at room temperature (180 Oe), nearly two orders of magnitude larger that the coercive field expected for a sputtered permalloy film. Thus the Py layer is pinned by the NiO substrate and acts as a hard magnetic layer. Moreover, it has been shown for sputtered Py/NiO(11 l) films

SYNCHROTRON STUDY OF OXIDES AND METALS that the room temperature exchange field decreases with increasing NiO grain size [254], again highlighting the idea that the large increase in coercivity is a phenomenon that is more intrinsic to the exchange coupling than the exchange field, which is related to the grain boundaries in the antiferromagnet. It is thus likely that the uncompensated spins at the grain boundaries have a major role in the hysteresis loop unidirectional shift. Large coercive fields and exchange fields appearing only at low temperature seem to be characteristic for single crystalline ferromagnetic/antiferromagnetic interfaces. As in the case of the Co/NiO interface, the coupling energy J was calculated (J = Ms0pyHc, where Ms is the spontaneous magnetization of the Py layer, 800 emu/cm 3 for the bulk Py). The value obtained for J is as large as ~0.12 erg/cm2; it is in fact fully comparable to the coupling energy of a sputtered Co/NiO interface (0.11 erg/cm 2 [238]). Hence, from a magnetic point of view, a single crystalline Py/NiO(111) interface is worth a sputtered Co/NiO(111) interface, and, thus, our Py layers can be used as pinned hard magnetic layers in fully epitaxial spin valves [255]. To summarize, growth conditions able to provide single crystalline 2D Py layers on NiO(111) were determined. The p(2 x 2) reconstruction of NiO(111) is confirmed to vanish through metallization. Annealing above 650 K leads to a spinel interfacial compound because of the diffusion of Fe into the NiO(111) substrate. The full characterization of the diffuse interface was only possible through the combination of GIXD, HR-TEM, and EF-TEM. The magnetic properties of the single crystalline Py/NiO(111) interface are surprising and allow the use of Py as a hard magnetic layer.

6. GROWTH OF NICKEL OXIDE

6.1. NiO(111)/r

(0001)

In Section 5 we have seen that ferromagnetic films deposited on single crystalline NiO(111) have interesting magnetic properties. In particular, giant coercive fields can be obtained through exchange coupling, allowing for the use of fairly large ferromagnetic film thickness. Such a situation is very favorable with respect to device elaboration, because the final spin valve would be less sensitive to surface defects and pinholes. Because sputtered NiO(111) films were reported on ot-A1203(0001) [256-258], it was interesting to investigate the MBE growth of NiO on this surface to determine the best growth conditions (if they exist) for obtaining single crystalline NiO(111) films. Moreover, for sputtered NiO(111) films, the influence of the crystalline quality on the magnetic properties for NiO films was investigated in previous studies [215,216, 232, 234, 235, 239, 259, 260]. However, the crystallographic quantitative analysis of such films is quite difficult. In contrast, the use of MBE prepared films allows for a quantitative characterization because of their better crystallographic quality. We have thus undertaken the structural study of MBE-grown NiO(111) films on ot-A1203 (0001) with respect to the growth temperature (320-700~ and to the thickness (29-200 nm).

585

Several samples were prepared, at four different deposition temperatures: 620, 700, 800, and 1000 K. NiO films were obtained by Ni evaporation in an oxygen atmosphere, by electron bombarding a metallic Ni rod of 99.99% purity. During Ni evaporation, the oxygen pressure was kept constant at 2 x 10 -4 Pa, as was the deposition flux of the Ni source (0.2 nm/min, calibrated with a quartz microbalance). A thickness of 200 nm was achieved for all temperatures. Three additional samples were prepared with different thicknesses: 30 nm and 150 nm at 700 K and 170 nm at 1000 K. The thicknesses were checked by X-ray reflectivity. The reflectivity signal rapidly damps, showing that the prepared NiO surfaces are rough. Polished and cleaned ot-A1203 (0001) substrates were used. All of our substrates were annealed at 1170 K under an oxygen pressure of p(O2) = 5 x 10 -3 Pa for 10 min and then checked by LEED and by X-rays: well-crystallized samples were obtained, with a near-surface mosaic spread of 0.0040-0.009 ~ (for more details, see the preparation of sapphire substrates, Section 3.3). LEED patterns were recorded for each sample at the end of the deposition, whereas the morphology was investigated by tapping-mode air-AFM. The crystallographic structure of the samples was then investigated by ex situ GIXD. The measurements were performed with a four-circle GMT diffractometer on the BM32 beamline at ESRF [ 15]. To reduce the absorption of X-rays by air, the samples were mounted in a small vacuum chamber (pressure in the 10 -3 Pa range), basically consisting of a beryllium cylinder. In GIXD, the samples were illuminated by a well-focused (size at sample: 350/~m horizontal • 500/~m vertical FWHM) 18-keV X-ray beam under an incidence angle on the order of the critical angle for total external reflection of the sample. The penetration depth can easily be varied from a few nanometers up to tens of nanometers by increasing the incidence angle. An incidence angle of 0.3 ~ larger than the critical angles for total external reflection Ore of NiO (0.17 ~ and ot-A1203 (0.13~ was used, to get the signal from the whole NiO film, even for thicknesses of tens of nanometers. At large incidence angles the ot-A1203 substrate signal was also detected. The reciprocal in-plane unit cells of ot-A1203 (0001) and relaxed NiO(111) are shown in Figure 77. The intersections of different CTRs with the surface plane are also indicated. The in-plane Bragg peaks unambiguously permit to identification of the presence of different in-plane orientational relationships between NiO and ot-A1203 (0001). LEED patterns were taken in situ before and after oxygen annealing of the sapphire substrate, as well as once the targeted thickness of the NiO film was achieved. The typical patterns before and after the deposition of a film at 1000 K are shown in Figure 78 for the same sample. The reciprocal unit vectors of the substrate and of the NiO film are rotated by 30 ~ Moreover, the NiO film exhibits a six-fold symmetry. Compared with the possible epitaxial relationships (Fig. 77), the LEED patterns correspond to a FCC plus twinned FCC NiO(111) film on ot-A1203 (0001), with the NiO(111) in-plane cell rotated by

586

BARBIER ET AL.

Fig. 77. In-plane view of the reciprocal space of the NiO/A1203(0001) interface. Different epitaxial relationships are shown. Represented reciprocal unit cells: A1203(0001) (OABC circles, continuous line); a possible orientation of NiO(001) (gray squares); NiO(lll)R0 ~ (ODEF, grey hexagonal cell with (lll)NiOIl(0001)sapphire (h00)NioIl(h000)sapphire); NiO(lll)R30 ~ (OGHI, dashed line, (111)NiOII(0001)sapphire (hh0)NiOII(h000)sapphire. For the sake of clarity, twinned orientations are not shown. They can easily be obtained by rotating the reciprocal unit cells of NiO by 60~ Symbols represent different types of NiO CTRs (in NiO r.l.u.): (1 le)-like rods (filled symbols), with Bragg peaks at e positions that can be expressed as e = 3 • K; (10e)-like rods (open symbols), with Bragg peaks at e = 3 x x + 1; and (01e)-like rods (gray symbols), with Bragg peaks at e = 3 x tc + 2.

Fig. 78. LEED patterns for (a) the oxygen-annealed substrate and (b) after NiO deposition at 700~ The projections in the surface plane of the reciprocal unit cells are also shown. Peaks appear at different energies after NiO deposition. 30 ~ with respect to the sapphire substrate. The FCC variant will be called R30 ~ and the twinned FCC variant (i.e., rotated by 90 ~ with respect to A1203), R90~ the respective epitaxial relationships are NiO(111)11ot-A1203 (0001), (110)NiO I1(1000)sapphire an d Ni O ( 111 ) II~- A 12O 3( 0001 ), (110) NiO II (~- 100) sapphire. A F M images were taken for all samples to determine the morphology of the NiO films. Some of the investigated situations are shown in Figure 79a-f. For all of our samples, a background layer made of triangular pyramids, which have different dimensions, depending on the preparation conditions, is found. The roughness of the NiO films varies with the thickness and deposition temperature. The smallest roughness is found

for the thinner NiO layer deposited at 1000 K, probably because the NiO islands are just about to be formed. The 200-nm thickness samples are very rough; the height of the NiO islands can be several tens of nanometers. The general trend is an increase in the roughness of the film with temperatures above 700 K. For the same thickness of NiO (200 nm) prepared at different temperatures, the sample prepared at 700 K has the smallest roughness. Figure 79a-e shows the morphology for two situations: the 200-nm NiO deposit at 620 K and 700 K. The images obtained for the other samples are quite similar. The shape and dimensions of the islands may change, as seen by AFM. Note that the color scale used in Figure 7 9 c - f (i.e., where the height scale is not reported) does not represent the real measured heights but the variation in the amplitude of the vibrating AFM tip. In this case, the contrast is enhanced for small details in the morphology. Several features are visible. In images similar to Figure 79d the angle of the facets with respect to the surface plane can easily be measured. The quantitative measurement was made on real height images; these facets are found to form an angle of 54 ~ 4- 4 ~ with respect to the mean surface plane. In addition, the angles between the comers of the triangular facets were found to be close to 120 ~ 4- 10 ~ (threefold symmetry). Indeed, the angle between the (111) and (100) planes is 54.7 ~ The pyramid has a threefold symmetry axis perpendicular to the (111) plane; a top view shows angles between comers of facets of 120 ~ The pyramids thus expose (100) facets of NiO(111). (110) facets (expected angle of 35.26 ~ were not found.

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 79. Tapping-mode air images for different samples. The thickness of the NiO film and preparation temperature (Tdeposit) are shown on each image, as is the scanned size. (a)arid (b) real heights grayscale maps. (c) (100) faceted pyramids (FCC and twinned FCC, marked by arrows; the arrow on the right side of the figure shows two neighboring islands rotated with respect to each other by 60~ square (100) facets (.), and square corner-truncated (o) islands. (d) The angle measured along the OM direction is 54 ~ 4- 4 ~ and AOB = 120 ~ 4- 10~ (e) Hexagonal islands (.) on the triangular pyramid background layer. (f) Triangular pyramids (FCC and twinned FCC) with (100) facets tilted by 54 ~ 4- 4 ~ (e.g., along the OM direction) and square (100) facets with AIOB f = 90 ~ 4- 7 ~

The shape of the islands strongly depends on the preparation conditions. We first notice flat hexagonal-like shapes for the 700 K prepared samples, which can be assigned to the (111) NiO surface plane. AFM images show a tilt of about 12 ~ 4- 5 ~ between the surface of these hexagons and the basal surface plane, along directions having again a threefold symmetry. Square islands, probably (100) facets, are also present for extreme preparation conditions (200 nm at 640 K and samples at 1000 K). In this case, the in-plane orientation cannot be addressed by AFM measurements. Some of these (100) facets have corners truncated by (111) facets (Fig. 79c and f). Concerning the majority NiO structure, NiO(111), the presence of twins can be identified even in AFM images. Indeed, the triangular (100) faceted NiO islands, having a (111)NiO basal plane, will show different orientations of facets if twins are present. For example, in Figure 79c, two types of islands, with

587

facets rotated by 60 ~ with respect to each other, can be seen. On the fight-hand side of the image, an arrow shows two neighboring triangular islands with their bases rotated by 60 ~. The morphological analysis thus indicates the presence of twinned NiO(111) on the prepared layers. If the AFM images allow the determination of the morphology of the NiO film and some crystallographic features, the epitaxial relationships mentioned in Figure 77 cannot be distinguished. This is due to the lack of information in AFM about the crystallographic orientation in the ot-A1203(0001) substrate with respect to the recorded image. Indeed, atomic resolution is not possible, and the substrate is completely covered by the NiO film. Moreover, only a very small surface fraction is investigated in AFM. To fully characterize the NiO films, X-ray diffraction was used to probe their crystallographic structure. The ot-A1203 (0001) triangular unit cell parameters were a - b - 4.754 ,~, c - 12.99 A, ot = /3 - 90 ~, and F -- 120~ (see Section 3.3). Because the LEED patterns support the (111) epitaxy of NiO (Fig. 78), we describe NiO by the usual triangular unit cell, with acube -- 4.177 ,~, so the unit cell vectors are a - b -- 2.95 ,~ and c - 7.235 ,~, with ot = fl = 90 ~ and F = 120~ The in-plane cell parameter misfit is thus ( 4 . 7 5 4 - 2.95)/4.754 = 37.9%. Figure 77 illustrates how the different possible crystallographic structures and orientations of the NiO layer can be distinguished. Along a CTR of NiO(111), the Bragg peaks lay out of the plane of the surface, and they are well separated for the FCC and twinned FCC structures. The stacking perpendicular to the surface can be extracted from the specular (00~) rod. The characteristic interplane distances in the samples are determined from the peak positions. Particular expected out-of-plane distances are 7.235 ,~ (c axis of the NiO(lll)IIA1203(0001) FCC and twinned FCC stacking, giving peaks at s = 5.4 • x, expressed in A1203 reciprocal lattice units (r.l.u.), where x is an integer) and 4.177 ,i, (c axis of NiO(100)11A1203 (0001), giving FCC characteristic peaks at ~ = 2 x 3.1 x x A1203 r.l.u., where tc is an integer). However, the in-plane orientation of the (111) or (100) NiO plane with respect to the substrate cannot be assessed from (00~) measurements. For that purpose, large inplane rocking scans, with constant Q II, for example, along the circular segment EH in Figure 77 and radial scans along (h00) or (hhO) directions, are necessary. The two sets of measurements were performed for all of our samples. Both NiO(100) and NiO(111) stacking was observed along the specular (00~) rod. In the following, if not otherwise specified, ot-Al203 r.l.u. are used. In all cases, along the (h00) direction of sapphire, Bragg peaks were found at h = 1.61 ~ -- 2.78 r.l.u., indicating an in-plane NiO unit cell rotated by 30 ~ with respect to that of the sapphire. This confirms not only that the LEED result is due to the surface layers, but that the structure is characteristic of the whole film. The NiO rod (at 2.78/3 = 0.93 r.l.u., (0.93 0.93 ~) at point I in Fig. 77) crosses Bragg peaks, which are distinct for FFC (~ = (3 x x + 1) • 1.8) and twinned FCC stacking (~ = (3 • tc + 2) x 1.8, where tc is an integer; Fig. 80b). Rocking scans at FCC and twinned FCC positions permit an estimation of the

588

BARBIER ET AL.

Fig. 81. Rocking scans at Qll = 2.78 c~-A1203 r.l.u. Peaks denoted by NiO(111)R30 ~ and NiO(111)R0 ~ correspond to H and E points in Figure 77.

Fig. 80. X-ray intensities measured along different directions in the reciprocal space. (a) (0, 0, s Tdeposit -- 320~ (b) (0.93, 0.93, s Tdeposit -- 700~ (c) (h, 0, 0) and (h, h, 0) directions; Tdeposit = 700~ These scans were selected from different samples to highlight the possible NiO crystallographic structures with respect to the sapphire. Positions where scattering is expected are indicated.

quantity of both ways of stacking in the film. For all of our prepared films, the FCC and twinned FCC NiO(111) structures were found to be present in about the same proportion, with a small preference for the twin orientation (NiO(111) R90~ This result contrasts strongly with the Co and Py growths on NiO(111) (Sections 5.2 and 5.3). Indeed, in the present case the substrate is six-fold and the epilayer has three-fold symmetry. A resulting 1 : 1 nucleation rate of the two variants is thus not surprising. Large in-plane rocking scans at all = 1.61~/3 = 2.78 r.l.u. indicate the presence of unrotated NiO(111)R0 ~ Corresponding twins of this unrotated structure are also present (R60 ~ in Fig. 81). Integrated intensifies show that less than 0.9% of the NiO layer adopts this unrotated structure for samples prepared in extreme conditions (620 K and 1000 K deposits). This is also confirmed by in-plane scans along the (hhO) direction, where the NiO(111)R0 ~ peak is expected at the (1.61, 1.61, 0) position in reciprocal space. Moreover, scanning along the (hhO) in-plane direction, a small peak is present at h = k =

1.61 ~/~ = 0.93 r.l.u. ("I" point in Fig. 77: it is the intersection of a NiO(111)R30 ~ CTR with the surface plane), showing the presence of the a (111) surface of FCC NiO(111). It confirms the existence of some relatively flat portions of a (111) surface for the deposited NiO. Figure 80 shows examples of measured intensities along different directions in the reciprocal space. The positions where scattering is expected for the different structures are shown. The quality of different NiO variants of the film can be addressed by analyzing the peak widths at different in-plane Q Ii positions to deduce the mosaicity and the diffracting domain size. The NiO(111) fraction (either FCC or twinned FCC) has a similar quality for all of the films: a mosaic spread between 0.8 and 1.7 ~ and a diffracting domain size generally larger than 10 nm. The NiO(100) variant, when present, is of very poor crystallographic quality; the intensity of the signal is spread out over several degrees (5-8~ We did not find any preferential in-plane orientation of NiO(100) with respect to the sapphire unit cell. It is likely that the observed signal on the specular rod (yielding to characteristic distances in NiO(100)) comes, in fact, from (100) stacking faults in NiO(111) or from very small NiO(100) crystallites embedded in NiO(111). Let us now discuss these results with respect to other NiO films. Sputtered NiO(111) films have already been used as pinning AF layers to elaborate spin-valve read heads [127, 202, 224]. For industrial applications, this preparation method is faster and cheaper than MBE, and the films obtained are much smoother. Relatively high deposition rates lead to sandwiches of several well-defined layers without pinholes between them, permitting the elaboration of functioning devices. However, this method also has some drawbacks; the NiO target crystallizes easily and may become rapidly unusable. It did not permit a complete understanding of the structure of the interfaces during growth or the role of each parameter (roughness, texture, diffusion at interface, etc.). Indeed, some of the reported resuits contradict each other. Generally, the exchange coupling is

SYNCHROTRON STUDY OF OXIDES AND METALS believed to be an interface effect [211], although some studies report different assumptions [228]. Some authors claim, in contradiction to existing theories [215, 216, 235, 246, 247], that the NiO texture, for the spin-compensated as well as for the uncompensated planes, does not really influence the exchange coupling. On the other hand, other studies report increases or decreases in the coupling when the uncompensated (111) surface of the NiO is used [232, 237]. Except for the better crystalline quality and the identification of all stacking, our resuits are comparable to similar studies of sputtered NiO films or NiO-CoO multilayers elaborated on sapphire [257,258], where the presence of twins was explained as being induced by steps on the surface of the substrate. This structural behavior is thus likely to be intrinsic to the interface. MBE-grown films represent an alternative approach in which films of good crystallographic quality can be expected at smaller deposition rates. One can also expect to better control each parameter. Unfortunately, our NiO films are much too rough, whatever the temperature and thickness growth conditions, to be used as antiferromagnetic substrates in a spin-valve device. Their magnetic properties for sensors are thus not accessible. In the range of explored parameters, the 700 K prepared film looks to be the smoothest. Our GIXD data show that the growth of NiO on sapphire is epitaxial within a twinned FCC scheme and (100) stacking faults or inclusion of very small (100) crystallites. The NiO(111) unit cells are rotated by 30 ~ for the FCC and twinned FCC stacking with respect to the ct-A1203 (0001) unit cells. The low-temperature growth shows the additional presence of small quantities of NiO(111)R0 ~ The unit cell parameter evolution does not indicate strain in the NiO films, and only stoichiometric NiO was found, highlighting the high stability of this structure for nickel oxide. Quantitative measurements permitted estimation of the fraction of each structure as well as the corresponding crystallographic quality. The complementary use of LEED patterns, AFM images, and X-ray diffraction showed that the crystallographic quality of MBE-grown films is comparable to that of sputtered films. However, our films are rougher in the whole range of the parameters we have investigated. Indeed, the small deposition rate in our case (a few angstroms per minute) favors the formation of islands with complex morphologies during growth. Conditions in which the NiO film is perfectly 2D were not found. We do not expect a different magnetic behavior from our films with respect to sputtered ones (inasmuch as the qualities look comparable, except for the flatness of the surface), and because spin-valve elaboration needs flat interfaces it does not seem straightforward at all to build epitaxial spin valves on c~-A1203(0001). The elaboration of single crystalline spin valves is a challenge that seems difficult to tackle with NiO films on sapphire. The present results support a growth mode in which at the beginning, a layer made of micropyramids is formed. Depending on the growth conditions, these pyramids grow more or less homogeneously. Because the NiO(111) surface is polar and relatively stable (see Section 3.4), its surface energy remains very

589

large compared with that of NiO(100). For MBE growth of NiO films, this fact may prevent the elaboration of single crystalline NiO(111) epitaxial surfaces because of the onset of NiO(100) facets at small growth rates. 6.2. N i O ( l l l ) / A u ( l l l ) The NiO(111) single-crystal surface is a good insulator at room temperature, and its conductivity drops sharply when the temperature decreases [261], preventing any investigation with electron-based techniques because of charge build-up. As a matter of fact, NiO(111) thin films, which are more adapted to many techniques, were investigated well before the single crystals because of the very intriguing predictions [98, 105] stating that this polar surface could be stable through the Niterminated [98] p(2 x 2) octopolar reconstruction [105]. A p(2 x 2) LEED pattern was reported for films grown at 550 K on Au(111) [94, 107] and for films grown at room temperature on Ni(111) [ 108]. On NiO/Ni(111) films, the pattern disappeared when water was introduced into the chamber because of hydroxyl adsorption and was restored upon annealing. However, this result contradicts a previous LEED work on the oxidation of Ni(111), where only c(2 x 2) and (7 x 7) reconstructions were reported [262]. On the other hand, only the reconstruction pattern has been reported, and not the structure of the reconstruction itself. Thus it was interesting to know if these films, grown in out-of-equilibrium conditions, adopt the oxidized or reduced NiO(111)-p(2 x 2) surface reconstruction to achieve stabilization. Because the reported LEED patterns for NiO/Ni(111) showed poor order and NiO/Au(111) showed excellent contrast, we have chosen to investigate the NiO/Au(111) interface by GIXD [94], which has proved to work quite well for single crystals (see Section 3.4). The GIXD experiments were performed on the ID03 surface diffraction beamline at the ESRF [15] in ultra-high-vacuum conditions (10 -1~ mbar). The thin NiO film was measured at 17 keV and a 0.9 ~ incidence angle because the bulk scattering from the Au(111) substrate was weak in the regions of interest. The crystallographic basis vectors for the surface unit cell describe the triangular lattice of the reconstruction. They are related to the bulk basis by asurf = [110]Cube, bsurf = [011 ]Cube, and Csurf = [111]Cube. The h and k indexes describe the inplane momentum transfer (in reciprocal lattice units (r.l.u.) of the NiO(111) reconstruction), and s the perpendicular momentum transfer. The NiO(111) thin film was prepared in situ on Au(111) [ 107, 108]. The surface used for the growth had a mosaicity of 0.052 ~ and a domain size of 2600 A exhibiting the herringbone reconstruction [263]. During deposition the substrate was held at 615 K, which was found to be the optimal growth temperature, and the Ni was evaporated from an electron-bombarded Ni rod in a 2 x 10 -5 mbar partial pressure of 02. A perfect 2D growth has been observed (by reflection high-energy electron diffraction (RHEED) and GIXD) from three to eight monolayers before 3D crystallites formed. For the quantitative analysis we have chosen an intermediate thickness of 5 ML.

590

BARBIER ET AL.

Fig. 82. Comparison of the Patterson maps of a 5-ML NiO(111) film on Au(111) and of the single crystal (SC).

The NiO(111) thin film was in good epitaxy, of surprisingly good crystalline quality, completely relaxed and p(2 x 2) reconstructed with 0.106 ~ mosaicity. It had a domain size of 550 A, was intense throughout the accessible region of reciprocal space, and had a perfect Lorentzian shape. This behavior is very different from the metal growth we discussed in Sections 4 and 5, which exhibited large mosaicities (several degrees) in the early stages of growth. The in-plane scattering of the p(2 x 2) pattern was measured quantitatively by rocking scans at all accessible positions belonging to the reconstruction in reciprocal space. Fifty-nine nonzero in-plane peaks were measured at s = 0.3, and the diffraction pattern has P3m 1 symmetry, leaving 32 nonequivalent peaks with a systematic error level of 11%. The largely different symmetries between the P6mm single crystal and the thin film cannot be explained by the small s difference, but indicate rather a different p(2 • 2) structure. In fact, both symmetries should be P6mm in the strict s = 0 surface plane, but the thin film deviates more firmly from this in-plane symmetry than the single crystal does. A direct comparison of the Patterson maps for the thin film and the single crystal is reported in Figure 82, showing that the structures are unlike. Moreover, 13 diffraction rods with 322 nonzero structure factors were measured, and their periodicity along s clearly indicates a reconstruction that is three atomic layers thick, further evidence that the thin film structure cannot match any of the known single crystal reconstructions. As intuitively expected from these simple observations, the octopolar reconstruction cannot reproduce the in-plane data, regardless of the relaxations or the termination (X 2 > 8). A coherent juxtaposition of half Ni- and half O-terminated domains separated by single steps yields the experimental Patterson map (provided that the bases of the two octopoles have

Fig. 83. Top and side views of two possible octopolar reconstructions with Ni- or O-terminated terraces (left and right, respectively), separated by a single step (solid line). The octopoles, on both sides of the step, have identical orientations, as shown by the triangles at the top of the figure. Large circles are oxygen atoms, and small circles are nickel. For either termination, the top two layers are 75% and 25% vacant compared with the bulk lattice. The possible symmetry-compatible relaxations, 8 and (, are shown as arrows indicating a positive relaxation.

the same orientation). The structure was refined, as for the single crystal, with the use of the same relaxations plus a domain fraction, the roughness, and a scale factor. The structural model is shown in Figure 83. The symmetry-related atomic relaxations in each atomic layer are indexed with respect to p, where p = 0 for the apex layer of atoms. Three of the four atoms in layer p of the unit cell have symmetry-related vertical displacements ~'pS, whereas the independent atom has vertical displacement ~p. Likewise, 8pS defines a radial displacement of symmetry-related atoms away from the in-plane position of the apex atom. Because this model contains a large number of atoms, the convergence of the fitting procedure was difficult, mainly because of local minimums. We have thus preferred an approach with identical relaxations in the two domains, so that ~'0 is the perpendicular relaxation of both apex atoms, and so on (Fig. 83). The best stable solution remained essentially unchanged when we allowed independent relaxations in

SYNCHROTRON STUDY OF OXIDES AND METALS

Fig. 84. Comparison between the experimental and calculated structure factors for a model with Ni- and O-terminated octopoles separated by a single step. (a) Diffraction rods: from bottom to top, 90s 71s 51s 41s 33s 30s 70s 32s 10s 31s 50s 7is and 41s O and 0, experimental data points.--, calculated structure factors. (b) In-plane structure factors. Right, experimental; left, calculated.

the two domains. Only three relaxations were nonnegligible. The best agreement was obtained for 61s - 0.096 + 0.008 A, 62s = 0.078 + 0.007 i , and (0 = -0.103 4- 0.028 A, with 50% Ni- and 50% O-terminated domains, a 1 - i r.m.s, roughness, and a global X2 of 1.4, close to the ideal value of 1. This solution reproduced all of the data well, as can be seen in Figure 84. The agreement is very good up to large momentum transfers, definitively supporting this two-variant octopolar reconstruction. Note that, in contrast to double steps, the single step belongs to the model itself and thus will not influence the coherence length (550 i ) , i.e., the single steps may be located anywhere and do not necessarily form large continuous step edges. This might explain why STM investigations, although for thinner layers, have mainly reported double steps, because they really define the step edges [107]. Here again, Wolf's octopolar reconstruction is the basis needed for the interpretation of the data. However, the sin-

591

gle crystal exhibits only Ni-terminated double steps, and the thin film can adopt both terminations and therefore single steps as well. We note that the thin film was grown under nonequilibrium conditions. At 615 K, Ni has a limited mobility on NiO, inasmuch as Ni clusters appear only at higher temperatures on NiO [91, 93]. The atomic flux ratio of O" Ni was roughly 1000" 1 on the surface. For these reasons, the growing surface necessarily passes through nonequilibrium structures to fill the incomplete lower layers. Indeed, a perfect Ni-terminated octopolar domain could be transformed into O termination via incorporation of a half-monolayer of nickel and a half-monolayer of oxygen atoms. We propose that the observed O-terminated regions are relatively stable metastable domains that are achieved during the special conditions of growth. Because Au does not easily oxidize, we can assume that the interfacial layer is Ni. Ni- and O-terminated octopolar structures are electrostatically equivalent. For the thin film, each Au(111) step will place unlike layers at the same height, causing an accumulated electrostatic energy that may be responsible for the sudden change from two- to three-dimensional growth after 8 ML. An alternative approach to the trial-and-error method for which the structure is guessed and the corresponding structure factors are calculated is the so-called direct methods. Information about the phases of the structure factors that is lost in a diffraction experiment is needed to restore the charge density. In the last few years, the direct methods approach has been adapted to 2D X-ray diffraction [264-266]. This method solves the phase problem by exploiting probability relationships between the amplitudes and the phases of the diffracted beams to determine a plausible initial solution. The method used for the p(2 x 2) NiO (111) structure (with the GIXD data under discussion) involved a minimum relative entropy algorithm combined with a genetic algorithm for global optimization [267,268]. The algorithm searches for the set of phases with the lowest figures of merit. The corresponding solutions are used to create electron density maps that obey the imposed symmetry. In the final step, the atomic positions were refined by the least-squares method. This approach cannot handle several structural domains but reaches an acceptable solution with a similar X2 of 1.37 over all of the data [269]. The corresponding structural model is drawn in Figure 85. It is essentially made of a particular combination of two embedded octopoles. The apex atom of the underlying O-terminated octopole is included in the basal plane of a more external Ni-terminated octopole (they are thus naturally oriented the same way). The net result is a 75% Ni vacant top plane, a full O plane, a 25% Ni vacant plane, and then bulk NiO(111). The relaxations are small. Thus the basic units needed to construct the two models are the same and the agreements are close. Here we hit another limitation of GIXD: the possible nonuniqueness of the model, even with good X2 values, due mainly to the fact that the phase information is lost. The direct methods model, however, exhibits 25% vacancies in the third layer, which does not seem easy to understand within

592

BARBIER ET AL. films may thus only be carefully extrapolated to the bulk surface.

7. CONCLUSIONS

Fig. 85. Structuralmodelfor a 5-MLNiO(111)filmon Au(111)derivedfrom the direct methods approach. The patterned squares highlight the vacant Ni atoms in the third layer.

a growth process, and it is hardly of any help to explain the onset of 3D growth after 8 ML. On the other hand, the growth was performed at 615 K, and limited atomic mobility exists. Additional experiments would be necessary to unambiguously differentiate between the two possible models. In particular, the direct methods model would lead to ferromagnetic oxygen because of the vacancies. Unfortunately, a dichroism experiment seems very difficult to carry out on the O K-edge because of the tiny cross section, and the total expected magnetization is well below the detectable level of the most sensitive magnetometers. Thus we should conclude that unlike the NiO(111) single crystal, which exhibits a clear Ni-terminated octopolar reconstruction after air annealing, the NiO(111) thin film has another p(2 x 2) surface reconstruction that combines in one way or another the two octopolar terminations with small relaxation. The stability of this surface against hydroxylation was tested by extensively dosing the surface with up to 106 Langmuir of H20 at a partial pressure of 3 x 10 -5 mbar at room temperature. Similarly to the single crystal case, no structural effect could be detected. This stands in contrast to the NiO(111) films of poor structural quality made by oxidation of Ni(111) [ 108, 270], which were found to be unstable against hydroxylation. We thus suggest that the reactivity of NiO(111) against water takes place mainly at defects (as for MgO [271]), which are almost absent on our surfaces and thin films. Our main conclusion is that NiO(111) is terminated and stabilized by a p(2 x 2) reconstruction, but the internal configuration may change a great deal from one experimental condition to another. The electrostatic criterion is always fulfilled, however, and because the electrostatic driving force is strong enough to stabilize the surface reconstruction, even in air or water (only metallization seems to be more stable), it is clear that this criterion is very important when polar surfaces are considered. Interestingly, the octopolar reconstruction prediction and the observation of the p(2 x 2) surface cell were not enough to understand the polar NiO(111) surface. Note also that oxide thin films may not exhibit the same surface structure as their bulk counterpart. The studies carded out on thin oxide

Let us now re-examine the questions raised in the Introduction concerning the structure and morphology of growing interfaces. For all systems we have determined the growth modes, the crystalline quality of the epilayer, and the epitaxial relationships and quantitatively discussed the morphology with respect to the deposited thickness. For exchange-coupled interfaces we have seen that the structure plays a determining role in the overall properties of the heterostructure. Several relaxation mechanisms of the interfacial strain due to lattice mismatch were observed: well-ordered dislocation networks at the buffed Ag and Pd on MgO(001) interfaces; several epitaxial relationships and variants that cancel the strain in Ni on MgO(001), and plastic deformation of the interface with growth of an interfacial compound in Py/NiO(111). For the Ag, Pd, and Ni on MgO(001), we have identified the O epitaxial site. The use of surfactants was also questioned, although the extrapolation from homoepitaxy to heteroepitaxy must be taken with care and some reactions like O with Co may only mimic a surfactant effect. The crystalline quality of the NiO(111) substrates on the nucleation of Co clusters was quantitatively investigated. In the present review we have thus discussed a number of typical situations that may arise during growth, on substrates that are insulating or not. We have shown that in situ synchrotron radiation investigations are often able to draw clear and quantitative answers, for a very wide range of situations, ranging from perfectly sharp interfaces (metal/MgO(001)) to highly reactive ones (Py/NiO(111)) and from single crystalline 2D epitaxial growth (NiO(111)/Au(111)) to fairly polycrystalline islands (Co/NiO(lll)). Thus these studies show that grazing incidence X-ray diffraction is not limited to the wellestablished description of surface reconstructions and relaxation, although this works nicely for oxides too, as seen for MgO(001), NiO(111), or tz-A1203 (0001). Describing the growth of metals or oxides on metals or oxides, especially when coupled to GISAXS, AFM, or TEM, can be described with a high level of detail. Thus although the number of techniques is reduced for insulating materials, the now available in situ synchrotron radiation techniques are really powerful and allow investigation of this class of materials with a high level of confidence and accuracy.

ACKNOWLEDGMENTS Parts of this report are based on the work of former Ph.D. students of the group and, in particular, P. Gu6nard and O. Robach. Y. Samson and P. Bayle-Guillemaud, respectively, are gratefully acknowledged for their excellent AFM and TEM images and active participation in illuminating the dark zones of the GIXD data. The SP2M/NM laboratory is acknowledged for

SYNCHROTRON STUDY OF OXIDES AND METALS giving us the o p p o r t u n i t y to use m u c h of their m a g n e t i c characterization e q u i p m e n t . M. N o b l e t and O. Ulrich are acknowle d g e d for efficient technical assistance d u r i n g the e x p e r i m e n t s on B M 3 2 - S U V . T h e staffs of b e a m l i n e s B M 3 2 , ID32, and ID03 are a c k n o w l e d g e d for h e l p and assistance during the experiments. E. Vlieg is a c k n o w l e d g e d for p r o v i d i n g the R O D software that was largely used in this work. We are also p l e a s e d to t h a n k m a n y e x p e r i m e n t a l i s t s w h o participated in one or several of the e x p e r i m e n t s r e p o r t e d here: J. Jupille, M. GautierSoyer, A. Stierle, K. Peters, H. K u h l e n b e c k , B. Richter, and O. Robach. It is difficult to cite here all of the scientists with w h o m we had i l l u m i n a t i n g discussions or fruitful collaborations, in particular we wish to t h a n k J. Jupille, C. N o g u e r a , H.-J. F r e u n d , M. Gautier-Soyer, E H u m b e r t , C. A. Ventrice, Jr., L. D. Marks, and B. Dieny. Finally we are i n d e b t e d to Prof. H. S. N a l w a for inviting us to write this chapter.

REFERENCES 1. R. Feidenhansl, Surf. Sci. Rep. 10, 105 (1989). 2. A. Guinier, "X-Ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies." Dover, New York, 1994. 3. R.W. James, 'q'he Optical Principles of the Diffraction of X-Rays." Cornell Univ. Press, Ithaca, NY, 1965. 4. G. Renaud, Surf. Sci. Rep. 32, 1 (1998). 5. I.K. Robinson and D. J. Tweet, Rep. Prog. Phys. 55, 599 (1992). 6. B.E. Waren, "X-Ray Diffraction." Addison-Wesley, Reading, MA, 1969. 7. I.K. Robinson, "Surface Crystallography," Vol. 3, pp. 221-266. Elsevier, Amsterdam/New York, 1991. 8. M. M. Woolfson, "An Introduction to X-Ray Crystallography." Cambridge Univ. Press, Cambridge, UK, 1970. 9. W. Borchardt-Ott, "Crystallography," 2nd ed. Springer-Vedag, Berlin, 1995. 10. T. E Russel, "Small-Angle Scattering" Vol. 3, pp. 379-470. Elsevier, Amsterdam/New York, 1991. 11. E Debye, Ann. Phys. (Leipzig) 43, 49 (1914). 12. I.K. Robinson, Phys. Rev. Lett. 50, 1145 (1983). 13. I.K. Robinson, Phys. Rev. B: Solid State 33, 3830 (1986). 14. T. Harada, M. Asano, and Y. Mizumati, J. Cryst. Growth 116, 243 (1992). 15. ESRF, avaible at http://www.esrf.fr. 16. A. Akimoto, J. Mizuki, I. Hirosawa, and J. Matsui, Rev. Sci. Instrum. 60, 2362 (1989). 17. R. Baudoing-Savois, G. Renaud, M. De Santis, A. Barbier, O. Robach, E Taunier, E Jeantet, O. Ulrich, J. E Roux, M. C. Saint-Lager, A. Barski, O. Geaymond, G. Berard, E Dolle, M. Noblet, and A. Mougin, Nucl. Instrum. Methods Phys. Res., Sect. B 149, 213 (1999). 18. S. Brennan and E Eisenberger, Nucl. Instrum. Methods 222, 164 (1984). 19. E Claverie, J. Massies, R. Pinchaux, M. Sauvage-Simkin, J. Frouin, J. Bonnet, and N. Jedrecy, Rev. Sci. Instrum. 60, 2369 (1989). 20. P.H. Fuoss and I. K. Robinson, Nucl. Instrum. Methods 222, 171 (1984). 21. S. Ferrer and E Comin, Rev. Sci. Instrum. 66, 1674 (1995). 22. G. Renaud, B. Villette, and E Gu6nard, Nucl. Instrum. Methods Phys. Res., Sect. B 95,422 (1995). 23. E. Vlieg, Van't Ent, A. E de Jongh, H. Neerings, and J. E Van der Veen, Nucl. Instrum. Methods Phys. Res., Sect. A 262, 522 (1987). 24. A. Munkholm and S. Brennan, J. Appl. Crystallogr. 32, 143 (1999). 25. A. Munkholm, S. Brennan, and E. C. Carr, J. Appl. Phys. 82, 2944 (1997). 26. C. Schamper, H. L. Meyerheim, and W. Moritz, J. Appl. Crystallogr. 26, 687 (1993). 27. M. E Toney and D. G. Wiesler, Acta Crystallogr., Sect. A 49, 624 (1993). 28. E. Vlieg, J. Appl. Crystalogr. 30, 532 (1997).

593

29. O. Robach, Y. Garreau, K. Aid, and M. B. V&on-Jolliot, J. Appl. Cryst. 33, 1006 (2000). 30. E. Vlieg, J. Appl. Crystallogr. 31,198 (1998). 31. J. R. Levine, J. B. Cohen, Y. W. Chung, and E Georgopoulos, J, Appl. Crystallogr. 22, 528 (1989). 32. A. Naudon and D. Thiaudi~re, J. Appl. Crystallogr. 30, 822 (1997). 33. D. Babonneau, A. Naudon, D. Thiaudi&e, and S. Lequien, J. Appl. Crystallogr. 32, 226 (1999). 34. G. Renaud, M. Noblet, A. Barbier, C. Revenant, O. Ulrich, Y. Borensztein, R. Lazzari, J. Jupille, and C. Henry, to be published. 35. G. Renaud, M. Noblet, A. Barbier, J. E Deville, O. Fruchart, and E Scheurer, unpublished results (2000), 36. G. Porod, "Small Angle X-ray Scattering," p. 37. Academic Press, San Diego, 1982. 37. J.R. Levine, J. B. Cohen, and Y. W. Chung, Surf. Sci. 248, 215 (1991). 38. A. Naudon, D. Babonneau, E Petroff, and A. Vaur~s, Thin Solid Films 319, 81 (1998). 39. M. Schmidbauer, T. Wiebach, H. Raidt, M. Hanke, R. K6hler, and H. Wawra, J. Phys. D: Appl. Phys. 32, A230 (1999). 40. D. Babonneau, J. Briatico, E Petroff, T. Cabioc'h, and A. Naudon, J. Appl. Phys. 87, 3432 (2000). 41. H. You,K. G. Huang, and R. T. Kampwirth, Physica B 221, 77 (1996). 42. M. Rauscher, R. Paniago, H. Meyzger, Z. Kovats, J. Dornke, J. Peisl, H. D. Pfannes, J. Schulze, and I. Eisele, J. Appl. Phys. 86, 6763 (1999). 43. O. Robach, G. Renaud, and A. Barbier, Surf. Sci. 401,227 (1998). 44. E Gu6nard, G. Renaud, and B. Villette, Physica B 221,205 (1996). 45. Y.C. Lee, E Tong, and E A. Montano, Surf. Sci. 181,559 (1987). 46. C. Li, R. Wu, A. J. Freeman, and C. L. Fu, Phys. Rev. B: Solid State 48, 8317 (1993). 47. G. Bordier and C. Nogu6ra, Phys. Rev. B: Solid State 44, 6361 (1991). 48. M. Causa, R. Dovesi, C. Pisani, and C. Roetti, Surf. Sci. 175, 551 (1986). 49. E W. de Wette, W. Kress, and U. Schr6der, Phys. Rev. B: Solid State 32, 4143 (1985). 50. J. Goniakowski and C. Noguera, Surf. Sci. 323, 129 (1995). 51. J. E LaFemina and C. B. Duke, J. Vac. Sci. Technol. A 9, 1847 (1991). 52. G.V. Lewis and C. R. A. Catlow, J. Phys. C: Solid State Phys. 18, 1149 (1985). 53. A.J. Martin and H. Bilz, Phys. Rev. B: Solid State 19, 6593 (1979). 54. G. Pacchioni, T. Mierva, and P. S. Bagus, Su~ Sci. 275, 450 (1992). 55. P.W. Tasker and D. M. Duffy, Surf. Sci. 137, 91 (1984). 56. D. L. Blanchard, D. L. Lessor, J. P. LaFemina, D. R. Baer, W. K. Ford, and T. Guo, J. Vac. Sci. Technol., A 9, 1814 (1991). 57. C.G. Kinniburgh, J. Phys. C: Solid State Phys. 9, 2695 (1976). 58. E A. Maksym, Surf. Sci. 149, 157 (1985). 59. H. Nakamatsu, A. Sudo, and S. Kawai, Surf. Sci. 194, 265 (1988). 60. M. Prutton, J. A. Walker, M. R. Welton-Cook, R. C. Felton, and Ramsey, Surf. Sci. 89, 95 (1979). 61. K.H. Rieder, Surf. Sci. 188, 57 (1982). 62. A. Santoni, D. B. Tran Thoai, and J. Urban, Solid State Commun. 68, 1039 (1988). 63. T. Urano and T. Kanaji, Surf. Sci. 134, 109 (1983). 64. M.R. Welton-Cook and W. Berndt, J. Phys. C: Solid State Phys. 15, 5691 (1982). 65. J.B. Zhou, H. C. Lu, T. Gustafsson, and P. H~iberle, S u ~ Sci. 302, 350 (1994). 66. V.E. Henrich, G. Dresselhaus, and H. J. Zeiger, Phys. Rev. B: Solid State 22, 4764 (1980). 67. C. Duriez, C. Chapon, C. R. Henry, and J. M. Rickard, Surf. Sci. 230, 123 (1990). 68. T. Gotoh, S. Murakami, K. Kinosita, and Y. Murata, J. Phys. Soc. Jpn. 50, 2063 (1981). 69. P. Gu6nard, G. Renaud, A. Barbier, and M. Gautier-Soyer, S u ~ Rev. Lett. 5, 321 (1998). 70. P. Gu6nard, G. Renaud, A. Barbier, and M. Gautier-Soyer, Mater. Res. Soc. Symp. Proc. 437, 15 (1996). 71. M. Gautier, J. P. Duraud, and L. Pham Van, Surf. Sci. Lett. 249, L327 (1991).

594

BARBIER ET AL.

72. J. Guo, D. E. Ellis, and D. J. Lam, Phys. Rev. B: Solid State 45, 13647 (1992). 73. W. C. Mackrodt, R. J. Davey, S. N. Black, and R. Docherty, J. Cryst. Growth 80, 441 (1987). 74. I. Manassidis and M. J. Gillan, Surf. Sci. Lett. 285, L517 (1993). 75. I. Manassidis and M. J. Gillan, J. Am. Ceram. Soc. 77, 335 (1994). 76. M. Cause, R. Dovesi, C. Pisani, and C. Roetti, Surf. Sci. 215, 259 (1989). 77. T.J. Godin and J. P. LaFemina, Phys. Rev. B: Solid State 49, 7691 (1994). 78. A. Kirfel and K. Eichhom, Acta Crystallogr., Sect. A 46, 271 (1990). 79. G. C. Ndubuisi, J. Liu, and J. M. Cowley, Micross. Res. Tech. 20, 439 (1992). 80. V. E. Puchin, J. D. Gale, A. L. Shluger, E. A. Kotomin, J. Giinster, M. Brause, and V. Kempter, Surf. Sci. 370, 190 (1997). 81. J. Ahn, and J. W. Rabalais, Surf. Sci. 388, 121 (1997). 82. G. Renaud, B. Villette, I. Vilfan, and A. Bourret, Phys. Rev. Lett. 73, 1825 (1994). 83. M. Gautier, J. P. Duraud, L. Pham Van, and M. J. Guittet, Surf. Sci. 250, 71 (1991). 84. S. Baik, D. E. Fowler, J. M. Blakeley, and R. Raj, J. Am. Ceram. Soc. 68, 281 (1985). 85. T.M. French and G. A. Somorjai, J. Phys. Chem. 74, 12 (1970). 86. H. Shiba, J. Phys. Soc. Jpn. 48, 211 (1980). 87. A.D. Novaco and J. P. McTague, Phys. Rev. Lett. 38, 1286 (1977). 88. E. Gillet and B. Ealet, Surf. Sci. 273, 427 (1992). 89. M. Vermeersch, R. Sporken, Ph. Lambin, and R. Caudano, Surf. Sci. 235, 5 (1990). 90. G. Renaud, M. Gautier-Soyer, and A. Barbier, unpublished results (2000). 91. A. Barbier and G. Renaud, Surf. Sci. Lett. 392, L15-20 (1997). 92. A. Barbier, G. Renaud, and A. Stierle, S u ~ Sci. 402-404, 757 (1998). 93. A. Barbier, G. Renaud, C. Mocuta, and A. Stierle, Surf. Sci. 433-435, 761 (1999). 94. A. Barbier, C. Mocuta, H. Kuhlenbeck, K. F. Peters, B. Richter, and G. Renaud, Phys. Rev. Lett. 84, 2897 (2000). 95. A. Barbier, C. Mocuta, and G. Renaud, Phys. Rev. B 62, 16056 (2000). 96. J.J.M. Pothuizen, O. Cohen, and G. A. Sawatzky, Mater. Res. Soc. Symp. Proc. 401, 501 (1996). 97. V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, J. Phys.: Condens. Matter 9, 767 (1997). 98. P.M. Oliver, G. W. Watson, and S. C. Parker, Phys. Rev. B: Solid State 52, 5323 (1995). 99. C. Nogu6ra, "Physics, and Chemistry at Oxide Surfaces." Cambridge Univ. Press, Cambridge, UK, 1996. 100. P.W. Tasker, J. Phys. C: Solid State Phys. 12, 4977 (1979). 101. V.E. Henrich, Surf. Sci. 57, 385 (1976). 102. D. Cappus, C. Xu, D. Ehrlich, B. Dillmann, C. A. Ventrice, Jr., K. A1Shamery, H. Kuhlenbeck, and H. J. Freund, Chem. Phys. 177, 533 (1993). 103. W.H. Meiklejohn, J. Appl. Phys. 33, 1328 (1962). 104. S. Soeya, S. Nakamura, T. Imagawa, and S. Narishige, J. Appl. Phys. 77, 5838 (1995). 105. D. Wolf, Phys. Rev. Lett. 68, 3315 (1992). 106. J.M. Cowley, Surf. Sci. 114,587 (1982). 107. C.A. Ventrice, Jr., Th. Bertrams, H. Hannemann, A. Brodde, and H. Neddermeyer, Phys. Rev. B: Solid State 49, 5773 (1994). 108. F. Rohr, K. Wirth, J. Libuda, D. Cappus, M. B~iumer, and H. J. Freund, Surf. Sci. Lett. 315, L977 (1994). 109. N. Floquet and L. C. Dufour, Surf. Sci. 126, 543 (1983). 110. M. Finazzi, N. B. Brookes, and F. M. F. de Groot, Phys. Rev. B: Solid State 59, 9933 (1999). 111. J.P. Hill, C. C. Kao, and D. F. McMorrow, Phys. Rev. B: Solid State 55, R8662 (1997). 112. G. Ju, A. V. Nurmikko, R. F. C. Farrow, R. F. Marks, M. J. Carey, and B. A. Gurney, Phys. Rev. B: Solid State 58, R11857 (1998). 113. V. Fernandez, C. Vettier, F. de Bergevin, C. Giles, and W. Neubeck, Phys. Rev. B: Solid State 57, 7870 (1998). 114. A. Barbier, G. Renaud, C. Mocuta, and A. Stierle, Adv. Sci. TechnoL 19, 149(1999).

115. C. Mocuta, A. Barbier, and G. Renaud, AppL Surf. Sci. 162-163, 56 (2000). 116. T. Shishidou and T. Jo, J. Phys. Soc. Jpn. 67, 2637 (1998). l l Z W.L. Roth, J. Appl. Phys. 31, 2000 (1960). 118. T.R. McGuire and T. S. Plaskett, J. Appl. Phys. 75, 6537 (1994). 119. R.P. Michel, A. Chaiken, and C. T. Wang, J. Appl. Phys. 81, 5374 (1997). 120. M. Tan, H.-C. Tong, S.-I. Tan, and R. Rottmayer, J. Appl. Phys. 79, 5012 (1996). 121. M.J. Carey and A. E. Berkowitz, Appl. Phys. Lett. 60, 3060 (1992). 122. M.J. Carey and A. E. Berkowitz, J. AppL Phys. 73, 6892 (1993). 123. M.J. Carey, A. E. Berkowitz, J. A. Borchers, and R. W. Erwin, Phys. Rev. B: Solid State 47, 9952 (1993). 124. H. Yamane and M. Kobayashi, J. AppI. Phys. 83, 4862 (1998). 125. F. Voges, H. De Gronckel, C. Osthover, R. Schreiber, and P. Grunberg, J. Magn. Magn. Mater. 190, 183 (1998). 126. J. B. Restorff, M. Wun-Fogle, and S. F. Cheng, J. Appl. Phys. 81, 5218 (1997). 12Z K. Nakamoto, Y. Kawato, Y. Suzuki, Y. Hamakawa, T. Kawabe, K. Fujimoto, M. Fuyama, and Y. Sugita, IEEE Trans. Magn. 32, 3374 (1996). 128. W.F. Egelhoff, Jr., T. Ha, R. D. K. Misra, Y. Kadmon, J. Nir, C. J. Powel, M. D. Stiles, R. D. McMichael, C. L. Lin, J. M. Sivertsen, J. H. Judy, K. Takano, A. E. Berkowitz, T. C. Anthony, and J. A. Brug, J. Appl. Phys. 78, 273 (1995). 129. D. M. Lind, S. P. Tay, S. D. Berry, J. A. Borchers, and R. W. Erwin, J. Appl. Phys. 73, 6886 (1993). 130. A.R. Ball, A. J. G. Leenaers, P. J. Van der Zaag, K. A. Shaw, B. Singer, D. M. Lind, H. Frederizike, and M. T. Rekveldt, Appl. Phys. Lett. 69, 1489 (1996). 131. P. Stoyanov, A. Gottschalk, and D. M. Lind, J. AppI. Phys. 81, 5010 (1997). 132. C. Mocuta, A. Barbier, G. Renaud, and B. Dieny, Thin Solid Films 336, 160 (1998). 133. A. Barbier, P. Ohresser, V. Da Costa, B. Carri~re, and J.-P. Deville, Surf. Sci. 405, 298 (1998). 134. N.W. Nydegger, G. Couderc, and M. A. Langell, Appl. Surf. Sci. 147, 58 (1999). 135. J.H. Van der Merwe, Philos. Mag. A 45, 159 (1982). 136. J.H. Van der Merwe, Philos. Mag. A 45, 127 (1982). 137. J.H. Van der Merwe, Philos. Mag. A 45, 145 (1982). 138. T. Epicier and C. Esnouf, J. Phys. III 4, 1811 (1994). 139. R.H. Hoel, Surf. Sci. 169, 317 (1986). 140. R.H. Hoel, H. U. Habermeier, and M. Riihle, J. Phys. 46, C4 (1989). 141. R.H. Hoel, J. M. Penisson, and H. U. Habermeier, J. Phys. 51, C1 (1990). 142. F. Ernst, P. Pirouz, and A. H. Heuer, Philos. Mag. A 63, 259 (1991). 143. G. Necker and W. Mader, Philos. Mag. Lett. 58, 205 (1988). 144. G. Renaud, O. Robach, and A. Barbier, Faraday Discuss. 114, 157 (1999). 145. O. Robach, G. Renaud, A. Barbier, and P. Gu6nard, Surf. Rev. Lett. 5, 359 (1998). 146. O. Robach, G. Renaud, and A. Barbier, Phys. Rev. B: Solid State 60, 5858 (1999). 147. U. Schonberger, O. K. Andersen, and M. Methfessel, Acta Metall. Mater. 40, S 1 (1992). 148. P. B16chl, "Metal-Ceramic Interfaces." Pergamon, Oxford, 1990. 149. J.R. Smith, T. Hong, and D. J. Srolovitz, Phys. Rev. Lett. 72, 4021 (1994). 150. A. M. Flanck, R. Delaunay, P. Lagarde, M. Pompa, and J. Jupille, Condens. Matter 53, 1737 (1996). 151. L. Spiess, Surf. Rev. Lett. 3, 1365 (1997). 152. A. Trampert, F. Ernst, C. P. Flynn, H. F. Fischmeister, and M. Riihle, Acta Metall. Mater. 40, $227 (1992). 153. H. A. Van der Vegt, H. M. Van Pinxteren, M. Lohmeier, E. Vlieg, and J. M. C. Thornton, Phys. Rev. Lett. 68, 3335 (1992). 154. H.A. Van der Vegt, W. J. Huisman, P. B. Howes, and E. Vlieg, S u ~ Sci. 330, 101 (1995). 155. H. AI Van der Vegt, J. Alvarez, X. Torrelles, S. Ferrer, and E. Vlieg, Phys. Rev. B: Solid State 52, 17443 (1995).

SYNCHROTRON STUDY OF OXIDES AND METALS 156. G. Renaud, E Gu6nard, and A. Barbier, Phys. Rev. B: Solid State 58, 7310 (1998). 157. E Gu6nard, G. Renand, B. Vilette, M. H. Yang, and C, R Flynn, Scripta Metall. Mater 31, t221 (1994). 158. M.S. Patterson, J. Appl. Phys. 8, 805 (1952). 159. "Handbook of Thermophysical Properties of Solid Materials." Macmillan, New York, 1961. 160. R. Bonnet and J. L. Verger-Gaugry, Philos. Mag. A 66, 849 (1992). 161. R. Bonnet, Philos. Mag. A 43, 1165 (1981). 162. A. Barbier, G. Renaud, and J. Jupille, Surf Sci. 454-456, 979 (2000). 163. A. Barbier, Surf. Sci. 406, 69 (1998). 164. E Didier and J. Jupille, Surf. Sci. 307-309, 587 (1994). 165. G. Renaud and A. Barbier, Surf. Sei. 433-435, 142 (1999). 166. G. Renaud, A. Barbier, and O. Robach, Phys. Rev. B: Solid State 60, 5872 (1999). 167. G. Renaud and A. Barbier, Appl. Surf. Sci. 142, 14 (1999). 168. C. Goyhenex, C. R. Hem3",mad J. Urban, Philos. Mag. A 69, 1073 (1994). 169. C. Goyhenex, M. Croci, C. Claeys, and C. R. Henry, Surf. Sei. 353, 475 (1996). 170. C. Goyhenex, M. Meunier, and C. R. Henry, Surf Sci. 350, 103 (1996). 171. C. R. Henry, C. Chapon, C. Duriez, and S. Giorgio, Surf. Sei. 253, 177 (1991). 172. C.R. Henry, M. Meunier, and S. Morel, J. CrysL Growth 129, 416 (1993). 173. C.R. Henry, Surf. Sci. Rep. 31,231 (1998). 174. S. G. Giorgio, C. Chapon, C. R. Henry, and G. Nihoul, Philos. Mag. B 67, 773 (1993). 175. S. Bartuschat and J. Urban, Philos. Mag. A 76, 783 (1997). 176. E Lu and E Cosandey, Aeta MetaU. Mater. 40, $259 (1992). 177. K. Heinemann, T. Osaka, H. Poppa, and M. Avalos-Borja, J. CataL 83, 61 (1983). 178. H. Fomander, J. Birch, L. Hultman, L. G. Petersson, and J. E. Sundgren, AppL Phys. Lett. 68, 2636 (1996). 179. C. Goyhenex and C. R. Henry, J. Electron Speetrose. Relat. Phenom. 61, 65 (1992). 180. J. Goniakovski, Phys. Rev. B: Solid State 57, 1 (1998). 181. A. Barbier, G. Renaud, and O. Robach, £ AppL Phys. 84, 4259 (1998). 182. G. Pacchioni and N. Rtisch, J. Chem. Phys. 104, 7329 (1996). 183. N. RSsch and G. Pacchioni, "Chemisorpfion and Reactivity on Supported Clusters, and Thin Films." Kluwer Academic, Dordrecht, 1997. 184. H. Bialas and K. Heneka, Vacuum 45, 79 (1994). 185. E Reniers, M. P. Delplancke, A. Asskali, V. Rooryck, and O. Van Sinay, Appl. Surf. Sci. 92, 35 (1996). 186. G. Raatz and J. Woltersdorf, Phys. Status SolidiA 113, 131 (1989). 187. H. Nakai, H. Qiu, M. Adarnik, G. SLfran, P. B. Barna, and M. Hashimoto, Thin Solid Films 263, 159 (1995). 188. H. Sato, R. S. Toth, andR. W. Astrue, J. Appl. Phys. 33, 1113 (1962). 189. A.A. Hussain, Z Phys.: Condens. Matter 1, 9833 (1989). 190. H. Bialas and Li-Shing Li, Phys. Status Solidi A 42, 125 (1977). 191. N.I. Kiselev, Yu. 1. Man'kov, and V. G. Pyn'ko, SoY: Phys. SolidState 31, 685 (1989). 192. H. Mamyama, H. Qiu, H. Nakai, and M. Hashimoto, J. Vac. Sci Technol., A 13, 2157 (1995). 193. H. Qiu, A. Kosuge, H. Maruyama, M. Adamik, G. Safran, E B. Barna, and M. Hashimoto, Thin Solid Films 241, 9 (1994). 194. M.R. Fitzsimrnons, G. S. Smith, R. Pynn, M. A. Nastasi, and E. Burkel, Physica B 198, 169 (1994). 195. G. Simmons and H. Wang, "Single Crystal Elastic Constants and Calculated Aggregated Properties." MIT Press, Cambridge, MA, 1971. 196. W.H. Meiklejohn and C. E Bean, Phys. Rev. 105,904 (1957). 197. W.H. Meiklejohn and C. R Bean, Phys. Rev. 102, 1413 (1956). 198. W. H. Meiklejohn, J. AppL Phys. 33, 1328 (1962). 199. B. Dieny, V. S. Speriosu, S. S. E Parkin, B. A. Gume, D. R. Wilhoit, and D. Manri, Phys. Rev. B: Solid State 43, 1297 (1991), 200. J.C.S. Kools, S. Lardoux, and E Roozeboom, Appl. Phys. Lett. 72, 611 (1998). 201. C. Tsang and Kenneth Lee, J. AppL Phys. 53, 2605 (t982).

595

202. S.L. Burkett, S. Kora, J. L. Bresowar, J. C. Lusth, B. H. Pirkle, and M. R, Parker, J. AppL Phys. 81, 4912 (1997). 203. W.C. Cain, W. H. Meiklejohn, and M. H. Kryder, J, AppL Phys. 61, 4170 (1987). 204. G. Choe and S. Gupta, AppL Phys. Lett. 70, 1766 (1997). 205. T. Lin, D. Mauri, N. Staud, and C. Hwang, AppL Phys. Len. 65, 1183 (t994). 206. Harsh Deep Chopra, B. J. Hockey, E J. Chen, W. E Egelhoff, Jr., M. Wutting, and S. Z. Hua, Phys. Re~. B: Solid State 55, 8390 (1997). 20Z H.J.M. Swatgen, G. J. Strijkers, R J. H. Bloemen, M. M. H. WiUekens, and W. J. M. De Jnnge, Phys. Re~: B: Solid State 53, 9108 (1996). 208. Z.-H. Lu, T. Li, J.-J. Qiu, K. Xnn, H.-L. Sben, Z.-Y. Li, and D.-E Shen, Chin. Phys. Lett. 16, 65 (1999). 209. Y. Kawawake, Y. Sugita, M. Satomi, and H. Sakakima, J. Appl. Phys. 85, 5O24 (1999). 210. T. Ambrose, K. Leifer, K. J. Hemker, and C. L. Chien, J. Appl. Phys. 81, 5007 (1997). 211. C. Tsang, N. Heiman, and K. Lee, J. Appl. Phys. 52, 2471 (1981). 212. R. Jnngblut, R. Coehoorn, M. T. Johnson, J. aan de Stegge, and A. Reinders, J. AppL Phys, 75, 6659 (1994). 213. O. Allegranza and M.-M. Chen, J. AppL Phys. 73, 6218 (1993). 214. J. Ding and J.-G. Zhu, J. Appt. Phys. 79, 5892 (1996). 215. D.-H. Han, J.-G. Zhu, and J. H. Judy, J. AppL Phys. 81, 4996 (1997). 216. D.-H. Han, J.-G. Zhu, J. H. Judy, and J. M. Sivertsen, Jr. Appt. Phys. 81, 340 (1997). 217. D.-H. Han, J.-G. Zhu, J. H. Judy, and J. M. Sivertsen, Appl. Phys. Lett. 70, 664 (1997). 218. D.-H. Hart, J.-G. Zhu, J. H. Judy, and J. M. Sivertsen, J. AppL Phys. 81, 4519 (1997). 219. T. J. Moran, J. M. Galtego, and I. K. Schuller, J. AppL Phys. 78, 1887 (1995). 220. T.J. Moran and L K. Schuller, J. Appl. Phys. 79, 5109 (1996). 221. H. D. Chopra, B. J. Hockey, E J. Chen, R. D. McMichael, and W. E Egelhoff, Jr.,./. AppL Phys. 81, 4017 (1997). 222. S. E Cheng, J. E Teter, R Lubitz, M. M. Miller, L. Hoines, J. J. Krebs, D. M. Schaefer, and G. A. Prinz, J. AppL Phys. 79, 6234 (1996). 223. T. Lin, C. Tsang, R. E. Fontana, and J. K. Howard, IEEE Trans. Magn, 3t, 2585 (1995). 224. Y. Hamakawa, H. Hoshiya, T. Kawabe, Y. Suzuki, R. Arai, K. Nakamoto, M. Fuyama, and K. Sugita, IEEE Trans. Magn. 32, 149 (1996). 225. READRITE, available at http://www, readrite, com. 226. IBM, available at http:llwwwxesearch.ibm.com/storage/oem/tech/ eraheads.htm. 227. SEAGATE, available at http://www.seagate.com. 228. N. J. G6kemeijer, T. Ambrose, C. L. Chien, N. Wang, and K. K. Fung, J. Appl. Phys. 81, 4999 (1997). 229. D. G. Hwang, S. S. Lee, and C. M. Park, AppL Phys. Lett. 72, 2162 (1998). 230. D.G. Hwang, C. M. Park, and S. S. Lee, J. Magn. Magn. Mater 186, 265 (1998). 231. C.-M. Park, C.-L Min, and C. H. Shin, 1EEE Trans. Magn. 32, 3422 (1996). 232. J.X. Shen and M. T. Kief, J. AppL Phys. 79, 5008 (1996). 233. C.-H. Lai, H. Matsuyama, R. White, T. C. Anthony, and G. G. Bush, J. Appl. Phys. 79, 6389 (1996). 234. C.-H. Lai, T. J. Regan, R. L. White, and T. C. Anthony, J, Appl. Phys. 81, 3989 (1997). 235. S.-S. Lee, D.-G. Hwang, C. M. Park, K. A. Lee, and J. R, Rhee, J. AppL Phys. 81, 5298 (1997). 236. J. Nogues, D. Lederman, T. J. Moran, and I. K. Schuller, Phys. Rev. Lett. 76, 4624 (1996). 237. O. Kitakami, H. Takashima, and Y. Shimada, J. Magn. Magn. Mater 164, 43 (1996). 238. C. Cowache, B. Dieny, S. Auffret, M. Cartier, R. H. Taylor, R. O'Barr, and S. S. Yamamoto, 1EEE Trans. Magn. 34, 843 (1998). 239. M.-H. Lee, S. Lee, and K. Sin, Thin Solid Films 320, 298 (1998).

596

BARBIER ET AL.

240. S. Soeya, M. Fuyama, S. Tadokoro, and T. Imagawa, J. Appl. Phys. 79, 1604 (1996). 241. C.-M. Park, K.-I. Min, and K. H. Shin, J. AppL Phys. 79, 6228 (1996). 242. J. Nogues and I. K. Schuller, J. Magn. Magn. Mater. 192, 203 (1999). 243. J.C.S. Kools, IEEE Trans. Magn. 32, 3165 (1996). 244. B.A. Everitt, D. Wang, and j. M. Daughton, IEEE Trans. Magn. 32, 4657 (1996). 245. K. Matsuyama, H. Asada, S. Ikeda, K. Umezu, and K. Tauiguchi, IEEE Trans. Magn. 32, 4612 (1996). 246. G. Chern, D. S. Lee, H. C. Chang, and T.-H. Wu, J. Magn. Magn. Mater. 193, 497 (1999). 247. K. Takano, R. H. Kodama, A. E. Berkowitz, W. Cao, and G. Thomas, Phys. Rev. Lett. 79, 1130 (1997). 248. S. Soeya, S. Tadokoro, T. Imagawa, and M. Fuyama, J. Appl. Phys. 77, 5838 (1995). 249. S.R. Andrews and R. A. Cowley, J. Phys. C: Solid State Phys. 18, 6427 (1985). 250. W. E Egelhoff, Jr., P. J. Chen, C. J. Powell, M. D. Stiles, R. D. McMichael, J. H. Judy, K. Takano, and A. E. Berkowitz, J. Appl. Phys. 82, 6142 (1997). 251. W. F. Egelhoff, Jr., P. J. Chen, C. J. Powell, M. D. Stiles, and R. D. McMichael, J. Appl. Phys. 79, 2491 (1996). 252. W. F. Egelhoff, Jr., P. J. Chen, C. J. PoweU, M. D. Stiles, R. D. McMichael, C. L. Lin, J. M. Sivertsen, J. H. Judy, K. Takano, and A. E. Berkowitz, J. Appl. Phys. 80, 5183 (1996). 253. P. Bayle-Guillemaud, A. Barbier, and C. Mocuta, Ultramicroscopy 88, 99 (2001). 254. C.-H. Lai, T. C. Anthony, E. Iwamura, and R. L. White, IEEE Trans. Magn. 32, 3419 (1996). 255. C. Mocuta, A. Barbier, S. Lafaye, P. Bayle-Guillemaud, Mater. Res. Sac. Syrup. Proc., in press.

256. C. Mocuta, A. Barbier, G. Renaud, Y. Samson, and M. Noblet, J. Magn. Magn. Mater. 211,283 (2000). 257. M. J. Carey, E E. Spada, A. E. Berkowitz, W. Cao, and G. Thomas, J. Mater. Res. 6, 2680 (1991). 258. W. Cao, G. Thomas, M. J. Carey, and A. E. Berkowitz, Scripta Metal. Mater. 25, 2633 (1991). 259. C.-H. Lai, H. Matsuyama, and R. L. White, IEEE Trans. Magn. 31, 2609 (1995). 260. R. P. Michel, A. Chaiken, C. T. Wang, and L. E. Johnson, Phys. Rev. B: Solid State 58, 8566 (1998). 261. J. E. Keem, J. M. Honig, and L. L. Van Zandt, Philos. Mag. B 37, 537 (1978). 262. W.D. Wang, N. J. Wu, and P. A. Thiel, Chem. Phys. 92, 2025 (1990). 263. A.R. Sandy, S. G. J. Mochrie, D. M. Zehner, K. G. Huang, and D. Gibbs, Phys. Rev. B: Solid State 43, 4667 (1991). 264. L. D. Marks, Phys. Rev. B: Solid State 60, 2771 (1999). 265. L. D. Marks, E. Bengu, C. CoUazo-Davila, D. Grozea, E. Landree, C. Leslie, and W. Sinkler, Surf Rev. Lett. 5, 1087 (1998). 266. L. D. Marks, W. Sinkler, and E. Landree, Acta Crystallogr. 55, 601 (1999). 267. C. Collazo-Davila, D. Grozea, L. D. Marks, R. Feidenhans'l, M. Nielsen, L. Seehofer, L. Lottermoser, G. Falkenberg, R. L. Johnson, M. Gothelid, and U. Karlsson, Su~ Sci. 418, 395 (1998). 268. L.D. Marks, D. Grozea, R. Feidenhans'l, M. Nielsen, and R. L. Johnson, Surf Rev. Lett. 5,459 (1998). 269. N. Erdman, O. Warschkow, A. Barbier, D. E. Ellis, and L. D. Marks, submitted for publication. 270. N. Kitakatsu, V. Maurice, and P. Marcus, Surf. Sci, 411,215 (1998). 271. P. Liu, T. Kendelewicz, and G. E. Brown, Jr., Surf. Sci. 412, 315 (1998).

Chapter 12 OPERATOR FORMALISM IN POLARIZATION-NONLINEAR OPTICS AND SPECTROSCOPY OF POLARIZATION-INHOMOGENEOUS MEDIA I. I. Gancheryonok, A. V. Lavrinenko Department of Physics, Belarusian State University, E Skariny av. 4, Minsk 2220080, Belarus

Contents 1. 2. 3. 4. 5. 6.

7.

8.

9. 10.

11.

12. 13.

14.

Fundamentals of the Theory of Ineraction of Vector Light Fields with Nonlinear Media . . . . . . . . 598 Tensor-Operator Approach to the Description of Photoanisotropic Media . . . . . . . . . . . . . . . . 599 Fedorov's Light Beam Tensor Formalism for Description of Vector Field Polarization . . . . . . . . . 602 Propagation of Polarized Radiation in an Anisotropic Medium: Evolution of Probe Wave Intensity . . 605 Saturation Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Nonlinear Polarization Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 6.1. Wave Operator Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 6.2. Reflection from Media with Light-Induced Anisotropy . . . . . . . . . . . . . . . . . . . . . . 609 6.3. Reflection Configuration for a Nonlinear Polarization Spectroscopy Detection Scheme . . . . 611 6.4. Noncollinear Geometry in Polarization-Sensitive Spectroscopy . . . . . . . . . . . . . . . . . 612 Spectroscopy of Optical Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612 7.1. Linearly and Circularly Polarized Pump and Probe Waves . . . . . . . . . . . . . . . . . . . . 612 7.2. Elliptically Polarized Interacting Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Principle of Nonlinear Spectroscopic Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 8.1. Polarization Changes of the Probe Wave during Propagation in a Medium with LightInduced Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Numerical Evaluation of an Effective Nonlinear Susceptibility in the Framework of NSE . . . . . . . 619 The Concept of Normal Waves in Photoanisotropic Media . . . . . . . . . . . . . . . . . . . . . . . . 619 10.1. Real K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 10.2. Small K or Nearly Linear Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 10.3. Non-Collinear EllipticaUy Polarized Pump Wave . . . . . . . . . . . . . . . . . . . . . . . . . 621 Method of Combination Waves in NSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 11.1. Codirected Pump and Probe Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 11.2. Noncollinear Geometry of Interacting Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 625 11.3. Informativeness of a Variant NSE Based on the Measurement of the Ratio of Eigenvalues of the Tensor of Parametric Coupling . . . . . . . . . . . . . . . . . . . . . . . . . 627 Nonlinear Optical Ellipsometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628 Nonlinear Light-Induced Anisotropy of an Isotropic Medium with Partially Polarized Light . . . . . . 629 13.1. Saturation Spectroscopy . . . . . . . . . . . . . . . . . . . . ................... 630 13.2. Nonlinear Polarization Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630 13.3. Spectroscopy of Optical Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631 13.4. Linear Pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632 13.5. Circular Pumping . . . . . . . . . . , ................................ 632 Methods for Measuring Nonlinear Susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 2: Characterization and Spectroscopy of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512910-6/$35.00

597

598

GANCHERYONOK AND LAVRINENKO

1. FUNDAMENTALS OF THE THEORY OF INERACTION OF VECTOR LIGHT FIELDS WITH NONLINEAR MEDIA In the general frame work the description of process of propagation of electromagnetic radiation in a medium is reduced to seeking the self-consistent solution of equations describing the action of radiation on a substance, and the influence of the latter on the radiation field. For complete correspondence of the theory and experiment it is necessary to undertake a quantum description of the medium as well as of the electromagnetic field. Indeed, in some only quantum effects can be exhibited: photon antigrouping, generation of squeezed states, etc. However, for a wide range of phenomena good consistency between theory and experiment is achieved with the use of a semiclassical description, i.e., description of the medium by the quantum equations, and of the radiation field by the classical Maxwell's equations. Further simplifications can be made under special conditions on the properties of the medium and the radiation. Let us consider nonmagnetic electrically neutral media, which include the majority substances that are isotropic in the linear approximation. Then the character of light-matter interaction will be characterized first of all by the electric field E, and instead of Maxwell's equations it is convenient to use the wave equations [ 1] O2E + O2p+ (V x (V x E+)) +/zoeo~ Ot 2 = -lZo Ot 2 (1.1a) V . eo~E + = - V

. P+

(1.1b)

where E + is the positive-frequency amplitude of the electric field E = E + + E - , and E - = (E+)*; ~ is the complex dielectric permittivity, defining the linear polarization of the medium P ~ = e0(~ - 1)E+; P+ is the positive-frequency part of the nonlinear polarization of the medium; e0 and/z0 are the electric and magnetic vacuum permittivities, respectively; and an asterisk denotes the complex conjugate. In resonant media it is convenient to consider P+ as the vector of polarization response associated with the resonant transitions [1 ]. The nonlinearity of this vector is considerable even for rather low radiation fields. Therefore dividing it into linear and nonlinear parts is frequently not meaningful. Then one can consider ~ as a permittivity determined by all nonresonant transitions of the medium. The polarization associated with these transitions remains linear even at very high radiation electric field; therefore, as a rule, ~ can be considered independent of E. It should be taken into account that, because their effects are small, the optical nonlinearities have been observed only under the action of radiation of high spectral density [2], which is produced as a rule by lasers. Then the radiation field is conveniently presented as

E+(r, t) = Z E+ exp(-iwjt + ikj . r)

(1.2)

J

where E + are complex amplitudes depending weakly [in comparison with e x p ( - i o o j t + i k j 9 r)] on coordinates r and time

t; j is the index numbering the waves distinguished by their frequency and direction of propagation; and kj and wj are the wave vector and frequency of the j th wave, respectively. The representation (1.2), in principle, can be used for any radiation field; however, it is the most convenient for laser radiation, owing to the restricted number of longitudinal modes. The decomposition (1.2) is also useful when it is known that the light beams are statistically independent and that their independence is not broken by interaction with the medium. Let us restrict ourselves to the case of quasi-homogeneous and quasi-stationary radiation and present these requirements in the following way:

>>, '

IAE+ I ~ e p m p when 010 : re/4, curve 1, q = 0; curve 2, Req = -0.75, Imq = 0.40; curve 3, from [32]. Circles, triangles, and small squares show experimental values for MB, CV, and RB, respectively. The bars indicate typical errors of measurements.

I

-45o

O"

AINPs

""••-,\ 9 the angle 10101 : 7r/4 is not optimum in the sense of obtaining maximum signal when the polarization of the pump wave is close to circular; 9 the shape of the plot of A INPS essentially depends on sign(Im q) (see Figure 1a and b, which differ only in the sign of Im q). We proceed now to the analysis of the c a s e s 010 : Then (6.2) can rewritten as follows: F = c o s 2 2epmp q-- Iq 12 :F Im q sin 4 e p m p

-+-zr/4.

Im q > 0:

Imq < 0:

_max_

epmp - - -max

1

1 2 Imq ~ arctan 1 -- Iq 12 2 Im q

pmp = ~ arctan i -- ~ i 2

min _ max _} 7r 8prop 8pmp 4 min

_max

~,, ,

7t"

epmp - e pmp (6.7)

Therefore, in the case of Hermitian S the maximum signal will be observed with linearly polarized pumping, and the minimum when the exciting radiation is circularly polarized. It is important to point out that the measurement of epmp ^max(min) allows one to determine the real and imaginary parts of q, which are spectroscopically informative quantities [21 ]. Another important feature of such measurements is that the measured parameters are independent of the pump power. In Figure 2 the results of our experiment [ 19] on aqueous solutions of three dyes [crystal violet (CV), methyline blue (MB), and rhodamine-B (RB)] are shown, which are in good accord with the theoretical dependence (6.6) (curve 1) and are in obvious contrast with the theoretical (curve 3) and experimental data on an aqueous solution of a dye (malachite green (MG)) from [32]. Curve 2 corresponds to characteristic parameters of the 992 cm-1 line of benzole, so that 8pm pmax ~, 18 ~ and 8pmpmin~, 27 o. It is necessary to point out that curve 1 is constructed on the assumption q = O, which (taking into consideration symmetry

J ~-~ J-1 (1'-3') J=l.$ (1-3) ,I--2 dp#d'

R=0.99(1');O(2');-1{3') -45~

l t l~ O" 8pmp

P,=111);0 ('2);-1 O) 4S"

(b)

(6.6)

This expression differs significantly from Eq. (15) of [32], in which the authors derive another expression within the same approach. From (6.6) it is easy to see that the behavior of AINps while scanning the elliptically of pumping is necessarily nonmonotonic. Its extreme values are reached at

4b~

(a)

Fig. 3. Theoretical dependences of the normalized value of the NPS signal on the angle of ellipticity of the pump wave for ensembles of two-level particles. See text.

of tensor index permutations) leads to equality of three components of the cubic susceptibility tensor: X12 = X44 = X43- Thus, there is strong evidence of Kleinman symmetry of the resonant tensor )~(3) in aqueous solutions of the dyes CV, MB, RB. The small values for Re q and Im q obtained in [32] hardly can be a basis for inferring violation of that symmetry in aqueous solutions of MG (and other dyes as reported in [32]). Moreover, the errors found in the fitting of theoretical to experimental values Re q and Im q are not indicated. We now address atomic systems. The essential dependencies are displayed in Figure 3a, where effects of interatomic collisions and radiation trapping in an ensemble of two-level particles are neglected, and the decay rates for the levels are supposed to be approximately equal. The curves in Figure 3b are free from the limitation imposed by the last supposition, and parameter k is determined as -

R -

AJ(yb--Ya)

IAJI(Ya + Yb)

(6.8)

It is easy to see from Figure 3 that the shape of the curves of A INps is characterized by strong J-dependence for small J, which can be utilized for identification of unknown transitions as well as in the analysis of three-level cascade systems [30]. In [30] the corresponding analysis was made for the following models: (i) J - 0 --+ J - 1 ~ J = 0; (ii)neon

608

GANCHERYONOK AND LAVRINENKO

atom [ls4(J = 1) ~ 2p4(J -- 2) --+ 3SE(J --- 1)], and (iii) J - 1 ~ J ~ J + l orJ+l --+ J ~ J - 1. The values of q are 1, 15/7, and - 5 respectively. For model (i) AINPs(epmp) = const was obtained, as well as for the following cascade systems: J + 1 --+ J --+ J and J --+ J --+ J + 1 for J = 3. We now give explicit forms of the function F for other polarization conditions. If the probe wave is circularly polarized, then F - - c o s 2 2epmp

(6.9)

i.e., in media with Kleinman symmetry of the )~(3) components, the expressions (6.2) and (6.9) coincide. If the probe wave is elliptically polarized with the semimajor axis of the ellipse of polarization along the X-axis, and the strong wave has linear polarization, then F ~ f(epmp), F = sin E 2epo,

eo.ex :

e0 II ex

or

2 e0 II ey

(6.10)

Here ePO is the angle of ellipticity of el0. Let us remark that in the previously examined cases with circularly and elliptically polarized probe radiation, the use of circular and elliptical analyzers, respectively, was assumed. Finally, we take a look at the dependence of a NPS signal on ~ in collinear geometry of the interacting waves. The dependence can be described by the following function: F~ = exp(-trl ~)[ 1 - exp(-cro~) ]2

(6.11)

From (6.11) it follows that the maximum NPS signal will be observed at ~max :

ln[(2cro + O'1)/O'1] or0

evolution of the field vector amplitudes of an electromagnetic wave during propagation in anisotropic and gyrotropic media. The surface impedance and normal refraction operators are very useful in the theory of electromagnetic or elastic wave propagation in stratified anisotropic media [45, 46]. The boundary value problem in such media can be rigorously formulated in terms of the operators ~ and N, which depend on the characteristics of the incident waves and the properties of the corresponding media. Thus, the operator method of solving various boundary value problem, including reflection and transmission of waves at a single plane interface, may be applied to calculations where high precision is needed. Let the first medium, from which the plane harmonic wave (of frequency 09) E (r, t) -- Ei exp [i ( k m . r - ogt)]

is obliquely incident onto the second one, be isotropic, and the other medium be anisotropic and described by the permittivity tensor ~ and permeability tensor/2. Here, Ei is the complex vector amplitude of the electric field strength, k = w / c , c is the velocity of the light in vacuum, m = b + m n q is the refraction vector [37] with tangential component b and normal component m n q , and q is the unit vector normal to the interface. The refraction vector m is connected with the wave normal n through an index of refraction n" m

6.1. Wave Operator Formalism Let us consider in detail the application of Fresnel's wave operator formalism to the problem of nonlinear polarization spectroscopy. The principles of this formalism have been given in a number of papers (see, for example, [37-39] and the literature cited therein). A surface impedance operator f (this is a linear operator of matrix form, so it may be considered as a tensor) is one of the fundamental concepts of this theory. The operator generalizes a scalar surface impedance that has been widely known in optics and radio-wave theory for many years [40--42]. Another important concept is a normal refraction operator N, which generalizes the refractive index operator [43, 44]. This operator (or tensor, as we showed earlier) describes the space

=

(6.14)

nn

It is convenient, especially in nonmagnetic media, to use the vector of magnetic field strength H and its tangential component Ht (relative to the interface) [37-39]. It is well known that for the plane waves (6.15)

H = m • E = m•

(6.12)

In NPS the frequency detuning of interacting waves as a rule is small, so that the corresponding optimum optical density can be estimated as Dopt = ZrnaxCr0 ~ In 3 ~ 1.1. In [32] Dopt was found to be 0.48. In a series of experimental works on NPS of dye solutions [35, 19, 36] the samples under study had D a little higher than Dopt from [32].

(6.13)

where m • E denotes the vector product of m and E, and m • is the antisymmetric second-rank tensor dual to the vector m [ 12]. The projection operator (~ is applied to project vectors on the tangential plane: (6.16)

Ht -- CJH

With the help of the dyadic q | q and unit tensor ~? one can easily find that (~ = I - q x q. We follow the intrinsic notation [12], meaning in (6.16) contraction of tensor t~ with vector H: ( H t ) i = E ~ = I Gij H i . T h e direct manipulation with tensors and vectors as in (6.16) simplifies the final expressions and provides results of great generality, eliminating the use of any coordinate system. Moreover, the results obtained are suitable for computer use. One can find the complex vector amplitudes of the reflected waves (Htr) and transmitted waves (H a) as shown in [37-39]: H t --rHt,

Htd:dHt,

r q- G - - d

(6.17)

^

where ~ and d are Fresnel's reflection and transmission operators, respectively. These operators are expressed by means of the surface impedance operators for incident (~i), reflected

OPERATOR FORMALISM IN POLARIZATION-NONLINEAR OPTICS

(~r),

and transmitted (9)d) radiation as follows: . ~ r ) - ( ~ i __ ~d), ~ _. (~d __ ~ r ) - ( ~ i

_. (~d

~r)

(6.18) where (~d _ ~ r ) - is a pseudo-inverse operator ("pseudo" because Fresnel's operators ~ and d are planar tensors, acting in the two-dimensional subspace, of the plane interface, so the ordinary inverse for these operators is not defined). The pseudoinverse operator 8 t can be found through the algorithm presented in [37-39]"

609

where lel is the determinant of ~. The total field of refracted waves, H ff (r, t) --- H d (0) exp [i (kb. r - wt)] exp(ikzbl)

(6.24)

contains an exponential operator oo

exp ( i k z N ) k -- E

[(ikz)k/k!] l~lk

k=0

where z = q 9r, and

^

,,_ ott G - 6t % = _

where &t denotes the trace of the adjoint tensor [12]. The surface impedance tensor ~ is introduced as a linear operator transforming the vector Ht into the vector q • E" q x E = 9)Ht

(6.20)

These vectors lie at the plane interface. It has been shown [38, 39] that the surface impedance satisfies the Riccati tensor equation

=o

(6.21)

where the tensor coefficients are

= ~ 1 GeG - - l b 1 = -ma

1 | a - ~q

= ---a eq

|

8q -- q ~q ,

x~ fzq X

lZq

(6.22)

IZq

~ia

- - b2

7%

(m~-lm)(m~z-lm) + (~-lmX~z-lmX)t + 1 = 0

(~ = / } ( t ~ -

D/}-,4)

(6.27)

(6.28)

Some complicated cases with degenerate tensor N, where refracted waves with linear, quadratic, and cubic dependence on coordinates appear, are considered in detail in the papers [47, 48].

where the dyadic r = a0 | a0 is a projective operator in the direction orthogonal to the plane of incidence, a0 = b0 x q, b = Ibl, and bo = b/b. In an anisotropic medium two partial waves are excited [47]. They have different polarizations and refraction vectors m T = b + m~nq. Therefore, an operator (6.20) connects the vectors Ht and q x E, which characterize a superposition of harmonic fields of both refracted waves. In the particular case when the crystal is nonmagnetic (/2 - (~) and is cut in such a way that q is an eigenvector of the k (q~ = ~q = eqq), the tensor })a is expressed in the following form: qx~-lqx ))d "- (mn+ + m n ) -1 G - m + n m n l _ a ~ _ l a

eqm+mn

-

a ~ a ) fa]

Let us consider an initially isotropic nonlinear medium in which uniaxial anisotropy is induced by a powerful plane monochromatic pump wave normally incident from vacuum. If the pump wave is linearly polarized, then the dielectric permittivity tensor may be written in the form [49] = e0[(1 + X0 + X1)I + x1Cc | c]

mn

+

(fi O)t)mn + ~t - - 0 (6.26) or one can find them by solving the equation of normals [ 12]

6.2. Reflection from Media with Light-Induced Anisotropy

l~q = q ~zq

})i __ __})r __

(-~q

" 3 + ( l ~ t _ O t ) m n _ 2+ . ( e t O t mn4 _ Ptmn

_ ---Cafzq | b

in which a tilde denotes the transposed operator. For a harmonic wave (6.13) in an isotropic medium the surface impedance is given by [39]

-

The eigenvalues and eigenvectors of the normal refraction operator (6.25) yield the normal components m n4- of the refraction vector and the polarization states of harmonic partial refracted waves. The m n4- are the solutions of the quartic algebraic equation

/3 = / ] + B b / } - ,

|

#q

8q

(6.25)

The tensor coefficients/3 and Q in (6.25) are derived from A,

1 x ~q | a - 1_~b | q/2r = __q 8q lZq 8q

= / ] + / } 1)

(6.19)

O~t

(6.29)

where e0 is the dielectric constant, X0 is the linear scalar susceptibility, Xl = X1221, C = (X1122 + X1212)/X1, Xijkl are the components of the fourth-rank tensor of the third-order nonlinear susceptibility, and c is the unit vector along the induced optical axis (c is also the polarization vector of the pump field). Since the incident pump wave normal is perpendicular to the plane interface, the optical axis of the MLIA is in the plane interface. Therefore, one can write c = cos r a0 + sin q9b0

(6.30)

where q9 is the azimuth measured from the direction of a0, which is perpendicular to the incidence plane. We point out that the substitution of c (6.30) into (6.29) yields (6.23)

~q = q~ = 8qq

(6.31)

610

GANCHERYONOK AND LAVRINENKO

i.e., q is the eigenvector of the dielectric permittivity tensor (6.29) with eigenvalue,

el, and they give small additions to the expression for the tensor in the case of an isotropic dielectric:

(6.32)

Eq = 60(1 + X0 + )~1)

Therefore, we may use the exact analytical expression (6.23) for the surface impedance tensor, substituting in it the following formula for the permittivity tensor ~ (6.29): (6.33)

--" 8q + 81~c

where 81 --" 80X1C, "cc denotes the projective dyadic operator e | e, and we imply that the scalar eq is multiplied by a unit tensor G, which from now we shall drop. A simple but cumbersome calculation gives us an expression for the impedance tensor of the MLIA:

mn

^

X

m+mn

X + 81~c

m + + mn

F

+

8q(m+n + ran)

(6.34)

1

(6.35)

and by F we denote

(6.41)

Now we are ready to derive Fresnel's reflection and transmission operators. Using the approximate formulae (6.38) and (6.41), it is easy to obtain from (6.18) tensors of reflection and transmission, generalizing the usual Fresnel coefficients. One has t~ = t~0 d-- t~l,

~'b = b0 | b0

^

= _ ~ r = mn~a -+- ~ 7 5 b mn

where the tensor X is " 2.~a X =Sq~b +m n ,

(6.40)

Eq

This expression follows from (6.34) for the case of an isotropic medium. In vacuum or, with high accuracy, in air (ei = G, /2i = (~, n = 1), the refraction vector m and wave normal n coincide. Let us rewrite the relation (6.38) on that assumption (ran = cos Oi, b = sin 01)"

^

~d=

l_.~b+m ~ rna^

~,d=

(6.42)

? = ?0 + rl

where the norms of the tensors d0 and ?0 are much greater than those of the t e n s o r s t~l and 71" lid111 > l"a, and 1/m n >> 1-'b, l-'a, 1-'b, ~,; thus 1-'a, r'b, ~, are quantities of first order in the small parameter

which means that the tangential components of the magnetic field strength vector are continuous across the boundaries in the main approximation. Taking into account the second equality in (6.17), we can write rl -- dl

(6.47)

OPERATOR FORMALISM IN POLARIZATION-NONLINEAR OPTICS so it is sufficient to find the first-order approximation for the reflection operator. Further calculation yields the formula rl .

2 [ .m n A F. a ~ a -~ . V

g F b ~ b - k ~ ' ( ~a mnA mn

mn'~b ) q• 1

(6.48) With the help of (6.39) and (6.45) this expression is reduced to the following form: rl =

RE -- l)rrm x

Substituting the relations for ~r (6.53), for ? (6.51), and for the tensor m ix dual to the refraction vector of the incident wave ( m x = b • + m n q • into (6.55) gives us the final formula: R E -- m n r a b ( - a ~ ) ( ~ q

e l m n s i n 2 ~ o q X [ ( 1 / m n ) ~ b -- mn~a]

2(mn + m n ) ( S q m n + m n )

rl -- rla~a + rlb~b + rlab

(6.49)

(6.50)

2 = da~a + db~b + ~1 rb -- rOb q- rlb,

da -- doa -[- r l a ,

db -- dob -[- rib

(6.51)

Our subsequent scheme includes the following procedures: 1. Deduce the vector Hi (6.15) from the given vector amplitude E of the incident wave and the refraction vectors m i . 2. Project the vector amplitude Hi on the plane interface of the two media according to (6.16), depending on the vector q. 3. Calculate the tangential component H r t of the reflected wave (or transmitted wave if that is what is needed) with the help of (6.50), (6.51). 4. Recover the electric field strength vector of reflected wave E r from the vector l'Irt using the operator ~ [39]: ~) = - q •

1

~, + - - q @ (a + q~q• ~,) 8q

(6.52) Taking into account that the first medium is isotropic and Yr = - ~ (6.41), we may simplify (6.52):

1

l)r --- m n q x ~a -+- ~ q •

mn

fb + q @ a

(6.53)

(6.57)

This expression is in a very useful form for applied calculations, because all quantities are explicitly connected with the natural basis of the boundary value problem, (a0, b0, q).

6.3. Reflection Configuration for a Nonlinear Polarization Spectroscopy Detection Scheme Now, we apply the obtained results to the reflection-transmission problem in the scheme of nonlinear polarization spectroscopy. A powerful normally incident pump wave induces anisotropy in a nonlinear medium. This anisotropy is taken properly into account through the complex dielectric permittivity tensor ~ (6.29). Thus, we use the covariant expression (6.56) to derive the vector amplitude of the reflected probe wave. Let an obliquely incident plane wave E0 pass through a linear polarizer described by the unit vector Up. So we have the incident (on the MLIA) wave in the form Ei = P Eo, where the dyadic - Up | Up is related to the polarizer action. If the reflected beam E r - R E fi E o

(6.54)

(6.58)

is blocked by a crossed analyzer described by the dyadic operator A = u A | UA, where UA is parallel to the analyzer axis, we may write the detected field as E--

A E r -- .4RE f i E o

(6.59)

For definiteness let us take one of the characteristic polarizations of the incident wave, for example, a TE wave of unit intensity. The polarizer transmits this wave without losses, which means that E0 -'- a0,

Up -- ao,

E i -- P E o = (Up. ao)Up -- ao

Then from (6.54)-(6.56) it follows that E r = R e a o = (--rbfa - crmnq • Za q- trb x fa)ao = --rbao - - t r m n ( q x ao) q - t x ( b x ao) -- --rbao -- tX(mnbo + b q )

Finally, we obtain the desired expression connecting the electric fields of the incident and reflected waves by combing Eq. (6.15)-(6.17), (6.53)" Er -- RE Ei

(6.56)

2 ( m n -k- m n ) ( e q m n nt- m n )

where rla, rib are scalar coefficients and rlab is a secondrank tensor. The initial tensors of reflection and transmissions and dr can be obtained by combining Eq. (6.42)-(6.45), (6.47), and (6.50):

ra -- rOa -k- rla ,

81 mn sin 2q)

tr =

or with appropriate notation

E--f)Ht,

2

q- ~b) -- mnraZb -1- rab2~q - rbra

where

8 1 m n ( s i n 2 qg(cos 00 + sin 20i) - 1) ^ Zb m n ( m n -k- m n ) 2

r -:- ra'Ca -+- rbZb q- rl,

(6.55)

-- crmnq x (~a -- ~b) -+- ~.b x (~a q- ~q)

m n (Sqmn -+- m n ) 2 "Ca

+

E r -- l)r H r t ,

where the amplitude reflection operator for the electric field is defined as

81mn sin 2 tpcos 20i ^

-

611

(6.60)

Here, we have taken into consideration that fbaO = fqao -- 0, faaO = ao, q • ao = bo, bo • ao = - q . The projective dyadic of the crossed analyzer has an axis UA -- - c o s O i b - sinOiq = - m n b o - b q

(6.61)

612

GANCHERYONOK AND LAVRINENKO

Therefore, the resulting electric field behind the analyzer is deduced from (6.59), (6.61) to be Eex = AEr

= (UA'Er)UA

=

(trm2n+ t r b 2 ) U A

= crUA (6.62)

Finally, for the detected signal in our approximations we have 2 /NPS

IO"12 ---

e1

2(ran + mn)(eqmn + ran)

m n2

sin 2 2~

(6.63) Here we have taken into account that el and m n may be complex quantities due to absorbing properties of nonlinear medium. Thus, we have verified theoretically the possibility in principle of using the reflection scheme in nonlinear polarization spectroscopy as proposed for the first time in [51 ]. On the other hand, the general theoretical expressions obtained seem to be very useful in the light of experimental research on nonlinear selective reflection [52, 53].

6.4. Noncollinear Geometry in Polarization-Sensitive Spectroscopy The geometry of interacting waves is basic in nonlinear spectroscopy. Nevertheless, only a rather small amount of theoretical and experimental work has been dedicated to detailed study of that problem. Examples are the works of Saican [54] and Levenson's group [55], and the report [20]. In [54] the author limited himself to consideration of the scheme of backward four wave mixing. The authors of [55] offered a new experimental scheme ensuring full collineary of the interacting pump and probe beams in NPS. In [20] the geometry of a possible experiment with a cell of cylindrical form was described, the diameter of which substantially exceeds the cross-sectional dimensions of the light beams, for elimination of polarization changes of the beams during oblique passage through walls of the cell (see also Section 10). Another scheme of polarizationsensitive spectroscopy [31 ] has, however, continued in common use, where probing and exciting beams are incident on a cell of standard form (fight parallelepiped), containing the investigated substance, at a small angle arccos(n0 9n 1), thus providing their spatial separation. The angle can be from several degrees [56] down to several milliradians [57]. Evidently, even at such small angles, the polarization state of radiation (pumping in the standard version of NPS, or probing in the version of NPS for observation of out-of-Doppler dichroism and birefringence induced by laser radiation [58]) in the investigated medium with unperturbed refractive index nm will in general differ from the initial state in a medium with refractive index fi after passing through a plane wall of the cell made of a substance with refractive index new. So the interaction that actually takes place is, for example, not with the circularly polarized radiation of the pump beam, but with an elliptically polarized wave. Note in this connection that the elliptical polarization, as a rule, is not constant and tends to shift during propagation in a nonlinear medium to a steady polarization state, which can be circular or linear [4]. On the other hand, even when the mentioned

polarization changes are small, they can have rather large significance in polarization-sensitive spectroscopy (especially for optically thin media), particularly in the quantitative interpretation of polarization spectra containing hyperfine structure of molecular lines [31]. Thus the investigations proposed in the following are realistic. Let the exciting radiation have circular polarization in an isotropic medium surrounding the cell. Then, by applying Fresnel's operator formalism (6.42)-(6.45), it is possible to show that for arccos(n0 9n l) 7 nm (optimal conditions) can be resolved, and a distance of > 9 nm can be resolved under routine conditions. However, estimation of the confidence level is an important factor for reliable results, and more work is still required in this direction. Such methods generally reconstruct the original distribution, given the measured distribution and some parameters of the analytical conditions. In this way it is claimed that TRIMDYNAMIC codes, which simulate layer broadening, could be reversed and successfully reconstruct the original distribution of metal layers in Si and Ge matrices [15]. Similarly, SIMS profiles of quantum wells and superlattice of III-V semiconductors have been modeled by convolving the true profiles with an analytical response function [ 118].

8. ION IMAGING WITH SIMS High-speed acquisition of SIMS data by computerized systems is not only providing better and faster analysis, but also the possibility of storing and reproducing the acquired information. Consequently, a computer can be used to scan the primary beam on the surface of the sample, scan the secondary optics accordingly to secure stable transmission, switch between the masses at the mass analyzer, and store the acquired data. Scanning in two dimensions for one element is very fast and can be visualized in realtime on a computer screen. Stored data for multiple elements or isotopes can be retrieved and visualized in two or three dimensions. However, correct representation of the data fully depends upon the correct interpretation of the collected single analyses with the methods discussed in the previous sections for quantification and depth profiling. Furthermore, initial topography further affects overall resolution of the imaged area by differential sputtering. It is suggested that correlations between SIMS images and topography (obtained, for example, with an AFM instrument) should be studied to assist in the correct visualization of two- or three-dimensional SIMS data [ 144]. It has also been shown that, when instrumental factors are not involved, image correlation spectroscopy (ICS) or image cross-correlation spectroscopy (ICCS) can successfully confirm spatial relationships by comparing two-dimensional SIMS images acquired during depth profiling [145]. This is a mathematical approach and it is useful mainly when features close to the size of the resolution are considered. Three-dimensional imaging, free of matrix effects due to the use of MCs + ions and correction with RSF Values, is demonstrated in [49]. However, a true three-dimensional reconstruction, suggested in [ 144], has to use information related to the original topography. Finally, correlations between images of different elements in two or three dimensions, line scans, and depth profiles of the analyzed volume are easy to plot by retrieving them for the existing three-dimensional data.

9. APPLICATIONS TO THIN FILM CHARACTERIZATION 9.1. Introduction

The high sensitivity of the SIMS technique is an advantage for thin film characterization. Thin films are low-volume materials with properties that are sometimes different from these of their bulkier counterparts. It is obvious, then, why precise control of their chemistry and their structural characteristics is so important. SIMS has been extensively used for the characterization of thin films. However, recognizing the difficulties of acquiring quantitative results, it is mainly treated as a qualitative or semiquantitative technique, always supported by other physical techniques for analysis and characterization. In these cases, one will find only basic information on how SIMS has been applied in the specific case, such as that of the primary ion beam species, its energy, possibly the type of charge compensation used when insulating samples are analyzed, and in the mode in which it was operated, something that sometimes is straightforward from the application. This may give the reader the impression of a routine technique. In many cases, though, a detailed methodology of the analyses is given and the problems are discussed, and some are treated in a systematic way in the search for possible relations. These research works treat the technique with great care and support their findings with results from other techniques. Consequently, all researchers still treat the technique consciously and the reader is advised also to do so. Still, one must stress once again the following advantages, also summarized in [146]: (a) SIMS can detect all of the elements of the periodic table, including hydrogen, and their molecular combinations; (b) SIMS has the lowest detection limit of all analytical techniques; (c) because it is a mass spectrometric technique, only isotopes are analyzed with applications in diffusion studies; (d) static and Tof-SIMS can give information on one monolayer and they are excellent tools for surface analysis; (e) ToF-SIMS is also a good tool for organic materials and can provide information on their chemical structure; and (f) SIMS requires minimal or no sample preparation. SIMS instruments can be used (a) for dynamic analysis for bulk composition of very small structures; (b) in static mode to analyze surfaces and monolayers; (c) for profile analysis of one dimension, either in depth or across a line on the surface, (d) for two-dimensional analysis of an area of the surface; and

SECONDARY ION MASS SPECTROMETRY (e) for three-dimensional analysis by combining the previous two, giving structural information (element distribution, interfaces, dissolution reactions, etc.). SIMS has also been used on devices that result from thin films. Many of these applications, however, are scattered work, related only to individual materials, and only in a few cases is more systematic work on certain areas present. There is also a lack of information on specific applications, because of the industrial interest of the materials (e.g., the semiconductor industry). Consequently, the following work has to follow this structure. Moreover, the list of applications and examples is not exhaustive or even restrictive. The purpose of this work is to give a basic idea of the advantages and the problems encountered when the technique is used and the areas in which it has been used, supported by some examples. It is expected that the user will be able to apply the technique in new areas and in a correct way, taking the maximum amount of information that it can provide. Thematically, SIMS has been used in materials science, surface science, and technology. In materials science, SIMS has been used to chemically and structurally characterize films, to optimize their growth procedures, and to control the growth environment, possible impurities, and sources of contamination. Types of layered materials that are more systematically studied are superconductors and, more specifically, YBCO films, to which a long paragraph is devoted here. New materials, such as synthetic diamonds or extra hard materials, are also very important, and their properties depend on their detailed chemistry. Other applications include the optimization of film alloys to produce electrodes and studies of the homogeneity of chemical coatings and some properties of polymers such as wettability or chemical changes and contamination of their surfaces. Surface characteristics of bulk materials are enhanced with thin films, and improvements in corrosion resistance or tribological properties are useful in aerospace technology or the production of biocompatible materials for artificial implants. SIMS has been also used to enhance the surface properties of substrates to improve the adhesion of films. Finally, some post-processing, such as annealing or doping, is common, and SIMS has been extensively used to study or control the effect on films. Very important technological materials are the materials used to fabricate microelectronic and optoelectronic devices. These devices are generally multiply layered structures, and for completeness they are treated here as thin films. One would encounter applications such as radiation filtering and detection in the fabrication of devices such as thermistors, capacitors, and memories. SIMS was also used to improve insulators, optimize VLSI metallization, fabricate advanced buffer layers, or investigate new materials such as semiconducting diamonds or SiGe HBT heterostructures. New technologies demand high integration of high-quality devices and SIMS has found applications in high-density recording media, fabrication of LCD displays, the improvement of solar cells, quality testing of lithographic patterning, and, more recently, microelectro-mechanical systems (MEMS) assembly and packaging. Environmental aspects in-

665

clude applications to the search for thin-film gas sensors or the catalysis of automotive exhaustion.

9.2. Characterization and Optimization of Materials and Processes by SIMS New and advanced materials, including thin films, should be designed and optimized with respect to their function, and with the purpose of finding technological applications. SIMS, because of its high sensitivity and high depth resolution, can assist in the chemical and structural optimization of thin films through the study of the films themselves, their method of growth, and the growth environment, and, finally, their stability during further processing (e.g., doping or annealing) or further testing. Briefly, by studying the surfaces of the substrates one can optimize them to improve growth, adhesion, and mechanical, thermal, or chemical stability at the interfaces. Compositional studies of films can provide detailed information on traces, impurities, and major chemistry with direct applications to the properties and the quality of the films. Further processing of the films, such as thermal treatment, might also result in selforganization or phase separation effects, which can be useful in the fabrication of quantum wells, etch stop layers or diffusion barriers. Furthermore, it is very common that thin films are used to alter or improve the surfaces of substrates. For example, oxide thin films grown on glasses improve their chemical and physical properties while they maintain transparency. Despite the sensitivity and the advantages over similar analytical techniques, SIMS must be supported by other techniques [ 147], such as SNMS, RBS, AES, and other spectroscopic techniques.

9.2.1. Control of Growth and the Growth Environment An example where very good control of the initial steps of growth is expected to enhance the properties of grown films is in high-density recording (magnetic) media. A method of ultraclean (UC) sputtering of NiP/A1 substrates was studied, in which Cr, CoNiCr, and CoCrTa films were deposited by DC magnetron sputtering [ 148]. Ultraclean conditions are achieved by dry etching with Ar just before film deposition. Magnetic measurements have shown that the coercive force Hc (the resistance of a magnetic material to changes in magnetization, measured as the field intensity necessary to demagnetize it when it is fully magnetized) increases with etching time. Systematic studies of ultracleaned and untreated samples made by SIMS (Fig. 19) have shown that this effect is related to oxygen that is absorbed on the substrate surface. The oxygen concentration is significantly reduced, even with slight cleaning, and results in an increase in Hc and the deterioration of magnetic properties. The readsorption of oxygen and other gas impurities on the surface does not reverse the effect. During growth, impurities have to be minimized to acquire good materials with optimized properties. Because of its high sensitivity, SIMS is a good tool for studying impurities, and this will be demonstrated here with an example, the synthesis of n-type semiconducting diamond [149]. P-doped diamond

666

CHATZITHEODORIDIS ET AL.

Fig. 19. Profiles showing how ultraclean sputtering, which is used as a cleaning procedure on substrates, can affect the oxygen content of surfaces. From [148] with permission from the author and Elsevier Science.

because of mechanical polishing. The film itself had reduced H content. The effect of the growth technique and of the growth environment is demonstrated in the growth of Si3N4 films [150]. These films are chemically inert and thermally and mechanically stable, and they are hard and have good dielectric properties. Microelectronics and other technologies take advantage of these properties to fabricate oxidation masks, gate dielectrics, insulating layers, and passivation layers. When these films are grown by chemical vapor deposition (CVD), hydrogen is trapped in the films and the physical properties of the films deteriorate. Hydrogen is contained both in the Sill4 target used by CVD and in the NH3 atmosphere. Rf-magnetron sputtering, however, uses a Si target in a reactive nitrogen-argon atmosphere (N2-Ar) and the hydrogen or oxygen involved comes from residual moisture in the environment. SIMS has helped to find the relation between bias voltage and hydrogen and oxygen content in the films, resulting in the observation that with increased voltage bias during sputtering deposition the hydrogen or oxygen content decreases to concentrations lower than 4 x 1020 atoms/cm 3 [150].

9.2.2. Optimizing Surface Properties and Adhesion with Thin Films

Fig. 20. A positive-ion SIMS depth profile of P-doped epitaxial diamond thin film (300-nm thickness) on a nondoped, synthetic diamond substrate. The higher content of hydrogen at 0.3 ~tm indicates that the interface with the substrate (shaded area) has been reached. The hydrogen content is higher because of contamination of the mechanically treated substrate surface. From [149] with permission from the author and the American Institute of Physics.

films were synthesized at high and low temperatures with vapor growth methods on diamond substrates, which were synthetic and mechanically polished. Because growth is performed from the vapor phase with PH3/CH4 precursors, the level of incorporated hydrogen is expected to be high, reducing the conduction properties of the diamond film. Optimized growth with the appropriate PH3/CH4 ratio and under substrate heating at very high temperatures has reduced the hydrogen content in the films [ 149]. The films have been characterized by SIMS depth profiling of the P and H elements (Fig. 20). Positive ions of the above elements were extracted with an O + primary beam. Quantification of the 1000 ppm P in the diamond films was estimated from RSF values, measured at an absolute concentration of 2.5 x 1019 cm -3. Structurally, the depth profiles show an almost constant P composition, implying uniform implantation. SIMS revealed that hydrogen was high only at the interface with the substrate, which was possibly caused by trapping of H at the imperfections of the substrate, which were numerous

In many technological applications thin films are used to enhance the mechanical, chemical, electrical, optical, and other properties of substrate surfaces. However, to maintain these properties, the thin film should stably adhere to the surface of the substrate. Possible influences on the adhesion of thin films to substrates are the structural, topographical, and chemical properties of the substrate itself. SIMS can be used to study chemical properties, and it is known that generally gases or hydrocarbons form contamination layers that reduce adhesion. SIMS, for example, was used to study the contamination that affects the adhesion of carbon, aluminum, chromium, and tungsten films deposited on steel and polished TA6V titanium alloy substrates. Oxygen and hydroxide radicals (O, OH) were detected, and it was demonstrated that sputter cleaning, with, for example, an argon ion beam, can reduce these effects [151]. Moisture diffused at the interfaces at room temperature is in a similar way the reason for reduced cohesion between TiN films and SiO2, and sequences of ion images taken with SIMS provided the opportunity to visualize and study the effect in detail [ 152]. Adherence of a film can also be improved when the chemistry between the substrate surface and the film does not change abruptly. Implantation of some elements in the substrate may create the appropriate conditions to improve adherence. C and N elements have been implanted in Ti alloys [153]. Ti alloys are generally used in the aerospace technology and for biomedical purposes, and although they have many good properties, such as a low density, high corrosion resistance, and good mechanical properties, their tribological characteristics, such as friction and their wear resistance, are very weak. Thin films of

SECONDARY ION MASS SPECTROMETRY nitride, carbide, and carbonitride can also improve these qualities. After implantation, SIMS depth profiling and RBS have demonstrated [ 153] that the independent implantation of C and N has reached the same depth, ensuring homogeneity, but the outermost Ti layer was partially oxidized. A material commonly used to cover the surfaces of stainless steel is a film of tungsten carbide (WC). Tungsten carbide is a hard material (2200 HV) with a high melting point (about 2800~ and a high thermal conductivity (1.2 J/(cm s K)) and, after diamond, has the highest modulus of elasticity (highly elastic), which is well above 700 GN/m 2. To further improve its hardness, it is doped with Ni. Estimations of the thickness of the grown films and compositional depth profiles have been acquired by SIMS [ 154], demonstrating that W, C, and Ni are uniform with depth. W and C are stoichiometric, allowing only for a slightly lower C signal, which is probably due to its lower ionization efficiency. SIMS has also revealed Co impurities, which probably have migrated from the stainless steel substrate, of which it is a component.

9.2.3. Post-Processing of Materials and the Resulting Effects

Sil_x_yGexCy alloy is a material that is applied in thin films on different substrates and can produce transistors and infrared detectors or high electron mobility devices. In the first case heterojunction bipolar transistors (HBT) with cut-off frequencies exceeding 100 GHz can be produced [155] by introducing carbon into the SiGe thin film, which is grown on Si. Sil_x_yGexCy alloy has a better lattice match with Si than with SiGe. Studies of SIMS and other methods have revealed a carbon self-organization into g-films [ 155]. These fine films might have technological applications such as quantum wells, etch stops, or diffusion barriers. However, growing Sil_x_yGexCy alloy films is difficult with molecular beam epitaxy (MBE) or RTCVD (rapid thermal CVD) methods because of the low solubility of C in Si and the tendency for SiC to preferentially precipitate [156]. Films that were grown by MBE and further treated by high-temperature (950~ rapid thermal oxidation (RTO) have been studied by SIMS and have shown that this treatment outgasses carbon and reduces the C content, especially close to the surface, but also deeper at the interface with the SiO2 [ 156]. Furthermore, this introduces compressive stress. SIMS has also revealed a slight increase in carbon concentration close to the interface with the Si substrate [ 157] when these films are grown at about 450-560~ Thin films can be also produced by post-processing of another film by the induction of phase separation. Such processing, for example, has technological advantages because at the same time it separates films of Ti and Co alloy in a twin layer of a silicide (e.g., CoSi2), which is a diffusion barrier of the Si from the substrate, and a surface transitional contact layer (TCL) film [158]. The first is functioning as a diffusion barrier layer (DBL) and the second as a TCL. Phase separation occurs in a N atmosphere; the gas reacts with the substrate to form the two layers. In the above study, SIMS was used mainly because of its advantages over AES, such as the higher sensitivity and

667

the capability to analyze molecular ions (CoTi +, CoSi +, and TiSi + when an O + primary beam is used, or SIN-, TiN- with a Cs + primary ion beam). Furthermore, qualitative SIMS depth profiles were acquired to understand the interaction between Si and the thin films of Ti-Co and Ti-Co-N during thermal annealing. It has been observed that reaction of TiCo thin films with Si results in the formation of ternary silicide compounds CoTiSi instead of CoSi2. With the introduction of N, a phase separation in Ti-Co-N thin films into two films occurs, resulting into a bottom CoSi2 film and an upper TiN film. An excess of N will form Si3N4 at the top of the surface. SIMS, also supported by AES and XRD (X-ray diffraction), has suggested a number of possible reactions during annealing at 850~ which lead to the thin film separation. Migration of elements during post-processing is also demonstrated in the following two cases. Annealing is a common post-processing technique for thin films. It is used mainly to remove stress formed in the thin films during growth, to convert an amorphous film into a polycrystalline, to outgas volatiles that are trapped in the films during growth, etc. However, it can also initiate other chemical effects, and SIMS is capable of revealing these changes. For example, annealing has mobilized Si to diffuse from the substrate to the surface of the Fe film, which was deposited on Si [159]. It is common that transition metal thin films (Fe, Co, Ni, and others) deposited on Si substrates form various silicides after annealing. The effect of annealing on the element migration is graphically demonstrated in Figure 21. Diamond-like or carbon-based composite films are promising divertor materials for the new generation fusion energy reactors because of their excellent thermal properties. Trapping of 4He+ or H + is an important safety parameter for their use in such applications. SIMS depth profiling has demonstrated that migration of H starts at 700~ and, finally, H is broadened to the whole thickness of the film [ 160]. Prior bombardment with He did not change the above behavior.

Fig. 21. The effect of annealing at different temperatures on hydrogen concentration profiles in carbon-based composite films, obtained by SIMS. From [160] with permission from the author and the American Institute of Physics.

668

CHATZITHEODORIDIS ET AL.

9.2.4. Investigating Physical Properties of Materials Corrosion effects can be enhanced by diffusion of elements into the materials in question. However, barrier layers can improve resistance to corrosion, and in harsh environments they are sometimes unintentionally grown, however, enhancing the properties of the used materials. The study of these materials in such environments is useful, and because these layers are generally thin and are present on the surfaces of the materials, they are also mentioned here. As a first example, oxide layers can be formed by oxidation as a result of oxygen diffusion, and with the intention of studying corrosion effects of reactor water on Zircaloy fuel rod claddings in pressurized water reactors, SIMS depth profiling and ion imaging were used to analyze these oxide layers [161]. In these reactors pH and reactivity are controlled by adding LiOH and H3BO3 to water. Li and B were found to diffuse in the < 10 ~tm thin oxide layer, which is formed on the fuel rod claddings. It was also observed that Li concentrates closer to the surface of the oxide (in touch with the water), leaving a dense oxide layer closer to the metal/oxide interface to control corrosion, and because it was present at a low concentration, it could not initiate corrosion reactions. Corrosion resistance of titanium alloys to an NaC1 environment was also increased by implanting in them a specific quantity of nitrogen [162]. SIMS depth profiling helped to optimize the above material. In the same way, with the incorporation of yttrium into Fe-Ni-Cr alloys, oxide scales are formed at the surface of the alloys, protecting them from oxidation at hightemperatures [163]. In this study, SIMS was capable of seeing the depth distribution of yttrium and of demonstrating the presence of an Y203 oxide 35 nm from the surface of the alloy, preventing further penetration of oxygen deeper into the sample. Similar studies have been performed for alumina or chromia alloys, but with less effect from yttrium [ 164]. Aluminum alloys can also be protected from corrosion when Ni is incorporated into the outer hydrated aluminum oxide; SIMS was used to study the properties of these films [165]. Corrosive-resistant Fe films could also be deposited at room temperature on Si wafers, and SIMS studies have shown a highpurity layer [ 166]. Corrosion preventions mechanical contact, such as between heads and hard disks, is increased by closer contact and the demand for higher storage densities. Among many techniques, ToF-SIMS was the most sensitive to cobalt migration toward the thin protective layer of the hard disk surface [ 167]. The effect is more pronounced for thinner protective layers and at normal humidity and temperature conditions of hard disk operation.

9.3. Superconducting Materials The perfect conducting properties of the high-Tc superconducting films increase their technological potential as ideal chip and device interconnects. However, compatibility with other materials, such as doping materials or substrate materials, must first be achieved for optimized performance. Furthermore, growth procedures and environments must be improved. SIMS has

helped researchers to study several aspects of YBCO films, such as their structural or chemical composition, the possible contamination from sources mainly related to the growth procedures, the migration and interdiffusion of doping elements between the layers or of elements from the substrate, optimization of their chemistry after doping with the aim of improving their electrical properties at even higher temperatures or their magneto-resistance properties. In the following subsection, a list of characteristic cases is presented to demonstrate the amount of information that can be acquired from the YBCO films during SIMS characterization.

9.3.1. Annealing Effects on Doped Elements and on the Interfaces of YBCO Heterostructures When YBCO heterostructures are doped with different materials they acquire their superconducting properties. A usual step after doping is annealing, which, however, has an effect on the doping materials: they tend to migrate from the doped to the nondoped layers. In a similar way, elements from the substrate can also migrate to the neighboring layers. Both effects cause the deterioration of the efficiency of the structures and the choice of doping elements or of the substrates and the annealing conditions can be optimized and standardized by iterating between chemical characterization and characterizations of the electrical or other properties of the films. Because YBCO films are multilayered thin films, chemical characterization can easily be performed with depth profiling SIMS or SNMS, generally assisted by other techniques. For example, SNMS has been used in comparison with AES techniques to show that when YBCO films are doped with rare earths there is no migration observed at annealing temperatures of 900~ [ 102]. SNMS was the technique chosen here to reduce the matrix effects introduced by SIMS. Y and Pr rare earths were the doping elements, and CVD techniques ware used to grow the heterostructures of YBa2Cu3OT-~ , PrBa2Cu307_8, and (YBa2Cu3OT-~/PrBa2Cu307_8)n films. Depth profiling of both annealed and as-deposited films has additionally demonstrated that CVD growth does not cause the deterioration of the interface quality of the heterostructures. This is depicted in Figure 22, where the depth profiles of the doping elements (Y and Pr) are compared with primary film elements (Cu and Ba) and the substrate (Ti and Sr). In this figure, two main YBCO layers can be distinguished (one doped with Y and a second with Pr), as can their interface at about 0.14 ~tm. The SNMS measurements have been performed for comparison on both powder and single crystals of these materials, and the acquired RSF values were identical. These values were used for the quantitative depth-profile characterization of the films and are available in [ 102]. From the previous sections it can be seen that Y and Pr are doping elements that produce films with stable chemistry and good electrical properties. Another doping element, Ag, can also increase the overall critical-current density (Jc) while at the same time giving to the films better mechanical characteristics. SIMS depth profiling, however, has shown that it is

SECONDARY ION MASS S P E C T R O M E T R Y _

__

....

~ .. . . . . . ~.....

, .......

,

1

.,,,

,,

.....

0.10

Cu

......

I

~

669 I

'

I

I

I

I

I

I

Ti (a)

O~

g

Ba

!'~-v ""

25:

0

~

201

is7

~

Pr

x,._. o.w

IB

/

0.05

o.to

o.is

o.zo

0.25

0.30

;:

II

i~1

,

.,,

I

, I

1.5 pm YBCO # Ag on LAO (100)

depth (l.tm)

Fig. 22. An SNMS depth profile of YBa2Cu307-~/ PrBa2Cu307-8 heterostructures. Ti and Sr belong to the substrate, Cu and Ba are at high concentrations throughout the film, and Y is in the first layer and Pr is in the second. One interface of the heterostructures is seen here at about 0.14 lxm. From [102] with permission from the author and Springer-Verlag.

II

I'

/

.

. I

I

,

,t

.....

-O.I

~.

(b)

0.025

4"

-0J

highly mobile [168], a feature that makes Ag a less than useful doping element. More precisely, Ag-doped Y B C O targets were used to grow thick Y B C O films (> 2 txm) on LaA103 substrates by pulsed laser deposition (PLD) with the purpose of producing coat conductors with increased current-carrying capabilities [168], which are useful for high-current applications in electrical engineering and power distribution. These films were characterized by X-ray fluorescence (XRF) and SIMS depth profiling. XRF was used for quantification purposes; it was estimated that Ag was contained in concentrations of 1 at.% over the entire surface of the samples, which had Tc > 70 K. SIMS depth profiling of several films demonstrated that this concentration decreases with depth (Fig. 23). It is possible that the observed nonuniformity of Ag with depth can explain the

1.20

1.00

l 87

'1'

I H

I

I 91

I

! 9~

TEMPERATURE (K)

Fig. 24. Imaginary (a) and real (b) part of ac susceptibility curves of Agdoped YBCO films. The values of the imaginary part (a) show a second peak probably attributed to a second high-Tc component (at about 93 K) for the same film. SIMS has shown a migration of Ag to the surface layers, which possibly produces this effect. From [168] with permission from Elsevier Science.

multiple high-Tc components of some thick films (Fig. 24). The high mobility and surface energy of Ag forces it to migrate to the surface of the films, a phenomenon enhanced under substrate heating. Furthermore, Ag has a low solubility in YBCO, and it concentrates at the boundary grains, which are larger at the surface of the film [ 168].

9.3.2. Doping by Ion Implantation

~r~ 0.80

o

l M

0.60

0.40

0.20

o.oo 0

I 500

I 1000

I 1500

. . . .

I 2000

2500

3000

t

3500

4000

Depth (nm)

Fig. 23. A simple SIMS depth profile of Ag in a YBCO film, demonstrating how concentration of a doped element drops with depth. From [168] with permission from Elsevier Science.

Doped YBCO films are not only produced from predoped material sources, but also by ion implantation methods. However, ion implantation can severely affect the internal structure of the films, by the creation of nonuniform, Gaussian-shaped deposition profiles, crystal damage, or both. A variety of elements can be implanted at a variety of energies; each case must be studied individually. The first example is the case of YBCO films grown on a LaA103 substrate and implanted with protons (H+), oxygen (O), and gold (Au) at ion energies ranging between keV and MeV [ 169]. The purpose was to create thin film superconductor devices that would be used as magnetic thin film devices employing colossal magneto-resistance (CMR). TEM (tunneling electron microscopy), X T E M (cross-sectional

670

CHATZITHEODORIDIS ET AL.

TEM), SEM, XRD, and SIMS were used together to study the structural changes. SIMS depth profiling in particular was used to study the distribution of the implanted ions. The profiles were calibrated for depth by measuring the sputtering time and calculated against the depth of the formed craters, which was measured with a stylus profilometer. As anticipated, depth profiles measured by SIMS of low-energy (50 keV) implantation of H + in a heavy matrix (such as the YBCO film) produced a Gaussian profile with a changing slope at the leading edge. Comparison of SIMS profiles for other implants, such as oxygen and gold, with TRIM simulations (see Section 2.2.) have shown that Gaussian profiles become more symmetrical and compare well with each other. This is attributed to reductions in the original crystallinity with increasing atomic mass of the bombarding species (TRIM simulations are more precise for amorphous materials). Within the same work [169] the proton mass transport in YBCO films was obtained by SIMS depth profiling, through the study of H - and OH-. The Gaussian profile is also skewed, with a change of slope at the leading edge, reflecting pre-existing protons, which have diffused into the film before implantation. They give rise to a surface layer with a higher effective stopping power for the deuterons, and during implantation these protons are well mixed into a layer with uniform concentration, giving the step at mass 17 signal (probably 16OH-). Diffusion of O [169] and deuterium (D or 2H) [170] into the YBCO film (Fig. 25a) seems to occur easily inside or outside of the film and redistributes. Especially during annealing, protons diffuse without using OH as a carrier, whereas O diffuses in the film, keeping the initial concentration. D, however, is bonded to oxygen and OH shows a declining "diffusion-controlled" distribution to a similar depth of 150 nm within the as-received YBCO film [ 170]. Heavier atoms, such as Au implants, show no redistribution at temperatures lower than or equal to 650~ (Fig. 25b, [169]), although surface crystallization started. However, redistribution occurs at temperatures between 650~ and 700~ Similar temperatures for 2H and 180 are about 175~ and 250-300~ respectively. Finally, in [169] a good example is provided that demonstrates the difficulties introduced during the interpretation of the acquired SIMS data. The problem is mass interference, observed as a mass-18 signal higher than expected from the natural abundance of 180. This is attributed to protons (2H) combined with 160 to form 18(1602H ). 9.3.3. Contamination Sources

Contamination is an important parameter, significantly affecting the quality of superconducting properties. It is mainly related to growth procedures, the growth environment, and contamination or reaction phases originating from the substrate. Common contamination coming from the environment was found in YBCO films that are deposited by codeposition sputtering of four ion beams and three targets (Cu20, Y203, and BaCO3) on SrTiO3 substrates [ 171]. The fourth ion beam was supplying low-energy oxygen. Static SIMS was used, together

0.08

O

YBCO 0.06

O

oO 0.04 0.02

0.00 0.0

(a)

0.2

0.4

0.6

1021 '

%

~ o c

< 102o (

0.8

1.0

1'. As-impl 2. 500 ~ 3. 700 ~ 4. 8 4 0 ~

Z

_(2 n" FZ

0

'

1018

'

Z

o

~ i 1017

0.0

(b)

YBCO I

I

I

0.2

0.4

0.6

tr RI i--z I1

0.8

DEPTH ( micron )

Fig. 25. Redistributionand peak wideningof oxygenin a YBCO film at different annealing temperatures. (a) Three SIMS profiles show 180 in YBCO before annealing (curve 1), after annealing at 300~ for 1 h (curve 2), and after rapid thermal annealing at 450~ for 2 min (curve 3). (b) The same effect is also observedfor Au, but at higher temperatures. From [169] with permission from the author and Elsevier Science.

with AES and ESCA-XPS, to characterize the top monolayers of the surfaces of the films and compare them with monocrystal reference materials of the same composition. In the monocrystal reference materials traces of A1 were found to be coming from the alumina crucible that was used during preparation. In contrast, the sputter codeposited samples have shown traces of residual gases, such as C, CO, CO2, and H. Also in the mass spectra, CO was interfering with Si, which came from bulk diffusion during sputter deposition at 650 ~ AES and SIMS have shown identical results for the two samples. Metal-organic chemical vapor deposition (MOCVD) is a well-established technique in the production of III-VI semiconductor optoelectronic devices (e.g., UHB-LEDs, ultra-highbrightness LEDs) or solar cells. Such a high-mass production technique could also be used in the production of cost-effective YBCO superconducting films [ 172, 173]. During the deposition procedures of the YBCO film, fluorinated precursors are used, which result in a quantity of fluorine remaining in the film [ 173, 174], which has to be removed by annealing [ 172] or reduced by the introduction of water into the flow of oxygen gas during growth [173]. SIMS demonstrated that annealing for 1 h in 10 mbar nitrogen at 800~ can reduce the original fluorine con-

SECONDARY ION MASS SPECTROMETRY centration from 250 ppm to about 50 ppm by evaporation [ 172]. The effect of a number of substrates, such as A1203, MgO, SrTiO3, ZrO2-Y203 (YSZ), and BaF2, on the superconducting transition temperature (Tc) on YBCO films has been studied. Superconducting films can be deposited by ion-beam sputtering and e-beam evaporation [ 175], or even by pulsed injection CVD from an organometallic vapor [ 176]. SIMS depth profiling alone or in combination with other characterization methods has resolved several interface materials and the interdiffusion of elements that affect the Tc properties of the superconducting film. MgO substrates show little interaction between the phases, but Tc was again reduced. YSZ substrates, although they interact to form BaZrO3 perovskite and although Zr was diffused in the film, have a small effect on the Tc properties [175]. However, an intermediate layer of CeO2 can stop the Zr diffusion and improve epitaxy and the other electrical properties of the films [ 176]. Compatibility with the substrates and the doping materials and contamination sources are not the only parameters that should be monitored. Superconducting materials like YBCO are applied in multilayer devices and circuit structures, thus they have to be patterned and a lithographical step will be involved. Consequently, not only compatible insulating materials, but also an appropriate patterning process and etching materials have to be found. A first study [177] has shown that the SrTiO3 (STO) can be considered a promising insulating layer in YBCO/STO/YBCO crossover structures. It was used with SIMS to study the interfaces and optimize the compatibility with the material photolithographic techniques and wet-etching process.

9.3.4. Proximity Effect and Other Superconductors A type of periodically layered superconducting film based on Nb/Pb and Nb/Cu multilayers has properties that depend on the proximity effect, and consequently the quality of the interface and the presence of possible transition layers are also important. Generally, the Nb layers are about 20 nm thick, whereas the metallic layers range from less than 2 nm to 17 nm. The structures are deposited on Si substrates with magnetically enhanced sputtering methods. Very high-resolution SIMS depth profiling has been used effectively together with X-ray specular reflectivity (XSR) to study the above structures [129]. In this study, high depth resolution is achieved by very low intensity, highly grazing primary oxygen and cesium ion beams (< 2 keV and 5.5 keV, respectively) and has revealed all of the periods of the multilayer structure. SIMS has shown that residual oxygen from the growth chamber is trapped preferentially at the interface between Pb and Nb layers and with Nb (NbO), mainly because of its high reactivity. Preliminary experiments with the same multilayer films but grown in UHV by MBE do not show NbO formation. Furthermore, Nb matrix effects due to oxygen are not present in the SIMS profiles of the MBEgrown structures, whereas they are observed as high yields of Nb where Nb oxide was deposited in sputter-deposited layers.

671

Thin film superconducting oxide (SCO) materials are another type of interesting superconducting materials that can now be produced with a variety of methods as thin films. SIMS has been used to find compositional differences between the thin-film SCOs and the bulk SCOs that are produced by conventional methods [ 178].

9.4. Applications in Electronics, Optoelectronics, and Light Sensors SIMS is a very common characterization technique in the semiconductor industry, mainly because of the very low detection limits compared with other techniques. It is possible to attain a detection limit as low as 2 ppb (= 1014 atoms/cm3). This is achievable because of the larger area of analysis. However, for semiconductor VLSI, or UVLSI applications, the feature sizes are a challenge for the technique. VLSI, for example, requires a lateral resolution of 0.2 ~tm for doping elements of 1014 atoms/cm 3 concentration [179], which results in a detection limit of 200 ppm. Thus, higher currents at finer primary ion beams have to be adopted. A solution can be created by applying liquid metal ion beams that can be focused into submicron scales (generally less than 0.2 ~tm). To improve the secondary signal analyzed, a ToF instrument can also be used, which has high transmission, and post-ionization methods using lasers are also possible [ 179]. Because semiconductor devices are patterned structures, they may not be considered as thin films by the strict definition. However, a selection of examples is presented here, such as when special layers or interfaces are studied. Such materials can be, for example, silane agents (organo-silicates), of which only one monomolecular layer is enough to improve surface properties such as adhesion; when they are deposited in more molecular layers they are used for coupling. In both cases ToFSIMS was used to study the quality and the effect of the layer on the substrates (see [ 180] and references therein). The areas in which SIMS can assist semiconductor research are mainly diffusion, migration, and segregation of elements between the different layers and the substrates, as well as chemical purity, doping concentration, and interface chemistry and structure. SIMS ion imaging has also been used to check the selectivity of deposition during lithographic patterning processes. Following is a selection of examples demonstrating the above studies for different devices.

9.4.1. Light Emission and Detection Devices In optoelectronics, MBE-grown, the fabrication of ZnSe-based (II-VI) heterostructures have recently found many applications in devices emitting in the blue-green region of the optical spectrum. To achieve the above emission properties, layers containing Cd are deposited to generate the active quantum well regions. However, interdiffusion of these elements between the layers but also with the substrates (generally GaAs) reduces the quality of the devices [ 181 ]. Moreover, the diffusion of Ga

672

CHATZITHEODORIDIS ET AL.

into the ZnSe layer produces complex chemistry, which generates two more photoluminescence (PL) peaks at 2.0 and 2.3 eV. SIMS studies have demonstrated sharp compositional changes in the different layers before annealing. However, annealing induces interdiffusion of Ga from the substrate. Moreover, Cd from the Cd-containing layers broadens into the other layers. According to experiments and confirmation by SIMS, it has been demonstrated that thicker films do not reduce the effect. On the contrary, they give enough space between Cd and Ga from the substrate that they do not reach each other and improve the thermal stability of the device. High-performance optoelectronic devices such as laser diodes emitting blue/UV light under room temperature conditions and continuous-wave operations with long lifetimes (> 10,000 h) [182] can be based on III-nitride semiconductors (e.g., GaN) [183]. Immediate applications of these structures are in the next generation digital video disk (DVD)players. GaN was deposited on sapphire substrates by MOCVD, and a thin (200nm) layer (cap layer) of dielectric SiO2 was deposited on top by electron beam evaporation [ 182, 183]. Previous results have shown that oxygen easily enters GaN and creates shallow donors equal in number to the concentration of the free electrons [182]. SIMS depth profiles (Fig. 26) were used to show that oxygen content in SiO2-capped GaN has increased by an order of magnitude [182]. The reason for the degradation is oxygen impurities coming from the SiO2 cap and not the Si, because when SixNy is used instead of SiO2 no significant degradation of the PL intensity is observed. Measurements have shown that in addition to the PL performance degradation of the devices, electrical effects also occur with increases in the electron density and mobility of GaN epilayers. Oxygen from SiO2 seems to be the possible cause of this, and rapid thermal processing (RTP) under different annealing temperatures can recover the effect and improve PL. A common impurity in GaN films is carbon. Taking advantage of the high sensitivity of SIMS, nondoped 5.5-txm-thick

films were characterized for carbon impurities [ 183]. However, 13C- ions are difficult to ionize, but the detection of CN- ions has improved the ion yield and, consequently, the sensitivity of the analysis by at least two orders of magnitude. It is expected that carbon detection can be improved in other films as well, such as Si3N4 or TiN, when measurement of CN- ions is utilized. Lasing materials can also be based on highly doped Alx Gal_xAs/GaAs heterostructures, which are grown by MBE. These structures can not only lase but can operate as waveguides as well. Such structures have been investigated by SIMS depth profiling [184] and were calibrated with RSF factors. Depth profiles have demonstrated that Be outdiffuses significantly and segregates at growth directions during the growth of films. Although the high quantities of A1 can hold higher concentrations of dopant Be, the Be diffuses to GaAs layers, deteriorating the quality of the structures. Upper doping limits must be followed to reduce redistribution. Far-IR light can be detected by thin films of Ir and its silicides (IrSil-IrSil.75) grown on a Si substrate. The highest efficiency of the detector is achieved when the films are very thin, in the range of 2-3 nm, and the materials are of high purity. SIMS is capable of characterizing both of the above aspects. In [138] it is suggested that very low primary energies must be used to resolve the films, which will still be extended in thickness by half of their original thickness because of effects intrinsic to the SIMS techniques, such as recoil mixing. Quantification investigations, calibration curves, and comparisons with thicker samples suggest that the measurement acquired just before going through the film can be safely taken as the correct concentration. IR and far-IR detection can also be achieved by S- and Si-doped GaSb films. These films can also have other optical applications or can be used to fabricate laser diodes operating in the 0.8-2.5-~tm range. When GaSb is doped with S or Si, it changes from a p-type to an n-type conductivity. These elements are used for doping [ 185] to avoid amorphization by the use of heavier ions (such as Te and Se), which later requires higher temperatures to anneal the low-melting-point GaSb (about 710~ SIMS depth profiling of Si has shown that there is no redistribution, even at annealing temperatures as high as 600~ Light-emitting materials have also been fabricated by doping of a film of SiO2 with S and N [186]. SIMS could show good N distributions inside the films, which were not affected by annealing.

9.4.2. Filter Coatings and Waveguides

Fig. 26. A SIMSdepthprofilemeasurementshowinga low-oxygendepthprofile in as-grown GaN films and higher-oxygenGaN films capped with a SiO2 film. From [182] with permissionfromthe author and the AmericanInstitute of Physics.

Metal oxide multilayers are widely used as filter coatings in optical technology and industry. The chemical purity of these films results in better quality of the optical systems. In [100] the interfaces of SiO2-TiO2 and SiO2-ZrO2 multilayer combinations have been studied by SIMS and SNMS. Enhancement of the Zr + and Ti + ion signals has been observed, and this is attributed to the depletion of oxygen at the interfaces with the SiO2 layer, which is a result of the preferential sputtering of

SECONDARY ION MASS SPECTROMETRY oxygen compared with the two metals. This effect is not observed for SiO2. High-quality optical waveguides or optical coatings can be grown epitaxially from dielectric IIA fluorides (CaF2, BaF2, SrF2, and their mixtures). Further applications of the same materials are found in microelectronics as insulators, gate dielectrics in field-effect transistors and lattice matching buffer layers, etc. They are promising for optoelectronic devices. The cubic fluorite structure is optically isotropic and has excellent transmission properties for wavelengths in the range of 0.3-5 ~m. Contamination with carbon or oxygen during the deposition deteriorates these properties and has to be investigated. SIMS profiling has been used [ 187] to study epitaxially grown BaF2 films. It is suggested that C and O are observed only at background levels, and the quality of the films is very high. Optical waveguides can be fabricated by depositing and diffusing Ti into lithographically patterned LiNbO3 substrates. It seems that the relationship between composition (acquired with SIMS depth profiling) and optical properties, such as the refractive index, is related to the difference in polarizability between titanium and lithium ions, but the strain induced by Ti in the crystal plays a minor effect [ 188].

9.4.3. Other Microelectronic and Electronic Materials

In microelectronic devices, the increased functionality at higher speeds with reduced energy consumption leads to ultra-largescale integrated (ULSI) devices with ever smaller feature sizes. A primary requirement is technological developments not only in lithographic technologies, but also in materials science and growth techniques. Most structures are grown epitaxially into thin-layered structures (or, in other words, thin films), which are then patterned with small features by lithography. The application of SIMS in microelectronics has been already reviewed [ 180], with examples of studies of surface contamination, which originates from the different etching, lithographical, and metallization processes; of induced surface modifications such as silane growth for adhesion enhancement or protection against corrosion; and of the inspection of doping processes or growth control. Similar applications and examples selected from the recent literature are briefly reported here as well. A way to dope silicon thin films is through the use of a gas mixture of silane and biborane (B2H6) or phosphine (PH3) during their growth, which can be made by different CVD methods. It is useful to know which ratio of the above mixtures must be used to fabricate films with a defined concentration of the doping element. Such a study has been performed with the use of SIMS depth profiling [189], but a straightforward relationship of the precursor gas ratios with the final concentration of dopants in the solid thin film could not be defined. Depth profiles show a completely different behavior of the B and P dopants in the silicon film. In semiconductor films, as with other thin films, element diffusion, migration, and segregation between layers and at interfaces can occur with or without further processing, such as

673

annealing. Gallium arsenide (GaAs) is a widely used semiconductor generally doped with Zn and Be, which tend to diffuse. More specifically, SIMS depth profiling has shown that there is significant interdiffusion of P and Sb between strained GaAsP/GaAs and GaAsSn/GaAs superlattices [190]. In both cases the interdiffusion was enhanced during annealing at increasing arsenic vapor pressures. Moreover, the interdiffusion coefficients were estimated at a variety of annealing temperatures and time periods, until a complete intermixing was reached. Anisotropic diffusion of A1 from the middle to the other layers of sandwiched structures of ZnSTe/ZnSTe:A1/ZnSTe is observed to occur, which can probably be attributed to channeling effects [ 191 ]. The studied structures were grown on GaAs substrates of different crystallographic orientations by MBE; the Al-doped layer was grown in a one-step process. SIMS depth profiling was performed with the use of two different instruments, and the measurements were calibrated by RSF functions. These measurements have shown that A1 is stable at growth temperatures of up to 300~ Annealing at 450~ and 550~ however, initiates diffusion of A1 to the neighboring barren layers. It was also observed that crystallographic orientation has an effect on the relative ratio of matrix atoms to A1 during growth. To understand the effect of epitaxial silicide layers such as CoSi2 on the diffusion of B and Sb in the underlying Si, SIMS has been utilized to profile the two elements. It has been observed that Sb diffusion is enhanced, whereas B diffusion is highly reduced by the epitaxial silicide layer [192]. Consequently, stable nanoelectronic structures based on the LOCOSI process (local oxidation of silicide) can be produced (thin Si layers within CoSi2 layers). Copper germanides are now used for microelectronic interconnects because of their improved electrical characteristics and reduced oxidation effects, replacing Cu silicides. Cu germanides can be fabricated by diffusion of polycrystalline Cu thin films (poly-Cu) that are deposited on amorphous Ge (a-Ge) films followed by annealing [193]. Among other techniques, SIMS has been used for depth profiling and revealed that at annealing temperatures higher than about 430~ Si from nonoxidized wafers diffuses through Ge, causing a change in resistivity of the multilayer structures. At lower annealing temperatures a stable Cu3Ge thin film with fixed stoichiometry and abrupt interfaces is created. Segregation and diffusion of P from in situ doped Sil-xGex epitaxial films on Si at 750-850~ have been demonstrated with the use of SIMS depth profiling [ 194]. Depth profiles show that P diffuses and segregates in Si. Furthermore, segregation concentrations are higher in films with a high Ge/Si ratio. Impurities affect the properties of semiconductor devices, as in the study of F impurities in Si-doped InA1As/InGaAs heterojunction FETs (field-effect transistor), which are related to their electrical characteristics. Structures with and without SiN passivation layers were studied [195]. SIMS has shown that there is no significant diffusion of F impurities in the structure after removal of the passivation layer with a HF solution. How-

674

CHATZITHEODORIDIS ET AL.

ever, in the case of SiN passivated structures, F accumulates in the Si-doped n-type InA1As layer of the structure, affecting the electrical characteristics. Impurities are also introduced during growth of the film microelectronic structures. The thinner the film and the smaller the structure, the higher is the effect of the impurities on the properties of the film. Gate dielectrics are an example that follows this trend for minimization. Silicon oxynitrides can replace silicon dioxide because they perform better and can be thinner [ 196]. Moreover, oxynitrides are grown in a N20 ambient, and hydrogen contaminant is reduced because NH3 is now avoided. SIMS depth profiling studies [ 196] have shown that nitrogen accumulates in high amounts at the oxynitridesilicon interface and has also been used to model the growth process. Patterning with lithographic techniques is an important step in the fabrication of microelectronic devices. It is used in conjunction with deposition techniques to fabricate complicated layered structures. Deposition has to be highly selective; otherwise the operation and the efficiency of the device may be affected. An example, where a soft lithographic with polymer protection patterning in conjunction with additive CVD metallization is used, is given in [197], where micron-scale electronic Schottky diode devices are fabricated, based on Pt/Ptsilicide/Si-substrate arrangements. The involved steps are: (a) patterning of a 30 x 10 array of micron-scale diode features on a silicon substrate with the use of a polymeric film, which was prepared by micro-moulding in capillaries (MIMIC), a soft lithographic patterning technique; (b) etching that removed the oxide from the substrate surface; and (c) metallization by selective platinum CVD that was used to form rectifying contacts with the substrate. The polymeric film successfully served both as an oxide-etch resist before metallization and as a deposition-inhibiting surface for the selective deposition of platinum. SIMS ion imaging of Pt and C was used to confirm the selectivity of deposition. Pt represents the metallized areas and C the polymer areas [ 197]. Abrupt surfaces and interfaces are required in most electronic devices, and MBE or MOCVD techniques are generally used. These techniques are also used for the fabrication of heterostructures, superlattices, and quantum wells of the III-V semiconductors. In [ 118], GaAs/InGaAs/GaAs and A1GaAs/InGaAs/A1GaAs quantum-well (QW) structures and InGaAs/AllnAs superlattice (SL) structures were studied with SIMS using O + and Cs + ion beams and by monitoring the MCs + ions. In this work, depth resolution was a critical characterization parameter, and techniques such as reduced bombardment energy and initial good surface topography were adopted to improve depth resolution. Consequently, depth profiles of the QW structure managed to resolve In peaks after small differences in erosion speed were taken into account. It also demonstrated that the depth resolution can be preserved with depth, keeping the interfaces abrupt, and only a small shoulder is observed, corresponding to slower increase in signal at

the front edge, which can be also attributed to memory effects during growth. In [ 118], the highest resolution is also achieved using SIMS depth profiling on InGaAs/GaAs multiple-QW, demonstrating a 0.62-nm resolution at the leading edge and a 1.30-nm resolution at the trailing edge. The SIMS profiles have been modeled by convolving the true profiles with an analytical response function and calibrated using measurements from TEM. Effects such as blurring with increased depth, especially after 400 nm, which degrades the depth resolution, have also been observed. Topography roughness (ripples, cones, pyramids, and terraces) is also introduced and is related to impact angle and bombardment energy (down to 2 kV). Diffusion and segregation at the interfaces were also studied using SIMS, and a combination of high depth resolution and high sensitivity is suggested as the best tool to resolve them: segregation of In occurs at the front edge between the A1GaAs and InGaAs interfaces. Finally, MCs + molecular ions were used to minimize the matrix effects, and, together with the use of reference materials and RSF functions, concentration accuracies better than 2% were achieved.

9.5. Other Technological Materials In this paragraph, thin film materials of special technological interest are described. This interest relies either on their mechanical and chemical properties or a combination of these and electrical properties. Consequently, hard materials such as diamonds and diamond-like and carbon nitride films are presented together. Because such materials are used as tools for mechanical processing of other materials, SIMS was used to study their interaction, a process that is mainly chemical diffusion of elements due to the high temperatures involved during cutting. SIMS also assisted in defining the exact chemistry of new materials of that kind. Thin-film transistor displays, solar cells, transparent conducting films, and gas sensors are treated mainly as devices of technological interest, and therefore they are presented here. SIMS has been used to study parameters that will optimize the operation or efficiency of these devices. Perovskites are also mentioned here because of their multiple applications in technology, which are not only electronic or optical but mechanical as well. The section concludes with examples from organic films and processes in microsystems and chemical technology that involve films and interfaces. 9.5.1. Diamond and Other Hard Films Diamond-like carbon films (DLC) or carbon-based composite films are promising divertor materials for the new generation of fusion energy reactors because of their excellent thermal properties. However, it is important to know the processes of hydrogen implantation, trapping, and transport in these films as well as possible contamination. These studies are performed by SIMS, among other techniques [ 160]. Diamond film materials are used for coatings of cutting tools because of their hardness. However, diamond is solu-

SECONDARY ION MASS SPECTROMETRY ble in ferrous metals, and it cannot be used to cut them. The ternary boron-carbon-nitrogen system can produce super hard phases when it is deposited in films by microwave-CVD from a B(N(CH3)2)3 precursor [198]. Their characterization by SIMS threw up new problems that required solution. These included the charging of the BN phases, which was eliminated by computer-controlled sample potential changes, and the low secondary ionization efficiencies of N, which required the analysis of molecular N-bearing species. The most significant problem was the matrix effect; quantification is not possible, even with the use of standards, and other techniques must be used. Other SIMS depth profiling studies [ 199] have shown that at high temperatures during cutting there is also an exchange of elements through diffusion processes between cubic boron nitride (cBN) tools and compacted graphite iron (CGI) materials, which reach a depth of about 20 ~tm. Similar diamond films have been grown by CVD deposition from a B(C2Hs)3 gas precursor on a pretreated silicon substrate [200]. On these samples, the B/C ratio has been investigated with SIMS one- and three-dimensional depth profiling and ion imaging. It has been observed that B is five times higher in concentration when films are grown along {111 } rather than {100}. Furthermore, the {111 } samples have shown contamination from A1 and Na traces. Cr traces are homogeneously distributed in the diamond films. Hard materials with a variety of applications in optics, electronics, and coating are the oxynitride films of silicon and aluminum. A combination of technologies, including SIMS and rf-SNMS, has been used to study these film materials [109] and optimize their composition to achieve better film properties. SIMS has proved to be useful for low-concentration measurements, albeit with some disadvantages due to charging and extensive calculations for quantification. The rf-SNMS method is easier than SIMS at higher concentrations (e.g., for oxygen contents higher than 10 wt%) and can share the same RSF values with SIMS. Carbon nitride (C3N4) films have been studied because of their mechanical properties; they are very hard and, in some cases, harder than diamond [201]. The films can be grown with reactive magnetron sputtering from a high-purity graphite target in nitrogen plasma. Understanding the chemical composition and bonding in these materials is of great interest; ToF-SIMS with a Cs + primary ion beam was used to sputter molecular fragments such as CN, C2N, CN2, C3N, C3N2, and C4N3. These fragments and their relative intensities have been compared with the characteristic spectra of other diamond, diamond-like, or graphite materials, and there are no similarities, indicating that the film is a highly N-rich material [201 ]. 9.5.2. Thin Film Transistor Display Materials

Technological developments of thin film transistor (TFT) displays are based on achieving high purity in the growth materials on large areas of appropriate substrates and optimization of the electrical properties (and in effect the optical properties) by controlling the impurity content and distribution. A commonly

675

used material is silicon, either amorphous or polycrystalline (polysilicon). The following application examples show that SIMS depth profiling can successfully be used to investigate and optimize the above devices. Thin films of amorphous silicon (a-Si:H) for TFT display applications can be grown over large areas by plasma CVD (PCVD) and other techniques. Then these are doped either by if-ion sources [202] or by laser [203], where an KrF excimer laser at 248 nm is used to initiate doping due to good absorption by amorphous silicon and easy surface melting and crystallization. Common doping elements are hydrogen, phosphorous, and boron, which are used to create the required n+ or p + junctions. SIMS depth profiling was used to analyze the doped films and to acquire information on the distribution of the doped elements. The results were used to compare experimental data with Monte Carlo simulations [202] and to optimize the number of laser pulses for more efficient doping [203]. This comparison is always useful because the doping effect can be calculated and the properties can be predicted. Furthermore, it was observed that peak positions (highest concentrations) of the phosphorus (31p+) profiles are observed at 6 nm and 25 nm, when doping occurs with energies of 6 kV and 30 kV, respectively, and 50 nm and 150 nm for hydrogen [202]. It was expected that hydrogen would have broader profiles relative to phosphorus because of its high mobility. However, both profiles are shallower relative to the calculated profiles, possibly because of etching, the last step in the process, which removed some surface material. The growth of polysilicon thin films was optimized in [204] for lower temperatures with a new PCVD technique, at 450~ This makes the growth process possible on ordinary glass substrates, which cannot tolerate high processing temperatures (> 600~ However, impurities of oxygen in the grown films are demonstrated by qualitative SIMS. These impurities are probably introduced from the conventional vacuum chamber used for the growth process [204]. Further work has demonstrated that an in situ cleaning procedure, using fluorine or fluorine together with hydrogen in the plasma, eliminates the oxygen impurities in the films. From such reactants amorphous silicon has been developed elsewhere. SIMS helped to relate fluorine content with crystal size [205] and to investigate atomic-scale smooth interfaces and growth from a highly crystalline seed [206]. The way in which impurities and their distribution can affect the electrical and, as a consequence, the optical properties of the thin film diode liquid-crystal displays (TFD-LCD) is demonstrated in [207]. TFD-LCDs show an after-image effect, which can be reduced to levels that are not visible to the human eye when the current-voltage relation is improved. SIMS was then used and proved capable of revealing these impurity/compositional asymmetries, which cause the asymmetries between current and voltage during the Schottky effect conductivity of the TFD displays. Impurity atom species, such as C and P, are incorporated between the Ti and Ta electrodes during the deposition of the TaO2 insulating films from the electrolyte solutions. From a variety of such anodizing solutions, only ammonium borate has shown that B atoms remain at the very surface of the film and reduce the after-image effect.

676

CHATZITHEODORIDIS ET AL.

9.5.3. Solar Cells, Quantum Wells, and Conducting, Transparent Films Solar cell structures can be fabricated from different materials and their structured combinations, such as QW Inl_xGaxAsy Pl_y/InP heterostructures [208], polycrystalline CdTe-CdS heterojunctions [19, 209], alternating layers of semiconducting and metallic materials [101], and hydrogenated/z-crystalline silicon (/zc-Si:H, low band gap) film on an amorphous silicon (a-Si:H, high band gap) semiconductor [210]. To complete the devices they must be covered on one side with a metallic contact layer, such as Ag, and on the other side, to allow light go through, with a transparent film of low resistivity, such ITO (indium-titanium oxide), or an Al-doped ZnO, or an F-doped SnO2 layer [ 101, 211 ]. The structures are fine and complicated, and impurities or structural quality might affect their efficiency. Once again, SIMS can provide a considerable amount of information on the structural and compositional status of these materials and has been used to help improve solar cell devices. The following are some selective examples from the literature explaining the above characterization procedures and the problems encountered during SIMS analysis. Polycrystalline CdTe-CdS heterojunctions have been investigated [209] as new materials, that can be used for the production of low-cost solar cells. However, there is a problem: the interdiffusion of S between the films that form a layer of CdSxTel-x, which reduces the efficiency of the cell by increasing light absorption. Depth profiling with nuclear reaction analysis (NRA) and SIMS has provided insight into the S diffusion in a CdTe monocrystal and in CdTe/CdS films, which is produced by thermal evaporation and during annealing. Both methods suggest that diffusion of S from CdS thin films to CdTe thin films is less than the diffusion occurring by thermal diffusion into the monocrystal of CdTe, and this is attributed to initial, stable chemical bonding in CdS thin films. SIMS profiles, despite the difficulties introduced by sample charging effects, have generally given more accurate diffusion coefficients and revealed a Si component in the films, which is a constituent during the sample (gas diffused) preparation phase. CdTe thin films have also been successfully grown by MBE on InSb substrates [19] because of effective lattice matching. However, the quality of CdTe films is affected by the substrate growth temperature, the preparation of its surface before growth, and other growth parameters. Moreover, in diffuses from the substrate to the film. SIMS was used in this work to study depth profiles of the involved elements. A matrix effect was observed as a sudden increase in Cd + at the interface while all of the other elements changed abruptly. Monitoring of InTe +, InTe + and In2Te~- signals suggests that the In2Te3 phase is probably present, because the above ions are possibly secondary ions that are produced from this phase; however, matrix effects cannot be ignored. Furthermore, for samples grown at high temperatures In diffuses (following Fick's second law) from the substrate and concentrates on the surface of CdTe. Only some Te diffuses into InSb.

Another type of solar cell is fabricated when several layers of C- or H-d0ped amorphous Si with different thicknesses are altered with metallic layers [101]. Such a p-i-n diode structure is completed by a metallic back layer, generally Ag, and a transparent but conducting front oxide film (TCO), such as an Al-doped ZnO, an F-doped SnO2 layer or an ITO. The whole structure is supported by a glass substrate. It is important to know whether elements from the TCO layers contaminate the p-layers by diffusion. SIMS depth profiles have shown that there is no Zn contamination of the p-layers [17, 101], but SNMS studies [18] could not clearly resolve the differences between SnO2 and ZnO. Furthermore, SIMS profiles of 2D (deuterium) have shown that at different temperatures and for different plasma exposure times, only limited surface diffusion occurs, and, consequently, it is expected that the optical properties of ZnO will not be affected by diffusion of H from the p-doped layers [101]. At interfaces such as ZnO/SnO2, SNMS profiles have shown a plasma pressure-dependent diffusion of Sn into ZnO, during ZnO sputter deposition. Finally, SNMS and high-mass-resolution SIMS depth profiles could not resolve possible P diffusion from the n-layer (P-doped a-Si:H) into the i-layer (a-Si:H). Technically, the high resolution was achieved by analyzing model systems comprising of simple parts of the complete structure [ 101 ]. The initial surface roughness of real TCO systems reduces depth resolution, and better studies were conducted with models with smoother surfaces. It is once again observed that SNMS profiles provide better results compared with SIMS because of the reduced matrix effects at the interfaces. A hydrogenated/z-crystalline silicon (/zc-Si:H, low band gap) film on an amorphous silicon (a-Si:H, high-band gap) semiconductor can produce efficient solar cells [212]. Such structures are easily oxidized when exposed to atmospheric conditions, which results in increasing dark conductivity (ordark) with time up to a saturation value, and porosity increases surface contamination from elements such as O, N, and C. SIMS has been used to investigate these effects ([ref:210] and references therein). QW Inl-xGaxAsyPl-y/InPheterostructures have found applications in ultrafast lasers, electro-optic modulators, infrared detectors, and solar cells. Multiple quantum wells (MQWs) of such heterostructures have been grown by low-pressure metallographic CVD (MOCVD) [208]. One of the samples, the SIMS profile of which is depicted in Figure 27, had the following structure: substrate of p-type InP(001), 500 nm Zn-doped (p-doped) InP, 50 nm of nonintentionally doped InP, 16 layers of GaSP/InP forming a total 310 nm layer, 50 nm of InP and a layer of Si-doped (n-doped) InP emitter. This sample had gold contacts, and, a similar one had no contacts. SIMS depth profiling was used for both samples. It has been demonstrated that gold diffuses into the sample layers, resulting in electric field inconsistencies between the samples (not seen in the figure). Also, both SIMS (Fig. 27) and Franz-Keldysh oscillations (FKOs) suggest interdiffusion of Zn from the p-region to the iregion of the sample (16 layers).

SECONDARY ION MASS SPECTROMETRY 10

9

' .....

I

'

I

I

i

'

I

'

I

'

I

'

I

1

9.5.4. Gas Sensors

. . . . . . . .

0o

g 0.1

6 c

I~

0.01

0

'200'

'

' 400'

'

'

' 600

800

1~o 0

'

'

1~o 0

'

1400

Depth (nm)

10

,

i

I

'~

...........

"

I

~ .....

I

I

'

'

I

'

I

"

I

,

Sample Bcontrol E

7

O v tO .=,= t_

r--

0.1

O O

(b

'., .,,!~

t--

1

N ...."

Cat) 0,01 i

I

0

677

200

i

I

400

m

I

~

600

I

,

800

I

1000

,

I 1200

~

I 1400

Depth (nm) Fig. 27. SIMS profiles for (a) sample AMQW and (b) sample BCONTROL. The solid line is element Zn, the dotted line is Si, and the dark solid line is As (see text for more details). From [208] with permission from the author and the American Institute of Physics.

High-efficiency solar devices for selective solar thermal collection can be fabricated by depositing TiOxNy thin films on Si or Cu substrates [97]. Efficiency is reduced at operating temperatures higher than 200~ when elements of the substrate migrate to the surface of the film and degrade its optical properties. In the case of Cu substrates, for example, SIMS depth profiles have shown that at about 350~ copper migrates to the free surface of the film and forms an oxide, which is also covered by a nitrogen-rich layer. ITO coatings are materials that are applied to LCDs, solar cells, and photodetectors because of their visible light transparency and low resistivity. The substrate glasses usually contain Na, and during deposition or annealing, Na diffuses into the ITO films, reducing their optical properties. SIMS profiles have demonstrated that several nanometers sol-gel deposited TiO2-SiO2 barrier layers (T) prevent the diffusion of Na into the ITO films and that they are more efficient than SiO2 layers alone [211 ].

Different combinations of materials, especially in the form of thin films, are used because of their selective sensitivity to different gases. The conductivity behavior of these materials, when in contact with these gases, is used to fabricate devices that can sense the presence of gases. The demand for sensitive gas sensing is increasing all the time, especially when one considers the consequences of modern pollution for the environment. Easy and quick sensing of a variety of gas pollutants is required in small and efficient devices for continuous monitoring. Such gases are the group of nitrogen oxides (NO and NO2), which are significant pollutants. Thin-film sensors of tungsten trioxide (WO3) deposited by sputtering on glass substrates are sensitive to NOx [213]. SIMS depth profiling has been used to study the composition of films and their structural characteristics as element distribution with depth. The purpose of this has been to achieve a homogeneous and constant distribution of the elements in the film and to ensure high quality and good properties. During these studies, the matrix effect of SIMS was again observed at the transition from the film to the substrate as a peak shape that recovers soon. NO2 (but also CO2, SO2, C12, CO, NH3, and H2) can be sensed by Al-doped and Al-coated NiO layers [214]. In [214] structural and chemical properties have been studied by a variety of techniques. SIMS was used to study the implantation profile of Al-doped NiO, and it was observed that there is an improvement of the gas sensor characteristics, such as sensitivity, selectivity, and signal quality. It was additionally observed that doped devices show better characteristics than the coated ones. Another type of material used to sense CO, H2, and C12 gases is tin oxide (SnO2). Tin oxide can be deposited as thin films by rf sputtering [215] on a silicon substrate, in polycrystalline form or with atomic layer epitaxy (ALE) [119]. To enhance its gas-sensing properties, this film can be doped either with Cu by dc sputtering with an additional surface activation by Pt doping [215] or with Sn to form an n-type semiconductor [119]. Doping with Sb in particular has not only increased conductivity but also improved the structural properties. In the first case the film was doped with different quantities of Cu to optimize the device in combination with SIMS, TEM, and XPS studies. SIMS and XPS have shown a constant concentration of Cu throughout the film; however, Pt is only observed as a very thin film on the surface of the SnO2. Consequently, any electrical properties inside the film are independent of Pt but only on Cu. A small concentration of Cu enhances the sensing properties of SnO2 and can control the selectivity for gases. In the second case [ 119], comparison of SIMS, XRF, and proton-induced X-ray emission (PIXE) compositional analyses of well-defined samples shows that SIMS is more sensitive at low concentrations, and it compares well with the other techniques at higher concentrations. However, uncertainty of measurements ranges between 8% and 22%. Depth profiles of SIMS can show that the growth of Sb inside SnO2 can be defined precisely down to very fine layers with the pulsing-ratio method of ALE (variable number of pulses constantly altered for the two starting materials,

678

CHATZITHEODORIDIS ET AL.

SnC14 and SbC15, during deposition, e.g., alternating 1 : 150 pulses, 1 : 600 pulses, etc.). SIMS required calibration sampies, which were made by ion implantation of matrix-matched substrates. Another complication with the SIMS measurements was the difficulty of seeing the surface layer due to the first phase of sputtering limitations (preferential sputtering) or increased charging. Sensor base materials used to detect reduced gases can be fabricated from n-type semiconducting polycrystalline Ga203 thin films by doping with SnO2 [216]. To acquire the n-type character, the films are doped with Ti 4+ or Zr 4+. The gas sensitivity can be improved by increasing the conductivity, and, consequently, Sn 4+ was tested as a doping material. SIMS was used to profile 2-ktm-thick films. After annealing, these films show a homogeneous distribution of SnO2 throughout their thickness. Doping with Sn 4+ has increased the conductivity of the films, with direct applications to chip size and energy consumption. Thin-film metal halides, such as CuBr, are promising alternatives to metal oxides for gas sensing at low temperatures, and their easy preparation by dc sputtering is an advantage [217]. However, the nonohmic behavior of Au/CuBr/Au and Au/CuBr/Cu structures cannot be explained, and the authors recognize the significance of the SIMS technique and propose compositional measurements with SIMS depth profiling. 9.5.5. Perovskites

The significance of perovskites as technological materials is due to their multitude of applications. Sensors, actuators for micromotors and micropumps, memories, high-value capacitors, thermistors, infrared detectors, SAW delay lines, optical switches, field-effect transistors, high-frequency transducers, and buffer layers for superconducting films are some of the applications. Some common compositions are Pb/Zr/Ti (PZT), Pb/La/Zr/Ti (PLZT), and Ba/Sr/Ti oxides. Properties that make these materials important are their high ferroelectric and the piezoelectric properties. Perovskites can be deposited as thin or thick films by a variety of techniques. Following are some examples of how SIMS has been applied to improve these materials. Thick films of PZT thin films (Pb(Zr, Ti)O3) are difficult to preserve after annealing because of decreased mechanical stability [218]. It has been found, however, that increased growth pressure (for example, during sputtering) improves the stability of the films and their ferroelectric properties. With the use of SIMS analysis the lead, titanium and zirconium profiles have been measured before annealing. Despite sample charging problems due to the primary beam (O2-), several profiles at thin films deposited under different conditions have shown that the content of Pb increases during growth and that there is a reverse relationship with the sputtering pressure. Consequently, higher growth pressures result in lower Pb content in the film, also increasing its mechanical stability due to reduced gradients with depth.

The above materials were also grown on Si(100), Au on Si(100), and TiN coated Si(100) substrates [219]. In this case, the SIMS technique was used, proving that diffusion between the TiN-coated Si(100) substrate and the film was less than that observed for the other combinations. Although all studied samples show piezoelectric properties without poling, the effective deposition of PZT on TiN-coated silicon substrates is reported. The enhanced properties of perovskites are sensitive to composition, particularly to high Si content, which generally diffuses from the Si substrates [220]. Increased Si content affects the resistivity in electrical stress of the films, and intermediate materials (buffer layers) must be used to reduce this effect. PZT (PbZrxTil-xO3), PLZT ((Pbl_xLax)(Zrl-yTiy)l-x/403), BaTiO3, and Bi4Ti3012 thin films have been deposited on a variety of substrates, and the effects of a direct contact or of the presence of Pt/Ti/SiO2 and SrTiO3 buffer layers have been studied. Positive and negative SIMS-depth profiles have shown that films of 0.1 ~tm of SrTiO3 can effectively prevent Si diffusion in perovskite films. In display applications, such as thin-film electroluminescent displays (TFELs), highly transparent films of BaTiO3 and SrTiO3 perovskites and their solid solution, (BaSr)TiO3, are grown on ITO films by CVD, and they play an insulating role. The ITO films are grown on glass substrates by rf-magnetron sputtering. As seen previously, the effect of the substrates on the properties of the perovskite films is significant and SIMS was used to determine it as a function of deposition temperature [221]. Depth compositional profiles of (BaSr)TiO2 films at their interface with ITO have been made to check for possible interdiffusion at structures grown at 350~ and 550~ Some technical problems, such as charging, occurred, especially when researchers tried to pass a beam through the glass substrate. The two profiles have shown some interdiffusion phenomena between the two interfaces (perovskite/ITO and ITO/glass), which are strongly expressed at the higher temperature. It is suggested that a buffer layer has to be developed to prevent diffusion. For devices such as thermistors, high-k capacitors, fieldeffect transistor nonvolatile memories and high-frequency transducers, a high dielectric constant is required. A high dielectric constant improves the storage capacity and at the same time reduces the price of the driving electronics. Perovskites of the composition (BaxSrl-x)TiO3 combine the high dielectric constant of Ba in the crystal and the structural stability of SrTiO3, properties that are significant to the production of large TFEL display panels [222]. For this study, such thin films were deposited on ITO layers, with buffer layers of 50-60 nm Y203 and Si3N4. SIMS depth profiles (Fig. 28) of buffered and nonbuffered structures have shown that Y203 acts as a better buffer for Sr (faster drop of the profile curve). Moreover, Si3N4 acts better with oxygen, which tends to diffuse into the substrate, leaving behind vacancies, which might be one of the reasons for the previously observed increase in the dissipation factor. The new structures show a reduction of the dielectric constant, but this is compensated for by the uniformity of structural and electrical properties throughout the film.

SECONDARY ION MASS SPECTROMETRY 107 10 e

Ir

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 I 9 ! "

I

a) (BaSr)TiO3/ITO

105

'

9.5.6. Other Technological Materials

-.o-- Sr --.o-- Ba --x-- T'i ~+~0

O'.-O-,,----O--.-.,,--~ - ~

......o

~I04

O.---,--,~.--~

o

/

,,o--o--o=~

"-'111"-- SFI

I!

...... ,n

~' 103

8 102 101 10 o 200

400

600

800

1000

Time (s)

10 7

: .

,

9 ......... , . . . . . . . .

,

.

. ....,. . . . . .

106 t b) (BaSr)TiO3/Y203/ITO

-.o---Q~ Ba.~ Sr ]

4

~

lOS I0

~1 OC

~176176176 X--------X

X" X--------X ~

~

X ~

X

~ 9

-+-"

Sn

"--- ye.

X~X-X

~=8 1~

I 100 0

. . . . . . . . . . . . . . . .

....

, .. 200

, 400

. 600

800 "

679

1000

Time (s)

Fig. 28. The effect of buffering in producing high-quality electronic structures: SIMS depth profiles of compositional changes around the interface layers of nonbuffered, Y203 buffered and Si3N4-buffered (BaSr)TiO 3 thin films (440 nm in thickness). From [222] with permission from the author and the American Institute of Physics.

SrTiO3 can also be doped with Ta. A film of 50-nm Ta205 is deposited on a SrTiO3 film or sandwiched between two of these films, treated at 1100~ for 10-40 h and characterized by conductivity measurements and SIMS and Auger depth profiling [223]. The last two were used to study interdiffusion of the two layers after the thermal treatment. Experiments have shown that thermal diffusion is completed with treatment at 1100~ for 40 h. The origin of oxygen in formed PbTiO3 (PT) perovskite films was investigated with the use of oxygen isotopes [224, 225]. At the same time, improvements to the deposition method were made, a method based on pulsed laser deposition (PLD). Parameters such as the cooling step of the film in an oxygen atmosphere after deposition, the laser repetition rate, and the gas phase reactions have been optimized. The studies showed that during the cooling, between the laser pulses, about 15 % of total oxygen content of the film originates from ambient gas, which is possibly attributable to surface exchange and vacancy diffusion.

Contamination from detergents, airborne particles, or volatile organic compounds is introduced into microelectronic components during handling, assembly or treatment. Furthermore, it is common that polymer surfaces are reconstructed [226]. Such effects can be efficiently analyzed or even visualized by ion imaging, with static SIMS [227] or ToF-SIMS. It is demonstrated [228, 229] that ToF-SIMS is especially useful in the study of polymers and other organic materials, because information on the chemical structure can be acquired. Quantitative studies of organic materials can also be made just by using relative peak intensities only when the appropriate peaks from the ToF spectra are chosen [230], and the oligomer fragments of a monomer can be recognized in the ToF spectra, a significant aspect of the study of segregation problems [231]. This was demonstrated for the PEG part of a PEGMA monomer (poly(ethylene glycol)methacrylate) [230]. The damage to polymers such as PVC and PMMA during ion bombarding is considered important. In [232] a study of the change in ToF-SIMS positive and negative ion spectra is performed as a function of ion dose. Finally, SIMS help to reveal the phase decomposition undergone by some polymers, observed as layered structures with well-defined interfaces [226]. Instrumental aspects of how to effectively analyze organic and biological materials are described in [233], showing in particular that SF~- primary ions can enhance secondary ion yields of characteristic molecular ions during operation at very high resolution. Both are demonstrated for a benzo(ghi)perylene and a cocaine ionic molecule by ion imaging. Further advantages of SF + sputtering are that sputtering rates from a glutamate film were about 37 times faster with primary ions compared with Ar + bombardment and that penetration and consequent damage are probably reduced with SF + molecular primary ions. Cleaning of surfaces of organics from common contamination by SF~- bombardment is demonstrated with PMMA [233]. In microsystems and photonics, assembly and packaging are commonly done by flip-chip solder bonding. To solder bond two surfaces of semiconductors an initial metallic layer is required, which is generally a Pt film, because it is free from oxides. SnPb60/40 solder balls are then used to connect two Ptmetallized surfaces. SIMS was used to investigate Pt diffusion in SbPb60/40 soldering, and the sputtering rate was calibrated by sputtering from the back side which was actually an etchable InP wafer substrate with a 200-nm InGaAs layer as an etch-stop layer followed by three pairs of 10-nm InP and 10-nm InGaAs layers [234]. From run to run of SIMS depth profiling (Fig. 29), the sputtering rates could be compared and the depth resolution was estimated. Ti/Pt metallization is shown in a SIMS peak that is initially high because of matrix effects, just after penetration of the calibration layers, but then reaches equilibrium. Signals drop again when the Pt is shown to be intermixed with Sn and just after the increase in the Pb signal. The Pt dissolution into the solder follows the parabolic diffusion law. The consumption of Pt during soldering shows good temperature and time values, suggesting a stable top surface metallization layer for flip-chip (FC) bonding applications.

680

CHATZITHEODORIDIS ET AL.

Fig. 29. (a) A SIMS depth profile from the back side of heat-treated sampies: An InP wafer was etched away, and as a first layer InGaAs (200 nm) was followed by three quantum wells of InP(10 nm)/InGaAs(10 nm) with accurate thickness, to be used for an estimation of sputtering rates. Then a Ti(20 nm)/Pt(300 nm) metallization was sputtered, and then a SnPb60/40 foil of about 100 ~tm was placed on the InAs substrate which with heat treatment wetted the Pt metallized areas of the structure. A matrix effect is apparent in the profile, that is the high increase of Ti ions also increases the Pt ion yields, which later drop to equilibrium. (b) For comparison with the SIMS profiles, the TEM image of PtSn4, which is the intermetaUic phase formed at the interface between SnPb60/40 and Pt. EDX (energy dispersive X-ray ) and X-ray goniometry have confirmed this material. From [234] with permission from the author and Elsevier Science.

In chemistry silicon is used to fabricate thin-film microelectrode arrays. These have higher efficiency relative to conventional macro-electrodes because of their improved diffusion and increased current density. ToF-SIMS reveals traces of A1 and Ag impurities on the Pt microelectrode surfaces [235]. A1 is probably introduced by an adhesive layer used before Pt deposition, which can be cleaned with dichromate-sulfuric acid. However, Cr is then introduced. Organic contaminants have not been detected.

REFERENCES 1. E L. Arnot and J. C. Milligan, Proc. Roy Soc. London Ser. A 156, 538 (1937). 2. H. Liebl and R. E K. Herzog, J. Appl. Phys. 34, 2893 (1963).

3. Y. Homma, E Tohjou, A. Masamoto, M. Shibata, H. Shichi, Y. Yoshioka, T. Adachi, T. Akai, Y. Gao, M. Hirano, T. Hirano, A. Ihara, T. Kamejima, H. Koyama, M. Maier, S. Matsumoto, H. Matsunaga, T. Nakamura, T. Obata, K. Okuno, S. Sadayama, K. Sasa, K. Sasakawa, Y. Shimanuki, S. Suzuki, D. E. Sykes, I. Tachikawa, H. Takase, T. Tanigaki, M. Tomita, H. Tosho, and S. Kurosawa, Surf. Interface Anal. 26, 144 (1998). 4. R. G. Wilson and S. W. Novak, J. Appl. Phys. 69, 466 (1991). 5. S.W. Novak and R. G. Wilson, J. Appl. Phys. 69, 463 (1991). 6. R.G. Wilson, Int. J. Mass Spectrom. Ion Processes 143, 43 (1995). 7. R. G. Wilson, G. E. Lux, and C. L. Kirschbaum, J. Appl. Phys. 73, 2524 (1993). 8. A.A. Salem, G. Stingeder, M. Grasserbauer, M. Shreiner, K. H. Giessler, and E Rauch, J. Mater Sci. 7, 373 (1996). 9. A. Havette and G. Slodzian, J. Phys. Lett. 41, L247 (1980). 10. R.W. Hinton, Chem. Geol. 83, 11 (1990). 11. E. Zinner and C. Crozaz, Int. J. Mass Spectrum. Ion Processes 69, 17 (1986). 12. R. G. Wilson, E A. Stevie, and P. H. Kahora, Secondary Ion Mass Spectrom. 487 (1992). 13. N. Shimizu and S. R. Hart, Annu. Rev. Earth Planet. Sci. 10, 483 (1982). 14. A. Benninghoven, E G. Rtidenauer, and H. W. Werner, in "Chemical Analysis" (P. J. Eking and J. D. Winefordner, Eds.), Vol. 86. Wiley, New York, 1987. 15. J. Biersack, NucL Instrum. Methods Phys. Res. Sect. B 153, 398 (1999). 16. Z. Jurela, Radiat. Effects 19, 175 (1973). 17. A. Eicke and B. Bilger, Surf. Interface Anal. 12, 344 (1988). 18. H.C. Weller, R. H. Mauch, and G. H. Bauer, Sol. Energy Mater. Sol. Cells 27, 217 (1992). 19. A.T.S. Weet, Z. C. Feng, H. H. Hng, K. L. Tan, R. E C. Farrow, and W. J. Choyke, J. Phys.: Condens. Matter 7, 4359 (1995). 20. J.C. Lorin, A. Havette, and G. Slodzian, Secondary Ion Mass Spectrom. 3, 140(1982). 21. M. Bernheim and G. Slodzian, Secondary Ion Mass Spectrom. 3, 151 (1982). 22. H.A. Storms, K. E Brown, and J. D. Stein, Anal. Chem. 49, 2023 (1997). 23. S.Y. Tang, E. W. Rothe, and G. P. Reck, Int. J. Mass Spectrom. Ion Phys. 14, 79 (1974). 24. C.A. Andersen, Int. J. Mass Spectrom. Ion Phys. 2, 61 (1969). 25. E. Chatzitheodoridis, The Development of a Multi-Collector Ion Microprobe for the Study of Oxygen Isotopes in Nature. Ph.D. Thesis, Manchester Univ., U.K., 1994. 26. G. Carter, M. J. Nobes, G. W. Lewis, J. L. Whitton, and G. Kiriakidis, Vacuum 34, 167 (1984). 27. G. W. Lewis, G. Kiriakidis, G. Carter, and M. J. Nobes, Surf. Interface Anal. 4, 141 (1982). 28. G. Carter, M. J. Nobes, I. V. Katardjiev, J. L. Whitton, and G. Kiriakidis, Nucl. Instrum. Methods Phys. Res. Sect. B 18, 529 (1987). 29. J.L. Whitton, G. Kiriakidis, G. Carter, G. W. Lewis, and M. J. Nobes, Nucl. Instrum. Methods Phys. Res. Sect. B 230, 640 (1984). 30. R. Smith and J. M. Walls, in "Methods of Surface Analysis, Techniques and Applications" (J. M. Walls, Ed.). Cambridge Univ. Press, Cambridge, U.K., 1989. 31. P. Konarski and M. Hautala, Vacuum 47, 1111 (1996). 32. H.C. Eun, Thin Solid Films 220, 197 (1992). 33. A.S. Hofmann, Rep. Prog. Phys. 61,827 (1998). 34. S.J. Guilfoyle, A. Chew, N. E. Moiseiwitsch, D. E. Sykes, and M. Petty, J. Phys.: Condens. Matter 10, 1699 (1998). 35. Y. Higashi, T. Maruo, and Y. Homma, Surf Interface Anal 26, 220 (1998). 36. D.E. Sykes, Surf. Interface Anal. 28, 49 (1999). 37. G. Prudon, B. Gautier, J. C. Dupuy, C. Dubois, M. Bonneau, J. Delmas, J. P. Vallard, G. Bremond, and R. Brenier, Thin Solid Films 294, 54 (1997). 38. E. Taglauer, Appl. Surf. Sci. 13, 80 (1982). 39. A.J.T. Jull, Int. J. Mass Spectrom. Ion Phys. 41,135 (1982). 40. E. Zinner, in "Proceedings of the 13th Annual Conference of the Microbeam Analysis Society" 1978. 41. H. Gnaser and I. D. Hutcheon, Surf. Sci. 195,499 (1988).

SECONDARY ION MASS SPECTROMETRY 42. W.A. Russell, D. A. Papanastassiou, and T. A. Tombrello, Radiat. Effects 52, 41 (1980). 43. H. Gnaser and I. D. Hutcheon, Phys. Rev. B: Condensed Matter 35, 877 (1987). 44. H.J. Kang, J. H. Kim, J. C. Lee, and D. W. Moon, Radiat. Eft. Defects Solids 142, 369 (1997). 45. C.A. Andersen, Int. J. Mass Spectrom. Ion Phys. 3,413 (1970). 46. V.R. Deline, W. Katz, C. A. Evans, Jr., and P. Williams, Appl. Phys. Lett. 33, 832 (1978). 47. R. Laurent and C. Slodzian, Radiat. Effects 19, 181 (1973). 48. G. Kiriakidis, An Investigation of Materials by Secondary Ion Emission (SIMS), Ph.D. Thesis, Univ. of Salford, U.K. (1979). 49. H. Gnaser, Fresenius J. Anal. Chem. 358, 171 (1997). 50. H. Gnaser and H. Oechsner, Fresenius J. Anal. Chem. 341, 54 (1991). 51. Y. Gao, J. Appl. Phys. 64, 3760 (1988). 52. H. Gnaser, W. Bock, H. Oechsner, and T. K. Bhattacharayya, Appl. Surf. Sci. 70-71, 44 (1993). 53. P. Willich and U. Wischmann, Mikrochim. Acta Suppl. 15, 141 (1998). 54. H. Gnaser and H. Oechsner, J. Appl. Phys. 64, 257 (1994). 55. H. Gnaser, J. Vac. Sci. Technol. A 12, 452 (1994). 56. U. Breuer, H. Holzbrecher, M. Gastel, J. S. Becker, and H.-J. Dietze, Fresenius' J. Anal Chem. 353, 372 (1995). 57. H.W. Werner, Surf. Interface Anal. 2, 56 (1980). 58. R.L. Hervig, R. M. Thomas, and P. Williams, in "New Frontiers in Stable Isotopic Research: Laser Probes, Ion Probes, and Small-Sample Analysis" (W. C. Shanks III, and R. E. Criss, Eds.), U.S. Geol. Surv. Bull. 1890, 137 (1988). 59. H.W. Werner and A. E. Morgan, J. Appl. Phys. 47, 1232 (1976). 60. R.L. Hervig, P. Williams, R. M. Thomas, S. N. Schauer, and L. M. Steele, Int. J. Mass Spectrom. Ion Processes 120, 45 (1992). 61. N. Reger, F. J. Stadermann, and H. M. Ortner, Fresenius' J. Anal. Chem. 358, 143 (1997). 62. W. Steiger and E G. Rfidenauer, Vacuum 25, 409 (1975). 63. W. Steiger, E G. R0denauer, J. Antal, and S. Kugler, Vacuum 33, 321 (1983). 64. E Degr~ve, R. Figareet, and P. Laty, Int. J. Mass Spectrom. Ion Phys. 29, 351 (1979). 65. D. K. Bakale, B. N. Colby, and C. A. Evans Jr., Anal. Chem. 47, 1532 (1975). 66. H. Gnaser, Surf. Interface Anal. 25,737 (1997). 67. P. Williams, Appl. Surf. Sci. 13, 241 (1982). 68. P. Williams, Surf. Sci. 90, 588 (1979). 69. P. Joyes, J. Phys.: Condens. Matter 29, 774 (1968). 70. P. Joyes, J. Phys.: Condens. Matter 30, 243 (1969). 71. P. Joyes, J. Phys.: Condens. Matter 30, 483 (1969). 72. G. Blaise and G. Slodzian, J. Phys.: Condens. Matter 31, 93 (1970). 73. G. Blaise and G. Slodzian, J. Phys.: Condens. Matter 35, 237 (1974). 74. G. Blaise and G. Slodzian, J. Phys.: Condens. Matter 35, 243 (1974). 75. Z. Sroubek, Surf. Sci. 44, 47 (1974). 76. J.M. Schroeer, T. N. Rhodin, and R. C. Bradley, Surf. Sci. 34, 571 (1973). 77. W.H. Giles, Int. J. Mass Spectrom. Ion Phys. 17, 77 (1975). 78. C.A. Andersen and J. R. Hinthorne, Science 175, 853 (1972). 79. C.A. Andersen and J. R. Hinthorne, Anal. Chem. 45, 1421 (1973). 80. D. S. Simons, J. E. Baker, and C. A. Evans, Jr., Anal. Chem. 48, 1341 (1976). 81. E G. Ruedenauer and W. Steiger, Vacuum 26, 537 (1976). 82. C. A. Andersen and J. R. Hinthorne, in "Proceedings XL VIII 253," Carnegie-Mellon University, Pittsburgh, PA, 1972, p. 39A/4. 83. C. Slodzian, J. C. Lorin, and A. Havette, J. Physique Lett. 41, L555 (1980). 84. E. Zinner, in "New Frontiers in Stable Isotope Research: Laser Probes, Ion Probes, and Small-Sample Analysis" (W. C. Shanks III and R. E. Criss, Eds.). U.S. Geol. Surv. Bull. 1890, 145 (1988). 85. T. Kawada, K. Masuda, J. Suzuki, A. Kaimai, K. Kawamura, Y. Nigara, J. Mizusaki, H. Yugami, H. Arashi, N. Sakai, and H. Yokokawa, Solid State lonics 21, 271 (1999). 86. R. J. Rosenberg, R. Zilliacus, E. L. Lakomaa, A. Rautiainen, and A. Maekelae, Fresenius' J. Anal. Chem. 354, 6 (1996).

681

87. S.L. Antonov, V. I. Belevsky, I. V. Gusev, A. A. Orlikovsky, K. A. Valiev, and A. G. Vasiliev, Vacuum 43, 635 (1992). 88. K. Wittmaack, Secondary Ion Mass Spectrom. 10, 657 (1996). 89. V. R. Deline, C. A. Evans-Jr, and P. Williams, Appl. Phys. Lett. 33, 578 (1978). 90. C.A. Andersen and J. R. Hinthorne, Science 175,853 (1972). 91. P. Williams, Secondary Ion Mass Spectrom. 7, 15 (1990). 92. R. G. Wilson, E A. Stevie, and C. W. Magee, "Secondary Ion Mass Spectrometry: A Practical Handbook for Depth Profiling and Bulk Impurity Analysis." Wiley, New York, 1989. 93. G.E. Lux, E E. Stevie, P. M. Kahora, R. G. Wilson, and G. W. Cochran, J. Vac. Sci. Technol., A 11, 2373 (1993). 94. R.G. Wilson, J. Appl. Phys. 63, 5121 (1988). 95. H. Gnaser, Surf. Interface Anal. 24, 483 (1996). 96. R. Yue, Y. Wang, Y. Wang, and C. Chen, Surf. Interface Anal. 27, 98 (1999). 97. J.B. Metson and K. E. Prince, Surf. Interface Anal. 28, 159 (1999). 98. H. Oechsner, Secondary Ion Mass Spectrom. 3, 106 (1982). 99. K.H. Miiller and H. Oechsner, Mikrochim. Acta. 10 (Suppl.), 51 (1983). 100. T. Albers, M. Neumann, D. Lipinsky, and A. Benninghoven, Appl. Surf. Sci. 70-71, 49 (1993). 101. M. Gastel, U. Breuer, H. Holzbrecher, J. S. Becker, H. J. Dietze, and H. Wagner, Fresenius' J. AnaL Chem. 358, 207 (1997). 102. C. Dubourdieu, N. Didier, O. Thomas, J. P. S6nateur, N. Valignat, Y. Rebane, T. Kouznetsova, A. Gaskov, J. Hartmann and B. Stritzker, Fresenius' J. Anal. Chem. 357, 1061 (1997). 103. M. Bersani, M. Fedrizzi, M. Sbetti, and M. Anderle, in "Characterization and Metrology for ULSI Technology: 1998 International Conference" (D. G. Seiler, A. C. Diebold, T. J. Shaffner, R. McDonald, W. M. Bullis, P. J. Smith, and E. M. Secula, Eds.). American Institute of Physics, New York, 1998, p. 892. 104. T. Maruo, Y. Higashi, T. Tanaka, and Y. Homma, J. Vac. Sci. Technol. A 11, 2614 (1993). 105. Y. Higashi, T. Maruo, Y. Homma, J. Kodate, and M. Miyake, Appl. Phys. Lett. 64, 2391 (1994). 106. Y. Higashi, Spectrochim. Acta, Part B 54, 109 (1999). 107. A.R. Bayly, J. Wolstenholme, and C. R. Petts, Surf. Interface Anal. 21, 414 (1994). 108. A. Wucher, Mater. Sci. Forum 287-288, 61 (1998). 109. S. Dreer, Fresenius' J. Anal. Chem. 365, 85 (1999). 110. U. Breuer, H. Holzbrecber, M. Gastel, J. S. Becker, and H. J. Dietze, Fresenius' J. Anal. Chem. 358, 47 (1997). 111. R. Bacon, S. Crain, L. Van Vaeck, and G. Williams, J. Anal. At. Spectrom. 13, 171R (1998). 112. A. G. Fitzgerald, H. L. L. Watton, B. E. Storey, J. S. Colligon, and H. Kheyrandish, Surf. Interface Anal. 22, 69 (1994). 113. H. Paulus, S. Kornely, J. Giber, and K. H. Muller, Mikrochim. Acta 125, 223 (1997). 114. R. Schmitz, G. H. Frischat, H. Paulus, and K. H. Mtiller, Fresenius' J. Anal. Chem. 358, 42 (1997). 115. H. Yamazaki and M. Takahashi, Surf. Interface AnaL 25, 937 (1997). 116. E. Zinner, Scanning 3, 57 (1980). 117. K. Wetzig, S. Baunack, V. Hoffmann, S. Oswald, and F. Prassler, Fresenius" J. Anal. Chem. 358, 25 (1997). 118. C. Gerardi, Surf. Interface Anal. 25, 397 (1997). 119. S. Lehto, R. Lappalainen, H. Viirola, and L. Niinist6, Fresenius' J. Anal, Chem. 355, 129 (1996). 120. H. Gnaser, Secondary Ion Mass Spectrom. 10, 335 (1996). 121. K. Yoshihara, D. W. Moon, D. Fujita, K. J. Kim, and K. Kajiwara, Surf. Interface Anal. 20, 1061 (1993). 122. K.J. Kim and D. W. Moon, Surf. Interface Anal. 26, 9 (1998). 123. K. Wittmaack, Surf. Interface Anal 26, 290 (1998). 124. S. Oswald, V. Hoffmann, and G. Ehrlich, Spectrochim. Acta, Part B 49, 1123 (1994). 125. R. Voigtmann and W. Moldenhauer, Surf. Interface Anal 13, 167 (1988). 126. J.E. Kempf and H. H. Wagner, in "Thin Film and Depth Profile Analysis" (H. Oechsner, Ed.). Springer-Verlag, Berlin/New York, 1984.

682

CHATZITHEODORIDIS

127. J. E Moulder, S. R. Bryan, and U. Roll, Fresenius' J. Anal Chem. 365, 83 (1999). 128. N.J. Montgomery, J. L. MacManus-Driscoll, D. S. McPhail, R. J. Chater, B. Moeckly and K. Char, Thin Solid Films 317, 237 (1998). 129. C. Gerardi, M. A. Tagliente, A. Del-Vecchio, L. Tapfer, C. Coccorese, C. Attanasio, L. V. Mercaldo, L. Maritato, J. M. Slaughter, and C. M. Falco, J. Appl. Phys. 87, 717 (2000). 130. K. Wittmaack, S. B. Patel, and S. E Corcoran, in "Characterization and Metrology for ULSI Technology: 1998 International Conference" (D. G. Seiler, A. C. Diebold, T. J. Shaffner, R. McDonald, W. M. Bullis, P. J. Smith, and E. M. Secula, Eds.). American Institute of Physics, New York, CP449, 1998, p. 791. 131. P. C. Zalm, J. Vriezema, D. J. Gravesteijn, G. E A. van de Walle, and W. B. de Boer, Surf. Interface Anal. 17, 556 (1991). 132. W. Vandervorst and T. Clarysee, J. Vac. Sci. Technol., B 10, 307 (1992). 133. P.C. Zalm, Secondary Ion Mass Spectrom. 10, 73 (1996). 134. J.B. Clegg, N. S. Smith, M. G. Dowsett, M. J. J. Theunissen, and W. B. de Boer, J. Vac. Sci. Technol., A 14, 2645 (1996). 135. H. J. Kang, W. S. Kim, D. W. Moon, H. Y. Lee, S. T. Kang, and R. Shimizu, Nucl. Instrum. Methods Phys. Res., Sect. B 153,429 (1999). 136. Z.-X. Jiang, P. E A. Alkemade, E. Algra, and S. Radelaar, Surf. Interface Anal. 25, 285 (1997). 137. M.G. Dowsett and D. P. Chu, J. Vac. Sci. Technol., B 16, 377 (1998). 138. J. M. Blanco, J. J. Serrano, J. Jim6nez-Leube, T-R-M. Aguilar and R. Gwilliam, Nucl. Instrum. Methods Phys,,Res., Sect. B 113, 530 (1996). 139. N.J. Montgomery, J. L. MacManus-Driscoll, D. S. McPhail, B. Moeckly and K. Char, J. Alloys Compounds 251,355 (1997). 140. P. Konarski, M. A. Herman, A. V. Kozhukhov, and V. I. Obodnikov, Thin Solid Films 267, 114 (1995). 141. B. Gautier, G. Prudon, and J. C. Dupuy, Surf. Interface Anal. 26, 974 (1998). 142. B. Gautie, J. C. Dupuy, B. Semmache, and G. Prudon, Nucl. Instrum. Methods Phys. Res., Sect. B 142, 361 (1998). 143. B. Gautier, J. C. Dupuy, R. Prost, and G. Prudon, Surf. Interface Anal. 25, 464 (1997). 144. M. L. Wagter, A. H. Clarke, K. E Taylor, P. A. W. van der Heide, and N. S. Mclntyre, Surf. Interface Anal. 25, 788 (1997). 145. M. Srivastava, N. O. Petersen, G. R. Mount, D. M. Kingston, and N. S. Mclntyre, Surf. Interface Anal. 26, 188 (1998). 146. H.W. Werner, Mater. Sci. Engin. 42, 1 (1980). 147. K. Bange, Fresenius' J. Anal. Chem. 353,240 (1995). 148. S. Kawakita, T. Sakurai, A. Kikuchi, T. Shimatsu, and M. Takahashi, J. Magn. Magn. Mater. 155, 172 (1996). 149. S. Koizumi, M. Kamo, Y. Sato, H. Ozaki, and T. Inuzuka, Appl. Phys. Lett. 71, 1065 (1997). 150. J.H. Kim and K. W. Chung, J. Appl. Phys. 83, 5831 (1998). 151. K. Koski, J. H61s~i, J. Ernoult, and A. Rouzaud, Surf. Coat. Techn. 80, 195 (1996). 152. G. Xu, M.-Y. He and D. R. Clarke, Acta Materialia 47, 4131 (1999). 153. M. Guemmaz, A. Mosser, J. J. Grob, J. C. Sens, and R. Stuck, Surf. Coat. Techn. 80, 53 (1996). 154. G. Zambrano, P. Prieto, E Perez, C. Rincon, H. Galindo, L. Cota-Araiza, J. Esteve, and E. Martinez, Surf. Coat. Techn. 108-109, 323 (1998). 155. C. Guedj, X. Portier, A. Hairie, D. Bouchier, G. Calvarin, B. Piriou, B. Gautier, and J. C. Dupuy, J. Appl. Phys. 83, 5251 (1998). 156. W.K. Choi, J. H. Chen, L. K. Bera, W. Feng, K. L. Pey, J. Mi, C. Y. Yang, A. Ramam, S. J. Chua, J. S. Pan, A. T. S. Wee, and R. Liu, J. Appl. Phys. 87, 192 (2000). 157. S. Hearne, N. Herbots, J. Xiang, P. Ye, and H. Jacobsson, Nucl. Instrum. Methods Phys. Res., Sect. B 118, 88 (1996). 158. D. G. Gromov, A. I. Mochalov, V. P. Pugachevich, E. P. Kirilenko, and A. Yu. Trifonov, Appl. Phys. A 64, 517 (1997). 159. S. Banerjee, G. Raghavan, and M. K. Sanyal, J. Appl. Phys. 85, 7135 (1999). 160. E. Vainonen, J. Likonen, T. Ahlgren, P. Haussalo, J. Keinonen, and C. H. Wu, J. Appl. Phys. 82, 3791 (1997). 161. O. Gebhardt, Fresenius' J. Anal. Chem. 365, 117 (1999).

ET AL.

162. D. Krupa, J. Baszkiewicz, E. Jezierska, J. Mizera, T. Wierzchon, A. Barcz and R. Fillit, Surf. Coat. Technol. 111, 86 (1999). 163. E. Caudron, H. Buscail, Y. P. Jacob, C. Josse-Courty, E Rabaste, and M. E Stroosnijder, Nucl. Instrum. Methods Phys. Res., Sect. B 155, 91 (1999). 164. A. M. Huntz, S. C. Tsai, J. Balmain, K. Messaoudi, B. Lesage, and C. Dolin, Mater. Sci. Forum 251-254, 313 (1997). 165. A.N. Rider, D. R. Arnott, A. R. Wilson, I. Danilidis, and P. J. K. Paterson, Surf. Interface Anal. 24, 293 (1996). 166. K. Miyake and K. Ohashi, Mater. Chem. Phys. 54, 321 (1998). 167. C. Gao, Mater. Res. Innovations 1,238 (1998). 168. C. Varanasi, R. Biggers, I. Maartense, T. L. Peterson, J. Solomon, E. K. Moser, D. Dempsey, J. Busbee, D. Liptak, G. Kozlowski, R. Nekkanti, and C. E. Oberly, Physica C 297, 262 (1998). 169. J. A. Kilner and Y. Li, NucL Instrum. Methods Phys. Res., Sect. B 139, 108 (1998). 170. Y. Li, J. A. Kilner, T. J. Tate, M. J. Lee, Y. H. Li, and P. G. Quincey, NucL Instrum. Methods Phys. Res., Sect. B 99, 627 (1995). 171. A. Gauzzi, H. J. Mathieu, J. H. James, and B. Kellett, Vacuum 41,870 (1990). 172. B. Schulte, B. C. Richards, and S. L. Cook, J. Alloys Compd. 251,360 (1997). 173. Y. Ito, Y. Yoshida, Y. Mizushima, I. Hirabayashi, H. Nagai, and Y. Takai, Jpn. J. Appl. Phys., Part 2 35, L825 (1996). 174. B. Pignataro, S. Panebianco, C. Consalvo, and A. Licciardello, Surf. Interface Anal 27, 396 (1999). 175. J.J. Cuomo, M. E Chisholm, D. S. Yee, D. J. Mikalsen, P. B. Madakson, R. A. Roy, E. Giess, and G. Scilla, AlP Conf. Proc. 165, 141 (1988). 176. A. Abrutis, V. Plau~inaitiene, A. Tei~erskis, V. Kubilius, J.-P. Senateur, and E Weiss, Chem. Vapor Deposition 5, 171 (1999). 177. J. A. Beall, M. W. Cromar, T. E. Harvey, M. E. Johansson, R. H. Ono, C. D. Reintsema, D. A. Rudman, S. E. Asher, A. J. Nelson, and A. B. Switzerlander, IEEE Trans. Magn. 27, 1596 (1991). 178. D.E. Ramaker, S. M. Hues, and E L. Hutson, in "Pittsburgh Conference and Exposition on Analytical Chemistry and Applied Spectroscopy (Abstracts)," Pittsburgh, PA, Technical Paper 1234, 1988. 179. H.W. Werner and A. Torrisi, Fresenius' J. Anal. Chem. 337, 594 (1990). 180. H.W. Werner and H. van der WeI, Anal. Methods Instrum. 2, 111 (1995). 181. R.C. Tu, Y. K. Su, Y. S. Huang, and S. T. Chou, J. Appl. Phys. 84, 6017 (1998). 182. X.C. Wang, S. J. Xu, S. J. Chua, K. Li, X. H. Zhang, Z. H. Zhang, K. B. Chong and X. Zhang, Appl. Phys. Lett. 74, 818 (1999). 183. C. Takakuwa-Hongo and M. Tomita, Surf. Interface Anal. 25,966 (1997). 184. A. Gaymann, M. Maier, and K. K/Shler, J. Appl. Phys. 86, 4312 (1999). 185. M. V. Rao, A. K. Berry, T. Q. Do, M. C. Ridgway, P. H. Chi, and J. Waterman, J. Appl. Phys. 86, 6068 (1999). 186. J. Zhao, D. S. Mao, Z. X. Lin, X. Z. Ding, B. Y. Jiang, Y. H. Yu, X. H. Liu, and G. Q. Yang, Nucl. Instrum. Methods Phys. Res., Sect. B 149, 325 (1999). 187. H. Sato and S. Sugawara, Jpn. J. Appl. Phys. Part 2 32, L799 (1993). 188. E Caccavale, A. Morbiato, M. Natali, C. Sada, and E Segato, J. Appl. Phys. 87, 1007 (2000). 189. S.K. Wong, N. Du, P. K. John, and B. Y. Tong, J. Non-Cryst. Solids 11 O, 179 (1989). 190. U. Egger, M. Schultz, P. Werner, O. Breitenstein, T. Y. Tan, U. G6sele, R. Franzheld, M. Uematsu, and H. Ito, J. Appl. Phys. 81, 6056 (1997). 191. Z.H. Ma, T. Smith, and I. K. Sou, J. Appl. Phys. 86, 2505 (1999). 192. A. K. Tyagi, U. Breuer, H. Holzbrecher, J. S. Becker, H.-J. Dietze, L. Kappius, H. L. Bay, and S. Mantl, Fresenius' J. Anal. Chem. 365, 282 (1999). 193. Z. Wang, G. Ramanath, L. H. Allen, A. Rockett, J. P. Doyle, and B. G. Svensson, J. Appl. Phys. 82, 3281 (1997). 194. S. Kobayashi, M. Iizuka, T. Aoki, N. Mikoshiba, M. Sakuraba, T. Matsuura, and J. Murota, J. Appl. Phys. 86, 5480 (1999). 195. A. Wakejima, K. Onda, Y. Ando, A. Fujihara, E. Mizuki, T. Nakayama, H. Miyamoto, and M. Kuzuhara, J. Appl. Phys. 81, 1311 (1997). 196. S. Singhvi and C. G. Takoudis, J. Appl. Phys. 82, 442 (1997). 197. M. K. Erhardt and R. G. Nuzzo, Langmuir 15, 2188 (1999).

SECONDARY ION MASS SPECTROMETRY 198. M. Griesser, H. Hutter, M. Grasserbauer, W. Kalss, R. Haubner, and B. Lux, Fresenius' J. Anal. Chem. 358, 293 (1997). 199. M. Gastel, U. Reuter, H. Schulz, and H. M. Ortner, Fresenius' J. Anal. Chem. 365, 142 (1999). 200. T. Kolber, K. Piplits, R. Haubner, and H. Hutter, Fresenius' J. Anal Chem. 365, 636 (1999). 201. S. Lopez, H. M. Dunlop, M. Benmalek, G. Tourillon, M.-S. Wong, and W. D. Sproul, Surf. Interface AnaL 25, 827 (1997). 202. A. Yoshida, M. Kitagawa, and T. Hirao, Jpn. J. Appl. Phys. Part 1 32, 2147 (1993). 203. E.A. A1-Nuaimy, J. M. Marshall, and S. Muhl, J. Non-Cryst. Solids 227230, 949 (1998). 204. T. Nagahara, K. Fujimoto, N. Kohno, Y. Kashiwagi, and H. Kakinoki, Jpn. J. Appl. Phys. Part I 31, 4555 (1992). 205. L.J. Quinn, B. Lee, P. T. Baine, S. J. N. Mitchell, B. M. Armstrong, and H. S. Gamble, Thin Solid Films 296, 7 (1997). 206. T. Akasaka, D. He, Y. Miyamoto, N. Kitazawa, and R. Shimizu, Thin Solid Films 296, 2 (1997). 207. T. Hirai, K. Miyake, T. Nakamura, S. Kamagami, and H. Morita, Jpn. J. Appl. Phys., Part 1 31, 4582 (1992). 208. A. Jaeger, W. D. Sun, E H. Pollak, C. L. Reynolds Jr., M. Geva, D. V. Stampone, M. W. Focht, O. Y. Raisky, W. B. Wang, and R. R. Alfano, J. Appl. Phys. 85, 1921 (1999). 209. D.W. Lane, G. J. Conibeer, S. Romani, M. J. E Healy, and K. D. Rogers, Nucl. Instrum. Methods Phys. Res., Sect. B 136-138, 225 (1998). 210. J. Meier, S. Dubail, J. Cuperus, U. Kroll, R. Platz, P. Torres, J. A. AnnaSelvan, P. Pernet, N. Beck, N. Pellaton-Vaucher, Ch. Hof, D. Fischer, H. Keppner, and A. Shah, J. Non-Cryst. Solids 227-230, 1250 (1998). 211. R.-Y. Tsai, E-C. Ho, and M.-Y. Hua, Opt. Engin. 36, 2335 (1997). 212. G. Kiriakidis, M. Marder, and Z. Hatzopoulos, Sol. Energ. Mater 17, 25 (1988). 213. M. Penza, M. A. Tagliente, L. Mirenghi, C. Gerardi, C. Martucci, and G. Cassano, Sens. Actuators, B 50, 9 (1998). 214. M. B6gner, A. Fuchs, K. Schamagl, R. Winter, T. Doll, and I. Eisele, Sens. Actuators, B 47, 145 (1998). 215. A. Galdikas, V. Jasutis, S. Ka6iulis, G. Mattogno, A. Mironas, V. Olevano, D. Senuliene, and A. Setkus, Sens. Actuators, B 43, 140 (1997).

683

216. J. Frank, M. Fleischer, H. Meixner, and A. Feltz, Sens. Actuators, B 49, 110 (1998). 217. J.L. Seguin, M. Bendahan, P. Lauque, C. Jacolin, M. Pasquinelli, and P. Knauth, Sens. Actuators, A 74, 237 (1999). 218. E. Defa~, B. Semmache, C. Dubois, M. LeBerre, and D. Barbier, Sens. Actuators, A 74, 77 (1999). 219. P. Verardi, M. Dinescu, E Craciun, R. Dinu, V. Sandu, L. Tapfer, and A. Cappello, Sens. Actuators, A 74, 41 (1999). 220. Y.C. Ling, J. P. Wang, M. H. Yeh, K. S. Liu, and I. N. Lin, Appl. Phys. Lett. 66, 156 (1995). 221. T.S. Kim, M. H. Oh, and C. H. Kim, Jpn. J. Appl. Phys. Part 1 32, 2837 (1993). 222. T.S. Kim, C. H. Kim, and M. H. Oh, J. Appl. Phys. 76, 4316 (1994). 223. E.B. Varhegyi, S. Jonda, I. V. Perczel, and H. Meixner, Sens. Actuators, B 47, 164 (1998). 224. N. Chaoui, E. Millon, J. E Muller, P. Ecker, W. Bieck, and H. N. Migeon, Mater. Chem. Phys. 59, 114 (1999). 225. N. Chaoui, E. Millon, J. E Muller, P. Ecker, W. Bieck, and H. N. Migeon, Appl. Surf. Sci. 138-139, 256 (1999). 226. J. Rysz, H. Ermer, A. Budkowski, M. Lekka, A. Bernasik, S. Wr6bel, R. Brenn, J. Lekki, and J. Jedliski, Vacuum 54, 303 (1999). 227. L. Van Vaeck, A. Adriaens, and R. Gijbels, Mass Spectrom. Rev. 18, 1 (1999). 228. B.A. Keller and P. Hug, AnaL Chim. Acta 393, 201 (1999). 229. D. Pleul, H. Simon, and J. Jacobasch, Fresenius' J. Anal. Chem. 357, 684 (1997). 230. D. Briggs and M. C. Davies, Surf. Interface Anal. 25, 725 (1997). 231. S.D. Hanton, P. A. Cornelio Clark, and K. G. Owens, J. Am. Soc. Mass Spectrom. 10, 104 (1999). 232. D. Briggs and I. W. Fletcher, Surf. Interface Anal. 25, 167 (1997). 233. G. Gillen and S. Roberson, Rapid Commun. Mass Spectrom. 12, 1303 (1998). 234. J. E Kuhmann, C.-H. Chiang, P. Harde, F. Reier, W. Oesterle, I. Urban, and A. Klein, Mater. Sci. Engin., A 242, 22 (1998). 235. M. Wittkampf, K. Cammann, M. Amrein, and R. Reichelt, Sens. Actuators, B 40, 79 (1997).

Chapter 14 A SOLID-STATE APPROACH TO LANGMUIR MONOLAYERS, THEIR PHASES, PHASE TRANSITIONS, AND DESIGN Craig J. Eckhardt Department of Chemistry, Center for Materials Research and Analysis, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

Tadeusz Luty Institute of Physical and Theoretical Chemistry, Technical University of Wroctaw, Wroctaw, Poland

Contents 1.

2.

3.

4.

5.

6.

7.

8.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. General Characterization of Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Representative Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Order Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Rotational Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Translational-Rotational Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Translational Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Effective Orientational Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Orientational Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Thermoelastic and Structural Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferroelasticity of Langmuir Monolayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Strain-State Calculations For Stearic Acid: An Illustration of Translational-Rotational Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Elastic Dipoles as a Measure of Orientational Fluctuations . . . . . . . . . . . . . . . . . . . . 4.3. Elastic Domains in Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Elastic Dipole Density Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Ferroelasticity in a Quasi-Two-Dimensional System . . . . . . . . . . . . . . . . . . . . . . . . Free Energy and Order Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Generalized Free Energy Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Natural Order Parameters: Dipolar and Quadrupolar . . . . . . . . . . . . . . . . . . . . . . . 5.3. Observations on the Microscopic Development of Order Parameters . . . . . . . . . . . . . . . Application of the General Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Generalized Free Energy Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. The Orientational Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. The Swiveling Transition (L 2 ~ L~) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. An Internal Stress Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extensions of the Solid-State Theory of Langmuir Film Phases . . . . . . . . . . . . . . . . . . . . . . 7.1. Implications for Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Implications for Diffuse X-Ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computer Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

686 686 687 689 691 692 694 695 695 695 696 699 700 700 705 708 709 710 711 711 713 715 715 715 716 717 718 718 720 720 721 722

Handbook of Thin Film Materials, edited by H.S. Nalwa Volume 2: Characterization and Spectroscopy of Thin Films Copyright 9 2002 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-512910-6/$35.00

685

686

ECKHARDT AND LUTY 8.1. Calculationof Packing of Model Amphiphilesand Selected Fatty Acids . . . . . . . . . . . . 8.2. Controlof Planar Packingby the Design of an Amphiphile's Cross Section . . . . . . . . . . . 8.3. CrossSectionPotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4. Extensionof the Cross SectionPotential to Simulationof the S ~ LS Transition . . . . . . . 8.5. BeadPotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. ClosingRemarkson the Solid-StateModelfor LangmuirFilms . . . . . . . . . . . . . . . . . . . . . 10. Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1. SymmetryAspectsof the 2-D HexagonalClose-PackedLattice . . . . . . . . . . . . . . . . . 10.2. The Local Stress CorrelationFunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. INTRODUCTION 1.1. General Characterization of Phases Langmuir monolayers at the air-water interface exhibit very rich thermodynamic behavior [1]. They form a variety of phases with different degrees of translational and orientational disorder, from gas-like to solid-like phases. Although these phenomena have been known for a long time, recent progress in experimental techniques requires an understanding of the microscopic origins that lead to such fascinating thermodynamic processes. Phenomenological Landau-type theory [2] does not address this problem and treats the system only from the point of view of global symmetry. The richness of phases indicates that Langmuir monolayers are frustrated systems where local and global structures compete, as do their respective equilibria. Frustration arises because the cross-sectional area of the head groups is different, in general, from that of the attached alkane chain, making it impossible to fill space without introducing some strain into the layer configuration or into the molecule itself. This factor plays an even more important, if not essential, role for amphiphiles with large molecular groups attached to the tails. There are ongoing experimental, theoretical, and numerical attempts to gain knowledge of the ordering and molecular nature of the different phases and the transitions between them. In this chapter, we focus on the molecular origin, symmetry, and nature of intermolecular forces that determine translational and orientational order as well as fluctuations and instabilities in the Langmuir monolayers [3-7]. We will show the value of solid-state concepts in understanding these systems. The detailed determination [8-10] of the phase behavior of these systems may be attributed to the advent of new techniques for their study: synchrotron X-ray diffraction [11, 12], atomic force microscopy [13], second harmonic generation [14], and Brewster angle [15] and polarized fluorescence [8] microscopies. (For a review of structural studies of ordered monolayers using atomic force microscopy, see [13].) These methods have significantly augmented the more traditional surface pressure (zr)-area (A) isotherms [16, 17]. In particular, recent X-ray diffraction experiments have shown that Langmuir monolayer phases exhibit a variety of structures [10, 18-20]. (For a review of 2-D crystallography of Langmuir monolayers, see [12].)

722 723 724 725 726 728 730 730 731 731 731

The current view is that the phase behavior of a monolayer displays, in addition to gas-like and low-density liquid-like phases, mesomorphic and solid states and that the subtle and almost continuous changes between these phases even admit amorphous states. This is based on monolayer phase behavior of "classical" fatty acid amphiphiles that are taken to reveal the most subtleties in Langmuir film phase behavior [ 1]. Current theoretical approaches almost exclusively emphasize similarities of the monolayers to liquid-crystalline phases [21] rather than to crystalline properties and give significantly less consideration to the early observation [22] of great similarities to three-dimensional (3-D) crystalline phases. Within this framework it has been suggested that mesophases of Langmuir monolayers, observed in high-temperature regimes, are hexatic phases that display long-range orientational (algebraically decaying) and short-range translational (exponentially decaying) order. Crystalline phases that have algebraically decaying translational order are indeed observed at low temperatures. Although there are many factors that may lead to detailed structure in the phase diagram arising from differences in translational and orientational order, predominant are the chemical nature, shape, and flexibility of the amphiphiles. This is exemplified by the striking difference in crystallinity at room temperature between amphiphiles comprising alkane chains and those that are perfluorinated [23, 24]. This has been attributed to the higher rigidity and interchain van der Waals interaction of the latter [25]. Moreover, for the homologous series of n-alkanoic acid molecules, the extent of two-dimensional (2-D) crystalline order is larger for systems with more attractive lattice potentials [25]. Thus, longer molecules favor crystallinity. Langmuir monolayers are, therefore, unusual systems; they combine features of 2-D and 3-D systems in a rather complicated way. The quasi-two-dimensionality may be attributed to the molecular tails that, by the very nature of their orientational flexibility, couple the 2-D system of heads with the 3-D system of tails. This combination makes Langmuir monolayers very exciting systems for the study of a variety of phase behaviors. Grazing incidence X-ray diffraction experiments [18] have shown the monolayers to be crystalline in both compressed and uncompressed states. These crystalline films, essentially 2-D "powders," are weak X-ray scatterers [18, 26], and making a distinction between the "powder" and mesophases is neither easy nor definite. As noted by Peterson and Kenn [27], the mosaic structure of highly ordered mesophases is essentially

LANGMUIR MONOLAYERS indistinguishable from a polycrystalline texture, and the latter is the one that occurs commonly in alkanes. So, as noted in reference to the X-ray studies, the single peak of the "powder" sample has been interpreted as the triply degenerate peak of a hexatic [28]. But in fact, hexatic order has not been directly observed for Langmuir monolayers, and there is significant doubt that mesophases can be rigorously treated as hexatics [29]. Recent elegant studies of the shear elasticity of monolayers [30, 31] have confirmed that these phases are more crystalline in nature than hexatic. Furthermore, from a fundamental point of view, the intrinsic head-tail asymmetry of Langmuir monolayer molecules makes the system quasi-two-dimensional rather than strictly 2-D, the only dimensionality for which hexatics are defined. Hexatic structure obtains as a result of exponential decay of the displacement-displacement correlation function in 2-D systems composed of objects without rotational degrees of freedom. Molecular monolayers are quite different! The molecules interact with the aqueous subphase by hydrogen bonding of the head groups and the molecular tails are orientationally flexible. As shown by X-ray diffraction studies, the ordering of head groups on the water surface differs from that of the molecular tails in the air (viz. geometrical frustration mentioned above) [18-20]. Recent Monte Carlo simulations for a system of surfactant molecules grafted at interfaces suggest that mesophases of Langmuir monolayers, apparently intermediate between crystalline and liquid phases, are characterized by frozen crystalline head groups and fluidized tails of the molecules. Crystalline phases are characterized by ordering of both head groups and tails, whereas in liquid phases both head groups and molecular tails are fluidized. The melting of a crystalline Langmuir monolayer may go through mesophases considered to be a mixture of "clusters," i.e., domains of mesoscopic dimension [7]. The size of the domains depends on the length of the molecular tails that determine the direct coupling for the orientational ordering [7]. The shorter the tails and the smaller the clusters, the more easily they are fluidized, and the system approximates a 2-D net. Thus, if any Langmuir monolayer structures were hexatic-like, they would most likely be those formed by short tail amphiphiles. This conclusion has been treated more extensively by Kats and Lajzerowicz, who illustrate this finding with a schematic phase diagram [32]. Langmuir films are formed by the deposition of amphiphiles on a fluid subphase which we take to be pure water. The amphiphiles, molecules comprised of a polar or ionic "head" group and a hydrophobic "tail" terminating structure, are initially dissolved in a volatile solvent of minimal solubility in water. Upon evaporation of the solvent the amphiphiles, here taken to be alkanoic acids or alcohols, are singly and randomly distributed on the surface of the surface of the water with intermolecular separations much larger than their molecular size. Even under these conditions, aggregation may occur. However, at this point of no applied surface pressure, the molecules behave as a 2D ideal gas. The surface pressure is monitored by a so-called Wilhelmy plate, which may be a known size of filter paper or a platinum

687

foil, attached to a sensitive balance. The film on the surface exerts an effective force on the plate that can be related to the difference between the surface tension of the water and the monolayer film and is commonly referred to as the surface pressure of the film. By closing barriers, usually made of Teflon, that enclose the film, the amphiphile intermolecular distances are decreased and liquid-like behavior is observed. This is reflected in the surface isotherm, the plot of surface pressure vs. area/molecule, by a rise in the surface pressure and decrease of the intermolecular distances to the order of molecular dimensions. Subsequent compression forces the amphiphiles to pack more closely together such that the "tails" are, on average, tilted to some angle from the normal to the surface with intermolecular distances small compared to the molecular "tail" cross section diameter. At this point, the film may be regarded as a 2D solid. From a rigorous geometrical view, of course, the film is a 3D system since the molecule has finite extension of its "tail" out of the surface. However, from the physical standpoint, especially if we want to consider the film as a solid, another definition based on symmetry used, as long as only a monolayer is studied, no translation symmetry of the motif exist in the direction perpendicular to the surface thereby rendering the system physically 2D. With sufficiently high applied surface pressure, the amphiphiles achieve a vertical arrangement thereby reaching the closest packing possible. Upon application of additional pressure, the film collapses and irreversibly forms a bilayer leading to a constant surface pressure but decreasing molecular area with decreasing distance between the moveable barriers. By repeating this measurement at different temperatures a phase diagram can be obtained that exhibits many phases. The various solid phases are distinguished by the amphiphiles' degree of tilt and the directions in which the tilting occurs. It is this rich phase behavior that has occupied the interest of many experimentalists and theorists.

1.2. Representative Phase Diagrams A generalized phase diagram for n-alkanoic acids is presented in Figure 1. It represents a rather inclusive compilation [33] based on a variety of measurements. Some phases, denoted by italics, require further confirmation but are included because most are consistent with the theory that will be developed here [3, 4]. The structural information for the depicted phases is displayed in Table I. This phase diagram can be further partitioned according to the method of measurement employed in the de! I! termination of each phase. Phases LS, L2, L 2, L 2, and CS are found by surface isotherm studies. All of these phases and two others, Ov and S, have been observed by optical methods such as Brewster angle microscopy and polarized fluorescence mi! croscopy [33]. In addition, the three phases L 1, L2d, and L2h within the L2 phase have been observed by X-ray scattering, as have the phases S' and L~ within the L~ phase. To characterize the phases shown by the phase diagram, and for a clearer distinction of theoretical models relevant to the

688

ECKHARDT AND LUTY

Fig. 1. Schematic phase diagram for n-alkanoic acids. The heavy phase equilibrium lines represent determinations by X-ray, optical, and surface isotherm measurements. The light phase equilibrium lines have been located by X-ray and optical methods. The broken phase equilibrium lines have been found only 9by X-ray measurement. Italic letters denote those phases that require further confirmation but are consistent with the proposed theoretical development. Table I.

Characterization of n-Alkanoic Langmuir Monolayer Phases of Figure le Backbone order

Tilt order

Phase

Lattice

(related to T scale)

(related to Jr scale)

LS

Hexagonal

Rotational disorder

Vertical

Ov

Rect/hex a

Rotational disorder

NNN

L2d

Rect/hex a

Rotational disorder

NN

L]

Rect/hex a

Rotational disorder

NN^NNN

S

Rectangular

Static disorder b

Vertical

L~

Rectangular

Parallel order c

NNN

L2h

Rectangular

Parallel order a

NN

CS

Rect/oblique d

Herringbone order

Vertical

St

Rect/oblique d

Herringbone order

NNN

L~

Rect/oblique d

Herringbone order

NN

aMolecules form a hexagonal, close-packed lattice in the plane perpendicular to their long axis. bMolecular backbones are in two equivalent orientations in every lattice site. CMolecular backbones are ordered parallel to each other. dlt is not certain if the herringbone order of molecular backbones is realized on a rectangular or oblique lattice. eltalics indicate unconfirmed phases that do not appear in the phase diagram.

ensuing discussion, introduction of angles and directors specifying the orientation of molecules in the monolayer is desirable. These are defined in Figure 2, where the molecular chain is modeled as a rigid rod. In addition to two polar angles (0, 40, there is the angle v formed by one crystallographic hexagonal axis (a so-called bond) with the x axis of the coordinate system. The latter has been introduced to characterize hexatic order [34,

Fig. 2. Representation of the axes, angles, and directors used in the description of the orientation of rigid rod model n-alkanoic acid molecules, x, y, and z define the Cartesian coordinate system with polar angles 0 and 4~. v is the angle formed by a crystallographic hexagonal "bond" axis with the x axis.

35], and it may be neglected in characterizing the aforementioned phases, i.e., by assuming hexatic rigidity, v = 0. In the LS phase the molecules are, on average, not tilted ((0) = 0), and indirect evidence suggests that the molecules are almost free rotors [ 18]. Those mesophases differing in the orientation of the c director (see Fig. 2) have (0) ~- 0 and are characterized by the azimuthal angle q~. In the L] phase [10], (4~) = -+-or + 2re/6, where c~ is the angle intermediate between 0 (molecules tilted in the direction toward nearest neighbors (NN), e.g., L2h and L2d phases) and zr/6 (molecules tilted toward next nearest neighbors (NNN), e.g., Ov and L~ phases). The distinction between the L~ and L~ phases is based on the tilt azimuth order and, for subphases within the L I2 and L2 phases, is based on the order of the molecular backbones (see Table I). A coupling between the tilt azimuth order and the distortion [36] observed for these phases is clear evidence for translational-rotational coupling. Although not conclusive, transitions between LS and L2 phases are believed to be continuous [ 1]. In the low-temperature regime, phases possess a higher degree of crystallinity. The S phase contains vertical molecules, thought to be orientationally disordered, on a distorted hexagonal lattice, which is, more precisely, a centered rectangular net [ 18]. The CS phase shows the long-range translational and orientational order of the spines of the molecules [9], but the pattern of the molecular backbones is not uniquely determined. It is believed that in the low-temperature regime the molecules are packed in a herringbone pattern analogous to such structures in 3-D solids [29]. Thus, lowering the temperature has the effect of reducing the symmetry of the high-pressure phase from hexagonal (LS) to centered rectangular (S) and, finally, to the possibly oblique superstructure (CS). This symmetry reduction

LANGMUIR MONOLAYERS is, no doubt, also related to translational-rotational coupling because the molecules become hindered rotors with decreasing temperature. All three phases, CS, S, and LS, may be compared with the 3-D crystalline structures of alkanes: herringbone crystal, distorted rotator without long-range herringbone order, and hexagonal rotator phases, respectively [29]. The order-disorder transition from the S to the CS phase is completely analogous to orientational transitions in molecular solids. It has also been shown that tilted phases can be associated with the same three categories as 3-D phases regarding the distortion and herringbone order that characterize the untilted phases [29]. The phase diagram presented in Figure 1 can be viewed as resulting from two tendencies in the thermodynamic behavior of the system. First, with decreasing temperature, there is an increasing order of molecular backbones, and the system passes from a rotationally disordered state to herringbone order through a centered rectangular lattice. Second, the effect of increasing the 2-D pressure is to suppress tilting of molecules, and the system evolves from NN tilting to the vertical structure by passing through a state with NNN tilting. Both types of orientational ordering are coupled to distortion of the hexagonal net. The two tendencies, in conjunction with the principle of continuity, provide a conceptual basis for an understanding of the formation of all phases. In this chapter we develop a general theory of the n-alkanoic acid Langmuir film phase diagram based on an intermolecular interaction model [3-5]. To illustrate the above-mentioned two tendencies in the diagram, we consider in detail two transitions: the swiveling transition, illustrating the mechanism of tilt change [6], and the orientational LS - S transition, to illustrate the orientational ordering within untilted phases [7]. Molecular dynamics [37-45] and Monte Carlo [46-49] simulations performed for Langmuir monolayers have involved a variety of approximations, ranging from conceptualization of the monolayer as a system of rods grafted onto a surface, through the inclusion of different interactions such as chain-chain and chain-surface, to different modelings of intermolecular potentials ranging from the idealized to the realistic. Most of these numerical experiments have concentrated on hexatic phases, with results supportive of the collective tilt measurement of experiment but with less attention being paid to the hexagonal lattice distortion. It remains for studies to focus on the microscopic aspects of the stabilities, structures, and transitions of Langmuir monolayer phases. Computer simulations using realistic potentials offer much more accurate descriptions of monolayer ordering for specific systems than do microscopic and mean-field theories, but they cannot yield powerful analytical solutions available from the latter and thus fail to provide the broad conceptualizations and trends desired for understanding the phase behavior of Langmuir monolayers. Moreover, such theories are essential for better interpretation of both physical and computer experiments. In an extensive study comparing intermolecular forces of Langmuir monolayers of perhydro and perfluoro amphiphiles, Cai and Rice [50, 51 ] developed a molecular theory based on density functional formalism to describe transitions between

689

untilted (LS) and tilted mesophases. Numerical calculations [51, 52] using realistic Lennard-Jones potentials for reasonably strong molecule-surface interactions have shown that a mesophase with vertical molecules is the most stable. Thus, a delicate balance between the potential and chain-chain interaction dictates the tilting characteristics for the mesophases. The nature of the transitions depends critically on the intermolecular interactions. For perfluorinated amphiphiles, only a first-order phase transition between the ordered and disordered dilute phases is found, with no evidence of a continuous tilt transition. However, a continuous tilt transition is commonly found for perhydro systems. The crystallinity of Langmuir films of molecules without polar groups [53] may be attributed to the assumed increased rigidity of perfluoro chains over that of perhydro chains. The model of grafted rods, where molecules are approximated by rigid, rodlike particles attached to a planar, impenetrable surface, has been most extensively studied [54-59]. The discrete version of the model, based on a spin-1 Isingvariable Hamiltonian, has been solved by mean-field [54] and renormalization-group [55] methods. The results deal with competing roles of interparticle and particle-surface interactions but are limited to transitions between LS and isotropic liquid phases. This model, augmented by continuous orientational variables, has been proposed by Somoza and Desai [59]. The advantage of the spin-1 model is that it is able to mimic two successive phase transitions, whereas all phenomenological models based on Landau theory introduce "coupling of phase transitions" [2, 60]. Phases are characterized by assumed order parameters, without a necessary relation to microscopic properties of the system. 1.3. Order Parameters

Consideration of the problem of order parameters used in the theoretical studies is crucial, and it is useful, at this point, to emphasize their importance to existing theories and to the one subsequently developed here. Following the theory of phase transitions, phases are conveniently characterized by order parameters and their symmetries, but these parameters have to be related to intermolecular interactions in the system. Let us represent a density of a system at any point, p(x), as a sum of spatially and temporally averaged densities, P0, and its fluctuation, 8p (x), p (x) = P0 + ~P (x)

(1.1)

A new phase is characterized by a nonzero, thermally averaged fluctuation, (Sp(x)) ~ 0, that can be treated as a generalized order parameter. To see how the density fluctuation is related to the degrees of freedom of a system, we consider the density at point x at a global equilibrium,

p(x)-po[exp(-flE(x))/v-l f dVexp(-flE(x))]

(1.2)

where fl = 1/kT (k is Boltzmann's constant, T is temperature), V is the volume of the system, and E (x) is the interaction

690

ECKHARDT AND LUTY

energy of a molecule at x with the surrounding field formed by the rest of the system. The energy will be written in terms of variables {Yi } and fields, {Fi }, E(x) = -Yi(x)Fi(x)

(1.3)

The field, F(x), is a sum of macroscopic, uniform fields and a local field due to fluctuations in the degrees of freedom of the surrounding molecules, F(x) = F + 8F(x)

(1.4)

where

8 F/(x) -- E

Kij (x, x') yj (xt)

(1.5)

x :fix' gij (x, x t) is the correlation function for the fluctuating fields, Kij (x, x') = fl (8 Fi (x)8 Fj (x'))

(1.6)

The density of the molecular degrees of freedom at site x t is

yj (x') -- 8p (x') Yj (x')

(1.7)

The interaction energy is assumed to be smaller than the thermal energy. This requirement can be satisfied by taking the external field, F, to be sufficiently small (see Eq. (1.3)). With this approximation and the global equilibrium condition (Eq. (1.2)), the density fluctuation becomes

,~,o(x) =/~,oo Y~(x) V~(x)

(1.8)

This relation is valid for a field-free system and, in the case of Langmuir monolayers, the global equilibrium will appear after the system relaxes to such a state. This process is known to be rather slow and thus can be taken as the reference state. In the situation where an experiment on Langmuir monolayers is performed without allowing the system to relax to the global equilibrium, the condition for local equilibrium must be employed. Thus for the density fluctuation,

8p(x) -- --flp0[Si(x) -- (Si(x))]Fi(x)

(1.9)

where (Yi(x)) is the thermal average of the variable within the local system at x. This equation demonstrates that, when a system is in local thermodynamic equilibrium (e.g., within a mesoscopic domain), the density fluctuation of the local degrees of freedom is determined only by the local fluctuation in these variables. For further discussion, global equilibrium is assumed, although the same treatment can be executed for the case of local equilibrium. Now, it becomes evident that the density fluctuation is related to intermolecular interactions and the molecular degrees of freedom. Thus, the average (Sp(x))can be expressed as (Sp(x))-- E

ai(Yi(x)) 2

(1.10)

i

(Yi (x)) and (Y].x Yi (x)) act as the local and global order parameters, respectively. Thus, the order parameters are just averages of fluctuations in the variables of a system. For the crystalline phases of Langmuir monolayers, these are the translational and orientational degrees of freedom of the amphiphilic molecules,

whereas for mesophases the order parameter may be the amplitude, pq, of the density fluctuation wave, 8p(x) = N -1 E Pq exp(iqx) q

(1.11)

characterized by the wave vector, q. This amplitude is called the "weak crystallization" order parameter [2, 32]. For liquid-like and gas-like phases, it is just an isotropic density fluctuation, 8p = p - Pc, where Pc stands for the critical density of the system. With these order parameters, we can describe a sequence of Langmuir monolayer phases as a continuous process of ordering, going from a gas-like phase (Sp < 0 ), through a liquid-like phase (Sp > 0), then mesophases, and finally crystalline phases (pq :/: O, (Yi(q)), (Yi), (Yi(x))). Despite a large number of models and theories, orientational order in monolayers is usually studied by imposing azimuthal symmetry and examining the nematic order parameter, which, following the standard formulation [61 ], has the form Qu# - Q(T)(nant~ - (1/3)8~/~)

(1.12)

where the n are unit vectors linked to the molecule, the subscripts refer to the laboratory frame, and 8 is the Kroenecker symbol. In the context of Langmuir monolayers, the Q33 component ((3 cos 2 0 - 1)) is not the symmetry-breaking parameter, and the 2-D version of Eq. (1.12) has been used [2, 62-64]. We show that this limitation has no justification in microscopic considerations. Models that have discrete orientational degrees of freedom [54, 55] have used the nematic order parameter and have sought the so-called biaxial order associated with 2D nematics, where the tilt order of molecules was neglected. Thus, Somoza and Desai [59] focused on tilt order but neglected biaxial order. They introduced the tilt order parameter, I/ = (sin0 cos4~). This arises naturally from using spherical harmonics for the description of a molecular orientational probability distribution function [59]. We, too, shah develop a description in terms of spherical harmonics and show their convenience and power for both microscopic theory and the free-energy expansion [3, 4]. Kaganer and co-workers [2, 62-64] have advocated a phenomenological Landau free-energy expansion with the use of two orientational order parameters, I/ to characterize tilt and a 2-D version of Qat~ to characterize molecular backbone orientation, and two other parameters to characterize the density wave and, separately, the herringbone ordering, associated with so-called weak crystallization order parameters. Coupled to each other, and based on purely phenomenological arguments, these parameters were used to characterize phases shown by the genetic phase diagram [33]. The phenomenological description of Kaganer et al. has no relation to and does not attempt to connect the theory with microscopic origins of the stabilities or instabilities of Langmuir film phases. Furthermore, a recent review article by Kaganer et al. [2] incorrectly characterizes the microscopic molecular theories as being "severely restricted by the use of lattice models, i.e., the mass centers of the molecules are assumed to be fixed on a hexagonal lattice and the transition occurs between orientationally disordered

LANGMUIR MONOLAYERS and ordered states in the translationally ordered system." To the contrary, the essential point of the microscopic molecular model is that it does not place the amphiphile's centers of mass on a hexagonal lattice, but rather the head groups of the amphiphilic molecules form the hexagonal lattice and their tails possess orientational freedom [3-5]. In this context, we demonstrate that spherical harmonics offer a natural and logical set of variables to define vector and higher-rank tensor order parameters for Langmuir monolayer phases. In another conclusion, Kaganer et al. state that in Langmuir monolayers "translational and orientational ordering occur simultaneously, which demands off-lattice models for herringbone ordering" [2]. Antithetically, we show that Fourier transforms of the spherical harmonics may be exploited to describe translational ordering of the crystalline phases instead of the assumed separate weak crystallization order parameters. The translational and orientational ordering, their coupling and molecular origin, are very important to Langmuir monolayers, and, for this reason, a microscopic theory has to be developed [3, 4]. Numerical calculations have shown that tilting/nontilting transitions follow from competition between chain-chain and chain-surface interaction. Strong chain-surface interaction is needed to impair collective tilting. In the microscopic theory, which will be presented here, this is consistently explained by competition between rotational-rotational and rotationaltranslational coupling. On the other hand, the phenomenological description based on Landau theory "is not sensitive to the difference between a hexatic and a 2-D hexagonal crystal," as noted by Kaganer et al. [2], and thus, the important aspect of simultaneous translational and orientational ordering is missing in the studies using a phenomenological free-energy expansion based on the global symmetry of a system. This contribution demonstrates and stresses the microscopic theory of Langmuir monolayer phases and their transitions by viewing them as essentially solid-state phenomena and describing them by exploiting their full symmetry. This leads to a microscopic theory that provides a consistent framework for understanding Langmuir monolayers and their phase behavior [3-7]. A series of steps is used to achieve this. First, we consistently use surface harmonics to describe fluctuations in molecular orientations. This produces a quite compact treatment of the rotational degrees of freedom, allows description of orientational fluctuations of any symmetry or magnitude, and gives a consistent and logical set of order parameters for the phase transitions. Second, we explicitly treat translationalrotational coupling, calculate effective rotational interactions, and analyze possible orientational instabilities from generalized rotational susceptibilities. Third, we calculate thermoelastic properties and find the free energy of the system in terms of the orientational order parameters that are average values of the surface harmonics [3]. In the next step, we discuss elastic aspects of the system by expressing the free energy alternatively in terms of strain tensor components and by exploiting the concept of elastic dipoles [4, 6]. This permits discussion of important macroscopic and mesoscopic aspects of the ferroelasticity of the Langmuir monolayers [7]. Finally, we describe

691

how the microscopic theory can be approximated and mapped onto a three-state spin-1 lattice gas model. Contrary to most current theories of Langmuir monolayer phases that are formulated from a liquid-state viewpoint, this approach may be identified with well-established solid-state methods. We exploit physical concepts employed in describing translational-rotational coupling in molecular crystals with orientational disorder [65-70]. This approach may, on first consideration, appear to contradict the idea of making comparisons to mesophases. However, recognizing that all Langmuir monolayer phase transitions are related to orientational fluctuations, a powerful method for describing these must first be identified. It is this that generates the similarity to orientational disorder in solids. When we approach the hexatic phases and their transformations from this point of view, we concentrate on similarities between the mesophases and the 2-D solid state rather than on their differences. We begin by defining the n-alkanoic Langmuir monolayer as a system of close-packed rigid rods of global hexagonal symmetry. The potential energy is then partitioned explicitly for single-molecule orientational potential and intermolecular couplings: rotational-rotational, translational-rotational, and translational-translational. Every part of the potential is derived for hexagonal symmetry, and the five lowest surface harmonics are used to describe the orientational fluctuations. The coupling matrices are expressed as Fourier transforms, thus forming a dynamical matrix for the system. With the expression of the translational-translational part in terms of elastic constants, the effective orientational potential is found. With this potential we calculate the rotational susceptibility matrix and analyze possible orientational instabilities related to different orientational fluctuations. Initially, the instabilities for not breaking translational symmetry are discussed and expected symmetry changes are predicted. Subsequently, we consider orientational instabilities with translational symmetry breaking and conclude with phase transitions to a superlattice with herringbone ordering. We show how the predicted orientational instabilities may drive phase transitions between the different phases found in the experimental phase diagram. Next we calculate the thermoelastic properties of the monolayer system and show how the structural (elastic) instabilities are driven by orientational ones. We then employ the concept of the elastic dipole and discuss the ferroelasticity of Langmuir monolayers as well as the swiveling transition.

2. MOLECULAR MODEL BUILDING We now derive a model [3] that accounts for several features of the Langmuir monolayers relevant to the phase diagram of the system. The following concepts are employed in the modelbuilding procedures: i. The phase transitions result from instabilities that follow from a competition between intermolecular interactions. The competing interactions are identified

692

ECKHARDT AND LUTY and, in particular, focus is placed on direct and indirect (lattice-mediated) rotational interactions. ii. Rotational degrees of freedom are important variables in the system and may be represented in terms of spherical harmonics. iii. The sites of the 2-D lattice are noncentrosymmetric by the very nature of the Langmuir monolayer, and various translational-rotational couplings appear. These couplings are taken as the driving force for orientational and structural instabilities in the system.

The Langmuir monolayer model system is defined as a hexagonal planar lattice with the amphiphiles' tails perpendicular to the net. This clearly removes the molecular centers of mass from the hexagonal planar lattice. The amphiphiles' head groups are attached to the impenetrable lattice at the sites. To keep the model reasonably general, the detailed structure and chemical nature of the molecules are neglected. In principle, the cross section of a rigid-rod molecule mimics the structure and chemical nature of a particular molecule reasonably well [62]. The closest packed structure of such a Langmuir monolayer has C6v point group symmetry that reflects the local environment around a molecular site. This is the symmetry of the so-called hexatic (LS) phase (see the Appendix for details), with one molecule in a planar primitive unit cell of the 2-D space group p6m [71, 72]. The crystalline model of the LS phase assumes hexatic rigidity (the "bond" angle v = 0, Fig. 2), but it should be kept in mind that it is only a reference structure, a network. The crystallinity of a phase depends on the correlation length that is determined by intermolecular couplings and temperature. At nonzero temperatures, fluctuations destroy the long-range order, and regions of uniform crystallinity will extend only over finite correlation lengths, Lx and Ly, which are, in general, different and vary from tenths to tens of thousands of times the size of the hexagonal lattice constant [18]. The correlation lengths can be used to define a discrete set of wave vectors, q, in reciprocal space. The final size of the crystallinity of the LS phase, which serves as the reference structure, will then give a particular meaning to the special points of the Brillouin zone defined for the lattice (see the Appendix). The position of the kth molecule on the 2-D lattice is denoted by X(k). This is where the head group of a molecule is grafted onto the impenetrable subphase lattice. Momentary displacements, u(k), are described relative to R(k), a well-defined equilibrium position, X(k) = R(k) + u(k)

(2.1)

The orientation of a rigid-rod molecule is given by f2 (k), which contains the polar angles, 0 and 4) (see Fig. 2). The potential energy of the system is 1

V - -~ ~ ~ V (kk') k

k'

(2.2)

which is approximated by the molecule-molecule pair potential,

v(~:h:') - v[x(~:), x(~:'); a (~:), a(~:')]

(2.3)

This potential can be modeled by any kind of (semi)empirical atom-atom potential, where details of the molecules are taken into account, or by nonrealistic potentials, where molecules are represented by some geometrical objects, as is often done in computer experiments. We expand the potential in (2.2) to second order in translational displacements. The harmonic approximation for the displacements is incorporated into the potential, V = V R + V TR + V T

(2.4)

which is written as the sum of a purely rotational part, V R, a translational-rotational part, V TR (first-order in the displacement, u), and a translational part, V x, as the second-order term. These three contributions to the total energy may now be derived.

2.1. Rotational Potential

The rotational potential corresponds to the zeroth-order term in the expansion in (2.4) with respect to translational displacements, u. Therefore, for the rotational potential we have vR = ~1 Z k

~

V[R(k) - R(U); ~2(k), ~2(U)]

(2.5)

U

which describes the interaction of molecules in orientations ~2(k) and ~2(U), which are at equilibrium positions on the lattice. The potential is further decomposed into the singlemolecule orienting potential, V~ (the term with k = U in the summation, Eq. (2.5)), and the rotational interaction, 1

vR = v0R+ 5 ~ Z V[a (k), f2(k')]

(2.6)

kCU

where

vg = Z

(2.7>

k

The single-molecule orientational potential is the sum of constituent orienting potentials experienced by a molecule at site k when all surrounding molecules are kept in their equilibrium positions, R(kl), and with orientations f2 (U) = (0 = 0, ~ = 0). This potential contains a contribution from the subphase of the monolayer. The single-molecule potential (Eq. (2.7)) possesses full hexagonal symmetry (C6v). The most convenient way to specify the potential, VR, is to expand it in terms of spherical harmonics [73] that transform according to the totally symmetric representation of the C6v point group. In principle, one has to expand the single-molecule orientational potential in terms of symmetry-adapted rotator functions. (For the theory of symmetry-adapted rotator functions that were originally introduced for solid methane [74],

LANGMUIR MONOLAYERS see [75-77].) The symmetry-adapted rotator functions transform according to the irreducible representations of the product of the site group and point group of a molecule [76]. This becomes important for nonlinear molecules when one wants to take into account, explicitly, the symmetry of the molecule. It has been shown [76] that for the case of a linear rod molecule (C~v symmetry), the symmetry-adapted functions depend on the spherical coordinates of the long molecular axis and, therefore, are just surface harmonics [73] relative to the site group. For molecules in a Langmuir monolayer, the molecular axis vector spans only the upper half space (z > 0) above the surface. As pointed out by Somoza and Desai [59], expansion of the rotational potential with the full set of spherical harmonics, Yl,m(O, ~), leads to a problem of redundancy or overcompleteness. Thus, following their suggestion, we restrict the set of spherical harmonics in problems of Langmuir monolayers to those for which

(OYl'm(O'dP)) O0

--O

vR R _ 1

- -2 E E Ya(k)Jae(kk')Ye(k')

where summation over repeated indices is assumed. The vector, Y(k){Y~[f2(k)]}, represents a set of surface harmonics that describe orientational fluctuations of the kth molecule, J (kU), with elements, J,~ (kU), that represent the matrix of rotationalrotational coupling constants that couple the otth harmonic of the kth molecule to the flth harmonic of the Uth molecule. Equation (2.13) is a condensed notation for a more general form of the interaction potential between molecules [78, 79]. The coupling constants, J~f(k, U), can be calculated from an assumed intermolecular potential between two molecules, k and U, and, with the use of the orthogonality properties of the surface harmonics,

Jaf(kk') --

(2.9)

V ~ ( ~ ) -- ao § E an sin 2n0 n=l...

210,

n=l...

The orientational probability distribution, P (~), for a molecule at the C6v symmetry site is -- ZO 1 exp[--flvR(f2)]

(2.11)

and the single-molecule rotational partition function is Z0 -- f d ~ exp[--flvR(f2)]

f dr2 (k) x f dr2 (k') V[R(k) - R(k'); f2 (k), f2 (k')]

where y6c _ (YI,6 + Yl,-6)/'v/~ and at, fit, are the coefficients of the expansion. More explicitly, the orientational potential (2.9) is written in the form

+( nSin42n0) cos60+

(2.13)

k :/=U

(2.8)

i.e., limited to harmonics with I + m -- even. For the site symmetry, C6v, the single-molecule orientational potential, is written as

e(a)

interaction in the form

0=~

W~(~'2) --" Ol0 § Z OllYl,o(") § Z fit y6c(~2) + . . l=2,4 l=6,8

693

(2.12)

For a strong orientational potential (Eq. (2.9)), molecules are localized in quasidiscrete states (pocket states [78]) that often are further approximated by discrete states. The spin-1 model Hamiltonian considered for the Langmuir monolayer [54, 55] corresponds to such an approximation. By keeping the orientational potential expressed in terms of spherical harmonics, we allow a continuous change in molecular orientation. The rotational-rotational coupling term, the second in Eq. (2.6), describes direct coupling between orientational fluctuations of different molecules (k ~ k'). Expressing the fluctuations in terms of surface harmonics [73], we write the

x Yo~[a(k)]Ye[a(k') ]

(2.14)

The coefficients Jag(k, k') consist of contributions from electrostatic, induction, dispersion, and repulsion interactions. For long molecules it is convenient to partition the potential into attractive and repulsive parts and relate the latter to the excluded area [59], A[f2(k)f2(U)] (the area excluded by molecule k in orientation f2 (k) as seen by another molecule U in orientation S2(U)). Consequently, the rotational-rotational coupling constants will be a sum of the corresponding contributions. At this point we specify the set of surface harmonics describing the rigid rods' orientational fluctuations. Besause there is no symmetry constraint imposed on the set, the number of these variables depends on how much rotational freedom one expects for the molecules, i.e., on the strength of the singlemolecule orientational potential. For Langmuir monolayers we do not expect a very strong single-molecule orientational potential, and, to keep the formalism reasonably clear, we limit consideration to surface harmonics with I = 2. Following the constraint (Eq. (2.8)), we take the following surface harmonics to represent variables of the orientational fluctuations of molecules, (YI,1 + Y1,-1)

(El)

Y1 --

= cx

(El)

Y2 -- - i

(A1)

Y3 = Y2,0 -- c'(2z 2 - x 2 - y2)

(E2)

Y4 --

(Y2,2 + r2,-2) -~

c.(x 2 -

(E2)

Y5 --

(Y22 -- Y2,-2) ' =

c"xy

(El 1 - Y1,-1) '

(2.15)

=cy

(2.16) (2.17) y2)

(2.18)

(2.19)

where c - (3/4zr) l/e, c' - (5/16rr) 1/2 and c" = (15/16zr) 1/e. Irreducible representations of the C6v point group are given, and

694

ECKHARDT AND LUTY

the Cartesian coordinates are x = sin 0 cos 4~, Y = sin 0 sin tp, and z - cos 0. This set of surface harmonics is representative of the problem and contains the lowest surface harmonics important to the description of different symmetries of the orientational fluctuations. The functions Y1 and Y2 belong to the doubly degenerate E1 irreducible representation of the C6v point group and transform as the x and y components of a vector. The function Y3 belongs to the totally symmetric representation A1 and transforms as the symmetric components of a second-rank tensor. Finally, the functions Y4 and I15 belong to the doubly degenerate E2 representation and transform as the nonsymmetric (deviatoric) part of a second-rank tensor. The symmetry properties of the harmonics are important because they permit relation of every observable property, vectorial or tensorial, to statistical averages of the corresponding surface harmonics. We shall refer to this when discussing order parameters. Note that Y1 and Y2 are also used to represent the angular distribution of atomic orbitals, px and py, respectively, and Y3, Y4, and Y5 are similarly associated with the dz2, dx2_y2, and dxy orbitals, respectively. This analogy will be helpful as the discussion proceeds. With the set of surface harmonics (Eqs. (2.15)-(2.19)) we shall be able to define orientational order parameters of A1 (non-symmetry-breaking) and E1 and E2 (symmetry-breaking) symmetries. Still, for a more complete set of surface harmonics, and the order parameters corresponding to them, the surface harmonics Y6 = (Y3,3 + Y3,-3)/~/-2 of B1 symmetry, Y7 "- - i ( Y 3 , 3 - Y 3 , - 3 ) / ~ / ~ o f B2 s y m m e t r y , a n d Y8 -i(Y6,6 -

Y 6 , - 6 ) / ~ / ~ o f A2 s y m m e t r y n e e d to b e i n c l u d e d .

The surface harmonic Y8 is a natural choice for the chiral order parameter. Here, we limit ourselves to the set given by Eqs. (2.15)-(2.19). We introduce the Fourier transforms, Ya(q)

= N-89 Z Ya(k) exp[iqR(k)]

(2.20)

2.2. Translational-Rotational Coupling The translational-rotational coupling term, VTR, is the first term in the expansion of the total potential with respect to translational displacement, u (Eq. (2.4)). It is vTR = Z Z V/[R(k)- R(U); ~ k

(k)]ui(k t)

(2.23)

k~

where V/stands for the ith component of a force acting between the k and U molecules at the equilibrium distance, R ( k ) - R ( U ) , when molecule U is in its equilibrium orientation, f2 (U), and molecule k is in the orientation f2 (k). The force is calculated as

V/(kk'; ~ ( k ) ) =

(aV[kk'; ~2(k~, ~ (k')]) O~//(-~) -

(2.24) n(k')=0

and represents an angular distribution. Therefore, we express the force in terms of orientational fluctuations of the kth molecule, e.g., in terms of the surface harmonics [65],

Vi'[kk'; f2(k)] = E I,%t(kk')Ya(k)

(2.25)

a

The coupling constant Via(kk') couples the k'th molecule being displaced by the uith component of the displacement vector with the kth molecule with the orientational fluctuation Ya. This constant is evaluated at the equilibrium distance between the molecules and is given by the equation

=f

(2.26,

With the introduction of Fourier transforms, ui(q)

-- N-89 E ui(k) exp[iqR(k)]

(2.27)

k and considering the translational-rotational coupling matrix, Via(q) = Z

~a(kk')exp[iq(R(k)- R(k'))]

(2.28)

kI

k

the translational-rotational part of the energy becomes

and Jae(q) = ~

Jae(kk') exp[iq(R(k) - R(k'))]

V TR - -

(2.21)

vRR

1 - 2 E

(2.29)

Heeding the symmetry of the system (see Appendix), taking into account the translational-rotational coupling between nearest neighbors, and denoting the constants between molecules located at (0, 0) and (a, 0) as Via, we construct the V(q) matrix (Eq. (2.30)), V (q) = { 2Vll fl (q) 0

\

Ya (q) Ja/~(q) Y~( - q )

Ui(q) Via (q) Ya ( - q )

q

k'

where q is the wave vector for the simple hexagonal planar lattice. There is a finite set of wave vectors determined by the extent of crystallinity of the reference phase. For such a set, the Fourier transform in Eq. (2.20) is equivalent to the "weak crystallization" parameter [2, 62-64]. The direct rotationalrotational part of the energy in reciprocal space is

~

0 2Vllfl(q)

2v13 f2 (q) 2~/~v13f3 (q)

(2.22)

q

The matrix, J(q) can be calculated for six nearest neighbors by symmetry arguments (see the Appendix), and the elements of the matrix are specified in the Appendix. For q :=~ 0 the rotational-rotational matrix is diagonal, as required by C6v point-group symmetry.

2v14f2(q) -2~/~v14f3 (q)

2~/3v14f3(q) ~ (2.30) 2v14f2(q)

J

where fl (q) = cos 2c~ + 2 cos or cos fl - 3, f2(q) = / ( s i n 2c~ + sina cos fl), and f3(q) = i(sint~ sin fl), where c~ = (1/2)qxa and fl = (ff3/2)qya. a is the hexagonal lattice constant, and qx and qy are components of the wave vector in the orthogonal

LANGMUIR MONOLAYERS axis system (see the Appendix). In the limit q ==~ 0, there is no translational-rotational coupling for harmonics Y1 and Y2. This is due to the translational invariance of the system potential, which requires ~ l,%t(kk') = 0 for every (iot) component [80]. At q ::~ 0, the system has C6v symmetry, and the orientational fluctuations of type E1 (Y1 and Y2 harmonics) can couple bilinearly to a displacement vector, u, which transforms also as the E1 representation. This coupling, a force, is compensated for when the system is at equilibrium. At q ~ 0, the system has lower symmetry than C6v, and fluctuations of type E2 and A1 can couple bilinearly to the molecular displacements. In the limit q =:~ 0, the translationalrotational coupling matrix is approximated as

V(q =O) = i3a (O 0 0

0

vl3qx vl3qy

vl4qx --vl4qy

vl4qy )

(2.31)

E ui(q)Mij(q)uj(-q)

(2.32)

q

For the 2-D system, the dynamical matrix is 2 • 2 and consists of Fourier transform elements of translational-translational force constants (second derivatives of the energy with respect to displacements) between molecules. Explicitly, the matrix elements are

Mll(q) = 2Mll(COS2C~ - 1) + (Mll + 3M22) x (cos ot cos/3 - 1)

(2.33)

M22(q) -- 2M22(cos 2c~ -- 1) + (M22 + 3Mll)

K R and K T represent the kinetic energy of the rotational and translational degrees of freedom, respectively. For linear rigid rotors, L2(k)

KR = k

where L 2 -- (p2 We also have

+ p~/sin 2 0)

(2.38)

21

and I is the moment of inertia. PZ(k) 2m

KT-'E

(2.39)

k

where p is the momentum operator and m is the molecular mass. In the total Hamiltonian, V0R is described by Eqs. (2.9) and (2.10), and the other terms are written in the compact form, Y(q)J(q)Y(-q)

(2.40)

vTR = E u ( q ) V ( q ) Y ( - q ) q v T = ~1 ~ u ( q ) M ( q ) u ( - q ) q

(2.41)

(2.42)

The matrices of coupling constants form a 7 • 7 dynamical matrix for the system.

3. T H E R M O D Y N A M I C S

First, we derive the effective orientational potential and susceptibilities. Next, we discuss possible orientational instabilities with and without translational symmetry breaking. Finally, we will analyze thermoelastic properties and derive the free energy for the system.

(2.34)

• (cos ot cos fl - 1) M12(q) -- ~/-3(M22 - Mll) sinot sin fl

(2.35)

where the Mii are force constants between nearest molecules located at (0, 0) and (a, 0). When there are only central forces acting between the molecules, there is an interrelation between the M11 and Mee components and the dynamical matrix can be expressed in terms of only one parameter. The dynamical matrix, M(q), can be conveniently expressed in terms of elastic constants in the limit q =:~ 0. For the hexagonal lattice, the simplest form is

q2 + lqy 2qxqy

(2.37)

q

The purely translational part of the system potential is conveniently expressed in terms of a translational-translational dynamical matrix, M (q),

a2m -1 C~

H - K R + K T + V0R + V RR + V TR + V T

Vm~_ 1 -- 2 Z

2.3. Translational Potential

M(q) --

Collecting all contributions to the potential energy, we write the total Hamiltonian for the system,

vl4qx.

Better insight into the physical meaning of the translationalrotational matrix in the limit q =:~ 0 can be gained from elasticity theory and the elastic dipole concept.

vT__ 1

695

2qxqy -~qx 1 2 + qy2

(2.36)

where m is a molecular mass and C~ is the bare elastic constant. We have assumed central forces between the molecules and that the Cauchy relation ( c O - c O ) is obeyed.

3.1. Effective Orientational Potential

The general structure of the Hamiltonian, as given by Eqs. (2.37~ -(2.42), is similar to that used in describing spin-phonon coupling [81 ]. We follow this formalism and decouple the translations and rotations. The u(q) displacement is divided into two parts, u(q) = uel(q) + w(q)

(3.1)

where U el (q) denotes the elastic lattice displacement for a given orientational configuration {Y} and w(q) is the vibrational part about the equilibrium position with the thermal average taken with the total Hamiltonian, (w(q)) = 0. Substituting Eq. (3.1) into Eqs. (2.41) and (2.42) and minimizing the Hamiltonian with respect to u el (q), we find uel(q) = - M -1 ( q ) V ( - q ) Y ( q )

(3.2)

696

ECKHARDT AND LUTY

Substituting this back into the Hamiltonian, we obtain H = HT+ HR

(3.3)

The statistical averages are taken with the total rotational Hamiltonian, (Ya ( q ) ) - Z -1

with

1 HT = KT + 2 E w(q)M(q)w(-q) q H R = K R + V R + V RR 1 2 E Y(q)L(q)Y(-q) q

(3.4)

where

L(q) - V(q)M - l ( q ) V ( - q )

(3.6)

This matrix, L(q), gives indirect, lattice-mediated coupling between orientational fluctuations of the molecules. One can understand this interaction in the following way. When the molecular orientation fluctuates, it produces a perturbation, which is transferred to other molecules through the translational-rotational coupling mechanism. Then, the surrounding molecules react and contribute to the orientational potential experienced by a reference molecule. The indirect rotational-rotational coupling contributes to the singlemolecule orientational potential with the last term of the equation,

d a Y,~( q ) e x p [ - f l H R]

(3.11)

where Z-

(3.5)

f

(3.12)

f dr2 e x p [ - f l H R]

Equation (3.11) defines order parameters corresponding to particular surface harmonics and their symmetries. The mean-field generalized susceptibility is given by [67] X (q) - X~

- L'(q)X~ -1

(3.13)

where I is the diagonal unit matrix, L'(q) = L(q) - J(q) - LS(q)

(3.14)

and X ~ is the single-molecule rotational susceptibility calculated with the effective orientational potential, V R (Eq. (3.7)). The matrix X ~ is diagonal by symmetry and is X0

--/~[X1, X1, X3, X4, X4]

(3.15)

where X~ - (Y~) is a weak function of temperature.

3.2. Orientational Instabilities vR -" V0R - Yc~LS~ Y~

(3.7)

which gives the effective single-molecule orienting potential. The self-energy term is determined by the matrix,

We now seek the orientational instabilities of the system. They can be identified from the condition X(q) ==~ c~, e.g., detl(x~ -1 - LZ(q) I = 0

L s = N-1 E L(q) q

(3.8)

In the mesoscopic limit (q =~ 0) only orientational fluctuations of E2 and A1 symmetries are coupled by the indirect interaction. However, the matrix L(q =~ 0) is not well defined because, as seen from Eq. (2.36), M(q) cx q2 and V(q) cx q (see Eq. (2.31)). This important point has been discussed in the context of translational-rotational coupling in alkali cyanide crystals [66] and is analogous to dipolar interactions [82]. The value of the matrix L(q =~ 0) depends upon the direction from which the q :=~ 0 (I" point) is approached. It thus depends on the shape of the system and is related to the domain problem and should not be confused with textures. We write the effective rotational Hamiltonian, HR

=

KR -[- vR

1 _ ~ - "~z..Y,q, ~ q

x [L(q) - J ( q ) - L S ] y ( - q )

X,#~(q) = fl[(Y~(q)Yl3(-q))-

(r~ (q) )(r~ (- q) )]

So, we have to find eigenvalues of the matrix. In principle, we should diagonalize the matrix for every q vector. This is possible and important when one considers a particular system for which the matrix elements are given numerically. Here, we analyze the instabilities in the model system for which only the symmetry is defined, and, therefore, we are constrained to those points in q-space for which instabilities might be relevant to phase transitions in Langmuir monolayers. We shall consider the center of the Brillouin zone, the F-point (q :=~ 0), the E direction (q -- (0, qy)), and the M-point (q - (0, 2yr/a~/3)) [72]. (See the Appendix for details.) First, we consider the orientational instabilities, which might drive phase transitions without translational symmetry breaking. These transitions seem to be most often found in the Langmuir monolayer systems in the high-temperature regime. We calculate L(q =, 0), and from Eqs. (3.6), (2.36), and (2.31) we find

(3.9)

The subtraction of the self-energy term, L s, recognizes that the indirect interaction between a molecule and itself cannot contribute to the ordering of the molecules. Using a well-known procedure of statistical mechanics, we calculate the rotational susceptibility matrix, X(q), with elements defined as (3.10)

(3.16)

L(qx =~ 0) = ~ vlav14 0 where ~ = 3m(C~ is

v14 0

0)

0 6v24

(3.17)

For the orthogonal direction, the matrix (

I)23

L(qy =:~ 0) = 8 --1)131)14 0

--1)131)14 0 ) 1)14 0 0 61)24

(3.18)

LANGMUIR MONOLAYERS Introducing these matrices into Eq. (3.14) and calculating the inverse of the orientational susceptibility, x - l ( q :=~ 0), we find that the matrix is diagonal in Y1, Y2 (El symmetry), and Y5 (E2 symmetry) and well defined for q =, 0. There is a 2 x 2 matrix on the diagonal that corresponds to a coupling (i.e., a hybridization) of Y3 (A1 symmetry)and Y4 (E2 symmetry)surface harmonics, and this matrix depends on the direction from which the q =~ 0 point is approached (see Eqs. (3.17) and (3.18)). Therefore, there are three possibilities for which our model of the Langmuir monolayer will become unstable without translational symmetry breaking: (i) orientational fluctuations of E1 symmetry, (ii) orientational fluctuations of E2 symmetry, and (iii) orientational fluctuations of hybridized A1 and E2 symmetries. For the E1 symmetry fluctuations, the inverse of the orientational susceptibility is X - l ( q :=> 0; El)

o

= ((flX1)-I + 03(Jll + J22)

)

(flXl) -1 + 3(Jll + J22) (3.19) From Eq. (3.16) we find that the instability takes place at the temperature, To(E1), To(E1) -- --kB 1X1(T0)3(Jll + J22)

(3.20)

and that it is a result of competition between the singlemolecule orientational potential that determines xI(To) and direct rotational-rotational interactions between molecules. This instability can happen only when the system gains enough energy by molecules tilting collectively ((Jll + J22) < 0). Thus, it represents only the kind of orientational-dependent intermolecular potential, whether it arises from short- or long-range interactions, that gives rise to a dipolar-like interaction (Y1 and Y2 represent the dipolar angular distributions) that will cause the instability. Moreover, the gain of energy must be large enough to overcome the influence of the single-particle orienting potential, which tends to keep molecules in a perpendicular orientation (X1 > 0). This is a general result that is independent of the assumption of the nature of the intermolecular potential. At To(E1) the system becomes simultaneously unstable against fluctuations described by both Y1 and Y2. We define the order parameter for the transition driven by this instability as

r/(E1) -- al (Y1) -+- a2(Y2)

(3.21)

i.e., a linear combination of parameters (Y1) and (Y2). For the general case, al,a2 5~ 0, 0(El) measures the collective tilt of molecules in an arbitrary direction as seen from the more explicit form of the order parameter: 0(El) = c(sinO)(al(cosdp) + a2(sin~b)); see Eqs. (2.15) and (2.16). Because the instability (Eq. (3.20)) is due to competition between the single-molecule orientational potential and direct rotational-rotational interaction, translational degrees of freedom do not contribute and there is no lattice deformation involved. The phase that would result from this instability will contain tilted molecules on the hexagonal, undeformed lattice.

697

When a l and a2 ~ 0, the symmetry change at the transition is C6v =~ C1, with the resulting phase reminiscent of L I1 on the phase diagram (Fig. 1). For al = 1, a2 = 0, and r/(E1) = (Y1), molecules in the corresponding phase are tilted toward NN in an angular distribution analogous to a px orbital. For a l - 0, a2 = 1, and r/(E1) = (Y2), molecules are tilted toward NNN. The symmetry change in both cases is C6v =:~ Cs, with the phase suggestive of L2a((Y1)) and Ov ((Y2)) in the schematic phase diagram (Fig. 1). This designation of phases is not final, because the observed tilt phases are all on a deformed lattice and a coupling with a lattice deformation will make the assignment more specific. Phenomenologically, one can understand a coupling of Eltype tilting with a deformation as a breaking of the hexagonal symmetry. The susceptibility matrix (Eq. (3.19)) then contains off-diagonal terms proportional to the symmetry-breaking deformation exy and (exx - e y y ) components of the strain tensor. Consequently, the degeneracy of the tilting instabilities of E1 type is lifted, and discrimination between tilts toward NN and NNN is obtained. The deformation of the lattice will determine which of the instabilities will occur first; this can be analyzed from the 2 • 2 susceptibility matrix. The conclusion is that the elasticity of the system will dictate which of the instabilities will take place. Therefore, the interaction of the molecules with the subphase can be important. Next, we discuss the instability of our Langmuir monolayer model system with respect to the orientational fluctuation of E2 symmetry without translational symmetry breaking. This instability is expected when (X (q =~ 0))51 -- 0, and its temperature is calculated as

T/j(E2) -- kB1X4(To)[6~V?4

- L44 - 3(J44 + J55)]

(3.22)

This instability arises from a competition between the singlemolecule orientational potential, which determines X4, and the effective rotational-rotational interaction. The indirect, latticemediated coupling between orientational fluctuations, Ys, helps the system to gain energy when molecules are collectively reoriented in the pattern described by the surface harmonic, Ys. The energy gain measured by the first term in the square brackets of Eq. (3.22) is inversely proportional to the system elasticity (C~ and critically depends on the strength of the translational-rotational coupling. The indirect rotationalrotational interaction should be very important in Langmuir monolayer systems and will be responsible for the orientational instabilities. For systems where direct interactions are described by quadrupolar-like interactions, more specifically by the xy component of a quadrupole, (J44 + J55) < 0, the indirect interaction increases the temperature of the instability. If an instability of the E2 type takes place, the new phase is characterized by the order parameter, r/(E2) -- (Y5)

(3.23)

and the symmetry change expected at the transition is C6v C2v. In this case, molecules are tilted collectively at every site with equal probability in the four directions, [1, 1], [ 1 , - 1 ] , [ - 1 , 1], and [ - 1 , - 1] (in the orthogonal axial system), and

698

ECKHARDT AND LUTY

with the hexagonal lattice deformed according to the xy strain component. The deformation of the hexagonal lattice is involved in the E2-type instability because the lattice-mediated indirect interaction contributes to the instability (Eq. (3.22)). For symmetry reasons, such a phase can be associated with the S region of the phase diagram (Fig. 1). The pattern of orientational disorder assumed for phase S, due to two mutually orthogonal orientations of a molecular backbone, is completely similar to the pattern of tilt reorientations described by Ys. The harmonics Y3, Y4, and Y5 transform as components of a second-rank tensor; therefore, every observable tensorial property will be described by its thermal averages. Quantitative relations for macroscopic strain components are derived at the end of this section. Here, we relate these averages to the mean cross section of a molecule. The cross section of a rigid rod that models a molecule can be represented as a 2-D second rank tensor similar to the nematic order parameter Eq. (1.1). Therefore, the statistical averages of the surface harmonics, (Y3), (Y4), and (Ys), can be a measure of an average cross section of the rigid rod. Furthermore, this cross section would correspond to an average orientation of a molecular backbone. Physically, this means that a rigid rod with circular cross section represents a molecule rotating around the long axis, and the rotation becomes hindered by a hexagonal lattice deformation and/or tilt of the molecule. This is reflected in nonzero orientational order parameters, with the tensorial parameters interpreted as indicating the angular distribution of the molecular backbones. Finally, for instabilities without translational symmetry changes, we shall discuss an instability due to coupled (Y3 (A1) and Y4 (E2)) harmonics. The inverse susceptibility submatrix corresponding to this is

x-l(q =~ 0; a l , E2) =

X31

X~1

(3.24)

X331 = /~-1 X3 1 _ 8V73 + LS3 q_ 6J33

(3.25)

where

X,~41 = f l - l x 4 1

-8V24 + L s + 3(J44 + J55) (3.26)

X31(qx =~ 0)

= t~V13Wl4

(3.27)

X31 (qy :=~ 0)

-- - S V 1 3 V 1 4

(3.28)

where we note the difference in the off-diagonal terms for approaching the F-point (tl =~ 0) from the x and y directions. The instability condition (Eq. (3.16)) X331 (T0)X~ 1(To) = (X31)2

(3.29)

determines the instability temperature, To. At this temperature, the lowest eigenvalue of the matrix (Eq. (3.24)) becomes zero, and the system is unstable against orientational fluctuations described by the corresponding eigenvector, x = Y3 cos tp -k- Y4 sin ~o

(3.30)

when approaching the F-point from the x direction and Y -- -- Y3 sin ~0 + Y4 cos ~0

(3.31)

for the y direction, where tan 2~0 = 21X311(X331 --X441) -1 . T h e eigenvectors express hybridization of the orientational fluctuations described by the Y3 and Y4 surface harmonics. The order parameters corresponding to the instability are defined as statistical averages of the eigenvectors, r/x (A1, Ea) = (~x);

JTY(A1,E2)

= (~Y)

(3.32)

Note that the order parameters are orthogonal. It is this indirect, lattice-mediated, rotational interaction that makes the difference in the ordering of molecules, depending on the direction of approach to the F-point (see Eqs. (3.27) and (3.28)). This is a well-known problem in solids with magnetic or electrical dipolar interactions. Here, the lattice-mediated, indirect, interaction described by the matrix L(q) represents the interaction of elastic dipoles [66], and this aspect will be discussed subsequently [4]. Therefore, we can expect a shape dependence for the interaction. Because a real system breaks up into domains, no shape dependence can be observed for the system as a whole. However, the domains themselves would have the most favorable shapes, because in this way the system can lower its free energy. Detailed analysis of the shape dependence problem would require lengthy considerations and derivations, but some insight into the preferred shapes of domains can be developed. Clearly, Eq. (3.32) defines order parameters for two domains of the same phase. The domain with the ox order parameter is formed with relative dimensions Ly >> Lx, and, conversely, the domain characterized by the order parameter r/Y has relative dimensions Lx >> Ly. In other words, the phase with the order parameter that is a hybrid of (I13) and (Y4) will split into two kinds of domains with mutually perpendicular stripes as their favored shapes. Indeed, it has been found that monolayer crystallites are stripes elongated perpendicular to the molecular tilt direction [ 18]. Every domain will be characterized by C2v symmetry because the (Y4) component is responsible for the symmetry breaking. Because of the lattice-mediated interactions that take part in the instability mechanism, the phase transition would be accompanied by a lattice distortion measured by a linear combination of (egg + eyy) (A1 symmetry) and (egg + eyy) (Ea symmetry) strain tensor components. Later, we shall elaborate this aspect in greater detail and show that the Langmuir mesophases can be viewed as elastically interacting domains [7]. Discussion of the orientational instabilities concludes with the case of broken translational symmetry. Consider the direction E(0, qy) with the end point M(0, 2zr/4'-3a) at the Brillouin zone boundary (see the Appendix). For this direction, the J(q) matrix, as well as the matrix of indirect couplings, L(q), is specified in the Appendix. It follows from the symmetry of the matrix, L(q) in the E direction that there is a coupling between Y1 and I15 and between Y2, Y3, and Y4. Consequently, the inverse susceptibility matrix, X-1 (E), is decomposed into 2 x 2 and 3 x 3 submatrices. For practical reasons, we analyze the 2 x 2 matrix corresponding to hybridization between Y1 and Y5 in the E direction. A related orientational instability will be

LANGMUIR MONOLAYERS where we have used

determined by the lowest eigenvalue of the matrix,

x(z)

=

M - l ( q ) -- fl(w(q)w(q))

l{Xlll + X51 -- [(XH 1 -- X5112 + 4(X~-51)2] 89 }

(3.33)

where the elements of the inverse susceptibility submatrix are X l l 1 -" f l - l x l l

- t l l ( ] ~ ) -~- J l l ( ~ )

(3.34)

X11 = - L 1 5 ( E )

(3.35)

X51 -- / ~ - l x 4 1 - L55(E) + J55(E)

(3.36)

One then finds that the minimum eigenvalue is obtained for the wave vector, qy = 2zc/~/3a, e.g., for the M-point that is the end of the Brillouin zone in the E direction. At this point, Y1 and Y5 are decoupled. Moreover, the indirect interactions are nonzero only for the Y1 and Y2 fluctuations. Because the interaction is larger for the Y1 harmonic, the instability temperature is found from

+

(3J22 - J l l ) ]

( Cllq2+C66q2 l(CllWC22)qxqY)2

(3.38)

(see Eq. (2.15)). This phase is characterized by the tilt of molecules in the direction of NN (x), with a modulation described by exp[iq(m)R(k)]. The modulation term may be interpreted as equivalent to the "weak crystallization" order parameter [2, 62-64]. The transition to this phase results in a doubling of the unit cell and creation of a herringbone pattern of molecular backbones. The new phase can be assigned to L 2II of the schematic phase diagram (Fig. 1). The symmetry change would be p6m => pg[72, 73]. 3.3. Thermoelastic and Structural Instabilities

Thermoelasticity implies a temperature dependence of the elastic properties of a system, and, thus, we calculate effective (T-dependent) elastic constants for a Langmuir film. We define the translational susceptibility matrix, D - l ( q ) = / 3 [ ( u ( q ) u ( q ) ) - (u(q))(u(q))]

(3.39)

The thermal averages of the displacement variables are calculated with the total Hamiltonian of the system (Eq. (2.37)). On introducing Eqs. (3.1) and (3.2) into the above equation, we get D-l(q) = M-l(q)[I + V(q)X(q)V(-q)M-l(q)]

I ( C l l + Cz2)qxqy

1C66q2 + Cllqy (3.42)

In principle, the effective elastic constants should be calculated from the exact equation, Eq. (3.40). However, this is tedious, and instead we use an approximate equation that gives insight into the renormalization of the elasticity due to the translational-rotational coupling. We use, as an approximation to (3.40),

(3.37)

If (3J22 - Jll) < 0, then the instability at the M-point will be preferred only when 488 V21 > 1(3 J22 - Jll)l. In this case, the instability at the M-point is a result of successful competition between the indirect and direct rotational interaction. It would be favored for a sufficiently soft lattice, which gives a large coefficient. In the case (3J22 - Jll) > 0, the instability related to the Y1 orientational fluctuation will be preferred at the M-point, and the new phase will be characterized by the order parameter, r/(E1, M) = (Y1 (M))

(3.41)

In the limit q =~ 0, Eq. (3.40) gives a link between the rotational susceptibility, X(q), and the elastic constants in the presence of the translational-rotational coupling, V(q). Matrix D(q) has exactly the same form as matrix M(q), with bare elastic constants replaced by the effective constants. Without the central force assumption, the matrix takes the form

D - l ( q => 0) =

T0(M) -- kB 1Xl(TO)[48~V?l

699

(3.40)

D(q :=~ 0) = M(q =~ 0) - V (q =~ 0)X (q = 0)V(q =~ 0) (3.43) The rotational susceptibility, X(q = 0), is determined by direct interactions and self-interactions only and is diagonal, as required by the symmetry of the C6v point group. The result of calculations for the effective elastic constants is Cll - C 0, - 9(X33 V23 + X44 V24)

(3.44)

C66 -- C~ - 18X44 V?4

(3.45)

Cll -]- C12 -

(C~ -q- C~

- 18X33V?3

(3.46)

where the rotational susceptibilities are

X33 = I t - I x 3 1 -1- (J33(0)-F LS3)] -I

(3.47)

X44 = [t-'X41 + (J44(0)+ Ls4)] -I

(3.48)

(3.48) The susceptibilities increase with decreasing temperature, consequently making the effective elastic constants smaller. The thermoelasticity makes the system softer with decreasing temperature, an effect totally due to translationalrotational coupling. An elastic instability occurs when one of the eigenvalues of the effective dynamical matrix, D(q) (Eq. (3.42)), becomes zero. The diagonalization of the matrix for q = (qx, 0) and q - (0, qy) yields the same eigenvalues, and the lowest one corresponds to the C66 elastic constant. Thus, the elastic instability in the system will be determined by the condition, C66 ~ 0. This means that the system becomes unstable against a shear strain of the 2-D lattice, e.g., the exy ~= e6 component of the strain tensor. For the hexagonal lattice, the relation C66 -- ( 1 / 2 ) ( C l l - C12) implies that the hexagonal lattice also becomes unstable with respect to the (exx - eyy) =- (el - e2) strain. Both strains transform according to the E2 irreducible rerpresentation and will cause a corresponding lattice symmetry change: C6v =r C2v. The elastic instability will take

700

ECKHARDT AND LUTY

place simultaneously with the orientational instability, causing E2 type symmetry changes as discussed above. This is due to the translational-rotational coupling effect, and, as a result, phases characterized by the orientational order parameters, as defined in Eqs. (3.23) and (3.32), will show lattice deformations measured by e6 and (el - e2) strains, respectively. They are equivalent to the orientational order parameters of E2 symmetry.

4. F E R R O E L A S T I C I T Y OF L A N G M U I R MONOLAYERS Ferroelasticity commonly refers to the interaction between anisotropic defects in elastic media that become correlated through the elastic interaction of a medium that is deformed by the presence of the defects. According to our model of the Langmuir monolayer, the molecular tails, characterized by orientational degrees of freedom, are "defects" grafted onto a 2-D elastic medium with translational order of head groups [3]. Ferroelasticity would therefore mean a correlation of orientations of molecular tails through the elastic interaction of the translationally ordered head groups. First, we shall illustrate this coupling by numerical calculations, then we shall introduce the concept of elastic dipoles.

4.1. Strain-State Calculations For Stearic Acid: An Illustration of Translational-Rotational Coupling This section is devoted to illustrating, by detailed numerical calculations, the importance of translational-rotational coupling in a Langmuir monolayer of stearic acid [5]. We retain the model of orientationally free tails grafted to a 2-D net formed by the head groups of the amphiphilic molecules. Following the above microscopic derivation, the system energy can be described as

V({E}, {~}) -- vR({~}) -~- vTR({6}, {~})-if- vT({•})

(4.1)

where the first term is the contribution from the orientational degrees of freedom ({f2}), the third js the contribution from the translational degrees of freedom ({e}), and the second term represents the coupling between these two types of variables. Although the appropriate dynamical orientational variables for these systems are spherical harmonics, in these calculations we consider small fluctuations, and so three orientational angles are used: {f2} = {Rx, Ry, Rz }, i.e., rotation about the orthogonal crystallographic x, y, and z axes, respectively. Thus, Rz is a rotation about the film normal and is analogous to the azimuthal angle, ~p, when either Rx or Ry is negligible. It is convenient to describe the translational subsystem via strain variables ({e}) appropriate to a given 2-D lattice. The translational contribution to the energy in Eq. (4.1) may be written as

vT({e})- vT({E})+ VTT({e})

(4.1a)

where the first term denotes contributions from the head groups, and the second denotes contributions from the tails. The translational energy contribution of the tails is crucial to the determination of the global energy minimum and to subsequent local

minimizations with respect to the area. The head-group contribution is not directly calculated, but is instead attributed to a rescaling of the translational energy by a zrA contribution to the total energy. Nonetheless, the translational variables remain two-dimensional, even when tail interactions are included; there are no translations allowed along the film normal. The total system may be considered as a connected stack of two-dimensional subsystems consisting of various cross sections of the film. The orientational fluctuations are expected to follow, or quickly reach equilibrium, for a particular set of strains. The above energy may therefore be minimized with respect to f2, where the braces indicating a set of variables have been dropped, 0v -

E

+ %(.*)

= 0

(4.2)

and the resulting expression is solved for f2* (e), the equilibrium orientation that minimizes V(f2*(e)) in Eq. (4.1). The solution f2* (e), which is a type of stress-strain relation, shows the energetically most favorable path for reorientation of the molecules due to a two-dimensional strain. The energy along this path was investigated. Intermolecular interactions between the tail groups are calculated as for rigid molecules, with the use of 6-exp atom-atom potentials [83]. This is a reasonable approximation for condensed phases that is supported by the fact that tilt of the molecule as a whole is shown experimentally to be preferred over conformational rearrangement for these systems [84]. Head-group and surface interactions are not directly calculated, but are not ignored. Surface interactions are implied, because the molecules are constrained to a plane [85], and head-group interactions are implicit in the value of the strain variables chosen. These may be rescaled by adding a surface pressure-area (Jr A) term to the potential energy [86]. With the use of geometrical parameters appropriate for a fatty acid molecule, it can be shown that the two-dimensional Gibbs free energy (Jr A) contribution from a surface tension of 1 mN/m is on the order of that exerted by a three-dimensional pressure of 1 kbar. The calculative procedure consists of several steps: 1. The global minimum with respect to all strain and orientational variables is determined. All lattice parameters and orientational degrees of freedom are minimized. For example, this involves minimizing a structure with an assumed fatty acid molecular structure [87] in a two-dimensional crystal with either one or two molecules per unit cell. 2. Strain states relative to this global minimum are calculated. This is done by utilizing the dependence of the strain on the lattice parameters as described below. The states calculated depend on the symmetry of the particular system investigated. 3. The symmetries (phases) of the states from step 2 are determined. It was found in every case presented here that the phase space can be separated into various

LANGMUIR MONOLAYERS

For two molecules per unit cell, the reference state chosen is centered rectangular, and the strain variables are of the form

partitions characterized by a specific symmetry, as determined by a set of orientational variables. 4. A complete set of strain states for each symmetry (phase) is calculated, meaning that the energy V(f2*(e)) is determined for the most important set of strain variables. Once this procedure has been completed, the contribution to the strain state partition function [88] may be computed for each phase from step 3 according to Qe = Y~alle exp(-flV(f2*(e))). It is then straightforward to calculate the strain state contribution to the free energy for a given phase as F ~ 1 In Qe A plot of this free energy against temperature gives an estimate of the transition temperature between phases. Combinations of the three two-dimensional strains exx, eyy, and exy are considered. The last is a pure shear strain and is denoted as e6, to be compatible with Voigt notation, exx + eyy is proportional to the change in area and is defined as el. This leaves e2 = exx - eyy as the remaining strain variable. It is straightforward to express the strain variables in terms of the lattice parameters [89]. The third dimension is not relevant to the present model, and the equations reduce to m

exx =

a 1 sin Yl* ao sin y~ bl

eyy

=

(4.3a)

1

bo

a l cos Yl* _

--

-2

L

.

-- 1

1 [ b l cot y~ exy

fl

ao sin yff

bo

/

where a and b are the lengths of the lattice vectors and 9/* is the angle between the lattice vectors in reciprocal space. The subscripts 0 and 1 denote states before and after deformation, respectively. The strain variables introduced above take the following form for a hexagonal (C6v) reference cell:

el

--

exx +

e2

--

exx

e6 -

eyy

--

-- eyy

--

vii2 a---o

--~al

sin Yl* + bl

a---s ---~al sin YI* - bl

]

- 2 (4.3b)

1 exy -- 2~/-3a0 [bl - 2al cos Yl*]

Table II.

Phase

Energy (kcal/mol)

Vertical (1 mol/u.c.) Herringbone (pg)

701

el

--

exx + eyy

-

1 [al a----O

e2

--

exx

--

1 [al sin Yl* - b l ] a---o

e6

-- exy ---

-- eyy

sin gl* + bl] - 2 (4.3c)

2 ~ ao cos y

For either reference state, three variables must be specified. This is done by scanning e2 and e6 relative to the global minimum and minimizing the energy for these various states with respect to el (and the three orientational variables). In other words, the area of the minimized system provides the third necessary constraint. This is implemented by letting a -- a(y*) and b = b(v*), according to the equations above, and by minimizing the lattice with respect to the one remaining independent variable, y*. The system chosen for initial calculation is a monolayer composed of stearic acid amphiphiles in the conformation found in form C [87]. The calculation with one molecule per unit cell most clearly illustrates this method. The calculated minimum energy (Table II) is determined with respect to all degrees of freedom for an ordered lattice. A quasi-hexagonal (planar group p6m, point group C6v) reference state may then be defined by appropriately distorting the lattice according to Eqs. (4.3b) above. This symmetry can apply to the reported high-pressure, high-temperature LS phase if one considers a vertical molecule averaged over all orientations about the film normal [3]. In a system of p 6 m symmetry el is totally symmetric and e2 and e6 transform according to the irreducible representation E2. The energy V(f2*(e)) is then identical with respect to a scan over either e2 or e6, because these orthogonal variables couple bilinearly with appropriate orthogonal spherical harmonics of identical E2 symmetry [3]. Fatty acids in an ordered phase, however, are never of higher symmetry than C~, which leads to planar groups of lower symmetry. In general this necessitates consideration of a complete set of states, including e6 and e2 as well as el. In practice, the lowest energy states for this system accompany changes in e6, and so this variable is studied in detail with e2 set to 0. If this reduced set contains the lowest energy states and the lowest energy path between them, it will give a good first-order prediction of the phase behavior of this system, as well as being less complicated to interpret and

Results for Calculated Phases of Stearic Acid Langmuir Film Area/molecule

A

B

y

(A)

(A)

(A)

(degrees)

-26.31

18.28

4.303

4.581

112.00

-26.27

18.32

5.027

7.288

90.00

Tilted (1 mol/u.c.)

-26.01

19.09

4.695

5.289

129.76

Tilted antiparallel (pm)

-25.89

18.95

5.149

7.413

96.73

702

ECKHARDT AND LUTY -18

'

J

I

'

-~9

,

-20

,

3.5

'

,~,~

'verucar - ~ \

3

"f"

2.5

\

,

-21

-~

~ ~ -~

.-,

2 1.5

-"

t

m

4-

i -25

"*, \ '~.

-26

-27 -0.3

/

~,

'

~

'

~

+ I . -0.1

1 -0.2

\

// \

~

~ .

~

"

.

.

Shear

~

'

. 0 Strain

+

f

It

'

,

..........

0

"

01.1

01.2

o

-5

-10

-15

Shear

0 Strain,

-0.3

,

=

-0.2

-0.1

i Shear

,"

1 -0.1

-1

0.3

_a

, -0.2

-..

-0.5

5

-20 -0.3

0.5

,+"

Fig. 3. Strain-state curves for vertical and tilted phases, one molecule per unit cell, plotting energy versus shear strain, e6. The vertical and tilted phase curves are found by fixing the tilt magnitude to 0 and 14.69 ~ respectively. The lower curve at every point is found when minimizing with respect to all degrees of freedom.

20

~

,. 01

1. 02

0.3

Fig. 4. Tilt angle Ry versus shear strain e 6. The average magnitude of the two nonzero portions of the plot defines the tilted phase geometry.

much more efficient to calculate. The effect of el is included in the minimization of the area, which in practice changes only slightly along the minimum energy path. By scanning the shear strain e6 over all states while minimizing the energy with respect to the orientational degrees of freedom and el, we obtained the results in Figure 3. There is a sudden change in the tilt angle Ry at shear strain ~ 0.19, from 0 ~ to 14.69 ~ (Fig. 4). Because Rx is nearly 0 for the entire set of states scanned (Fig. 5), Ry corresponds to the tilt angle and Rz to the azimuthal angle (Fig. 6). This allows the separation of phase space into two and the definition of a vertical and a tilted phase, with the magnitude of the tilt angle Ry fixed at 0 ~ and 14.69 ~ respectively. The remaining energies for these two defined phases were then calculated; complete curves are shown in Figure 3.

Fig. 5. angle.

Tilt angle

0 Strain,

,

0.1

012

0.3

Rx versus shear strain e6. Note the small magnitude of this

The curves in Figure 3 were fit to a 16th-order polynomial by a X2 minimization. This was then used to calculate the strain state partition function as the integral Q~ lone period exp(-/~ V (~* (e)))de. Because the pure shear strain e6 results in a periodic function (Fig. 3), the integral is performed over one period. These functions are sufficiently simple that they may be integrated by Romberg integration [90]. These curves show that the shear elastic constant C66 is negative for the reference hexagonal system, and, therefore, the hexagonal phase is obviously unstable with respect to shear strain due to the coupling with the orientational fluctuations. Because the alkane chain has no more than Ca symmetry, it cannot be accommodated in an ordered phase by a C6v translational subsystem. Furthermore, any translational-rotational coupling will lead to a breaking of C6v symmetry. The one-molecule unit cell results have been introduced above. Surprisingly, tilting behavior is quite discontinuous with respect to shear strain, indicating nonlinear coupling between the tilt angle Ry and e6 (see Fig. 4). Because there are two phases found with respect to a scan of e6, vertical and tilted, these were treated separately to determine the ground state and possible transitions. There is considerably more linear coupling between Rz (the azimuthal angle) and e6, as shown in Figure 6. This coupling results in the continuum of states shown in Figure 3. Free energy contributions were calculated as described above. Calculations including no numerically applied pressure indicate that the stable phase at all temperatures is the vertical phase (Fig. 7). A negative surface pressure must be introduced to produce a tilted phase. This rescaling is attributed to the effect of head-group and surface interactions that can cause the film to expand [91]. The magnitude of the surface pressure difference applied here is similar to that required to produce a vertical phase on the aqueous surface. Estimates of the transition temperature were calculated as shown in Figure 8, indicating a transition from a vertical to a tilted phase with increasing temperature [54]. Although this transition temperature

LANGMUIR MONOLAYERS

Fig. 6. Azimuthalangle Rx versus shear strain e6. This plot is considerably more linear than that of Rx and Ry.

703

Fig. 8. Strain-statefree energycontributionsfor vertical and tilted phases (one molecule per unit cell) at an applied surface pressure of -50. The sign of this pressure is attributed to a rescaling due to surface and head group interactions.

Fig. 7. Strain-statefree energycontributionsfor vertical and tilted phases (one molecule per unit cell) at 0 applied surface pressure.

is unobtainable in practice, it increases with decreasing applied pressure. The calculated minimum for a two-molecule unit cell (as proposed for the CS phase [ 1, 84]) is essentially identical in energy to that found for a one-molecule unit cell (Table II, Figs. 9 and 10). Two phases are again found by scanning •6, a vertical herringbone phase of symmetry pg, and a tilted phase of symmetry pm. The herringbone p g phase contains a crystallographic glide plane between the molecules, whereas in the tilted p m phase this is replaced by a mirror plane coincident with the mirror plane containing the fatty acid chain. A twofold axis is found between the tilted molecules and parallel to their long axis, but not coincident with a crystallographic axis. The long axes of these molecules are therefore parallel, but the rotation about them differs by 180 ~ This phase is therefore denoted as the antiparallel phase. A third phase of higher energy is also found that exhibits a crystallographic twofold axis between pairs of molecules of

Fig. 9. Projectionof the vertical phase (one molecule per unit cell).

significant tilt magnitude. This nonuniformly tilted p m phase was not investigated in detail. The antiparallel p m phase is extremely similar to the original tilted phase of one molecule per unit cell (Figs. 11 and 12), as is clearly demonstrated by viewing these phases down the long axes of the molecules. The closest distance between molecular centers in the plane perpendicular to the long molecular axis is 4.11 and 4.14 ~ for the tilted and antiparallel phases, respectively. The corresponding tilt angles are 74.2 ~ and 76.6 ~ Because reorienting a given molecule in these two phases by 180 ~ with respect to its surrounding molecules makes little energetic difference, it seems highly unlikely that such phases will exhibit long coherence lengths in the condensed phase. The results from two-molecule per unit cell systems are shown in Figure 13. A clear transition between the pg her-

704

Fig. 10. cell).

ECKHARDT AND LUTY

Projection of the herring bone (pg) phase (two molecules per unit

Fig. 11. Perspective projection along the long axis of the molecule of the tilted phase (one molecule per unit cell).

Fig. 12. Perspective projection along the long axis of the molecule of the tilted antiparallel (pm) phase (two molecules per unit cell). The orientation of the molecules depicted in the center row is rotated 180~ about the long axis.

Fig. 13. Strain-state free energy contributions for herring bone (pg) and tilted antiparallel (pm) phases (two molecules per unit cell) at 0 applied surface pressure.

ringbone and the pm tilted antiparallel phase is found with increasing pressure. This may be compared to a CS-S t transition [ 1]. The slopes of these curves are considerably different at the crossing point. This indicates a high entropy of transition (~ 3 cal/mol.K) and, therefore, a first-order transition that is in agreement with phase coexistence reports in the literature [84]. Concluding this section, we stress that these calculations should be viewed as modeling Langmuir monolayers by a realistic potential while exploiting the underlying order and symmetry of these systems to arrive at reasonable predictions of the most likely phases. We intend to illustrate the feasibility of such an approach, which requires several extensions for quantitative agreement with experiment. These include a more detailed description of the interaction of the head groups with the substrate, especially their chemical nature and their relation to the surface pressure. Orientational disorder about the tail axis, as well as conformational disorder, should also be modeled [92, 93]. As such, conclusions from this work must still be expressed qualitatively, although they arise from potentials that are considered to be realistic. The results for one molecule per unit cell are illustrative and clear but are not directly comparable to most zr-T phase diagrams that describe ordered condensed phase unit cells as containing two molecules. Nonetheless, the high surface pressure calculations predict no transition between vertical and tilted phases with respect to temperature, and the qualitatively necessary result of tilt with decreasing surface pressure is obtained. Further data are necessary to determine the slope of the line separating vertical and tilted phases at intermediate pressures. There is nonlinear coupling between the tilt magnitude and the shear strain (Fig. 4), but this is a much more linear coupling with what, in practice, is the azimuthal angle of the amphiphile (Fig. 6). The graph of V(~*(e)) in Figure 3 allows straightforward determination of the shear elastic constant C66 by this methodology. It also may facilitate the calculation of coupling constants involving ~6 and orientational variables (f2i)

LANGMUIR MONOLAYERS in the Landau expansion. By sequentially setting 6i and then ~i to zero and performing further scans involving the remaining variables, one may quantitatively obtain all of the constants in the Landau expansion. Systems of two molecules per unit cell exhibit a tilting transition with respect to temperature, and the considerable divergence of the two free energy contribution curves indicates that this is a first-order transition. It may be compared with the recently reported coexistence of similar phases [84]. Details of the potential are important, because the potential energy surface is, in general, quite flat with many close-lying local minima. The curves in Figure 3 provide a unique view of fatty acid monolayers. They indicate that at low temperatures the monolayer is ferroelastic, as predicted [3]. Stress is caused by orientational fluctuations, although these calculations derive this necessary stress by first fixing the strain. Clearly, a tilted amphiphile introduces an elastic dipole, which is a local stress, into the system [5]. Domains represented by minima in the double-well potential decrease in size with increasing temperature until, finally, a phase that has average hexagonal symmetry results. This mesophase is reached when the barrier between the minima is overcome, although there remains a higher barrier to larger shear strain. At a high enough temperature, this barrier is also overcome, and a truly liquid state is obtained. Aside from this qualitative picture, this investigation of stress-strain relationships has reproduced several features of the fatty acid phase diagram. Extensions, including the chemical nature of the head groups, the disorder of the tail groups, and the explicit contributions of the other strain variables will further improve the quantitative predictions of these preliminary calculations. This methodology may prove to be well suited to inclusion compounds such as alkane derivatives in urea, which have been analyzed in this context [94, 95]. Here the neglect of interalkane translational contributions may be justified, and the explicit calculation of contributions from the urea cage are not complicated by solvent interactions, as in the case of head groups considered here. This makes calculation of vT({e}) straightforward. The remaining parts of the energy are similarly accessible computationally. 4.2. Elastic Dipoles as a Measure of Orientational Fluctuations

In this section the theoretical description of the translationalrotational coupling is reconsidered to introduce the concept of local stress. As shown in Section 3, Langmuir monolayer phases are characterized by both strain and orientational order parameters [3] that are related to each other through the elasticity of the system. This suggests that molecular tilt can be conveniently described by the concept of elastic dipoles embedded in an isotropic 2-D elastic medium. The elastic multipoles were originally introduced as a model for the interaction of defects and impurities in a bulk solid [96, 97]. They have been shown to be a very useful and elegant concept for orientational glasses [98, 99] and crystals with orientational disorder [66, 100]. Very recently elastic multipoles have been adopted

705

for a theory of solid-state reactions in a quantitative description of the mechanical characteristics of the reaction cavity [ 101]. The concept of elastic multipoles, which describe a force distribution around a molecule, is thus convenient for modeling molecular systems. Individual molecules can be treated as objects immersed in an isotropic elastic medium. The objects are characterized by a multipole moment that is a measure of the extent to which an object embedded in the elastic medium disturbs the medium by deviating from sphericity. The model is especially suitable for molecular systems where molecular shape [46] rather than chemical nature determines the predominant interaction and packing. It is reminiscent of the well-known "close-packing" principle commonly believed to govern the structures of simple molecular solids. Langmuir monolayers are appropriate for modeling by elastic multipoles, and we are unaware of any other attempts to do so, although mechanical models are commonly used to mimic monolayer molecules (e.g., grafted rods). Here, we demonstrate how the elastic multipole concept models the Langmuir monolayer by representing the molecules as elastic multipoles and by taking the interaction between them as that between multipoles. The model can be extended, and molecular compressibility can be introduced, which, for the amphiphilic molecules, would be a measure of aliphatic chain flexibility. This will allow inclusion of coupling between molecular tilt and chain conformation. Following the approach proposed in Section 2, we treat the LS phase as a hexagonal crystal-like phase, the equilibrium behavior of which is described by continuum elasticity theory. We rewrite Eq. (2.25) as a Fourier transform in the elastic limit, Vi t (q) =

i Viot(q) Y~(q)

(4.4)

It is possible to determine the form of the (2 • 5) coupling matrix V(q){Vi,~} from the requirement that V TR must have full hexagonal symmetry and, in the elastic limit, V(q) = 3 a

(0 0 Aqx Bqx 0 0 Aqy -Bqy

Bqy ) Bqx

(4.5)

where a is the hexagonal lattice constant and A and B are coupling constants for nearest neighbor molecules located at (0, 0) and (a, 0). The fact that there is no translational-rotational coupling for harmonics Y1 and Y2 indicates that forces due to translational displacements along x and y are balanced at equilibrium by molecular torques associated with orientational fluctuations described by Y1 and Y2. Equation (4.4) is now written in the form V/'(q) - - i N

-1 ~ Pij(k)qj exp[iqR(k)]

(4.6)

k where we have used the elastic limit of the translationalrotational coupling and the Fourier transform of the surface harmonics. We define Pij

(k) = a~ A~ Yo~(k)

(4.7)

as the elastic dipole of the kth molecule induced by orientational fluctuations specified by the surface harmonics. A~ equals A for ot = 3 and equals B for c~ = 4.5 and represents

706

ECKHARDT AND LUTY

the translational-rotational coupling constants (see Eq. (2.17)). The a are elements of real, spherical unit tensors [97]. In writing Eq. (4.7), we have represented a force distribution around a reorienting molecule, k, by the elastic dipole. With Eq. (4.7), we can write the translational-rotational part of the energy, Eq. (2.29), as V TR - - i N - 8 9

~ q

ui(q) Z

Pij(k)qjexp iqR(k)

(4.8)

k

the result

Gij(kk') = -[4zr/z(21z + ~.)]-1 [ (3/z + ~.)Sij lnR -- ([d + ~.)Ci Cj ]

(4.16)

where R = IR(k) - R(k')l/a and ci = elastic coupling between the dipoles,

Ri/R. We calculate the

aijkl(kkt) -- [4~r/z(2/x + ~.)]-1R-2{(3/z 4- ~.)[~ik~jl

(4.9)

-- CjCi~ik] -- (ft 4- ~.)[~il~kj 4- ~ij~kl -- 2(~ijCkCl 4- t~kjCiCl 4- t~jlCiCk 4- ~ilCkCj -- ~klCiCj) 4- 8CiCjCkCl]} (4.17)

When calculated from the Fourier transform of the translational displacement, u (q) can be used to write Eq. (4.8) in the compact form,

It is convenient to represent the indirect interaction, Eq. (4.15), in spherical coordinates rather than Cartesian ones. We split the elastic dipoles into components, Pij = a~. Pot, where Pc~ = Aa Y~ defines the transformed couplings between dipoles,

vTR : E eij(k)Pij(k) k

Got~(kk') = a~ Gijkl(kkt)aflkl

with the strain tensor components defined as

1 Oui (k) ! Ouj(k))

eij (k) : -~ 0 n j (k)

0 gi (k)

(4.10)

This shows that the translational-rotational part of the energy is conveniently represented as a sum over sites of products: local strain times local stress. This gives a simple interpretation of an elastic dipole as a local stress generated by a molecular tilt. As in elasticity theory, we define the elastic Green's function [102],

Gij(kkt)

: Z Mij(q)exp(iq[R(k) - R(U)])

which satisfies the relation Gij(kkt)Mil(ktk tt) -- Sil(kk"). We can express elastic displacement and local strain as

sel(k) -- Gijk(kkt)ejk(k t)

(4.12)

eij(k) : Gijkl(kkt)ekl(k t)

(4.13)

where the nonlocal response functions are corresponding derivatives of the Green's function, e.g., 02 (4.14)

Relation (4.14) implies that the above response function has the meaning of nonlocal compliance. With this identification, we write

1

Vind : ~ Z Z eij(k)Gijkl(kkt)ekl(kt) k k~

with the transformed elastic compliance,

~ =

S~

(419)

The indirect interaction is

1

Vind --- --~ Z E k :/:U

Pa(k)[ N-1S'~~ 4-Ga#(kk')]P#(k') (4.20)

(4.11)

q

Gijkl(kk') -- ORj(k)ORi(k') Gik(kk')

(4.18)

(4.15)

This indicates that the indirect rotational energy is the lattice deformation energy due to local stresses induced by the reorientation of molecules. In the equation, the summation runs over all molecular sites and includes the term k = k t, which is the energy of creation of an elastic dipole in the elastic medium, E. The energy is Ec = Pij SOkl ekl, where SO = (C~ -1 is the bare elastic compliance tensor. The elastic Green's function for a 2-D hexagonal (isotropic) system can be calculated following the procedure in [103] with

This interaction is highly anisotropic. To see this, we consider the interaction of two elastic dipoles, separated by the vector, R, in the direction of the x axis. The result is [ 2/z(/24-~.) ] Vind(Rllx) = --(4/z) -12/z 4- ~. 1 4/z 4- ~. yr(2/z 4- ~,)2R2 x (A 4- B)2[y3(0) 4- Y4(O)][Y3(R)

4- Y4(R)]

)~ [14-(2/24-3~.)(/x4-)0] /z + ~. zr (2/z 4- ~.)ZR 2 x (a-

B)Z[Y3(0)-

Y4(O)][Y3(R)- Y4(R)]

[ (5/24-32) ] 4- 1 4- 4zr(2U 4- ~.)R2 BZYs(O)Ys(R) (4.21) It is convenient to use the linear combination [Y3 + Y4]/2 for the (xx) component of the elastic dipole and [Y3 - Y4]/2 for the (yy) component of the elastic dipole. We conclude that a tilt of molecules in the direction perpendicular to the vector R is highly unlikely (viz. the second term), and the molecules will tend to tilt in the direction of the vector, which joins them. This supports the analogy to the interaction of electric dipoles, where a "head-to-tail" orientation is favored over a parallel arrangement of dipoles. This analogy can be further extended by considering elastic compliance as an analog of the macroscopic dielectric constant and the nonlocal compliance as corresponding to the dielectric function. Now we can calculate the indirect potential for a system of hexagonal symmetry. The summation over interacting nearest

LANGMUIR MONOLAYERS neighbors, which are at distance R, gives 1 [ 6(/z2 - ~,2) ]A2 Vind(R) - - 2 ( / z 4- ~.) 1 4- yr/z(2/z 4- ~.)R 2 x [3cos 2 | 1 [ 14-

2/z

1][3 cos 2 t 0 ( R ) - 1] 3 ( / z - ~ ' ) ] B2 4re (2# + )0R

x sin e 0(0) sin 20(R) cos 2[q~(0) - 4~(R)] (4.22) This equation gives two contributions to the total energy of a system (Eq. (4.1)). The indirect potential should be understood as an increase (decrease) in energy of the system with respect to the energy of the 2-D elastic medium, because surfactant molecules are long and are oriented at the interface. The first term in the indirect potential gives the interaction of the elastic dipole components (zz) along the long axes of molecules forming the Langmuir monolayer. Because molecules are oriented at the air-water interface, this term is nonzero and is largest for a phase with vertical molecules. The second term describes the interaction of (xx) and (yy) components of the elastic dipoles, which are related to the effective cross sections of the molecules. This term prefers the molecules to be tilted. For/z = ~., which corresponds to the Cauchy relation between elastic constants, and when there are only central forces between molecules, the indirect interactions in the hexagonal system are R-independent. Moreover, while the energy is independent of the tilt direction of molecules, it prefers them to be tilted, 0 ~ 0. For the general case, however, as long as [(8yr + 3)-/z + (4zr - 3). ~.] > 0, the elastic dipole interaction prefers the molecules to be tilted in such a way as to maintain the smallest difference between tilted directions of neighboring molecules. This tendency may change, depending on the elastic properties of the system and, in particular, on the interrelation between the elastic constants,/z and ~.. Notice that the interaction is critically dependent on the shear modulus # and is important for soft systems. When the system reaches an elastic instability (/z =, 0), the interaction becomes extremely attractive, provided the translational-rotational coupling constants A and B, are nonzero. If the elastic instability drives the system toward melting, the couplings diminish (there is no static translational-rotational coupling in an isotropic liquid) as well, and the elastic dipole interaction does not influence the collective orientation of the molecules. However, the elastic instability, # :=~ 0, might drive a transition toward a solid phase or mesophase where the coupling still exists. Then the elastic dipole interaction becomes attractive to the extent that it overcomes direct rotational interactions and leads to a collective tilt of the molecules. This creates a new phase with correlated (ordered) elastic dipoles, a ferroelastic phase. Now, we analyze how results are modified when one considers mesophases. Instead of a system with long-range translational order where the continuum elastic limit can be used, we deal with a system with a mesoscopic range of the translational order. Following an approach adopted for the glassy

707

state, we use the microscopic Hamiltonian from Section 2 as a guideline for a phenomenological coarse-graining procedure. There are reasons why such a phenomenological procedure is needed. A mesophase is characterized by large fluctuations predominantly in translational displacements on microscopic length scales. Therefore, standard procedures for extracting elastic properties (e.g., by gradient expansions) cannot be used here. Second, the reorientation of a molecule in a translationally disordered system is a strongly anharmonic process on microscopic length scales. It is hard to estimate it from first principles. In a mesophase we consider ranges of thermodynamic parameters for regions where the correlation length x of thermal orientational fluctuations is much larger than the NN distance, i.e., x >> a. A coarse-graining procedure should lead to an effective Hamiltonian, Heff, for long-wavelength fluctuations. The form of Heft is restricted by the following simplifying assumptions: (i) The range of all direct intermolecular forces is short compared with the mesoscopic coarse-graining length ~0 (a < ~0 < ~), with the possible exception of direct interactions between molecules due to electrical multipoles. This assumption is well satisfied for Langmuir monolayers where the predominant interaction is between aliphatic chains and is of short range. As a consequence of this assumption, Heft should consist of terms and their derivatives that are local in a coarse-grained displacement field, u(x). (ii) On mesoscopic length scales, the system behaves like an elastic medium, so that Heff is at most quadratic in u(x). This does not imply the harmonic approximation at shorter length scales, where a system with translational disorder, such as a mesophase, is anharmonic in molecular displacements. (iii) The coarse-graining procedure divides the system into mesoscopic grains of size x. Within a grain, the system is considered to possess hexagonal, C6v point group symmetry. Given these three simplifying assumptions, the simplest effective Hamiltonian takes the form

Heft-- Z(~eij(x)COklekl(X)4-eij[~(x)]eij(x)) x

1

+ ~Z x

Z

vR[ f2 (x)' ~2(x')]

(4.23)

x t

The summation extends over the points of a coarse-grained 2-D net with hexagonal, C6v point group symmetry. The three terms can be identified as corresponding to the microscopic terms. In particular, the second term corresponds to Eq. (3.11). The stress on the mesoscopic length scale, P[f2 (x)], depends on the orientation of molecules within the grain x and is expressed in terms of spherical harmonics. The elastic constants are those on the mesoscopic coarse-graining scale. The direct rotational potential can be decomposed into a potential that denotes local orientational anisotropy, vR[f2 (x)], and couplings x r x'. The coupling between grains will, in general contain contributions from direct electrical multipole interactions as well as indirect interactions mediated by lattice distortions on the short length scales, )~ < ~0. For Langmuir monolayers, the coupling in the

708

ECKHARDT AND LUTY

effective Hamiltonian (Eq. (4.1)) is essentially the indirect interaction, Vind, found in the previous section. Thermodynamic properties of the model can be obtained from the partition function with the Hamiltonian, Heff, by integrating over e(x) and f2(x). It is convenient to decompose the strain into a homogeneous part, e, and an inhomogeneous one, e(x) = e. + 8e(x). Minimization of the partition function with respect to homogeneous strain gives

N - 1 E (Pij(x)) = Cijkl(ekl) o

(4.24)

X

where, as follows from Eq. (3.8), (Pij(x)) - a~jaa(Ya(x)). The orientationally ordered phase ((Ya) = 0) is always accompanied by a homogeneous deformation, which is characteristic of ferroelasticity. This is a deformation of the 2-D elastic medium formed by the head groups, and Eq. (4.24) tells us that Langmuir monolayers with orientationally ordered tails are always strained 2-D systems. In particular, for the phase with vertical tails, (Yc~) ~ 0, and consequently from Eq. (4.24), the totally symmetric strain (ell + e22) ~ 0. If this phase serves as a reference for a Landau free energy expansion, (Yc~) should not be considered as the orientational order parameter. However, if the reference state is the 2-D elastic medium of the molecular head groups, Eq. (4.24) gives the linear relation between the orientational order parameter (Y~) and macroscopic strain. If orientations within grains are frozen into random directions such as Y~x (Pij(x)), which corresponds to fluidized molecular tails whose head groups are frozen in a crystalline arrangement, the macroscopic deformation vanishes. But there are randomly frozen inhomogeneous strains, 8e(x), within every grain. This can be found by minimization of the partition function with respect to displacement, u (x), yielding

(ui(x))-- Ex' Gij(xxt)(O(ejk(x')) ) OXtk

(4.25)

and inhomogeneous strain can be calculated from Eq. (4.9). The elastic Green's function is that calculated above, because the elastic 2-D medium is the crystalline arrangement