Nano- and Micromaterials

advances in materials research 9 advances in materials research Series Editor-in-Chief: Y. Kawazoe Series Editors: M...

Author: Kaoru Ohno | Kaoru Ohno | Masatoshi Tanaka | Jun Takeda | Yoshiyuki Kawazoe

137 downloads 1610 Views 14MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

advances in materials research

9

advances in materials research Series Editor-in-Chief: Y. Kawazoe Series Editors: M. Hasegawa

A. Inoue

N. Kobayashi

T. Sakurai

L. Wille

The series Advances in Materials Research reports in a systematic and comprehensive way on the latest progress in basic materials sciences. It contains both theoretically and experimentally oriented texts written by leading experts in the f ield. Advances in Materials Research is a continuation of the series Research Institute of Tohoku University (RITU). 1

Mesoscopic Dynamics of Fracture Computational Materials Design Editors: H. Kitagawa, T. Aihara, Jr., and Y. Kawazoe

2

Advances in Scanning Probe Microscopy Editors: T. Sakurai and Y. Watanabe

3

Amorphous and Nanocrystalline Materials Preparation, Properties, and Applications Editors: A. Inoue and K. Hashimoto

4

Materials Science in Static High Magnetic Fields Editors: K. Watanabe and M. Motokawa

5

Structure and Properties of Aperiodic Materials Editors: Y. Kawazoe and Y. Waseda

6

Fiber Crystal Growth from the Melt Editors: T. Fukuda, P. Rudolph, and S. Uda

7

Advanced Materials Characterization for Corrosion Products Formed on the Steel Surface Editors: Y. Waseda and S. Suzuki

8

Shaped Crystals Growth by Micro-Pulling-Down Technique Editors: T. Fukuda and V.I. Chani

9

Nano- and Micromaterials Editors: K. Ohno, M. Tanaka, J. Takeda, and Y. Kawazoe

Kaoru Ohno Masatoshi Tanaka Jun Takeda Yoshiyuki Kawazoe (Eds.)

Nano- and Micromaterials With 204 Figures

123

Professor Dr. Kaoru Ohno Professor Dr. Masatoshi Tanaka Professor Jun Takeda Yokohama National University, Graduate School of Engineering, Department of Physics Tokiwadai, Hodogaya, Yokohama 240-8501, Japan E-Mail: [email protected], [email protected], [email protected]

Professor Dr. Yoshiyuki Kawazoe Tohoku University, Institute of Materials Research Katahira, Sendai 980-8577, Japan E-Mail: [email protected]

Series Editor-in-Chief:

Professor Yoshiyuki Kawazoe Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

Series Editors: Professor Masayuki Hasegawa Professor Akihisa Inoue Professor Norio Kobayashi Professor Toshio Sakurai Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

Professor Luc Wille Department of Physics, Florida Atlantic University 777 Glades Road, Boca Raton, FL 33431, USA

ISSN 1435-1889 ISBN 978-3-540-74556 Springer Berlin Heidelberg New York Library of Congress Control Number: 2007938884

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media. springer.com © Springer Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data prepared by SPi using a Springer LATEX macro package Cover: eStudio Calmar Steinen Printed on acid-free paper

SPIN: 12031894

57/3180/SPi

-543210

Preface

In nanotechnology to date, much emphasis is placed on the creation of the nanostructures by means of micro- and atomic manipulations. This research field has been highly respected and promoted by the society, polytics, and economics. Rapid progress in this field has been greatly stimulated by more fundamental study on nano- and micromaterials. In this respect, the scientists and engineers in different fields of physics, chemistry, materials science, and information technology including experimentalists, theorists, and also researchers doing computer simulations have collaborated to form a new interdisciplinary field. This book covers the recent advances in this growing research field, in particular, those developed mainly in the interdisciplinary research project named “Materials science for nano- and microscale control: Creation of new structures and functions,” which was formed in 2004 in the Graduate School of Engineering of Yokohama National University in collaboration with the Institute for Materials Research, Tohoku University and other universities. The topics described in this book are as follows. In computational materials design, first-principles calculations and simulations can give reliable guidelines for structural and functional controls of nanomaterials. In this respect, the development of new computational methods, in particular, for the excited states of materials, is highly desirable to investigate atomic and electronic dynamics on the nano- and microscales. The state-of-the-art GW and T -matrix calculations, transport calculations, and lattice dynamics calculations will be explained in detail in this book. From experimental point of view, in particular from the viewpoint of structural controls, the use of the self-organization of surface or local nanostructures controlled by light or heat is described in detail, in which a variety of useful structures appear through grain boundary motions on submicron scales. Such novel nanointegration technologies are particularly useful to create quantum dots or quantum well devices, and such applications are also described in detail. Also a variety of interesting optically controlled chemical or catalytic reactions, and phase transitions are described in detail for

VI

Preface

particular interesting systems. Moreover, the functionalities of quantum dots, the creation of micro-/nanomachines using microstereolithography, and the development of new techniques of laser spectroscopy to observe dynamical processes related to optic functionalities are described in detail. We hope that this book would be benefit to not only the scientists or engineers in this field but also the researchers in other fields to see what is going on in the researches of nano- and micromaterials. Finally, we would like to thank C.E. Ascheron and his coworkers at Springer-Verlag in Heidelberg for their continuous help in completing this book. Yokohama, Sendai January 2008

Kaoru Ohno Masatoshi Tanaka Jun Takeda Yoshiyuki Kawazoe

Contents

1 General Introduction K. Ohno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Nanometer-Scale Structure Formation on Solid Surfaces M. Tanaka, K. Shudo, and S. Ohno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Atomic Layer Etching Processes on Silicon Surfaces . . . . . . . . . . . . . 2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Real-Time Optical Measurements . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Adsorption of Halogen Atoms: Sticking Coefficient and Potential Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Site-Selective Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Desorption of Silicon Halides and Restoration of the DAS Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Nanoscale Fabrication Processes of Silicon Surfaces with Halogens . 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Scanning Tunneling Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Thermal Desorption Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Cluster Alignment by Passive Fabrication . . . . . . . . . . . . . . . . 2.3.5 Active Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Self-Organized Nanopattern Formation on Copper Surfaces . . . . . . . 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Novel Phenomena on Cu(001)–c(2×2)N . . . . . . . . . . . . . . . . . . 2.4.4 Nanopattern Formation at Vicinal Surfaces . . . . . . . . . . . . . . 2.4.5 Strain-Dependent Nucleation of Metal Islands . . . . . . . . . . . . 2.4.6 Strain-Dependent Dissociation of Oxygen Molecules . . . . . . . 2.4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19 19 21 21 24 26 34 39 48 50 50 53 56 62 68 76 77 77 78 79 79 82 85 88 89

VIII

Contents

3 Ultrafast Laser Spectroscopy Applicable to Nano- and Micromaterials J. Takeda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.2 Femtosecond Optical Kerr Gate Luminescence Spectroscopy . . . . . . 97 3.2.1 Time-Resolved Luminescence Spectroscopy: Up-Conversion Technique vs. Opical Kerr Gate Method . . . 97 3.2.2 Femtosecond OKG Method: Experimental Setup and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.3 Femtosecond Transient Grating Spectroscopy Combined with a Phase Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.3.1 Principle of Transient Grating Spectroscopy . . . . . . . . . . . . . . 105 3.3.2 Transient Grating Spectroscopy Combined with a Phase Mask: Experimental Setup and Results . . . . . . . . . . . . . . . . . . 107 3.4 Femtosecond Real-Time Pump-Probe Imaging Spectroscopy . . . . . . 109 3.4.1 Principle of Real-Time Pump-Probe Imaging Spectroscopy . 109 3.4.2 Experimental Demonstrations of Real-Time Pump-Probe Imaging Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4 Defects in Anatase Titanium Dioxide T. Sekiya and S. Kurita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.2 Growth of Anatase Single Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4.3 Control of Defect States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.3.1 Heat Treatment Under Oxygen Pressure . . . . . . . . . . . . . . . . . 123 4.3.2 Heat Treatment Under Hydrogen Atmosphere . . . . . . . . . . . . 124 4.4 Properties of Anatase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.4.1 Absorption Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.4.2 Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4.3 EPR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.4.4 Electric Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4.5 Carrier Control by Photoirradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.5.1 Photoconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.5.2 EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5 Organic Radical 1,3,5-Trithia-2,4,6-Triazapentalenyl (TTTA) as Strongly Correlated Electronic Systems: Experiment and Theory J. Takeda, Y. Noguchi, S. Ishii, and K. Ohno . . . . . . . . . . . . . . . . . . . . . . . . 143 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 5.2 Crystalline Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Contents

IX

5.3

Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.3.1 Paramagnetic Susceptibility and Electron Spin Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.3.2 Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.3.3 Photoinduced Magnetic Phase Transition . . . . . . . . . . . . . . . . 151 5.4 Electronic Structure Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.4.1 Results Within the LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.4.2 Breakdown of the LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 5.4.3 T -Matrix Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 5.4.4 Results in the T -Matrix Theory . . . . . . . . . . . . . . . . . . . . . . . . 164 5.4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 6 Ab Initio GW Calculations Using an All-Electron Approach S. Ishii, K. Ohno, and Y. Kawazoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.2 Many-Body Perturbation Theory and GW Approximation . . . . . . . . 172 6.3 Choice of Basis-Set Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 6.4 Application to Clusters and Molecules . . . . . . . . . . . . . . . . . . . . . . . . . 176 6.4.1 Alkali-Metal Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 6.4.2 Semiconductor Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 6.4.3 Gallium Arsenide Clusters and Crystal . . . . . . . . . . . . . . . . . . 180 6.4.4 Benzene Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 6.4.5 Why Are LDA Eigenvalues of HOMO Level Shallower Than Experiments? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.5 Self-Consistent GW vs. First Iterative GW (G0 W0 ) . . . . . . . . . . . . . . 184 6.6 Appendix: Proof of WT Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 7 First-Principles Calculations Involving Two-Particle Excited States of Atoms and Molecules Using T -Matrix Theory Y. Noguchi, S. Ishii, and K. Ohno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 7.2 Methodology: T -Matrix Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 7.3 Double Electron Affinity of Alkali-Metal Clusters . . . . . . . . . . . . . . . . 193 7.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 7.3.2 Effect of the Coulomb Interaction in the DEA Spectra . . . . . 193 7.3.3 Short-Range Repulsive Coulomb Interaction Within the T -Matrix Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 7.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 7.4 Double Ionization Energy Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 7.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 7.4.2 Two-Valence-Electron Systems . . . . . . . . . . . . . . . . . . . . . . . . . 198

X

Contents

7.4.3 Inert Gas Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7.4.4 CO and C2 H2 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 7.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 7.5 Two-Electron Distribution Functions and Short-Range Electron Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 7.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 7.5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 7.5.3 Ar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 7.5.4 CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 7.5.5 CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 7.5.6 C2 H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 7.5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 7.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 7.7.1 Fourier Transformation of Green’s Function . . . . . . . . . . . . . . 213 7.7.2 Fourier Transformation of K-Matrix . . . . . . . . . . . . . . . . . . . . 214 7.7.3 Fourier Transformation of T -Matrix . . . . . . . . . . . . . . . . . . . . . 215 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 8 Green’s Function Formulation of Electronic Transport at Nanoscale A.A. Farajian, O.V. Pupysheva, B.I. Yakobson, and Y. Kawazoe . . . . . . . 219 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 8.2 Landauer’s Transport Formalism: The Green’s Function Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 8.2.1 Multichannel Landauer’s Formula . . . . . . . . . . . . . . . . . . . . . . . 220 8.2.2 Surface Green’s Function Matching Method . . . . . . . . . . . . . . 221 8.2.3 Scattering Matrix and Transport Properties . . . . . . . . . . . . . . 223 8.2.4 Alternative Formulation of the Total Conductance . . . . . . . . 226 8.3 Carbon Nanotube Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 8.3.1 Conductance of Nanotubes with Vacancy or Pentagon–Heptagon Defects . . . . . . . . . . . . . . . . . . . . . . . . . 227 8.3.2 Doped Nanotube Junctions: Rectification and Novel Mechanism for Negative Differential Resistance . . . . . . . . . . . 230 8.3.3 Effects of Random Disorder on Transport of Nanotubes . . . . 234 8.4 Functional Molecule Between Two Metallic Contacts . . . . . . . . . . . . 235 8.4.1 Transport Through Xylyl-Dithiol Molecule Attached to Two Gold Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 8.4.2 Transport Through Benzene-Dithiol Molecule Attached to Two Gold Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Contents

XI

9 Self-Assembled Quantum Dot Structure Composed of III–V Compound Semiconductors K. Mukai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 9.2 Control of QD Structure by Growth Condition . . . . . . . . . . . . . . . . . . 244 9.2.1 Control of Growth Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 244 9.2.2 Closely Stacked QDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 9.2.3 QD Buried in Strained Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 9.3 Growth Process of QD Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 9.4 Analysis of QD Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 9.4.1 Grazing Incidence X-Ray Scattering . . . . . . . . . . . . . . . . . . . . . 256 9.4.2 Scanning Tunneling Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . 258 9.5 Summary and Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 10 Potential-Tailored Quantum Wells for High- Performance Optical Modulators/Switches T. Arakawa and K. Tada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 10.2 Parabolic Potential Quantum Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 10.3 Graded-Gap Quantum Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 10.4 Asymmetric Coupled Quantum Well . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 10.5 Intermixing Quantum Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 11 Thermodynamic Properties of Materials Using Lattice-Gas Models with Renormalized Potentials R. Sahara, H. Mizuseki, K. Ohno, and Y. Kawazoe . . . . . . . . . . . . . . . . . . . 275 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 11.2 Scheme of the Potential Renormalization . . . . . . . . . . . . . . . . . . . . . . . 276 11.3 Application of the Potential Renormalization . . . . . . . . . . . . . . . . . . . 278 11.3.1 Application to Melting Behavior of Si . . . . . . . . . . . . . . . . . . . 278 11.3.2 Application to Cu–Au Phase Diagram . . . . . . . . . . . . . . . . . . . 282 11.3.3 Application to Transition and Noble Metals . . . . . . . . . . . . . . 286 11.3.4 Order–Disorder Phase Transition of L10 FePt Alloy Using the Renormalized Potential Combined with First-Principles Calculations . . . . . . . . . . . . . . . . . . . . . . . 287 11.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 12 Optically Driven Micromachines for Biochip Application S. Maruo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 12.1.1 Two-Photon Microstereolithography for Production of 3D Micromachines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

XII

Contents

12.1.2 Assembly-Free, Single-Step Fabrication Process of Movable Microparts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 12.2 Optically Driven Micromachines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 12.2.1 Optical Trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 12.2.2 Optical Driving Method of Multiple Micromachines . . . . . . . 298 12.2.3 Optimization of Time-Divided Laser Scanning . . . . . . . . . . . . 300 12.2.4 Cooperative Control of Micromanipulators . . . . . . . . . . . . . . . 302 12.2.5 Optically Driven Micropump . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 12.2.6 Concept of All-Optically Controlled Biochip . . . . . . . . . . . . . . 307 12.3 Conclusion and Future Prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 13 Study of Complex Plasmas M. Shindo and O. Ishihara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 13.1 Overview of Complex Plasma Research . . . . . . . . . . . . . . . . . . . . . . . . 311 13.2 Charging of a Dust Particle in a Plasma . . . . . . . . . . . . . . . . . . . . . . . 312 13.3 Measurements of the Charge of Dust Particles Levitating in Electron Beam Plasma [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 13.4 Various Approaches to Plasma-Aided Design of Microparticles System in Ion Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 315 13.4.1 Analysis of Ion Trajectories Around a Dust Particle in Ion Flow [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 13.4.2 Wake Potential Formation to Bind Dust Particles Aligned Along Ion Flow . . . . . . . . . . . 318 13.4.3 Attractive Force Between Dust Particles Aligned Perpendicular to Ion Flow [30] . . . . . . . . . . . . . . . . . . . . . . . . . . 320 13.5 Simulation Study of Cluster Design of Charged Dust Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 13.6 Complex Plasma Experiment in Cryogenic Environment [38] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 13.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

List of Contributors

Taro Arakawa Department of Electrical and Computer Engineering Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected]

Yoshiyuki Kawazoe Institute for Materials Research Tohoku University 2-1-1 Katahira, Aoba-ku Sendai 980-8577, Japan [email protected]

Amir A. Farajian Department of Mechanical Engineering and Materials Science Rice University Houston, TX 77005, USA [email protected]

Susumu Kurita Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokoham 240-8501, Japan

Osamu Ishihara Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected] Soh Ishii Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected]

Shoji Maruo Department of Mechanical Engineering Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan PRESTO Japan Science and Technology Agency 5 Sanbancho, Chiyoda-ku Tokyo 102-0075, Japan [email protected]

XIV


Hiroshi Mizuseki Institute for Materials Research Tohoku University Sendai 980-8577, Japan [email protected]

Kohki Mukai Department of Solid State Materials and Engineering Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected]

Yoshifumi Noguchi Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan Research Fellow (DC2) of Japan Society for the Promotion of Science Yokohama National University Yokohama 240-8501, Japan Computational Materials Science Center (CMSC) National Institute for Materials Science (NIMS) 1-2-1 Sengen, Tsukuba Ibaraki 305-0047, Japan [email protected]

Kaoru Ohno Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected]

Shin-ya Ohno Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokoham 240-8501, Japan [email protected] Olga V. Pupysheva Department of Mechanical Engineering and Materials Science Rice University Houston, TX 77005, USA [email protected] Ryoji Sahara Institute for Materials Research Tohoku University Sendai 980-8577, Japan [email protected] Takao Sekiya Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokoham 240-8501, Japan [email protected] Masako Shindo Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected] Ken-ichi Shudo Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokoham 240-8501, Japan [email protected]


Kunio Tada Graduate School of Engineering Kanazawa Institute of Technology 1-3-4 Atago, Minato-ku Tokyo 105-0002, Japan [email protected] Jun Takeda Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokohama 240-8501, Japan [email protected]

XV

Masatoshi Tanaka Department of Physics Graduate School of Engineering Yokohama National University 79-5 Tokiwadai, Hodogaya-ku Yokoham 240-8501, Japan [email protected] Boris I. Yakobson Department of Mechanical Engineering and Materials Science Rice University Houston, TX 77005, USA [email protected]

1 General Introduction K. Ohno

In a fundamental part of the field of nano- and microscale science, revolutional progress has been made since last two decades, in a way highly respected by the society, politics, and economics. In this stream, scientists and engineers from different fields of physics, chemistry, materials science, and information technology, including experimentalists, theorists, and researchers doing computer simulations, have collaborated to form a new interdisciplinary field called nanotechnology. In the field of electronics, for example, since the invent of the transistor by Shockley, Brattain, and Bardeen in 1940s, downsizing of the electronic devices has been continued. According to the so-called Moore’s law, the density or the number of transistors per unit area on an integrated circuit is doubled every 2 years; in other words, the size of transistors decreases by a factor of 1/8 every decade starting from 1 cm in 1950, and it is certainly ∼ 50 nm in 2007 as shown in Fig. 1.1. Figure 1.2 shows the atomic structure of the interface between Si and SiO2 [1, 2]. For example, a titanium deposition on top of silicon surfaces (Fig. 1.3) [3] is considered as a way to increase the mobility of the electronic devices. A lot of experimental and theoretical efforts have been devoted to these and many related but different systems. However, it is anticipated that the fabrication of electronic devices based on the present-day semiconductor technology will soon face the technical limit, and the use of nanolithography or self-organization controlled by light or heat (see Chap. 2), or the use of new idea such as quantum dots or molecular devices is highly expected. As a related topic, microstereolithography (Chap. 12) will be useful to manipulate micromachines. When the size or the dimension of materials decreases, a variety of new phenomena which have never been expected in bulk materials will appear. It would be a tremendous idea to use them as the future devices. First of all, when the size decreases, the quantum effect becomes, in general, dominant as pointed out by Kubo in 1962 [4], and this is often called as the Kubo effect. Consider for example metals. Near the Fermi level, metals have continuum spectra and the splitting between adjacent quantum levels is quite small and

2

K. Ohno

Fig. 1.1. Moore’s law of the minimum size of transistor used in the integrated circuit

Fig. 1.2. Si/SiO2 interface

(a)

(b)

Fig. 1.3. Ti on Si (001) surface. (a) Pedestal site and (b) dimer vacancy site [3]

1 General Introduction

3

Fig. 1.4. Ionization potential (IP) and electron affinity (EA) and their relation to the energy levels

negligible. However, in clusters made of small number of atoms, the splitting between adjacent quantum levels is finite, and in general this splitting increases when the number of atoms in the cluster decreases or equivalently when the size of the cluster decreases. This is true not only for semiconductor clusters but also metal clusters. For neutral clusters and molecules, the electron affinity (EA) is defined as the maximum energy gain to attach an electron from infinitely apart to the lowest unoccupied molecular orbital (LUMO), and the ionization potential (IP) is defined as the minimum energy required to detach an electron from the highest occupied molecular orbital (HOMO) to infinitely apart. The absolute values of the LUMO and HOMO energies correspond EA and IP, respectively, and the IP minus EA gives the energy gap; see Fig. 1.4. There is a general tendency that the energy gap increases when the size of the cluster decreases although there are exceptions due to the irregular geometries of the bond between atoms. For the GW approximation, see Chap. 6. Experimentally, quantum levels of bulk samples are measured by the photoemission or inverse photoemission experiment. The photoemission determines the quantum levels of the occupied states from the absorbed photon energy minus the emitted excited electron, while the inverse photoemission determines those of the empty states from the absorbed electron energy minus the emitted photon energy. For clusters, the mass of charged clusters is separated by the time-of-flight (TOF) method, which uses the acceleration proportional to e/m under an applied electric field. Simultaneously, by photoirradiation, the electron affinity (EA) is measured as the threshold value of a photon energy with which the negatively charged clusters is photodetached and neutralized. Irrespective to bulk or cluster, optical absorption spectra is different from the photoemission and inverse photoemission spectra. This is because, in the optical absorption process, the excited electron does not go away from the

4

K. Ohno

cluster but still trapped inside the cluster, forming an electron–hole pair called exciton. Due to the binding energy of the Coulomb attraction between the electron and hole, the threshold energy of the optical absorption is generally smaller than the energy gap. For semiconductor clusters, the phenomenon that the photoluminescence energy is smaller than the optical absorption energy, i.e., the photoluminescence has longer wavelength than the optical absorption, is called the Stokes shift. This phenomenon occurs because the relaxation of atomic geometry takes place in each process. Then because the wavelength of the photoluminescence is different from the incident light, it can be detected distinctly from everywhere the cluster exists. Moreover, the color of the photoluminescence depends on the cluster size. The clusters showing strong luminescence are therefore useful to mark particular biomolecule, for example, since the luminescence with different wavelengths is controlled by the cluster size. In this respect, CdSe clusters are often used in biomedical experiments. Since the zero-dimensional system inside which charged carriers and excitations are confined is called the quantum dot, these clusters are often called quantum dots. (More commonly the term “quantum dot” is used in electron transport problems explained later.) Stable structures and optical absorption spectra of small CdSe clusters (Fig. 1.5) have been calculated from first principles [5–7]. For passivated nonstoichiometric CdSe clusters, the result of the state-of-the-art first-principles calculation solving the Bethe–Salpeter equation for the twoparticle Green’s function is compared with the result of the time-dependent density functional theory in [8]. The wavelength of the absorption peaks is strongly size dependent and monotonically increases as the size of the cluster decreases. The majority of the clusters have a series of dark transitions before the first bright transition. This may explain the long radiative life times observed experimentally. For an example of metal clusters, FePt clusters have attracted considerable interest because it can be used for magnetic thin films with high coercivity. Figure 1.6 shows the structure of FePt cluster with a diameter of 17 nm at 3,000 K determined by a fcc-lattice Monte Carlo simulation using the total

Fig. 1.5. Most stable structure of (CdSe)13 and (CdSe)34 . After Noguchi et al. [5] and Kasuya et al. [6]


5

Fig. 1.6. Structure of FePt cluster with a diameter of 17 nm at 3,000 K

energies determined by a first-principles calculation (see Chap. 11) [9, 10]. Au clusters are also of much current interest because it was found to exhibit catalytic behavior [11, 12]. To control the energy gap in p–n junction has been crucially important in semiconductor technology. This idea may be directly used to create the high performance solar battery. The tuning of the optical absorption spectra to the spectra of sun light is basically possible by combining different sized clusters. Another example is the photosynthesis in chlorophyll or light-harvesting property in dendrimers (see Chap. 3). Figure 1.7 is a π-conjugated dendrimer, star-shaped stilbenoid phthalocyanine (SSS1Pc) with oligo (p-phenylenevinylene) peripheries, which shows a light-harvesting property [13–16]. The calculated wavefunctions [16] are shown in Fig. 1.8, in which the levels are clearly separated to those belonging to the peripheries (P) and those belonging to the core (C). When an electron is selectively excited in the periphery (P), electron and hole transfer from the periphery to the core through π-conjugated network as shown in Fig. 1.9. From dynamics simulation [16], it has been found that the one-way electron and hole transfer occurs more easily in dendrimers with planar structure than in those with steric hindrance because π-conjugation is well maintained in the planar structure. This results well explain the experiments by Akai et al. [13,14] and Takeda et al. [15]. Another example of the gap control is a photocatalysis. In this respect, metal oxide such as anatase TiO2 (see Fig. 1.10) has been widely investigated (see Chap. 4). In particular, the doping of transition metal impurity is quite important in controlling the energy gap suitably.

6

K. Ohno

Fig. 1.7. Structure of (a) SSS1Pc-1 and (b) SSS1Pc-2. In both (a) and (b), upper figures show the front view and lower figures show the side view. The structure of SSS1Pc-2 (b) is three-dimensional due to steric hindrance between the peripheries

Fig. 1.8. (Color online) Amplitude of the wave function at the ground state of SSS1Pc-2. The cubes are the unit cells. For each level, the points at the center and the upper right side show the core and the periphery, respectively. Gray and black areas denote the positive and negative values of the wave function, respectively

For example, the dissociation of H2 O by solar energy would be one of the wonderful applications in the photocatalytic reaction. Figure 1.11a shows the absorption of H2 O on the surface of anatase crystal. Figure 1.11b, c shows the geometry and wavefunction of the most stable, adsorbed ground state [17].


7

Energy eigenvalue (eV)

0 −1

Periphery (P)

Core (C)

P-LUMO

−2

C-LUMO

−3

hv C-HOMO

−4

P-HOMO

−5

Fig. 1.9. The energy eigenvalues of SSS1Pc-2. Black and white circles denote electrons and holes, respectively. First, an electron is excited from the (almost doubly degenerate) P-HOMO levels to the (doubly degenerate) P-LUMO levels on the periphery side (solid line with an arrow ). Then, the electron is transferred from the P-LUMO levels to the (doubly degenerate) C-LUMO levels (dashed line with an arrow ), and the hole is transferred from the P-HOMO levels to the C-HOMO level (dotted line with an arrow )

(a)

(b)

Fig. 1.10. (a) The unit cell of anatase (TiO2 ) crystal. Large and small circles correspond, respectively, to oxygen and titanium atoms. (b) The supercell for treating the surface of anatase (TiO2 ) crystal

Figure 1.12 shows a schematic diagram of the dissociation of H2 O molecule by photocatalyst. Figure 1.12a is the simplest scheme, in which four holes created by light absorption induce a reaction 2H2 O → 4H+ + O2 + 4e− and produce an oxygen molecule, while two electrons induce a reaction 2H+ + 2e− → H2 and produce a hydrogen molecule. Figure 1.12b is a combination of two independent reactions using different catalysts can induce oxygen and hydrogen molecules separately, called the Z scheme [18].

8

K. Ohno

(a)

(b)

(c)

Fig. 1.11. Reaction between H2 O molecule and the surface of anatase crystal

Transition metal oxides are well-known strongly correlated systems, whose electronic structure is hardly treated by the standard band structure calculation. Similar and related topic is a synthetic metals and organic Mott insulators. For example, the high-temperature phase of an organic radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) crystal exhibits a Mott insulator phase [19] (see Chap. 5). The state-of-the-art T -matrix calculation solving the Bethe–Salpeter equation can handle the multiple scattering and short-range correlations between electrons, and enables us to evaluate the on-site Coulomb energy U of this material (see Chaps. 5 and 7). By this method, it is demonstrated that the so-called “Coulomb hole” plays a very important role in the problem of short-range electron correlations. Quantum dots are more commonly considered in the electron transport problem in confined area (see Chaps. 8 and 9). The electron transport through a quite small structure such as quantum dots is governed by the quantum effects. For example consider a spherical particle with a diameter of d embedded in the medium of dielectric constant ε. Then the capacitance of this particle is given by C = 2πεd,

(1.1)

and the energy required to charge up this particle with one excess electron (or hole) is given by E=

e2 e2 = . 2C 4πεd

(1.2)

(If we consider a Cooper pair in a superconductor, e2 should be replaced by 4e2 .) When the size d (and therefore the capacitance C) of this cluster becomes


O

O

H+

H

H

O

H+

H

H

H

H

Pt

O H

hν

H

H+

Fe e+

3+

H

hν

e+

2+

A

H O

O

hν

e−

e+ e−

H

H

H H+

9

Fe

e−

B

3+

Fe

Fe

H

H

H H+ O

H+

H

Pt

hν H+

H

H

O

H H+

H

H

e+ e−

O

H

A

H

Fe3+

H

H

O

H

(a)

A H H

H hν 2+

e− Fe

H2 H

3+

O2

O O O O

O H

H

Fe

B

H Pt H

O O

O

e+

Fe2+

e+

O2

O

hν

e–

H O

2+

B

H2

(b)

Fig. 1.12. (a) The simplest scheme of the dissociation of H2 O by photo-catalyst. Four holes created by light absorption induce a reaction 2H2 O→ 4H+ +O2 +4e− and produce an oxygen molecule, while two electrons induce a reaction 2H+ + 2e− →H2 and produce a hydrogen molecule. (b) Two independent reactions using different catalysts can induce oxygen and hydrogen molecules separately

extremely small, this energy E becomes large and exceed the thermal energy kB T . In this case, the electron transfer (i.e., the conductance) is blocked. This phenomenon is called “Coulomb blockade.” Then, according to the bias voltage, the electric current jumps up stepwise. This anomalous conducting behavior can be observed in nanometer-sized metal clusters embedded in the oxide tunnel junction sandwiched by metal conductors at quite low temperature. The origin of E in (1.2) is the electron–electron repulsive interaction inside the quantum dot, and this problem is related to the problem of strongly correlated electrons. Such an problem can be treated by the T -matrix theory (see Chaps. 5 and 7). When the confined area is two-dimensional, the structure is called “quantum well” (see Chap. 10). The density of states in two-dimensional materials is much sharper than in three-dimensional materials, and therefore quantum

10

K. Ohno

Fig. 1.13. TTTA crystal in which the electronic charge distribution shaded by blue clouds is restricted inside each molecule in the HT phase or between the dimerized molecules in the LT phase

wells are widely used as diode lasers. They are used also for the heterostructure field effect transistor (HFET) which is called also as the high electron mobility transistor (HEMT). Related but completely new idea in the physics of nanotechnology is based on the wavefunction control instead of the energy gap control. One example is the quantum computing, which uses, for example, the quantum spin states | ↑ and | ↓ called “qubits.” Although there are still many problems to be solved, quantum dot may be used as a qubit in the future. Qubits may be also realized by constructing three Josephson junctions in a superconducting circuit (see Fig. 1.14) [20, 22]. In the classical von Neumann-type computer, this information is used just as 0 or 1. In contrast, in the quantum computer, the mixture of the two quantum states is also used, and certain problems such as integer factorization is expected to be solved exponentially faster than the classical computer. Another example is the use of the Aharonov–Bohm (AB) effect. A well-known example of the AB effect is as follows: The wavefunction of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field though the magnetic field is zero in the region through which the particle passes. As is seen in this example, the electron wavefunction may become physical quantity and may be used to develop completely new electric devices in the future.


11

(b)

(a)

Fig. 1.14. (a) Josephson junction of 800 nm wide and (b) superconducting loop including three Josephson junctions working as a qubit. Both of them are made of aluminum. Courtesy of Shimazu [20]

(a)

(b)

(c)

Fig. 1.15. Structure created in dust plasma. (a) is the side view, while (b) and (c) are the cross section view. After Ishihara [21]

A completely different but very interesting topic is a complex plasma known also as a dust plasma. It includes fine particles of size ranging from nanometers to micrometers in size. What is interesting is the creation of hollow structure of dust particles despite the Coulomb repulsive interaction between dust particles. Figure 1.15 is a computer simulation image of the structure. See Chap. 13 for more details. As a new kind of low-dimensional materials, fullerenes and nanotubes made of only carbon atoms have attracted considerable interests since the discovery of C60 by Kroto et al. in 1985 [23]. By laser ablation or arc discharge experiments using a graphite rod, carbon chain molecules are aggregated in a plasma state. Fullerenes are created when the plasma is cooled down in a helium gas atmosphere. Fullerenes a hollow, closed cage structure made of

12

K. Ohno

(a)

(b)

(c)

Fig. 1.16. Na insertion into carbon nanotube

spherical network of six- and five-membered rings. It is well-known that, due to mathematical Euler theorem, the number of five-membered rings is always 12. The most abundant fullerene is C60 , which has a soccer ball shape. The next abundant fullerene is C70 , which has a rugby (foot) ball shape, and there are many higher fullerenes such as C74 , C76 , C78 , C82 , C84 , C90 , C94 , . . .. On the other hand, carbon nanotubes have a hollow cylindrical tube structure formed from a rolled graphite sheet and therefore made of six-membered rings only [24]. Carbon nanotubes have very high tensile strength and elastic moduli due to the covalent sp2 bonds between adjacent carbon atoms. The encapsulation of foreign atoms or molecules inside fullerenes and carbon nanotubes has been also investigated. Figure 1.16 represents the snapshots of the first-principles molecular dynamics simulation of inserting a sodium atom with 70 eV kinetic energy into a single-walled carbon nanotube [25], although no such experiment has been performed yet. If these materials could be created experimentally, they would be applied to a molecule-based diode or conductor as well as the gold nanowires [26]. For the calculation of transport properties of these materials, see Chap. 8. It has also been revealed that a polyyne molecule (C10 H2 ) can be put inside an open-ended single-walled carbon nanotube [27]. There is an energy gain of about 1.7 eV when C10 H2 . The bonding between C10 H2 and SWNT is due to the large area of weak overlap of the wave functions in the intermolecular region inside the SWNT [28]; see Fig. 1.17. A recent related experiment showing the molecular motion inside SWNT has been reported in [29]. The so-called endohedral fullerene, which has at least one foreign atom inside the cage of the fullerene, have attracted interested. Experimentally, it has been confirmed that at least one lanthanum, yttrium, or scandium atom can be encapsulated inside C82 or C84 using arc-discharge vaporization of composite rods made of graphite and the metal oxide [30]. The creation of endohedral C60 is possible, though the creation rate is very low, by using a nuclear recoil of isotope nuclear reaction [31]. Figure 1.18 represents a snapshots of a first-principles molecular dynamics simulation of the insertion of Po atom with 40 eV kinetic energy into C60 . It is quite amazing that such a heavy element as Po can be successfully encapsulated inside C60 with such low energy. Experimentally, the existence of Po@C60 in the solvent was certainly


13

polyyne molecule

Fig. 1.17. Wave function of the HOMO level of C10 H2 @SWNT

Fig. 1.18. Snapshots of a first-principles molecular dynamics simulation of a Po atom insertion into C60 with 40 eV kinetic energy

confirmed in the synchronized measurements using high-performance liquid chromatography and UV detector [31]. As a related topic, the electron capture (EC) decay rate of 7 Be encapsulated in C60 was measured using a reference method comparing with the rate in Be metal crystal, and it was found that the half-life of 7 Be endohedral C60 (7 Be@C60 ) decreases about 0.83% than inside Be metal crystal [32, 33].

14

K. Ohno

Fig. 1.19. Structure of the 3D polymers crosslinked by [2 + 2] cycloadditional four-membered rings

(a)

(b)

Fig. 1.20. Optimized 3D structure of peanut-shaped polymers crosslinked by eightmembered rings in a monoclinic unit cell. (a) is a side view and (b) is a view of the cross section of this structure

The decay rate is further accelerated when the 7 Be@C60 sample is cooled down at liquid helium temperature (its half-life is 1.5% shorter than Be metal) [34]. This phenomenon can be explained theoretically by the calculation of the electron density at the 7 Be nucleus position inside the C60 cage and in the Be metal crystal. The theoretical estimates are in fair agreement with the experimental observations [34, 35].


15

Fig. 1.21. Structure of polymer

Fullerene polymers made of C60 are also interesting [36]. Figure 1.19 represents C60 polymer networks crosslinked by [2+2] cycloadditional fourmembered rings, and Fig. 1.20 represents a peanut-shaped fused C60 polymer chains crosslinked by eight-membered rings, which are considered as a model for the electron beam irradiated C60 samples [37]. Owing to the overlap of wave functions as well as the hybrid networks of sp2 -like (threefold coordinated) and sp3 -like (fourfold coordinated) carbon atoms, the electronic structure is considerably different from each other. The resulting electronic structure is either semiconductor or semimetal depending on the spatial dimensionality of materials [36]. Another interesting topic in nano- and micromaterials is soft materials like flexible polymers, although they are not described in detail in this book. For example, micelle formation of AB block-copolymers can be used as a drag delivery system (DDS) in biomedical applications. Figure 1.21 represents an example of the mixture of water, oil, and amphiphilic polymers [38].

References 1. A. Pasquarello, M.S. Hybertsen, R. Car, Appl. Surf. Sci. 104/105, 317 (1996) 2. T. Morisato, K. Ohno, Y. Kawazoe, unpublished 3. B.D. Yu, Y. Miyamoto, O. Sugino, T. Sasaki, T. Ohno, Phys. Rev. B 58, 3549 (1998) 4. R. Kubo, J. Phys. Soc. Jpn. 17, 975 (1962)

16

K. Ohno

5. Y. Noguchi, K. Ohno, V. Kumar, Y. Kawazoe, Y. Barnakov, A. Kasuya, Trans. Mater. Res. Soc. Jpn. 29, 3723 (2004) 6. A. Kasuya, R. Sivamohan, Y.A. Barnakov, I.M. Dmitruk, T. Nirasawa, V.R. Romanyuk, V. Kumar, S.V. Mamyukin, K. Tohji, B. Jeyadevan, K. Shinoda, T. Kubo, O. Terasaki, Z. Liu, R.V. Belosludov, V. Sundararajan, Y. Kawazoe, Nat. Mater. 3, 99 (2004) 7. S. Botti, M.A.L. Marques, Phys. Rev. B 75, 035311 (2007) 8. M.L. del Puerto, M.L. Tiago, J.R. Chelikowsky, Phys. Rev. Lett. 97, 096401 (2006) 9. S. Masatsuji, Master Thesis, Yokohama National University, 2006 10. Y. Misumi, S. Masatsuji, S. Ishii, K. Ohno, MRS fall meeting, 2007 11. M. Haruta, N. Yamada, T. Kobayashi, S. Iijima, J. Catl. 115, 301 (1989) 12. M. Valden, Z. Lai, D.W. Goodman, Science 281, 1647 (1998) 13. I. Akai, H. Nakao, K. Kanemoto, T. Karasawa, H. Hashimoto, M. Kimura, J. Lumin, 112, 449 (2005) 14. I. Akai, A. Okada, K. Kanemoto, T. Karasawa, H. Hashimoto, M. Kimura, J. Lumin, 119–120, 283 (2006) 15. A. Ishida, Y. Makishima, A. Okada, I. Akai, K. Kanemoto, T. Karawasa, M. Kimura, J. Takeda, preprint (DPC07) 16. Y. Kodama, S. Ishii, K. Ohno, J. Phys. Condens. Matter. 19, 365242 (2007) 17. J. Shiga, S. Ishii, K. Ohno, unpublished 18. H. Kato, M. Hori, H. Sugihara, K. Domen, Chem. Lett. 33, 1348 (2004) 19. K. Ohno, Y. Noguchi, T. Yokoi, S. Ishii, J. Takeda, M. Furuya, Chemphyschem 7, 1820 (2006) 20. Y. Shimazu, J.E. Mooij, in Towards the Controllable Quantum States, ed. by H. Takayanagi, J. Nitta (World Scientific, Singapore, 2003) pp. 353–358 21. O. Ishihara, J. Phy. D: Appl. Phys. 40, R121 (2007) 22. J.E. Mooij, T.P. Orlando, L. Levitov, L. Tian, C.H. van der Wal, S. Lloyd, Science 285, 1036 (1999) 23. H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smaley, Nature 318, 162 (1985) 24. S. Iijima, I. Ichihashi, Y. Ando, Nature 356, 776 (1992) 25. A.A. Farajian, K. Ohno, K. Esfarjani, Y. Maruyama, Y. Kawazoe, J. Chem. Phys. 111, 2164 (1999) 26. Y. Kondo, K. Takayanagi, Science 289, 606 (2000) 27. D. Nishide, H. Dohi, T. Wakabayashi, E. Nishibori, S. Aoyagi, M. Ishida, S. Kikuchi, R. Kitaura, T. Sugai, M. Sakata, H. Shinohara, Chem. Phys. Lett. 386, 279 (2004) 28. R. Kuwahara, Y. Kudo, T. Morisato, S. Ishii, K. Ohno, unpublished 29. M. Koshino, T. Tanaka, N. Solin, K. Suenaga, H. Isobe, E. Nakamura, Science 316, 853 (2007) 30. H. Shinohara, H. Sato, M. Ohkohchi, Y. Ando, T. Kodama, T. Shida, T. Kato, Y. Saito, Nature 357, 52 (1992) 31. T. Ohtsuki, K. Ohno, Phys. Rev. B 72, 153411-1 (2005) 32. T. Ohtsuki, H. Yuki, M. Muto, J. Kasagi, K. Ohno, 33. H. Pllcher, Nature 431, 412 (2004) 34. T. Ohtsuki, K. Ohno, T. Morisato, T. Mitsugashira, K. Hirose, H. Yuki, J. Kasagi, Phys. Rev. Lett. 98, 252501 (2007), to be published online on 20 June 2007


17

35. T. Morisato, K. Ohno, T. Ohtsuki, K. Hirose, Y. Kawazoe, Phys. Rev. B, in submission 36. S. Ueda, K. Ohno, Y. Noguchi, S. Ishii, J. Onoe, J. Phys. Chem. B 110, 22347 (2006) 37. J. Onoe, T. Ito, S.-I. Kimura, K. Ohno, Y. Noguchi, S. Ueda, Phys. Rev. B 75, 233410 (2007) 38. N. Nakagawa and K. Ohno, in AIP Proceedings on the 5th International Workshop on Complex Systems (IWCS2007), in print

2 Nanometer-Scale Structure Formation on Solid Surfaces M. Tanaka, K. Shudo, and S. Ohno

2.1 Introduction Nanostructured materials have been extensively studied for more than 10 years because of tremendous potential to application in a variety of technology, such as electronics, materials science, and biotechnology. Although a large part of these studies concerns nanostructures in three dimensions, this section focuses on nanostructures in rather lower dimensions, on solid surfaces. Moreover, “nano-” usually means the range of a few to hundreds of nm; however, we concentrate on the structures one order smaller than usual, in other words, the structures in “atomic scale” rather than “nanometer scale,” especially those formed on well-characterized surfaces under ultrahigh vacuum (UHV) conditions. Even in this scale, nanostructures can be formed both by selforganization and by ultrafine machining. Before we present our latest studies, some categories of this kind of nanostructures are introduced in this section. We do not attempt to present a detailed review with reference to huge number of articles, but give a few examples of each category with emphasis on the initial works or fundamental studies. Self-organization process can potentially produce uniform nanostructures in wide area. It is more attractive in fabricating nanodevices if the controllability is achieved. Self-organized nanostructures are classified into some categories, for instance, those on metal surfaces are different from those on semiconductor surfaces [1]. Surface reconstruction on a (110) surface of face-centered-cubic metals (Ni, Cu, Pd, Ag, Ie, Pt, Au) is probably oldest known self-organized nanostructures on surfaces [2]. Added row and missing row reconstructions are found on diatomic gas molecule-adsorbed surfaces and on alkali-metal adsorbed surfaces as well as on clean surfaces [3]. The driving force of this kind of reconstruction is simply thought to be surface energy; however, the reconstruction is as a result of subtle energy balance between electronic energy and surface energy. Very low coverage of gas molecule or alkali-metal induces the reconstruction, which means that local coordination number and nonlocal

20

M. Tanaka et al.

charge distribution of transferred charge play important roles of the reconstruction. Prototype of nanopatterned metal surfaces is observed on vicinal Au(111) and nitrogen-covered Cu(001), and the pattern formation is explained by the elastic continuum model [4]. Long-range elasticity is dominant to form not only these prototypes but also all kinds of adlayers, and can be a tool for self-organization [5]. These structures are used as templates for growing one-dimensional (1D) and two-dimensional (2D) structures. Metal epitaxy on metal surfaces, such as Cu/Ru(0001) and Au/Ni(111), exhibits also nanopatterns [6]. Self-organized nanostructure formation on semiconductor surfaces, especially IV group semiconductors [7] and III–V group semiconductors [8], has been more extensively studied than that on metal surfaces because of potential applications in industries. As for IV group semiconductors, elongated Ag islands with aspect ratios greater than 50:1 were formed on Si(001) and the formation of this 1D structure was a result of elastic relaxation of the strained layer [9]. The 1D structures are found also in other systems. Self-assembled Ge nanowires were grown on Si(113) by molecular beam epitaxy [10]. Bi line structures were formed on Si(001) in the vicinity of its desorption temperature [11]. The 2D structures, such as the growth of Ge layers on Si surface, have been a subject of greater interest than these 1D structures. Ge nanoislands were formed by taking advantage of the Stranski–Krastanow (SK) growth mode [12,13]. Coherent SK growth was explained in terms of elastic deformation around the islands. The island size and spacing grow progressively more uniform, when Si layers and Si0.25 Ge0.75 layers are formed alternately on these nanoislands [14]. An approach toward nanointegration through the control of self-organization processes of surface structures – such as surface reconstruction, atomic steps, and the phase boundaries of reconstructed domains – was proposed [15]. On the other hand, as for III–V group semiconductors, the flat (211), (311), and (111) GaAs surfaces break up into regular facets and make superlattices with lateral corrugation of the interfaces during multilayer molecular beam epitaxy [16]. Quantum dots have been developed since dislocation-free strained In0.5 Ga0.5 As islands were found during the growth on a GaAs(001) substrate [17]. More practical methods to obtain highly uniform dot size and density were proposed [18, 19]. The prototype of the ultrafine machining is the method using Ga+ focused ion beam (FIB) with a diameter of only 100 nm [20]. Significant progress has been made in FIB technology and it is now a powerful tool in lithography, etching, deposition, doping, and even 3D nanostructures [21]. However, the dimension of nanostructures produced with this method is still beyond the scale focused in this section. Best spatial resolution in ultrafine machining is achieved with a scanning tunneling microscopy (STM) which can manipulate atoms one by one. Atom manipulation was first demonstrated by sliding Xe atoms on Ni(110) at 4 K to form an “IBM” logo where each letter was written by a collection of atoms [22]. Anther example is excision of S atoms from MoS2 surface by field

2 Nanometer-Scale Structure Formation on Solid Surfaces

21

evaporation to form characters at room temperature (RT) [23]. Nanometerscale modification of H-passivated Si(111) surface in air was also reported [24]. Under UHV condition, nanoscale patterning of H-passivated Si(100) surface was achieved by local desorption of hydrogen due to tunneling current, and only the patterned area was subsequently oxidized [25]. Tunneling electrons not only manipulate an atom, but also form an effective excitation source for inducing chemical reaction. The concept of bond-selective chemistry using this mechanism was proposed with the examples of single O2 molecule dissociation on Pt(111) and displacement of Si adatoms on Si(111) [26]. Fe(CO) molecules were formed starting from Fe atoms and CO molecules adsorbed on a Ag(110) surface [27]. The feasibility of inducing all the steps of a surface chemical reaction by using the STM tips was shown by the synthesis of biphenyl molecules starting from iodobenzene adsorbed on Cu(111) [28, 29]. Although spatial resolution of surface modifications using STM is perfect, it cannot be applied directly to the production of devices. As a more practical way, possibility of nanostructuring the surface by inelastic processes, induced by electrons or photons, has been widely discussed. Modification of materials by electronic excitation is becoming attractive due to recent advances in laser and synchrotron radiation [30]. In this section, we present our latest studies on nanometer-scale structure formation on solid surfaces since 2002 in the following sections. In Sect. 2.2, the fundamental processes of layer-by-layer etching of a Si(111) surface are described. Nanostructures in the lateral direction are also found: Halogen atoms are adsorbed at selective sites, and clusters are formed during the desorption process. In Sect. 2.3, how to control silicon surface at the atomic scale is described with regard to the dynamic processes, for example, passive fabrication due to thermal process to align nanoclusters and active fabrication via nonequilibrium reaction pathways due to electronic excitation. In Sect. 2.4, an example of self-organization on a metal surface is introduced: Nitrogen adsorption on Cu(001) surface induced strain and forms patch patterns which are used as a template for nanoscale arrangements.

2.2 Atomic Layer Etching Processes on Silicon Surfaces 2.2.1 Introduction Etching with halogen gases is the widely used process to fabricate semiconductor surfaces, and the usual industrial process is thermally induced etching in ambient chlorine gas. To understand the process, adsorption and desorption of chlorine at silicon surfaces have been studied [31, 32]; but because the current technology requires ultrahigh precision [33], the importance of study at the atomic scale is growing. Halogen etching is also a promising candidate method for atomic layer etching, which is one of the basic techniques

22

M. Tanaka et al.

to fabricate nanometer-scale structures [34]. Reaction between halogens and semiconductor surfaces has therefore attracted much attention in the recent years. Halogen etching consists of several stages; adsorption of halogen atoms on the surface, desorption of silicon halides, and reconstruction of the clean surface. Understanding of the atomic-scale mechanisms of these fundamental processes will be useful to optimize etching conditions and necessary for future development of atomic-scale etching. Although atomic-scale etching itself is a kind of ultrafine machining, our studies on the fundamental processes of the etching have revealed that they involve self-organizing processes, for instance, halogen atoms can be adsorbed at selective sites to form adsorbate patterns and nanoclusters can be formed by the thermal treatment of halogen-covered surface. In this section, the atomic-scale mechanisms of these fundamental processes are elucidated mainly by means of real-time optical measurements. Etching of the Si(001) surface is preferentially studied in connection with industrial applications, but etching of the Si(111) surface is also of interest, because the dimer-adatom-stacking fault (DAS) structure [35] has a variety of sites with different chemical reactivity [36]. The DAS model is illustrated in the left half of Fig. 2.1. STM has greatly improved our understanding of chemical processes at the atomic scale, and most studies have focused on the electronic states or the morphology mainly of the Si adatoms. However, another type of dangling bond on the rest-atoms which are not accessed by STM must have some role in surface reactions. The static properties at each stage in the fundamental processes of halogen etching have been revealed by a variety of methods. It is known that chlorine atoms first react with adatom sites to form monochlorides and remove dangling bond states near EF at low coverage [37, 38], while further exposure produces SiCl2 and SiCl3 species [39, 40]. These polychlorides tend to be formed on the center adatom sites [41]. On the other hand, there is little direct evidence for the presence of polybromide species, although their presence is generally accepted. In the right half of Fig. 2.1, the chloride species are schematically shown. When a dichloride is formed, the back-bond of the adatom is broken and a new dangling bond appears on the rest-atom, as illustrated in Fig. 2.1. With further chlorine, the second back-bond is broken to form a trichloride. Annealing at about 700 K for a Cl-saturated surface and at 500–650 K for a Br-saturated surface removes Si adatoms, and the rest-surface (the surface consisting of rest-atoms; see Figs. 2.37 and 2.41) covered with halogen atoms takes a 1×1 structure as in Fig. 2.27 [37–39, 42, 43]. Ultraviolet laser irradiation also produces this kind of rest-surface [41, 44]. X-ray photoelectron spectroscopy [39, 40] and surface-enhanced X-ray absorption fine structure [45] studies confirmed that only monochloride species remain after annealing above 673 K. In accordance with the above observations, a thermal desorption spectroscopy (TDS) study revealed that polychlorides species are desorbed as a peak at 690 K, and a laser-induced thermal desorption (LITD) study showed that the SiCl3 species almost disappears above 630 K [46]. On

2 Nanometer-Scale Structure Formation on Solid Surfaces Clean

Top View

Cl-adsorbed

a

M

a

M

r

a

N

M

N

D

E

a

23

r

N

D a

r

T T

E

T

E

a

Si adatom Si restatom

M

Cl atom

Side View a r

a

b

r

M

a

E

Si adatom Cl atoms

D

N

ND

E E

T T

T

Adsorption Emerging dangling bond Relaxing

Si restatoms (with native d.b.)

Si restatoms (bonded to the adatom originally)

Fig. 2.1. (a) Structural model of clean (left half ) and Cl-adsorbed Si(111)–7×7 DAS surfaces (right half ). a and r indicate the dangling bonds on Si adatoms and Si rest-atoms, respectively. Mono-, di-, and trichlorides are marked as M , D, and T , respectively. Hatched Cl atoms terminate the adatom dangling bonds (N ) or the newly emerging dangling bonds (E) at the rest-atoms. (b) Dichloride formation from a Si monochloride. The back-bond of the adatom is broken and a new dangling emerges at the rest-atom

the 1×1 Br-terminated rest-surface, many bilayer islands and clusters are found [43, 47]. When the halogen-covered rest-surface is heated above 900 K, halogen atoms are desorbed mainly as SiCl2 [40,46] and SiBr2 [48], as shown by a TDS study. As for the desorption mechanism, an STM study indicated that spontaneous Br etching of Si(111) at 700–900 K results in step retreat [43]. In this way, one Si layer is taken off, and a clean 7×7 DAS structure is subsequently restored. In spite of these studies, the dynamic processes of the desorption of silicon chlorides and the reconstruction to form the 7×7 DAS structure are still poorly understood, and need to be established before the relative reactivity of halogens on the Si(111) surface can be discussed.

24

M. Tanaka et al.

2.2.2 Real-Time Optical Measurements Real-time in situ observation is essential to investigate the kinetics. Optical methods are superior to others, because they are noninvasive, nondestructive, and capable of very rapid response. The optical responses of the surfaces are related to the surface electronic states [49–53]. Studies on halogen-etching processes on Si(111) introduced in this section were investigated by means of two optical methods: surface differential reflectivity (SDR) spectroscopy and second harmonic generation (SHG). These optical methods were combined with TDS which gives the total halogen coverage. These experimental techniques are not so popular compared with standard techniques for surface analysis such as electron spectroscopy. Accordingly, principles of these techniques are briefly introduced and their experimental procedures are described. Surface Differential Reflectivity Spectroscopy SDR spectroscopy was proved to be a powerful tool for the real-time study of hydrogen adsorption on Si(111) [49]. Differential reflectivity is defined as ∆R/R ≡ (Ra − Rc )/Rc , where Ra and Rc are the reflectivities of the Hcovered and clean surfaces, respectively. Spectral features of adsorption on adatom dangling bonds and breaking of adatom back-bonds were identified from the calculation of the ∆R/R spectrum for the hydrogenated 7×7 surface [54, 55]. These spectral features arise from the surface states of the clean surface, so that the SDR spectrum is considered not to depend on the adsorbate. These features develop with time during adsorption processes, whereas in the desorption processes, they decay with time as the clean surface structure is restored. Magnitudes of the SDR spectral features is interpreted to be proportional to the densities of saturated dangling bonds and broken bond breakage. The schematic diagram of the experimental setup is shown in Fig. 2.2 [56]. Measurements reported in this section were performed in an UHV chamber at a base pressure of 2 × 10−8 Pa. The 7×7 structure of the clean surface Powermeter

Q - Switched N d : YAG Laser λ/2

Imaging Assembly Monochro mator PDA

F1 LS1

Quartz Plate

SHG F3

AgCl Electrochemical Cell

Monochromator

F4

P1 LS2

P2 F2

Controller

PM

PM

Preamplifier

SDR

Si(111) Digital Oscilloscope

PC QMS

PC

Fig. 2.2. Experimental setup for SDR and SHG. See [56] for detail


25

was confirmed by low-energy electron diffraction. Halogen gas was generated in the vacuum with a AgX (X = Cl, Br) electrochemical cell doped with CdX2 (5% wt) [57]. The electrochemical cell produces more atoms than molecules [58]. The setup for the SDR measurement is as follows. Light from a halogen tungsten lamp (LS1) or a deuterium lamp (LS2) was polarized horizontally with a Glan-Taylor prism (P1), and separated into a probe beam (90%) and a reference beam (10%). The p-polarized probe beam was introduced into the vacuum chamber and incident on the surface at an angle of 70◦ from the surface normal. The specularly reflected probe beam and the reference beam were introduced via optical fibers to a grating spectrograph with an imaging assembly correcting astigmatism. The spectra of both beams were detected by a dual photodiode array, and the intensity of the reflected spectrum was normalized with respect to the reference spectrum. Photoinduced electrons in the diode array were accumulated at each pixel for 10 s to improve the signal-to-noise ratio. Second Harmonic Generation SHG has been employed more extensively than SDR to observe the kinetics of adsorption [51, 59] and desorption [60, 61] on Si(111). When the fundamental wave of a Nd:YAG laser is used as a pump laser, the two-photon energy of the fundamental wave is resonant to the S3 –U1 transition [52], where S3 and U1 states are attributed to the adatom back-bond and the adatom dangling bond, respectively. The nonlinear susceptibility χ(2) then decreases linearly with the coverage at low coverage. The adsorption process on adatom dangling bonds at low coverage is therefore detected more sensitively by SHG, and vice versa at high coverage. However, SDR is superior rather than complementary to SHG as a tool of real-time measurement, because SDR reveals the adsorption process in the full exposure range and provides information about not only the adsorption on adatom dangling bonds, but also the breaking of adatom back-bonds. In the SHG measurement, the fundamental wave (1,064 nm, 8 ns) of a Qswitched Nd:YAG laser was used as a pumping laser. The duration of the light pulse of the fundamental wave was 8 ns. The laser radiation polarized along the [211] direction with a half-wave plate was incident on the surface of the specimen with an incident angle of about 20◦ . The reflected second harmonic (SH) signal was passed through another polarizer, purified with a bandpass filter (F3) and a monochromator, and detected by a photomultiplier and gate integrated with a digitizing oscilloscope. Part of the incident light was directed to a quartz plate which produced strong SH signal used as a reference signal. The SH intensity was numerically obtained from the reflected signal divided by the reference signal.

26

M. Tanaka et al.

Coverage Evaluation by Thermal Desorption Spectroscopy The total halogen coverage was determined by means of TDS. TDS spectra were measured with a quadrupole mass spectrometer located in front of the specimen. The target mass was 63 and 107 for SiCl+ and SiBr+ ions, respectively. These species are considered to be cracked from SiCl2 and SiBr2 by the electron ionizer in the mass spectrometer. It was found that about 10% of the X atoms are desorbed around 600–700 K and about 90% are desorbed around 1,000 K when the coverage is above 60% of the saturation [46,48]. The former component arose from polyhalides, the amount of which could not be evaluated quantitatively. Accordingly, the specimen was annealed at 743 K for 2 min (Cl) or at 673 K for 3 min (Br) before the TDS measurement to eliminate polyhalides. After the annealing, all polyhalides including Si adatoms are desorbed [48] and the adatom layer disappears [43, 47]. Instead, the Xterminated rest-surface appears together with clusters including halogenated adatoms [43, 47], and this surface partially reconstructs a X-terminated 1×1 bulk-like surface [38]. In the measurements of isothermal desorption (SDR, SHG), desorption from this “1×1” rest-surface was observed. TDS was measured also from this surface with typical heating rate of 10 K s−1 . The total coverage was calculated from the area of the SiX+ . TDS spectrum between 850 and 1,200 K (Cl) or 770 and 1,170 K (Br), as the additional 10%, is taken into account when the coverage is above 60% of the saturation. The saturation of TDS is normalized to 1.35 ML (= 66/49), where 36 halogen atoms are on the adatoms and 30 halogen atoms are on the rest-atoms. 2.2.3 Adsorption of Halogen Atoms: Sticking Coefficient and Potential Barrier The adsorption processes of chlorine and bromine on Si(111)–7×7 were investigated by temperature dependence of adsorption on adatom dangling bonds and breaking of adatom back-bonds [56, 62]. The process was observed by means of real-time SDR spectroscopy and SHG measurements. The interpretation of SDR spectra is based on the results of the calculation of optical responses [63]. The kinetics of the adsorption process is discussed from the point of view of the direct adsorption of atoms. The analysis yields the sticking probability on an adatom dangling bond and the breaking probability of an adatom back-bond. Temperature dependence of these probabilities reveals the adsorption process and the breaking process with regard to potential energy. The difference in the reactivity of chlorine and bromine on Si(111) is discussed in terms of the interaction between adsorbates. Surface Differential Reflectivity Spectroscopy Figure 2.3 shows the relative variation of p-polarized SDR spectra for several Cl exposures at 300 K. The vertical axis corresponds to ∆R/R ≡ (Ra − Rc )/Rc ,


27

0.01 1L

0

4L

0

8L

0

15L

R/R

0

30L

0

E C

60L

0 -0.01

D

-0.02 -0.03

A

1

2

B

3

4

5

6

Photon Energy (eV)

Fig. 2.3. Variation of p-polarized reflectance spectra for several Cl exposures at room temperature. Data are taken from [56] 0.02 0.01

∆R / R

0.00 -0.01 -0.02

SB SA

-0.03 -0.04

1

2

3 4 Photon Energy (eV)

5

6

Fig. 2.4. Decomposition of the ∆R/R spectrum at 60 L in Fig. 2.3 (gray line) into two component spectra SA (solid line) and SB (dashed line). See [56] for detail

where Ra and Rc are the reflectances from the Cl-covered and clean surfaces, respectively. The ∆R/R spectrum at the exposure of 1 Langmuir (L) (1 L = 1.33 × 10−4 Pa s) has only a negative peak A located at 1.8 eV. At 8 L, a shoulder B at 2.4 eV becomes apparent as well as small structures above 3.3 eV. The peak A is almost saturated at 8 L, whereas B is saturated above 60 L. Each spectrum in Fig. 2.3 is reproduced by a linear combination (aA SA + bA SB ) of two component spectra SA and SB representing the structures A and B, respectively. For example, as shown in Fig. 2.4, the experimental plot (gray line) at 60 L is well reproduced by the sum of SA (solid line) and SB (dashed line). The magnitudes of SA and SB are determined so as to reproduce the spectra at 60 L with aA = 1 and aB = 1.

28

M. Tanaka et al. adatom

(a) Clean(Si21H27)

(b) Cl - adsorbed (Si21H27Cl)

H

Si

Cl

Fig. 2.5. Geometric structure of the Si(111) clusters: (a) clean surface cluster (Si21 H27 ), (b) Cl-adsorbed surface cluster (Si21 H27 Cl), and (c) dichloride surface cluster (Si21 H27 Cl2 ) (d) Calc. (H) 1.4eV

2.1eV

2.8eV

∆R/R

(c) Exp. (H)

2.8eV

(b) Calc. (Cl) 2.2eV 1.55eV

(a) Exp. SA (Cl)

1

2 3 4 Photon Energy (eV)

Fig. 2.6. SA component of the SDR spectrum for the monochloride Si(111) (a) and the spectrum obtained by calculation (b). The experimental (c) and calculated (d) spectra of monohydride Si(111) [54] are plotted for comparison

The optical responses of clean and Cl-adsorbed Si(111) surfaces have been calculated using time-dependent density functional theory (TD-DFT). The electronic states of three model clusters were calculated after optimizing the geometry. The geometric structures of the clusters are shown in Fig. 2.5. They represent the clean surface, and the surfaces with monochloride and dichloride. The SDR spectrum was obtained from the reflectance derived from the transition probability of each model with the aid of an extrapolation to the photon-energy range dominated by the bulk transition. Figure 2.6 compares SA component of Fig. 2.4 in (a) with that of the calculated spectrum in (b). The spectrum in (b) is obtained by subtracting the reflectivity for Fig. 2.5a


29

(d) Calc. (H)

∆R/R

(c) Exp. (H)

(b) Calc. (Cl)

(a) Exp. SB (Cl) 1

2 3 Phoeon Energy (eV)

4

Fig. 2.7. SB component of the SDR spectrum for the dichloride Si(111) (a) and the spectrum obtained by calculation (b). Experimental (c) and calculated (d) spectra for the dihydride [55] are also shown for comparison 1.2

aA , bA

1.0 aA

0.8 0.6

Br Cl

bA

0.4 0.2 0.0

0

1

2

3

4

5

6

7

8

9

10

11

Ni

Fig. 2.8. Development of the coefficients aA and bA vs. Ni at room temperature. Solid symbols are for Br adsorption, whereas open symbols are for Cl adsorption. Solid and dashed lines are the best-fit curves for direct adsorption of atoms

from that for Fig. 2.5b. The results for hydrogen adsorption are also plotted in (c) and (d) [54]. The calculated feature at 1.55 eV is assigned to the transition from adatom back-bond states to antibonding adatom dangling bond states. The same comparison for the SB component is shown in Fig. 2.7. The spectrum in (b) is obtained by subtracting the reflectivity for Fig. 2.5b from that for Fig. 2.5c. All the spectra in Fig. 2.7 contain a negative peak at around 2.6 eV or about 3.0 eV. This peak can be assigned to the loss of the transition at adatoms owing to the missing of adatom back-bonds. Above assignments allow us to commonly interpret that SA and SB represent the adsorption on the adatom dangling bonds and the breaking of adatom back-bonds, respectively. The coefficient aA and bA are plotted against the accumulated number of atoms impinging on the area of the 1×1 unit, Ni , in Fig. 2.8. Open and closed symbols represent the coefficients for Cl adsorption and Br adsorption,

30

M. Tanaka et al.

respectively. Figure 2.8 reveals the development of adsorption on the adatom dangling bonds and the development of breaking of the adatom back-bonds. It is known that the halogen gas produced by the electrochemical cell involves more atoms than molecules [58]. In the case of direct adsorption of halogen atoms without migration, the rate equation is as follows: dnA = αni (1 − nA ). dt

(2.1)

Here, nA is the normalized density of adatoms bonded to at least one halogen atom, α is the sticking probability of halogen atoms on the adatom dangling bond, and ni is the number of halogen atoms impinging on the area of the 1×1 unit cell per second. Solutions of (2.1) fit to aA are shown by dashed and solid lines in Fig. 2.8 for Cl and Br, respectively. On the other hand, the adatom back-bond is assumed to be broken only when the adatom dangling bond is terminated by at least one halogen atom. In the case of direct adsorption of atoms without migration, the rate equation is as follows dnB = βni (NB nA − nB ), dt

(2.2)

where β is the breaking probability of adatom back-bond by halogen atoms, nB is the normalized density of broken adatom back-bond, and NB is the saturated number of nB . NB should be smaller than 2 because adatoms are not removed by the halogen exposure. Solutions of (2.2) fit to bA are shown in Fig. 2.8. Thus obtained sticking probability on the adatom is αSDR = 0.7 and 1.20 ± 0.2 for Cl and Br adsorption, respectively, and the breaking probability is βSDR = 0.2 and 0.49 ± 0.04 for Cl and Br adsorption, respectively. These results at room temperature are summarized in Table 2.1. The sticking probability αSDR for Br adsorption is 1.7 times as large as αSDR for Cl adsorption. Larger αSDR for Br adsorption can be at least partially explained by the larger atomic radius of the Br atom (0.115 nm for Br and 0.100 nm for Cl) [64], because the cross section of the collision to the adatom dangling bond is larger for larger impinging atoms. However, the ratio of the atomic radius, Table 2.1. Summary of SDR results for the adsorption process of halogens on Si(111)–7×7

Sticking probability on the adatom dangling bond (feature A) Breaking probability of the adatom back-bond (feature B) Activation energies Adsorption on the adatom dangling bond Breaking of the adatom back-bond

Cl

Br

0.7

1.2 ± 0.2

0.2

0.49 ± 0.04

−8 ± 14 meV −38 ± 7 meV

−2 ± 16 meV −39 ± 19 meV


31

1 SDR

SHG

SDR

0.1 2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

1000/T (1/K)

Fig. 2.9. Logarithmic plots of the sticking probability αSDR (solid square), αSHG (open square) and the breaking probability βSDR (solid circle) for Cl adsorption. Dashed line, dash-dotted line, and solid line are the best-fit straight lines for αSDR , αSHG , and βSDR , respectively

1.15, is smaller than the ratio of αSDR , 1.7, so that this explanation seems insufficient. The breaking probability βSDR for Br adsorption is 2.5 times as large as βSDR for Cl adsorption. This means that the back-bond is broken more easily by bromine than by chlorine. In other words, polybromide species are produced more easily than polychloride species. More detailed information will be obtained in the following section by means of extended SDR studies combined with TDS. The ∆R/R spectra for Cl adsorption were measured between 310 and 423 K, and αSDR and βSDR are determined at each temperature. Figure 2.9 shows the logarithmic plots of and against 1/T . Nominal activation energies determined from the slopes of the straight lines are −8 ± 14 meV for the adsorption on adatom dangling bond and −38 ± 7 meV for the breaking adatom back-bond as shown in Table 2.1. SDR results for Br adsorption are quite similar to those for Cl adsorption. Activation energies for the adsorption on adatom dangling bond and for the breaking adatom back-bond are determined as −2 ± 16 and −39 ± 19 meV, respectively [65]. These activation energies agree well with those for Cl adsorption, so that the process of Br adsorption is essentially the same as that of Cl adsorption. However, this is not true as shown in the following section. Second Harmonic Generation The nonlinear susceptibility χ(2) decreases linearly with the coverage at low coverage when the fundamental wave of a Nd:YAG laser is used as a pump laser. In the case of H adsorption on Si(111), the linearity holds up to 0.15 ML (1 monolayer (ML) is defined as 49 atoms per unit cell, namely 1 ML = 7.81 atoms cm−2 ), and χ(2) becomes nonlinear above 0.15 ML even if adatom back-bonds are not broken [61]. The relationship between the SH

32

M. Tanaka et al.

IS H G (arb.unit)

1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Coverage (ML)

Fig. 2.10. Dependence of SH intensity on Cl coverage determined from TDS. Solid line is determined so as to fit a linear combination of two exponential functions to the experimental plot

Coverage (ML)

0.2

0.1

0.0

0

1

2

3

Exposure (L)

Fig. 2.11. Development of the Cl coverage determined from SH intensity at room temperature. Solid line is the best-fit curve for direct adsorption of atoms

intensity and the coverage can therefore be determined with the aid of TDS before the results of the SHG measurement are analyzed. Figure 2.10 shows the coverage dependence of the SH intensity. There are at least two coverage regimes: linear and nonlinear. A linear combination of two exponential functions is therefore used for approximation. A solid line shown in Fig. 2.10 is determined to fit the function to the plot of χ(2) data vs. coverage. The SH intensity is then transformed to the coverage by using this curve. The development of coverage against chlorine exposure at 300 K is shown in Fig. 2.11. The solution of (2.1) is fit to the plot in Fig. 2.11, which yields the sticking probability αSHG = 0.51. The SH intensities were measured between 310 and 423 K. From a logarithmic plot of αSHG against 1/T , nominal activation energy was determined as −9 ± 8 meV. This is nearly the same as −8 ± 14 meV obtained from SDR. Adsorption on Adatom Dangling Bonds and Breaking of Adatom Back-Bonds The activation energy for the halogen adsorption on the adatom dangling bond is found to be almost zero. This indicates that the adsorption is not thermally activated, and there is no potential barrier in the adsorption. This is reasonable because adsorption of atoms on dangling bonds does not require the breaking of any chemical bond. The above experiments present direct evidence


33

V(z)

~44meV

z E*

Ea

ka

k*

kd

Fig. 2.12. Potential energy for the breaking of adatom back-bonds

for this expectation. On the other hand, the activation energy for the breaking of adatom back-bonds is determined as about −40 meV from the SDR. Negative activation energy indicates that the breaking of adatom back-bonds is not thermally activated, and that there is no potential barrier for the bondbreaking. In the analysis related to (2.2), the adatom back-bond has been assumed to be broken only when the adatom dangling bond is terminated by at least one halogen atom. This assumption means that the potential barrier for the breaking of adatom back-bonds is high compared with thermal energy when the adatom dangling bond is present, and that the barrier becomes much lower when the adatom dangling bond is removed due to the halogen adsorption. The experimental result indicating no potential barrier is compatible with this assumption. Moreover, negative activation energy reveals that the potential curve has a small hump, and that a metastable state exists at the position where the bond length is slightly larger than that of the chemisorption state. The potential energy for the atom incident on the adatom terminated by a halogen atom is schematically shown in Fig. 2.12 [56]. The horizontal axis corresponds to the distance from the surface. The breaking probability of back-bonds via the metastable state is determined from three rate constants: the adsorption rate from the metastable state to the chemisorption state (ka ), the restoring rate from the chemisorption state to the metastable state (kd ), and the desorption rate from the metastable state (k ∗ ) [66]. At the initial stage of the breaking, the restoration from the chemisorption state can be ignored. The initial breaking probability is therefore evaluated without kd , namely β = ka /(k ∗ + ka ). Since ka and k ∗ are expressed as ka0 exp(−Ea /kB T ) and k0∗ exp(−E ∗ /kB T ), respectively, using the height of the hump Ea and the depth of the metastable state E ∗ , Ea − E ∗ is obtained from the logarithmic plot of βSDR /(1 − βSDR ). The nominal activation energy for Cl adsorption, Ea − E ∗ , was determined to be −4 ± 48 meV, and this corresponds to the energy at the top of the hump.

34

M. Tanaka et al.

A theoretical study predicted the adsorption energy for Cl on Si(111), defined as the difference between the total energy at the adsorption site and the total energy at a distance far from the surface [67]. A first-principle calculation for the adsorption process and the breaking of the back-bond process indicates that both processes of adsorption on the dangling bond and breaking of the back-bond are barrierless [68]. The calculation also shows the possibility of a metastable state when a Cl atom is incident on the surface along the surface normal. It is reasonable to conclude that a small hump originating from the energy consumed to break back-bonds can appear in the potential curve for the Si–X bond breaking process. 2.2.4 Site-Selective Adsorption The adsorption process, especially the adsorption site preference, is focused in this section, which may be available for atomically controlled surface modification, site-selective etching, and so on. On Si(001), it has been already reported that halogen atoms have site preference in the adsorption process. For example, a patterning of larger halogen (Br or I) adsorbates was found in the form of stable c(4×2) structure at 0.5 ML [69, 70]. This phase involves adsorption on nonneighboring dimers under certain conditions at elevated temperature. At high coverage in Br adsorption, a (3×2) structure in which Si dimer rows alternate with atom vacancy lines is favored as a result of desorption of volatile SiBr2 [71, 72]. The roughening – under which dimer vacancies, dimer vacancy lines, pits, and Si regrowth are observed – occurs at temperatures below the threshold for SiX2 (X = Cl, Br) desorption [73–75]. Si epitaxial growth on Br–Si(001) produces ordered Si overlayer chain [76]. The results of these STM studies were interpreted in terms of repulsive interaction both experimentally and theoretically [77, 78]. However, this simple picture is not enough because the influence of adsorption on the properties of the underlying substrates should be taken into account. Patch formation on Cl–Si(001) was then explained by an attractive interaction between anticorrelated bare dimers on Si(001) [79]. However, interaction between adsorbates has not been well studied on Si(111). The STM study on halogen molecule adsorption at room temperature [80] showed that a Cl2 molecule with 0.05 eV translational energy tends to be adsorbed on center adatoms of the DAS structure to form a single chloride or a pair of chlorides. The neighboring pair of adsorbates seemingly suggests an attractive interaction between adsorbates. On the other hand, significant I–I interaction was seen at high coverage as the binding energy decreases in X-ray photoemission spectra [81]. Furthermore, in “Adsorption on Adatom Dangling Bonds and Breaking of Adatom Back-Bonds” section, we compared adsorption processes of Br atoms with that of Cl on Si(111), and found that the Br process yields a higher sticking probability on adatom dangling bonds and a higher breaking probability of adatom back-bonds. These results suggest


35

a repulsive interaction between Br adsorbates on Si(111). Thus, interactions of opposite directions were reported so far. The underlying interaction in the adsorption on Si(111) may be different from that on Si(001) because of different surface structure. The distance between center adatoms on Si(111) is 0.69 nm and much longer than 0.38 nm of the distance between dimers on Si(001). The latter is rather close to the distance between the adatom and the bare rest-atom on Si(111). The rest-atoms having dangling bonds are also reactive and the reaction of 6 rest-atoms in the unit cell cannot be negligible compared with that of 12 adatoms. However, Jensen et al. [80] assumed that the adatoms are the exclusive adsorption sites, and they proposed dissociative adsorption on the adatom–rest-atom pair contrarily in their previous paper [82]. The adsorption on the rest-atoms is therefore crucial to discuss interaction between adsorbates on Si(111). Restatom dangling bonds on Si(111) can hardly be accessed by an STM. The reaction of the rest-atoms is often neglected in studies on surface reactions, and the reactivity of rest-atoms has not yet been clarified. The question to be addressed is whether or not there is site preference as regards adsorption on the adatom and the rest-atom of Si(111) and, if there is a preference, whether or not the site preference in Br adsorption is different from that in Cl adsorption. Chemical trend of the site preference is expected because different halogens will react with a semiconductor surface in different ways because of different ionic radii and different electron affinities; for example, the sticking probabilities, the desorption rates, and their temperature dependences will be different. Understanding the chemical trend of halogen reactivity is crucial to optimize etching conditions. In this section, studies on the adsorption site preference on Si(111) [83, 84] by means of SDR spectroscopy and TDS [56] are introduced. Densities of Saturated Dangling Bonds and Broken Back-Bonds The coefficients aA and bA in Fig. 2.8 are proportional to the densities of saturated dangling bonds and broken back-bonds, respectively. There are 12 adatom dangling bonds in the 7×7 unit cell, so that aA is normalized to 0.24 ML (= 12/49), whereas bA is normalized to 0.49 ML (= 24/49) because two of three adatom back-bonds for each Si adatom are breakable. At each exposure, the SDR spectrum was first measured, and coefficients aA and bA were determined. The TDS spectrum was then measured so as to determine the total coverage θ. The densities of saturated dangling bonds and broken back-bonds for Br and Cl adsorption are plotted against the total coverage in Fig. 2.13a, b, respectively. Open squares represent the density of saturated dangling bonds, whereas solid squares represent the density of broken back-bonds. Apparently, Br and Cl adsorption follows different lines, which reveal a chemical trend in the adsorption processes. It has already been found that both the sticking probability on adatom dangling bonds and the breaking probability

36

M. Tanaka et al. 0.7 0.6

(a) Br

Density (ML)

0.5 0.4 0.3 0.2 0.1 saturated dangling bond broken back bond

0.0 0.7 0.6

(b) Cl

Density (ML)

0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Total Coverage (ML)

Fig. 2.13. Density of saturated dangling bonds aA (open squares) and that of broken back-bonds bA (solid squares) determined from SDR vs. total coverage determined from TDS. Part (a) is for Br and (b) is for Cl. Gray lines are shown merely as visual guides

of adatom back-bonds for Br adsorption are higher than those for Cl adsorption [62]. With the aid of TDS, the development of the adsorption process can be seen more quantitatively in relation to the total coverage in Fig. 2.13. This figure shows how many Br atoms are adsorbed on adatom dangling bonds and how many Br atoms break adatom back-bonds, when a specified number of Br atoms is adsorbed. Partial Coverages on the Adatoms and the Rest-Atoms A new dangling bond appears at the rest-atom upon breaking of the adatom back-bond as shown in Fig. 2.1b. Hereafter, we call it “emerging dangling bonds at the rest-atoms” which should be distinguished from “native dangling bonds at the rest-atoms” on the clean surface. A new dangling bond also appears at the adatom, however, it adsorbs the halogen atom immediately, because there is no evidence for asymmetric polyhalide in the STM observations [38]. Consequently, the partial coverage on the adatoms is evaluated as aA + bA . The partial coverage on the rest-atoms is then calculated as the difference between the total coverage and the partial coverage on the adatoms, θ − (aA + bA ). If all the adatoms form trihalides at saturation, the partial coverages on the adatoms and the rest-atoms can be as large as 12×3/49 = 0.73 ML and (6+12×2)/49 = 0.6 ML, respectively. Thus obtained


37

Partial Coverage (ML)

1.0 (a) Br 0.8 0.6 0.4 0.2

adatom rest atom

0.0 1.0 Partial Coverage (ML)

(b) Cl 0.8 0.6 0.4 0.2 0.0 0.0 0 .2

0.4 0 .6

0.8 1 .0

1.2

1.4

1.6

Total Coverage (ML)

Fig. 2.14. The partial coverage on the adatoms aA + bA (open squares) and the partial coverage on the rest-atoms θ − (aA + bA ) (solid squares) vs. total coverage. Part (a) is for Br and (b) is for Cl

partial coverage on the rest-atoms cannot be estimated with STM, and the present SDR–TDS method is the only available means to evaluate it. The partial coverages of Br are plotted against the total coverage in Fig. 2.14a. The result of Cl adsorption is shown in Fig. 2.14b. Open squares represent the partial coverage of the adatoms, whereas solid squares represent the partial coverage of the rest-atoms. Error bars correspond to the sum of the errors of densities of saturated dangling bonds and broken back-bonds shown in Fig. 2.13. Adsorption Site Preference The experimental results shown in Figs. 2.13 and 2.14 establish the adsorption site preference in the adsorption process. For Br adsorption, the slope of the partial coverage on the adatoms at the first stage is almost 1.0 and that on the rest-atoms is nearly 0, which means that all adsorbed Br atoms sit on the adatoms, and none on the rest-atoms. On the other hand, the slope of the partial coverage on the adatoms for Cl adsorption is almost 2/3 and that on the rest-atoms is nearly 1/3. This means that Cl atoms are adsorbed on both the adatoms and the rest-atoms with equal probability, because there are 12 dangling bonds at the adatoms and 6 native dangling bonds at the rest-atoms in a clean 7×7 unit cell. Cl atoms impinging to the surface will be adsorbed at the site where the collision occurs, no matter whether the target is the adatom or the rest-atom. The Cl adsorption on the rest-atom is thus suggested to be also barrierless because the adsorption on the adatom dangling bond is barrierless. As for the Br adsorption on the rest-atoms, both interaction between halogen adsorbates and interaction between halogen atoms and the

38

M. Tanaka et al.

rest-atoms should be taken into account at high coverage, however, only the latter is effective at low coverage. Since no Br atom sits on the rest-atoms even at very low coverage, there must be a potential barrier for Br atom to be adsorbed on the rest-atoms. In other words, there is repulsive interaction between Br atoms and the Si rest-atoms. At 0.1 ML in Br adsorption, about five adatoms per unit cell or 40% of the adatoms have adsorbed Br, while 60% of the adatoms have the dangling bonds. Nevertheless, the breaking of back-bonds begins. An electronstimulated desorption (ESD) study [85] reported that the desorption of SiBr+ 2 ions, suggesting polybromide formation, was apparent even at coverage as low as 0.1 ML for Br-covered Si(111), though no ion-containing Si was detected from Cl-covered Si(111) at such low coverage. This result agrees well with ours. There are two possibilities for the breaking of back-bonds at such an early stage. In case I, the SiBr species at the adatoms hinders other SiBr species at the adatoms, and one SiBr2 species is formed with a barrier lower than that to form an adjacent pair of SiBr species. A stronger repulsive interaction between Br adsorbates plays an essential role. In this case, a patterning in which Br atoms are adsorbed on every other adatom is expected. In case II, adsorption to the center adatoms is different from that to the corner adatoms as suggested for the adatom with low electron density to be favored [80]. Since the interaction with the adatom of low electron density is effectively attractive, the barrier for the process is expected to be low. If one SiBr2 species at the center adatoms is energetically preferred to the configuration with one SiBr species on the center adatom and the other SiBr species on the corner adatom, the breaking of back-bonds begins after six center adatoms in the 7×7 unit cell (0.12 ML) are adsorbed. Interaction between Br adsorbate and the Si adatom plays an essential role. In this case, a patterning decorated with adsorbates on the center adatoms is expected. In both cases, underlying interactions suggest patternings of adsorbates on the Si(111) surface. On the other hand, the onset of back-bond breaking in Cl adsorption is at 0.3 ML, i.e., about 15 atoms per unit cell. Back-bond breaking begins only after about 80% of dangling bonds at the adatoms and the rest-atoms have adsorbed Cl. We can see little trace of interaction between Cl adsorbates or interaction between Cl adsorbate and the Si adatom. The adsorption behavior above the onset of back-bond breaking is quite different from that below the onset. In the range of 0.1 < θ < 0.3 ML in Br adsorption, the rest-atoms remain intact (Fig. 2.14a) and the slopes of the densities of saturated dangling bonds and broken back-bonds are nearly equal (Fig. 2.13a). This means that about a half of impinging Br atoms are adsorbed on the dangling bonds of the adatoms and the other half breaks the adatom back-bonds. In other words, 50% form monobromide and 50% form dibromide at the adatoms, but none is on the rest-atoms. In the range of 0.3 < θ < 0.6 ML in Br adsorption, about 40% of newly adsorbed Br atoms are on the adatoms and about 60% are on the native or emerging dangling bonds at the rest-atoms (Fig. 2.14a). On the other hand,


39

in the range of 0.3 < θ < 0.6 ML in Cl adsorption, almost all the impinging Cl atoms break the adatom back-bonds and adsorbed on the adatoms (Fig. 2.13b). In other words, newly adsorbed Cl atoms preferentially form dichlorides at the expense of the Cl atoms on the rest-atoms, and the emerging dangling bonds on the rest-atoms remain intact. Terminating the emerging dangling bond seems to be more difficult than breaking the other back-bond. The breaking the back-bond is known to be barrierless, whereas di- or trichloride at the adatom may hinder the intrusion of the next chlorine. The intrusion requires the distortion of the adatom chlorides and probably involves a potential barrier. This kind of repulsive interaction between Cl adsorbates was seemingly strong in this range. Therefore, the repulsive interaction is not simply determined by the geometric size of the atom (0.115 nm for Br and 0.100 nm for Cl) [64], but it is determined by the total energy. The stronger repulsive interaction is a result of increase of the total energy due to distortion energy. This study provides the first direct evidence for adsorption site preference and suggests a pattern formation on a Si(111) surface. As mentioned in Sect. 2.3.2, STM study showed that, at coverage less than 0.03 ML, adsorbed bromine atoms were rarely isolated, while chlorine atoms showed a greater tendency to be adsorbed separately. Center adatoms had higher reactivity than the corner adatoms. As for the underlying interaction, interaction between Br adsorbate and the Si adatom with low electron density [80] (case II) seems plausible at the coverage range. In the case II, the rest-atoms have higher electron density, and hardly adsorb halogen atoms. Back-bond breaking by Br atoms occurs at lower coverage because back-bonds of Br-adsorbed Si adatom are more weakened than that of Cl-adsorbed Si adatom and SiBr2 can be formed more easily than SiCl2 , as shown in Si(001) [77]. 2.2.5 Desorption of Silicon Halides and Restoration of the DAS Structure The desorption process of silicon chloride and bromide from Cl- and Brterminated Si(111) rest-surfaces, respectively, was investigated in real time by means of SDR spectroscopy for the first time and SHG [62, 86, 87]. One should note that the structure of the rest-surface on which the desorption takes place is different from the 7×7 DAS structure on which the adsorption takes place. The chlorine and bromide desorption and subsequent restoration of the DAS structure were examined between 873 and 923 K. The time courses of the recoveries of the dangling bonds, the back-bonds, and SH intensity yield the rate constants, the order of reaction, and the activation energies in the desorption process. The kinetics of desorption and restoration processes are evaluated here from the bond density data. The cluster formation on the terrace is suggested from the consideration of the order of reaction. The difference in the reactivity of Cl and Br on Si(111) is discussed in terms of the interaction between adsorbates.

40

M. Tanaka et al.

Surface Differential Reflectivity Spectroscopy The thick lines in Fig. 2.15 show the relative variation of p-polarized reflectance spectra during the isothermal desorption at 903 K from the Cl-covered Si(111) surface. The vertical axis is ∆R/R = (Ra − Rc )/Rc , where Ra and Rc are the reflectances from the Cl-covered surface and the clean surface at 903 K, respectively. The spectrum at 20 s has a negative peak B at around 2.4 eV, and a negative shoulder A at around 1.7 eV. There are positive peaks at around 3.4 and 4.3 eV. The feature A is depressed faster than B , and almost disappears at 400 s, whereas B remains even at 800 s. These spectral features are quite similar to those observed for Cl adsorption at room temperature, except for the relative magnitude of the feature A [56, 88]. The transitions relevant to the features A and B are related to missing surface states of the clean 7×7 DAS structure. The decay of these features therefore corresponds to the restoration of the structure of the clean surface. Each ∆R/R spectrum in Fig. 2.15 is reproduced by a linear combination (aD SA + bD SB : shown by thick lines) of two component spectra, SA and SB , representing the features A and B , respectively. Thin lines represent the decomposition of each spectrum into two component spectra: aD SA and bD SB . Thus obtained aD and bD are plotted in Fig. 2.16a, b, respectively. They are normalized so that the values fitted by (2.5) described below are 1 at 0 s. The decay of aD represents the recovery of the adatom dangling bond, whereas the decay of bD represents the recovery of the adatom back-bond.

903 K

0.01

20 s

0.00

SA

SB

∆R / R

A

B

100 s

0.00

200 s

0.00

400 s

0.00

800 s

0.00 -0.01 1

2

3

4

5

6

Photon Energy (eV)

Fig. 2.15. Variation of p-polarized reflectance spectra during the isothermal chloride desorption at 903 K (thickest lines). Thick lines are the best-fit curves of aD SA + bD SB for the experimental plots, whereas thin lines represent component spectra aD SA and bD SB


41

1.0

aD

0.8 0.6 0.4 873 K 903 K

0.2 933 K 0.0

0

200

400

600

Time (s)

1.0

bD

0.8

873 K

0.6 903 K 0.4 933 K 0.2 0.0

0

200

400

600

Time (s)

Fig. 2.16. Time courses of the coefficients: (a) aD and (b) bD at 873 K (solid squares), 903 K (solid triangles), and 933 K (solid circles). Solid lines are best-fit curves for first-order kinetics

The decay rate Rd is expressed in terms of the rate constant κ(1) for a first-order process as Rd = −

dx(t) = κ(1) x(t), dt

(2.3)

where x stands for aD and bD . In the case of a thermally activated process, the temperature dependence of κ(1) can be expressed in terms of an activation energy Ed Ed (1) (1) , (2.4) κ = κ0 exp − kB T where kB and T are the Boltzmann’s constant and the temperature, respectively. The solution of (2.3) is written as x(t) = x0 e−κ

(1)

t

,

(2.5)

where x0 is the initial value of x. The solid lines in Fig. 2.16 are best-fit curves obtained by using (2.5). These curves reproduce well the overall features of the decay of aD and bD . The fit with higher order was worse than the fit with first order, indicating that these processes are dominated by first-order kinetics. The decay rates κa and κb were obtained from these fits at each temperature.

42

M. Tanaka et al.

Fig. 2.17. Logarithmic plots of the decay rates κa (solid circles) and κb (open circles). Solid lines are best linear fits to the plots Table 2.2. Summary of SDR results for the desorption process of halogens on Si(111)–7 × 7

(a)

(b)

Cl

Br

Recovery of the dangling bonds (feature A ) Order Rate constant at 903 K (s−1 ) Activation energy for the desorption (eV)

First 0.008 2.3 ± 0.3

First 0.01 1.8 ± 0.4

Recovery of the back-bonds (feature B ) Order Rate constant at 903 K (s−1 ) Activation energy for the reconstruction (eV)

First 0.004 2.8 ± 0.5

First 0.003 3.5 ± 0.6

κa corresponds to the recovery rate of the dangling bond, whereas κb corresponds to the recovery rate of the back-bond. The temperature dependences of κa and κb are shown in Fig. 2.17 with solid and open circles, respectively. The solid lines are the best linear fits to the plots. The activation energies in the recovery processes of the dangling bond and the back-bond were determined from the slopes of the solid lines as 2.3 ± 0.3 and 2.8 ± 0.5 eV, respectively. General feature of the desorption process on Br-covered Si(111) surface is almost the same as that of chloride [62]. The activation energies in the recovery process of the dangling bonds and the back-bonds for the Br-saturated surface are determined as 1.8 ± 0.4 and 3.5 ± 0.6 eV, respectively. These rate constants and activation energies are summarized in Table 2.2. Second Harmonic Generation Figure 2.18 shows the time courses of the SH intensities of the Cl-terminated Si(111)–“1×1” surface in the isothermal desorption process. The horizontal axis corresponds the time (t) after the indicated temperature (T ) had


43

been achieved. On the vertical axis, the intensity, I(T ), is referred to the SH intensity of the clean 7×7 DAS surface, I0 (T ) at the respective temperature. Note that the intensity I0 (T ) decreases as the sample temperature increases, because the resonant wavelength of SHG shifts owing to lattice expansion and electron–phonon interaction [89]. The initial increase of I(T )/I0 (T ) within around 80 s at 943 K or 500 s at 873 K is named “fast” recovery. The subsequent very gradual increase in intensity will be referred to as “slow” recovery hereafter. If the slow recovery is ignored, Fig. 2.18 can be taken as showing only fast recovery to a specified SH intensity, I0 (T ) = γI0 (T ), where γ = 0.82 at 943 K, for example. The Cl coverage was evaluated under the condition that SH intensity saturates at I0 (T ) when the chlorides are desorbed out. Figure 2.19 shows that a decay of the coverage is quite similar to isothermal

0.8 0.6

SHG Intensity I(T)/I0 (T)

0.4

873K

0.2 0.0 0.8 0.6 903K

0.4 0.2 0.0 0.8 0.6

943K

0.4 0.2 0.0

0

200

400

600

800

Time (s)

Fig. 2.18. Time courses of SH intensity in isothermal chloride desorption. A fast recovery in the intensity is followed by a very slow recovery. The gray curves are the best-fit product of two exponential decays 0.20

Coverage (ML)

(a) 966K 0.15

(b) 913K (c) 893K

0.10

(d) 873K

0.05 (d) 0.00

(a) 0

(c)

(b) 100

200

300 400 Time (s)

500

600

Fig. 2.19. Time courses of the Cl coverage during the isothermal desorption at four temperatures. The coverages were obtained from Fig. 2.18 using the relation in Fig. 2.10. Each curve can be well fit with a single exponential curve (gray curve)

44

M. Tanaka et al.

desorption monitored by SDR. We take the desorption process to be first order, and fit the time course in Fig. 2.19 with an exponential function exp(−κ1 t),

(2.6)

where κ1 is the decay rate of the Cl coverage. Form an Arrhenius plot of κ1 , the barrier height for the chloride desorption is Ed = 2.1 eV. After chlorides have been substantially desorbed, the surface is reconstructed to the 7×7 DAS structure. The slow component therefore corresponds to the surface reconstruction. In fact, with the laser wavelength we employed, SHG is capable of monitoring the reconstruction back to 7×7 [90]. Accordingly, each curve in Fig. 2.18 is fitted by the product of two exponential functions (gray curves) {1 − exp(−κ1 t)}{1 − exp(−κ2 t)},

(2.7)

where κ1 and κ2 are the SH recovery rates by the desorption (fast component) and the reconstruction (slow component), respectively. It is assumed that the reconstruction produces an exponential recovery in SH intensity. The barrier height for the reconstruction step can be estimated from the Arrhenius plot for κ2 , and we estimate the value to be 2.4 eV. Recovery of the Dangling Bond The results of the SDR and SHG experiments for the chloride desorption are summarized in Table 2.3 together with the results of other isothermal desorption studies on Cl-saturated Si(111). The order of the process, the rate constant at 903 K, and the activation energy are listed. For the recovery of Table 2.3. The order of the process, the rate constant, and the activation energy for the isothermal desorption determined by several methods Method

Order

Rate constant at 903 K (s−1 )

Activation energy (eV)

(a) Recovery of the dangling bond SDR (feature A) UPS (Cl 3p) [91] AES (Cl LMM) [92] SHG (fast)

First First – First

8 × 10−3 7 × 10−3 7 × 10−3 2 × 10−2

2.3 ± 0.3 2.2 – 2.1

(b) Recovery of the back-bond SDR (feature B) SHG (slow)

First First

4 × 10−3 2 × 10−4

2.8 ± 0.5 2.4


45

the dangling bond, the rate constants determined from SDR (feature A ) and SHG (fast component) are compared with those from ultraviolet photoelectron spectroscopy (UPS) [91] and Auger electron spectroscopy (AES) [92]. UPS and AES detect the density of the chlorine atom remaining on the surface, whereas SDR (feature A ) and SHG detect the density of the dangling bond. The result of SDR (feature A ) agrees well with the results of other methods. This agreement means that the same microscopic process is detected by the three different techniques. UPS and AES directly respond to the desorption of chlorides, which produce the dangling bond on the rest-surface. If the dangling bond on the rest-surface is also reflected in the SDR spectrum, the feature A can decay with the same rate as those of UPS and AES before the adatom is formed. Actually, the peak energy difference between the dangling bond states of the relaxed 1×1 surface [93] and the 7×7 DAS structure [55] estimated to be less than 0.4 eV is smaller than the band width of the feature A of 1.2 eV [49]. Consequently, the appearance of the dangling bond on the rest-surface yields nearly the same decay of A as the appearance of the adatom dangling bond does. Meanwhile, the recovery rate of the dangling bond determined from SHG is two or three times larger than that from other methods. The SHG intensity is dominated by not only the dangling bond density, but also the resonance factor. The resonance width for the SHG pumped at around 1,064 nm is about 0.3 eV [52]. SHG can therefore detect the difference between the dangling bond state of the rest-surface and that of the DAS structure, or even the difference between 5 × 5 DAS and 7×7 DAS structures. The rate constant estimated from the SHG intensity is not necessarily the same as the recovery rate of the dangling bond density. TDS studies showed that the main desorption species from the Cl-saturated Si(111) surface above 873 K is SiCl2 [39]. If randomly distributed monochloride species diffuse freely on the surface and two of them recombine to form the volatile SiCl2 species, the process obeys second-order kinetics. Moreover, 4.23 eV is required to extract the Si atom on the rest-surface [68]. This disagrees with the experimentally obtained activation energy, 2.3 eV. Consequently, the desorption of SiCl2 from an ideally Cl-covered rest-surface is unlikely, and defects such as steps and craters should be taken into account. Desorption at the step has already been proposed in the STM study on the bromine etching of a Si(111) surface [94]. The edge of these defects has 1D nature, and a monochloride species bound on the step inevitably recombines with other monochloride species irrespective of the Cl density on the step. The desorption rate is therefore proportional to the density on the step, which means that it is a first-order process. The corresponding activation energy represents the energy required to form a volatile SiCl2 molecule at defects such as steps, craters, and pits, because the energy barrier for the Cl diffusion is estimated to be low, 0.9 eV [95]. The value of 2.3 eV is close to the calculated etching energy, 2.4 eV, which is energy difference between a surface species and a single molecule in the vacuum [67].

46

M. Tanaka et al.

SDR, SHG, and UPS detect the surface density of the dangling bond and the Cl atom, and they revealed first-order kinetics for the isothermal desorption. On the other hand, the methods that detect desorbed species, such as LITD [96], TDS [46], and monitoring the signal of the mass spectrometer in steady-state spontaneous etching [97], revealed second-order kinetics. The LITD study on isothermal desorption is considered first. The characteristic of second-order kinetics in isothermal desorption compared with first-order kinetics is long-lived desorption. A significant amounts of clusters that come from adatoms are sustained on the rest-surface after annealing at about 700 K of a halogen-saturated Si(111) surface, as observed by STM [38,47]. We therefore speculate that the desorption from the SiClx cluster lasts longer than that from the step. SDR, SHG, and UPS are highly sensitive to the surface and cannot detect halogen atoms in clusters. The signal of these methods therefore disappears when Cl atoms on the terrace are almost exhausted, although the desorption from the clusters that can be detected by the LITD study continues. Consequently, LITD can see a second-order kinetics, even when SDR, SHG, and UPS see first-order kinetics. The results of TDS and the steady-state spontaneous etching are also interpreted by the model that the desorption from the cluster with larger activation energy lasts longer than that from the defect [62]. Thus proposed desorption model is schematically illustrated in Fig. 2.20. Chemical trend of the recovery of the dangling bond is shown in Table 2.2. The activation energy for bromide desorption, 1.8 eV, is smaller than that for the chloride desorption, 2.3 eV. The local structure of the dimer at the step edge on Si(111) is similar to that of the dimer on Si(001) [43]. According to ab initio electronic structure calculation on Si(001) [77], the desorption energy for SiBr2 (2.31 eV) is smaller than that for SiCl2 (3.11 eV). The smaller desorption energy of SiBr2 was assigned mainly to the larger strain due to the repulsive interaction between monobromide species and not to a decrease in the bond charge. On the other hand, TDS studies of bromide and chloride desorption from Si(001) showed that the activation energy for SiBr2 is 1.9 eV and that for SiCl2 is 2.4 eV [98,99]. The activation energies on Si(001) are quite similar to our results on Si(111), so that the smaller activation energy for SiBr2 on

volatile SiX2

(X = Cl, Br)

crater cluster step

Fig. 2.20. Proposed desorption mechanism. There are two types of desorption: desorption from defects on the rest-surface, such as steps and craters, and desorption from clusters. See [62] for detail


47

Si(111) can also be assigned to the larger strain due to the repulsive interaction between Br adsorbates. Recovery of the Adatom Back-Bond The rate constant determined from SDR (feature B ) is about 20 times larger than the recovery rate of the slow component of SHG, as shown in Table 2.3. According to the calculated reflectance spectra [100], the reflectance spectrum for the 3×3 DAS structure exhibits a peak at around 2.5 eV due to the back-bond contribution. On the other hand, the reflectance spectrum for the 2×2 adatom–rest-atom structure exhibits only a broad feature in that energy region. The feature B therefore does not disappear upon adatom formation, but disappears when the DAS structure is formed. Various n×n DAS structures have been found during reconstruction from the quenched 1×1 phase and the 7×7 DAS structure is formed through the size change process [101–103]. Between 5×5 and 7×7 structures, for instance, the electronic state of Si adatom dangling bonds differs by 0.4 eV [104], which is lower than the resonance width in SDR (1.2 eV) and higher than that in SHG (0.3 eV). Consequently, it is reasonable to consider that the decay of B corresponds to the formation of a DAS structure, such as 5×5, 7×7, and 9×9 structures, whereas the recovery of SH intensity corresponds to the completion of the 7×7 DAS structure. It takes a certain period of time to form the exact 7×7 DAS structure, so that the recovery of SHG intensity is much slower than that of decay of the feature B . Meanwhile, the recovery of the adatom backbond followed first-order kinetics. This result suggests that the restoration of DAS structure is an independent event that takes place randomly on the surface, so that the recovery rate of DAS structure is proportional to the area without DAS structure. Actually, random nucleation and uniform growth of domains were observed by STM on extended terraces when the DAS structure is formed during Cl desorption [105]. The activation energy for the recovery of the back-bond corresponds to the energy required for the DAS structure formation, because the energy needed for the diffusion of Si clusters is estimated to be lower than 1.5 eV [106, 107]. Although the DAS structure consists of several elements – such as dimers, a corner hole, and stacking faults – these elements are inherently inseparable [101]. Accordingly, the obtained activation energy should be compared with the formation energy for a faulted half-unit cell, which is reported as 2.6 eV [106]. The activation energy for the recovery of the back-bond cannot be distinguished from 2.6 eV because of the large experimental error. On the other hand, the activation energy for the slow recovery in SH intensity is a little lower than 2.6 eV. The activation energies to form various DAS structures are reported to be between 1.7 and 2.3 eV for the observed structures [102]. This seems to correspond to the activation energy for the slow recovery of SH intensity. In the temperature range of our experiments, the surface concurrently undergoes fluctuation in the DAS size and stacking-fault formation [108]. Our

48

M. Tanaka et al.

estimated value, 2.4 eV, may represent the combined effect of DAS size change with about 2.0 eV and stacking-fault formation with 2.6 eV. Chemical trend of the recovery of the adatom back-bond is shown in Table 2.2. The activation energy for recovery of the back-bond after Br etching was found to be 3.5 ± 0.6 eV. This value is meaningfully larger than that for the formation energy for a faulted half-unit cell, 2.6 eV. Additional mechanisms giving higher activation energy should be taken into account for the surface reconstruction after bromide desorption. Although the nature of such a mechanism cannot be determined from the SDR results, surface morphology could affect the process of DAS structure formation, as pointed out in [109]. 2.2.6 Summary As the first step of Cl and Br etching of the Si(111) surface, the adsorption process has been investigated by means of in situ real-time SDR and SHG spectroscopy. The developments of the adsorption on the dangling bond and the breaking of back-bonds yield the sticking probability and the breaking probability. From the temperature dependence of these probabilities, the activation energy for the adsorption on dangling bonds is found to be almost zero and that for the breaking of back-bonds is approximately determined as −40 meV. Cl coverage on the adatom dangling bond was also evaluated from SH intensity with the aid of TDS. The sticking probability and its temperature dependence are almost the same as those determined from SDR. The activation energies for the adatom dangling bond and the breaking of the adatom back-bond reveal that both processes are barrierless. Moreover, it also reveals that there is a metastable state in the breaking process of the adatom back-bond, and the energy of the top of the hump in the potential energy is evaluated as about −45 meV. This hump may originate from the energy consumed to break the back-bond. The mechanism of the Br adsorption process was found to be qualitatively the same as that of the Cl adsorption, but quantitatively different. Both the sticking probability on dangling bonds and the breaking probability of back-bonds for Br adsorption are larger than those for Cl adsorption. This chemical trend is presumed to arise from larger strain due to repulsive interaction between Br adsorbates. The site preference of halogen atoms has been quantitatively studied by means of SDR and TDS. Partial coverages on the adatoms and the rest-atoms, which cannot be estimated by other techniques, even STM, reveal the adsorption site preference of bromine atoms. At the initial stage below 0.1 ML, Br atoms are adsorbed selectively on dangling bonds of the Si adatoms, but not on those at the rest-atoms, and, at the later stage, dibromide species are formed on adatoms before monobromides reach 40% of the adatoms. On the other hand, Cl atoms are adsorbed randomly on the dangling bonds at both the adatoms and the rest-atoms. This chemical trend is well interpreted in terms of repulsive interaction between halogen adsorbates or the interaction between halogen adsorbate and the Si adatom. In the range of 0.3 < θ < 0.6 ML,


49

newly adsorbed Cl atoms preferentially form dichlorides at the expense of the Cl atoms on the rest-atoms, and the emerging dangling bonds on the rest-atoms remain intact. The site preference of Cl is explained by a kind of steric hindrance due to polychloride on the adatom which prevents Cl atom from intruding to the rest-atom. As the second step of Cl and Br etching of the Si(111) surface, isothermal desorption of silicon halides from a halogen-terminated Si(111) rest-surface and subsequent restoration of the DAS structure have been investigated by means of in situ real-time SDR and SHG spectroscopy. The rate constant and the order of reaction are determined from the time courses of the dangling bond recovery, the back-bond recovery, and the SH intensity recovery. The activation energies evaluated from the temperature dependence of the rate constants are compared with the results obtained by other methods. The dangling bond contribution to the SDR spectrum recovers on the rest-surface as a result of the desorption of silicon chlorides. The time course of this decay reveals first-order kinetics, which suggests the associated desorption of SiCl2 at defects such as steps, craters, and pits. The long-lived desorption from clusters is also suggested to explain the second-order kinetics observed by TDS, etc. The activation energy is ascribed to the energy required to form a volatile SiCl2 molecule at the defects. The activation energy for bromide desorption is smaller than that for chloride desorption, which is interpreted in terms of larger strain due to repulsive interaction between Br adsorbates. On the other hand, the back-bond contribution to the SDR spectrum recovers when the DAS structure is formed. The activation energy is ascribed to the energy required to form a faulted half-unit cell. Time course of the SH intensity involves fast recovery and slow recovery. The fast recovery corresponds to the recovery of the adatom dangling bonds. The slow recovery corresponds to the completion of the 7×7 DAS structure. The activation energy for this process is suggested to represent the combined effect of DAS size change and stacking-fault formation. In this section, atomic-scale mechanisms underlying layer-by-layer etching of Si(111) surface with halogen atoms and their chemical trend have been elucidated. This should be useful information to optimize etching conditions, as well as to improve out understanding of the fundamental processes in the halogen etching of Si surfaces. Our results suggest that Br etching is superior to Cl etching, because the smaller desorption energy means better controllability of the etching process, and the larger interaction between adsorbates may be used for site-selective etching. The site preference and cluster formation suggested in this section could be utilized to achieve site-selective etching and could be applied as a template to immobilize large molecules, such as biomolecules.

50

M. Tanaka et al.

2.3 Nanoscale Fabrication Processes of Silicon Surfaces with Halogens 2.3.1 Introduction In this chapter, with regard to the dynamic process of structure control of silicon surface at the atomic scale, the recent developments of studies are reviewed. The fabrication of silicon surface is of the great importance in semiconductor technology. The processes are divided into two parts: decrease and increase of the surface component. In industrial use, the surface is often etched with halogen plasma at high temperatures, and the growth on it is done by means of deposition of such evaporated gas as silane. The former process is simply recognized as the scrape of semiconductor surface. After the process, what structure will be formed? It will lead to novel technique to make microstructures on the semiconductor surfaces if the surface structure could be controlled only by etching of the wafer. Before the construction of functional devices at nanometer scale, well-defined surface is required at the atomic scale. At the microscopic aspect, we can recognize the etching process of the surface as the elemental physical/chemical phenomena for fabricating the semiconductor surface. In this section, the most typical and well-defined cases are addressed mainly in terms of desorption. The most primitive and fundamental process of etching of silicon is desorption from halogenated surface, because the reactive halogen gasses are most frequently used in industrial purpose to weaken the Si–Si bond near the surface when they are adsorbed on the surfaces. The fabrication with halogens is usually promoted in energetic excitations, such as plasma state of chemical compound gas. These excitations are generally of high efficiency, and for the homogeneity the reaction is often held at high temperature during the gas (or plasma) exposure. However, this kind of processes are too complicated to be analyzed, and be empirically optimized in real industry. The diffusive process on the surface may destroy the surface structure. This is why this excitation method is not good at structure control of the surfaces at the atomic scale. Thus, to study well-defined process on the surface, we introduce the halogenadsorbed silicon surfaces as the simplest model systems, which are, at the same time, applicable to the industrial purpose. The physical interpretation of the surface phenomena may open the gate to atomic arrangement of the surface structure. It is not a dream to control of the nanometer-scale structure on silicon surface. The most advanced integrated circuits are made of thinner lines than 90 nm in commercial products, and they are realized by means of lithography methods with resist layers. The optical lithography with far-ultraviolet exposure is capable to construct 45 nm lines [110], which contains only countable number of silicon atoms at the order of several hundreds (see Fig. 2.21). Along this trend, the wavelength of the light is becoming shorter, while the reduction of aberration of the microlenses is of great interest in engineering field. On


51

Fig. 2.21. Isolated 30 nm lines by means of lithography with resist at height of 90 nm [110]. The light was provided by a laser-produced plasma in xenon-fueled pinched gas jet [111], and was focused by optics with numerical aperture (NA) of 0.3

Fig. 2.22. Basic idea of the lithography and self-organized processes (illustration referred to [112]). The hole is prepared in conventional lithography, and the following heating of the sample causes the step retreat. Then, viewed in the wider scale, the steps are bunched along the hole patterns

the other hand, the limit of the method in this trend will be soon attacked by diffraction limit of the light and diffusive destruction on the surface. To overcome these limitations, several methods are proposed. Among them, the combination of such conventional lithography and self-organized process is beginning to be focused in this century [112], where the diffusive tendency of chemical species under reaction is positively utilized to form certain structures by spontaneous motion (see Fig. 2.22). In the combinative method, the fundamental mechanisms – such as surface diffusion, step motion and step bunching, reconstruction, or strain near the heterointerfaces – are important. In this review, the recent results of such fundamental mechanisms are discussed. We introduce a good example to utilize the self-organization process. Figure 2.23a shows the domain boundary on Si(111) surface oriented to [112] direction, perpendicular to the steps. This can be obtained when Si is deposited to 20 nm on the surface at ∼923 K [113]. This type of surface arrangement to construct nanopattern is addressed in the following sections, where the strain associated with surface reconstruction is discussed. Using other material such as Ge, the morphology of the clean surface can be

52

M. Tanaka et al.

(a)

step

step DB

(b) DB

bend

[112]

1 µm step DB

(c)

(d)

[112] 1 µm

(e)

[112]

1 µm

step

[112]

DB

2 µm

DB step

[112]

2 µm

Fig. 2.23. Regularly arranged grid pattern on Si(111) surface observed with AFM. Steps and the domain boundaries of 7×7 DAS structure (denoted as “DB”) are aligned, to show meshed nanopattern on the Si-deposited Si(111) surface (a). The solid phase epitaxy of germanium forms clusters (bright spots) after heating at 750◦ C , and they are distributed at the step edges and domain boundaries. The size of the clusters is controlled by the deposition thickness [114]. Nanopattern reveals different morphology dependent on the thickness of the deposited Si: (b) 1 ML, (c) 1 nm, (d) 50 nm, and (e) 100 nm. The images are taken from [115]

controlled. When Ge is deposited onto the surface at the high temperature of 1,023 K, the Ge forms clusters and they are preferentially trapped at the domain boundary and the step edges. The shape changes with the thickness of Si layer deposited prior to the Ge deposition, as shown in Fig. 2.23b–e. The asymmetric diffusive process bents the steps and the spacing of the boundaries to minimize the energy of the phase boundaries. In the process of halogen etching of Si(111) surface, the regular alignment of Si clusters due to the strain


53

by reconstruction is found, shown later. The initial scratch made by “active” fabrication, that may be electron impact or photoirradiation with laser for example, would be utilized in the fabrication process of the artificial patterns on silicon surfaces. In this section, the thermally induced desorption process from halogenated surface is introduced first, because the processes at high temperatures are practically very important. The temperature dependence of the desorption yield classifies the desorption path, and the results rise discussions of the reaction at the atomic scale. The quantitative analysis of the desorption yield will rise the discussion of energetic interpretation of the process. Then, as processes applicable to the surface fabrication, the passive process induced by heating is discussed. At high temperature, the motion of step retreat changes the morphology. In the wide terrace, the competition of the diffusive process and reconstruction will cause the pattern on the surface. Finally the active process induced by electronic excitation will be overviewed. 2.3.2 Scanning Tunneling Microscopy In the fabrication technology, the findings about the microscopic aspect of the physical phenomena will contribute to the development of the combinative fabrication methods. However, the inhomogeneity of the surface structure is actively introduced. The microstructure without periodicity is difficult to be observed by means of diffraction method and discussed in reciprocal space. Fortunately, the microscopic observation at nanometer scale is now popular, and the images may give the information about the arranged structures through self-organization mechanism. Among them, STM is capable to give atomic structure at the surface of conductors or semiconductors. Nowadays its family, so-called scanning probe microscopy (SPM), is a widespread techniques to observe the surface structure, for example, in terms of local electronic state with scanning tunneling spectroscopy (STS), and insulator structure with atomic force microscopy (AFM). The surface of Si(111) has triangular periodicity. There is a Si in the topmost layer (refereed to adatoms) supported by three Si atoms in the second layer (refereed to rest-atoms) through the back-bond (see Fig. 2.24). Due to the large electron affinity of halogen atoms, the charge transfer from halogen to the rest-atom weakens the back-bonds. This is the chief reason of frequent utilization of halogen (or halogen compounds) in the etching process of silicon surface. In the early stage of the development of STM, Boland et al. [42] showed that the dangling bond of Si(111) surface disappears after termination of halogen atoms in STS, because an STM images the integration of local density of states near Fermi level. Contrarily, at the sample bias of 3 V, formation of antibonding states by the overlap between the dangling bond at the adatom Si and the adsorbed Br 4p orbitals leads to the bright appearance of the bromine adsorption [38, 43]. The STM image of Cl-adsorbed surface by less than one atomic monolayer is shown in Fig. 2.25. In Fig. 2.25a, the

54

M. Tanaka et al. dangling bond rest - atom Si

halogen

−δ weaken

adatom Si

+δ

+δ +δ back - bond

Fig. 2.24. The dangling bond (a) into the vacuum from adatom Si, in the topmost layer, is terminated by halogen X atom to form Si–X bonding state (b). The dangling bond state is located energetically near Fermi level, while the Si–X is far from the level

Fig. 2.25. STM topograph of Si(111)–(7×7) exposed to bromine gas. Bromine is adsorbed 0.04 ML (after Boland). The size of the area is 15×15 nm2 . The diamondlike area in white lines is a unit cell of 7×7, in which DAS structure can be recognized. The tunneling current was 0.1 nA. Each spherical dot corresponds one adatom. (a) Sample bias was +1 V. The dark dots are bromine adsorbates, while the nonreacted sites are bright. (b) Sample bias was +3 V. Bromine-adsorbed sites are brighter than the unreacted sites

55

Density of polybromine [ML]


Coverage [ML]

Fig. 2.26. Correlation of the densities of chlorine adsorbed on Si(111) surface estimated in optical SDR spectroscopy (vertical axis) and STM images (horizontal axis). Note that the fluctuation of STM results is larger than the averaged density obtained by means of SDR. The data are taken from [117]

bright spheres are the dangling bonds at the adatoms, while the dark spheres indicate where the dangling bonds disappeared. The change of the electronic state near the surface can be detected optically also. When chlorine atoms impact on the Si(111)–(7×7) surface (see Sect. 2.1 for detail of DAS structure of this surface), they react first with the Si adatom dangling bond to form monochloride (SiCl) at low coverage, while higher coverage leads to the formation of dichloride (SiCl2 ) and trichloride (SiCl3 ) [83]. It is possible to distinguish the various types of chlorides from the displacements in STM images [116]. The surface density of the polybromide species estimated from the STM images has good correlation with that from the SDR spectra, as shown in Fig. 2.26. SDR is a powerful optical tool to evaluate the density of adsorbates in real time, even during high-pressure gas exposure. This method gives quantitative information about the averaged densities of various adsorbates at different reaction site (see Sect. 2.2 for detail of SDR). Although the density of adatom dangling bonds identified as polybromide varied by about ±20% depending on the image processing, it remains to fluctuate by ∼±30% among the areas that was imaged. The densities obtained with STM coincide reasonably well with the SDR results. It is important to note that the optical response shows the averaged properties over the macroscopic area of the surface. On the other hand, the fluctuation of the statistical results from the STM images indicates that the distribution of the adsorbates varies greatly at the atomic scale. The correlation of the adsorption sites with the bond breaking/formation, suggested by the optical findings, has been confirmed at the atomic level by means of the microscopic method. The STM is capable to find a sole particle on the surface. Atoms, clusters, and island play essential role in the diffusive process on the surface. The idea of island/cluster formation [47] and reconstruction strain [119] are proposed on Si(111) surface. The stability and instability of halogenated species formed on the surface are the clue whether the desorption of halogenated silicon

56

M. Tanaka et al.

Fig. 2.27. Island of Br-adsorbed Si(111) surface after annealing at 673 K. The 1×1 structure is seen in the plateau of the island and near the island, while 7×7 remains in the far region. The image is shadowed to enhance solidity after taken from [118]

occurs or not [67]. The thermal reactions of silicon (111) and (001) surfaces are explained in detail by Weaver et al. [120] in terms of local structure of bonding configuration. They pointed out that the desorption occurs chiefly at the step edges on the surface, while the spectacle nucleation of migrating silicon halide may change the surface morphology. At the same time, the (111) surface reconstructs between 7×7 and 1×1 structure at high temperature (see Fig. 2.27). The clusters of silicon halides are seen on 1×1 region both on the island and outside the island. The binding energy of the clusters on 1×1 is larger than 7×7 by 0.3 eV [47]. 2.3.3 Thermal Desorption Process Adsorption and desorption at semiconductor surfaces have been widely studied, often with the aid of TDS, because this method is relatively simple. The desorption rate is measured during heating the sample with the temperature raised. The features of the TDS signal allow quantitative classification of the reaction path [121], and TDS has often been utilized in studies of catalysis on metals, as well as semiconductor processes. However, the desorption rate is generally difficult to determine precisely unless it is sufficiently high. Generally the S/N is not necessarily enhanced even if the sensitivity is increased. For example, to obtain an activation energy, the decay of desorption is important, and so a wide dynamic range is required. We present results obtained with isothermal and TDS methods utilizing a very sensitive mass spectrometer with a wide dynamic range [48]. With this apparatus, quantitative analysis of the desorption yield from an active surface enables us to evaluate the density of the surface adsorbates. Based on the relation of the density with the desorption rate, one can discuss the mechanisms of the desorption processes in terms of activation energy and reaction order. Results of TDS from Cl-saturated Si(111) surface are shown in Fig. 2.28. The detected mass is tuned to 63 amu, corresponding to SiCl ion. The signals + of 133 and 168 amu (due to SiCl+ 3 and SiCl4 , respectively) can be assigned


57

Temperature (°C) 300 400 500 600 700 800 900 1000

Desorption Rate (Arb. Units)

A SiCl+ C

B

+

SiCl2

SiCl3+

SiCl4+

500 600 700 800 900 1000 1100 1200 1300 Temperature (K)

Fig. 2.28. TDS of the Cl-saturated Si(111) surface. The ions were selected by quadrupole mass spectrometer. The shape for SiCl+ is quiet the same as that of SiCl+ 2 when vertically scaled. The plot is taken from [122]

to a mixture of SiCl3 and SiCl4 . Surface species from the Si adatoms have been classified into monochloride (SiCl) or polychlorides (SiCln with n = 2 or 3) [39, 40]. Three peaks, A, B, and C, are found. These are clearly split with the highly sensitive mass spectroscopy system. The largest peak A, which appears at the highest temperature region, has been assigned to desorption of monochlorides formed on the surface, and peak C to polychlorides formed on the surface at high levels of chloride [39, 42, 46]. Although the origins of the + SiCl+ 3 and SiCl4 signals remain unclear, these two species could be related to surface defects [122]. The desorbed species for peaks A and B is mainly SiCl2 . At 900 K and higher, it has been associated with retreat of steps where SiCl2 is generated from monochloride species [120]. It is concluded [48] that peak B is associated with surface reconstruction from 7×7 into Cl-terminated “1×1,” whose structure has been observed with an STM [47, 118]. The three processes, originating each peak, involve independent mechanisms corresponding to each temperature region. Once the Cl-saturated surface has been heated to a temperature of 600–700 K, subsequent TDS measurement from room temperature gives only peaks A and B. After this thermal treatment, peak B is missing because the structure becomes Cl-terminated 1×1, and polychlorides have been desorbed out around the temperature region for peak C. Similarly, only peak A appeared from the Cl-exposed surface after the surface had been heated to 800 K. Remaining peak(s) (A and B for 600–700 K heating; only A for 800 K heating) had the same height(s) as the peak height(s)

58

M. Tanaka et al.

Desorption (Arb. Unit)

TDS of Cl-saturated Si(111)

A

B C

As Cl-exposed

After annealing to ~800 K

400

500

600

700

800

900

1000

Temperature (K)

Fig. 2.29. Comparison of the TDS results from Cl-saturated Si(111) surface (filled circles) with that of Cl-adsorbed sample after annealing at ≈800 K for a few minutes (open and gray circles). Peaks B and C disappear once after heating to the temperature in the region of peak A. The curve of peak A from the Cl-saturated 7×7 surface precisely traces that from 1×1 surface appeared after the heating. Data are taken from [123]

obtained without such thermal treatment, as shown in Fig. 2.29 [123]. During the heating of 7×7 surface, the process of peak A must be overlapped partially by that of peak B. This means that the rate of peak A is not affected by the surface periodic structure (reconstruction in peak B). And the remaining polychlorides, if any, after peak C, do not change the dominant process of peak A. We will focus chiefly on peak A for the energetic discussion based on the time dependence of desorption rate, so-called isothermal desorption measurement. Figure 2.30a shows the results of isothermal process for peak A of SiBr+ , which is obtained after 6-min heating at ∼800 K for removing the contribution of peaks B and C. The desorption rates were reduced to almost zero in a few hundred seconds. We used the following procedure to analyze the time dependence, based on Polanyi–Wigner’s rate equation [124, 125]. The rate of desorption, Rd , from unit surface area with an adsorbate density of N is given by the following rate equation Rd = −

dN = uN m , dt

(2.8)

where m is the order of the desorption process and u is a temperaturedependent coefficient. Analytic solutions of (2.8) are given by for m = 1, uN0 e−ut , Rd = (2.9) (1−m) (1/(1−m))−1 u[(m − 1)ut + N0 ] , for m > 1, where N = N0 at t = 0. Fitting of the experimental results with Rd for m = 1 and m = 2 gives the curves in Fig. 2.30a. The curve for m = 2 agrees better with the experimental plots. From the parameters for the fitted curves,


59

Desorption Rate, R (arb. unit)

Isothermal desorption of Cl / Si(111)

993 K

918 K (x3) 843 K (x3) 0

20

40

60

80

100

Time (s) Temperature (°C)

ln u(T) (arb. unit)

0

782

694

619

556

−2

Ed = 2.18 eV

−4 −6 −8 −10 −12 11.0

11.5

12.0

12.5

13.0

13.5

14.0

1/(kBT) (eV)−1

Fig. 2.30. Isothermal desorption for the major process (peak A in Fig. 2.28). (a) The time course of desorption rate for each temperature. Filled circles indicate the obtained data, while the gray and thin curves show the fitting for the first-order (m = 1) and the second-order (m = 2) process, respectively. (b) Arrhenius plot of prefactor coefficient for the second-order process fitted to (a). The data are taken from [122]

Fig. 2.30b shows the relation between log10 u and 1/kB T (so-called Arrhenius plot ) for m = 2. When u(T ) has the Boltzmann distribution u(T ) = u0 e−Ed /kB T ,

(2.10)

where Ed , kB , T , and u0 are the desorption potential barrier, the Boltzmann’s constant, the absolute temperature, and a preexponential constant, respectively, the fitting gives Ed = 2.18± ∼ 0.1 eV [126]. The desorption energy of SiBr2 is obtained in the similar method on Si(111), found to be

60

M. Tanaka et al.

Ed = 2.6 eV [48]. This desorption energy for bromine, smaller than that for SiCl2 , implies that the bromine-etching speed can easily be controlled by temperature in comparison with chlorine etching. In case of bromine-adsorbed Si(111), the value of Ed is very close to a desorption energy of 2.6 eV reported from the TDS experiment of Br/Si(001) at about 950 K [127]. The agreement suggests that the back-bond of the dimer on a Si(001) structure is similar to the back-bond of dimer at the step edge on a Si(111) surface [43, 94, 120]. To discuss the activation energy for the desorption process, the shape of the curve can provide information about the nature of the surface process, on the assumption of the first- and second-order processes. In case of the most simple spontaneous mechanism, each TDS curve was fitted to the solution to the Polanyi–Wigner’s rate equation (2.8) for a first-order process −

dN = uN, dt

(2.11)

where u is a constant at a given temperature. However, the solution for a second-order process, −

dN = uN 2 , dt

(2.12)

representing the simple associative mechanism. In many TDS experiments, socalled Readhead analysis is often adopted to obtain the experimental values from a few TDS curves, in which merely the peak temperature is considered. For example, the desorption energy for the Cl/Si(111)–1×1 surface at ∼900 K was 2.9 eV [96]. This is different value for our result above. The discrepancy is resolved in the estimation of whole shape of TDS spectra [126]. TDS with various parameters in Fig. 2.31a shows the coverage dependence, where chlorine exposure was changed. The surface was saturated with chlorine between 0.3 and 0.6 L. During the Cl exposure, monochloride is formed on the surface first, and polychloride later [40]. Correspondingly, peak A appears first at lower exposure, and is followed successively by peaks B and C. It should be noted that peak A shifts to lower temperature as the coverage is increased, while peak B shifts to higher temperature. The process leading to peak A was second order (see [126] for detail). The process resulting in peak B is too complex to allow analysis from the peak shape, because it includes reconstruction [48]. Figure 2.31b shows the TDS result when the heating rate, η ≡ dT /dt, was varied. The desorption rate is defined as r(t) ≡ −σ(dN (t)/dt), where N (t) is the surface density (Cl coverage) at time t and σ is the sensitivity of the detection system. It was normalized with η, and the vertical axis is R(T )/η, where r = r(t) at time t is transformed into the desorption rate R(T ) at temperature T (t) to satisfy r(t) = R(T (t)). As all the measurements were started from a Cl-saturated surface, the total coverage at the initial time, t = 0, must be the same for all heating rates 1 ∞ 1 ∞ R(T ) Nsat = − dN = dT. (2.13) r(t)dt = σ t=0 σ T =RT η


61

Temperature (°C) 300 400 500 600 700 800 900 1000

Desorption Rate, R (Arb. Unit)

(a)

A

B

C

0.6 L 0.3 L 0.10 L 0.025 L 0.010 L

500 600 700 800 900 1000110012001300

Temperature (K) Temperature (°C) 300 400 500 600 700 800 900 1000

A

Desorption Rate, R / η (Arb. Unit)

(b)

Heating Rate B

0.5 K/s

1.0 K/s 1.5 K/s 2.0 K/s 5.0 K/s C

10 K/s

500 600 700 800 900 1000 1100 1200 1300

Temperature (K)

Fig. 2.31. TDS of Cl-adsorbed Si(111) surfaces. The spectra with the Cl coverage varied (a) and TDS of Cl-saturated surface with the heating rate varied (b). Peak A shifts to the lower temperature as the coverage is increased, while peak B to higher. On the other hand, both peaks shift to lower temperature as the heating rate decreased. The plot is taken from [122]

Indeed, the heights and widths of the three peaks are similar to each other at various heating rates. To analyze the shapes of the TDS curves, we define θ(T ) as the surface Cl coverage at a temperature, T , so N (t) ≡ θ(T (t)), where T = T (t). Then, from integration of the desorption rate, θ(T ) = −

∞

T

1 dθ ≈ ση

Tmax

R(T )dT .

(2.14)

T

Numerical integration allows a discussion of the energetics. As the reaction order m = 2, the results in Fig. 2.31a were converted into a plot of ln(R/θ2 ) against 1/(kB T ), as shown in Fig. 2.31a. The plot is linear even when the

62

M. Tanaka et al.

starting coverage is varied, and the slope of the line again indicates the barrier for the desorption. The value obtained was 2.17 eV. The values obtained in the analysis for whole spectral shape have good agreement to the value of the isothermal result, Ed = 2.18 eV. Note that the plots of ln(R/θ) for the first-order model are not straight both for Fig. 2.31a, b, suggesting that m = 1 is not the case for the desorption process. 2.3.4 Cluster Alignment by Passive Fabrication At the atomic scale, adsorption and desorption processes are fundamental stages, and the structures on the surfaces made with such processes have been well examined. For example, atomic level dynamics on silicon surface under halogen etching has been deeply elucidated, where STM was chiefly utilized [120]. The fundamental chemical reactions at local sites are known from the surface structures in STM images, usually observed at room temperature after such process. The local chemistry affects the surface morphology. However, most of the processes are done at high temperature. Although the importance of diffusion has been discussed on the halogen–silicon systems [95], little results are presented experimentally about the motion of surface species. On halogen-adsorbed surface, the diffusing species may be silicon halide, or atomic silicon detached from the surface. During the processes, in situ observation at the high temperature will reveal what happen on the surface to form nanostructures as results of surface strain and diffusion. Recently, nanoclusters of silicon carbide are found to be aligned as concentric circles on oxidized Si(111) surface [128]. The bond of Si–C is apt to be formed at step edges at high temperature [129], and multiple-step holes appear nucleated around the oxygen-free pits [130]. At the every stages in the whole process, surface diffusion and reconstruction play essential roles. We here address formation of the regularly organized structures on silicon surface using halogen desorption. In the process, the pinning of surface species and step retreat due to the desorption are important, as can be suggested the thermal desorption process described above. There is another factor, surface strain, due to reconstruction. The silicon clusters are aligned on the terrace through halogen etching. The formation mechanisms, from the STM images observed at high temperature, will serve the methodology of self-organization techniques on silicon surfaces, which are not obtained static structure observed at room temperature. In all the images in this section, the sample was started to be processed from clean Si(111)–7×7 DAS surface to which Cl gas was exposed to the saturation coverage at room temperature. The coverage was estimated to be 1.62 ML, where 1 ML has 49 atoms in a 7×7 unit cell [40]. Figure 2.32a shows STM images observed at room temperature after 873 K heating. This image is obtained after heating for 540 s. Many steps are found. Along the diagonal line from the left bottom to the right top, there are about 30 diatomic steps, and some multiple steps among them can be only recognized in the image.


63

(a)

(b)

A D

E

C

B

Fig. 2.32. (a) Nanoclusters formed at apexes of the step edges. STM image of aligned clusters on Si(111) surface observed at room temperature, obtained after 873 K heating of Cl-adsorbed sample at the saturation coverage. The area is 200×200 nm2 . Tunneling current was 0.1 nA and the sample bias was +2.5 V. (b) Clusters (near “A” and “C”) pinning the step retreat (“E”) and bunched steps (dashed bands at “D” and “B”) observed at high temperature. The process finally aligns the clusters at the apex of the bunched steps as in image (a)

This is not the average morphology of the surface due to inhomogeneity, but it was a typical area where the step density was high. At the most of apexes of the step edges, clusters are found. Typical size of the clusters is 8 nm in diameter and 2–4 nm in height. The clusters apparently grow at the edges of the multiple steps whose height was 4–6 diatomic-step height (∼1.5 nm). We do not consider that the clusters simply grow at the apexes, but clusters pin the step motion [123]. With the isothermal decay recalled (see Fig. 2.30 and Sect. 2.3.3), the main process of the desorption seems almost finished at Fig. 2.32a. That is, after the desorption, the diffusion of the chlorides on the terrace consists chiefly of movement among the clusters. We consider it,

64

M. Tanaka et al.

so far, that the surface structure reconstructs back to 7×7 with the clusters deformed, while very slight desorption occurs at the cluster edges as well as the step edges. The STM images at room temperature may not provide enough information about the diffusive process, because the cooling process would anneal the surface structure. The surface structure in the actual desorption process at high temperature may differ from the cooled one. We observed the surface at 673 K, corresponding to peak B. However, no clusters but some double steps are seen on Cl-terminated 1×1 surface in any image of the surface during the thermal treatment up to 30 min. The shape of step curves looked changed between scans, suggesting only the dissociation or association of chlorides at the step edges. Figure 2.32b was observed at ∼160 s after the temperature rising to ∼803 K, at which process of peak A begins. At this time, the desorption is the slowest as the process for peak A. Many clusters are formed at this temperature, but some should be called islands because the height is of one double step. Deep craters are formed near mark A and B in the image. Both craters draw step bunches to the left. Larger clusters marked C and D are identified at the upper sides of the bunches near the craters A and B, respectively. Hence, a model is presented here as shown in Fig. 2.33. The surface phenomena of the cluster alignment at the apexes of the step edges as follows: in consideration that associative reaction of surface chlorides was proposed in the context of the polychloride desorption ascribed to the second-order process. (1) The clusters prevented the movement of the steps which were growing or retreating. Or, (2) the migrating chlorides are preferentially collected at the terrace edges at the upper sides of the bunches, to let the clusters grow there. Bey-shaped pit, E in Fig. 2.32b for example, may thus develop between the pinned clusters around C. Desorption has been ascribed to be related to the step structure [47, 118], and the movement of the steps at high temperatures can be assigned to desorption at the edge proposed in a step-retreat model [43,120]. Our cluster alignment occurred because some interaction regulates the seeds of clusters. Consequently, randomly distributed steps have regular spacing and the clusters are seen aligned in a line. In similar alignment of bunched steps, the pinning of step motion can be done by holes made with

Fig. 2.33. Model of pinning of the step retreat to describe the high-temperature process (Fig. 2.32b) for formation of the regularly aligned clusters seen in Fig. 2.32a


65

Fig. 2.34. Nanoclusters formed on a wide terrace. Only a single step is seen. STM images of aligned clusters on Si(111) surface were observed at room temperature, obtained after 873 K heating of Cl-adsorbed sample at the saturation coverage. The area is 200×200 nm2 . Tunneling current was 0.1 nA and the sample bias was +2.5 V

photolithograph as well [112]. This mechanism is one of general methods to the fabrication of the surfaces on which diffusive species remain or the steps are very active. In turn, we consider the wide terrace. Figure 2.34 was obtained after 873 K heating for ∼1,200 s. In the image, only one step can be seen. Some clusters were grown at the step edges, while much more were on the terrace. The clusters were wider but their height was smaller than in Fig. 2.32. One notes that the clusters are aligned in the direction indicated by the white arrow. And the spacing between them is ∼30 nm. This suggests that there are some mechanisms, other than the step motion and pinning, to determine where the clusters grow. The surface during the high-temperature treatment is presented for the sake of examination of the cluster alignment on the terrace. In Fig. 2.35a, some 7×7 DAS areas are seen, and other areas seem structureless. The areas of 7×7 were found at the upper sides of the steps, and they grew into the terrace. It takes several minutes to reconstruct most of the surface, and the size of the structureless regions converges to a temperature-dependent fraction of the whole surface. Some part of the regions had very thin width to form the domain boundary (black line) of adjacent 7×7 regions, and they can be finally called two-dimensional dislocation. The boundary had got its width thinner as the heating time is longer, and the reduction of the width was faster as the temperature was higher. On the surface after quenched, the structureless area is indeed not periodic structure except for 5×5 region near the step. Thus we conclude that the structureless area is so-called 1×1 at high temperature,

66

M. Tanaka et al. (a)

(b)

(c)

Fig. 2.35. (a) An STM image of Cl/Si(111) at 873 K heated approximately for 2,500 s. (b) The sample cooled from 913 to 773 K. The images were successively obtained at 773 K. The area of the image was 22×33 nm2 , sample bias was about +2.8 V, and tunneling current was 0.8 nA. (c) The sample cooled from 913 to 663 K. The area of the image is 200×200 nm2 . The 7×7 phase boundary was emphasized with black lines. The boundary had tendency to be oriented as the direction of arrows, along which the clusters are nucleated


67

i.e., silicon adatoms are moving on the flat 1×1 surface. The “1×1” surface reconstructs into 7×7 from the upper side of the step edge. When we observed Fig. 2.35a, temporarily 5×5 or 9×9 were seen at the front of 7×7 expansion during the high-temperature observation, indicating that the reconstruction took place into 7×7 through such periodic structures. From the observation, the lifetime of the metastable structures was about a few seconds, so that even quick scan rarely gave a clear image of the metastable structure. Next, it should be noted that no cluster was in any high-temperature images like Fig. 2.35a, so far as the temperature was monotonously raised. After the very long heating, the “1×1” area converged into a size that was smaller as the temperature was the higher. The area would be shaped into triangular. However long we keep the sample at the high temperature, no cluster appeared (in several hours of heating). To search the origin of the clusters, we quenched the sample down to 773 K successively after enough long heating time at 916 K. Then the images were obtained as in Fig. 2.35b. In the images, there is a step, whose lower side was “1×1” structure. The shape of the step changes, indicating detachment/attachment of the silicon atoms diffusing on the surface [131]. And the domain boundary of 7×7 regions is seen to start from the concave corner of the step into the terrace. The shape of the boundary changes from the curved, then the fluctuated, and finally the straight. There is a force to make the domain boundary straight along the dimer row of DAS perimeters. At the domain boundary, there are mismatch in the stacking-fault layer and broken stabilization at the corner hole symmetry [132]. Thus, the literal anisotropy contains strain, and it is larger if the boundary is bent. This larger strain is weakened through the thermal excitation during the 7×7 reconstruction. Then one finds clusters (small protrusions) along the domain boundary in Fig. 2.35b. The height was less than a single diatomic step, indicating that they were isolated silicon atoms. While the clusters also detach from and attach to the boundary, the boundary shape was changing. So far as the silicon clusters were relatively small as seen in the figure, they changed their positions. Some horizontal flashes of noise are seen near the boundary only. These are interpreted as temporary stay of silicon adatoms. No flash was observed on the wider terrace, indicating that the diffusing velocity is much higher than the scanning probe. The potential of the lateral motion may be lower near the boundary. The 2D adatom gas was overcooled, and a part of the gaseous atoms, exceeding the density of the 2D vapor, condensated near the boundary or the step. Finally the surface structure is shown in Fig. 2.35c, observed at 663 K. The sample was heated at 913 K for enough time, and annealed to the temperature (it took several seconds to cool down to 663 K). The surface on the terrace was covered with 7×7 DAS structure. To guide the phase boundaries, segmented lines are drawn. The lines connect the protrusions about 5–8 nm in the diameter. The heights of the protrusions are all ∼0.3 nm, corresponding to the single diatomic step. As time went on, the boundary was oriented to a direction. This is caused by the mechanism, shown in Fig. 2.35b, to make the domain boundary straight

68

M. Tanaka et al.

from the step edge to the terrace. The length of the segmented straight lines was 20–40 nm, which may be the tolerance to the strain at the temperature. The size of clusters tends to larger as the temperature was lower. However, it was determined not only by the temperature but also by the width of boundary and annealing rate. After the clusters had grown larger, we did not see any case that they moved to be aligned. The larger clusters, once formed, are crystalline [123] and may smoothly match with the substrate crystal. In the recent years, the limitations of the lithography and plasma process themselves have been turned out. The fluctuation of the fabricated structures is of the most serious problem (suggested by, for example, the optical and microscopic discrepancies at the atomic scale, in Fig. 2.26). On the other hand, the functional region of the semiconductor devices is of the size of a few nanometer scale. The self-organization can be introduced to control the surface structure on mere silicon surfaces, a typical system of homogeneous material, that may contain the strain near the surface due to the reconstruction described above. The heterointerfaces are much more important for the functional devices constructed by oxide insulator on the semiconductor surfaces, metal junction to the semiconductor, or semiconductor–semiconductor junction such as Ge, Alx Ga1−x As, GaN, InP, and so on. The conflict between materials due to the mismatch of the lattice will cause the distortion of the structure. However, such strains proved to reveal the patterning near the interface (see the example patterns in Fig. 2.36), and in the industrial use the reliability is nowadays discussed in the high performance of the electronic state-strained region of the interface layer [134, 135] as it has already been at the stage of real mass production. The high-temperature observations have shown this kind of mechanism at the atomic scale. The local strain will be soon much elucidated to utilize the relaxation and patterning in thermal treatment such as etching and growth process. The patterning at the nanometer scale on metal surfaces is presented elsewhere in Sect. 2.4. 2.3.5 Active Fabrication In this section, some results are introduced for the surface-etching process induced by electronic excitation. This kind of reaction may include usually desorption of the surface species, so that the mechanism is frequently referred to “desorption induced by electronic transition (DIET).” In the case of halogenated silicon, one could obtain the surface structure that can never been obtained by thermal process. The “active” fabrication means the surface process that one stimulates the surface with some excitation and the process goes through the path nonequilibrium. This indicates that one can obtain a surface with different structure or morphology obtained through a high-temperature process. The structure may be controlled if the excitation is caused selectively. In consideration of the self-organized patterns like in Figs. 2.32 and 2.34, the mechanisms of diffusion and strain (see Figs. 2.23 and 2.36, for example) will be adopted to construct to fabricate the surface process beyond


69

Fig. 2.36. TEM image of patterning at heterointerface of silicon-on-insulator structure, composed of α-Si, Ge layers on insulating SiO2 . A sample (thickness Si:Ge = 17:35 nm) after annealing at 1,373 K for (a) 2 min, (b) 20 min, and (c) 60 min, and another sample (thickness Si:Ge = 10:26 nm) after annealing for (d) 2 min, (e) 20 min, and (f ) 60 min. The images are taken from [133]

the lithography. The aligned clusters are not unique method for the template of nanopatterns. We should examine the detail of dynamic process at the atomic scale to fabricate the surface actively. The artificial scratches (wellcontrolled defects) or regularly aligned local structures can be made with electronic excitation, which obeys the selection rule. The pioneering work of the dynamics of electronic excitation is done by a Japanese on 1942 before the daybreak of surface science [136]. Since that, the desorption kinetics has been understood in terms of electronic excitation [137]. The initial excitation has been chiefly electron impact, which possesses the tunable energy. Now photon is also available as the coherent and tunable excitation source to elucidate the surface processes. The photoexcitation has advantage in selectivity, while electron beam can be focused into smaller area easily. These sources should be chosen according to the design of the surface processes. On Si(111) surface, Cl adsorption weakens the bonding energy of the adatom to the rest-atom. This is favorable to control the structure of the atomic layers only near the surface. The energy of the polychloride species is much weaker than that of the monochloride [67]. We show STM images that

70

M. Tanaka et al.

(a)

(b)

Fig. 2.37. An STM image of Cl-adsorbed Si(111) taken after UV irradiation of photon energy at 4.7 eV. The regions in white lines indicate unit cells of 7×7 surface. (a) The Cl exposure was ≈ 1.5 L. The sample bias voltage was +2.5 V. Some adatoms are recognized, while some are collected like clusters. Rest-atoms can be seen where the adatoms are missing. (b) The Cl was adsorbed to the saturation coverage (exposure was ≈ 10 L). There are six atoms at the perimeter of the triangle of the unit cell. The stacking-faulted and -unfaulted halves have different brightness, corresponding to the heights of the electronic state. It should be focused that this rest-surface contains many point defects. See [44] for detail

were obtained after weak irradiation (below the ablation fluence) of UV light with the photon energy of 4.7 eV (Nd:YAG pulsed laser, time duration was ∼5 ns). In Fig. 2.37a, some of rest-atoms are identified from the STM image, and many adatoms are seen as bright spheres. Note that the 7×7 unit cell is recognized in the white diamond frame and the adatoms are placed at the position close to the DAS geometry. However, some adatoms are gathered into cluster. At the same time, there are some regions in which no adatoms are seen. That is, the adatoms are desorbed and rest-atoms can be seen. In the image, the “rest-atoms” indicate six rest-atoms along the perimeter of the unit cell, which is the very configuration of DAS model (Fig. 2.1). This is interpreted


71

that the monochloride (identified from STM images) remains on the surface, while polychlorides are desorbed by the photon [44]. The difference from the thermally induced process is the remaining stacking-faulted 7×7 structure. When chlorine is adsorbed to the saturation coverage, the image in Fig. 2.37b shows a beautiful rest-surface (only consisting of rest-atoms in the top-most layer). At the saturation, nearly all the adatoms were polychlorinated. When the chlorination is imperfect, photoirradiation cause the surface migration due to the removal of the adatom chlorides until they are nucleated into the clusters as in Fig. 2.37a. From the STM images, reader should note the difference from Fig. 2.27; in the thermal process, no defect is seen, and the stacking fault was removed into 1×1 periodicity. However, the image in Fig. 2.37b contains the DAS periodicity, and many defects are created in the rest-surface. This suggests that the pulsed photoirradiation lets DIET to occur on Cl-adsorbed Si(111) surface. It is true that the photoirradiation may raise the temperature. The increase of temperature may induce thermal desorption. The energy of photons is injected to the system through the electronic transition, and the heat increases chiefly the temperature of electron system, not the lattice vibronic system. When the laser pulse has the time width of ns order, the desorption occurs on Cl-adsorbed Si(111) surface with the photon energy in the range from 2.3 to 6.4 eV, but it is indetective at 1.2 eV [138, 139]. This implies that the desorption is induced by the excited electron from the photo-absorbed substrate of the silicon bulk. In a report of the desorption closely examined with the photon energy varied from 3.8 to 5.4 eV, two peaks are found at 4.28 and 5.06 eV [140]. The optical absorption of silicon crystal has its peak at 4.28 eV to support the desorption caused by the bulk excitation. When we irradiated infrared laser (1.55 eV) with fs and ps duration, the desorption from the surface was not much [109, 122], but the change of components of the surface species was found shown in Fig. 2.38. There are apparent differences between TDS of Cl-saturated Si(111) before and after irradiation (thick and dashed curves, respectively). This spectra can never be obtained after thermal pro+ cess as in Fig. 2.27. Peak A in SiCl2 (observed as SiCl+ 2 and cracked SiCl ) is reduced at the same time peak B or C remains. The increase of peak C in SiCl4 implies the creation of the defects on the surface or the irregular chloride clusters as in Fig. 2.37a. The long-time irradiation (∼ minutes) of IR pulses may cause the desorption from the sample at room temperature, but not at 150 K [122]. This means that the desorption is coupled with the thermal excitation, but the change of the surface occurs on the sample at 150 K. Before the increase of the temperature, the modification, known form of the surface structure, was finished. In case of laser irradiation of ps pulse at 800 nm [141], the irradiation changes TDS like Fig. 2.38. Time-of-flight (TOF) measurement of the desorbed species gives the information of the energy of the desorbed species. The TOF of SiCl+ differs from that of SiCl+ 2 , interpreted as the desorption of SiCl from the surface. The ratio of the desorbed species was also different from the ratio for

72

M. Tanaka et al. A Desorption yield (arb. units)

C

SiCl+

B A

C

B

SiCl2+ (X 3) SiCl3+ (X 30)

SiCl4+ (X 30)

600

800 1000 1200 Temperature (K)

Fig. 2.38. TDS spectra of the Cl-saturated Si(111) surface. The change can be seen before (solid curves) and after laser irradiation (gray curves) of IR pulses (80 fs) at the fluence of ≈90 nJ cm−2 for 500 s. The repetition rate was 80 MHz. Each ions are selected by quadrupole mass spectrometer. The data are taken from [122]

the cracked species in TDS. This suggests that there are at least two species on the surface to be desorbed. The desorption ratio suggests that the two species are monochloride adatom and polychloride adatom. There is discrepancy from these results for femtoseconds [141] to the case of nanoseconds [44]. The very intensive attack from the bulk within femtoseconds may break the binding of the SiCl and SiCl2 to the surface. The desorption rate was compared with the two ions, and the desorption rate R was not proportional to the laser fluence I. 3.9 , respectively. As shown in Fig. 2.39, R(SiCl+ ) = αI 4.7 and R(SiCl+ 2 ) = αI Although the meaning of the power factor (p) are not still clear, the nonlinearity indicates that the process requires multiple excitation. Two possible mechanisms were suggested for the hot carrier-induced process from experimental and theoretical approaches: desorption induced by multiple electronic transition (DIMET) [142–144] and desorption due to nonadiabatic vibronic excitation [145–148] for the process with very short pulse lasers comparable to the lifetime of the excited carriers in the conduction band [149, 150]. The pulse duration remarkably affected desorbed species and rate, and especially the very short pulses are possible tool for surface fabrication other than equilibrium heating. Recalling the cases of photoinduced desorption with ns pulses (the previous paragraph), we note here that the photons with energies of 5.06 and 6.4 eV give the desorption yield proportional to the incident fluence [139, 140]. However, the photons at 4.28 eV give hyperlinearly increased yield [140]. This derives that there are at least two paths to relaxation of the excited electron at the surface to lead to the desorption, linear and nonlinear mechanisms. However, these have not been related to the surface species yet. Next we change the topic with the source of excitation from photon beam (laser) to electron beam (e-beam). The electron-impacted processes have been


73

104

Desorption yield (counts)

103

102

p = 4.7

4

5

SiCl+

6 7 8 910

103

102

p = 3.9

101

SiCl2+

4 5 6 7 8 910 Laser fluence (mJ/cm2)

Fig. 2.39. Desorption yield of SiCl+ and SiCl+ 2 ions with various fluence of ps laser (λ = 400 nm). Note that the vertical scale is logarithmic and the relation is nonlinear, suggesting multiple electronic excitation. The data points are from [141]

one of major field of surface science, and still keep the importance especially for semiconductor technology because electron impact is an important factor in the plasma etching/deposition and lithography is often done with e-beam. This kind of process is often referred to electron-stimulated desorption. Among them, the system of silicon with halogen is of the most importance. The desorption of bromine was measured with the primary energy of e-beam varied. When the surface coverage of bromine was not high, the desorbed species was ion of atomic bromine (Br+ ). As shown in Fig. 2.40, the desorption was increased between 200 and 300 eV, corresponding to the excitation of M shell electrons in bromine. From highly bromine-covered surface, silicon bromides are desorbed as ionic state (SiBr+ x ; x = 0, 1, 2). The kinetic energy of the desorbed ion was not so high (3–4 eV) irrespective of the primary energy. The process through the core excitation is understood in terms of the Knotek– Feibelman (KF) model where there is a transition state before the desorption. The transition state in KF model is two (or more) holes in the valence band after the relaxation of the initial core hole through Auger process. However, none can discuss further on the excitation in the bulk or at the surface unless the initial and transition states were separately discriminated [151]. In turn, we consider that the case with e-beam has no high energy. STM can inject ultimately narrow e-beam into the surface at the atomic scale. The STM current, in which the electron energy is typically within ±4 eV from Fermi level, may induce the excitation required for chemical reaction including desorption. The halogen atoms adsorbed to Si surface can be removed from the

74

M. Tanaka et al.

Fig. 2.40. The desorption yield of Br+ ion from a Br-adsorbed Si(111) surface under electron irradiation at various primary energies. The arrows show the absorption edge of the indicated electronic states. The data points are taken from [85]

40 30 20 10 0 0

10

20 (a)

30

40 nm (b)

Fig. 2.41. STM images of a Cl-saturated Si(111) surface. The sample bias was +2.5 V. (a) An image of the central area of 40 × 20 nm2 with the bias at 5.0 V. (b) A magnified image of the area surrounded by the rectangle in (a). The image is taken from [155]

surface [152, 153]. This indicates that the e-beam may cut the bond between the adsorbed halogen and the silicon atom in the top-most layer. This kind of desorption is reported to have threshold bias voltages at +1.5 V for bromine and ∼+5 V for chlorine. They are ascribed to the antibonding state between the halogen and the silicon. Once the antibonding electrons are injected, the halogen atoms slide away along the adiabatic potential like classic mechanics. This picture is referred to Menzel–Gomer–Readhead (MGR) model [154]. The advantage of e-beam from STM is the polarity of the bias voltage. That is, the occupied electron in the valence state is removable from the atoms near the surface. Figure 2.41a shows the rest-surface obtained with tunneling current of 0.8 nA at the bias of +2.5 V after scanning in the inside area at −5.0 V. The inside area is found to the structure is different from


75

the outside. The magnified image in the inside area is shown in Fig. 2.41b, which has obviously the same structure as in Fig. 2.37. Both images reveal the feature of electronically created rest-surface. This process, namely hole injection, may be resonant to the back-bond between adatom Si and restatom Si. However, all the three back-bonds are broken. Consider that the STM current at ∼nA supplies one hole in every 0.1 ns, which is at the same order of lifetime of a surface state on the semiconductor at longest [149, 150] and it can rarely fill all the three back-bonds at the same time. Then, we have another model. We propose the inelastic scattering that enhances the local vibration [156, 157]. The energy required to desorb the surface species must have more than a single vibronic quantum. The first excited vibration has lifetime at ∼10 ps, while higher-order excited vibration may be prolonged up to ∼ns due to the unharmonicity [158]. Then the multiple vibronic excitation accounts for the hole-injected desorption (negative bias), and this is also applicable to the electron-impacted desorption (positive bias). Close examination of the atomic desorption of hydrogen adsorbed on Si(001) surface, the desorption dependence on the bias voltage and the tunnel current concluded the multiple excitation of the local vibrational model due to the hole/electron scattering [159]. The difference of the multiple vibronic excitation from the conventional thermal excitation is whether the system near the surface (especially the atomic motion) can be said equilibrium with the electronic state (chiefly in the bulk) or the lattice phonon (over the substrate). The energetic distribution is described in terms of temperature, and time evolution of the temperatures of each system may be good indicator of the energy transfer. On the metal surface, the transient temperatures of each nearly independent system consistently give indeed good picture of the desorption process induced by photoexcitation [160]. In this sense, this model can be adopted not only to the e-beam process, but also to the photoinduced process. The hyperlinearity in the laser-induced cases has been explained two-hole localization due to the surface plasma vibration [161], but the multiple vibronic excitation can explain the mechanism as well. DIMET model also assumes the antibonding adiabatic potential curve like simple MGR model. However, the antibonding state is not always found, and the photon-energy dependence of the etching rate at the chlorinated surface implies that the resonant excitation is not necessary. The vibration of the surface species through the electronic antibonding state can be replaced by that by the electron–local phonon scattering at the surface. Then the difference may disappear between DIMET and the multiple excitation after some modification. The rate of inelastic scattering at the surface species depends on the energy spacing of the vibronic steps and the energetic threshold of the injected electron in the ladder-climbing process [162]. Anyway, in the change of the bonding due to active excitation near the surface, the clue is the dissipation path of the energy and the process of the electronic relaxation. In this concept, findings about the mechanism of the dynamic reaction, desorptions typically, induced by the active excitation will

76

M. Tanaka et al.

generally serve for the technology to the controlled and precise fabrication processes on the surface. 2.3.6 Summary In this section, microscopic aspects are reviewed on the surface processes on silicon surface in association of halogens. From the viewpoint of physical phenomena on semiconductor surface, etching process is the most fundamental. The quantitative analysis of desorption by means of TDS gives rise to the good pictures to interpret the surface phenomena, and the energetic discussion becomes possible with the aid of optical results to determine the surface density of the adsorbed species. This approach is widely applicable to deposition, structural change, and surface reaction of other material, that may be semiconductor or other material, onto the silicon wafers. Self-organization processes have drawn many researchers’ interest in the recent years for their possibility in fabrication of semiconductor surfaces, because the required size for electronic devices will soon be nanometer scale, smaller than the limit of optical lithography. Scanning probe technique is one of the good crafts to control a single atom on the surface [163], as well as it is very powerful tool to analyze the surface structure, electronic state, and so on. However, the scanning probe techniques are not suitable for industrial use, in which mass production and reliability are required. This situation promotes the discussion of combinations of chemical/physical techniques such as etching, deposition, and lithography [112]. In the combination, the mechanism of the strain is important to assembly the surface structure by self-organization. No matter what material homo- or heterospecies makes on them, the product structure is ruled by the mismatch at the interfaces in heteroepitaxy. In this section, we present the simplest system, the structural growth of silicon on the surface of silicon single crystal. It is pointed out here again [123,164] that in the alignment of the silicon clusters, the desorption mechanisms (step motion and reconstruction, typically) are competing, and that regular structures emerge as the result of the balance between them. Finally, processes actively induced on silicon surfaces are addressed. Electric excitation, which used to be electron impact in the early era of surface technology, can be selectively induced today using tunable light source, typically laser and synchrotron. They are often pulsed into ultrashort time duration from fs to ns, and they are utilized to understand the ultrafast dynamics [165]. The application of such light sources is introduced in other chapters. Lastly, we comment that the detailed dynamics at the atomic scale in terms of electronic excitation [166] will be soon developed to the actual fabrication at the micrometer to nanometer scale.


77

2.4 Self-Organized Nanopattern Formation on Copper Surfaces 2.4.1 Introduction As the scale of integrated circuits continues to diminish, reaching the scale of a few nanometers in lateral dimension, it is of great importance to design nextgeneration nanoelectronic devices based on a bottom-up approach, namely precise control of the atomic processes on surfaces. Thus, fabrication of low-dimensional structures such as nanoclusters [167], nanowires [168], and nanopatterns [112] has been intensively studied for decades. Formation process of these nanostructures through self-organizations is of particular interest to produce uniform structures over a macroscopic range on surfaces [169]. In this section, we review a particular system as one of the examples of such studies, focusing on nitrogen-covered Cu(001) surface (Cu(001)–c(2×2)N). It has been discovered for over a decade ago that this surface produces a novel periodic nanopattern as shown in Fig. 2.42. In this image, bright lines with the average width of about 2 nm represent clean Cu area separated with a square patches of c(2×2)N structure with the size of 5×5 nm2 . Formation mechanism of nanopattern on this surface has been investigated by STM [170– 174], spot profile analyzing low-energy electron diffraction (SPA-LEED) [175], Rutherford backscattering spectroscopy (RBS) [176], grazing incidence X-ray diffraction (GIXD) [177], and first-principles calculations [178]. The elastic effects on surfaces are important to understand formation mechanism of such a nanopattern. The displacement of the Cu lattice covered

Fig. 2.42. A surface with regularly arranged c(2×2)N patches (dark area) separated by 2 nm wide Cu lines on average (bright square grids). The nitrogen coverage is 0.25 ML (the full coverage corresponds to 0.50 ML), and the image size is 100 × 100 nm2

78

M. Tanaka et al.

with N was calculated based on the elastic model, and a good accordance with GIXD results was obtained [177]. The lattice distortion near the boundary of the c(2×2)N patches was visualized by STM [174]. More recently, shrinkage of lattice constant at the clean Cu area surrounded with c(2×2)N patches was experimentally confirmed by angle-resolved ultraviolet photoelectron spectroscopy (ARUPS) [179]. This study showed that upward shift of the Tamm state toward the Fermi level coincides with a slight shift of the folding point at M along the Γ –M line, and is ascribed to the strain at the clean Cu area on the grid pattern. The periodic pattern on this surface provides us with a template for fabricating periodic nanostructures on a relatively wide terrace. Formation of nanodot array and stripes was reported for magnetic metals such as Fe [180–182], Co [183], and Ni [184]. Novel magnetic properties and electronic properties were investigated with surface magneto-optical Kerr effect (SMOKE) [185] and magnetic linear/circular dichroism (MLD/MCD) [186]. The inhomogeneity of electronic properties on this surface governs not only the growth process but also dissociative adsorption of molecules. It turned out that inhomogeneous strain can cause significant change in the dissociation probability and diffusion rate [187]. Active role of oxygen coadsorption on the surface stress distribution has been further investigated with GIXD [188]. Fundamental understanding of these phenomena will be the basis of the bottom-up approach to create controlled nanostructures at the atomic level. Here, our recent studies on strain-induced nanopattern formation, growth process, and dissociative adsorption are summarized. 2.4.2 Experiments The experiments were carried out in an UHV apparatus, equipped with STM, LEED, AES apparatus, and ion gun. The base pressure was better than 5×10−11 Torr. We used the chemically polished Cu(001) surface of a columnshaped single crystal with the diameter of 4 mm at the surface and the height of 2 mm at the side. The STM used for this study was a commercial Omicron Vakuumphysik micro-STM. All the STM images were recorded in a constantcurrent mode with a tungsten tip at RT. The Cu(001) surface was cleaned by repeated cycles of Ar+ sputtering (500–1,000 eV) and annealing at 600 K until no sign of contamination by AES was observed. A nitrogen-covered c(2×2) surface was prepared exposing the clean Cu(001) surface to nitrogen activated by an ion gun (400–500 eV), followed by annealing up to 600–690 K. Pure iron (99.998%) was deposited on the surface at RT from a resistively heated alumina crucible at a rate of 2.0 ML min−1 . The stability of evaporation rate was confirmed using the quartz crystal microbalance. The pressure during the deposition was better than 3×10−10 Torr. The surface was exposed to oxygen gas at the amount less than 300 L (1 L = 1×10−6 Torr s).


79

2.4.3 Novel Phenomena on Cu(001)–c(2×2)N At low coverage of N, inhomogeneous displacement of Cu atoms from the bulk position was observed by STM [174]. Such an inhomogeneous strain may play crucial roles in the nanopattern formation and kinetic processes of adsorbates. We address here three novel phenomena observed on Cu(001)–c(2×2)N: 1. Nanopattern formation at vicinal surfaces 2. Strain-dependent nucleation of metal islands 3. Strain-dependent dissociation of oxygen molecules 2.4.4 Nanopattern Formation at Vicinal Surfaces Figure 2.43 shows STM images for a Cu(001)–c(2×2)N surface vicinal to the [110] direction prepared by annealing up to 620 K. Nitrogen coverage was 0.33±0.03 ML on average. In these images, bright lines indicate a clean Cu surface and the dark areas indicate the N-adsorbed surface. The clean Cu lines are 1.1±0.2 nm wide along the 110 direction. In Fig. 2.43a, the shape and size of the N-covered surface are not homogeneous on most of the terraces. We call this structure a “labyrinth pattern.” We also note small domains with a stripe pattern in Fig. 2.43a, such as the area indicated as S. A magnified image around the stripe pattern is shown in Fig. 2.43b. The width of the terrace with the stripe pattern is always over 20 nm. In Fig. 2.43c, we show the cross-sectional line of the STM image along the line A–B in Fig. 2.43b. The apparent height of the Cu lines of the labyrinth pattern is about 0.09 nm compared with the level of the N-adsorbed surface. At the step edges along the 110 direction, bright lines with the width of 0.90±0.05 nm are observed. Their apparent height is higher than the level of the N-adsorbed surface by about 0.06 nm. Thus we consider that these step edges are made of clean Cu lines. When we exclude the area S in Fig. 2.43a, the total length of the Cu lines parallel to the [110] direction (L[110] ) is longer than that parallel to the [110] direction (L[110] ) by the ratio of L[110] /L[110] ≈ 1.5. The clean Cu lines along the 110 direction become straighter and form the stripe pattern when we increase the annealing temperature as shown in Fig. 2.44. The nitrogen coverage is the same as that for the surface with the labyrinth pattern. This STM image was obtained after subsequent annealing of the surface shown in Fig. 2.43 up to 660 K. The surface is dominantly covered with the stripe patterns. On this surface we can see two domains on the same terrace. One consists of the Cu lines parallel to the [110] direction and the other consists of those parallel to the [110] direction. The area of the former domain is about three times larger than that of the latter domain. Thus, we call the former the “major stripe domain” and the latter the “minor stripe domain.” The step of the major stripe domain is straight and aligned parallel to the [110] direction while that of the minor stripe domain is rounded. The step edges for the major stripe domain consist of clean Cu lines like those in the labyrinth pattern.

80

M. Tanaka et al.

(a)

S

[110]

[110]

(b)

A

[110]

[110]

Height (nm)

B

0.2 0.1 0.0 0 A

5

10 Distance (nm)

15

20 B

(c) Fig. 2.43. (a) An STM image of the labyrinth pattern formed on the Cu(001)– c(2×2)N surface vicinal to the [110] direction. The size of the image is 100×100 nm2 . A surrounded area (S ) indicates the stripe pattern on this surface. (b) A magnified image around the stripe pattern. The size of the image is 40 × 40 nm2 . (c) The cross-sectional profile along the line A–B in (b)

The average width and length of the clean Cu lines and the N-adsorbed stripes, perpendicular (⊥) or parallel ( ) to the [110] direction in Fig. 2.44a, are summarized in Table 2.4. The width of the Cu lines is almost the same for both directions while that of the N-adsorbed stripes is smaller in the minor


81

G G

G [110] [110]

(a)

[110] [110]

(b) Fig. 2.44. (a) An STM image of the double-domain stripe pattern on the Cu(001)– c(2×2)N surface vicinal to the [110] direction. The size of the image is 100×100 nm2 . Surrounded areas (Gs) indicate the grid pattern on this surface. (b) A magnified image at the boundary between the different stripe domains. The size of the image is 33 × 33 nm2 Table 2.4. Widths and lengths of the Cu lines and the N-adsorbed stripes

Cu lines (⊥) Cu lines () N-adsorbed stripes (⊥) N-adsorbed stripes ()

Width (nm)

Length (nm)

1.0 ± 0.1 1.1 ± 0.1 1.6 ± 0.2 2.2 ± 0.2

Nano- and Micromaterials

Molecular- and Nano-Tubes

Nano Mechanics and Materials

Nano- and Biocomposites

Nano and Micromachining

Nano- and microelectromechanical systems fundamentals of nano- and microengineering

Nano-technology

Nano World

The Nano-Micro Interface: Bridging the Micro and Nano Worlds

Nano, Quantum And Molecular Computing

Nano and Molecular Electronics Handbook

Nano-Architectured and Nanostructured Materials

Nano Materials

Nano and Molecular Electronics Handbook

Colloids for Nano- and Biotechnology

Nano Technology - Ethic and Society

3 Nano Flower

Nano - Nanotecnologia En Espana

The Nano Flower (Mindstar)

The Nano Flower

The Nano Flower

Principles of Nano-Optics

iPod nano Руководство пользователя

Principles of nano-optics

Nano-Bio-Sensing

Nano: The Essentials

The Nano Flower

The Nano Flower

MACRO TO NANO SPECTROSCOPY

Nano-Surface Chemistry

The Nano Flower

Nano- and Micromaterials

Molecular- and Nano-Tubes

Nano Mechanics and Materials

Nano- and Biocomposites

Nano and Micromachining

Nano- and microelectromechanical systems fundamentals of nano- and microengineering

Nano-technology

Nano World

The Nano-Micro Interface: Bridging the Micro and Nano Worlds

Nano, Quantum And Molecular Computing

Nano and Molecular Electronics Handbook

Nano-Architectured and Nanostructured Materials

Nano Materials

Nano and Molecular Electronics Handbook

Colloids for Nano- and Biotechnology

Nano Technology - Ethic and Society

3 Nano Flower

Nano - Nanotecnologia En Espana

The Nano Flower (Mindstar)

The Nano Flower

The Nano Flower

Principles of Nano-Optics

iPod nano Руководство пользователя

Principles of nano-optics

Nano-Bio-Sensing

Nano: The Essentials

The Nano Flower

The Nano Flower

MACRO TO NANO SPECTROSCOPY

Nano-Surface Chemistry

The Nano Flower

Recommend Documents