THE C H E M I C A L PHYSICS OF SOLID SURFACES
THE C H E M I C A L P H Y S I C S OF S O L I D S U R F A C E S
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THE C H E M I C A L PHYSICS OF SOLID SURFACES
THE C H E M I C A L P H Y S I C S OF S O L I D S U R F A C E S
Volume 1 CLEAN SOLID SURFACES Volume 2 A D S O R P T I O N AT S O L I D S U R F A C E S Volume 3 CHEMISORPTION SYSTEMS Volume 4 F U N D A M E N T A L S T U D I E S OF H E T E R O G E N E O U S CATALYSIS Volume 5 SURFACE P R O P E R T I E S OF E L E C T R O N I C M A T E R I A L S Volume 6 C O A D S O R P T I O N , P R O M O T E R S AND P O I S O N S Volume 7 P H A S E T R A N S I T I O N S AND A D S O R B A T E R E S T R U C T U R I N I N G AT METAL S U R F A C E S Volume 8 G R O W T H AND P R O P E R T I E S OF U L T R A T H I N E P I T A X I A L LAYERS
TH ECH EMICAL PHYSICS OF SOLI D SU RFACES
EDITED B Y
D.A. KING B.Sc., P h . D . ( R a n d ) , Sc.D. ( E a s t A n g l i a ) , F.R.S.
1920 Professor of Physical Chemistry, University of Cambridge AND
D.P. WOODRUFF B.Sc. ( B r i s t o l ) , P h . D . , D . S c . ( W a r w i c k )
Professor of Physics, University of Warwick
VOLUME 8
G ROWTH AN D PROPE RT! ES OF U LTRATH !N EPITAXlAL LAYERS
ELSEVIER AMSTERDAM - LAUSANNE
- NEW YORK - OXFORD 1997
- SHANNON
- TOKYO
ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands
ISBN 0-444-82768-4 (Vol. 8) ISBN 0-444-41971-3 (Series) 9 1997 ELSEVIER SCIENCE B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), 222 ROSEWOOD DRIVE, DANVERS, MA 01923. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science B.V., unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands.
Contributors to Volume 8
E. BAUER
Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287-1504, USA
F. BESENBACHER
Institute of Physics and Astronomy and Center for Atomic-scale Materials Physics, University of Aarhus, DK-8000 Aarhus C, Denmark
J.A.C. BLAND
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, UK
H. BRUNE
Institut de Physique Exp6rimentale, Ecole Polytechnique F6d6rale de Lausanne CH- 1015 Lausanne, Switzerland
C. CHEN
Texas Center of Superconductivity, University of Houston, Houston, TX 77204, USA
G. COMSA
Institut for Grenzfl~ichenforschung und Vacuumphysik, Forschungszentrum Jiilich, D-52425 Jiilich, Germany
H.-J. FREUND
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Abteilung Chemische Physik, Faradayweg 4-6, 14195 Berlin, Germany
D.W. GOODMAN
Department of Chemistry, Texas A&M University, College Station, TX 77843, USA
P.D. JOHNSON
Physics Department, Brookhaven National Laboratory, NY 11973, USA
vi K. KERN
Institut de Physique Exp6rimentale, Ecole Polytechnique F6d6rale de Lausanne CH- 1015 Lausanne, Switzerland
R. KOCH
Institut fOr Experimentalphysik, Freie Universit/it Berlin, Arnimallee 14, D- 14195 Berlin, Germany
H. KUHLENBECK
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Abteilung Chemische Physik, Faradayweg 4-6, 14195 Berlin, Germany
M.G. LAGALLY
University of Wisconsin, Madison, WI 53706, USA
G. LE LAY
CRMC2-CNRS Campus de Luminy Case 913, 13288 Marseille Cedex 09, France and UFR Sciences de la Mati6re, Universit6 de Provence, Marseille, France
E LIU
University of Wisconsin, Madison, WI 53706, USA
T.E. MADEY
Laboratory for Surface Modification and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, PO Box 849, Piscataway, NJ 08855, USA
vii L.P. NIELSEN
Institute of Physics and Astronomy and Center for Atomic-scale Materials Physics, University of Aarhus, DK-8000 Aarhus C, Denmark and Haldor Topsoe Research Laboratories, Haldor Topsoe A/S, Nymollevej 55, 2800 Lyngby, Denmark
R. PERSAUD
Laboratory for Surface Modification and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, PO Box 849, Piscataway, NJ 08855, USA
B. POELSEMA
Faculty of Applied Physics and Centre for Materials Research (CMO), University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
C. RATSCH
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D- 14195 Berlin-Dahlem, Germany
G. ROSENFELD
Institut fiir Grenzfl/ichenforschung und Vacuumphysik, Forschungszentrum Jtilich, D-52425 Jiilich, Germany
P. RUGGERONE
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D- 14195 Berlin-Dahlem, Germany
M. SCHEFFLER
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D- 14195 Berlin-Dahlem, Germany
viii P.T. SPRUNGER
Institute of Physics and Astronomy and Center for Atomic-scale Materials Physics, University of Aarhus, DK-8000 Aarhus C, Denmark and Center for Advanced Microstructure and Devices (CAMD), Louisiana State University, Baton Rouge, Louisiana 70803, USA
S.C. STREET
Department of Chemistry, Texas A&M University, College Station, TX 77843, USA
T.T. TSONG
Institute of Physics, Academia Sinica, Taipei, Taiwan, 11529 ROC
J.A. VENABLES
Department of Physics and Astronomy, Arizona State University, Tempe, Arizona 85287, U.S.A. and School of Chemistry, Physics and Environmental Sciences, University of Sussex, Brighton BN1 9QH, U.K.
ix
Preface During the late 1960s and 1970s the commercial availability of ultra-high vacuum (UHV) systems allowed the development of a plethora of new techniques which were devised to probe materials in a surface-specific fashion, and this in turn led to the creation of modern surface science; the study of the structural, electronic and chemical properties of extremely well-characterised surfaces on an atomic scale. When this series of volumes was first conceived in the late 1970s our objective was to recognise the growing maturity of this new scientific discipline which was already starting to apply these techniques in a combined fashion to understand surface processes. One important type of surface phenomenon which has a wide range of potential applications is epitaxial growth, both homoepitaxy (A on A) of relevance to growing pure single crystals, and heteroepitaxy (A on B) of relevance in a many interfacial phenomena including electronic and magnetic 'devices' and synergetic effects in heterogeneous catalysis. Much of the early work on epitaxial growth was conducted under 'technical' or 'high' vacuum conditions, but subsequent UHV studies have shown clearly that many results were heavily influenced by surface contamination. Although there has been steady progress in understanding aspects of epitaxial growth throughout the last 30 years of modern surface science, work in this area has intensified greatly in the last 5 years or so. A number of factors have contributed to this expansion. One has been the general trend in surface science to tackle problems of increasing complexity as confidence is gained in the methodology, so for example, the role of oxide/metal interfaces in determining the properties of many practical supported catalysts is now being explored in greater detail. A second factor is the recognition of the potential importance of artificial multilayer materials not only in semiconductor devices but also in metal/metal systems because of their novel magnetic properties. Perhaps even more important than either of these application areas, however, is the newly-discovered power of scanning probe microscopies, and most notably scanning tunneling microscopy (STM), to provide the means to study epitaxial growth phenomena on an atomic scale under a wide range of conditions. These techniques have also contributed to revitalised interest in methods of fabricating and exploiting artificial structures (lateral as well as in layers) on a nanometre scale. This volume, on Growth and Properties of Ultrathin Epitaxial Layers, includes a collection of articles which reflect the present state of activity in this field. The emphasis is on metals and oxides rather than semiconductors, as
semiconductor growth and properties already received significant coverage in volume 5 of this series on Surface Properties of Electronic Materials. The first chapter by Venables, one of the pioneers of the field (along with, in particular, Bauer, the author of chapter 2) provides a general overview of our growing understanding of fundamental processes in epitaxial growth. Chapters 2 to 6 develop this theme with particular emphasis on metal-on-metal growth systems. Bauer (chapter 2) presents not only of some historical aspects of the problem but also demonstrates the important contribution his novel method of low energy electron microscopy has made to the field. Rosenfeld, Poelsema and Comsa discuss metal homoepitaxy and the way in which thermal helium atom scattering has helped to clarify mechanisms, while Tsong and Chen remind us of the important role played by field ion microscopy, an atomicscale microscopy which greatly predates STM, in identifying some key processes in surface diffusion and its role in growth. Both chapter 5 and 6 (Brune and Kern, and Besenbacher, Nielsen and Sprunger) illustrate the power of STM to investigate metal heteroepitaxy and identify key mechanisms including the role of strain and of very specifically limited mixing at the metal/metal interface to produce surface alloy phases having no bulk counterparts. Chapters 7 and 8 are concerned with semiconductor growth systems. Liu and Lagally describe the very detailed understanding of Si homoepitaxy which is emerging, while Le Lay describes some recent work on ultrathin metal overlayers on semiconductors and some of the novel properties of such surfaces. Chapters 9 to 11 are all concerned with metal/oxide growth systems, Kuhlenbeck and Freund, and Street and Goodman describing work on epitaxial oxides on metals, while Persaud and Madey discuss work on metal overlayers on one specific oxide, TiO 2. A rather different general aspect of epitaxial growth is presented by Koch in chapter 12, namely the role, characterisation and measurement of intrinsic stress in such films. In chapter 13, Ruggerone, Ratsch and Scheffler provide a description of the remarkable advances that are being made in theoretical descriptions of growth through the combined power of new theoretical methodologies and increasing computational power. Finally, in the last two chapters, Johnson and Bland describe the physical phenomena and magnetic properties which motivate one particular practical interest in metal/metal growth systems.
January 1997
D.A.King D. E Woodruff
xi Contents Preface
ix
Chapter 1 (J.A. Venables) Surface processes in epitaxial growth 1. Introduction 1.1 Growth modes and surface energies 1.2 Surface processes in crystal growth 1.3 Thermodynamics and kinetic arguments 2. Microscopy and surface physics techniques 2.1 Transmission and scanning electron microscopy 2.2 Surface-sensitive electron microscopy and analysis 2.3 Field ion microscopy 2.4 Tunnelling and force microscopies 3. Nucleation and growth theory 3.1 Rate equations for cluster densities 3.2 Adatom capture and regimes of condensation 3.3 Competing sinks: step capture and nucleation 3.4 Pattern formation: ripening and other effects 4. Island growth: metals on insulators 4.1 Ag, Au and Pd on alkali halides 4.2 Metals on oxide surfaces 4.3 Defect-induced nucleation on insulator surfaces 4.4 Comparison with theory 5. Layer growth: metal and semiconductor homoepitaxy 5.1 Metal-metal systems 5.2 Semiconductor homoepitaxy 5.3 Compound semiconductors and other compounds 6. Layer plus island growth examples 6.1 Metal heteroepitaxy: Ag/W, Ag/Fe(110) and Ag/Pt(111) 6.2 metal/semiconductor systems: Ag/Si and Ge(111) 6.3 Semiconductor heteroepitaxy: Ge/Si(100) 6.4 Metallic systems involving interdiffusion 7. Discussion and conclusions Acknowledgements References
1 2 3 5 7 7 8 9 10 11 11 13 15 17 19 19 21 22 24 24 24 27 29 31 31 33 36 39 41 42 42
xii
Chapter 2 (E. Bauer) The many facets of metal epitaxy 1. Introduction 2. Metals on metals 2.1 General considerations 2.2 The submonolayer range 2.2.1 The bcc(ll0) surface 2.2.2 The bcc(100) surface 2.3 Coverages above one monolayer 2.3.1 The bcc(110) surface 2.3.2 The bcc(100) surface 3. Metals on semiconductors 3.1 Some results from microscopic studies 4. Concluding remarks and acknowledgements References
46 48 48 48 48 52 53 53 56 59 59 62 63
Chapter 3 (G. Rosenfeld, B. Poelsema and G. Comsa) Epitaxial growth modes far from equilibrium 1. Introduction 2. A kinetic model for homoepitaxial growth 2.1 Ideal growth modes in homoepitaxy: intralayer versus interlayer mass transport 2.2 Atomistics of intra- and interlayer mass transport 2.3 Growth modes in real systems 2.4 Dependence of growth modes on deposition parameters 3. Experimental studies of metal homoepitaxy 3.1 Homoepitaxy on fcc(100) metal surfaces 3.2 Homoepitaxy on fcc(111) metal surfaces 3.3 A special system: the growth of Pt/Pt(111) 3.4 Discussion: why are fcc(100) and fcc(lll) metal surfaces so different? 4. Kinetic concepts for growth manipulation 4.1 Controlled reduction of the step-edge barrier 4.2 The concept of two mobilities 5. Conclusions Acknowledgements References
66 68 68 70 72 75 79 81 84 88 92 94 95 95 97 97 98
xiii
Chapter 4 (T.T. Tsong and C. Chen) Dynamics and diffusion of atoms at stepped surfaces 1. Introduction 2. Field ion microscopy 3. Random walk of single atoms and atom-clusters 3.1 Random walk of single atoms on a terrace 3.2 Mechanisms of atomic jumps: hopping vs. exchange-displacement 3.3 Field induced surface diffusion 3.4 Diffusion of clusters 4. Effects of lattice steps and defects 4.1 Step structures and ledge atom diffusion 4.2 Equilibrium island shape 4.3 Relative binding energy of ledge atoms at different steps 4.4 Descending steps 4.5 Ascending motion of step-edge atoms and in-layer atoms 4.6 Dissociation of step edge atoms to remain on the lower terrace 4.7 Impurity traps 5. Summary References
102 104 106 109 111 114 117 118 119 123 127 131 133 138 143 143 145
Chapter 5 (H. Brune, and K. Kern) Heteroepitaxial metal growth: the effects of strain 1. Introduction: heteroepitaxial metal growth 2. Thermodynamic growth mode and structural mismatch 3. Strain relief and strain induced structures 3.1 Dislocations and strain relief at hexagonal close-packed interfaces 3.2 Strain relief mechanisms at interfaces with square symmetry 3.3 Anisotropic strain relief 4. Effects of strain on nucleation kinetics in metal epitaxy 4.1 Nucleation and surface diffusion 4.2 Effect of isotropic strain on surface diffusion and nucleation 4.3 Nucleation on anisotropically strained substrates 4.4 Strain and interlayer diffusion Acknowledgement References
149 150 153 155 162 169 171 175 184 188 194 201 201
xiv
Chapter 6 (E Besenbacher, L.P. Nielsen and P.T. Sprunger)
Surface alloying in heteroepitaxial metal-on-metal growth 1. Introduction 2. Thermodynamic considerations 3. Growth of bulk miscible systems 3.1 Surface alloying of Pd on Cu(100) 3.2 Surface alloying of Pd on Cu(ll0) 4. growth of bulk immiscible systems 4.1 Surface alloying of Au on Ni(110) 4.2 Theoretical predictions for the Au-Ni system 4.3 Surface dealloying of Au on Ni(ll0) 4.4 Surface alloying of Au on N i ( l l l ) 4.5 Strain relief at the buried Au-Ni(111) interface 4.6 Surface alloying of Au on N i ( l l l ) at high Au coverages: Vegards law in 2-D 4.7 Surface alloying of Ag on Cu surfaces 4.7.1 Surface alloying of Ag on Cu(110) 4.7.2 Surface alloying of Ag on Cu(100) 4.7.3 Surface structure and alloying of Ag on C u ( l l l ) 4.7.4 Surface alloying of Ag-Cu on Ru(0001) 4.8 Surface alloying of Ag on Ni surfaces 4.8.1 Surface alloying of Ag on Ni(110) 4.8.2 Surface structure of Ag on N i ( l l l ) 4.9 Surface alloying of Pb on Cu surfaces 4.9.1 Pb on Cu(110) 4.9.2 Pb on Cu(100) 4.9.3 Pb on C u ( l l l ) 4.10 Surface alloying of alkali metals on AI(111) 5. Surface alloying: general trends 6. Implications for surface reactivity 7. Concluding remarks Acknowledgements References
207 210 213 213 214 215 216 217 221 222 224 226 229 230 231 233 234 236 236 237 238 238 240 240 242 243 248 251 252 252
XV
Chapter 7 (E Liu and M.G. Lagally) Epitaxial growth of Si on Si(001) 1. Introduction 2. Background 2.1 The silicon (001) surface 2.2 Kinetic processes during vapor deposition 3. Adatom adsorption: theoretical predictions 4. Direct measurement of Si self-diffusion with STM 4.1 Dependence of island number density and denuded-zone width on the diffusion coefficient 4.2 Diffusional anisotropy 4.3 Diffusion coefficient and activation energy 5. Nucleation: energetics and dynamics of Si ad-dimers 6. Growth: adatom-step interaction 7. Coarsening 8. Real-time measurements of kinetics of surface defects 8.1 Activation energy for step fluctuation and step motion 8.2 Dimer-vacancy migration 9. Thermodynamic properties and equilibrium surface morphology 9.1 Equilibrium shape of Si islands and energetics of steps 9.2 Equilibrium step configurations 9.2.1 Nominal surface 9.2.2 Vicinal surface 10. Conclusion References
258 259 259 261 262 264 265 269 271 274 277 280 283 284 286 288 288 289 289 290 292 293
Chapter 8 (G. Le Lay) Monolayer films of unreactive metals on semiconductors
1. Introduction 2. Ultra low metal coverage regime 2.1 Cs/InAs(110) 2.2 Pb/Si(111)7x7 at RT 3. Submonolayer regime 3.1 Pb, Sn/Si, Ge(111) mosaic phases 3.2 The R3 alpha phase 4. The dense 2D phases 4.1 RT structures 4.2 The R3f;zlxl phase transition
297 300 300 302 304 305 305 311 312 319
xvi 4.3 Equilibrium formation of 2D-adlayers 5. Thin metal films 5.1 Quantum size effects in thin Ag and Pb films 5.2 Hydrogen-termination effects 5.3 Influence of buried interface structures on Schottky-barrier heights 6. Unreactive metals on Si(001) 6.1 Bismuth adsorption 6.2 Lead adsorption 6.3 Thin silver (111) films on Si(100) 7. Future prospects References
320 322 322 323 326 328 329 330 334 335 336
Chapter 9 (H. Kuhlenbeck and H.-J. Freund) Structure and electronic properties of ultrathin oxide films on metallic substrates 1. Introduction 340 2. Preparation of thin oxide films 342 3. Experimental results for different oxide-metal systems 344 3.1 NiO(100)/Ni(100), N i O ( l l l ) / N i ( l l l ) and N i O ( l l l ) / A u ( l l l ) 344 3.1.1 Geometric structure 344 3.1.1.1 NiO(100)/Ni(100) 344 3.1.1.2 NiO(111)/Ni(111) 347 3.1.2 Electronic structure 352 3.1.2.1 Band structure of NiO(100)/Ni(100) 352 3.1.2.2 Electronic excitations 355 3.2 Cr203(0001)/Cr(110) 357 3.3 A1203(111)/NiAI(110) 364 4. Summary 370 Acknowledgements 371 References 371
o o
XVll
Chapter 10 (S.C. Street and D.W. Goodman) Chemical and spectroscopic studies of ultrathin oxide films 1. Introduction 375 2. Magnesium oxide 376 2.1 Synthesis and characterisation of MgO(100) ultrathin films 376 2.1.1 Adsorption of CO on MgO(100) ultrathin films 378 2.1.2 Acid/base and Li-doped properties of MgO(100) ultrathin films 378 2.2 Synthesis and characterisation of MgO(111) ultrathin films 381 2.2.1 Adsorption on MgO(111) ultrathin films 382 3. Nickel Oxide 384 3.1 Synthesis and characterisation of NIO(100) ultrathin films 384 3.1.1 Adsorption of CO on NiO(100) ultrathin films 384 3.1.2 Acid/base properties of NiO(100) ultrathin films 385 3.2 Synthesis and characterisation of NiO(111) ultrathin films 387 3.2.1 Adsorption on NiO(111) ultrathin films 388 4. Alumina 389 4.1 Synthesis and characterisation of A1203 ultrathin films 389 4.2 Interaction of benzene with AL203and MgO ultrathin films 390 5. Layered and mixed oxide ultrathin films 392 5.1 The MgO/NiO mixed oxide system 392 5.2 The CaO/NiO mixed oxide system and comparison to the NiO/MgO system 394 5.3 NiO ultrathin film supported on A1203 395 5.4 Mixed A1203/SiO2 ultrathin films 397 6. STM imaging of oxide surfaces 398 7. Oxide supported metal particles 401 9. Conclusion 402 References 404
Chapter 11 (R. Persaud and T.E. Madey) Growth, structure and reactivity of ultrathin metal films on TiO 2 surfaces 1. Introduction 2. Overview of metals on TiO2(110) 2.1 Stoichiometric TiO2(110) 2.2 2.3 2.4 2.5 2.6
Thermodynamics of metal/TiO 2 interactions Experimental procedures Growth modes for metals/TiO 2 Interfacial reactivity for metals/TiO2 Structure
407 408 408 411 414 414 417 419
xviii 2.7 Thermal stability of overlayer films: encapsulation 3. Element-by-element survey of metals on TiO 2 3.1 Non-transition metals on TiO2(110) 3.1.1 Alkali metals on TiO2(110) 3.1.1.1 Na/TiO2(110) 3.1.1.2 K/TiO 2 3.1.1.3 Cs/TiO2(110) 3.1.2 A1/TiO 2 3.2 Transition metals on TiO2(110) 3.2.1 Ti/TiO2(110) 3.2.2 Hf/TiO2(110) 3.2.3 V/TiO2(110) 3.2.4 Cr/TiO2(110) 3.2.5 Mn/TiO2(110) 3.2.6 Fe/TiO2(110) 3.2.7 Rh/TiO2(110) 3.2.8 Ni/TiO2(110) 3.2.9 Pd/TiO2(110) 3.2.10 Pt/TiO2(110) 3.2.11 Cu/TiO2(110) 3.2.12 Ag/TiO2(110) 3.2.13 Au/TiO2(110) 4. Summary and outlook Acknowledgements References
420 421 421 421 422 423 424 425 425 425 426 426 428 429 430 432 432 433 434 436 437 437 442 443 443
Chapter 12 (R. Koch) Intrinsic stress of epitaxial thin films and surface layers 1. Introduction 2. Nomenclature, definitions of stress 2.1 Intrinsic stress of thin films in one dimension 2.2 Intrinsic stress of thin films in three dimensions 2.3 Surface tension and surface stress 3. Measurement of misfit strain and stress 3.1 Techniques to determine misfit strain 3.2 Techniques to determine misfit stress 4. Intrinsic stress upon equilibrium epitaxy 4.1 Film growth in thermodynamic equilibrium 4.2 Volmer-Weber epitaxy
448 449 449 450 455 457 457 458 461 461 464
xix 4.3 Stranski-Krastanov epitaxy 4.4 Frank-Van der Merwe epitaxy 5. Intrinsic stress upon pyramidal growth 5.1 Film growth at presence of Ehrlich-Schwoebel barriers 6. Intrinsic stress of surface layers 6.1 Stress of clean surfaces 6.2 Changes of surface stress induced by adsorbates 7. Summarising discussion Acknowledgements References
471 475 477 477 482 482 483 484 486 486
Chapter 13 (E Ruggerone, C. Ratsch and M. Scheffler)
Density-functional theory of epitaxial growth of metals 1. Introduction 2. Atomistic processes and rate equations 2.1 Atomistic processes 2.2 Rate equations 2.3 Critical island area and the action of surfactants 3. Total energy and the description of growth 3.1 Bond-cutting methods 3.2 Density-functional theory 3.3 Implementation of DFT into state-of-the-art computations 3.4 Kinetic Monte Carlo approach 4. Results for fcc(111) and fcc(100) surfaces 4.1 Growth at AI(111) 4.1.1 Microscopic processes 4.1.2 Ab initio KMC study of growth 4.2 Ag(111) 4.2.1 The influence of strain on surface diffusion 4.2.2 The role of antimony as a surfactant 4.3 Microscopic processes at AI(100) 4.4 Ag(100) 4.4.1 Microscopic processes 4.4.2 The influence of strain on surface diffusion References
490 494 494 502 504 507 508 509 514 518 520 521 521 524 530 53O 533 536 537 537 539 540
XX
Chapter 14 (E D. Johnson) Electronic structure of ultrathin magnetic films 1. Introduction 2. Itinerant magnetism and the Stoner model 3. Transition metal films 3.1 Theoretical studies 3.2 Experimental studies 3.3 Other ultrathin ferromagnetic systems 4. Noble metal films on ferromagnetic substrates 4.1 The Ag/Fe(001) interface 4.2 The Cu/Co(001) interface 5. Summary Acknowledgements References
545 546 548 538 551 562 563 564 570 577 578 578
Chapter 15 (J.A.C.Bland) Uitrathin magnetic structures - magnetism and electronic properties 1. Introduction 2. Ultrathin magnetic film magnetometry 2.1 The magneto-optic Kerr effect: an introduction 2.2 The magneto-optic Kerr effect 2.3 A macroscopic description of the Kerr effect 2.4 Vector MOKE 2.5 Polarised neutron reflection: an introduction 2.6 Polarised neutron reflection 3 Absolute magnetic moments 3.1 3-d metal magnetic moments - an overview 3.2 Volume dependence of the magnetic moment 3.3 Magnetic moments and surface stability 3.4 Measurements of absolute magnetic moments in ultrathin transition metal films 3.5 X/Fe(001) films on Ag(001) substrates 3.6 Fe(ll0) films on W(ll0) substrates 4 The two dimensional magnetic phase transition 4.1 Critical behaviour of Co/Cu(001) 4.2 Effect of Cu overlayers on the magnetism of Co/Cu(001) 5 Thickness dependence of magnetic anisotropies and vector spin reversal processes
583 585 586 587 588 590 590 591 594 594 600 601 602 603 607 607 608 609 612
xxi 5.1 bcc Fe/GaAs 5.2 Vector switching processes in Fe/GaAs(001) 5.3 Vector spin reversal of coupled Fe/Cr/Fe trilayers 5.4 Anisotropy and reversal behaviour of Fe/Ag(001) 6 Conclusions Acknowledgements References
613 617 620 622 627 628 628
Index
635
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
Chapter 1 Surface processes in epitaxial g r o w t h
John A. Venables Department of Physics and Astronomy, Arizona State University, Tempe, Arizona 85287, U.S.A. and School of Chemistry, Physics and Environmental Sciences, University of Sussex, Brighton BN1 9QH, U.K. 1. INTRODUCTION This book 'Growth and Properties of Ultrathin Epitaxial Layers' is concerned with a whole range of phenomena which occur during the production and use of epitaxial thin films. As the editors have explained in the preface, thin films are currently used in a wide variety of technological situations, and there are many more applications in prospect. Thus we need, as 'materials' scientists, to understand the processes which occur in detail, and to pursue experiments which test the correctness of our current understanding. This chapter is concerned with the very earliest stages in the formation of thin epitaxial films, concentrating on deposition from the vapour. In many senses this is the simplest case, since it involves the formation of a dense, solid phase from a dilute, gaseous phase. The solid-vapour interface can be observed by an array of surface science and microscope-based experimental techniques. The theoretical formulations are also relatively simple: thermodynamic and statistical mechanical models can be formulated and tested by experiment. However, it should be clear at the outset that 'real life' is typically more complicated than these simple models. In particular, we are not discussing here how to make 'better' films for particular applications, but rather aimimg to introduce the language in which such efforts can be discussed. This initial section gives some of the underlying arguments, before we proceed in sections 2 and 3 to describe some of the experimental techniques and the theoretical formulations. Sections 4 to 6 give experimental examples of how nucleation, growth and surface diffusion can be studied in the various growth modes, followed by the discussion of section 7. Our aim in this chapter is to give the flavour of the subject, rather than to be comprehensive.
1.1 Growth modes and surface energies The first use of surface energies to describe the three modes of crystal growth was made by Bauer in 1958, and has been reviewed many times [1,2]. In the island, or Volmer-Weber mode, islands of the bulk deposit are initially formed on the bare substrate. Further deposition causes these islands to grow and maybe coarsen; they may sometimes rearrange extensively before forming a continuous film, and any epitaxial orientation may be established quite late in the growth process [1,3]. In the opposite case, layer, or Frank-van der Merwe growth, one layer is more or less complete before the next layer starts to form, and the epitaxial orientation is typically established within the first monolayer; after a relatively large thickness has been deposited, misfit dislocations and other defects may be introduced to relieve strain [3]. In the intermediate 'layer plus island', or Stranski-Krastanov (SK) growth, one or more (epitaxial) layers form first, but then further deposition is in the form of (usually epitaxial) islands. These distinctions can be understood qualitatively in terms of relative surface energies, YAand YB, as illustrated in Figure 1. If the deposit is A, and the substrate is B, the condition YA+ Y* < YB leads to layer growth, as shown in Fig. 1(a). The condition is therefore not satisfied if B is the deposit and A the substrate, and this leads to island growth, as illustrated in Fig. l(b). However, if we have layer growth initially, then it is often the case that the effective interfacial energy 7" increases with thickness of the layer, for example due to strain in this layer. In such a case, the thermodynamic conditions for layer growth are terminated after a certain layer thickness. Further growth of the layers is then in competition with growth of the more stable islands. This thermodynamic situation is very common, so that many crystal growth systems can be classified as SK growth. The above classification immediately tells us to expect trouble in the growth of A/B/A superlattices. Even if we assume no interdiffusion, or chemical reactions between A and B, then the interfaces A/B and B/A may well grow in a different mode, and one interface is likely to be more perfect than the other. But in many cases of technological interest there may well be interdiffusion and/or reactions and at the interfaces. In these cases, the reason why the end-product is not the equilibrium compound of A and B is due to kinetic limitations during and after deposition. One of the difficulties of describing the whole epitaxial growth process quantitatively, and the final structures of films in general, is that there are many possible types of kinetic effect, each with associated length and time scales which can be very different.
a
A
b ------i
~'A~ ./
}~,,
"-.
7B 7A
B Arrival (R)
C
Special sites
Re-evaporation
Surface diffusion
Binding, nucleation
Surface
Interdiffusion
Fig. 1.a) Growth of A on B, where YA< 'YB;misfit dislocations are introduced, or islands form after a few layers have been deposited; b) Growth of B directly onto A as islands. The interfacial energy y* represents the excess energy over bulk A and B integrated through the interface region; c) Surface processes and characteristic energies in nucleation and film growth.
1.2. Surface processes in crystal growth The atomistic processes responsible for nucleation and growth of epitaxial thin films are indicated in Fig. l(c). Atoms anive from the vapour at a deposition rate R (equivalent to a flux F, used in the recent literature) or at an equivalent gas pressure p, such that R = p/(2rclnkT) ~/2, where m is the atomic mass, k is Boltzmann's constant and T the absolute temperature of the source. This creates adatoms (or ad-molecules) on the surface, whose areal density n~(t) increases initially as n l = Rt. At the highest temperatures, these adatoms will only stay on the surface for a short time, the adsorption stay time "Ca.This time is determined by the adsorption energy, Ea, and is conventionally written as Ta "1 =
Va exp
(-Ea/kT)
(1)
where Va is an atomic vibration frequency, of order 1-10 THz. Before evaporating, the adatom will have moved, maybe quite a long way fiom its point of arrival, with a diffusion constant D. A simple expression for the diffusion
constant appropriate to two dimensional surface diffusion, in tenns of the diffusion energy Ea, is* D = (Vda2/4) exp (-Ed/kT)
(2)
where a is the jump distance, of order the surface repeat distance, say 0.2-0.5ran. The number of substrate sites visited by an adatom in time Ta is Dxa/No, where No is the areal density of such sites, of the same order as a -2. The nns displacement of the adatom from the arrival site before evaporation is x~ = (Dx,) 1/2 = a(Vd/Va)1/2 exp
{(Ea -
Ed)/2kT}.
(3)
Since Ea is typically several times Eo, (xJa) can be large at suitably low temperatures. Then, in their migration over the surface, the adatoms will encounter other atoms. Depending on the size of the binding energy between these atoms, and on their areal density n~, they will form small clusters, which may then grow to form large clusters of atoms on the surface, in the form of 2- or 3-dimensional islands. This binding energy between a pair of atoms, Eb, and the energy of the critical cluster, Ei, are centrally important to the understanding of nucleation and growth processes. Some simple cluster geometries are explored pictorially in ref [4]. Subsequently, surface- and inter-diffusion processes may occur, as illustrated on the right-hand side of Fig. l(c). It may also be that the migrating adatoms encotmter special sites, such as surface vacancies or the steps indicated at the let~-hand side of the figure. These processes may be more difficult to model in detail, because they are highly specific to the systems studied, such as the nature of any chemical reactions at the interface, or the exact orientation of the substrate surface. In most of this chapter, we will concentrate on understanding nucleation and growth processes in tenns of the 3 characteristic energies (E,, Eo and Eb) introduced in this section. But we should keep in mind that this is the simplest case, which we study first for ease of understanding. In pal~icular, interchange reactions at the surface are likely where the deposit is more strongly bound than the substrate, and/or where the substrate plane is more open. These topics are explored more fully in later sections and chapters; recently, exchange diffusion, and nucleation based on exchange processes, has been observed quite frequently. *Footnote: Formulae 1 and 2 are conventional, in the sense that they are valid over a limited temperature interval, but the various frequencies v are not necessarily the same in different expressions. In particular, consistency with eqn (4) requires a more complex form of v, in eqn (1), and the Vd in eqn (2) includes entropy of migration. This is discussed further in section 3.
1.3 Thermodynamic and kinetic arguments Despite the use of thermodynamic classification and argument, the growth of a thin epitaxial film is a non-equilibrium kinetic process in which one or more steps are rate-limiting. Two limit cases may be instructive. The thermodynamic limit is illustrated by the equilibrium vapour pressure, p~, of bulk material (A). In this case, by equating the chemical potential, la, of the low pressure vapour, which is exact, and an approximate description of the free energy of the solid (primarily due to the lattice vibrations), we can find an expression for p~. Using the Einstein approximation in the high temperature limit, for vibrations of frequency v, we obtain the standard result P e - (27tm)3/2 v3(kT) "1/2 exp(-L0/kT).
(4)
There are two points to make about this result in the present context. First, the vapour pressure is dominated by the sublimation energy L0, which is much larger than kT at all temperatures below the melting point. However, it is also influenced strongly (v 3) by the lattice vibrations, so that models which ignore such effects cannot be correct in detail. Second, this equilibrium result is independent of the state of the surface, which acts only as an intermediary between the vapour and the solid. When the vapour and solid are not in equilibrium, the nature of the surface does play a significant role, as first shown by Burton, Cabrera and Frank (BCF) in 1951 [5]. They argued that the condensation coefficient, ac, in the HertzKnudsen equation dn/dt = C~c(R- Re),
(5)
where n is the total areal density of atoms condensed, is a function of the step structure of the surface in the absence of island nucleation. At low supersaturation S, defined by p/p~ or R/R~, such that Ala = kT In S, they showed that ac = (2xs/d) tanh (d/2xs),
(6)
where d is the step separation and Xs- (Dx~)~/2 as in eqn. 3. This is equivalent, in the small-xs limit, to adatom capture in a zone of width Xs either side of a step, with re-evaporation of the adatoms which are further away from the step. When Xs >> d, all atoms are captured, and the condensation coefficient tends to unity. BCF went on to show that at low A~, growth did not occur at a measurable rate on a flat surface, but was mediated by (screw) dislocations which produce spiral arrays of steps at the surface [5-7].
At higher supersaturations, adatoms will come together before they reach the steps, and if they are botmd strongly enough, will fonn nuclei which can develop into islands. The rate limiting step is the formation of 'critical nuclei' of size i, which is defined as the size which is more likely to grow than decay [8]. As explained in more detail elsewhere [2], we can apply statistical mechanics, in either a 'classical' or an 'atomistic' version to calculate the density of critical nuclei, ni. The atomistic expression, in tenns of the single adatom density n~, and the (free) energy of the critical cluster, El, is ni/N0 =
Ci
(nl/N0) i exp (Ei/kT),
(7)
where Ci is a statistical weight of order 1-10. From now on, it is helpful to work in monolayer units (for the n's, R and D, etc) which means that we call drop the factor No from more complicated equations. The use of atomistic expressions was prompted by the realisation that, in many deposition experiments the driving force A~t call be so large that the critical nucleus is only a single atom [2,9]. Thus i - 1 represents the extreme kinetic limit on a perfect surface, a limiting case of 'general i' models, discussed in section 3. The case i - 0 can arise on a defective surface; this means that adatoms diffi~se to defect sites, and that clusters nucleate from such filled sites. This possibility is discussed further in section 4. Only for the lowest substrate temperatures is it possible to suppress surface diffusion of adatoms, and in this limit the film would grow simply by accreting atoms which stick where they fall! This does not happen at temperatures involved in the growth of less reactive thin fihns for practical purposes. But the observation of stationary single adatoms of refractory metals has been perfonned by Field Ion Microscopy (FIM) for many years [10,11]. More recently, scamling tunneling microscopy (STM) has been used to obselwe Xenon and Iron atoms, which, despite their low diffusion energy, do not move on liquid helium - cooled substrates, unless they are 'pushed' by the STM tip [12]. The use of microscopy to observe the nucleation patterns is described in the next section. Equivalent 'classical' expressions to equation (7) have been fonnulated in terms of surface energies for three-dimensional (3D) or 'edge' energies for 2D nuclei [1,2]. These become more realistic as the nuclei become large (many htmdreds of atoms), close to equilibrium conditions. In tiffs limit a reliable model has to be consistent with the equilibrium vapour pressure, and with all other types of considerations of 'detailed balance'. This is not entirely straightforward, and we need definitions of quantities such as Ci and Ei in (7), and others such as the adsorption stay time Za in (1), which do not introduce internal contradictions [13]. For initial purposes, it may be better to note such problems in passing, and to return to them at a later stage.
2. MICROSCOPY AND SURFACE PHYSICS TECHNIQUES Many experimental tools can be used to observe the earliest stages of the growth of thin films. Most important are the various forms of microscopy, and a range of surface sensitive techniques. These surface teclmiques can be sensitive to much less than the first monolayer (ML) of the deposit, measuring chemical composition, via (e.g.) Auger Electron Spectroscopy (AES), or crystallographic order, via Low Energy or Reflection High Energy Electron Diffraction (LEED or RHEED). Some familarity with these teclmiques mad the nomenclature of surface science is assumed in the descriptions which follow [14].
2.1 Transmission and scanning electron microscopy The observation of clusters in island growth by transmission electron microscopy (TEM) has a long history [1-4]. The number density of clusters can be observed, and their size and spatial distributions, as a function of the deposition variables R, T and time t. An example of Au deposited on NaCI(100), taken from work by the Robins group was given previously [4, Fig. 1]; there we see a time sequence of nucleation, growth m~d coalescence of islands. On the (100) terraces, the clusters seem to have nucleated at random, but we also see the strong decoration of individual surface steps. This decoration teclmique has been widely used [6,7] to study the step structure of alkali halide surfaces. A more recent use of TEM, to study small Pd particles deposited onto MgO, is illustrated here in Fig. 2, where we see high resolution pictures of the distribution of islands, coupled with the diffiaction pattern to detennine their epitaxial orientation. These pictures are used to identify differently shaped islands, and to measure nucleation densities and size distributions [15]. This island growth system is of interest as a model catalyst, and the work cited is a good example of transmission electron microscopy and diffraction used in combination with several surface science techniques. Experiments on metal/ insulator systems, performed to test ideas about nucleation and growth on the terraces, at steps and other defects are described in Sect. 4. In principle the same studies can be done using scamling electron microscopy (SEM), provided the spatial resolution is high enough. If crystal growth produces rough surfaces or relatively widely spaced or highly three-dimensional clusters, SEM can produce striking pictures of surface morphology. If these observations are made in nonnal vacuum TEM's mad SEM's, then the surfaces will be covered with contamination layers, and may otherwise react with the atmosphere. However, for most materials systems, the crucial point is that the deposition must
ns=2.98x1011 cm-2
d
L._
!
j
D=11.2nm o-=2A nm Ac=31%
-
]
-
r-r 5
lo
diameter (nm)
Fig 2. Epitaxial Pd particles on MgO: (a) TEM overview of particles after some coalescence has occurred; (b) higher magnificationview of particles with different shapes numbered 1-3; (c) transmission diffraction pattern, giving epitaxial orientation of all such islands; (d) size distribution histogram,nucleation density and other quantities derived t~om(b). From ref [15]. be done under clean (UHV-based) conditions; the restrictions during observation, while important, are somewhat less stringent. Development of surface sensitive microscopies, and in-situ growth studies, are considered next.
2.2 Surface-sensitive electron microscopy and analysis The scanning 'principle' is very versatile, and, in a 'clean' UHV-SEM, we can supplement the standard secondary electron 'pictures' with other surface analysis tools such as AES and RHEED. We can also use such techniques on a microscopic scale, for example, by analysing the layers and the islands separately in Stranski-Krastanov growth. The secondary electron (SE) signal is also surface sensitive, via changes in workfianction and other effects. Sub-ML sensitivity can be achieved simply by biassing the sample negatively to collect the low energy electrons which carry the contrast. An example of Ag deposited on W(ll0) is shown in Fig. 3, in which we see fiat, bright Ag islands which have grown on top of two Ag monolayers [16]. These 2ML can be made separately visible m biassed- SE images and in Auger line-scans, by depositing Ag past a mask edge. Auger spectra and linescans are useful in establishing the coverage of the first layer or layers, and the extent of lateral dif~sion [17].
Fig. 3. Biassed secondary electron image of flat Ag(111) islands growing (on top of 2ML of Ag) on W(ll0); 5ML deposit at R = 0.3ML/min at (a) T = 300~ and (b) = 400~ (c) Islands on a vicinal surface in the same experiment as (b); (d) thicker islands spanning multiple steps on facetted vicinal surface. From ref [ 16]. Several other in-situ microscopies have been developed, including Low Energy Electron Microscopy (LEEM), which produces surface sensitive images of growing crystals up to video rate [18]; examples are given here in the chapter by Bauer. UHV-TEM, UHV-ScanningTEM, and Reflection Electron Microscopy (REM) are also being actively developed and used in studies of vapour deposited samples [19]. A sketch of the capabilities of these techniques is given in [20].
2.3 Field ion microscopy Field Ion Microscopy (FIM) was the first technique to 'see' atoms of refractory metals on small terraces on a f'me tungsten tip. A major use of FIM is to study the migration of single adatoms and small clusters on individual terraces, and the interaction of such atoms with steps. Many interesting results have been obtained by the relatively few groups working in this field [10,11 ]. In particular, observations of linear rather than close-packed clusters, cluster diffusion, and adatom incorporation at steps by displacement mechanisms were all surprises when they were first discovered, and warn against us making over-simple assumptions. This work is discussed here in the chapter by Tsong and Chen.
10
2.4 Tunnelling and force microscopies The advent of STM and related spectroscopic techniques has had a dramatic effect on microscopic studies of surfaces, as explored thoroughly in subsequent chapters. After the first observations of surface reconstructions on Si(111) 7x7, and monolayer height steps, several groups have used STM to study the first stages of vapour deposition. These studies have revealed a wealth of detail, as illustrated in Fig. 4, for Ag deposited on Si(111)7x7 at room temperature [21]. This figure shows the underlying 7x7 structure, and a very high density (around 8 x 1012 cm 2) Ag islands of various thicknesses and shapes. The case of Ag/Si(111) is considered in more detail in Sect. 6. However, for now we should note that this picture represents a fairly extreme case of where kinetics is dominant in growing the film. First, the Ag has to break down the original reconstruction, since it would like to form its own (~/3x~/3R30 ~ surface reconstruction. But this doesn't occur rapidly below about 200~ so the Ag adatoms have lots of 'choices' to make. They can diffuse over the highly corrugated 7x7 surface, but will probably get trapped very soon. They can try to reconstruct the surface, but as more adatoms arrive, they will also want to cluster and form Ag islands. This concept of 'competitive capture' of adatoms is a useful unifying idea, which is elaborated in the next section.
Fig. 4. STM picture of 1/3ML Ag deposited on Si(111) 7x7 at room temperature. See text for discussion. From ref [21].
11 3. NUCLEATION AND G R O W T H THEORY This section describes an atomistic approach to the description of how clusters nucleate and grow on surfaces. The best case to consider initially is the island growth mode, where the critical nucleus size is small, and larger clusters have a 3-dimensional (3D) form. In this case all the rate-limiting processes occur on the original substrate surface. Later, we see how such approaches can be generalized to include the (2D) nucleation processes occurring in layer growth, and the (mostly 2D) processes which occur in Stranski- Krastanov growth.
3.1 Rate equations for cluster densities We follow the density of clusters containing j atoms, nj, by writing coupled differential equations describing the rate at which nj changes due to the various processes taking place on the surface. The simplest case is nl in the high temperature limit when only re-evaporation is considered. In this case, we can write dnl/dt = R - nl/'Ca,
(8)
and the solution, for times t >> "Ca,is simply n j = RT:a. If this is all that happens, nothing nucleates or grows on the surface, so we must consider additional processes. Just considering single adatoms to move, and all other clusters to be stationary, we find dnj/dt = Uj.,- Uj,
(9)
where Uj is the net rate of capture of adatoms by j-sized clusters. We may write Uj as the difference between a 'diffusion capture' tenn and a 'decay' term, Uj = ojDnlnj.l- nj(vdexp {-(AEj + Ed)/kT}).
(10)
Here, oj is a 'capture number', explained in section 3.2, and AE.i = Ej - E.i_~. If we substitute for the diffusion coefficient D from equation (2), and put U.i = 0 for all j < i, then by repeated application of equation (10) we obtain equation (7) for the density of i-sized clusters. This corresponds to the condition of local equilibrium between ni and n~. Equation (10) is a reminder that we need to be carefill about including 'back reactions' in our model, since failure to do so can result in inconsistencies with the thermodynamic limits. Equation (9) is also true for large clusters, but it is inconvenient to consider each individual atomic size in this case. We can therefore group clusters together, within a given size range, or even more drastically, lump all clusters j > i together as 'stable' clusters of density nx, resulting in dnx/d[ = Ui = oiDnlni.
(11)
12 The initial evolution of the nucleation density, nx(t), can therefore be obtained from the coupled equations (8) and (11) in the high temperature limit. A more detailed calculation of the cluster size distribution could be obtained from a more extensive set of coupled equations of the fonn (9). However, to be more realistic, we must include other processes. These include, at least, the loss of adatoms to growing clusters in (8), by diffusion capture and by 'direct impingement'. We also need to limit the cluster density in (11) by clusters coalescing. When these processes are included consistently, we obtain an equation for the maximum, or saturation, cluster density nx as a function of the experimemal variables R and T, and the energies introduced in the above equations, which can be compared with experimental observations [2,13]. With these processes included, the time evolution of n i and n~ is as shown schematically in Fig. 5. At high temperatures (Fig. 5a), nt is constant for t > T, as in equation (8), and nx increases linearly until coalescence sets m. The condensation coefficiem, i.e. the proportion of the impinging atomic dose which ends up in the deposit, ct(t), is initially very small. At low temperatures (Fig. 5b) when there is no re-evaporation so that ct = 1, n t increases linearly until it is limited by diffusion capture by the previously nucleated clusters, after a time ~. This is an example of'competitive capture' of adatoms, as described in the next section.
/.
log n
/
/
/
/
/..~..
log n
/
Rtcx
coalescence
/
n x
al.
I
I I I I Ta
a
1
log t
Tc
log t
b
Fig. 5. Evolution of the single-atom density (n~), the stable cluster density (n.0and the total number of atoms condensed (Rt) as a function of deposition time for (a) high temperatures and (b) low temperatures. The re-evaporation time x,, capture time x~ and the limitation of n~ by coalescence are indicated. From ref [2].
13
3.2 Adatom capture and regimes of condensation The processes considered in Fig. 5 can be visualised atomistically as shown in Fig. 6. Atoms arrive from the vapour. They may evaporate, but they may alternatively start the nucleation chain of small clusters. Once some stable clusters have been nucleated, this opens up another channel for loss of adatoms, namely diffusive capture by stable clusters. When these clusters cover a fraction, Z, of the substrate, then direct impingement from the vapour is also possible. These processes are introduced into the rate equations by writing dnl/dt = R(1-Z) - nl/'l;a -nl/7;n - nl/Tc.
(12)
The loss of adatoms during nucleation itself (r,,) is numerically negligible, so we may write the 'steady state' solution for n~(t) as nl = Rx(1-Z), with x -1 = Xa-1+ Xc-1+ ...
(13)
where the continuation ... means that we can consider adding other competing mechanisms, which will add like resistances in parallel. The loss of adatoms to stable clusters is characterised by "r~-1 = oxDn• and r = x,/Zc = oxDTanx,
(14)
where the capture number ~• is typically of order 5-10, as explained below. To complete the circle, we need a further equation to subtract the coalescence rate, U~, from equation (11), and to express it in tenns of Z. Using U~ - 2nxdZ/dt with dZ/dt given by all the cluster growth tenns in (13), and the shape of the clusters, then we can derive general expressions for the maximum cluster density [2,4,13]. Arrival
(R)
1 ~'~tt
,~Evaporat ion (T.,a)
9169
ni Fig. 6. Schematic illustration of the interaction between the nucleation and growth stages [ 13]. The adatom density nl determines the critical cluster density n~; however, nl is itself determined by the arrival rate R in conjunction with the various loss processes described in the text.
14 The nucleation density of 2D islands, n,,, is given by [13, equation 2.9] nx (g+ r) i (Z0 + r) = f (WD) i {exp (Ei/kT)} (tT~Dza)i+l,
(15)
where the (maximtun) density is limited by coalescence at island coverage Z0. For 3D islands, nx is replaced by nxx/2 on the left hand side of (15). For a given R and T, the critical nucleus size is that value which produces the lowest nucleation density, or nucleation rate, and is thus determined self consistently as an output, not an input, of the iterative calculation for all feasible assumed critical sizes. Equation (15) describes three regimes of condensation, within each of which (16)
nx--- (R/v) p exp (E/kT),
where the power laws p and energies E can be derived from (15), and are given in Table I for 2D and 3D clusters. In complete condensation re-evaporation is negligible, and r >> g, Z0, corresponding to adatom capture by an average stable cluster (suffix x) being much more probable than re-evaporation. In the extreme incomplete regime, growth by direct impingement is most important, with r, g 1. The transition from nucleation to no nucleation will be even sharper in this case. There are many other rate and diffi~sion equation treatments in the literature, which use slightly different non-linear terlns and botmdary conditions; some of these are given in refs [28]. In particular, Fuenzalida shows that one can solve numerically for the size and spatial distribution of clusters on the terraces, taking step motion into account consistently, for the case when both up- and down-steps are perfect sinks; Kajikawa et al. consider anisotropic diffi~sion. Depending on parameters, skewed cluster size and position distributions are produced; such effects may modify the constants in equations (20) and (21). The higher value of the concentration n~+ in equilibrium with a down- step is caused by the EhrlJch-Schwoebel [29] potential barrier to incorporation of such adatoms. At low temperatures when this barrier is effective, nuclei are formed on the upper terrace right up to the down-step. At higher temperatures, where the supersaturation is low, nucleation at the step edges is considered, as done by Roland and Gilmer [28], and at even higher temperatures, evaporation [30]. In heteropepitaxy, strain is also ilnportant, as considered by Ratsch et al. [28]. The question of the stability, or otherwise, of step motion in these various conditions has attracted a great deal of attention since the initial work of Schwoebel. Much recent work has been performed and reviewed by Villain and coworkers [30]. 3.4 Pattern formation: ripening and other effects In parts of the above discussion, we have asstuned that clusters with size j > i are 'stable', and that initial nucleation events, at least on large terraces, occur at random positions. These assumptions are good at relatively short times, but at longer times several subtle effects occur which modify our perception of what is going on, and of what is most important. As the deposition proceeds, and even more as the deposited film is left at elevated temperature for long times, a degree of 'self-organisation' asserts itself. Small differences in free energy can make themselves felt. Since this chapter is concerned with the early stages of film growth, we could reasonably ignore such effects, but it is perhaps better to indicate the link between the theory presented in this and subsequent chapters.
18 The film as deposited is rarely close to equilibrium, and it will therefore 'try' to approach such an equilibrium, albeit slowly. In the island growth mode, the equilibrium state is when all the deposited material is in one large island. The driving force to approach this equilibrium is the reduction in surface energy. Thus, for example, coalesence of two islands typically results in one island which reorganises its shape in an attempt to minimize its surface energy. Depending on the extent of (surface) diffusion around the island, the substrate will become reexposed. During the later stages of deposition, secondary nucleation may occur in the spaces, leading to various cycles of coalescence and re-nucleation [31 ]. A second example related to island growth can be seen in relation to Fig. 6. After the capture of adatoms by 'stable' clusters, the adatom concentration nl decreases with time as the rate of capture goes up, even though the typical effect via equation (14) implies a fairly slow variation. Thus, in this period, the critical nucleus size, i, increases, again slowly. This in turn means that clusters which were stable no longer are. The classical description of this effect is 'Ostwald Ripening' in which large clusters grow, and small clusters disappear, via exchange of adatoms. This process is likely to be important if the adatom density in equilibrium with the islands is high; this is the Gibbs-Thomson effect on the (2D) vapour pressure of the island, and depends on the island radius r, in contact with the substrate as nl~(r) = nl~ (1 + 27~/kTr),
(22)
where ~ is the atomic volume of the deposit, y is a suitable surface energy, which depends on cluster shape, and the density nl~, in equilibrium with a large island, is similar to nl~ in equation (19). This adatom density is governed by a (2D) evaporation energy, which is the difference between the sublimation energy L0 of the deposit and the adatom adsorption energy E,. When the transfer of atoms between the islands is diffusion, rather than interface limited, the rate of atom transfer between small and large islands is proportional to (n~D), and the activation energy for coarsening is simply (L0 - E~ + Ed). As noted previously [26], this is the same energy which governs the nucleation density when the lateral binding energy Eb is small, and hence the critical nucleus size is large. Incorporation of such effects into the description of nucleation processes is discussed by Zinke-Allmang [32]. The example of denuded zone formation at steps, discussed in the last section, is an example of pattern formation which is applicable to layer growth, and which has been observed in monolayer sensitive FIM and STM studies. There is also the possibility of exploiting steps, and artificially produced edges, to produce usefifl (linear) structures. Some examples of these types of pattem formation are described in the following sections.
19 4. ISLAND G R O W T H : METALS ON INSULATORS Many experiments have been done to test ideas about island growth, and to abstract energy values from a comparison of these experiments with the formulation presented in the previous section. Typically, they have used ex-situ Transmission Electron Microscopy (TEM) techniques to examine the deposit after preparation in UHV. In the case of the noble metal on alkali halides, which have been extensively studied [1-4,7,9], the island distribution is 'fixed' m-situ by evaporation of an amorphous carbon film. After removing the sample from the vacuum system, the substrate is dissolved in water, leaving the metal islands attached to the thin carbon film, which is then examined by TEM. 4.1 Ag, Au and Pd on alkali halides
A full review of early work on these noble metal systems has been given in ref. [2], where there is also an extensive tabulation of energy values deduced from experiment. For silver and gold, the adsorption energy, E~, of the atoms is in the range 0.5 - 0.9 e V, with the Au values somewhat higher than the Ag values, and errors for particular deposit- substrate combinations < 0.1 eV. These values are much lower than the binding energy of pairs of Ag or Au atoms in free space, which are accurately known, having values 1.65 + 0.06 and 2.29 + 0.02 eV respectively [33]. We can easily see from these values why we are dealing with island growth, and why the critical nucleus size is nearly always one atom. The Ag or Au adatoms re-evaporate readily above room temperature, but if they meet another adatom they form a stable nucleus which grows by adatom capture. Further experiments have been undertaken more recently to study the details of particular combinations. In addition to more accurate energy values, these experiments showed that several other surface processes can occur in addition to those considered explicitly in section 3. It is very difficult to tell, simply from looking at the TEM pictures, whether the nuclei form at random on the terraces, or whether they are nucleated at defect sites. The classic way to distinguish true random nucleation, with i = 1, is to check that the nucleation rate is proportional to R 2 at high temperatures when nl = R,a, as in equations (8) and (11). But there are several other possibilities, including the creation of surface defects during deposition, which might mimic this effect [2,9]. As substrate preparation techniques have improved, lower nucleation densities which saturate earlier in time have been observed. This has been associated with the absence of defects, and the mobility of small clusters. From detailed observations as a function of R,T and t, some energies for the motion of
20 these clusters have been extracted. Qualitatively, it is easy to see that if all the stable adatom pairs move quickly to join pre-existing larger clusters, then there will be a major suppression of the nucleation rate. Two further types of experiment are of interest. The first is the study of alloy deposits, which has now been perfonned for tluee binary alloy pairs, fonned from Ag, Au and Pd on NaCI(100) [34]. In such experiments the atoms with the higher value of E,, namely Au in Ag-Au, or Pd in Pd-Ag and Pd-Au, fonn nuclei preferentially, and the composition of the growing film is initially enriched in the element which is most strongly bound to the substrate. The composition of the films was measured by X-ray fluorescence and energy dispersive X-ray analysis, as shown for Ag-Au deposited at 300~ in Fig 8. The composition approaches that of the sources only at long times, or under complete condensation conditions. These experiments can be analysed to yield energy differences BE, where 8E = 8E,,, - ~SEy,and BE,,, BEy = (Ea-Ed)x,y for the two components. Values of 8E have been obtained for the pairs, namely Au-Ag: 0.11 + 0.03; Pd-Au: 0.12 + 0.03; Pd-Ag: 0.25 + 0.05 eV [34]. These experiments measure, very accurately, differences in integrated condensation coefficients, Ctx,y(t), which are determined by the diffusion distances (c.f. equation 3) of the corresponding adatoms.
I
-
Z
! 94
at.-%Au 80
'
60
at %Au
40 -
2O
.
.
10-8
.
.
.
1
10-7
..........
1,
10-6
,
,1 .
.
10.5
.
.
.
.
.
36
- 13 8'5
(gcm -2) 0
86
.
10-4
Fig. 8. Fractional Au content in Au-Ag alloys on NaCI(100), as a function of the total condensed mass per cm2. The compositions of the incoming atomic beams are shown on the fight-hand axis. RA~= 5.1013 atoms.cm2.s'l; RA, was varied; TN~c~= 573K. From ref [34].
21 Table II: Values (in eV) of E, and Ed of Ag, Au and Pd adatoms on NaCI(100) (abstracted from refs [9,34]. Values without error bars are derived from data combinations) Element/6E [34]
Ea
(Ea-Ed) 0.22
0.41
Ed 0.19
0.33 + 0102 [91
0.49 _+0.03 [9l
0.16 + 0.02 [91
0.45
0.78
0.33
Ag O.11 + 0.03 0.12+0.03 Pd 0.25 + 0.05 Ag
Coupled with nucleation density measurelnents, the data give particular values for E, and Ed for these three elements on NaCl(100), as given in Table II. A second interesting type of experiment concerns the interaction between nucleation on the terraces and on cleavage steps. A detailed analysis gave a value 0.23 + 0.03 eV for the binding energy of Au atoms to steps on NaCI(100) surfaces [35]. Studies of non-unifonn spatial distributions have been made, both on terraces and at steps, giving infonnation on cluster forces and mobility [36]. 4.2 Metals on oxide surfaces
Dispersed islands of specific transition metals oll various oxide surfaces are used as catalysts for a wide range of chemical processes. Studies of model catalysts are therefore of gTeat importance, and especially if microscopic observation is combined with gas reaction studies. A good example is the TEM study of the morphology of Pd particles grown on MgO, and the molecular beammass spectrometry study of the interaction of CO with these particles [ 15]. To make such a study quantitative, the shapes and size distributions were deterlnined as shown in Fig. 2. The Pd particles have (100) top faces, with different amounts of {111} and {110} inclined faces in contact with the substrate. The density, nx arotmd 3.10 ~ cm= is typical for deposition at T = 150200~ and the size distribution is characteristic of complete condensation, plus a small amount of coalesence. Surface diffi~sion around the islands is sufficient to form a polyhedral shape, but is low enough that coalesced islands remain elongated. The residence times of CO molecules on the Pd particles were determined as a ftmction of temperature, to deduce their adsorption energy. This value, 30.8 kcal/mole or 1.34 eV, was independent of particle size down to diameters arotmd 5 lUn, but rose sharply to around 1.6 eV for 2 nm particles.
22 Typically useful catalysts have particles in this smaller size range, and the adsorbing molecules can modify their geometry quite drastically during the life of the catalyst. In particular, the small metal particles can move and coalesce under the influence of the reacting gases, and the catalyst then needs to be regenerated, i.e. the particles needs to be redispersed to be effective again [37]. 4.3 Defect-induced nucleation on insulator surfaces
When the adsorption energy is small, the adatom concemration n~ call be extremely small even at moderate temperatures. In this situation, nucleation is a very unlikely evem on a perfect terrace, and nucleation at defect sites is likely to be dominaalt. Several examples of nucleation on defects have been demonstrated in the literature, for example Au deposited on mica, MgO, A1203 and graphite, and many examples of metals on alkali halides, as described in ref [2], section 3. Some of the earlier examples are discussed in more detail in ref [4], section C2. A defect nucleation model has been developed to explain recent high resolution UHV-SEM observations of the growth of nm-sized Fe and Co particles on various CaF2 surfaces, typically thin films on Si(111) [38]. In this work, the nucleation density, for Z0 = 0.2 close to the maximum density, was independent of temperature over the range 20-300~ This is not understandable if nucleation occurs on defect-flee terraces, but can be understood if defect trapping is strong enough. An equation for 3-dimensional islands oll defective substrates can be readily derived by considering the origin of the various terms in equation (15). The main effect of nt point defects (traps), with trapping energy Et, is to shift the balance strongly in favour of nuclemion on the defects. The right hand side of equation (15) is proportional to the nucleation rate (via the term in exp (Ei/kT)), which is enhanced by a ratio Bt = 1 + At with defects present. We can consider that local equilibrium will be established between adatoms oll the terraces (density nl) and on the defect sites (nit). The equilibrium which determines At has the form of a Langmuir adsorption isothenn, where we also take account of the clusters nucleated on traps (nxt) which block further adsorption. In the simplest case where the traps only act on the first atom which joins them, and entropic effects are ignored, we have At = A = nl exp(Et/kT), and nlt/(nt- llxt) = A/(1 +A), a high value of A gives strong trapping, in which almost all the sites unoccupied by clusters will be occupied by adatoms. However, this modification of equation (15) ensures that the defect processes are not linear. The clusters which form on the defect sites get established early on and thereby deplete the adatom density on the terraces. As a result, the overall
23
nucleation density, which appears in the left hand side of (15) grows only as a fractional power [typically 1/(i + 2.5) for complete condensation, see Table I] of the trap density. In this weak trapping limit, the main effect is the reduced diffusion constant D due to the time adatoms spend at traps. Nucleation on terrace sites is strongly suppressed, due to adatom capture by already nucleated clusters. But when n• > nt, there is little effect on the overall nucleation density. Comparison with experiments puts bounds on the energies Ea, El, and Et, all 1 eV, and suggests 0.1- 0.3 eV for Ea, as shown in Fig. 9(a), where the density llt = 0.01 ML, compared to perfect terrace nucleation in Fig 9(b). The latter case is assumed to be limited by an athennal mechansism at the observed density, but this 'explanation' is not convincing. The defect concerned is unknown, but is probably chemically specific (e.g. a fluorine vacancy), and is much less effective for Ag, whose nucleation density varies with temperature norlnally. These experiments [38] also fonned a usefid check on models of coalescence, which typically assume that the islands can rearrange instantaneously to the most compact fonn [31 ]. These models w e r e f o u n d t o be well obeyed for Ag, but not for Co and especially not for the Fe islands; it is clear that this ordering corresponds to decreasing surface diffusion coefficients. 300 200 ! ' i ,
14.5 / '
100 i
0 i"
'
Y(~
,
( a ) Traps /
N t-
300 200 , i , i ,
/
0.01
ME
100 i
0 i
,
T (~ '~
Ea=1.16
13.0
/
Eb--1.04
(b) e V / / ~
6
./''--
/
, .."/"
12.0
3ot
...... "
12.5 0.3 O. 12.0
t
11.5 ~
1.5
-
'
t
2.0
/
..""
0.2
11.o
0,~1 '
.-"
J
11.5
,,"
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10.5
E d values (eV) ,
I
2.5
,
I
3.0
,
I
3.5
,
i
4.0
,
I
4.5
,
I
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V) 1.5
,
,
2.0
2.5
I
3.0
I
3.5
1000/-I- (K) I
4.0
I
4.5
~
I
5.0
Fig. 9. Nucleation Density of Fe/CaF2 with Ea = 1.16 eV, Eb = 1.04 eV and Ed as indicated: a) in a defect trapping model, trap density nt = 0.01 ML and energy Et = 1 eV; b) on perfect terraces, with (arbitrary) limitation at 0.01 ML via athermal means. From ref [38].
24
4.4 Comparison with theory There is considerable scope for comparing energies deduced in these careful nucleation experiments with theoretical calculations of metal-insulator bonding. Several groups have used semi-empirical methods to obtain adsorption, diffusion and cluster mobility energies which have the right order of magnitude [39]; it is a considerable challenge to obtain answers which are accurate enough to detect the small variations indicated in Table II. Many interactions are very weak, hardly stronger than van der Waals forces. But the strong electric field over individual substrate ions reduces dipoles on the metal atoms, which can cause locally strong bonding, and thereby decrease the lateral binding energies between metal atom pairs. As these effects strengthen, we are following a path from physi- to chemisorption, and eventually this will lead to a transition to layer growth, which may occur for kinetic reasons before we reach the case of equilibrium layer growth. Such a case has been observed for Ag/MgO [40]; this kinetic effect can take place when the adsorption energy has an intermediate value, and the precise explanation is the subject of current work [41 ]. 5. LAYER G R O W T H : M E T A L & SEMICONDUCTOR H O M O E P I T A X Y The opposite case to island growth is layer growth. If there is a nucleation barrier, as there certainly is on a perfect terrace [2], then we have nucleation of 2D islands, followed by the completion of successive layers. In the simplest case, we might suppose that each layer is completed before the next one begins, but this would only happen if nucleation were extremely slow, and growth very rapid. In practice, therefore, there will a distribution of different heights over the surface, which corresponds to a surface which is more or less 'rough', typically for kinetic rather than thermodynamic [42] reasons. This roughness depends not only on diffusion over the terraces, but also on the mechanism by which the atoms can surmount energy barriers, and become incorporated at the edges of the ML-thick islands. Three examples, of monolayer sensitive experiments on metal, elemental and compound semiconductor homoepitaxy, are discusssed here.
5.1 Metal-metal systems Until the advent of the STM, it was very difficult to observe monolayer thick nuclei, except in special cases by REM and TEM, where high atomic number deposits were used [19]. A TEM example is shown in Fig 10 [7], where the Au ML islands have decorated the steps, and have also nucleated on the terraces.
25
33OC
N
0
.
5
~
0
N
I
81 ~
0.5 0 1
N 0.5 0 0
O.S
I
,--,__,_,_ o
k____
Fig. 10. Distribution of Au nuclei, in relation to steps on a Ag(111) surface, at the three temperatures indicated. The sense of the step train corresponds to the TEM image of the Au islands. Note that the up-steps are decorated with a continuous thin strip of Au, and what is plotted is the island position histogram on the terraces. From ref [7]. The accompanying diagrams show that the positions of the nuclei with respect to the steps have been measured, and that the island density peaks near the downsteps. This effect is temperature dependent in the range 33 - 105~ at the higher temperature, the down-step becomes almost as good a sink as the up-step, and the position distribution becomes more symmetric. This Au/Ag(111) system should approximate to Ag/Ag(111) within the first ML, but will of course show differences (e.g. interdiffusion, see section 6.4) at a later stage. This step effect has been implicated in Pt/Pt(111), where instead of the expected two regimes as a function of deposition temperature, originally seen by RHEED, four were actually seen by helium beam diffraction [43]. At the highest temperatures growth proceeds by step flow, with no diffraction oscillations. Next there is the expected transition to nucleation of monolayer islands on the terraces, m line with equations (20) and (21), which gives well defined oscillations. At lower temperatures, the oscillations disappear again. The authors associate such behaviour with a transition to a new kind of island growth, or a pronounced kinetic roughening, due to the retention of adatoms on the upper terraces, because of the potential barrier at the edge of the ML islands. At even lower temperatures, the oscillations characteristic of're-entrant layer' growth reappear.
26 Both FIM and STM studies have clarified what is going on in this case, and have also revealed an amazing degree of complexity, and a great variety of kinetic effects, operating within and on the first few ML of the deposit. Much of this work will be described in subsequent chapters; here we sketch some of the issues for Cu, Ag, Pt, Fe and Ni, summarizing Ed values obtained in Table III. First, there is the question of diffusion mechanisms. So far, we have tacitly assumed that surface diffusion proceeds via adatoms hopping from one site to the next, leaving the substrate unchanged. A series of FIM experiments [ 10] showed, via the use of 'site distribution maps', that hopping is norlnal for close-packed surfaces, but that it could be replaced by 'exchange' diffi~sion on more open surface planes. Thus for Pt and Ni(100), FIM has identified exchange diffusion by the fact that diffusion proceeds in directions rather than , and has a jump distance ~/2 times as long. As we shall see in section 6.4, homo- and hetero-epitaxy are very different: only in the former case is the substrate left unchanged by exchange diffusion. Second, adatoms on top of ML islands can fall over the edge to be incorporated into the first ML, in one of two ways. Either, they can jump over the Ehrlich-Schwoebel barrier, or they can displace atoms at the edge of the ML island, in an edge-specific maimer. In the case of fcc[ 111 } surfaces, there are two types of steps along , which have different displacement energies [44]. In the STM experiments on fcc{ 111 } surfaces, whole sequences of metastable ML island shapes have been discovered [44-46]. At the lowest temperatures, the edges of the monolayer islands are very irregular and the shapes become fractal; in this case gaps in the edge barrier become available. Coupled with the small size and close proximity of the islands, this results in the reappearance of a 'kinetically limited' layer growth at the lowest temperatures. Table III. Diffusion Energies from Nucleation and FIM Experiments Deposit Ag Pt
Substrate Ag(lll) Pt(lll)
Ea (eV) 0.10 + 0.01 0.26 + 0.02 0.25 hop 0.47 exchange 0.45 0.47 0.04 + 0.01 . 0.40 ,,,
Pt(100) i.
Fe Ni Cu
Fe(100) Ni(lO0) Cu(lll)
Cu(100)
,,,
Method, Reference STM, Brune [44] STM, Bott [46] VIM, Kellogg [10l FIM, Kellogg [ 10] STM, Stroscio [45] STM, Kopatzki [45] He, Wulfllekel [46] STM, Zuo [451
27 At successively higher deposition temperatures, other specific, crystallographic, edge mechanisms have been observed. The results serve as a reminder that the diffusion energy, Ed, is often very low, in the 0.1 eV range or less, so that it is impossible to suppress adatom diffusion at normal growth temperatures. The promotion of smoothness in epitaxial fihns via localized diffusion, 'downward funneling' and specific bonding geometries on fcc (100) surfaces is also important at high nucleation densities, and is discussed in refs [47].
5.2 Semiconductor homo-epitaxy The classic substrate for semiconductor growth is Si(100), since this has the simplest structure, and is the substrate used for growth of most practical devices. Typically device growers use a surface which is tilted off-axis by about 2-4 ~ to form a vicinal surface which contains a regular step array. The reason for this is precisely to promote step-flow growth, and to suppress randoln nucleation on terraces: nucleation is not wanted, because it increases the possibility of incorporating defects (e.g. threading dislocations) which have bad electrical properties! Si(100) has a basic (2xl) reconstruction, which arises from dimerization to reduce the density of dangling bonds. This reconstruction reduces the symmetry of the surface, and results in diffusion and growth properties which are very anisotropic, and alternate across single height steps (1ML - ao/4 = 0.13581un). Thus in general there are two orthogonal surface domains, and only surfaces with double height steps can give single domain surfaces. The steps are also rebonded in various ways, with two different single height steps, denoted SA and SB, which have very different step energies. In addition, for larger miscut angles, doubleheight steps are preferentially formed, and these may be more usefid for growing compound semiconductors such as GaAs on Si, since single steps produce antiphase boundaries, across which Ga and As are misplaced. Thus nucleation and growth on this surface is intrinsically quite complicated. Moreover, in principle, the dimer reconstruction has to be broken and reformed and redimerized as each layer is grown, so there can be nucleation barriers at many stages of growth. However, at nonnal growth temperatures (400-650~ dimerization is not the rate-limiting step. There have been several studies of Si/Si(100) growth, primarily using STM, in addition to spot profile analysis using LEED and RHEED. An example of the STM work, which shows many of the characteristic features, is shown in Fig. 11 [48]. In one detailed study, the nucleation density was observed as a function of R and T, and an analysis similar to that of section 3 performed, but taking into account the diffusion anisotropy, and the anisotropy in binding at the edges of the monolayer islands [49].
28
58 S B
SA
SA
.........
lOOnm
Fig. l 1. STM images of Si/Si(100) showing diffusional anisotropy of adatoms, and the effects of SA and SB steps, after 0.1 ML deposition at R = 0.15 ML/min and T = 563K (a) and T= 593K (b). The surface steps down from upper left to lower fight. In (a) anisotropic islands can be seen on all the terraces; the underlying dimer rows are orthogonal to these islands. In (b) diffusion is more rapid, so denuded zones are observed only on (2xl) terraces. From ref [48]. 714 10in
555
454
385
333
10 TM o v
Z
10 tt
10 TM ! /. 1.4
t 1.s
1/T
.
I.
I
2.2
2.s
.
Fig. 12. Nucleation density N(T) abstracted from STM images of sub-ML Si/Si(100) growth. From ref. [49].
z.o
(.lO-a K - t )
This N(T) data is shown in Fig. 12. The low temperature region, with a slope of 0.165 eV, is consistent with a critical nucleus size i = 1, and a d i ~ s i o n energy, m the 'easy' direction parallel to the dimer rows, Ed = 0.67 + 0.08 eV. At higher temperatures, there is a transition to a higher critical nucleus size, probably involving the breakup, and coarsening of, larger clusters into (stable) dimers, via
29 dimer motion. Subsequent work has shown that this system is indeed very complex; the Si(100) 2xl (and even more so the Si(111)7x7) surfaces are good examples of 'rugged energy landscapes', in which the difusion pathways themselves, and the measured activation energies, depend on temperature. In addition to these observations of nucleation on the (100) terraces, the expected nucleus-free, or denuded, zones next to steps are seen in Fig 11. In particular, the terraces to show denuded zones at lowest temperature have the (2xl) reconstruction, where the fast diffusion direction is towards the steps. In the case of anisotropic diffusion, the reduced dimensionality modifies the relation between diffusion coefficient and nucleation density; this detailed experimental work, and the burgeoning theoretical literature on the Si/Si(100) system, are discussed in the chapter by Liu and Lagally.
5.3 Compound semiconductors and other compounds The growth of compound semiconductors such as GaAs, by MBE and other tectmiques, has been reviewed many times [50]. Questions of layer growth versus nucleation on terraces have been addressed, as well as alloy segregation and pattern formation at steps. It is clear that the detailed atomic (diffi~sion-reactionincorporation) mechanisms are complicated, but calculations have developed to the point where the energies associated with the atomic and molecular kinetic processes can be studied in some detail [51]. Several groups have monitored the gaowth of GaAs in-situ using RHEED oscillations and a variety of light scattering techniques. Of particular interest in the present context are those studies which co~ielate surface and step stn~ctures observed by a microscopic teclmique, typically STM or AFM, with the real time monitoring teclmique. Of the many examples in the literature, one is illustrated here in Fig. 13. In panel (a), the starting buffer layer surface is shown in a large area STM scan containing a few steps in the 200x200 nln= field of view. Panel (b) shows a highly ramified step structttre after deposition to the point where the RHEED intensity shows its fourth maximum. Fingers of the upper terraces have grown out over the lower levels, the fingers being roughly perpendicular to the original steps. Similar data has been obtained at other doses, and the measured rouglmess correlated with the diffraction intensity [52]. Rough growth on wide terraces, for all the materials discussed in this section including GaAs, is caused by the Ehrlich-Schwoebel barrier [28,50,52]. As the strength of this barrier increases, straight steps become wavy, as illustrated in the calculation of Fig. 13(c); for larger baniers, well developed mounds are seen, as in panel (d). This is a fascinating example of pattern formation; in effect, the surface rearranges itself so that it Oust) creates conditions for step flow [52].
30
Fig 13. a) STM image of a GaAs buffer layer; b) after termination of growth at the fourth RHEED maximum. Scan range for a) and b) 200x200 mnZ; c) and d) Monte Carlo calculation after 50 layers deposition, original scale 200x200 sites2. Vicinal surface with slope = 0.1 in c), showing wavy steps, and on-axis surface in d), showing large mounds. Adapted from refs [52]. There is a substantial literature on epitaxial layer growth of other compounds, including alkali halides and rare gases [2, sections 5.1 mid 5.2], and oxides such as high temperature superconductors [37]. There is no space here to elaborate on such experiments and calculations, mid the reader is referred to the references quoted, and to the chapters on oxides in this volume, as a starting point.
31 6. LAYER PLUS ISLAND GROWTH EXAMPLES The Stranski-Krastanov, or layer plus island, growth mode occurs for many deposit-substrate combinations, including metals, semiconductors, gases condensed on layer compounds, and others. Indeed the name comes from a 1938 paper, in which the authors calculated, by doing the conesponding lattice sums, that the alkali halides MX condensing onto alkaline earth halides MX2 would grow in this mode [1,4]. Since then, the growth mode has been found to be very widespread. Here, three examples taken from metal, metal-semiconductor and semiconductor hetero-epitaxy are given in sections 6.1- 6.3; in section 6.4, the cases involving interdiffusion are described briefly. The competing processes are discussed, and some characteristic energy values are deduced.
6.1 Metal heteroepitaxy: Ag/W, Ag/Fe(ll0) and Ag/Pt(lll) The systems Ag/W(ll0) [16] and Ag/Fe(ll0) [53] have been examined in detail by UHV-SEM based techniques, as illustrated for Ag/W(110) in Fig. 3. In these systems, 2ML of Ag form first, and then flat Ag islands grow in (111) orientation. Ag/Pt(111) and related systems have been studied in detail by UHVSTM [44]. The nucleation density N(T) is a strong function of substrate temperature, and the results of several Ag/W(110) experiments are shown in Fig 14, in comparison with a nucleation calculation of the type outlined in sect. 3.2. The calculation derives from equation (15) and Table I in the following way. An assumption is made that the energy of the critical nucleus Ei can be expressed in terms of lateral pair-bonds of strength Eb, and that the important clusters, on top of the 2ML intermediate layer, are 2-dimensional, compact and quasihexagonal. Then, E~ can be expressed in terms of Eb by counting bonds. The critical nucleus size i is obtained self-consistently, by assuming a given value, calculating n• for that value, and repeating the calculation for all possible ivalues. The value which gives the lowest n~, or equivalently the lowest nucleation rate in equation (11), is the actual critcal nucleus size, since the cluster size with the lowest density (i.e. highest free energy) in equilibrium with the adatom population, then constitutes the 'nucleation barrier'. Condensation is complete in this system, except at the highest temperatures studied, and the critical nucleus size is in the range 6-34, increasing with substrate temperature. Energy values were deduced, Ea = 2.2 + 0.1, and the combination energy (Ed +2Eb) = 0.65 +_0.03 eV, within which Ed - 0.15 + 0.1 and Eb = 0.25-/+ 0.05 eV. STM studies of Ag/Pt(111) [44] obtained Ed values ~ 0.1 eV from N(T) data obtained at lower temperatures where i = 1.
32 T (K) 800 750 700
850
'
450
500
550
800
I
i
g.o
I
J 8.5
/
IO g
/ Los (N/Cm2)
108
8.0 7.5
/ 107
7.0
'
B. 5 B.O
N/Cm2
AS/W(110) Joneo ek o l .
(lggo)
T r i o n s l = s , ~,wo = a m p l e l
'oleon'
SClUOreo,
I = 34
Oiomondo,
5.5 I~!
1.2
-
I,.
1.4
,
!
1.8
l0 B
' oon~omlno~ed, o ~ e p p e d ' Spillar
I
1.8
........
Qk e l .
(1983)
I
I
2.0
2.2
,
IOOO/T ( I / K )
Fig. 14. Nucleation density N(T) from UHV-SEM images of Ag/W(110), with calculation for Ea = 2.1, Eb = 0.25 and Ed = 0.135 eV (full line) or 0.185 eV (dashed line). From ref. [16].
What, however, makes these values interesting is that they can be compared with the best available calculations of metallic binding. Comparison has been made with Effective Medium theory calculations, and the agreement is striking, as shown in Table IV. In particular, the results demonstrate the non-linearity of metallic binding with increasing coordination number. In the simplest nearest neighbour 'bond' model, the adsorption energy on (111) corresponds to 3 bonds, or half the sublimation energy for a fcc crystal. So for Ag, with L = 2.95 eV, such a model would give Ea = 1.47 eV, whereas the actual value is much larger. The same effect is at work in the high binding energy of Ag2 molecules, quoted in sect 4.1 in connection with island growth experiments. However, the last bonds to form are much weaker, so that in this case Eb iS much less than L/6 = 0.49 eV. This is a general feature of 'Effective Medium' or 'Embedded Atom' calculations on metals, which are finding wide application [44,47,54]. The results also demonstrate the important effects of strain in the SK growth mode. The Ag/Pt(111), Ag/1MLAg/Pt(111) and Ag/Ag(111) results show how sensitive Ed values are to strain, and probably, though not measured, to changes
33
Table IV. Ea, Ed and Eb for Ag from SEM and STM Experiments (Values in brackets are theoretical calculations, with references) Substrate 2 ML Ag/W(110) Ag(111) Pt(111) 1 ML Ag/Pt(111)
Ea (eV) 2.20 + 0.10 (2.23) [161 (2.94) [44]
g d (eV) 0.15+0.10 0.10 + 0.01 0.16 + 0.01 0.06 + 0.01
Ed +2Eb (eV) 0.65 + 0.03 (0.68) [161
Reference SEN [161 STM [441
in Ea between these systems. The comparison between Ag/W and Ag/Fe(110) shows that the first two layers are different crystallographically, with two distorted Ag(111)-like layers on W(110) [ 16], compared to a missing row c5xl structure for the first layer, followed by an Ag(111)-like second layer on Fe(110) [53]; but adatom behaviour on top of these two layers is very similar. There are still some curious features of these systems, including how the transition from 2D nucleation to 3D growth occurs, and the precise role of surface defects, including steps on such surfaces. The evidence to date is that the 2D3D transition occurs after nucleation is essentially complete, and that steps have a big effect on atomic motion within the first silver layers, but much less on top of these stable layers. The more perfect the substrate, the flatter the islands are. This is probably related to the difficulty of islands growing in height, without threading dislocations which may be generated at steps (c.f. Fig 3d and ref. [55]). Some effects in the first ML's of the related, but rather more reactive systems Cu and Au deposited onto W and Mo(110) have been studied by LEEM [56].
6.2 Metal/semiconductor systems" Ag/Si and Ge(111) These systems have been studied by many surface teclmiques, and by microscopy, including STM, as illustrated in Fig. 4 for growth of Ag/Si(111) at room temperature (RT) on the 7x7 reconstructed surface. Nucleation and growth of the islands has been extensively investigated in both systems by UHV-SEM [57-59] and STM [21,60]. At temperatures above 460 K for Si, and at RT and above for Ge, interlnediate layers with the (x/3xx/3)R30~ (called the x/3 structure for convenience), 4x4 and 3xl reconstructions are formed. The coverage of the x/3 layer, also studied by LEEM [61 ], has proved to be extremely controversial. One reason for the interest is that the metal-semiconductor interface is abrupt. Unlike other noble mid near-noble metals (Cu, Au, Ni, Pd and Pt) on silicon, there is no tendency for Ag and Si to intermix or form silicides, although Ge does dissolve to a small extent in Ag at high tempertaures [59].
34
In addition to nucleation and growth studies of the type described in the last section [57], UHV-SEM and AES techniques have been used to study the extent of surface diffusion, and the coverage of the intermediate layers. Diffusion can be studied by depositing the silver through a mask of holes, observing the width of the patch as a fimction of deposition and armealing treatments. Data for Ag/Si(111) is shown in Fig. 15a [58], and indicate that, using a 20 pm wide mask, there is a deposition temperature region around 750K where the observed width of a 'patch' with the ~/3 stnlcture is around 100 pm after a silver dose of 5ML. Diffusion distances of Ag on Si(111) 7x7 are very short, but diffusion distances on top of the ~/3 layer can be long, greater than 50 ~m. This is an almost macroscopic distance for an atomic process! Quantitative analysis of these results shows that at temperatures higher than this peak, the Ag adatoms diffuse rapidly, and also desorb, so that the measured diffusion length is just (Dz,) u2 in equation (3), and the temperature dependence gives (E~ - Ed) around 2.0 eV. However, at lower temperatures, the diffusion distance is limited by nucleation of islands and subsequent capture of the adatoms, as in equation (14). Similar data, taken both during deposition and amlealing, is available for Ag/Ge(111), which is more complex due to the low coverage 4x4 structure; the energies resulting from a comparison of both systems are given in Table V [59].
0.09 120
-.-
"9 R=0.43 x R=0.50 -...
110 co cO L. o
100
I
Eb=O. 10eV Eb=O.O5eV
ML/m[n
in
Ed=0.45 eV
0.07
90
-~
E 80 ,._i c~ 70
g
9
Eb=O.05 eV
0.06
0.05i
~-~0.04
~ 6O /~+ cO 5O 4_.1 121 4% 4O -~
O
",,,.~,.
8
• "'""-
X "'~"~'""'"'" "-..,..
•
I O00/T
(1/K)
0,03 0.02 0.01
X
........ I ......... I ......... | ......... i ......... i ......... i ......... i ....... ~'i ......... i ~........ i ......... 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65
a
E a = 2 . 4 5 eV
0.08
ML/.min
i
O.(X)
b
10
20
,30
40
50
60
70
80
90
100
pm
Fig. 15. Width of the ~/3 'patch' on Ag/Si(111) after at 5 ML dose through a 20 pm mask at various temperatures: a) experimental data at T - 700 K, showing a peak at around 770 K, with the patch width around 100 pm. Calculations for R = 1.41 ML/min, Ea = 2.45, Ed = 0.45 eV and Eb as indicated; b) calculated single adatom profiles during deposition, against patch width for dose increments 0 - 1/3 ML, for R and T as in (a). From ref. [58].
35 In these systems the critical nucleus size is quite large, of order 100 atoms in the temperature range considered, and this is associated with very low values of Eb < 0.1 eV. A calculation of the adatom concentration across such a patch as a function of dose is shown in Fig 15b, for the values Ea = 2.45, E d - 0.45 and Eb = 0.05 eV [58]. It can be seen that, for these values, the adatom concentration approaches 0.1 ML; the values are just sufficient to observe nucleation, in the centre of the patch only, at T - 700 K. Shifts in the parameters by + 0.05 eV will change this situation markedly; note that the upward curvature of the later curves indicate the re-evaporation is significant at this temperature. Isothermal desorption experiments have been used to measure the binding energy of the x/3 Ag/Si (111) layer (L3 --~ 3.05 eV), so that the ~/3 layer is more strongly bound than a silver island by about 0.1 e V, and than an adatom by around 0.6 eV, if Ea = 2.45 eV. These systems involve many aspects of competitive capture of adatoms: they can diffuse, evaporate, nucleate crystals, and also exchange with the intermediate (x/3, and 3xl, 4x4, and possibly other) layers. Fig. 4 shows that at RT, Ag islands form without disrupting the Si(111) 7x7; at T > 460 K, the ~/3 layer forms, but it has a coverage 0 < 1ML. At higher deposition temperatures > 650 K, 0 may approach 1ML, but above 800 K, this layer starts to desorb. The corresponding case of Ag/Ge(111) shows that many effects are similar to Ag/Si(111), but that the different starting reconstructions, and small differences in bonding make the comparison interesting. The details of the relatively subtle arguments outlined above are given in ref. [59]. Table V Energies from S E M N u c l e a t i o n - D i f f u s i o n E x p e r i m e n t s
Substrate ~/3 Ag/Si(111) /Ge(lll) 4x4 Ag/Ge(111)
a) Combination Energies from Experimem Ea-Ed (eV) Ed+3Eb (eV) L3-Ea4+Ed4(eV) 2.05 + 0.05 0.60 + 0.05 2.30 + 0.05 0.55 + 0.05 0.85 + 0.05
b) Individual Energies from Comparison with Model, with 0 4 - - 0.375 ML, v d - 1-2 Thz and L3 - 3.05 eV. Substrate Ea (eV) Eb (eV) Ed (eV) Ea4-Ed4(eV) ~/3 Ag/Si(111) 2.45 + 0.05 0.07 + 0.03 0.40 + 0.05 /Ge(111) 2.65 + 0.05 0.07 + 0.03 0.35 + 0.05 4x4 Ag/Ge(111) 2.20 + 0.05
36 Since we are dealing with kinetic processes, the history of the sample is important, and the balance between the competing effects can be shifted. For example, if the sample surface is defective, and nucleation is promoted, then we may expect that the ~/3 layer will not be completed when nucleation starts. The nucleation lowers the adatom concentration, which means that the driving force to complete the layer will be much reduced. This effect has also been seen for Ag on Si and Ge(100), where the layer coverage, measured variously between 0.25 and 1 ML, has both a thermodynamic mid a kinetic asw~t [21,57,62]. An asymmetry of this form between the adatom concentration during deposition and annealing is most marked. With the values given here, the adatom density during annealing (equation 22) is -~ 100 times less than that present during deposition (Fig 15b) for Ag/Si(111) at T = 700 K. The extra 0.25 eV in the combination energy (Ea-Eo) for Ag/Ge(111) is similarly associated with much faster annealing than for Ag/Si(111). Some of the conclusions in Table V can be reached directly from experiment, while others depend to a greater or lesser extent on the details of a rate-diffusion model, in which the equations presented in section 3 are supplemented by a diffusion term; the resulting equation is then integrated over a 1-dimensional grid. Rather than oversimplify this approach in the space available here, we refer the reader to the original literature [58, 59].
6.3 Semiconductor hetero-epitaxy" Ge/Si(100) In the above Ag/Si(111) example, the intermediate layer was a maximum of 1ML thick, has a quite different structure than either the substrate or the deposit, and should perhaps best be regarded as a monolayer compomad. At the other extreme, Ge on Si has the same structure, differing only in the lattice parameter by 4%, with the Ge slightly less strongly bound. This can be seen in the measured sublimation energies, L = 3.85 + 0.02 and 4.63 + 0.04 eV/atom, and in the binding energies of the diatomic molecules, 2.63 + 0.1 mad 3.21 + 0.1 e V for Ge2 and Si2 respectively [33]. Thus, the surface energy of Ge is expected to be lower than that of Si, and deposition of Ge will first occur in the form of layers. However, growth beyond the first few ML will build up substantial strain due to the 4% mismatch, and after a certain thickness, the Ge would prefer to grow as islands in which the strain has been relieved by misfit dislocations [see ref. 4, chapters 7 and 8]. The route to this state is quite complicated, but can be understood qualitatively by reference to Fig. 1a. The equilibrium Ge layer thickness has been measured, after annealing, to be 3ML [63-64]. But it is possible to grow much thicker coherent layers kinetically, or by using a surfactant; the first islands to form are also coherent with the underlying layers, not dislocated [65].
37 This can be seen in TEM pictures, taken ex-situ after UHV preparation, as shown in Fig 16a. The strong black-white contrast is due to the bending of the substrate (Si) lattice caused by the Ge island, and indicates a radial strain, which also has a component normal to the substrate [64]. At deposition temperatures above 500~ where surface diffusion is rapid, the size to which these coherent islands grow is markedly dependent on the presence of other sinks within the diffusion distance. Dislocated islands can be nucleated, prefentially from the larger coherent islands, or at impurity particles; once nucleated these islands form the strongest sinks, they grow rapidly and the supersaturation in the (0 > 3ML) Ge layer reduces. At a temperature of 500~ diffusion distances are of order 5 ~tm, whereas below 400~ this figure drops below 0.5 ~tm. An example of a facetted, dislocated island is shown in the UHV-STEM images in Figs 16(b) and (c). Similar effects are seen when Ge films, grown at RT to thicknesses above 3ML are annealed at comparable temperatures, although the detailed mechanisms and diffusion coefficients will be different. Fig 16(d) shows a series of size distributions taken at different annealing times at T = 375~ [64]. Initially, there are no large (> 10nm radius) islands, but as annealing proceeds the bigger islands grow rapidly, while the size distribution of the smaller islands (< 10nm rad.) stays constant. This evidence suggests that the material for the rapid growth of the dislocated islands occurs primarily from the supersaturated layer rather than from the coherent islands; in particular, their strain fields are effective in keeping out migrating adatoms [66]. Interest in SiGe alloys, in the form of superlattices, is high for optoelectronic applications. There is a large body of data on the structures of, and strain and defects in, the various layers; the references quoted here give a lead into the literature, mainly on mono- and few-layer level structural effects. Ge/Si(100), Si/Ge/Si(100) and (111), and the alloys have all been studied by STM, AFM, TEM and diffraction techniques [67, 68], and compared with the layer growth system Si/Si(100) [49]. These systems start out by 'looking' the same, but as growth proceeds, they have to diverge. The driving force is the need to expand the surface to accomodate the larger lattice parameter of bulk Ge; the initial structure may be a fine scale 'tippled' surface, leading to the formation of 'quanttun dots' [69], arrays of missing dimers [70], and/or an intermixed Ge/Si surface layer [71]. Various 'kinetic pathways' to the evolution of the final film have been identified, such as the 'hut clusters' illustrated in Fig 17 for Ge/Si(100) [67]. The kinetic processes may also be influenced by surfactants which have been added to prevent islands forming, i.e by less strongly bound atoms which 'float' to the surface during the (layer) growth process.
38
L
-~v
I. . . . .
25 ~ ~ 10~~
K
5 minutes
J................. 10 minutes ~'~
I..... "-- 20 minutes ~%, J'":"' ....... 4 0 minutes ~./J',"""" 120 minutes
.
r~.~
~===,1,
~N
RADIUS 0 ~l -----~
5
10
15 (NM) *
i
9 -
" ....
Fig. 16. Island formation in vicinal Ge/Si(100): a) ex-situ bright field TEM image, showing coherent islands. The strong black-white contrast parallel to the reflection g = 220 indicates a radial dilatational strain field: b) UHV-SEM and c) -STEM images of a single dislocated island, showing b) facets and c) moire fringes indicative of misfit dislocations; d) island size distributions on annealing a 5ML RT deposit to 375~ for the times indicated. From ref [64].
39
"
...................... "
100
"
. . . . . . . . . . .
"
lOnm
Fig. 17. STM images of the so-called 'hut clusters', which are formed in Ge/Si(100) between the islands seen by SEM/STEM (cf fig 19): a) top view; b) perspective view, showing the facets, identified as {510} type planes. From ref[67].
6.4 Metallic systems involving interdiffusion Many metal-metal deposition systems should follow the island growth mode, if the surface energy of the deposit is greater than that of the substrate. Since surface energies are strongly correlated with cohesive energies, the islands of the strongly bound material, once formed, could lower their energy by allowing themselves to be coated with a thin skin of substrate material! This corresponds to a curious form of interdif~sion, m which islands or layers, rather than single atoms, bury themselves m (i.e. burrow into) the substrate. At low temperatures this will not happen, because the substrate atoms will not diffuse. However, recent STM studies of surface steps on noble metals have shown that steps can move quite rapidly, even around RT. It is now fairly clear that the difficulties various groups have experienced in producing well-defined thin films of magnetic metals (Fe, Co, Cr, etc) on noble metal surfaces (Cu, Ag, etc) is related in some way to effects of this nature. Not only do such magnetic metals have higher surface energies, in general, than the substrates, but they also undergo structural phase changes with increasing thickness. Classical surface science techniques have been extensively applied to these systems, and microscopic studies are beginning to unravel the competing effects [72]. A case which has been studied recently by STM is Ni/Ag(111) [73]. Here Ni can both diffime by hopping over the surface, or, at higher T, can exchange with an Ag atom and become embedded. This immobile Ni atom now acts as a nucleus for further growth of Ni clusters. In a fixed deposition T experiment, this corresponds to creation of nuclei at a rate proportional to the adatom concentration, and, if the Ni-Ni bond is strong enough, to i = 0.
40
The temperature dependence of nx should enable both Ea and the energy for Ni-Ag exchange to be extracted via a quantitative model. Similar cases are Fe/Au (111), with a complex surface reconstruction, which orders the Fe crystals [74], and Fe/Cu(100), where subsurface and surface ML islands can co-exist [75]. Size distributions of clusters nucleated on these defects have been studied by KMC; a broad distribution is obtained, with a large proportion of small islands [76]. All these cases, both semiconductor (Si/Ge/Si or equivalent) and metallic (Fe/Ag/Fe or equivalent) take us back to Fig. 1, and the difficulty of making high quality multilayers from A/B/A systems: if one interface is 'good', typically an example of SK growth as described in this section, then the other interface is 'bad'. these systems may formally be an example of island growth, but active participation of the substrate makes this classification too naive at elevated temperatures. Nuclei form by exchanging deposit and substrate atoms; clusters of deposited atoms start to form, and then tend to get covered by a substrate 'skin'. Once one realises what is happening on a microscopic scale, the evidence is there clearly in the classical surface science results, e.g from AES as shown in Fig 18. In this case, the Ag signal in panel (a) breaks at 0.8 and 1.8 ML [53], and the Ag/Fe Auger ratio in panel (b) follows the layer growth curve initially, but breaks away from it between 1 and 2 ML at RT, and recovers further on annealing [77]. 1.0 ca') o._.
r-
9, ,
I ....
I ....
I ....
i ....
I*'"'1
....
1 ....
I ....
! ....
(1,} . m
R T deposition
9
250~
0.8
=,
Annealed to 2 5 0 ~
0.6
,~~_~_~_
Annealed to 3 0 0 ~ Auger layer calc.
t--"
t~
c:
to
- -
.
c--
O
r-"
0. This is the justification for neglecting upward diffusion in kinetically controlled homoepitaxy. If, however, the step-edge barrier vanishes, the barrier for upward diffusion is equal to the barrier for evaporation of an atom attached to the lower side of the step. In this case, step-up diffusion needs to be considered if evaporation of atoms from step edges is active on the time scale of the growth experiment. 2.3 G r o w t h m o d e s of a r e a l s y s t e m The step-edge barrier introduced in the previous section plays a key role for the understanding of the different growth modes far from equilibrium because it controls the amount of interlayer mass transport. It is, however, not straight-forward to quantify the influence of this barrier on the growth behaviour. The only case where this is possible without further thought is the case of an infinitely high barrier which obviously leads to ideal multilayer growth. The opposite case is not true: a vanishing barrier does not lead to ideal layer-by-layer growth. As we will see in this section, nucleation on a layer takes always place before the layer is completed. This deviation from the ideal behaviour has the consequence that, after deposition of many layers, any surface will eventually grow rough. Therefore, a simple qualitative distinction between growth modes is impossible for real systems: strictly speaking, there is always multilayer growth, and it is only the amount of roughness which makes the difference. A meaningful definition of growth modes for real systems must therefore be based on a criterion that quantifies the amount of interlayer mass transport or the film roughness and classifies the growth behaviour according to these quantities. It is clear that there are different possibilities for choosing such a criterion. In this work we will use a submonolayer criterion to classify the growth and to define different growth modes. The amount of interlayer mass transport is quantified by the (critical) coverage 0c at which nucleation on top of growing islands begins; and the different growth modes are defined by comparing this quantity to a certain fixed value. For this value we choose the coverage 0coal at which the islands coalesce to form a connected layer. This quantity is typically between 0.5 to 0.8. We will call the growth mode two-dimensional (2D-growth) if:
73 0 C ) Ocoal
(1)
and three-dimensional (3D-growth) if OC < Ocoal 9
(2)
This definition is motivated by the fact that for conventional homoepitaxy, nucleation on top of the growing layer m u s t take place shortly after coalescence as outlined below. Note, t h a t this definition possibly leads to a different classification of growth modes t h a n a definition based on a quantitative criterion (e.g., the n u m b e r of uncovered layers) after deposition of many monolayers. However, our definition has the advantage that the critical coverage for secondlayer nucleation in the submonolayer regime can be calculated quite easily because it depends only on a single characteristic length scale which is the average island separation. We will now illustrate the problems encountered in defining growth modes for real systems by following the growth of an atomic layer in time for the case of a vanishing step-edge barrier. The initial stages of monolayer growth are characterized by the nucleation process: the deposited atoms diffuse across the surface until they meet and form nuclei. After some time, a saturation density of stable nuclei is reached: the formation of new nuclei ceases when the n u m b e r of stable nuclei is large enough so t h a t the probability of an adatom to attach to an existing nucleus is greater t h a n the probability to form a new nucleus. After saturation has been reached, the film consists of a constant number of islands which grow in size as new material is deposited onto the surface. This is equivalent to the s t a t e m e n t t h a t every atom deposited in between islands can travel a distance of at least half the average island separation before forming a new nucleus. As saturation is reached at low coverages the separation of islands is to a good approximation equal to the average distance between island centres: hence, an adatom on top of an island has a m e a n free path high enough to reach the island edge. Therefore, if nothing prevents the adatom from jumping over the island edge, no nucleation should occur before coalescence. However, at the onset of coalescence, the characteristic length scale suddenly changes. The islands merge to form areas which are larger t h a n the average distance between nucleation centres. Hence, second-layer
74 nucleation is expected to occur some time after the onset of coalescence. A different argument leads to the same conclusion that, even in the case of a vanishing step-edge barrier, nucleation on top of a layer must take place before layer completion. It is assumed that some time after coalescence a connected layer has formed with two-dimensional holes. Because there is no step-edge barrier the step edges bordering these holes are sinks for adatoms on top of the incomplete layer. As long as the holes provide a sink density large enough to decrease the adatom density below a certain threshold value, nucleation is suppressed and the holes are filled. But as the number of holes, and hence the sink density decreases, nucleation must set in because of the same reason that explains the existence of a saturation density of nuclei in the early stages of monolayer growth: if nucleation on the substrate ceases when the number of stable nuclei (i.e., the density of sinks) has reached a certain value, it must start on top of the incomplete layer when the number of vacancy islands has decreased below a threshold value. The question at which coverage second-layer nucleation exactly starts in the case of a vanishing step-edge barrier is difficult to answer because the structure of the connected layer close to monolayer completion is harder to characterise than the structure of the layer before island coalescence. The (practical) definition of growth modes given above (equations (1) and (2)) circumvents these problems by choosing the coverage at which coalescence sets in as the dividing line. Before we discuss in detail the dependence of growth modes on the deposition parameters, i.e., substrate temperature and deposition rate, in detail we note that on the basis of the simple picture of submonolayer growth developed in this section, we can already make a couple of general statements. First, in the absence of a step-edge barrier one should have 2D-growth (according to our definition) independent of the deposition parameters, as no explicit parameter dependence was used in the arguments above. Second, as the occurrence of second-layer nucleation during early stages of growth is caused by a significant (reflecting) effect of step-edge barrier, one expects that a transition from 3D- to 2D-growth should occur with increasing substrate temperature which increases the transmission factor at the step edge. In the next section we will see that these general statements can be derived from a rigorous theory.
75 2.4 D e p e n d e n c e
of growth
modes on deposition
parameters
From our definition of growth modes it is clear t h a t calculating the dependence of growth modes on the deposition parameters is equivalent to calculating the parameter dependence of the critical coverage 0c at which nucleation on top of islands sets in. In this section we determine 0c by assuming circular islands and a steady-state adatom density profile on top of the islands. This t r e a t m e n t follows the approach of Stoyanov and Markov [15] and Tersoff et al. [16] who calculated a critical island radius for second-layer nucleation for special cases of small and high step-edge barrier. The steady-state diffusion equation with boundary conditions at the island edge (Neumann conditions, i.e., the flux across the island edge is specified with respect to the transmission factor s) is solved to obtain the adatom density on top of the growing island. From the adatom density, the average nucleation rate ~ on top of islands is calculated using standard nucleation theory [17]: ~2-
f
r
o~ 92~r'dr'
(3)
0
where r is the island radius, and co is the nucleation rate given by the Walton relation [18]: co- Ci nl i+l, where nl is the adatom density and Ci a factor depending on the size i of the critical nucleus. In the following, we will use dimensionless quantities for all lengths and densities, i.e., lengths are expressed in units of the lattice constant and densities (adatom and island density) in units of the density of lattice sites. Equation (3) is evaluated to yield [19]: --
oi 2 [(r 2 + r/2s )
~'(~iei 9 x 4 ( i + 2 ) ---~" 9
--
i+2 - [ r / ~
'-'2s'i+2
1
(4)
n 0
where s is the transmission factor introduced above, (~i is the capture number of the critical nucleus, nx is the saturation density of nuclei which is given by [17]" i
n x-n
o .ex
(i+2)kT
"
"
(5)
76 Here, E i is the binding energy of the critical cluster, R the deposition rate (in ML/s) and v d the diffusion frequency. The factor no depends on the critical island size and contains capture numbers. Moreover, we define an average island separation ~ by ~=l/~/nx. The critical coverage 0c is defined by the onset of second-layer nucleation, i.e., by the condition that a certain fraction f of the islands on a surface have nucleated an island on top. This fraction is given by:
f-1-exp(-~:~
) .
(6)
We will choose a fraction of f = 0.1 in the following to define the onset of nucleation. The integral in equation is evaluated to yield a relation between the critical coverage and the deposition parameters. One obtains a general solution of the form: F(0c) -
0c 0
~i+3
i+l
~2 dO - a ( i ) . , c "~k:o
bk(i). (s" ~)-k 9Ock/2 ,
(7)
where a(i) is a factor which depends on capture numbers and the size of the critical nucleus [20], whereas the coefficients bk(i) (0420) 77 80 - 5 0 0 300 100 - 5 0 0 300 - 480 300 100 - 5 0 0
r a n g e [K]* 3D-growth
2D-growth
210- 227t -
s t e p flow
Method
Ref.
200-480 77 170, 3 0 0
> 480 -
RHEED RHEED SPALEED
[32] [6] [33]
1 0 0 - 500 300 300 227- 420 77 80 - 4 0 0 300 100 - 4 3 0 300 - 4 8 0 300 100 - 4 5 0
> 500 > 420 > 400 > 430 > 450
TEAS X-rays STM TEAS RHEED TEAS X-rays TEAS RHEED STM LEED
[30] [34] [35] [36] [6] [37] [38] [31] [39] [40] [41]
* The t r a n s i t i o n t e m p e r a t u r e s given are a p p r o x i m a t e v a l u e s for a fixed deposition rate. T h e t r a n s i t i o n to step flow d e p e n d s on t h e step density, it is not an i n t r i n s i c p r o p e r t y of t h e crystal surface. Definition of 3D- (2D-) growth: absence ( a p p e a r a n c e ) of i n t e n s i t y oscillations for diffraction m e t h o d s ; for real-space m e t h o d s : second-layer n u c l e a t i o n before (after) coalescence. t This e a r l y r e s u l t could not be r e p r o d u c e d by o t h e r groups.
step-flow growth) is observed for the entire temperature range studied. Obviously, it is a general trend of fcc(100) metals to grow smoothly. This means, that the interlayer mass transport for these systems is quite effective, pointing to a low or even vanishing step-edge barrier. This behaviour is remarkably different from that of fcc(lll) surfaces as we will see in the next section. A striking characteristic of the growth of the fcc(100) surfaces is the fact that oscillations are present at the lowest temperatures where thermal diffusion of adatoms is hardly active. Moreover, even at these low temperatures, islands with characteristic sizes of several lattice spacings develop. To explain this puzzling phenomenon, several mechanisms have been suggested, which are related to the
84 dynamics of the deposition process. Egelhoff and Jacob suggested that a "deposited atom uses its latent heat of condensation to skip across the surface, preferentially coming to rest at growing island edges, to achieve quasi-layer-by-layer growth" [6]. For metal surfaces, this mechanism (transient mobility) could not be found so far for deposition onto a flat terrace, neither by molecular dynamics calculations [42] n o r by a detailed analysis of the spatial distribution of deposited atoms in FIM experiments [43]. There are, however, calculations which show that deposition of atoms close to step edges might trigger an exchange process (cf. Figure 3) which transports the atom into the lower layer and hence promotes interlayer mass transport even in the absence of thermal mobility [44]. Another process which promotes interlayer mass transport in the absence of thermal mobility was proposed by Evans et al. and termed "downward funnelling" [7]. This process is a natural consequence of the solid-on-solid condition for a real crystal for which the stacking sequence is not simple cubic. Because of the real stacking sequence, the edges or sides of islands are microfacets of finite width, and atoms deposited onto these edges are thought to slide down the microfacet to the lower layer. However, the true origin of the significant interlayer mass transport at low temperatures remains an open question. Also the formation of characteristic length scales of several lattice constant in the absence of adatom mobility is a matter of ongoing debate. Recent Monte-Carlo simulations suggest that island structures develop even in the absence of single adatom diffusion (both thermal and transient) if local rearrangement of connected island atoms is active [45]. 3.2 H o m o e p i t a x y on fcc(111) m e t a l s u r f a c e s At first sight, the growth of fcc(111) metal surfaces shows a greater variety than that of (100) surfaces. This is illustrated by Figures 9 and 10 which show deposition curves obtained during growth of Pt(111) and Ag(111). For Pt(111) several growth regimes are observed" below step flow there is a regime of layer-by-layer growth, characterized by long-lived oscillations, followed at lower temperatures by a regime of multilayer growth (monotonically decaying signal). At even lower temperature one finds is a regime of r e - e n t r a n t layer-by-layer growth with damped oscillations, but still of relatively high amplitude. The Ag(111) surface, on the other hand,
85 shows a different behaviour: below step flow one observes nothing but multilayer growth. These different growth modes of Pt(111) and Ag(111) have been observed by many groups. The first experimental results on P t ( l l l ) were obtained by of He-scattering [46,28], and meanwhile the existence of the different growth regimes has been confirmed by STM [47] and electron diffraction (SPALEED) [48]. Also the growth of A g ( l l l ) has been studied by both real space methods (electron microscopy, STM) and diffraction methods (RHEED, X-ray scattering, LEED, and TEAS), see Table 2. All these studies support the existence of multilayer growth below the transition temperature for step flow. First results on a third system, Cu/Cu(lll), made the situation even more complicated, because conflicting results were found. Henzler reported a behaviour qualitatively similar to that of P t / P t ( l l l ) : pronounced LEED oscillations indicating layer-by-layer growth at a high temperature of 370 K, a regime of multilayer growth at intermediate temperatures, and weak reentrant layer-bylayer growth at low temperatures, although the low temperature oscillations were of very low amplitude (less than 0.5 percent of the initial intensity) [48]. On the other hand, Dastoor et al. using TEAS, observed a behaviour completely similar to that of Ag(lll): no oscillations at all below step flow [49]. The discrepancy in the low temperature regime might easily be explained because of the different diffraction techniques used: very shallow oscillations during growth of small structures can be suppressed in the case of TEAS because of its high sensitivity to diffuse scattering. The conflicting results at high temperatures, however, could not be explained by the different techniques used. Additional studies using X-ray scattering [50] and TEAS [51] both supported the results of Dastoor et al., the oscillations reported by Henzler could not be reproduced, and hence, there is overwhelming evidence that the growth behaviour of C u ( l l l ) is identical to that of Ag(111). The general trend emerging from the studies reported so far is that growth on the fcc(lll) metal surfaces is much rougher than that on fcc(100) surfaces. Multilayer growth is either observed in a finite temperature window as in the case of P t ( l l l ) , or in the entire temperature regime below step flow as in the case of A g ( l l l ) and Cu(lll). This picture is further supported by preliminary results on Ni(111) [62]: STM scans of a Ni film grown on Ni(111) at room tem-
86
1.0
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I/Io 0.5
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621 K
0.5
900 K 0.0
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400
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271 K
0.5
0.0 0
0
400
135 K
O.5
200
400
0.0 0
200
..... 4(~0
deposition time (s)
Figure 9. Anti-phase deposition curves obtained by He-scattering during growth of Pt/Pt(111) at a deposition rate of 0.02 ML/s [46, 28, 52].
I/Io 0.5
1.0
1.0
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0.5
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OOo
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.0
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- --
----~-
9
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deposition time (s)
Figure 10. Anti-phase deposition curves obtained by He-scattering during growth of Ag/Ag(111) at a deposition rate of 0.01 ML/s [58].
87 Table 2 E x p e r i m e n t a l s t u d i e s on fcc(111) m e t a l surfaces T e m p e r a t u r e r a n g e [K]*
Pt(111) Pt(111) Pt(lll) Ag(lll) Ag(lll) Ag(lll) Ag(lll) Ag(lll) Ag(lll) Ag(lll) Ag(lll) Ag(lll) Cu(lll) Cu(lll) Cu(lll) Cu(lll) Ni(lll)
studied
3D-growth
100 - 900 200-800 130-750 300 200 - 780 1 7 5 - 575 300 100-600 130-200 220, 300 300 1 5 0 - 315 1 7 0 - 370 110-400 1 2 5 - 375 100-450 310
340 - 470 350-480 3 0 0 - 450 300 see footn.* 1 7 5 - 525 300 100-450 130-200 220, 300 300 1 5 0 - 315 200-300 110-350 1 2 5 - 375 100-420 310
2D-growth 525 X-rays STM > 450 TEAS SPALEED SPALEED STM RHEED SPALEED > 350 TEAS X-rays > 420 TEAS STM
>800 >700 > 700 -
-
< 190, 3 7 0 t
Method
Ref. [46,52] [47,53] [48,54] [55] [32] [56] [57] [58] [59] [60] [29] [61] [48] [49] [50] [51] [62]
* The transition temperatures given are approximate values for a fixed deposition rate. The transition to step flow depends on the step density, it is not an intrinsic property of the crystal surface. Definition of 3D- (2D-) growth: absence (appearance) of intensity oscillations for diffraction methods; for real-space methods: second-layer nucleation before (after) coalescence. ** The transition temperatures for 2D- and 3D-growth given here are based on a different criterion: a constant "growth number" after deposition of 5 ML [53]. This characteristic parameter is zero for 3D- and unity for 2D-growth [53]. The transition temperatures given here correspond to a value of the growth number of roughly 0.8. With this choice, the transition temperatures defined by the onset of He-intensity oscillations are reproduced. + "intensity oscillation has not been observed in the temperature range examined" [32] t This result is based on two measurements at a single temperature, it could not be reproduced by other groups [63].
perature show a rough film morphology, strikingly similar to that observed in STM work on Ag(lll) or in the multilayer regime of Pt(lll).
88 This general picture is further supported by the fact that the different behaviour of the P t ( l l l ) surface is due to a peculiarity of this surface which os not observed for the other fcc(lll) metal surfaces discussed. The high-temperature layer-by-layer growth regime is caused by an unusual effect: the reconstruction of the growing surface layer during deposition of Pt [64,65]. In the absence of this reconstruction, multilayer growth is observed. Therefore, P t ( l l l ) can be viewed as an exception from the general rule of multilayer growth of fcc(lll) metal surfaces, caused by special aspects of the Pt surface. In the next section we will describe the growth of P t / P t ( l l l ) and the origin of its different growth modes in more detail. 3D-growth is a result of limited interlayer mass transport, and hence the fcc(lll) surfaces must be characterized by a significant step-edge barrier opposing step-down diffusion in contrast to the case of the fcc(100) surfaces discussed in the previous section. The difference is presumably caused by fundamentally different mechanisms for step-down diffusion of the two types of surfaces. We will address this issue in further detail in section 3.4.
3.3 A special system: the growth of Pt/Pt(111) The Pt/Pt(111) system is the homoepitaxial metal system studied in greatest detail to date. As already clear from the previous paragraph it shows a variety of phenomena which are worth to be discussed although these phenomena might peculiarities of this particular metal. This subsection is devoted to a closer inspection of these aspects. Figure 11 is a summary of all the results obtained with He-scattering in our group. Each point in this mode diagram corresponds to one deposition experiment, its location in the diagram is determined by the deposition parameters used, i.e., substrate temperature and deposition rate. The data are classified according to the criterion discussed above, i.e., the appearance or non-appearance of oscillations, no matter how pronounced these oscillations are. Because of this classification, there appear sharp boundaries separating the different growth regimes although the transition between the growth modes is smooth. These boundaries are indicated by the dashed lines which serve as a guide to the eye. Note, that there is some scatter across the line separating the high-temperature layer-by-layer growth regime from the step-flow regime. This scattering is expected: the
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Figure 11. Growth mode diagram for Pt/Pt(111) as observed by He-scattering. transition to step flow is not an intrinsic property of the growth system, it depends on the initial step separation on the probed part of the crystal surface. A striking feature of this mode diagram is the transition line between the 3D-growth regime and the high-temperature 2D-growth regime at a temperature between 450 K and 500 K. The transition line is almost vertical, showing that the deposition rate has hardly any influence on the growth mode transition. This behaviour is unexpected: in the framework of the kinetic theory developed in this chapter one would expect a finite slope of this line. Indeed, assuming that the transition line corresponds to some constant value of the product s.k (cf. section 2.4), this line should be described by the relation (cf. equation 12): R ~ exp(-E/kT), where the energy E is given by: E - E s. (i + 2)/i + E i / i + E D . Using the slope of the transition line, a value of ED=0.26 eV [66] and a reasonable range of values for i and Ei, one obtains values of the step edge barrier Es of more than 1 eV. This clearly unphysical result suggests that the transition is not the usual transition from 3D- to 2D-growth with increasing temperature as predicted by the kinetic theory.
90 70 9
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9 9
9
eS, 9
50
go 9
9
9
Z' [A2] 40 30 9
20 10
~ 25o 36o 46o 56o 66o 76o 85o substrate temperature [K]
Figure 12. Effective cross section for diffuse He-scattering during the initial stages of growth of Pt/Pt(lll) [67]. The idea that the growth mode transition is a special feature of this system, was supported by the observation of an unusual nucleation phenomenon coinciding with the growth mode transition. It was found that the amount of diffuse scattering after deposition of submonolayers of Pt showed an irregular behaviour (cf. Figure 12) [67]. Below a growth temperature of 450 K, the total amount of diffuse scattering decreases with increasing growth temperature. This is the expected result because the diffuse scattering is caused by the edges of islands the number of which decreases with increasing growth temperature. However, between 450 K and 500 K, a sudden increase of the total amount of diffuse scattering by about one order of magnitude is observed. The high level of diffuse scattering is maintained in the entire high temperature 2D-growth regime before it drops off as the transition to step flow sets in. The sudden increase in diffuse scattering was initially interpreted by the formation of very small clusters of a "magic" size between 7 and 10 atoms [67]. Only a high density of clusters of this small size on an otherwise flat terrace could account for the observed amount of diffuse scattering. This explanation, however, proved to be wrong after the discovery of a new type of reconstruction which forms during deposition of Pt onto P t ( l l l ) at temperatures above 400 K
91
[64,65]. This reconstruction consists of fcc and hcp domains separated by a network of dislocation lines which presumably are responsible for the major part of the diffuse scattering increase observed with He-scattering. Essential for the 3D- to 2D-transiton is that the reconstruction does create an enhanced number density of Pt islands, only the enhancement factor is smaller than that estimated from the TEAS experiments. As demonstrated in [65] it is this enhancement of the island density which is the ultimate cause for the transition to the layer-by-layer growth regime at high temperatures, in conjunction with another characteristic of the reconstruction: the reconstruction is only observed on large terraces, but never on top of the growing islands. Therefore, the nucleation on top of islands is effectively suppressed: the island dimensions are reduced without reducing the mobility of adatoms on top of the islands. As a result, the atoms deposited on top of island visit the island edge at an enhanced rate, leading to an improved interlayer mass transport even in the presence of a high step-edge barrier. The possibility to turn rough growth into layer-bylayer growth by creating an enhanced island density without effecting the mobility of adatoms on top of islands has been demonstrated in controlled experiments for A g ( l l l ) [68] and will be discussed in section 4. This way to manipulate the growth of kinetically controlled systems is obviously naturally realized for the Pt(111) surface. The remaining point to be discussed with respect to the growth of P t / P t ( l l l ) is the origin of the transition from 3D- to 2D-growth at low temperatures. Also this transition cannot be explained within the simple kinetic model developed above which predicts improving growth only with increasing temperature. This apparent contradiction is solved by recalling that the model assumed compact, temperature-independent island shapes. This assumption is not valid for the low temperature transition. It was found by STM that the island shape changes from compact to fractal-like as the temperature is lowered from the 3D- to the 2D-growth regime [23]. Fractal islands naturally lead to an enhanced interlayer mass transport compared to compact islands of the same size. The number of edge sites is higher for fractal than for compact islands so that also in this case the frequency at which adatoms on top of islands visit the island edge is enhanced. However, this enhanced visiting frequency alone can presumably not account for the observed drastical improvement of
92 interlayer mass transport. Moreover, this effect cannot explain why exclusively P t ( l l l ) shows this pronounced reentrant layer-by-layer growth effect: both A g ( l l l ) and C u ( l l l ) exhibit a corresponding transition in island growth shapes from compact to fractal but do not show a distinct reentrant effect [51]. The cause for the low temperature layer-by-layer growth of P t ( l l l ) must be sought in special interlayer diffusion processes which are activated for Pt by the change in island shape but are unimportant for Ag and Cu. These processes are suggested to be exchange processes near kink sites, either of thermalized adatoms [69] as discussed in section 2.2 (Figure 3 d) or during the deposition process as discussed in the context of transient mobility in section 3.1 [70]. Indeed, Monte-Carlo simulations incorporating processes of this kind could reproduce the growth transition observed experimentally [69]. 3.4 D i s c u s s i o n : W h y a r e fcc(100) a n d f c c ( l l l ) m e t a l s u r f a c e s so different? The general trend apparent from the review of available data on homoepitaxy of single crystal metal surfaces is that fcc(100) surfaces grow r a t h e r smoothly while growth on fcc(111) surfaces is in general rough. In the framework of the simple kinetic model developed in section 2 of this chapter it follows that the step-edge barrier opposing interlayer mass transport must generally be small for fcc(100) surfaces and high for fcc(111) surfaces. To get an idea about the size of the step-edge barrier Es for the two types of surfaces let us recall that the conditions for 2D-growth and 3D-growth (equation 3) are fulfilled for s.~>l and s.~>l, a less conservative estimate of 0.035 eV is obtained. Similarly, taking P t ( l l l ) at room temperature as an example for fcc(lll) surfaces, the condition s.~-type and < 110>-type steps of the Ir(001) layer has been studied by Chen and Tsong [36]. They find that at the -type step edge, a ledge atom is not stable with respect to diffusion, i.e. at the temperature it can diffuse along the step edge, it can also dissociate to the terrace. It is therefore very difficult to measure the parameters of ledge atom diffusion along this step. For diffusion along the -type step, data analysis
121
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0
first bi-layer atoms
0 0
second bi-layer atoms
9 9
Fig. 7. One of the 56 possible different step structures of the Si (111) (7x7) surface. See Ref. 34 for details.
122
(a) fcc (001)
(b) fcc (111) Fig. 8. Structure of the basic step-types of the fcc (001) and (111) surface layers. In (b), we also show two possible ways a comer atom. can move from on step type to the other; one by atomic hopping and one by atomic exchange.
123 is completely the same as terrace diffusion in 1-D. Data derived for Ir/Ir (001), in the form of Arrhenius plot, is shown in Fig. 9. The activation energy of ledge atom diffusion, 0.62+0.05 eV, is considerably lower than that for terrace diffusion of 0.84+0.05 eV. Also, whereas self-diffusion on the terrace is achieved by atomic-exchange, ledge atom diffusion along the -type step is achieved by atomic hopping. In an attempt to explain a transition of island shape of Pt on the Pt (111) surface found in STM observations, Michely et. al. [37] assumed that the activation energies of atomic diffusion along the A-type and B-type step edges should be the same as those of adatom diffusion on the (113) and (331) surfaces, respectively, since they have identical n.n. and second n.n. atomic configurations. FIM studies of surface diffusion in general find that there are no simple rules relating the activation energies to the atomic configurations of the surfaces. For an example, whereas the smoothest surface on bcc tungsten is the (110) surface, activation energies of terrace diffusion of various 5-d transition metals on this surface are higher than those on other rougher surfaces such as the (112) and (123). Fu and Tsong [38] therefore made a comparison study of terrace diffusion on Ir (113) and (331) with ledge atom diffusion on the A- and B-type step edges. Their results, summarized in Table 1, show no resemblance of these diffusions. Not only is there no clear correspondence between the activation energies in terrace diffusion with those in ledge atom diffusion, their orders are actually reversed. At the present time, the cause of such behavior is not known. It is possible that in ledge atom diffusion, the effect of charge smoothing at step edges [39] can affect the activation energy of ledge atom diffusion more than the atomic configuration. Table 1. Diffusion Parameters Do (cm2/s) System Adatom on Ir(113) 1xlO "3~ Adatom on Ir(331) 1xlO "19~5 Ledge atom at A-type step of Ir(111) 1xl0 -3 (assumed) Ledge atom at B-type step of Ir(111) lxl0 "3 (assumed)
Ed (eV) 0.72+_0.02 0.91_+0.03
0.82___0.03 0.76_+0.03
4.2. Equilibrium island shape. The equilibrium shape of a crystal is related to surface free energy through Wulff plot. Likewise the equilibrium shape of an island is related to step free energy through 2-D Wulff plot. There is the interesting question of what is the equilibrium shape of an island, especially that of a nanometer size island. When a system is in thermodynamic equilibrium, the system as a whole is in the state of
124
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I
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3.5
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3.8
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IO00/T
Fig. 9. Field ion images showing random walk diffusion of Ir ledge atoms along the step edges of the Ir(001) layers and an Arrhenius plot obtained for Ir ledge atom diffusion. From the slope and intercept of this plot, data described in the text are derived.
125 lowest free energy in thermal contact with a heat reservoir. Although in a macroscopic system, many phases may co-exist and may also exchange atoms with one another, except for the thermal contact with the heat reservoir, the system is closed to the outside world, i.e. it does not exchange particles with outside. When we are discussing the equilibrium shapes of clusters or islands on a surface, we have to define our system explicitly. If we consider the entire surface to be our system, the surface will assume the lowest free energy state in thermodynamic equilibrium which is characterized by a certain distribution of steps, and cluster and island sizes and shapes. From the point of view of individual clusters or islands, their shapes can still change with time by exchanging atoms among them and with steps. In other words, there is a very large degeneracy of states which can give the same lowest free energy for the entire system, or the system is in dynamic equilibrium. The shape and size of individual islands, especially for nanometer size islands whose properties are very sensitive to the atomic size, can change with time. Their shapes may be affected by the rates of capture and detachment of atoms at different step edges. Thus it may be difficult to obtain information on step energies from these islands using principle of Wulff construction when a system is in dynamic equilibrium. Information on the binding energy of step atoms can, however, be more easily studied by considering one nanometer size island as our system and the substrate as the reservoir. In this case, we can consider the island shape as the equilibrium shape if and only if: 1, its does not exchange atoms with the outside world, and 2, the mobility of atoms along the step edges and within the island is rapid and the annealing time long enough to rearrange its shape to a stable shape which will no longer change with time by further annealing. These two conditions cannot always be satisfied unless the islands are nanometer in size since at the temperature where the mobility of layer atoms is high enough, step edge atoms can already detach from the island to terraces. Fortunately one realizes that it is the behavior of atoms in nanometer size islands which will determine the early stages of coarsening of the islands, the subsequent growth process and structure of ultra-thin films, and the morphology of the thin film surfaces finally formed. Another advantage for using nanometer size islands for our study of steps is that there exists only a few atomic configurations for atoms in step edge sites of such islands. Thus data analysis is considerably simpler. The equilibrium shape of nanometer size Ir islands on the It(001) surface has been studied by Chen and Tsong earlier [36]. The step energy is very anisotropic. They find that the shape of a small island of ~100 atoms, when annealed at a temperature below 420 K where dissociation of step-edge atoms to terraces occurs only very infrequently, the island shape is close to a square with
126 only a few kinks and with its sides consisting mostly the -type step, or the closely packed atomic rows. If the number of atoms in an island does not fit to a perfect square, then rectangular shape of unequal sides will most likely be formed. If this is not possible, then comers having the -type step will appear. At a temperature >500 K, hollow islands, i.e. islands with a vacancy or a void inside, can already be fonned. Thus the binding energy of an interior atom is not so different from that of a step edge atom of the < 110>-type step. On the other hand, the free energy of the < 100>-type step is considerably higher than that of the < 110>-type step. For nanometer size Ir islands on Ir(111), a study was reported by Fu et. al. [38] In their experiment, they strictly control the number of atoms in an island. This number can be controlled by addition or reduction of atoms to the original island by a combination of vapor deposition followed by surface diffusion, and low temperature field evaporation, a technique introduced into an FIM study of surface diffusion and adatom-adatom interactions by Tsong in 1972 [7]. They find that for small Ir islands, as long as the number of atoms can be arranged into a perfect hexagon, i.e. 7, 19, 37, 61, 91, .... etc., the island shape after annealing at 490-500 K for a sufficiently long period of time, is a perfect hexagon as shown in Fig. 10. These numbers, N=3n(n-1)+l with n being the atomic length of the sides, will be called the ideal numbers of nanometer size Ir islands on Ir(111) surface (likewise N=n 2 are the ideal numbers of nanometer size Ir islands on the Ir (001) surface). At this temperature, step-edge atoms can diffuse rapidly along the step, but dissociation of step edge atoms to terraces is still very infrequent. We find that once an island of ideal atom number reaches the shape of a perfect hexagon, its shape will no longer change by fi~rther annealing unless one or more step edge atoms are lost by dissociation to the terrace. This does not mean, however, that the equilibrium shape of the island can be easily reached since at this temperature, step-edge atoms can already dissociate to the terrace. Before reaching the equilibrium shape, atoms may be lost to the terrace. Nanometer size islands of ~100 atoms or less with a non-ideal atom number tend to arrange into a shape as close to a hexagon as possible but there is no fixed shape; the shape can change with time, or the length of the A- and B- type steps can change with time. When we want to compare the step energy of two type of steps, it is of course most ideal to have only these two step types present in the island. This observation of the equilibrium hexagonal shape, or the equal length of the A-type and B-type steps, indicates that the difference in the binding energy per step atorn of the two types of steps must be relatively small. Limited by the size of the islands in this FIM experiments, we can only conclude that the length difference is less than ~1/5, or about 20%. Five is the maximum length of
127 the sides of islands, excluding two comer sites, studied by these authors. This provides us an estimate of the binding energy difference of less than ~kTgn(6/5)z0.01 eV/atom for the A- and B-type steps. From this observation alone it is impossible to tell which of the two step types has the lower free energy, or larger binding energy of step edge atoms. However, a stable 36-atom island discussed in the next section has longer A-type steps. Thus the A-type step has the lower free energy, or the larger binding energy.
Fig. 10. FIM images of Ir islands on the Ir{ 111 } having the five lowest ideal atom numbers. 4.3. Relative binding energy of ledge atoms at different steps An unusual behavior noticed by Chen and Tsong in their study of steps of the Ir(001) layers is that a diffusing ledge atom tends to stick to the end sites of the -type steps. The site next to the end site shows only a slightly attractive behavior. The relative occupation numbers of one Ir ledge atom along a step
128
with a length of 9 sites at 280 K is shown in Fig. 1 l(a) and the relative binding energies of this ledge atom in these sites are shown in Fig. 11 (b). From the data one can easily see that within the uncertainty of the measurement of about +5 meV, the binding strength of a ledge atom at the -type step is fairly uniform except at the two end sites, which are 57+5 me V and 21 +5 me V larger than the rest of the sites. In this experiment, the (001) layer is not yet thermally annealed to reach the equilibrium shape.
500
I
I
(a)
450
,
i
,
,
i
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,
,
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SITE
Fig. 11. It is also found that Ir ledge atoms tend to sit more frequently in the end and next-to-end sites of the steps as shown for a step of nine sites. From these data, the relative binding energies of the ledge atom at different sites are derived.
129 A similar measurement has been done by Fu et. al. for Ir ledge atoms at the Atype steps of the Ir(111) layers. They find that at a temperature when a ledge atom can move fairly freely from one step to another, the ledge atom is almost always found at one of the A-type steps, indicating that the binding energy of a ledge atom at the A-type step is considerably larger than that at the B-type step. For an example, out of over 400 heating periods of observation with a hexagonal island of~100 atoms at 400 to 420 K, not once is the ledge atom found to sit at any of the B-type steps. At this temperature, the ledge atom can move around the step boundary fairly freely. Statistically reliable amounts of data are difficult to collect for this phenomenon since statistical error reduces with the inverse square root of the number of observations. The binding energy difference is a little too large for this technique to measure reliably, but from the available data, the difference in the binding energies of a ledge atom at the two types of steps is found to be greater than ~kT.gn (400/1) = 0.21 eV. The first impression is that this is a surprisingly large difference considering we have just shown in the last section that the difference in the binding energies per atom of the two step types is relatively small. At the moment, it is not clear how the binding energy of a ledge atom at the step edge is related to the binding energy per step atom. The binding energy per step atom refers to an atom at a uniform step whereas a ledge atom has no neighbor atoms along the step. It is also very surprising that a ledge atom at A-step and at B-step, both of which have a nearly identical atomic configuration with 5 n.n., can have such a large difference in the binding energy. This large difference in the ledge atom binding combined with the small difference in the step atom binding can produce a surprisingly interesting phenomenon. The shape symmetry of a nano-island can be reversed by addition of just one ledge atom. In Fig. 12(a), we show an island of 36 atoms prepared by low temperature field evaporation followed by annealing at 490 K. It has a truncated triangular shape. The long steps of five atoms each are the A-type steps and the short steps of three atom each are the Btype steps. This shape is stable with respect to further annealing up to ---490 K. When we add one Ir atom to the step edge of the island as seen in Fig. 12(b) by deposition-diffusion, the ledge atom is found to move fairly freely from one step edge to another already at 400 K, but it stay always at the A-type step edges as exemplified by (b) and (c). At this low temperature, only ledge atoms can diffuse along step edges, but the island shape remains unchanged. With the additional ledge atom, when the temperature is raised again to 490 K, however, the island starts to change its shape, first from (c) to (d) and then to (e). Although it is still a truncated triangle, the lengths of the A-type and B-type step edges are now
130
Fig. 12. (a) shows an island of 36 atoms prepared by low temperature field evaporation. Subsequent annealing at 400 K does not change the shape. The long sides are the A-type steps. An Ir atom is deposited on the surface which eventually diffuse and stick to an A-type edge. Upon heating to 400 K, the ledge atom moves from one A-edge to another but the island shape remains intact as exemplified by (b) and (c). Raising the temperature to ~490 K results in a gradual change of its shape from (c) to (e) and then stay in that shape. Now the lengths of the A-type and B-type edges are reversed. The ledge atoms still sticks only the A-type edges. reversed. This structure is still only a metastable one (the stable hexagon structure can be forlned if it is annealed for a sufficiently long period of time or at a slightly higher temperature), but it is in a lower free energy state. The ledge atom, however, still stays at the A-type step-edge always. Thus the addition of one ledge atom is enough to transform the symmetry of the island from one with longer A-steps to one with shorter A-steps. From this observation, the following relation can be derived.
131
(9 ea+3 e.8+66AB+e,a,)450 K. No attempt was made, however, to clarify why atoms appeared there although it is quite clear now that these atoms are either ascended from the step edges or the substrate layer. In a later study, Fu et. al. [33] find evidence that when an Ir(111) layer is heated above 500 K, step edge atoms can detach from the step and either remain at the lower terrace or ascend to the upper terrace. It is even more
135 surprising that above ---530 K, in-layer atoms can be found to move up the layer to the upper terrace. Thus after heating, occasionally one or two atoms may be found on top of the layer either at tlie step edge or in the middle of the terrace. Fig. 15 gives an example where a step edge atom has ascended the step. In these pictures, successive images of a surface layer, after preparation by field evaporation and then heating to 510 K for 20 s, are shown. In (a), a layer with a vacancy at the step edge can be seen. After another heating period, the length of the heating period being chosen so that at this temperature less than one ascended atom is found for the entire surface, an adatom appears on the terrace near the step edge of the upper terrace. Upon field evaporating this very bright adatom, we find a new vacancy at the step edge near the adatom. All other step edge atoms of the layer remain intact. Thus a step edge atom has ascended the step as illustrated in the line drawings. On the terrace of Ir(111), self-diffusion by atomic hopping can already occur around 100 K. However, the ascended atom at the step edge is found to diffuse only above -~270 K. The diffusion, aside from the occasional descending motion, is also found to be mostly along the step edge. The much higher diffusion temperature is due to the adatom-vacancy interaction, similar to diffusion of a dimer-vacancy complex [46]. At this temperature, once an edge atom ascends the step, three possible events can happen within the same heating period, a) The ascended atom at the step edge can descend the step and recombine again with the vacancy. When this happens, the ascending motion cannot be detected. b) In principle, it can escape from the interaction of the vacancy and diffuse on the upper terrace and be found elsewhere, but the diffi~sion of this adatom will be so fast at this temperature, it will most definitely be lost by descending to the lower terrace, c) It can stay at the site where it has ascended due to the adatomvacancy interaction, d) It can diffuse together with the vacancy. Only in the last two cases, can the event be observed. This diffusion occurs around 270 K. When the same surface is heated to above-~530 K, one or two adatoms can occasionally be found in the middle of the top surface layer. Of course, it is not possible to tell whether these adatoms are from step edges or from the upward movement of in-layer atoms. However, there is a way to find out. If they are adatoms ascended from step edges, or from the substrate layer and subsequently dissociated from the interaction of the vacancies, they should diffuse around 100 K. In fact adatom diffusion speed is so fast at ~530 K, it is unlikely one has any chance of finding an adatom ascended from the step edge. It will certainly encounter the step again and descend the step. What we find is that the ascended adatom in the middle of the plane starts to move only above ---200 K. This can only happen if they are from the upward motion of in-layer atoms and the
136 ascended in-layer atoms actually diffuse together with the vacancies in the layer, or the diffusion we have observed is really the diffusion of the adatom-vacancy complexes. Unfortunately, a vacancy in the Ir (111) surface cannot not be seen in the FIM image. The only way to detect this vacancy is to reduce the size of the layer by field evaporation. Even so, it is impossible to see it clearly when it is inside the layer. Only when it reaches the step edge, does it appear as shown in Fig. 16. The upward movement of in-layer atoms can much more clearly be seen if one uses a less densely packed surface where in layer atoms are much better resolved. In (c) and (d), we show an adatom-vacancy complex created on an Ir (113) from the upward movement of an in-layer atom by heating the sample to 450 K for 30 s. If adatom-vacancy dissociates and the adatom diffuses elsewhere, then only the vacancy can be observed. This, in fact, is also shown in (d). In this experiment we are able to measure the activation barrier heigl!t, or the activation energy, for the ascending motion of step edge atoms. For a layer with N~ step-edge atoms, if the heating period and temperature are chosen so that within a heating period less than one edge atom ascends the step, the probability of finding an ascended atom from the entire step in a heating period is given by
Eas
Pas - vvN~ e x p ( - - ~ ) ,
(11)
where v is the frequency factor, r is the length of the heating period, and E,,~ is the potential barrier height for the ascending motion. In our measurement, we use layers with N~ in the range of 30 to 40, or about 35, and r is 30 s. Our data, plotted in gn(p,,~) vs. 1000/T, are shown in Fig. 17. From the slope and intercept of this plot, we derive E,,~ and v to be 1.51+0.10 eV and 3.1x10 ~+~ s-~, respectively. Due to the cumbersome procedure, we have not yet measured the activation energy for the upward movement of in-layer atoms. From the temperature this process can occur, we estimate the energy barrier to be about 1.7+0.2 eV. The mechanisms for the ascending motion of step edge atoms cannot really be identified from our observations. Two mechanisms are possible, i.e. by direct atomic hopping or by atomic-exchange as illustrated by Fig. 18. For the upward motion of in-layer atoms, a substrate atom moves up by thennal activation as is also shown in the figure. In view of the ease of this last mechanism which can occur at about the same temperature, it is very likely that step edge atoms also ascend the step by atomic hopping.
137
Fig. 16. (a) An adatom appears on an Ir(111) layer after heating to 530 K for 30 s. (b) The layer has been reduced in size by field evaporation. At the digitized position of the adatom a vacancy is found at the step edge pointed by an arrow. (c) After heating a (113) surface to 450 K for 30 s, an adatom appears on the terrace. (d) By gradual field evaporation, two vacancies are found one of them (pointed by an arrow) is at the neighbor site of the adatom (see line drawings).
138
E
-
as
=1.51+0.i0
~/ =3.13xlOll•
(eV)
-1 I:1
-2
-3
\ I
I
I
I
1.85
1.90
1.95
2.00
Iooo/T (X-~)
,
Fig. 17. Data of Pas are plotted in an Arrhenius form from which Eas is derived to be 1.51+0.10 eV for the ascending motion of step edge atoms of the Ir(111).
I I
I II
-~
/
Fig. 18. The mechanisms of the ascending motion of step edge atoms and inlayer atoms. 4.6. Dissociation of step edge atoms to remain on the lower terrace. When a surface layer is heated to high temperature, step edge atoms may ascend the step to the upper terrace and in-layer atoms may move up to the upper terrace as described in the last section. The most commonly accepted view is, however, for the step edge atoms to detach, or dissociate, but remain on the lower terrace. Chen and Tsong [36] first reported a measurement of the
139 dissociation energy of step comer site atoms of the Ir(001) layer as well as the average dissociation energy of step edge atoms of the Ir(001) layer. In the case of step comer atoms, it is possible to pinpoint from field ion images which of the comer atoms are dissociated within a given heating period, thus the lifetime before dissociation at a given temperature can be measured. From such data, the dissociation energy can be derived with an Arrhenius-like plot. FIM images and data derived are shown in Fig. 19(a) and (b).
Fig. 19(a). FIM images showing dissociation of step comer atoms of an Ir(001) layer at 420 K. Arrows point to the atom dissociated during the next heating period. At this temperature, step edge atoms can move along the -type step. Once a comer atom dissociates, step edge atoms move to replenish a new comer site atom.
140 .
.
.
.
I
.
.
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.
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I
I
5 b.
4
3
(.~)
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I
I
2.05
I
2.10
I
2.15
2.20
I
2.25
2.30
IO00/T
10
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I
I
I
_
7
_
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-
1.5
(c)
4,
I
I
I
I
1.6
1.7
1.8
1.9
2.0
IO00/T
Fig. 19(b) and (c). Dissociation time data obtained for comer atoms are plotted in Arrhenius fonn shown in (b) from which the dissociation energy is derived to be 1.35+0.1 eV. In (c), the average dissociation energy of step edge atoms of the Ir (001) layer is measured from the dissolution time as function of temperature of Ir (001) layers. From such data, the average dissociation energy of step edge atoms is derived to be 1.40+0.1 eV. Time constants are respectively 2.5x10 13~176 s and 2.4xl 0 1~176176s, respectively.
141 For a macroscopic surface, it is difficult to tell whether an adatom is ascended from a step edge, from the upward movement of an in-layer atom or from dissociation of step edge atoms of the upper surface layer. Thus their potential barrier heights cannot be measured separately. For a field ion emitter, when it is heated to high temperature, the emitter will start to blunt and low index surfaces tend to grow in size. For fee metals, the size of the {111 } facets will grow into the largest ones followed by the {100} facets. What happens is atoms detached from the {111 } layers will eventually diffuse to either the tip shank or high index surfaces and be incorporated into the step edges of these surfaces. It is because of having such a tendency that we can estimate the dissociation energy of step edge atoms of low index surfaces by measuring the temperature dependence of the time needed to dissolve a small top surface layer of these low index surfaces. This method was first used by Chen and Tsong in a measurement of the average dissociation energy of step edge atoms of the Ir(001). The data obtained is shown in Fig. 19(c). A similar measurement for the Ir(111) was carried out by Fu et. al. [33]. In their study, they measure the temperature dependence of the time needed to dissolve a layer of about 100 atoms to about 40 atoms and plot the data in an Arrhenius form. From the slope, the average dissociation barrier height of step edge atoms of the Ir(111) is estimated to be 1.6+0.2 eV. The time constant obtained is 7x10 -~=+~ s. Although this energy appears to be slightly larger than the activation barrier height for the ascending motion of step edge atoms, in reality, the accuracy of both measurements is not high enough to tell which is larger. All we can say is that they are comparable. The fact that the layer eventually will be completely dissolved indicates that the dissociation barrier is most probably slightly lower than the ascending barrier. Dissociation of step edge atoms to remain on the lower terrace as well as the descending motion of adatoms can also be studied with the STM. In Fig. 20 we give an example for the Si(111) (7x7) surface. A small 3-D cluster of Si is created by applying a ms voltage pulse to the scanning tip. This island, at 500 ~ is seen to reduce in size as well as in height continuously. Obviously step edge atoms dissociate to the lower terrace gradually and at the same time these adatoms descend the steps and diffuse to other places. Some of these atoms are absorbed into the step edges of the lattice steps seen in the lower part of the large terrace. The dissociation rate is found to be greatly affected by the bias voltage of the scanning tip as well as the presence of the lattice steps nearby, making a quantitative study of dissociation rate very unreliable. The effect of the scanning tip can of course be alleviated by reducing the scanning bias voltage as has been done by Tanaka et. al. [47], but the effect of steps in the nearby is difficult to be
142
Fig. 20. At 500 "C, a nanometer size Si crystal on Si(111) gradually reduces in size by losing atoms from step edges. Some of these atoms are absorbed into the step edges seen in the field of view which is seen to grow slowly instead. The times lasted are also shown. Length scale can be inferred from the (7x7) unit cells. accounted for. At the present time, we believe the dissociation energy cannot be derived with a reliable accuracy, but we estimate it to be slightly less than 2 eV [48]. Tanaka et. al., however, ignore all these untraceable effects and have derived the activation energies of the decomposition of hillocks and filling of craters to be 1.6+0.2 and 1.7+0.1 eV, respectively, with a pre-exponential factor of 2.7x10 ~+-~/s for both processes. We believe the activation energy of refilling
143 a crater should really represent the activation energy of adatoms to descend a lattice step, but the energy obtained seems a little too high considering what we have already learned of metallic systems. Further study should clarify this apparent inconsistency.
4.7. Impurity traps Other point and line defects existing on a surface, such as substitution or interstitial impurities and grain and domain boundaries etc., can also affect the transport of atoms across the surface and thus can affect the epitaxial growth of thin film layers as well as the surface morphology of the grown thin film layers. An example is the trapping of diffusing adatoms by substitution impurities. Cowan and Tsong [49] reported a study of impurity trapping by studying the binding strength of a W adatom on the (110) surface of W-3%Re alloy. Using a site mapping technique they find that there is an attractive interaction of about 90 meV between a Re substitution atom and a diffusing W adatom at their closest equilibrium separation and a smaller repulsive interaction at the second closest separation. For studying impurity trapping, it is most ideal if one can embed an impurity atom into the substrate layer of a pure metal and study the interaction of this atom with a diffusing adatom. Tsong [51] recognized that a vapor deposited foreign atom can be embedded into the surface of an fcc metal by atomic exchange which can then be used for studying the impurity trapping. A detailed study was reported by Kellogg using Ir/Rh(100) system. At 255 to 260 K, a Rh adatom is found to be trapped by a substitution Ir atom. The movement of the Rh adatom is found to be confined to the four sites making direct contact with the substitution Ir atom. The position of the Ir atom is continued later from the position of the atom retained on the surface after the substrate layer is field evaporated. The strength of the trapping is found to be 0.12 eV. hnpurity atom trapping is obviously important in understanding the nucleation centers in crystal and epitaxial growth, as well as the active sites in surface promoted catalytic reactions on alloy surfaces. 5. SUMMARY Atomic processes important to epitaxy are diffusion of adatoms on terraces, how these atoms behave when they encounter the ever present lattice steps and the step edges of nanometer size islands already grown by aggregation of diffusing adatoms, diffusion of ledge atoms along step-edges, as well as how step edge atoms behave at different temperatures. In hetero-epitaxy, the growth
144 process and structure are going to be determined by the behavior of atoms at lattice steps and the step of nanometer size islands. Important factors are the rate of arrival of adatoms from the vapor phase, the fraction of atoms reflected at the step boundary of nanometer size islands compared to that moves down the steps, the fraction of atoms ascends to the upper layer from the step edges and from the in-layer atoms compared to that dissociates to the lower terrace, etc. The activation energies of many of these atomic processes have already been measured for Ir (001) and (111) surfaces. When the activation energies of all these atomic processes are known, the process of epitaxial growth as well as the morphology of the grown surface at a given temperature can be easily obtained by Monte Carlo simulations using these energies. But even without such detailed studies, one can already see some tendencies by considering the behavior of atoms we have already studied. In homo- and hetero-epitaxy, what we have to consider is which of these atomic processes is the rate limiting step, or the most important factor. There is no unique answer to this question but there are general n~les one can follow to find a reasonable answer. For an example, for Ir atoms on Ir(l 11) surface, when the temperature is below 200 K, only terrace diffi~sion of single adatoms along surface channels of the 2-D surface net can occur. Terrace diffusion will determine the island structure as well as the morphology of the surface. The island structure should be a diffusion limited aggregation of atoms, or it should have a fractal structure. Between 200 and 350 K, terrace diffusion is so rapid it is no longer a rate limiting factor; step edge diffusion and the binding energy of ledge atoms are. Island shapes will depend on the rate of the adatom deposition, and their capturing probabilities at different step edges. But, in general, the shape of the islands will be triangular with no obvious fractal features since ledge atom diffusion can already occur. The direction of the triangular islands may depend on the binding energy and diffusion speed of ledge atoms at the A- and B-type step edges. When the temperature is raised above ~400 K, ledge atom diffusion is so rapid, it will play much less important role. Now the island shape will be determined by step energy, kink energy and corner site energy, etc. The island shape will be hexagonal for small islands of ideal atom numbers and nearly hexagonal for others. Above 500 K, atomic steps of the ascending and descending motion of atoms as well as the rate of dissociation and association of atoms at the steps will play the dominant role. The island shape should be determined by how fast atoms detach and absorb at the edges of different types of steps. At even higher temperature when the rate of ascending motion is comparable to the rate of descending motion, the surface will start to roughen, or a roughening transition will set in. In general, the rate limiting atomic process is
145 the one having a mean square displacement of atoms, within the heating period of observation, comparable to the size of the feature we are interested. A detailed study of the mechanism of different atomic processes and their energetic will provide us with basic knowledge needed to judge the more important factors affecting the epitaxial growth and other phenomena involving the transport of deposited or surface atoms at the given temperature. A recent realization of considerable importance is that different "modes" of epitaxial growth can be much more naturally explained in terms of the reflection properties of different types of steps to diffusing adatoms and atom-clusters. In the past, the three dominant "modes" of growth have been interpreted to arise from different interface energies based on equilibrium thermodynamics. The fact that the growth structures are growth condition dependent already clearly indicates that any interpretation based on equilibrium thennodynamics is inappropriate. Another important realization is that the nature of atomic interactions at surfaces does not distinguish steps from "ascending" and "descending" steps (these names are still used in this article just for the purpose of convenience). In fact, from the potential energy curve shown in Fig. 13, one can easily see that those steps which do not reflect terrace diffusion adatoms, the "ascending motion" of step edge atoms to the "upper terrace" should be easier than dissociation to remain on the same terrace. Obviously, many effects of lattice steps remain to be discovered and studied. Experimental data available and interpretations we have now are all preliminary. It is in such an early stage of development of our understanding of the effects of steps that makes the study of atomic steps challenging and exciting.
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
149
Chapter 5 Heteroepitaxial metal growth" the effects of strain Harald Brune and Klaus Kern Institut de Physique Exp6rimentale, Ecole Polytechnique F6d6rale de Lausanne CH- 1015 Lausanne, Switzerland
1. INTRODUCTION: H E T E R O E P I T A X I A L M E T A L G R O W T H Epitaxial thin films have attracted considerable attention in recent years in the search for new materials. The growth of crystalline films on a crystalline substrate (epitaxy) offers the opportunity to create metastable structures with novel physical and chemical properties. The structure and the properties of the film can be manipulated by the geometric and electronic structure of the substrate. A topical example is the heteroepitaxial growth of Fe on the Cu(100) surface [ 1], in which the lattice misfit forces Fe films below a critical thickness to adopt the face-centered-cubic (fcc) structure of the Cu substrate, although under normal conditions Fe has a body-centered-cubic (bcc) structure. The fcc Fe-films are particularly interesting with respect to their magnetic properties [2]. In most cases heteroepitaxy involves lattice mismatch between deposit and substrate that will produce strain in the epitaxial layer. The presence of strain can not only force the heteroepitaxial layer into a metastable "artificial" structure but can also severely affect the layer morphology. When a heteroepitaxial layer is grown, initially a fiat surface might result under ideal growth conditions when internal defects are suppressed and the layer adopts a pseudomorphic structure. With increasing thickness the strain energy increases proportional to the coverage and the epitaxial film eventually will find a way to relieve the strain. Usually this occurs by the introduction of defects such as dislocations into the epilayer [3, 4] or by roughening of its surface [5, 6]. Since smooth epilayers with atomically abrupt interfaces are desired for most applications, the understanding and control of strain relief and its influence on the film morphology are of primary importance. In this review we discuss the effects of strain in heteroepitaxial metal growth and give some examples of the
150 variety of mechanisms nature has invented to relieve strain. The examples are mainly taken from the laboratory of the authors, concentrating on systems which grow phase separated. Systems in which interfacial alloying plays a dominant role are discussed in detail in the Chapter by Besenbacher et al. in this Volume. We illustrate in Section 3 that atomic scale surface probes like STM give unprecedented microscopic insights into growth phenomena and demonstrate that in most cases the scenario of strain relaxation is more complex than suggested by simple continuum models. While the importance of strain relief for the film structure and morphology has long been studied, the effect of strain on the kinetic processes has hardly been recognized. In molecular beam epitaxy (MBE), in particular for metals, however, thin films are usually grown under experimental conditions far from equilibrium [7] (see also Chapter by Rosenfeld and Comsa in this Volume). Film growth will then be governed by kinetic processes, e.g., adatom diffusion on terraces, along and across atomic steps, as well as the nucleation and dynamics of stable and unstable nuclei. Homoepitaxial systems were believed to be ideal model systems to study these kinetic processes in their pure form, without the complications arising from strain or different surface energies of substrate and film [8]. It was hoped that the knowledge gained for homoepitaxial systems could be simply transferred to heteroepitaxial systems. We recently demonstrated, however, that strain has a dramatic influence on the kinetics of the microscopic processes determining epitaxial growth [9-11]. In paragraph 4 we discuss in detail the effect of strain on the nucleation kinetics and on the interlayer mass transport. We also indicate how these strain effects can be exploited to tailor the growth morphology of the heteroepitaxial film.
0
THERMODYNAMIC GROWTH MODE AND STRUCTURAL MISMATCH
The growth mode of a film is usually classified according to the morphology [12, 13]. In the Frank-van der Merwe growth, also known as layer-by-layer (LBL) growth, the film forms a sequence of stable uniform layers with increasing coverage. In cluster or Volmer-Weber growth three-dimensional clusters of the deposit nucleate directly on top of the bare substrate. An intermediate situation is the Stranski-Krastanov growth in which the deposit grows initially in a few (often only one) uniform layers on top of which 3Dislands are formed. The growth modes are of great technological relevance as uniformity of film thickness and structural perfection are crucial in device fabrication. It is obvious that the growth of well-defined layer structures with abrupt interfaces requires the layer-by-layer growth mode.
151
In a naive picture the equilibrium configuration of a heteroepitaxial system is determined by the competition between the film-substrate interaction and the lateral adatom interaction in the film, describing the anisotropy of chemical bond strength parallel and perpendicular to the interface. Usual measures of these quantities are the isosteric heat of adsorption Vo and the lateral adatom attraction ee. Based on simple thermodynamics [14], it was argued that layer-bylayer growth should be observed for "strong" substrates, where the adsorbatesubstrate interaction Vo dominates the lateral film interaction ee "Weak" substrates, on the other hand, should favor 3D cluster growth. Physisorption experiments, designed to test these predictions [15, 16], revealed however, that layer-by-layer growth was restricted to a very narrow intermediate range of substrate strengths. Both small as well as large Vo/ee values resulted in cluster growth. A more rigorous thermodynamic treatment for the prediction of the growth mode of heteroepitaxial systems was given by Ernst Bauer many years ago [ 12]. In the case of a film composed of n-layers the criterion for layer-by-layer growth is given by ~rf(n) + ~ri(n)
- ~s ~
0
(1)
with Ys and ~rf(n) the surface energies of the semi-infinite substrate and the nmonolayer film and ~/i(n) the interfacial energy. Eq. (1) is rigorously fulfilled in the trivial case of homoepitaxy, when ]if(n) = ~/s and ~/i(n) = 0. In the heteroepitaxial case the obvious condition for LBL growth is that yf < Ys. The inequality has to be large enough to fulfill Eq. (1) because in general the interfacial energy has no reason to be negative, because substrate and deposit have different crystallographic structure, or at least different natural lattice parameters; thus in general '~f(1) --> '~ and/or ~/i(1) are positive and non negligible. Bauer and van der Merwe [ 17] have included in ]ri(n) the n-dependent strain energy of the film. In order to emphasize the role of the structure, Eq. (1) may be also written for each layer of the film as ~f(n) + ~i(n,n-1) - ~f(n- 1) --< 0
(2)
with ~i(n,n-1) the interfacial energy between the n-th layer and the (n-1)-th layer of the film. Because the surfaces of the layers n and n-1 consist of the same chemical species, ~f(n) = ~/f(n-1) with ](fin) slightly smaller if the n-th layer has a more "natural" structure than the (n-1)-th layer, which it certainly tends to have. However, if the structures of the two layers, n and n-1, differ significantly, the interfacial energy ]ri(n,n_l) becomes important and of course positive and Eq.
152
(2) is not fulfilled. We can thus conclude that even if "if < "ts is fulfilled, but the structure of the first monolayer differs appreciably from that of its own bulk, 3D growth may set in above the first monolayer and the f'llm grows in StranskiKrastanov mode. The onset of this growth mode may be retarded a few monolayers by long range influences of the substrate, but still there will be no layer-by-layer growth. The rather restrictive condition for layer-by-layer growth, that the structure of the first monolayer must be almost identical to that of its own bulk, is supported by a molecular dynamics simulation of Grabow and Gilmer [18]. Their result is summarized in a "phase diagram" in Fig. 1. The deposition on an fcc(100) substrate surface only occurs in a layer-by-layer mode for strong substrates Vo/e~ > 1 with negligible structural misfit m -- 0 (thick line). The importance of the structural mismatch is also evident in the phase boundary between the Stranski-Krastanov growth and Volmer-Weber growth which shifts substantially to larger substrate strengths with increasing lattice mismatch. LAYER BY LAYER iii[iiii!ii!iii:iiiiiiii~ii iiiiiiiiiiii!!iiiiii!iii',i~!i[ii!ii!ii:i!!iiiiiii!ii~ill :iiiii]iii ~iiiiiiii[ii!iiii~i!ii~iiiiii!iiil !iiiiiiii!iii[iiiiiiiiiiiiiiiiiiiii[iiiiiiiiii[!iiii!i[!i:iii!i~i i~i:iiiiiiiiiiiii[iiiii~ii:!iiii ':~
3~
i
.9.0
VOLMERI
I
.04
.08
WEBER I
!
.12 .16 MISFIT (m)
I
p
.20
Figure 1. Phase diagram of multilayer growth on an fcc(100) surface in the substrate strengthmisfit plane, according to ref. [ 18]. As already discussed in the introduction film growth from atoms deposited from the gas phase is a non-equilibrium phenomenon governed by the competition of thermodynamics and kinetics. The above considerations are only applicable for growth conditions close to thermodynamic equilibrium, i.e., at high substrate temperature and low deposition flux. With decreasing temperature and increasing flux, i.e., increasing supersaturation, kinetic effects become more
153 important and finally dominate film growth. In Section 4 we discuss in detail the atomic nature of the most relevant kinetic processes involved in epitaxial growth and explore their sensitivity to strain.
3. STRAIN R E L I E F AND STRAIN INDUCED S T R U C T U R E S Intuitively, it is obvious that the epitaxial growth of one metal on another is easiest, if the structural mismatch between the two metals is negligible. In Fig. 2a lattice matched growth, where the lattice parameter of the substrate a and that of the deposit b coincide, is illustrated. Unfortunately, lattice matched systems are the exception rather than the rule. Usually the crystal structure between substrate and deposit differs and strain effects become important. The usual measure to quantify the strain is the misfit m, defined as the relative difference of the lattice parameters m=(b-a)/a. The lattice mismatch between film and substrate material in heteroepitaxial growth leads to strain in the film until the film has adopted its bulk geometry through introduction of strain relieving defects. It is important to understand this strain relief, since the defects influence the morphology and the physical properties of the film. Frank and van der Merwe [3] were the first to address theoretically the strain relaxation in an epitaxial system. Based on the FrenkelKontorova approach [19] they modeled a monolayer of deposit atoms on a rigid substrate by a one-dimensional chain of atoms coupled by elastic springs subject to an external sinusoidal potential. Later, van der Merwe [20] and Jesser and Kuhlmann-Wilsdorf [21] developed a more sophisticated approach treating the substrate and adlayer as elastic media with an external sinusoidal stress imposed at the interface. bll = a c
bll = a b•
b,•
....> B
bll ~ a b,l, ~:a
c
(
Ill!
a
r
i ~ ! ~ !
a
lattice-matched
Ia
a
a
strained
a
dislocated
Figure 2. Interfacial structure in an heteroepitaxial system. Shown ar_.elattice matched growth (a), strained coherent growth (b), as well as dislocated growth (c), B stands for the burgers vector, and T for threading dislocation. In all cases a layer-by-layer growth mode is assumed.
154 The theoretical models predicted the existence of a critical misfit m = mc, depending on relative bond strengths, below which a pseudomorphic epilayer can grow (Fig. 2b). In the pseudomorphic state, the film lattice is homogeneously strained into registry with the substrate in the interfacial plane, but can distort tetragonally in the perpendicular direction in order to preserve the volume of the unit cell. The perpendicular lattice constant is given by Eq. (3) b• = a (l+m) (l+v) / (l-v)
(3)
Ev = 2 G (1 +v) m2/(l-v)
(4)
where v is the Poisson ratio of the deposit material. The elastic strain energy density in the pseudomorphic epilayer is given by Eq. (4), where G is the shear modulus of the deposit material. As the thickness of the pseudomorphic film increases, the elastic strain energy increases and the pseudomorphic epilayer finally becomes unstable at a critical thickness h = hc. Above the critical thickness it costs too much energy to strain the additional deposit layers into registry with the substrate and the strain is partially relieved by the introduction of misfit dislocations (Fig. 2c) [20, 21]. With further increasing film thickness the dislocation density increases until the average strain is eventually reduced to zero, i.e. the adlayer has relaxed towards its natural lattice parameter. The critical thickness he is determined by the elastic constant and the actual misfit m: hc/z = [ 8~ (1 +v) m ]-1 [ 1 + In { (l-v) z / 2~d } + In { 4 hc/z } ]
(5)
here d is the spacing between the atomic planes on each side of the interface and z is an "intermediate" lattice constant z = 2ab/(a+b). A very similar expression was derived by Matthews and Blakeslee [4] who developed a simple approach based on the stress acting on a pre-existing dislocation in the substrate which threads up through the epitaxial overlayer. For typical metal-metal systems he is calculated to vary from below 1 A (Iml > 10%) up to 10-200 ~ for small misfits (Iml < 2%) [21 ]. Qualitative and quantitative tests of the predictions of the pseudomorphic to strain relaxed transition have been made for numerous heteroepitaxial systems, including semiconductor/semiconductor, oxide/semiconductor and metal/metal interfaces [22]. While epitaxial combinations of semiconductors and oxides were usually found to exhibit critical thickness and residual strain far in excess of prediction, heteroepitaxial metal systems were believed to fit well with the
155 predictions. This agreement was ascribed to the fact that in metals the lattice offers less resistance to dislocation motion. It was, however, recently shown that also in the case of metal-on-metal systems substantial deviations between theory and experiment exist [23-27]. In the following paragraphs we will describe some of the relevant experiments and discuss the physical origin of this discrepancy.
3.1. Dislocations and the strain relief at hexagonal close-packed interfaces The continuum model for predicting the pseudomorphic film thickness completely ignores atomic details of the interface structure. Indeed, it has recently been found to fail in the description of hexagonal close packed interfaces [23-25]. This failure is related to the particular structure of closepacked metal surfaces with two favorable adsorption sites, fcc and hcp threefold hollow sites (Fig. 3a). While these two sites generally have similar adsorption energy, the occupation of bridge or on-top sites is associated with a large energy penalty. Strain at these interfaces can easily be accommodated by the introduction of fcc-hcp stacking faults acting as misfit dislocations (domain walls). Their density is higher or lower than that of the pseudomorphic areas depending on whether the strain is tensile or compressive, respectively. The first type of walls are called heavy, the latter are called light. Depending on the wall crossing energy, the walls may either form a striped pattern (Fig. 4a) or may cross each other yielding a triangular network (Fig. 4b, c). If the wall crossing energy is positive, crossings are energetically unfavorable and consequently a striped domain-wall system is formed. Instead, if the energy cost in the crossing area is negative, crossing becomes favorable and a node network is formed. Examples of both patterns have been observed in a number of metal-metal interfaces [23, 24, 28] and even on reconstructed clean metal surfaces [29-34].
fcc (111)
fcc (100)
J
i!.i!iil!i!! !i
m
ii~iiii~]~iii~!ii~ii~A;iii!~iiiiiii~iiiiii~iiiiiiiii~==iii!iii!=~]iiiii! fcc
hcp
fcc
Figure 3. Domain walls in a pseudomorphic adlayer on fcc(111) (a) and fcc(100) surfaces (b). Only in the first case a non-integer phase shift can be produced due to the fcc-hcp stacking fault. While in (a) the right stacking fault represents a light domain wall, the left represents a "super light" wall.
156 The most extensively studied of these systems is the Au(111) surface with its striped domain wall reconstruction [29, 30, 33]. The reconstruction of this surface is driven by the considerable tensile stress in the outermost layer. It consist in the introduction of a certain density of dense domain walls, or partial dislocations, between alternating fcc and hcp stacking regions. For Au(111) the 4% compression of the first layer is achieved by two partial dislocations per (~f3x22)-unit cell, each of which inserting one-half extra atom, thus leading to 23 atoms adsorbed on 22 second-layer atoms along the close-packed (1 ]-0)directions [33, 35]. Due to the difference in energy, more fcc than hcp sites are populated, giving rise to a pairwise arrangement of the (112)-oriented domain walls. Locally, the compression is unidirectional, however, on larger terraces a mesoscopic order of the domain walls is established. The domain walls bend by +120 ~ with a period of 250 ,~ [33] forming the so-called herringbone structure (see Fig. 4a) which reduces the anisotropy of the surface stress tensor [34].
(a)
(b)
(c)
Figure 4. Possible domain wall structures on fcc(111) surfaces, a) striped phase with mesoscopic bending into a herringbone structure, b) and c) trigonal networks with wall crossings. In epitaxial metal films on close-packed metal surfaces the low energy cost for the formation of the domain walls via hcp-fcc stacking faults essentially drops he to zero or just to the first monolayer. As examples we discuss the two epitaxial systems of Cu/Ru(0001) and Ag/Pt(111). Both systems have an atomic size mismatch of roughly 5% (-5.5%, and +4.3%, respectively), in the first system resulting in tensile strain while in the second system the adlayer atom is larger than the substrate atom and the strain is compressive. For both systems the continuum theory predicts a critical layer thickness of a few monolayers, while in experiment only the first monolayer is found to grow pseudomorphic. In Fig. 5 we show STM images of GUnther et al. [24] characterizing the growth of Cu thin films on Ru(0001). The first monolayer grows pseudomorphic; the corresponding STM image (Fig. 5a) only reveals the
157 hexagonal atomic corrugation with a periodicity identical to that of the substrate. With increasing coverage, however, the pseudomorphic state becomes unstable and the Cu fdm introduces strain relieving defects.
(a)
(b)
Figure 5. STM images characterizing a Cu monolayer (a) and multilayer (b) grown on Ru(0001). The nominal coverage of the Cu multilayer is 3 ML. The local thickness varies, however, from 2 ML and 3 ML to 4 ML from top left to bottom right. The image sizes are 7.7 nm x 40 nm (a) and 193 nm x 115 nm (b). From [24]. The corresponding strain relief patterns are clearly visible in the STM images. This is demonstrated in Fig. 5b showing a wedge type sample with Cu coverages increasing from 2 ML and 3 ML to 4 ML from top left to bottom fight. The Cu bilayer shows the well known stripe pattern consisting of bright double lines, i.e., heavy domain walls, running along (112). The pattern has a periodicity of--43 ]~ along (1]-0). High resolution images of the authors revealed the lateral displacement of surface atoms along (112) of 0.8 ,~,, demonstrating that the domain walls are indeed fcc-hcp stacking faults separating fcc regions (larger domains) from hcp regions (small domains inside the double lines). With increasing thickness the strain relief pattern changes markedly. The 3 ML film shows a domain wall network of triangular symmetry with wall crossings allowing for a more isotropic strain relaxation on a mesoscopic scale. Obviously, the crossing energy has become negative, while it was positive for the bilayer. With further increasing coverage the domain wall network disappears in favor of a moir6 pattern characterizing the growth of a weakly modulated incommensurate overlayer. This strain relief scenario is remarkably similar for the Ag/Pt(111) system, which is under 4.3% compressive strain. In Fig. 6a we show the misfit dislocations which develop upon growth of a 1.5 ML film at 300 K. The second layer reveals again the formation of a striped domain wall phase, where strain is
158 relieved anisotropically into one of the (1 ]0)-directions per domain which is accomplished by the introduction of a pair of partial misfit dislocations running perpendicular to this direction [23]. a) T = 3 0 0 K ,
(9=1.5ML
b) T A - 8 0 0 K ,
O-1.5ML
50 A
100 A I
I
Figure 6. Strain relief pattern of a Ag bilayer on Pt(111); integral coverage in both STM images 1.5 ML. At room temperature, the Ag bilayer adopts a metastable striped domain wall phase (a). Upon annealing to 750 K the striped phase transforms into a trigonal network phase (b). From [36]. The striped phase for the second Ag layer on Pt(111) is in fact quite similar to the (ff3x22)-reconstruction of A u ( l l l ) [30, 33, 37] and the Cu bilayer on Ru(0001) [24, 38, 39], discussed above, and has also been observed for Ag films on Ru(0001) [28]. Since the pseudomorphic stacking regions of the Ag layers are under compressive strain, the domain walls in which strain is relieved must represent areas of locally lower density, i.e. they are light walls [23]. Correspondingly the domain walls are imaged as dark depressions while the pseudomorphic domains are imaged bright. This is opposite to the Au(111) reconstruction and Cu/Ru(0001) where the dislocations are areas of locally increased density. Also in contrast to the Au(111) reconstruction and to our original interpretation [23], there are more hcp than fcc sites in this phase, as recently uncovered by X-ray photoelectron diffraction [40]; the large domains are hcp stacking regions while the small domains inside the double lines are fcc stacked. Notice that, in agreement with this finding, in Fig. 6a, the narrow areas are imaged lower by 0.09+0.02 A than the wider ones. This is in accordance
159 with the fact that fcc areas within the Au and Pt reconstruction have been imaged lower than hcp regions by about the same amount (0.08 ,~ and 0.09+0.02 ,~ for Au and Pt respectively) [32, 33]. The 1st Ag layer on Pt(111) is perfectly fiat as demonstrated in Fig. 6a where the tip clearly resolves the dislocations on the second layer while the first layer is imaged fiat. This demonstrates that the first layer, when almost completed, is bare of dislocations and hence pseudomorphic [41], analogous to the Cu/Ru(0001) system. The dislocations on the second layer appear dark in the STM topographs. Since atoms in dislocations are adsorbed on bridge sites this STM contrast is inverted to the geometry expected from a simple ball model. There are two ways to explain this STM contrast. The first is based on a reduced density of states at dislocations according to their reduced atomic density. The second evolved from Embedded Atom Method (EAM) calculations for Ag/Ru(0001), suggesting substrate buckling, which was not found in Effective Medium Theory (EMT) calculations for Ag/Pt(111) [42]. The striped phase of the second Ag layer on Pt(111) is metastable. Upon annealing to T > 700 K (or growth at T > 500 K) it converts into the equilibrium structure which is a trigonal network where the partial dislocations cross, allowing for more isotropic strain relieve [23]. With this transformation the population of sites also changes to the favor of fcc stacking as expected from their generally higher binding energy. Since the subsequent layers grow in fcc stacking with respect to the second layer, the growth or annealing temperature of the second layer determines whether the whole Ag film grows with or without stacking fault with respect to the Pt(111) substrate [40]. The triangular network shown in Fig. 6b is an example for isotropic strain relief still exhibiting different areas for fcc and hcp stacking. This is realized by shifting one class of domain walls relative to the crossing point of the two others so that crossing of all three domain walls does not occur (see also the model in Fig. 4c). The offset 5 generates the small triangles characterizing the structure in Fig. 6b and allows for an optimized ratio between fcc and hcp stacking areas A, according to Eq. (6), and thereby accounts for the actual energy difference between both sides. A(fcc) / A(hcp) = [1 + 2(8/a) - 2(8/a) 2] / [1 - 2(8/a) + 2(8/a) 2]
(6)
Trigonal networks of the type discussed above are found in a number of epitaxial systems, e.g., in surfactant mediated growth of Ge on Si(111) [43], for Na adsorption on Au(111) [44], and for the 13phase of Ga on Ge(111) [45, 46]. In all these cases the systems try to increase their fraction of ideal stacking with respect to the faulted one. For Na/Au(111) and Ga/Ge(111) the domain walls are crossing in one point. In the alkali-metal case, therefore, the domain walls bend
160 and thus incline altemafing smaller (hcp) and bigger (fcc) triangles (see Fig. 4b). In the latter case, the domain walls have different width, which allows for bigger fcc areas. The symmetry of the domain wall pattern changes from uniaxial to quasi hexagonal for Ag films thicker than 2 ML grown at 300 K. The third monolayer (see Fig. 7) exhibits a periodic structure consisting of hexagonally arranged protruding areas surrounded by darker lines which again mark well localized partial dislocations. The space in-between these hexagons is again devided by partial dislocations although less clearly visible in the STM topographs. He-
STM
diffraction
(0,1)
(0,0) 0.010., . . . . . ;'. clean
2ML
10000
()a
, ~l~;~,'~ ........... :~!-~ ...........
0.005
5000
0.000 ~---"J ~'--'--- 1 ML
0
~, 0.005 : o.ooo k J
3 ML
1000
~__
0
2 ML
500 .~
0.005 -
~2J 0.000
0
3 ML
0.oo5j!j 0.000
10 ML
"~
1000 0
10 ML
0.005 ~ , , ~
~ d _ ~
0.000 -0.0
2.3
0.0 0.5 Q (/~-1)
2.7 Q(A -1)
000 0
i 100 A I
Figure 7. Transition from a domain wall phase to a weakly modulated incommensurate phase with increasing layer thickness of Ag films on Pt(111). On the left hand side we show STM images and on the right hand side the corresponding He diffraction pattern. The Hewavelength was )~= 1.02 A. STM images from [36], He diffraction data from [47].
161 The unit cell of the third layer is a rhombus quite similar to that of the trigonal dislocation pattern characterizing the equilibrium structure of the second layer. Therefore the striped phase of the second layer is unstable towards transformation into a hexagonal dislocation network upon covering it with an additional Ag layer at 300 K. The hexagonal domain wall network persists up to about 10 ML thick films (see Figs. 7). Notice, however, the decrease in image contrast at 10 ML which is associated with less well localized domain walls indicating a transition to a moir6 like phase. Thicker films transform into a weakly modulated structure with Ag(111) interplanar lattice constant. This transition in film structure from a misfit dislocation network to a weakly modulated incommensurate structure has also been detected in high resolution He-diffraction measurements [47]. On the fight hand side of Fig. 7 we show that up to 3 ML the diffraction spectra exhibit a splitting of the (0,1) diffraction beam characteristic for a dislocation network with its ( l x l ) pseudomorphic domains and the localized strain relief in narrow domain walls of lower density (this splitting is seen up to 8 ML, not shown here). At a Ag film thickness of 10 ML and above no splitting of the (0,1) diffraction peak is detectable; only one diffraction peak corresponding to an interplanar lattice constant of 2.89A is measured indicating the growth of Ag layers with bulk Ag(111) structure. The transition from the pseudomorphic monolayer through a series of domain wall structures with more or less localized strain relief to a weakly modulated moir6 phase with increasing film thickness can be understood qualitatively within the simple Frank-van der Merwe picture discussed above [3]. The elastic strain energy increases proportionally to the film thickness. For the monolayer the elastic energy is smaller than the energy to relax the film and the adlayer adopts a pseudomorphic structure. As the thickness and associated strain energy increase, the film relaxes gradually to its natural bulk structure. Initially this is achieved through introduction of hcp-fcc stacking faults, where the strain is locally relieved. At close packed interfaces the introduction of these defects is energetically favorable. However, the domain wall structures still contain substantial residual in-plane elastic distortions. By the gradual transition from the anisotropic striped or trigonal structures to hexagonal networks with larger domain wall widths the residual in-plane strain is progressively lowered. Finally the relaxation is completely isotropic with no in-plane strain resulting in weakly modulated incommensurate structure (moir6) with the bulk lattice constant of the film. It is, however, important to note that the discussion of the strain relief structures in the framework of the Frank-van der Merwe model is largely simplified. In this model the substrate is assumed to be rigid and the entire relaxation is occurring in the adlayer. Although this might be a reasonable
162 assumption for rare gas adlayers on metals or graphite it is certainly less adequate for metal-on-metal systems. In these systems the adsorbate-substrate interaction is of the same order of magnitude as the lateral interactions in the film and in the substrate. It is thus natural to assume that not only the film atoms relax at the interface but also the substrate atoms, i.e. the substrate acts as flexible elastic lattice. There is indeed compelling theoretical evidence that this is the case. It is a challenging but not impossible experimental problem to measure quantitatively the atomic distortions in the substrate upon interface formation. Recent STM studies of Ag growth on Ru(0001) in combination with EAM-calculations [28], and of P b / C u ( l l l ) in combination with EMTcalculations [48], suggest a flexible response of the metal substrate surface; the evidence from the STM data was, however, only indirect since the correlation of imaging and geometric height can even for metals be not trivial. Direct evidence might come in the future from crystallographic studies using x-ray diffraction which can access buffed interfaces [49]. 3.2. Strain relief mechanisms at interfaces with square symmetry The strain relief mechanism via fcc-hcp stacking faults is symmetrically impossible at interfaces with square symmetry because there are no different sites with similar adsorption energy (see Fig. 3). For these interfaces many experimental studies have been reported which seem to be in agreement with the predictions of the simple continuum model [22]. We have recently demonstrated, however, that also for these systems atomic details of the interracial structures have to be considered, which can result in novel strain relief mechanism and substantial deviations from the "Matthews picture". In this paragraph we present again STM results for the strain relief scenarios for two metal-on-metal systems with misfit of opposite sign; i.e., we will compare the strain induced structures of compressively strained Cu films on Ni(100) (m = 2.4%) with those of Cu layers on Pd(100) which is under-7.2% tensile strain. In Fig. 8 we show a series of STM images characterizing the Cu multilayer growth on Ni(100) at 350 K. Already in the submonolayer range at coverages of about 0.25 ML (not shown here) long protruding stripes appear at the islands which have a typical size of 60 - 80 A. The stripes protrude by about 0.6 A., have a width o f - 6 .~ (which is the typical STM-imaging width of a single atom [50]) and traverse the entire islands. At a coverage of one monolayer the whole surface is covered by a network of stripes (see Fig. 8a). The stripes all have the same width and are all running along I1 TO) with an equal probability for the two orthogonal domains. This pattern is maintained up to coverages of about 20 monolayers. The width of the stripes grows linearly with the coverage. Their density and their average length, on the other hand, remain constant in this
163 coverage range. Note, the stripes do neither cross each other nor coalesce. a)
O=IML
C) O - 1 1 M L ii:il,i,i~84 ........,~ . ............:....::: . .......,,. ....i~: .. ~ i
/
b)
O-6ML
d)
O-24ML
84184
........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1250 A ! Figure 8. STM images characterizing the multilayer growth of Cu on Ni(100) at 350 K. From [26]. In ref. [26] we have introduced a simple model which accounts for the experimental observations. It is motivated by the fact that the compressive strain at the fcc(100) surface is highest in the close-packed (ll0)-directions. Therefore, intuitively it could be expected that chains of atoms are squeezed out from the adlayer and create protruding stripes. Due to the square symmetry, these stripes have to form with equal probability in both (ll0)-directions, perpendicular and parallel to the substrate step edges. The simplest way to generate such stripes is to shift Cu atoms from their four-fold hollow site to the two-fold bridge site (see Fig. 9a). Such a bridge site atom has a reduced number of nearest neighbors in the substrate but it gains binding energy in the adlayer since it is six-fold coordinated there. There are two nearest neighbors within the (1 i-0) atomic chain and, in addition, four lateral neighbors with a binding length which is only about 10 % larger. More importantly, the protruding atoms gain lateral freedom of expansion and the film can partially relieve its strain.
164 Obviously, this lateral freedom of expansion together with the increased lateral coordination overbalance the lowered binding energy to the substrate. An important experimental observation is the fact that stripes neither cross nor coalesce at all coverages below about 20 ML (see Fig. 8). This behavior is easy to understand in the proposed model. There are two domains of bridge sites on the square fcc(100) surface representing the two symmetrically equivalent directions of the stripes. At their potential junction, two orthogonal stripes are always separated by 1/~f~ of a lattice constant (i.e. 1/2 nearest neighbor distance) rendering crossing impossible (see Fig. 9). Coalescence is also unlikely as the distance between two parallel stripes is given by the lattice constant of the Ni substrate and the merging of two stripes would block further transverse relaxation. Therefore, at higher coverages one can find neighboring parallel stripes which have a smaller width than the other stripes at the same image (see Fig. 8 , O -- 11 ML). Only at high coverages close to 20 monolayers, where almost all of the surface is covered by relaxed stripes, neighboring as well as orthogonal stripes merge and thereby form a high density of bulk dislocations. O= 1ML
0=3
Ah
ML
\
[001]
All I I I
I I I
I I
I I
m
[110]
Figure 9. Internal faceting model describing the appearance of the stripes in the Cu monoand multilayers on Ni(100). The shaded circles represent the substrate atoms (Ni). The "dark atoms" (Cu) are placed at the fourfold hollow sites in pseudomorphic geometry. The "light atoms" (Cu) form the stripes and are placed at the twofold bridge sites. In the monolayer case one can clearly see the two orthogonal domains of bridge sites which renders crossing of the stripes impossible. From [26].
165 Fig. 9 also shows the model for the trilayer film. The height Ah is independent of coverage. Considering the most simple case of a hard sphere model, one obtains Ah = 0.4 ,~ for the example of Cu on Ni. The width D depends on the coverage, i.e., for one monolayer the stripes are exactly one atom wide, for two monolayers two atoms and so on. While the atoms, situated at the hollow sites (dark colored atoms), grow essentially pseudomorphic, the stripe atoms (light colored) can relieve strain at least perpendicular to the stripes [26]. In our model the density of the stripes and their length distribution is determined by the monolayer configuration. The subsequent growth stabilizes the pattern of stripes by the formation of internal { 111 } facets along the stripes. This is energetically favorable because the strain relaxation takes place by the formation of the highly stable close-packed internal { 111 } facets. The growth of thin Cu films on Ni(100) was also studied by Chambers et al. [51 ] by Auger Electron Diffraction (AED). The ratio of the in-plane to vertical lattice constant (transverse lattice expansion) was measured, which is directly related to the strain of the film. The authors compared their data with the predictions of the continuum model of Matthews and Crawford [52] (thin solid line). The continuum model predicts a critical thickness of hc = 14.8 ,~ = 8 ML. Up to this thickness Cu should grow pseudomorphic. Only at coverages above 8 ML the film should relax its strain spontaneously by the formation of bulk dislocations. Chambers et al. interpreted their experimental data as confirmation of the continuum model. Fig. 10 shows clearly that the AED data are much better described by the internal (111)faceting model than by the continuum model. Using the internal faceting model and the STM data we have calculated the mean values of the transverse lattice expansion. The fraction of the relaxed stripe volume is determined by adding up the stripe coverage in the individual layers as determined by the STM measurements. The relative weight of the individual layers for the AED experiment has been accounted for by the simple ansatz I = I0 exp(-| using an attenuation factor of O0 = 7 ML. Assuming the stripe atoms are fully relaxed and the copper between the stripes is pseudomorphically grown, one obtains the dashed line in Fig. 10. However, it is likely that the copper close to the stripe boundary is not perfectly pseudomorphic but partially relaxed. It is reasonable to assume (see inset in Fig. 10) that the additional relaxation at the stripe boundary, ~(O), depends linearly on the coverage. With ~,(O) = 0 . 2 0 [in atomic distances], we obtain the thick solid line in Fig. 10 which is in excellent agreement with the data of Chambers et al. This implies that most of the copper between the stripes is pseudomorphic and the film relieves its strain gradually in a layer-by-layer fashion.
166
Continuum M o d e l
Fa
P
0.03-
l lx105 should be analyzed in a linear regression. Thus a slightly lower barrier of Em = 157+10 meV (v0 = 6x1013.~~ S-1) has been obtained when the slope was analyzed including data down to 65 K [92], where it is seen from Fig. 18a that post-nucleation already decreases island densities. The evolution of the island density with coverage for our example of Ag/Pt(111) at 75 K is plotted in Fig. 18b (compare also STM images in Fig. 16). Again, there is perfect agreement with the self-consistent rate equation analysis. Since the analysis did not account for coalescence, an experimental value at 0.12 ML for the (hypothetical) island density without coalescence has been derived, which can be accomplished, since coalesced islands are discerned by their shape from those that grew from a single nucleus. Fig. 18b also shows KMC simulations performed on a square lattice with the same parameters as in the rate equations. They are in perfect agreement with experiment and rate theory. The results from KMC simulations performed on a hexagonal lattice accounting for the dendritic island shape [108] are hardly discerned from the KMC results shown here. In general, KMC simulations have served as valuable test for nucleation and scaling theories [106, 118-121]. For our example of Ag/Pt, Fig. 18b shows that the self-consistent rate equations are in quantitative agreement with these simulations and both perfectly describe the experiment. Another common approach is to integrate rate equations of nucleation within certain approximations for the capture numbers ~, significantly reducing the calculational effort [92, 93]. These approximations are compared in Fig. 18b to the exact solutions and KMC simulations discussed above. The capture numbers describe the capability of islands or monomers to capture diffusing adatoms. They generally involve solutions of two-dimensional diffusion problems. This is not the case in the geometrical concept [122] where capture numbers are assumed to scale with the island diameter seen by the approaching monomers. This concept, when applied to fractal islands, yields 6x = 2+x 1/1"7 (with x being the island size in atoms, the constant of 2 accounts for atoms diffusing towards sites adjacent to the island perimeter). This approximation has successfully been applied to calculate the evolution of island densities with coverage at a single temperature [92]. It has been shown, however, to be inconsistent in so far as it yields a higher slope in the Arrhenius representation of the island densities compared to the slope expected from Eq. (7) [93]. It was noted early that the
183 geometric concept gives even more inaccurate predictions than constant capture rates [123], which should therefore be preferred as the most simple approximation. A more elaborate approach is obtained from solving the diffusion equation in the lattice approximation [104, 123]. This yields an analytic expression for Ox (stable islands) that depends only upon coverage. For monomers, on the other hand, a constant value of O l = 3 corresponding to the geometrical concept can be used for simplicity. The rate equations for monomers and stable islands read for the case of metal epitaxy at low temperatures, i.e., for dimers being stable and immobile and neglecting reevaporation (compare Eqns. 2.3, 2.5, 2.6. and 2.8 in ref. [82]): dnl = F - 2o'1Dnl2 - O'xDnln - F ( F t - n I ) - 2Fn 1 dt x dn
x = O-lDnl2 + Fn 1 dt
(8)
(9)
The terms on the fight hand side of Eq. (8) denote the increase of monomer density due to deposition with flux F, their decrease due to the encounter of two diffusing atoms under creation of a dimer associated with the disappearance of the two atoms, the decrease occurring when a monomer is captured by a stable island, and the last two terms denote the decrease caused by direct impingement onto stable islands, respectively monomers. In Eq. (9) the terms on the right hand side account for the increase of stable island density nx due to creation of dimers, first when two monomers meet by diffusion, and second upon direct deposition onto a an adatom. For sake of comparison with the self-consistent analysis above, coalescence is neglected in Eq. (9); incorporation would add a further term -2nx(F-dnl/dt). The result from numerical integration of these equations within the lattice approximation (see dash-dotted curves in Fig. 18) is seen to compare well to self-consistent rate theory as well as to KMC simulations and experiment (apart from the small deviation in slope). In variance to this result, the lattice approximation has earlier been reported to yield slightly too high values [93]. This discrepancy might be ascribed to a small difference in the equations used by Bott et al., i.e., they did not account for direct impingement onto monomers expressed by the last terms in Eqns. (8) and (9). Note, that coalescence is not very accurately described by the coalescence term, e.g., for 1 ML the island density stays at a finite value. In summary, the straight forward analysis of island densities by mean-field nucleation theory by means of Eq. (7), when performed for D/F > 105 and a critical nucleus size of one, allows to determine the energy barriers and attempt
184 frequencies for surface diffusion with good accuracy. This precision can further be increased when comparing experimental data to self-consistent mean-field theory or to KMC simulations, which both are fully consistent to each other. In addition, nucleation theory has recently been subject of rather direct experimental tests which all underline its validity for isotropic substrates [9, 87, 92, 117]. This has placed its application for extracting parameters for surface diffusion from island densities on a firm basis. Also for anisotropic substrates, a mean-field treatment was put forward [97], and applied to estimate diffusion barriers [94, 95].. For these cases, however, generally more experimental information is needed to discern anisotropic terrace diffusion from anisotropic diffusion around and sticking to the island edges [95, 96]. For this purpose, and generally for cases where many diffusion processes are involved, as well as for island size and distance distributions, KMC simulations are a valid tool for comparison with experimental data and as a check for predictions from meanfield and scaling theories. 4.2. Effect of isotropic strain on surface diffusion and nucleation Isotropic strain, as it appears in the growth of pseudomorphic heteroepitaxial layers, is the variation of the in-plane lattice constant of the film material with respect to its bulk value. Theoretically, it has been pointed out several times that surface diffusion and thus nucleation should be altered by strain. Two molecular dynamics simulations were proposing that for semiconductor surfaces strain changes adatom mobilities [75, 76]. A theoretical study was explicitly investigating the effect of strain on the nucleation kinetics on vicinal surfaces [77] and there was even the suggestion to apply strain in order to influence the growth kinetics - with the goal to grow linear structures attached to the steps of a vicinal substrate [78]. Only very recently, however, the influence of strain on surface diffusion and nucleation has been addressed experimentally. The experiments showed that the barrier to surface migration on a pseudomorphic Ag monolayer on Pt(111) is significantly reduced with respect to that on a fully relaxed Ag(111) surface. This observation prompts the question whether this effect is indeed due to strain, or rather caused by the electronic adlayer-substrate coupling. Calculations within Effective Medium Theory (EMT) and very recent ab-initio calculations [124, 125] demonstrate that in fact strain is by far dominating electronic coupling. In this Section, we discuss these first experimental and theoretical results on surface diffusion on isotropically strained surfaces. For the system Ag/Pt(111) there is a strong layer dependence of island densities as becomes evident from inspection of Fig. 19. The three STM images were obtained for low temperature nucleation of Ag on Pt(111), on the first Ag
185
monolayer grown on Pt(111), and on Ag(111), respectively (see Figs. 19a- 19c). a)
b)
c)
I
d) - 1.5
i
i
100 A
I
!
,..l -2.0 .= - 2.5 =
-3.0 -
9
9
9
O .=~
-3.5 -4.0 O
Y
9
Ag/1MLAg/Pt(111)
i
-4.5 0.005
!
!
!
0.01
0.015
0.02
.,d
0.025
T - I [ K -1]
Figure 19. STM images showing the nucleation of submonolayer coverages of Ag on Pt(111) a), 1 M L A g / P t ( 1 1 1 )
b), a n d o n A g ( 1 1 1 )
c), r e s p e c t i v e l y . ((a) T = 65 K; (b) T = 6 5 K; (c) T =
60 K, size 307x307 A2). d) Arrhenius plot of saturationisland densities derived from STM for nucleation of Ag on Pt(111) (11), on 1MLAg adsorbed on Pt(111) (&), and on Ag(111) (O), respectively. From [9]. The lowest island density is observed on the first Ag layer. The structure of this layer is pseudomorphic with respect to the Pt(111) substrate [23, 40, 41, 126]. The Ag interatomic distance in this layer is therefore reduced by 4.3% with respect to the Ag bulk value. The Ag(111) surface has been prepared by deposition of a thick Ag film onto Pt(111) at 450 K and subsequent annealing to 800 K. This yields extended, perfectly flat terraces, giving rise to a single diffraction peak in high-resolution He-diffraction measurements which corresponds to the interplanar lattice constant of bulk Ag(111) of 2.89 A [47].
186 The temperature dependence of saturation island densities on these three substrates shows strongly differing slopes, indicative for differing migration barriers (see Arrhenius in Fig. 19d). Nucleation on the pseudomorphic Ag layer is characterized by the smallest slope, followed by Ag(111) and finally by Pt(111). These slopes directly yield the parameters for surface diffusion on these layers, since dimers are stable for the data shown here. This is indicated by the absence of bends in the Arrhenius and has also been verified by dimer annealing experiments. The resulting migration barriers Ern on the different isotropic layers amount to 168+10 meV for Ag/Pt (see preceding Section), 60+10 meV for the pseudomorphic Ag layer and finally 97+10 meV for Ag diffusion on a strainfree Ag(111) surface [9]. The most conspicuous effect uncovered by the STM experiment is the low barrier for Ag diffusion on the pseudomorphic Ag layer compared to unstrained Ag(111). Two effects are conceivable to cause the observed lowering. It may either be due to the 4.3% compressive strain or an effect of the electronic adlayer-substrate coupling. In order to decide which of both is dominant we consider the results from EMT [127, 128] calculations represented in Fig. 20. These calculations have been performed for a Ag atom adsorbed on a periodically repeated 6x6 cell of a 5 layer thick slab; the three upper layers of which were free to relax. The adatom is then pulled over this surface, allowing its position to relax freely in a plane perpendicular to the vector of displacement to find the minimum of total energy in course of this displacement. The diffusion barrier Em is then determined as the difference in total energy between the transition state (bridge site) and the preferred adsorption site (fcc- or hcphollow). In order to investigate the effect of strain on the diffusion barrier, the Ag(111) slab has been subjected to strain by changing its lateral dimensions while leaving it free to relax in the (111) direction. The EMT results presented in Fig. 20a clearly show that strain has a pronounced influence on migration barriers. For a compression of 4.3% the barrier is lowered from 67 to 40 meV, respectively by 40% This compares well to the experimentally observed lowering. Regarding absolute values, it is known that EMT underestimates diffusion barriers on close packed surfaces [ 129, 130], however, the order of the calculated barriers is in full agreement with the experimental values for our example [9]. The migration barrier for Ag on a pseudomorphic Ag monolayer on Pt(111), on the other hand, is found in the EMT calculations to be only slightly higher (50 meV) than the strained Ag(111) case. These calculations therefore suggest that electronic effects of the Pt substrate even slightly decrease the effect of strain, at the same time they identify strain as the dominant origin for the observed lowering of the migration barrier.
187 Rather good absolute values for migration barriers on close packed surfaces have recently been provided by ab-initio calculations, either performed within Local Density Approximation (LDA) or with Generalized Gradient Approximation (GGA). (For a review on ab-initio calculations of surface diffusion see Chapter by Ruggerone, Ratsch, and Scheffler in this Volume.) The barrier for Ag/Pt(111) has been calculated by Feibelman to 200 meV [ 131 ], and recently by Ratsch and Scheffler to 150 meV, both in good agreement with the experimental value. For Pt(111) self-diffusion, the theoretical values (380 meV [ 130], 390 meV [125]) lie above the established experimental result of 0.25 eV [93, 130]. For Ag(111) self-diffusion 100 meV has was calculated by J. J. Mortensen et al. using calculations with GGA [ 125] in agreement with the LDA value of 90 meV obtained by Ratsch and Scheffler [ 124] (a slightly higher value of 140 meV was reported in a recent LDA calculation [132]). As in the case for Ag/Pt, also these theoretical numbers are in good agreement with experiment (97+10 meV, see above). Therefore, it is particularly valuable that these more precise calculations are in agreement with the interpretation formerly deduced from the EMT results presented above. Ratsch and Scheffler find reduced diffusion barriers on the pseudomorphic Ag layer on Pt(111), 65 meV, as well as on a compressively strained (by 4.3%) Ag(111) slab, also 65 meV [124]. These values agree well with the experiment and fully support the interpretation that strain is the origin for the decrease in the diffusion barrier (40%) on a compressively strained Ag layer (4.3%) when compared to strain free Ag(111). This result is corroborated by Mortensen et al. who explicitly address the correlation of strain and diffusion barriers and calculate the derivative of Em with lattice mismatch for several transition metals [ 125]. 80.0
|
a)
b)
70.0 m
ii
IB
IB
~-~ -2.350
60.0
~ -2.4oo
E .~ 50.0
bridge site [ three fold hollow site
40.0
9 9
-2.450 30.0 0.90
,
0.95
1.00
I
l
1.05
,
1.10
0.90
i
0.95
,
,
1.00
i
1.05
,
1.10
lattice constant [aAg (EMT) = 4.075 ~]
Figure 20. EMT calculations of (a) the barrier for Ag self diffusion on a Ag(111) slab, and (b) binding energies in the transition (bridge) and binding (hollow) sites as a function of tensile or compressive strain. From [9].
188 The physical reason for the strong influence of strain on the diffusion barrier at a close packed surface can be analyzed on hand of EMT calculations. From Fig. 20b it is seen that the binding energy in the three-fold hollow site increases almost linearly with strain. The binding energy in the transition state, on the other hand, varies only little for strains in the range of +2%. Since the migration barrier is the difference between these two values, it varies almost linearly in that range; increasing for tensile and decreasing for compressive strain. The decrease of the diffusion barrier induced by compressive strain is mainly caused by a smaller binding energy in the hollow site. As expected, for tensile strain the binding energy in the hollow is increased, which leads to the increase in Em. For larger compressive strains, migration becomes increasingly fast, the barrier attains half of the unstrained value at 4.8% compression. At high tensile strain (> 3.5%) the transition state drastically decreases its energy which explains the bending of the curve and the second decrease in Em. This can be understood by the increasing softness of the layer with increasing lattice constant. Thus atoms involved in the bridge configuration corresponding to the transition state can relax more efficiently. The result is that the barrier attains a maximum (75 meV at 3.5% tensile strain) and then it drops upon further increase of the lattice constant. Ab-initio calculations don't find this second decrease of Em, apart from this they fully support the physical picture derived here from EMT [ 124]. The experimental results discussed in this Section, although available for only one system so far, suggest that isotropic strain in general may have a pronounced influence on adatom mobilities. This is supported by recent ab-initio calculations performed for self-diffusion on strained fcc(111) surfaces of several metals [125]. For all studied metals (Ni, Pd, Pt, Cu, Ag, Au) the authors find tendencies similar to that of A g / P t ( l l l ) , i.e., decreasing barriers for compressive, and increasing barriers for tensile strain. We will discuss in Section 4.4. below that strain also strongly influences interlayer diffusion. Therefore, the entire nucleation and growth kinetics of heteroepitaxial systems may be dominated by these strain effects. 4.3. Nucleation on anisotropically strained substrates As has been discussed in Section 2 of this chapter, the strain energy present in heteroepitaxial systems can lead to a transition from pseudomorphic to weakly incommensurate layers. Together with the substrate reconstructions these weakly incommensurate surfaces all have in common non-uniform interatomic distances, i.e., they reveal anisotropic strain. In the preceding Section we have seen how sensitive barriers for surface diffusion depend on isotropic strain, we therefore expect strong effects on the nucleation kinetics also for anisotropic strain. The example for Ni/Ru(0001) (see Fig. 15) already
189 showed that this is the case. In this Section we will discuss the effect of anisotropic strain in more detail in concentrating on the case of fcc(111) surfaces and the role played by their partial dislocations in nucleation kinetics. We will first show two examples for nucleation on the A u ( l l l ) surface with its reconstruction revealing a higher density of surface atoms. In comparison, we discuss an example of nucleation on a surface where the partial dislocations reduce the surface density, i.e., on a regular dislocation network of the second Ag layer on Pt(111). The (111) surfaces of Au and Pt are known to reconstruct, driven by the considerable tensile stress in the outermost layer. As discussed in detail in Sect. 3.1. these reconstructions consist in the introduction of a certain density of dense domain walls, or partial dislocations, between alternating fcc and hcp stacking regions. Chambliss and coworkers showed that the "elbows" at the Au(111) surface, where the partial dislocations bend act as sites of preferred nucleation for Ni deposited at room temperature [133-135]. This leads to quite regularly spaced islands accompanied by a narrow island size distribution (see Fig. 21).
2o0 h Figure 21. STM images of Ni nucleation on the (~/3x22)-reconstructed Au(lll) surface at room temperature, a) Large scale image showing the mofiolayer Ni islands aligned in rows along the .~ll2)-directions (| = 0.11 ML). b) Detail showing that islands are located at elbows of ttie herringbone reconstruction (| = 0.14 ML). From [133]. Preference of nucleation at, or close to elbows of the Au reconstruction was also observed for room temperature deposition of Fe [136, 137], Co [138], and Rh [139]. The case of A u ( l l l ) auto-epitaxy is less clear. In a study by
190 Chambliss et al., too few islands formed at room temperature precluding statistically significant statements [134]. In contrast, in an earlier work nucleation has been found at elbows, however, in that study the sample was transferred through air which is likely to invoke contamination problems [ 140]. For Ag, on the other hand, nucleation is homogeneous and independent of the mesoscopic order of the (~/3x22)-reconstmction [141,142]. The same is true for Cu [ 143] and also for A1 as we will discuss below. The distinctive anisotropy of the nucleation probability at elbows of the reconstruction, found so far for Ni, Fe, Co, and Rh, was ascribed by Chambliss et al. in the case of Ni/Au(111) to attractive potential wells located at elbows which effectively trap single diffusing atoms. It has been shown in a Monte-Carlo simulation that already small trapping probabilities at the elbows may be sufficient to cause the experimentally observed alignment of islands [ 133]. Very recently, the system Ni/Au(111) was revisited evolving an alternative explanation [ 144]. The authors demonstrated that the Ni adatoms perform a place exchange with Au surface atoms localized at the elbows, followed by preferential nucleation of Ni islands on top of substitutional Ni atoms. The elbows are areas of locally increased strain, since there a close packed atomic row terminates, as directly demonstrated on hand of STM images of these regions [133, 145]. As a result, there is one Au atom with only 5-fold lateral coordination. The reason for preferred place exchange at elbows is thought to be this reduced coordination in these highly strained areas rendering place exchange easier than throughout the terraces. A necessary condition for preferred nucleation at elbows, or in general at dislocations is that these can be reached by adatoms, which implies that the total binding energy must either stay constant or increase at these sites (the latter would render dislocations attractive). On the other hand, if the binding energy decreases at dislocations, they constitute repulsive barriers that may effectively reflect migrating adatoms. As an example for the latter case we discuss the nucleation of A1 again on the reconstructed Au(111) surface at low temperature [ 146]. From the STM image shown in Fig. 22 it is seen that at 150 K A1 islands nucleate in-between the partial dislocations of the otherwise unperturbed reconstructed Au(111) surface. In the Arrhenius plot of the saturation island density there are three regimes of nucleation clearly distinguished by their markedly different slope. For temperatures below 200 K, mean island distances lie below the distance between dislocations. (The corresponding island density is marked by the dashed horizontal line.) This indicates that also the mean free path of diffusing atoms is below this value and the adatoms predominantly diffuse and nucleate on the isotropic fcc and hcp areas and do not see much of the dislocations. For this regime a migration barrier of 30+5 meV is extracted
191 from the slope under the assumption of isotropic diffusion. This barrier compares well with results from density-functional-theory (DFT) calculations performed by Stumpf and Scheffler yielding a barrier of 40 meV for AI(111) self-diffusion [147]. Notice, however, that for Au(111) self-diffusion a much higher barrier (0.22+0.03 eV) has been calculated also with first principles methods [132]. 245 225 200 180 10-2 ~ " i ' ' l ' i i
"~
z
150
120
100
i
i
I
10- 3
&
10- 4
i
1200A i 10-5 4
5
6
7
8
9
10
[l/T] x 10.3 Figure 22. Arrhenius plot of saturation i~and ,densities deduced from variable-temperature
STM for the nucleation of A1 on the (~/3x22}-reconstructed Au(ll 1) surface (O = 0.100.15 ML, F = 3.1x10 -4 ML/s). The ins6t show's that islands nucleate in-between the partial dislocations (O = 0.04 ML, T = 150 K, F = 3.1x10-4 ML/s). From [ 146]. At temperatures above 200 K the adatoms cross dislocations as the mean island separation becomes larger than the dimensions of the (~f3x22)-unit cell. The diffusion over partial dislocations is associated with an increased barrier, reflected in the strongly increased second slope. Here, a quantitative analysis in order to extract an effective barrier for crossing dislocations would require a KMC simulation, since mean-field nucleation theory is no longer applicable for this particular case. We notice, however, that this barrier is significant, compared to the small barrier to diffusion on the pseudomorphic parts of the substrate. The finding that dislocations can represent repulsive barriers is corroborated by EMT calculations performed for P t ~ t ( l l l ) [148]. In these calculations, the binding energy of the Pt adatom is found to be decreased as it
192 approaches the partial dislocation. Even if the change in total energy is small (half the migration barrier), it is feasible to lead to drastic changes in diffusivity because atoms have to make successively several jumps into unfavorable directions to overcome a dislocation. This interpretation is supported by experimental evidence for a high effective barrier towards crossing of dislocations for Pt/Pt(111)recently reported from STM observations on the nucleation behavior of this system at 650 K [79]. At temperatures above 400 K the Pt(111) substrate surface is known to reconstruct in the presence of Pt adatoms [32]. The dislocations associated with the reconstruction are observed to lead to a strongly reduced mobility on the reconstructed substrate terraces. Since islands do not reconstruct, the mobility remains high on-top of them (see Fig. 14, we have the case where Dn >> Dn-1). Together with the fact that the interlayer barrier can readily be overcome above 400 K, this causes the most perfect layer-by-layer growth observed so far [71, 79]. The third nucleation regime of A1/Au(111) sets in at 245 K and is again clearly discerned by its slope in the Arrhenius in Fig. 22. It is due to modification of the reconstruction associated with alloy formation [149]. Alloy formation with the Au(111) surface has also been found for Pd from 240 K on [150], and for Rh on upon annealing to 670 K [139]. A case of nucleation on a regular network of dislocations of reduced density has been reported for Ag nucleation on the second Ag monolayer adsorbed on Pt(111) [9]. The second Ag layer transforms upon annealing to 800 K from a striped incommensurate phase into a trigonal network of crossing dislocations as discussed in detail in Sect. 3.1. Ag nucleation onto this surface at low temperature leads to a high density of islands where the majority is located away from dislocations [9]. This implies that they constitute repulsive barriers as in the preceding example. For increasing temperatures the island density approaches a minimum at 110 K, where only one island forms per network unit cell. Figs. 23 a) and b) show nucleation at 90 K and 110 K with on the average 1.3 and 1.1 islands per unit cell of the superstructure. Note that very few of the islands form on dislocations, the majority nucleate on the hexagons of the unit cell, which are pseudomorphic with fcc stacking [40]. These examples illustrate that dislocations in general strongly influence nucleation. They can constitute rather effective repulsive barriers, leading to an increased island density, even if diffusion on the homogeneously strained parts of the surface may be fast. Dislocations can also act as preferred nucleation sites which can be understood in terms of localized strain which either facilitates exchange or locally increases migration barriers, or binding energies. Whether dislocations act as nucleation sites or reflective barriers for migrating atoms depends on the variation in binding energy, the diffusion barrier when crossing
193 the dislocation, as well as the tendency to alloy formation, and has to be investigated for each particular system.
a)
b) ......:,,:!ii~!ii ~I!I~I!~ ~!~!!ii
I
100 ,/k
Figure 23. STM images showing nucleation of Ag on a regular trigonal network of dislocations formed by 2 ML Ag/Pt(111) after annealing to 800 K. a) T = 90 K, island density nx = 1.3 per unit cell of superstructure, O = 0.03 ML, (b) T = 110 K, nx= 1.1 per unit cell of superstructure, O = 0.12 ML. From [9]. Independent from the respective nature of the interaction, the influence of dislocations and in general anisotropic strain on nucleation can be applied to significantly decrease the width of island size- and distance distributions when compared to nucleation on isotropic substrates. Here, one takes advantage of the fact that there is generally a strong repulsive interaction between dislocations often leading to their arrangement in periodic patterns. Fig. 23b shows that quite regularly spaced islands with a narrow size distribution may result upon nucleation on such a network. Also in moir6 patterns, there are periodic variations in strain and/or adatom binding energy which may similarly lead to regular island spacing for nucleation on these layers. It has to be kept in mind, however, that, at least for the case of repulsive barriers, one is confronted with the fact that there is no plateau in temperature for the desired island density of one island per superstructure unit cell but rather a change in slope necessitating the careful choice of the deposition temperature. The influence of anisotropic
194 strain on surface diffusion can also be the key to understand anisotropic diffusion observed on hex-reconstructed fcc(100) surfaces [95, 96]. Finally, anisotropic strain is in general expected to strongly influence surface diffusion and nucleation. This has direct implications for growth morphologies of heteroepitaxial systems with lattice mismatch and even for homoepitaxial systems when they are unstable upon reconstruction due to their intrinsic tensile stress.
4.4. Strain and interlayer diffusion When an adatom approaches a descending step, it generally encounters an additional energy barrier for descend. This additional step edge barrier, AEs = Es - Em, is the energy barrier for an adatom to descend the step minus the diffusion barrier on a fiat terrace (see potential energy diagrams in Fig. 24). Although first experimental evidence for this barrier was observed already 30 years ago by Ehrlich and Hudda [151] and theoretical consequences were discussed at that time by Schwoebel and Shipsey [152, 153], quantitative measurements of AEs are rare [154, 155]. a)
Ag/Ag(111)
b)
Ag/Ag-Islands / Pt(111)
Em=60meV
li,--,i
>
AEs=120meV ~0.1 0
~JIEm=97me V I
~
@V~
0.17
-[ AEs=30meV
r---ll/A/ m=168me v
0
-
IV
"
"-'-
Figure 24. Potential energy diagrams (a) for Ag(lll) homo- and (b) for Ag/Pt(lll) heteroepitaxy of the first layer. From [ 10]. In addition to these direct measurements by FIM, there have been various approaches to derive estimates for AEs from the film morphology at a given coverage and temperature, mostly obtained from STM. In the absence of interlayer mass transport the exposed coverages in successive layers obey a Poisson distribution. The deviation of the layer occupancies from this distribution, due to a certain amount of interlayer transport, can be analyzed to estimate the additional step edge barrier. For this purpose typically a linear model for interlayer mass transport [156] is applied. In recent literature, this model has been refined to account for layer dependent interlayer [74] and also
195 intralayer diffusivity [157, 158]. Also a model based on the critical coverage for second layer nucleation has been applied to STM data [158]. Recently, Tersoff et al. used mean-field nucleation theory to show that the nucleation rate on-top of islands reveals a sharp transition from 0 to 1 with increasing island radius [ 159]. Based on this approach, a general method for the quantitative determination of the additional step edge barrier was developed [ 10]. From the measurement of the nucleation rate on-top of previously grown islands as a function of their size and substrate temperature, AEs and the corresponding attempt frequency can be inferred with high accuracy. As ingredients, one needs to know the parameters for terrace diffusion and the critical cluster size on-top of the islands. We discuss this method for the example of Ag(111) homoepitaxy which has frequently been addressed in recent literature [ 10, 74, 160, 161 ]. It reveals a considerable additional step edge barrier [10, 157, 158] and thus grows 3D below 400 K while it grows 2D (step flow) at elevated temperatures [74]. We will compare the results to Ag heteroepitaxy on Pt(111). As in the case of terrace diffusion, also interlayer diffusion is strongly influenced by strain. A fist step for the experiment is the preparation of a high abundance of circular 2D islands with a size distribution sufficiently broad to enable the study of the nucleation rate on-top of these islands as a function of their size. Such a distribution of islands can be synthesized in a simple way via Ostwald ripening [ 107]. Fig. 24 shows STM images of 2D Ag islands grown on a Pt(111) surface by annealing dimers and trimers created from a low temperature deposition experiment. There is a clear threshold temperature for the onset of Ostwald ripening as inferred from the graph in Fig. 25. This temperature is 100 K in our case of annealing periods lasting half an hour. This threshold bears valuable information on critical cluster sizes and their mobility; since dimer (and trimer) dissociation and their mobility would lead to detectable island coarsening, both can be excluded below this threshold. Annealing to higher temperatures leads to an exponential increase in mean island size due to Ostwald ripening, i.e., stronger evaporation from smaller islands leading to their decay in favor of larger ones. The islands of 6, 14, and 200 atoms average size are to a good approximation circular. Those containing 800 atoms on the average begin to approach the thermodynamic equilibrium shape, i.e., a distorted hexagon with the two kinds of close packed steps having different length's according to their free energy difference [ 107, 114]. The size distributions of Ostwald ripening satisfy a scaling law and are by a factor of 2 more narrow than those obtained from nucleation experiments [ 108]. As we will see below, the width is still sufficient to study the nucleation rate as a function of island size. Notice that this method of preparation of circular islands
196 by Ostwald ripening is generally applicable to a any epitaxial system that does not show intermixing at the required annealing temperatures. ll0K
n-6
140K
n=14
n=200
,'100A,,
ilO0 A I 280 K
230K
I 800 A i
n = 800 1000
9
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9
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9 deposition at 50K "~ .,,.,
100
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t~
1 50
I 8~176
I
,
100
I
150
,
I
200
i
I
250
,
300
annealing temperature TA [K]
Figure 25. STM images showing that compact 2D Ag islands with defined sizes are obtained via deposition of 0.1 ML Ag at 50 K on Pt(111) and subsequent annealing. The graph shows the exponential increase of the mean island size with annealing temperature due to Ostwald ripening. From [ 107]. To study the nucleation probability on these well prepared 2D islands, a submonolayer coverage is then deposited in a second step at a certain temperature. As can be seen from Fig. 26 only a fraction of the preexisting islands reveal second layer islands on-top, the smaller islands are mostly bare of second layer nuclei. In addition, the critical size for second layer nucleation increases with increasing temperature (compare Fig. 26 a and b, where the second deposition step has been performed at 60 K and 85 K, respectively). Due to the low coverage of the preexistent islands most of the deposited material
197 lands on the substrate surface (in our example 90%). These atoms then either form additional islands in-between those prepared by Ostwald ripening, as the case in Fig. 26, or they attach to the preexisting islands and contribute to their growth. These two cases will have to be distinguished in the analysis described below.
a)
T - 60 K
b)
I 200 A I
T = 85 K
I 200 A I
Figure 26. STM images showing the results of nucleation experiments, in which 0.1 ML Ag were deposited (F = 1.3x10-3 ML/s) on compact 2D Ag islands that have previously been prepared by Ostwald ripening on Pt(111). From [ 10]. The fraction of islands revealing second layer nucleation deduced from a large number of STM experiments, taken out at three different temperatures, is shown in two graphs in Fig. 27 for the case of Ag homoepitaxy and Ag/Pt(111) heteroepitaxy, respectively. It is clearly seen that there is a well defined transition for the nucleation probability from 0 to 1 as the island size increases. The curves show the best fits to the experiment resulting from a calculation applying mean-field nucleation theory [159]. This theory yields that the nucleation rate on-top of an adisland strongly depends on the 2D monomer density that builds up there (to the power of the stable island size). Under steady state conditions, i.e., the incident atom flux onto an island equals the downward flux from that island at its perimeter, and for circular islands, this density has a parabolic radial dependence. Its maximum is located at the island center and determined by the island size and the ratio of interlayerto terrace diffusion. This ratio is given by exp(-AEs/kT), where AEs is the additional step edge barrier introduced above. Integrating the nucleation rate over the island area in course of deposition yields the curves shown in Fig. 27. Depending on the mean-free path of adatoms on the substrate compared to the
198 mutual distance deposition step deposited on the island size when
of the preexistent islands these may grow during the second due to diffusion and attachment of material that has been substrate. This can be accounted for in including a variation of integrating the nucleation rate over time [ 10].
a)
Ag/A_A.g(111) I
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I
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I
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.-.
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,~ 0.0 I
,
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.
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Figure 27. Quantitative evaluation of the nucleation probability for Ag in 2D Ag islands on Ag(111) (a) and Pt(111) (b). The fraction of covered islands is shown as a function of island radius and deposition temperature determined from STM experiments in comparison to theoretical curves representing the best fits. From [ 10].
199 In analyzing STM data obtained at various temperatures one can clearly separate the attempt frequency form the additional barrier for interlayer diffusion. The first predominantly shifts the whole set of curves along the abscissa in Fig. 27, whereas the latter largely determines the horizontal distance between the curves for the various temperatures. The fits are rather sensitive to the only free parameters, v0 and AEs, especially to the choice of AEs, which in turn allows its precise determination. For Ag homoepitaxy an additional step edge barrier of AEs = 120!-_15 meV is obtained with this method. This is higher than the Ag adatom diffusion barrier of 97 meV (see Fig. 24) and explains the 3D growth of the homoepitaxial system experimentally observed below 400K [74]. The values estimated for Ag(111) in previous studies, either from layer occupancies (150+20 meV) [157] or from the critical coverage at the onset of second layer nucleation (0.19 - 0.23 eV) [158], are both slightly higher than the value for AEs determined above. Both evaluations are based on STM data obtained at a single temperature and therefore presumably reveal higher uncertainties than the value derived above from the temperature dependence of the nucleation rate on-top of preexistent islands. The additional activation energy for step-down diffusion in the strained heteroepitaxial system Ag/Ag islands/Pt(111) is determined to AF.s = 30+5 meV. This is only 25% of the barrier in the homoepitaxial case and thus remarkably small. There are two differences to the homoepitaxial case which are conceivable to cause the observed lowering of AEs. While in homoepitaxy both, upper and lower terrace are energetically on the same level, energy levels of successive layers may be different in heteroepitaxy. In the case of Ag/Pt(111) the binding energy for an Ag adatom on the 1st Ag layer is about 170 meV lower than on the Pt(111) substrate [ 126] (see Fig. 24). This energy difference might be thought to bend down the potential at the step, implying, however, that the energy gain must be available to the descending atom already in its transition state. Whether this is reasonable certainly depends on the microscopic mechanism for descend. The second difference with respect to A g ( l l l ) homoepitaxy is the substantial compressive strain of 4.3% inherent in the 1st Ag layer on Pt(111) [10]. The pseudomorphic islands preferentially relieve their strain at the edges where the Ag atoms are free to expand laterally. This edge relaxation can certainly favor exchange processes which have been suggested as the mechanism associated with the lowest barrier for atom descend on fcc(111) surfaces [129, 147, 162]. The strain argument is strongly corroborated by the observation that the low interlayer barrier is only observed where the Ag layer is free to relax at its edge. If this is not the case, e.g., where the Ag layer touches a former Pt step, atom descend is inhibited leading to the formation of pin holes at
200 steps [36]. Similarly to the first Ag layer, descend from the second Ag layer is found to have a reduced additional barrier of AEs = 60+20 meV as estimated from layer occupancies [36]. Presumably, also here the strain still present in the second layer is causing the slightly reduced barrier with respect to the strain free Ag(111 ) case. Strain can also be thought to be involved in the decrease of AEs caused by certain surfactants. As an example we consider the oxygen mediated layer-bylayer growth of Pt/Pt(111) [ 163]. Pt islands on Pt(111) are under tensile stress. Chemisorption of an electronegative adsorbate like oxygen at the island edge weakens the lateral bond of the edge atoms towards the island. This manifests itself in a detectable outward relaxation of the edge atoms [164]. Outward displacement of edge atoms constitutes the first step to adatom descend by exchange. Therefore, the outward relaxation of edges, either by strain or by electronegative adsorbates, can lower the barrier to interlayer diffusion. Notice, all values for interlayer diffusion discussed here represent effective barriers, they can not unambiguously be assigned to a microscopic diffusion process. These effective barriers, however, determine the growth morphology in a real deposition experiment and its precise measurement with the method outlined above is therefore rather valuable. The nucleation rate method is an alternative to FIM measurements for the determination of AEs. FIM studies generally allow to trace the atoms in their initial and final state before and after descend, in order to find the microscopic pathway. However, for interlayer diffusion, this is often hampered by edge diffusion immediately following descend [155]. In some cases, the effective barriers measured with the nucleation method can be related to a microscopic process. If there is an interlayer process associated with a particularly low barrier, than the measured effective barrier presumably reflects the activation energy for this most efficient process. For close packed surfaces, e.g., the process associated with the lowest barrier is likely to be exchange at B-steps, since there atoms move out more easily than at straight A-steps. The example of A g / P t ( l l l ) shows that the step-edge barrier on the pseudomorphic Ag-islands is found to be substantially lowered with respect to the homoepitaxial system. This lowering is related to relaxation effects at the edges of the compressively strained islands. It is likely that stain in general strongly influences adatom descend at steps. Due to the example discussed here compressive strain facilitates interlayer diffusion, which presumably takes place through exchange on fcc(111) surfaces. It is certainly very interesting to apply the method for the quantitative measurement of AEs described above to further study the influence of strain on interlayer diffusion. The results obtained so far, clearly indicate that strain effects can cause layer dependent interlayer barriers
201 which will have to be taken into account for modeling the kinetics in heteroepitaxial growth. Within the recent years considerable progress has been made in the quantitative understanding of the microscopic processes involved in epitaxial growth. New methods have been developed to determine their activation energies. They rely on the application of mean-field nucleation theory or Kinetic Monte-Carlo simulations to island densities obtained from measurements with variable-temperature STM. This technique supplements FIM measurements which so far have been the most important and precise source for activation energies for diffusion of single particles. Other than FIM, the new approach with variable temperature STM allows to study strain effects and diffusion on large areas. The examples reviewed in this Section are the first experimental indication that strain has a pronounced effect on terrace, as well as on interlayer diffusion. The activation energies obtained for various systems with this new technique are valuable for comparison with theoretical calculations which in the past improved considerably concerning absolute values. Together with theory, the recent progress in experimental study of the relevant microscopic processes has certainly increased our understanding of the kinetics of epitaxial growth. ACKNOWLEDGEMENTS We gratefully acknowledge valuable contributions of C. Boragno, K. Bromann, J. P. Bucher, B. Fischer, A. Fricke, E. Hahn, E. Kampshoff, B. MUller, L. Nedelmann, H. Rtider, C. Romainczyk, and N. W~ilchli to the experimental results presented here. We also acknowledge collaboration with J. Jacobsen, K. W. Jacobsen, P. Stoltze, and J. NCrskov in performing simulations with Effective Medium Theory, as well as with G. S. Bales concerning nucleation theory.
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
207
Chapter 6 Surface alloying in heteroepitaxial metal-on-metal g r o w t h
F. Besenbacher, L. Pleth Nielsen a and P.T. Sprunger b Institute of Physics and Astronomy and Center for Atomic-scale Materials Physics, University of Aarhus, DK-8000 Aarhus C, Denmark
1. INTRODUCTION For decades, scientists have studied the nucleation and growth involved in metal-onmetal thin-film epitaxial deposition. This interest has continually increased, partly because of the possibility of growing thin films with novel physical and chemical properties and partly because of the desire to understand the fundamental processes underlying nucleation and growth. When studying metal-on-metal growth, difficulties often arise in separating the influence of and the competition between the thermodynamics of the new solid phase formation and the involved growth kinetics. Whereas thermodynamics tends to drive the system into its minimum free energy configuration, the trend towards thermodynamic equilibrium is often hindered by kinetic limitations, i.e. processes that depend on temperature and time, such as rates of accommodation, diffusivity, and the removal of metal atoms. When metal atoms are evaporated onto a metal surface, a supersaturated gas phase of metal adatoms exists above the metal surface, and the higher this supersaturation, the more the nucleation and growth is dominated by kinetics. Previously metal-on-metal growth has often been characterized by the growth modes. Based on simple thermodynamic equilibrium arguments, it was suggested by Bauer [ 1] that the quantity which determines the growth mode may be written as: m~ = 'Ya + ~r
a
~r
Permanent address: Haldor TopsCe Research Laboratories, Haldor TopsCe A/S, Nymr 55, 2800 Lyngby,Denmark.
bPermanent address: Center for Advanced Microstructures and Devices (CAMD), Louisiana State University, Baton Rouge, Louisiana70803, USA.
(1)
208 also known as Young's equation [2]. Here ~a and Ys are the specific surface free energies of the adlayer/thin film and the substrate, respectively, whereas y~ is the specific interfacial free energy. Depending on the relative values of the interface energy and the surface free energies, the growth modes have historically been divided into three categories named after their original investigators [3]: (i)
(ii)
(iii)
Layer-by-layer or Frank van der Merwe (FM) growth [4]. In this case, the adlayer favours wetting the substrate, and one oveflayer is fully completed before the next layer starts to form, i.e. the condition Ay < 0 is fulfilled for every successive adlayer. This strict two-dimensional (2-D) growth mode is generally only possible for homoepitaxial growth where Ay = 0. Three-dimensional (3-D) or Volmer Weber (VW) growth (Ay > 0) [5]. In this case the metal adlayer does not wet the substrate, and small three-dimensional clusters will nucleate. Subsequently, a rough 3-D island growth mode will result. Layer-by-layer growth followed by island formation or Stranski Krastranov (SK) growth [6] (Ay < 0 for n adlayers). This mode is an intermediate between FM and VW growth. The adlayer wets the substrate in the beginning, but as the interface energy increases with increasing layer thickness, a transition from layer-by-layer to island growth is observed at a critical layer thickness n.
The above description of growth modes is valid only in the limit where thermodynamic equilibrium is established. Since, in many cases, metal-on-metal growth proceeds under conditions far from equilibrium, the growth is strongly influenced by kinetic effects, and deviations from these simple growth models often exist. From a fundamental point of view, one would ideally like to understand the atomistic processes which underlie and control the nucleation and growth. Single atoms or a small group of atoms arriving from the vapour phase diffuse on the substrate surface until they meet other adatoms and form stable, immobile clusters that subsequently grow into larger clusters/islands by further attachment of diffusing adatoms. With a high probability, diffusing adatoms may also be incorporated at step edges. Conversely, dissolution of small clusters can also occur, whereas desorption of adatoms or clusters to the gas phase is negligible in most cases. The rate at which these different processes proceed depends on extemal parameters such as evaporation rate, temperature, etc. In general, the overall surface morphology is dictated by the rate-limiting process. The experimental verification of how the individual atomic processes, and thereby the overall growth mode, actually proceed on an atomic scale has remained unanswered for quite some time. However, in recent years our atomistic understanding of the involved processes in metal-on-metal growth has improved considerably, as will be evident from the chapters in this book. Invaluable experimental insight into growth
209 phenomena has been gained from diffraction methods such as low energy electron microscopy (LEEM), spot-profile low energy electron diffraction (SPA-LEED), reflection high energy electron diffraction (RHEED), surface x-ray diffraction (SXRD), thermal energy atom (He) scattering (TEAS), and maybe especially from field ion microscopy (FIM) [7,8]. However, it is fair to say that recently the scanning tunnelling microscope (STM) has had a particularly significant impact on the field. One of the great advantages of an STM when studying metal-on-metal growth processes is the large dynamic range of spatial resolution, ranging from the atomic scale to several micrometers. The atomic-scale resolution is important for directly accessing the atomistic processes governing the growth kinetics such as motion of individual adatoms and clusters, critical nucleus sizes, shape and branch thicknesses of dendritic adatom islands, whereas scans over larger regions give information on island densities, defect and step densities, etc. In the present article we will discuss a growth mode which departs from being strictly categorized within the three traditional growth modes mentioned above. In the case of heteroepitaxial growth, the growing adlayer and the substrate may intermix, and it has recently become evident that this growth mode, referred to as surface alloying, is much more important than previously anticipated. It was to be expected that surface alloying occurs for metals that intermix in the bulk phase, i.e. for metals that have a negative enthalpy of bulk mixing and form stable bulk alloys. However, recently it has been discovered experimentally that, in the initial phases of metal-on-metal growth, surface alloying also occurs for metal systems which are known to be immiscible in the bulk phase, i.e. for metals where the heat of bulk alloy formation is high and positive. For these systems the alloy formation occurs in the outermost surface layer exclusively, and thus for these systems, new 2-D surface alloy phases are observed which have no bulk 3-D analog. The outline of the present article will be as follows. We will start out by briefly discussing the energetics of bulk alloy formation and by showing typical bulk binary phase-diagrams for systems known to be bulk miscible and immiscible, respectively. We will then briefly discuss surface alloy formation observed during metal-on-metal growth for so-called bulk miscible systems, exemplified by results for Pd on Cu, and continue with the main subject of the present article: surface alloy formation for bulk immiscible systems. Recent mainly STM results for the growth of Au on Ni, Ag on Cu and Ni, Pb on Cu, and alkali metals on A1 surfaces will be highlighted and discussed. These experimental findings will be related to recent theoretical calculations of the energetics of the surface alloy formation. Finally, we will comment on how the alloy formation of these novel 'surface alloys' may open up the possibility of 'model design' on the atomic scale- catalysts with particular catalytic properties.
210
2. THERMODYNAMIC CONSIDERATIONS Whether two metals are bulk miscible or not is often determined from their bulk phase-diagrams. In many binary metal systems, there exists at a given temperature a maximum concentration of solute atoms that may dissolve into the solvent, forming a solid solution, which defines the so-called solubility limit. It is often argued that two metals are bulk immiscible if the solubility limit is below for example ~ 1 at. %. If the solute atoms are added in excess of this limit, the binary system will phase separate into two phases with completely different atomic compositions, the relative amount of which is simply determined by the so-called lever rule [9]. For bulk miscible systems a homogeneous alloy may form in the entire solubility range and furthermore, there might exist certain well-ordered stoichiometric bulk alloyed structures which are energetically favourable. Figure 1 depicts examples of binary phase-diagrams for both bulk miscible and immiscible metal systems [9,10].
1200 (a)'
'
'
.'.
'
'
'
'
'
-
~800
13001
I
,
,
i
i
i
I
Liu,o
i
i
900
C-155-396A i I
-
rr 5OO
400
GO Cu
t
t 20
t
I t t t t 40 60 80 A T O M I C P E R C E N T Pd
t
t 100 Pd
10n..0 Au
20
40 60 ATOMIC PERCENT
80 Ni
100 Ni
Figure 1. Bulk phase-diagramsfor selected binary metal-metal systems. In (a) is depicted the phasediagram for Cu-Pd which is an example of a system miscible within the entire composition range. The phase-diagramof Au-Ni (b), on the other hand, is a representativeexample of an bulk immiscible system with a characteristic miscibility-gap [9].
The bulk phase-diagram for Cu-Pd (Fig. 1(a)) represents a model example of a binary metal system showing complete miscibility of the two constituents within the entire composition range. Cooling down from the liquid Pd-Cu phase, it is even possible to form stoichiometrically stable intermixed phases, e.g. PdCu and PdCu 3. A counter example is the highly immiscible Au-Ni (Fig. 1(b)) system, for which a large miscibility gap exist. Among other things this implies that only small amounts of Au can be alloyed into bulk Ni and vice versa at room temperature (RT).
211 In order to elucidate whether a binary metal system is miscible or immiscible in the bulk one has to consider Gibb's free energy (G), defined as G = H - T S , where H is the enthalpy, and S is the entropy which quantifies the degree of disorder within the system. The system is considered to be in equilibrium if the Gibb's free energy is at minimum, and for a binary system the change in Gibb's free energy upon mixing is given by AGmix
=
mnmix
-
T ASmi x
(2)
Here M-/m~ and A S ~ are the change in enthalpy and entropy, respectively, associated with the intermixing of the two species. If the change in enthalpy is assumed to depend only on the bond energy difference c between nearest neighbouring (NN) atoms, then: AHm~x o~ c = CAB -1//2(CAA "~" EBB), where cij is the bond energy between atoms of type i and type j, respectively [ 11 ]. If c > 0 there is a tendency to form separate type A and type B clusters, whereas if c < 0 the free energy can be lowered by increasing the number of mixed bonds. Consequently, AHmix is positive (negative) if the bond energies in the mixed system CAB are larger (smaller) than the average of the bond energies of the pure elements. The change in entropy can be estimated from Boltzmann's equation: S = kBIn f2, where k B is Boltzmann's constant and f2 is the number of different possible configurational states for the system. One can estimate ~ by considering a three-dimensional lattice with N 3 sites, populated by type A and type B atoms with concentrations N30A and N30B - N 3 (1-0 A), respectively. By means of Sterling's formula, AG ~ can for a large system be approximated by [12,13]:
AGmi x - AHmi x + NBkBT [0Aln0A + (1-0A)ln(1-0A) ]
(3)
The latter entropy term is always negative hence favouring intermixing for exothermic systems (AHmix< 0) independent of composition and temperature. On the contrary, for endothermic systems (AHmix > 0) the alloy formation depends critically on the relative size of the mixing enthalpy and the entropy (atomic composition as well as temperature). Table 1 lists the enthalpy of bulk mixing for various bimetallic systems [ 14]. For bulk alloys the very large prefactor on the entropy term favours incorporation of a small amount of solute atoms into the bulk of the solvent metal even in very endothermic systems where the mixing enthalpy is high and positive. For surface confined alloys
212
on the other hand, the number of lattice sites, and thus the entropy term, is reduced by a factor of N. Therefore it is less obvious that the entropy term can counterbalance the positive energy cost of intermixing for an endothermic system. This can be illustrated by the following simplified estimate: Consider a Ni(110) surface (300x300 A2) corresponding to ~ 10,000 atoms. Assume that n Au atoms are alloyed into the topmost Ni(110) layer at T = 300 K, and furthermore, that these Au atoms each contributes +0.34 eV/atom (Table 1) to the mixing enthalpy. It is then easy to verify that A G m i x (equation 3) is positive over the entire coverage range (Oau= n/N), i.e. based on simple thermodynamic considerations Au is expected to be immiscible in the topmost Ni(110) surface layer at RT.
Impurity surf. energy lattice const atomic radii
Ni
Pd
Pt
Cu
Ag
Au
2.66 J/m2 3.52 ,~ 1.25 A
1.89 J/m2 3.89 ,~, 1.38 A
2.42 J/m z 3.92 ,~, 1.39 ,~,
2.12 J/m2 3.61 ,~, 1.28 ,~
1.20 J/m2 4.09 ,a, 1.45 A
2.66 J/m2 4.08 ,~, 1.70 A
--,0 miscible
-0.23 miscible
+0.13 miscible
+0.70 immiscible
+0.34 immiscible
--0 miscible
-0.49 miscible*
-0.29 miscible
-0.20 miscible
-0.43 miscible*
-0.03 miscible*
+0.18 immiscible
+0.39 immiscible
-0.16 miscible*
Host Ni Bulk Pd Bulk
-0.09 miscible
Pt Bulk
-0,18 miscible
--0 miscible
Cu
Bulk
-0 miscible
-0.35 miscible*
-0.58 miscible
Ag Bulk
+0.80 immiscible
-0.30 miscible
-0.03 miscible*
+0.25 immiscible
An
+0.13 immiscible
-0.36 miscible
+0.17 immiscible
-0.13 miscible*
Bulk
-0.19 miscible -0.16 miscible
Table 1. The enthalpy of mixing in eV/atom for various permutations of the six metals: Ni, Pd, Pt, Cu, Ag, and Au [ 14,15]. With only one exception (Cu on Ni) the heat of mixing [ 14] confirms the miscibility/immiscibility deduced from the bulk 3-D phase-diagrams. Miscible (immiscible) states whether the constitutes are miscible (immiscible) in their bulk phase at RT, as judged from the binary phase-diagrams. An added asterisk (*) indicates that the binary metal system forms one or several stable stoichiometric mxBybulk alloys [9,10]. Included in the table are also the respective lattice constants (lattice const), the atomic radii calculated from the interatomic distances [ 16], as well as calculated surface free energies (surf. energy) [17].
213
3. GROWTH OF BULK MISCIBLE SYSTEMS In the following we will briefly address the nucleation and growth of heteroepitaxial systems which are bulk miscible, i.e. A H,~ < 0. We will do this by discussing only the representative model system, Pd on Cu, with special emphasis on the atomic-scale nucleation and growth. An overview of the numerous STM studies of such heteroepitaxial metal-on-metal systems can be found in recent reviews [18-23].
3.1. Surface alloying of Pd on Cu(100)
(a)
(b) .........
:
.
I
[oo ]
(c)
(d)
[o o1
Figure 2. (a) STM image (50• ,~2) of a Cu(100) surface after the deposition of 0.20 ML Pd at RT. The superimposed (1• 1) unit mesh shows that the Pd atoms (protrusions -0.2 ,~) are substituted into Cu(100). (b) STM image (1000• A2, 0ed= 0.20 ML) showing the formation of square Cu islands on terraces and a roughening at the step edges. The Cu islands originate from Cu 'squeezedout' during the surface alloy formation. (c) STM image ( 100x 100 A2) depicting the ordered c(2• Pd-Cu(100) alloy structure (0pd ~ 0.6 ML). (d) Schematic hard-ball model of the alloyed c(2• Pd-Cu(100) phase. The Pd/Cu atoms are heavily/lightly shaded circles [24,25].
214 The Pd-Cu system is bulk miscible, having a negative heat of alloy formation (A Hmu < 0). Well-ordered stoichiometric bulk alloys, e.g. PdCu3, are also known to form as seen from Fig. 1(a). At the Cu(100) surface, deposition of Pd atoms forms a c(2x2) structure [26-29]; this structure is indeed the surface equivalent of the PdCu 3 bulk phase. The nucleation and growth of the c(2x2) structure have been studied by Murray et al. [24,25]. Impinging Pd atoms are substituted into the topmost Cu(100) layer as seen from Fig. 2(a). Accompanying the intermixing of Pd atoms into the Cu(100) surface, one observes the agglomeration of the hereby expelled Cu atoms into compact islands on large terraces (Fig. 2(b)). In regions with a high step density, the ejected Cu atoms diffuse to the nearby step edges which act as sinks. The Pd coverage as determined by counting the protrusions in the STM images is slightly less than the Pd coverage determined from in situ high energy ion scattering (HEIS), indicating that some of the Pd atoms have been covered by the Cu islands. As more Pd atoms are alloyed into the Cu(100) surfaces, it is found that the Pd atoms are preferentially located in next nearest neighbour (NNN) positions, resulting in substitutional [001] and [010] directed Pd chains. Whenever these chains intersect locally, c(2x2) domains develop. Well-ordered domains of the c(2x2) structure, Fig. 2(c), were formed only when the Pd coverage was beyond 0.5 ML which is the expected saturation coverage for the c(2x2) structure, as seen from the hard-ball model displayed in Fig. 2(d). The reason for the higher Pd coverage is simply that some of the Pd atoms are located in subsurface sites, i.e. the Pd atoms are buried beneath the Cu islands growing on the terraces as stated above, as well as beneath the expelled Cu at step edges [24,25]. Many other miscible heteroepitaxial systems are found to nucleate and grow in a similar fashion [ 19,22,30-36]. 3.2. Surface alloying of Pd on C u ( l l 0 ) On the open Cu(110) surface, recent STM studies by Murray et aL [37] have shown that deposited Pd atoms, at low coverages (Opd "" 0.02 ML), alloy into the Cu(110) surface. As seen in Fig. 3(a), the substituted Pd atoms form ordered linear -Cu-Pdchains along the [ 110] direction. The protrusions in Fig. 3(a) are assigned to Pd atoms alloyed substitutionally into the surface layer. The periodicity of the Pd atoms along the chains corresponds to two NN distances and is equivalent to that found in a stoichiometric Cu3Pd bulk alloy. At higher Pd coverages, the linear chains disappear. The Pd atoms become incorporated in subsurface sites, i.e. they become covered, partly with substrate atoms squeezed out during additional surface alloying, and partly by substrate atoms removed from terraces. Since this mechanism requires more substrate Cu atoms to be displaced than Pd atoms deposited, this results in a rough surface morphology with a large number of islands and pits, as seen from Fig. 3(b). The islands (Fig. 3(c)) can be interpreted as regions with an ordered (2xl) PdCu structure in the
215 subsurface layer which is covered with a pure Cu layer. The island structure is identical to the equilibrium structure of CuaPd(110) which is also terminated by a Cu layer. This explains the 2:1 variation of the island area to Pd coverage found from a height histogram of large area images, such as Fig. 3(b). These conclusions have been confirmed by ab initio total energy calculations [37]. A subsurface growth mode has also been reported for the growth of Au on Ag(110) [38-40]. However, in this case the detailed mechanism of how the Au was incorporated into subsurface sites and the detailed atomic ordering was not revealed.
(a)
Co)
(c)
Figure 3. STM images for the growth of Pd on Cu(110). (a) Pd-Cu chains aligned along the [ 1T0] direction results after the deposition of small amounts (0ed ~ 0.02 ML) of Pd (70x70 ,~2). (b) Image (1000x 1000 ,~2) showing the development of islands and pits after deposition of larger amounts ofPd (0ed= 0.17 ML). The islands preferentiallyalign along the [l-l-0]direction. (c) An atom-resolved image (80x80/$,2)of an island showing features consistent with Cu(110). The ordered (2xl) PdCu alloy structure is buried underneath the capped Cu layer [37].
4. GROWTH OF BULK IMMISCIBLE SYSTEMS
We proceed with the main topic of this article: Surface alloy formation in heteroepitaxial metal-on-metal systems which are known to be bulk immiscible, i.e. we will discuss the nucleation and growth of metal-on-metal systems for which the heat of bulk alloy formation A H ~ is high and positive and for which a characteristic miscibility gap exists in the bulk (3-D) binary phase-diagram as depicted in, for instance, Fig. 1(b). In spite of this bulk miscibility gap, it appears from a number of recent studies to be the rule rather than the exception that these systems also do intermix in the topmost surface layer, resulting in the formation of novel 2-D confined surface alloys. This will initially be illustrated by discussing the Au-Ni system in some detail and
216 subsequently, the Au-Ni results will be compared with recent results for other bulk immiscible systems such as Ag-Ni, Ag-Cu, Pb-Cu, and alkali-A1. 4.1. Surface alloying of Au on Ni(ll0) Although the Au-Ni system belongs to the class of bulk immiscible systems (see Fig. l(b)), with the bulk heat of mixing AHm~ -- +0.34 eV/atom (see Table 1), STM studies [41-43] have revealed that, when Au atoms are deposited on the open Ni(110) surface at RT, a Au-Ni surface alloy develops in the topmost surface layer. The impinging Au atoms diffuse along the close-packed troughs of the Ni substrate, and at certain positions along the diffusion path, a concerted motion occurs in which Au atoms squeeze out Ni atoms from the surface layer, resulting in the incorporation of Au atoms into the topmost Ni(110) layer [41-43], see Fig. 4. For most tip configurations, the substituted Au atoms are imaged as apparent holes (depth --0.2 ,~). However, this imaging contrast depends strongly on the actual tip-apex configuration, and associated with a tip change, the imaging contrast of the substituted Au atoms can be reversibly changed into protrusions (height ~ 0.2/~) [40-43]. Intuitively one would expect that substituted Au atoms would be imaged as slight protrusions due to their larger atomic radii (see Table 1). In this context it is, however, important to realize that an STM image is a convolution of the local geometric as well as electronic structure of both the tip and the surface [44-46].
..........;*:::::~:!;:~:::~:::~~::!::i~:i::~:.:;::;~:!:~?.~"::? :? :..:.::..
(a)
i:
:
"
9 ....
': .........
:
(b)
(c)
Figure 4. STM images of the Ni(110) surface after RT deposition of: (a) 0.05 ML Au (47• ,~2) and (b) 0.35 ML Au (35x38 ,~2).The Au atoms are substituted into the Ni(110) surface layer and are imaged as apparent depressions (depth -0.2 ,~). (c) Large-scale STM image (1000• 1000 ,~2) of the Ni(110) surface after the deposition of -0.3 ML Au at RT, showing the anisotropic growth of 2-D Ni islands originatingfrom the Ni being 'squeezed-out' duringthe RT alloy formation [41-43].
217 The density of substitutional Au atoms in the surface layer increases linearly with the amount of deposited Au, as seen from a comparison of Figs. 4(a) and 4(b). Accompanying the alloy formation in the surface layer, STM results show that the ejected Ni atoms subsequently nucleate into Ni islands which are found to grow anisotropically along the close-packed [ 1 10] direction due to the strong NN bond energy (Fig. 4(c)). From a detailed analysis of the STM images, it was found that there exists a one-to-one correspondence between the area of the Ni islands and the density of substituted Au atoms [41]. That the islands are indeed formed by the expelled Ni atoms is confirmed by the fact that the islands reconstruct [47] into the well-known p(2• added row phase [48] upon oxygen exposure. The STM results thus clearly reveal the existence of a novel 2-D Au-Ni surface alloy at RT, despite the fact that Au is essentially immiscible in bulk Ni. The existence of a Au-Ni surface alloy has been verified by low-energy ion-scattering (LEIS) studies [49-51], which concluded that at very low Au coverages, the Au atoms are located in substitutional sites, 0.07/~ _+0.05 A above the Ni(110) surface plane.
4.2. Theoretical predictions for the Au-Ni system The existence of a Au-Ni surface alloy has been supported by calculations of the energetics of the system within the semi-empirical effective medium theory (EMT) [52-57]. In the simplest form of EMT, the total energy of the system can be written as:
Etot- ~ i
E, i (hi) + EAS + Elel
(4)
where the summation is over all the atoms within the system. Ec, i (Fl) is the cohesive function describing the variation of the energy of atom i as a function of the electron density around the atom stemming from the surroundings. The cohesive function can be calculated in a reference system where the calculation is simple, for instance as the embedding energy in a homogeneous electron gas as a function of electron gas density, or as the cohesive energy in a bulk crystal lattice as a function of the lattice constant. In general, the Ec function shows a minimum at the optimum electron density. The two last terms in equation (4) are correction terms describing the energy difference between the real system and the reference system. The atomic sphere correction (Eas) is the difference in electrostatic and exchange-correlation energy for the atoms in the system of interest and the reference system, whereas the other t e r m (Elel) is the difference in the sum of the one-electron energies in the two systems. In principle these correction terms can be calculated ab initio, and an accuracy comparable to selfconsistent calculations can be obtained, although such an approach is quite computer
218 intensive. Therefore Jacobsen, Stoltze and NCrskov [57] have introduced pair-potential approximations for Ele I , which leads to a simple, and in many cases quite useful, semiempirical parametrization of the total energy. Table 2 shows the energetics for a Au atom chemisorbed as well as substituted into the topmost Ni(110) layer and into the bulk, respectively, for the unrelaxed and the relaxed structures [41]. It is seen that the lowest energy configuration corresponds to the Au atom being embedded into the first Ni layer, consistent with the experimentally observed surface alloy formation. Clearly relaxations tend to stabilize the structures, but even the unrelaxed configurations show the correct trend. For the unrelaxed case, the total energy is sprit into contributions from the cohesive function for both Au and Ni as well as the atomic-sphere term, and it is seen that the E c term dominates and hence alone describes the observed trend in the total energies.
Chemisorption
Substitution
Bulk substitution
E~ (Ni)
-0.53
-0.36
+0.12
e, v
u~ %% %
-4.0 -
%%%
-4.5 0
I
3
I
6
%% I
9
I
12
15
NUMBER OF Ni NEIGHBOURS
Figure 5. The cohesive function Ec plotted as a function of the coordination number N for a Ni atom and a Au atom, in both cases surroundedby Ni neighbours at the equilibrium Ni bulk nearestneighbour distance [41 ]. Let us instead focus on the variation of the energy as seen for a Au atom surrounded by Ni atoms. A plot of the Au cohesive function Ec(Au) when plotted v e r s u s the Au coordination number in Au would look very much like the E c function for Ni shown in Fig. 5 and depicts an energy minimum at N = 12. However, since the lattice constant for Ni is much smaller than that of Au (see Table 1), a Au atom would feel an electron density contribution from a Ni atom at the equilibrium Ni-Ni distance that is considerably larger than that from a Au atom at the equilibrium Au-Au distance. For a Au atom surrounded by Ni atoms it is therefore more appropriate to plot Ec(Au ) as a function of the Ni coordination number in a Ni lattice. The result is shown in Fig. 5, and this curve has a minimum at N = 8 simply because eight Ni neighbours at the Ni-Ni distance
220 contribute as much electron density as twelve Au atoms at the equilibrium Au-Au distance. This means that for Au embedded in bulk Ni, where N = 12, the electron density is too large, and thus Au has a high energy, reflecting the high and positive heat of solution of Au in bulk Ni (0.34 eV/atom, see Table 1). On the other hand, for Au chemisorbed on the Ni(110) surface where N = 5, the electron density is too small and the energy of Au is also high. Alternatively for Au substituted into the Ni(110) surface layer, where N - 7, the Au atoms attain the minimum energy configuration. It is this trend for the E~(Ni/Au) functions that makes the Au most stable in the Ni(110) surface layer, and since this is a direct consequence of the non-linearity of the cohesive function, it is a tree many-body interaction effect [41, 54, 57] which cannot be described in a simple pair-wise interaction model. Thus within the EMT scheme the formation of a Au-Ni surface alloy is related to the fact that the Ni(110) surface atoms are highly under-coordinated, and that the Au atoms help to lower the Ni surface energy by giving the Ni surface atoms an effective higher coordination. Another semi-empirical approach for calculating the energetics of surface alloy formation for the Au-Ni(110) system has been published by Bozzolo-Ferrante-Smith (BFS) [58]. Within the BFS method, the alloy formation energy is calculated as a superposifion of individual contributions of local strain and a weighted chemical energy of the non-equivalent atoms in the surface alloy. Again it was found that the lowest energy configuration corresponds to the one where the Au atoms are substituted into the Ni surface layer. Tersoff has also addressed the theory for surface-confined alloy formation in immiscible systems and discussed particularly the Au-Ni system although he chose the Ni(100) surface [59]. Based on a highly simplified model containing only strain energy through pair-wise interactions, it was concluded that surface-confined mixing occurs, quite generally, in systems dominated by a large lattice mismatch, which for the present Au-Ni system is 16%. Tersoff argues that in general a misfitting atom will have a reduced strain energy at the surface relative to the bulk and furthermore, that this strain will cause a repulsion between two misfitting substitutional atoms in the surface layer. Thus in the limit where the energefics are dominated simply by strain effects, the model proposed by Tersoff would predict that two elements form an alloy confined to the uppermost surface layer, even though they are immiscible in the bulk. The distribution of the substituted Au atoms within the surface Ni layer is controlled by the size of the Au-Ni interface energy, ~?Au-Ni,and Monte-Carlo simulations show that for positive YAu-N~values a clustering of the Au atoms within the Ni surface layer is to be expected. The STM experiments for the growth of Au on Ni(110) discussed above indeed showed that approximately 95% of the intermixed Au atoms were found as [1-i-0] directed Au dimers (see Fig. 4(b)).
221
4.3. Surface dealloying of Au on Ni(ll0) As more Au is substituted into the Ni(110) surface layer, the total energy increases due to an increase in the compressive strain caused by the substituted larger Au atoms. When the Au coverage exceeds 0.40 ML, combined STM and HEIS results [43,60] have shown that the Au induced compressive strain becomes so high, that it is no longer energetically favourable for the Au atoms to be incorporated into the Ni(110)
At' 1'~
oc bcmb (a)
(b)
0.3 ML), we shall digress and discuss the nucleation and growth of Au on Ni(111) during RT Au deposition.
4.5. Strain relief at the buried Au-Ni(111) interface When Au is deposited on Ni(111) at RT, STM studies [64,65] have found that monatomic high Au islands nucleate and grow out from descending Ni step edges (Fig. 9(a)), and zooming in on these Au islands, a periodic network of triangles is revealed (Figs. 9(b) and 9(r The average distance between the triangles is found to be ~ 9.7 times the interatomic distance of the bare Ni(111) surface, i.e. very close to the distance expected for a simple Moir6 interference structure, d~ aau/(aau - aNi) 9, see equation (7) below. The distance between the Au atoms in the Au layer is measured to 2.80 A, i.e. slightly less than the Au-Au distance for an unreconstructed Au(111) surface (2.88 A) but very close to that for the "herringbone" reconstructed surface [66]. The local Au coverage in the islands corresponds to 0.8 ML measured relative to the atomic density on the Ni(111) surface (0.8 ~ (2.49/2.80)2). The triangular loops are seen to surround Au clusters of variable size (1, 3, 6, 10, ...) and furthermore, it is found (Fig. 9(d)) that protrusions of Au atoms are imaged within the troughs of the triangles. Both the Au atoms in the cluster regions and the Au atoms imaged lower in the triangular troughs are in registry with the unperturbed Au lattice separating the triangular regions. This indicates that the topmost Au layer is laterally uniform and only perturbed vertically in the triangular regions. From an interplay between STM experiments and EMT calculations it has been revealed that the triangular structure reflects the structure at the buried Au-Ni(111) interface [64]. As discussed above, when a homogeneous Au(111) layer is placed on top of the Ni(111) substrate, a Moir6 structure results where some of the Au atoms at periodic distances (d) are located in or very close to on-top positions with respect to the underlying substratc. The substratc on-top positions, however, are energetically very unfavourable and the Au atoms would prefer to sit in threefold hollow sites. o
225
(a)
(c)
.... ...................
....... ........
....
(b)
: .........
(d) .
.
.
.
Figure 9. (a) STM image (1450x 1570 ,~) after the deposition of 0.25 ML Au on Ni(111) showing that the Au islands grow out from descending Ni step edges at RT. (b) (145x160 A~) revealing the periodic -(9.7x9.7) triangular structure within the Au islands. (c) (100• A,~) and (d) (45x50 A ~) showing the atomic details of the triangular loop structure [64,65]. Ni::,subs~
~O
OO~-~t
B O 0 @ ~ @ ~
:
9 9~J~ O~ ~ O ~ O ~ ~ @ ,
Ni,subs~
~O ~ ~ , ~ ~ ~ |
Au:o~eflay~,
~!iii~'::::: ~',~:~:~:,~i:~ ::~!~,!!~,~~:: , ,:~|
~,~ ~ ~
~n,,sp~en~,,A:u,
: ~ ..... ::-:~*
, :~ ........~ ~*~:.......~:.~.:. ~ ~
Figure 10. Hard-ball model for the Au-Ni(111) superstructure. In (a), a row of five Ni atoms are squeezed out whereby the Ni atoms in the triangular region are shifted half a lattice constant, thus creating the dislocation loop in (b). When the Au layer is placed on top of this Ni surface (c), the Au atoms in the edges of the triangular regions adjust their heights. This results in the characteristic triangular structure of the Au layer, as observed experimentally. (d) Making the Au layer 'transparent', it is seen that all the Au atoms are located close to threefold hollow sites [61,64,65].
226 Already in 1949, Frank and van der Merwe [4] pointed out that lattice-mismatchinduced interfacial strain may be relieved by the formation of misfit dislocations, i.e. regions with large changes in the interatomic distances separating domains with more normal bond lengths. This is exactly what happens in the Au-Ni(111) system. The high interface strain, or equivalently the high interface energy, is reduced by forming an ordered array of vacancy misfit dislocation loops in the underlying Ni substrate. The atomistics of these dislocation loops are sketched in Fig. 10. A row of five Ni atoms is considered to be squeezed out, and the Ni vacancy line induces a shift of the ten Ni atoms within a triangular area from FCC sites into HCP sites. The triangular boundary separating the FCC and the faulted HCP regions is clearly a partial dislocation loop. The Au atoms in the Au(111) overlayer adjust their height at the border of the underlying dislocation loops, and the structure observed in the Au(111) overlayer (Fig. 9(d)) thus simply reflects the atomic structure of the restructured Au-Ni interface. Since more vacant space is available in the comers than along the triangular boundary of the loops, the Au atoms in the comers are imaged lower (-0.2 A). As a further confirmation of the triangular misfit dislocation model, it was found [65] that there is a one-to-one correspondence between the number of Ni atoms squeezed out of the surface layer in order to form the underlying dislocation loops and the number of Ni atoms, the 'white protrusions' in Figs. 9(b) and 9(c), alloyed into the Au(111) layer. In spite of the large and positive energy involved in forming the partial dislocation loops, the triangular misfit dislocation structure corresponds to the lowest energy configuration observed by STM at RT, the main reason being that the FCC-to-HCP shift of the Ni atoms in the faulted triangular area makes it possible for all the Au atoms in the overlayer to be in or close to threefold hollow sites, as opposed to the highly, energetically unfavourable substrate on-top sites. The reason that the vacancy dislocation loops are formed only at RT or above, as opposed to the simple Moir6 overlayer structure formed after low-temperature Au deposition, is simply that the energy barrier associated with the breaking of the Ni-Ni bond has to be overcome [64]. This example illustrates how in certain cases it is possible with an STM to determine not only the surface structure but also the atomic-scale structure of a buffed interface between two metals from the signature at the topmost layer. The importance of these results for the further discussion of surface alloying for Au on Ni(111) will become evident in the following section.
4.6. Surface alloying of Au on Ni(111) at high Au coverages: Vegards law in 2-D As discussed above the surface alloying of Au on Ni(111) is an activated process which occurs at elevated temperatures only. Recent STM studies [67] have revealed that if the amount of deposited Au alloyed into the Ni(111) surface is increased beyond
227 0A, = 0.30 ML (T > 425 K) a homogeneous network of triangles evolves, as seen in Fig. 11. The average distance between neighbouring triangles decreases with increasing Au coverage as revealed from Fig. 12(a) where the distance between neighbouring triangles is plotted as a function of the total amount of deposited Au, as measured
(a)
(b)
(c)
Figure 11. STM images (200x200 ,~2), after the deposition of Au at 700 K, depicting a periodic network of triangular misfit dislocation loops with a coverage dependent superstructure periodicity; (a) -- (20x20) 0Au= 0.35 ML, (b) -- (13x13) 0 a,= 0.50 MLand (c) -- (10xl0) 0 A~ 0.70 ML [67].
20
, -(a)
I
!
I
I
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I
I
I
I
2.9
I
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I
I
I
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C-155-397A
(b) 2.8
z 160 or) z w ~; 0
2.7
12-
aAu=2.80
A
\~
-
~
aN, 9,- 2 o49 A
o
2.6 2.5
",o
8 0.0
I
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0.2
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0.4
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0.6
Au COVERAGE (ML)
I
I
I
0.8
2.4 0.0
I
I
I
I
I
I
I
I
0.2 0.4 0.6 Au COVERAGE (ML)
I
I
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I
0.8
Figure 12. (a) The superstructure dimension as a function of the total amount of evaporated Au measured by ion scattering. (b) The effective lattice constant, ae~(0a,), of the alloyed Au-Ni(111) overlayer as a function of the amount of Au within the layer [67]. by ion scattering. A similar surface morphology was shown to develop if the RT deposited Au islands were annealed to elevated temperatures. The existence of this
228 triangular network with a Au coverage dependent superstructure periodicity can be rationalized as follows [67]. At low Au coverages (0au < 0.3 ML), the Au atoms are alloyed one-to-one into the topmost Ni(111) surface layer. These large Au atoms cause a build-up of compressive strain in the Ni surface layer. At low Au coverages the strain can be accommodated through a local relaxation of the surrounding NN Ni atoms. Similar to the growth of Au on Ni(110), at a certain Au coverage (Oau = 0.30 ML) the strain becomes too large and is consequently relieved upon further Au deposition/incorporation. Exceeding this critical Au coverage the strain relief occurs through an isotropic expansion of the alloyed topmost Au-Ni(111) layer. The expanded Au-Ni alloy surface layer 'floats' on top of the Ni substrate and consequently obtains its own effective lattice constant, aejf, depending critically on the actual Au coverage. This Au induced lattice mismatch implies that at certain regular positions, the atoms in the alloyed Au-Ni surface layer are located in or close to on-top positions with respect to the underlying Ni(111) lattice. As for the growth of Au on Ni(111) at RT discussed above, this subsequently results in a triangular network of partial vacancy dislocation loops in the underlying Ni layer. Also for the alloyed layer, the observed triangular superstructure periodicity reflects the atomic arrangement at the buried interface between in this case the isotropically expanded alloyed Au-Ni(111) surface layer and the underlying non-alloyed Ni(111) lattice. It has been shown [67] that the observed variation of the superstructure periodicity with Au coverage can be understood by applying Vegard's law [68] for bulk binary alloys to the case of 2-D surface alloys. Vegard's law states that for a binary alloy, the effective lattice constant, aeg, can be written as a simple concentration-dependent linear combination of the lattice parameters of the two constituents. In the case of Au alloyed into Ni(111) for Oau> 0.3 ML the effective lattice constant can be written as"
aefy(OAu ) - CAu(OAu) aAu + CNi(OAu) aNi
(5)
where the weight factors (CA,,, CNi) depend on the actual Au coverage OAu. It is known from the triangular misfit dislocation structure observed upon RT Au deposition that the lattice constant of the Au(111) layer is 2.80 ,~ and fia~ermore, that the Au coverage of the saturated Au(111) layer corresponds to 0.8 ML. Introducing this normalization factor (0.8) for the Au coverage, Vegard's law can explicitly be rewritten as:
a t'AAu'~ef-jx", - OAu OAu 0.8 aAu + (1 - 0.8) aNi
(6)
229 with the only variable parameter being the Au coverage OAu.The variation in the effective lattice constant of the alloyed Au-Ni surface layer as a function of Au coverage is depicted in Fig. 12(b). For a close-packed, non-rotated overlayer on top of a (111) substrate with mismatching lattice parameters ao and as, respectively, the superstructure beating distance or the Moir6 periodicity (d) is given by:
d -
a o
(7)
a~ - as
Since the effective lattice constant aey (OAu) of the alloyed Au-Ni layer depends on the Au coverage, the beating distance will also depend on Oau, and can be determined by combining equations (6) and (7), resulting in:
OAu
d(OAu)
aeff(OAu) =
aefj(OAu) - aNi
0.8 ( aau - aNi ) + aNi =
OAu 0.8( aAu - aNi )
(8)
As seen from Fig. 12(a), this expression gives a perfect fit to the experimentally observed superstructure periodicity for aug = 2.49 A, the lattice constant for Ni, and aAu - - 2 . 8 0 A, the Au-Au distance in the Au islands as measured in e.g. Fig. 9(d). Thus it can be concluded that the observed variable Au coverage dependent superstructure periodicity arises from a Au induced lattice mismatch between an alloyed Au-Ni overlayer with an effective lattice constant following Vegard's law and a non-alloyed Ni(111) substrate. As will become evident in the discussion below, many of the concepts relating to surface alloying discussed for the Au-Ni system have general applicability for a large number of other bulk immiscible metal-on-metal systems. o
4.7. Surface alloying of Ag on Cu surfaces For the Ag-Cu system there is also a large miscibility gap and a large lattice mismatch (13%) as in the Au-Ni system. Due to the very small surface free energy of silver, one would have expected, based on the simple thermodynamic arguments in section 2, that the first monolayer of silver would 'wet' the Cu surfaces. However, recent STM results show that also Ag and Cu form surface alloys, i.e. Ag atoms are alloyed into all three low-symmetry surface planes of Cu.
230
4.7.1. Surface alloying of Ag on Cu(110) The STM results for the Ag-Cu(110) system closely resemble those discussed above for the Au-Ni(110) system. However, since the Ag-Cu mobility is much larger than the Au-Ni mobility, low-temperature STM is required in order to extract detailed structural information [69]. Previous experimental studies by Taylor et al. [70] have yielded much information concerning the Ag-Cu(110) system, and simple non-alloyed Ag ovedayer structures were proposed. However, recent low-temperature STM data rebut these results and show that Ag atoms are alloyed into the open Cu(110) surface.
%
~}..
(c) Figure 13. STM images of Ag deposited on Cu(110), all acquired at 150 K: (a) after deposition of-0.25 ML of Ag at 200 K, showing growth of alloyed Ag-Cu islands on Cu terraces (2400x2400 A2);(b) afterannealing(a) to 350 K and recoolingto 150 K showingsurfacealloystructure(100xl00 ,~2);(c) afterdepositionof-0.4 ML of Ag at 400 K, showinginitial growth of zigzaggingAg chains (150x150 ,~2);(d) showingperiodicarrayof Ag [001]-chains at highercoverages(0.65 ML) (240x240 ~2) [69].
231 At submonolayer ~ (0.25 ML) Ag deposition, a surface alloying is observed to proceeA in which Cu atoms are squeezed out of the surface layer, resulting in a high density of small Cu islands out on the terraces, as depicted in Fig. 13(a). If this surface is annealed to 350 K and subsequently imaged at 150 K, the Cu islands have disappeared as a result of step flow, and moreover, atomically resolved images show that the substituted Ag atoms, imaged as protrusions, are preferentially aligned along the [001]direction (Fig. 13(b)). This shows that there exists an attractive Ag-Ag interaction which preferentially arranges the Ag atoms pseudomorphically within the Cu(110) surface perpendicular to the close-packed direction. For the anisotropic Cu(110) surface the Cu-Cu distance is 3.61 ,~ along the [001 ]-direction, whereas the nearest-neighbour distance is only 2.56 ,~ along the perpendicular [1-i-0] direction. Thus the substitutionally alloyed Ag atoms, having a bulk Ag-Ag lattice parameter of 2.89/~, are compressed along the [1 10] direction, and in order to minimize this strain, the Ag atoms orient in substitutional chains predominately along the [001 ]-direction [69]. If the Ag coverage is increased further ( > 0.4 ML), a 'dealloying process' is observed as for the Au-Ni(110) system. Figure 13(c) shows an STM image, recorded at 150 K, after deposition of -~0.4 ML of Ag at 400 K. The emergence of the characteristic zigzagging dimer-trimer chains is immediately noticed. Between the chains small protrusions corresponding to alloyed Ag atoms remaining within the Cu surface are observed. As outlined in Section 4.3, the driving force for the formation of the chains is the reduction of surface strain caused by the substituted Ag atoms, and as a result vacancies stabilizing the chains are formed in the topmost surface layer. At higher Ag coverages (~0.5-0.8 ML) the chains forms an ordered structure (Fig. 13(d)), which implies that there exists a net chain-chain repulsion along the [ 1 10] direction as in the Au-Ni(110) system. Increasing the Ag coverage even further leads to a coalescence of the Ag chains into a simple hexagonal Ag(111) overlayer (Oag N 1.3 ML) resting on top of a nonalloyed substrate analogous to the Au on Ni(110) system.
4.7.2. Surface alloying of Ag on Cu(lO0) Previous experimental studies of the Ag-Cu(100) system employing LEED [71 ], EELS [72], ARUPS [73], and PED [74] have concluded that there is no indication of surface alloying. Recent STM studies [75] seem to support of this conclusion since at low substrate temperatures (T < 250 K) Ag deposition results in a c(10• overlayer structure (Fig. 14(a)) on Cu(100). Atomically resolved images of this low-temperature structure reveal monatomic height, nearly hexagonal Ag islands surrounded by the bare non-alloyed Cu(100) substrate. The Ag-c(10• structure is highly buckled due to the large interfacial mismatch arising when the hexagonal Ag overlayer is placed on top of the square substrate lattice (Fig. 14(b)). However the reason that no surface
232 alloying is observed at lower temperatures is that the activation barrier is larger than the available thermal energy associated with the exchange mechanism.
(a)
(b)
9
(c)
(d)
Figure 14. STM images of Ag deposited on Cu(100): (a) image, acquired at 160 K after deposition of 0.4 ML of Ag at 225 K, showing growth of hexagonal Ag-c(10x2) overlayer islands on Cu terraces and at step edges (800x800/k2); (b) atomically resolved details of the Ag-c(10x2) superstructure and local pseudo-hexagonal arrangement(see superimposed grids) (42x44,g2); (c) image, acquired at 170 K, of same surface as shown in (a) after annealing to 425 K, showing Ag-c(10x2) patches within Cu surface (see arrows) surroundedby Ag-Cu alloy (120x120 ,~2); (d) image, acquired at 180 K, of the Cu(100) surface deposited with only 0.07 ML of Ag at 440 K showing single Ag atoms (protrusions) pseudomorphically alloyed into Cu(100) surface (56x56 ~2) [75].
If, on the other hand, Ag is deposited at RT and subsequently imaged at lower temperatures (< 200 K), STM results show, see Fig. 14(c), that silver atoms are substitutionally alloyed into Cu(100) [75]. In Fig. 14(c) where 0Ag = 0.4 ML, a small density of Ag-c(10• domains similar to the Ag-c(10x2) low-temperature structure
233 are observed, but in this case the Ag-c(10x2) islands are located within the first Cu layer, as revealed from the measured height difference between the Ag islands and the surrounding Cu substrate. Moreover, in the interstitial regions between these hexagonal Ag domains atom-size depressions, attributed to individual Ag atoms being alloyed into the Cu(100) surface, are revealed. This shows the coexistence of two silver phases within the Cu surface: (i) individual Ag atoms alloyed into the surface and (ii) domains of phase-separated c(10x2) hexagonal Ag islands. Figure 14(d) shows an STM image, acquired at 180 K, in which ~0.07 ML of Ag has been deposited at 440 K. At this low Ag coverage only individual Ag atoms, substitutionally arranged within the Cu(100) surface lattice, are depicted, while no hexagonal Ag-c(10x2) islands are observed. From a series of STM measurements where successively increasing amounts of Ag were deposited at elevated temperatures and subsequently imaged at low temperatures, it can be concluded that a critical Ag coverage of ~0.13 ML exists at which a phase separation occurs into coexisting areas of the alloyed Ag-Cu(100) phase and hexagonal Ag-c(10x2) islands. Similar to the Au-Ni system, this phase separation is driven by the increased compressive strain caused by the substitution of the larger Ag atoms. As the surface alloy composition of Ag increases, the compressive strain energy of the surface increases, and at a critical Ag concentration (~0.13 ML) the energy of the system is minimized by the creation of Ag-c(10x2) domains within the Cu(100) surface, and the density of the Ag hexagonal domains increases with increasing Ag coverage. At the Ag saturation coverage (0agN0.9 ML) the surface is completely covered by a nearly perfect hexagonal Ag(111) overlayer on top of a non-alloyed substrate, analogous to the Au-Ni(110) and Ag-Cu(110) systems.
4.7.3. Surface structure and alloying of Ag on Cu(lll) Silver forms a hexagonal overlayer structure on Cu(111) at low temperatures (~ 170 K), analogous to the systems described above [76]. As seen from Fig. 15(a), the unstrained Ag(111) overlayer forms an incommensurate Moir6 structure, rotated by 2.4 ~relative to the underlying substrate, with a spot-spot distance corresponding to a-(9x9) superstructure. In contrast, if Ag is deposited at submonolayer coverages on Cu(111) at RT, STM images reveal a quite different structural phase. Although details of the local atomic structure previously has been studied with RT-STM [77], the structural details of this phase are again most easily imaged at low temperatures (~ 200 K) due to the high dynamical motion of the Ag/Cu layers. From the easily identifiable triangular structures depicted in Fig. 15(b), and the results presented in Section 4.5, the structure can be attributed to atomic arrangement at the buried Ag-Cu(111) interface where misfit dislocation loops are formed in the underlying topmost Cu(111) layer. Similar to the arguments presented for the Au-Ni(111) system, these dislocation loops arise due
234 to the minimization of the large interfacial energy associated with Ag atoms near substrate on-top positions.
Figure 15. STM imagesof Ag depositedon Cu(111):(a) image,acquiredat 170 K afterAg deposition at 225 K, showinglocal atomicstructureand Moir6superstructure(48x52 A2);(b) image,acquired at 165 K after Ag deposition at RT, showing triangular misfit dislocation structure (56x56 ,~2); (c) Ag at submonolayercoveragealloyedinto the Cu(111) terrace at 775 K; the image is acquired at RT (84x88 A2) [76].
STM images reveal that no Ag-Cu(111) surface alloying has taken place at temperatures up to 400 K. However, if a submonolayer coverage of Ag is deposited at even higher temperatures (> 425 K), STM images (Fig. 15(c)) directly depict the formation of a Ag-Cu surface alloy, where the substituted Ag atoms are imaged as depressions within the surface. This implies that the Ag-Cu(111) surface alloy formation is thermally activated as for the Au-Ni(111) system. An important point is that in the temperature ranges between 425 and 600 K, the local concentration of alloyed Ag atoms is atthe highest equal to 8%. Depositing more than ~0.1 ML of Ag at elevated temperatures results in coexisting phases of the concentration limited (8%) Ag-Cu surface alloy and nearly hexagonal Ag islands decorated by the triangular misfit dislocation structure. In contrast to the Au-Ni(111) system, there appears to be a constant superstructure periodicity of the misfit dislocations independently of the Ag coverage, implying that the Ag overlayer is non-alloyed.
4. 7.4. Surface alloying of Ag-Cu on Ru(O001) As outlined above, unequivocal evidence has been presented that Ag forms surfacealloys on all three low-symmetry Cu surfaces. In order to elucidate the effects of the underlying substrate the aUoying process of a mixed Ag-Cu overlayer has been studied
235 on Ru(0001) [78,79]. This system is tailored to such studies since no substrate alloying is observed, and furthermore, there is a large positive as well as negative atomic mismatch between the adatoms and the substrate (Cu/Ru, -6%; Ag/Ru, +7%; Ag/Cu, +13%). In a study employing TDS, LEED, and ARUPS, it was concluded that, within the monolayer film, Ag/Cu on Ru(0001) are in fact miscible down to a temperature of 250 K (bulk Ag-Cu mixing occurs at a temperature above 2000 K) [78]. In the bulk, theoretical studies of binary hard sphere mixtures have predicted that segregation (mixing) should occur in compounds with a size mismatch greater (smaller) than 15% (6%) [80]. In the Ag/Cu monolayer film, the induced strain is more easily accommodated, due to the reduced coordination number, resulting in the formation of an alloy phase. Using RT-STM, Stevens and Hwang have investigated the structure of the Ag/Cu overlayer on Ru(0001) [79]. Whereas the monolayer structure of Ag on Ru(0001) is reminiscent of the Au(111) herringbone structure [81 ], co-adsorption of Cu and Ag results in a series of mixed monolayer structures resulting from a Ag/Cu strain stabilization on the Ru surface.
(a)
(b)
Figure 16. STM images of a Ru(0001) surface with Ag and Cu co-deposited (0o,/0Ag = 0.42) following an annealing to 823 K. (a) Two domains (labelledA and B) of the alloy are separated by domain walls made up of a pure Ag phase (1000x1000 ,~2). (b) Atomically resolved details of the alloy domain structure and domain walls (200x200 ,h2) [79].
At medium concentrations of Cu within the Ag/Cu monolayer (Oc,,/OAg 0.42), STM reveals (Fig. 16(a)) a network of triangular shaped domains separated by stripes (domain walls). Atomically resolved images of this alloyed monolayer indicate domain walls (approximately 20 A wide), separating regions with areas with HCP and FCC -
"
236 stacking, which are composed of Ag atoms only. However, within the domain walls the Ag and Cu atoms intermix in small chainlike clusters, i.e. no long-range ordering within the alloy is observed (Fig. 16(b)). The average stoichiometry within these triangular shaped domains is consistent with a composition of Ocu/Oag= 0.5. Within a simple hard-baU atomic model, this leads to an effective lattice constant nearly equal to the underlying Ru lattice (2.71 ,~). In analogy with the Au-Ni(111) system described in Section 4.6, the binary composition of the Ag/Cu-Ru(0001) system within the triangular domains follows directly from Vegard's law. In the present case the mixed ahoy adopts an average composition in which the local strain energy is minimized, that is, an average lattice spacing close to that of the underlying substrate.
4.8. Surface alloying of Ag on Ni surfaces The Ag-Ni system has also a large miscibility gap as well as a large lattice mismatch (16%), and furthermore, the surface free energy of Ag is again significantly lower than that of Ni (see Table 1). According to the simple thermodynamic considerations described in Section 2, one would therefore have assumed that the first monolayer of silver completely 'wets' the Ni substrate. However, like the other systems described in this article, this is not the case, and instead surface alloys are formed.
4.8.1. Surface alloying of Ag on Ni(llO) STM results clearly show that RT deposition of Ag on Ni(110) results in the formation of a surface alloy [82]. As seen from Fig. 17(a) deposition of 0.2 ML of Ag on Ni(ll0)
Figure 17. STM images acquired at RT of Ag deposited on Ni(110): (a) image showing alloyed Ag-Ni islandformationupon depositionof--0.2 ML of Ag at RT (482x522,~2);(b) imageof (10xl) string structure formed at coverages between 0.5-0.8 ML (840x883 ,~2); (c) atomically resolved imageof (b) showingdetailsof [11--0]-buckledstringstructurewitha Ni-(1x 1)unit grid superimposed (42• ,~1) [82].
237 at RT results in the formation of monatomic height Ni islands on the terraces, with a one-to-one density equal to the Ag coverage. These islands are formed by the Ni atoms expelled during the substitutional alloy mechanism, and atomically resolved images reveal a pseudomorphic surface alloyed structure. At slightly higher coverages (0ag~0.3 ME) a new structural phase begins to evolve. Similar to the Ag-Cu(110) system, alloyed Ag atoms locally cluster along the [001Jdirection and are accompanied by an outward buckling, along the [1 10J-direction, of the Ag-Ni surface in response to the increased local compressive strain. This effect can be identified more easily at even higher coverages (-0.5-0.8 ML) wherein this buckling locks into a superperiodicity. As shown in Fig. 17(b), the strain-induced buckling, with an oscillation amplitude of-0.4 A, form a periodic arrangement with a separation of ten Ni[1 10] units. Atomically resolved images of this anisotropically buckled structure (Fig. 17(c)) indicates that, as in the lower coverage phase, the Ag surface alloyed atoms are pseudomorphically arranged with respect to the underlying substrate. From the STM images, the local arrangement of the Ag atoms within the Ag-Ni surface cannot be determined, i.e. whether the higher (lower) portions of the buckling oscillation correspond to preferentially larger (smaller) local Ag concentrations. o
4.8.2. Surface structure of Ag on N i ( l l l ) From the results presented above concerning the propensity of alloy formation versus surface coordination, it appears that surface alloys do form even for bulk immiscible systems, but the activation energy for surface alloy formation varies strongly with the specific surface face. However, the growth of Ag on Ni(111) appears to be an exception since STM measurements have shown that, in this case, no alloy formation occurs, and instead Ag forms a 'simple' overlayer structure on Ni(111) [83].
Figure 18. STM image of Ag monolayer on Ni(111) at RT showing both local atomic structure and Moir6 superstructure (59x62/~2) [83].
238 As seen from Fig. 18, the deposition of Ag on Ni(111) at RT causes the nucleation and growth of monatomic Ag islands at descending Ni step edges, and the unstrained Ag(111) overlayer is accompanied by a Moir6 superstructure, with a spot-spot distance corresponding to an incommensurable --(7x7) superstructure. The Moir6 lattice is found from the STM images to be rotated -2 ~with respect to the underlying Ni(111) substrate, and this rotation arises again from a minimization of the interfacial energy. From a detailed analysis of the superstructure corrugation of the Moir6 pattern it is found that the regions with depressions and protrusions correspond to Ag atoms occupying near on-top and hollow sites, respectively, i.e. there is a height reversal between what one would naively expect from a simple hard-ball model. A similar Moir6 structure was found after low-temperature deposition of Au on Ni(111) and Ag on Cu(111), and also in these cases the corrugation reversal was found. Theoretical total energy calculations of the Ag-Ni(111) [84] and the Ag-Cu(111) [85] systems corroborate this height 'reversal' as being caused by substrate relaxation arouad the energetically unfavourable on-top sites. 4.9. Surface alloying of Pb on Cu surfaces The Pb-Cu system is another example of a bulk immiscible system. The lattice mismatch for Pb (apb = 4.95 ,~) and Cu (a c~= 3.62 ,~) is very large (37%), the surface free energy of Pb (~'eb ~ 0.50 J/m/) is four times smaller than that of Cu (YCu ~ 1.96 J/m 2) and furthermore, the Pb-Cu interfacial energy is, for the (111) plane, estimated to be Ypb-c~- 0.3 J/m 2 [86]. Thus, although one would, from simple thermodynamic considerations, expect Pb to grow on top of the Cu surfaces, recent STM studies [36,87,93] have revealed that impinging Pb atoms intermix with the Cu surfaces, resulting in Pb-Cu surface alloys.
4.9.1. Pb on Cu(11 O) For the deposition of submonolayer amounts of Pb on Cu(110) at RT, an alloyed Pb-Cu(110) lattice gas phase is formed. Due to the high mobility of the Pb adatoms, it has not been possible to resolve this phase by STM at RT [87]. Atom-resolved STM images of Pb-Cu structures can, however, be obtained at higher Pb adlayer coverages in which case the Pb atoms are locked into a myriad of well-ordered structures" c(2x2) at Opb -- 0.50 ML [87-89], p(nxl) n = 2, 4, 5, 6, 8, 9, 12 and 13 for 0.75 ML < Opb 1. The fines in Fig. 22(b) show the theoretical dependence given by equation (9), and clearly the model quantitatively describes the variation of the sticking probability with the Au coverage
C-155-401
150
'
ia>
i.0
(b)
9
T.,=l ,= 1050K
13
T,,=l = ffi 550 K
0.8
100 0.6 t:m
~
9~
50
0.4
"o.
"~ o~ "
"
~
~
o
0
v
-10
-5 0 5 Reaction coordinate
10
Z: 0.0 0.0
0.1
0.2
0.3
0.4
0.5
Au coverage ( M L )
Figure 22. (a) The calculated energy along the reaction path for CH4 dissociating over a Ni atom on a Ni(111) surface. The geometries of the CH4 along the reaction path include full structural relaxation of the C H 3 group. The rightmost dashed data points refer to infinite separation of the dissociated H and C H 3 group on the surface. For the Au-Ni system the Au and the surrounding Ni atoms have been allowed to relax, but the reaction path is kept the same as over the clean Ni. The total energies are calculated within the local densityapproximation (LDA) augmentedby non-local corrections in the so-called generalized gradient approximation (GGA). (b) The measured initial sticking coefficient of methane on Au-Ni(111) surface is shown, as function of Au coverage, for two molecular beams with approximately the same translational energy (~ 75 kJ/mol) but with different nozzle (vibrational) temperature. The lines show the theoretical dependence given by equation 9, where the sticking coefficients have been weighted with their appropriate probabilities Po(Oa,) and P,(Oau), (see Fig. 7) [180].
251 These results reveal how it has now become possible to quantitatively predict trends in reactivity by combining theoretically calculated activation energies with an experimental determination of the atomic distribution of the reactions sites. Furthermore this shows that although the ensemble control is an important aspect of alloy catalysis, the surface atoms of an alloy do not retain their clean metal properties, not even for reactions that take place over a single atom. This allows for a much finer tuning of metal reactivity than the differences between the elemental metals offer. Therefore one of the ultimate goals of surface science, i.e. to be able to model design - on an atomic scale - surfaces with particular catalytic properties is now within reach.
7. CONCLUDING REMARKS
Over the last decade, the surface/materials science community has been wimessing a flood of studies which specifically address the novel electronic, magnetic and catalytic properties of bimetallic surfaces. Whether prepared by "cleaving" bulk alloy crystals or by heteroepitaxially growing metal-on-metal systems via vapour deposition techniques, studies have shown that the physics and chemistry of the near surface region of the alloys can be radically different from their bulk counterparts. A general phenomenon which has been identified is that the compositional phase-diagrams of many bimetallic surfaces are quite different from those of the bulk. As highlighted in this review, this extends to systems wherein the formation of surface metal alloys are identified for metals which, in the bulk, are highly immiscible. As elaborated earlier, our ever-increasing understanding of this class of systems has been greatly facilitated by the use of the scanning tunnelling microscope. Using data primarily acquired with this unique atomic-scale technique, we have endeavoured to overview some of the relevant properties of a broad range of 2-D "surface alloy" systems. As outlined above, there are some "general trends" which have emerged through a comparison of experimental results from differing systems. But many of these conclusion has come to fruition only through a direct interplay between experiment and theory. With this in mind, we now look toward the future scientific ventures for surface alloys of bulk immiscible systems. Utilizing ever more powerful computational facilities, many new theoretical schemes have recently emerged which show great promise with regard to predicting various properties of surface alloys. As more studies emerge which holistically probe our fundamental understanding of these systems, we will be able to predict and correlate with greater certainty their various unique properties. With this ability, we will be better able to judiciously design and engineer surfaces whose
252 properties have no bulk analog and yet are tuned to yield a given structural, electronic, magnetic, or catalytic property to help solve the technological hurdles of tomorrow.
8. A C K N O W L E D G E M E N T S It is a pleasure to thank a number of our colleagues including, I. Stensgaard, E. Laegsgaard, P. Murray, S. H. Christensen, J.K. NCrskov, K.W. Jacobsen, J. Jacobsen, P. Stoltze, T. Rasmussen, I. Chorkendorff, P.M. Holmblad, J. Hvolb~ek Larsen, B. Hammer and P. Kratzer for their contribution to the present article. We gratefully acknowledge D.L. Adams, M. Schmid, P. Varga and R. Hwang who kindly provided us with illustrations for inclusion in this article. We are also indebted to Randi Mosegaard for patient assistance in the preparation of this manuscript. Finally, we acknowledge the financial support from the Danish National Research Foundation through the Center for Atomic-scale Materials Physics (CAMP), the Danish Research Councils through the Center for Surface Reactivity and the Center for Nanotribologi, the Knud Hcjgaard and the VELUX Foundation.
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258
91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
Chapter 7 Epitaxial growth of Si on Si(001) Feng Liu and M.G. Lagally University of Wisconsin, Madison, WI 53706, USA 1. I N T R O D U C T I O N The development of modem techniques of thin-film growth and characterization has remarkably advanced our understanding and knowledge of growth mechanisms and surface properties. Scanned-probe microscopy allows us to observe not only static surfaces but also dynamic processes of growth at the atomic level. Among the variety of systems under investigation, the silicon (001) surface has attracted the most interest. Not only is silicon the foundation of modem semiconductor technology, but it displays a wealth of fascinating and intriguing phenomena that make it an ideal model system. Several reviews [1] of research on this surface have appeared, but they have been limited to its static properties. In this chapter, we review the most recent results on epitaxial growth of Si on Si(001), focusing on the microscopic aspects of growth kinetics rather than the thermodynamic properties of equilibrium surface morphologies. Because of limited space, we will concentrate on films grown by molecular beam epitaxy (MBE), using scanning tunneling microscopy (STM) as the major probing technique combined with theoretical modeling and simulation for quantitative data analysis. The chapter is organized as follows: In section 2 we give an overview of the Si(001) surface and kinetic processes involved during vapor deposition and introduce the necessary notations for later discussion. Sections 3 to 7 cover the various kinetic aspects including adatom adsorption (section 3), self-diffusion (4), nucleation (5), growth (6), and coarsening (7). The kinetics of surface defects (steps and dimer-vacancies) are discussed in section 8. In section 9, for completeness, we include a brief discussion of the thermodynamic properties of equilibrium surface morphologies, such as the equilibrium shape of Si islands, the energetics of steps and kinks, and step configurations on nominal and vicinal surfaces. Section 10 concludes the chapter.
259 2. B A C K G R O U N D
2.1 The Silicon (001) surface At room temperature, Si(001) displays a (2xl) reconstruction [1]: surface atoms dimerize, eliminating one dangling bond per atom at the expense of introducing an additional anisotropic surface stress, to lower the surface energy by --1.0 eV per atom. The dimerization was first proposed by R.E. Schlier and H.E. Farnsworth [2] and was first 'seen' directly by STM in 1985 [3]. Fig. 1 shows a schematic view of the surface. The reconstruction, which establishes two characteristic directions on the surface, either along or perpendicular to the surface dimer rows, in orthogonal directions, leads to many interesting surface property anisotropies, such as surface diffusion, surface stress, and interaction between adatoms and substrate steps.
0
0
0
m
Figure. 1. Side view (top panel, [1 1 0] projection) and top view (bottom panel) of the (2xl) reconstructed Si(001) surface. The dark rectangle depicts a 2xl unit cell of dimension 7.70 ,~ x 3.85 ,~. The dimer bond length is about 2.2 ,~. Because of the tetrahedral bonding configuration in the diamond structure, the dimer direction is orthogonal on terraces separated by an odd number of monatomic steps, giving rise to both (2xl) and (lx2) domains. There are two types of monatomic steps: step segments for which the upperterrace dimer rows are parallel (perpendicular) to the step are called SA (SB) [4]. On vicinal surfaces miscut toward a direction the two types of steps alternate. Usually, SA steps appear smooth while SB steps appear rough, containing many kinks and segments of SA termination. For simplicity, however, we still call a step nominally SA (SB) if it is oriented in the
260 direction and step segments along the average edge are SA (SB). We call terraces on the upper side of the rough SB steps (2xl) and the other orientation (lx2). Surfaces with miscut toward the [100] direction are comprised of steps that mn nominally at 45 ~ to the dimers, and in this case all the steps and terraces are indistinguishable and the (2xl), (lx2) nomenclature becomes arbitrary. If the surface is miscut by more than -1.5 ~ toward , doubleatomic-height steps begin to form and their fraction increases with increasing miscut angle [1,5]. Although there can be two types of double steps (DA and DB) [4], only DB steps form [5], leading to a predominance of (2xl) domains over (lx2) domains. The B-type of steps (SB and DB) can have two kinds of edge structures: rebonded or non-rebonded. Experiments [5,6] show that the rebonded SB and DB step edges appear much more frequently than their nonrebonded counterparts on natural surfaces, in agreement with total-energy calculations [4]. Fig. 2 shows schematic views of the atomic structure of single- and double-atomic-height steps. r'SB
S
.
(a)
r'DB
-
(b)
Figure. 2. Side view of (a) single- and (b) double-atomic-height steps on Si(001). Prefixes n- and r- denote non-rebonded and rebonded steps. Horizontal bonds are dimers of 2xl terrace; solid circles denote projection of dimers of lx2 terrace, which are normal to the plane of the figure.
At low temperature (below -200 K), surface dimer buckling begins to appear, forming c(4x2) and p(2x2) domains, and the number of buckled dimers increases with decreasing temperature [7]. Surface defects and steps are also observed to induce dimer buckling, in a way to release surface strain energy [7]. At high temperature, where most growth processes are carried out, surface dimers rapidly switch orientation, leading to an averaged symmetric appearance in STM. Ab initio calculations [8-11] show that the surface energy of buckled dimers is indeed lower than that of symmetric dimers, but the energy difference is very small.
261
2.2 Kinetic processes during vapor deposition The advantage of vapor deposition growth techniques, such as MBE, is that structures that are far from equilibrium can be made by choosing a proper growth temperature and deposition rate and selectively freezing kinetic processes. The key is to enhance the desirable kinetic processes and suppress the unwanted ones. In order to achieve this goal of manipulating growth kinetics, one must first understand quantitatively the microscopic kinetics of growth at the atomic level. During vapor deposition, a substrate is placed in a vacuum chamber and exposed to the vapor of the growth materials. In MBE, fluxes of atoms or molecules of material being grown are generated by evaporation from either a solid or liquid. As the adatoms are continuously deposited onto the substrate, the system is driven into supersaturation, i.e., the two-dimensional (2D) vapor pressure of the adatoms is higher than that at equilibrium. A condensed phase, e.g. 2D or 3D islands, will then form to relax the system back to equilibrium. There are three major processes in the formation of a condensed phase from a 2D vapor: nucleation, growth, and coarsening [12,13]. Arriving adatoms make a random walk on the surface and, when meeting each other, form islands. This is the nucleation process whose rate limiting step is the formation of the critical nucleus, which is defined as the island that is more likely grow than to decay [14]. The nucleated islands grow by further addition of adatoms, and the lateral accommodation kinetics determine the growth shape of the islands. The growth process continues until the deposition is interrupted. Thereafter, coarsening, in which small islands laterally "evaporate" and the atoms go to larger islands, controls the dynamics of further ordering. The driving force for coarsening is the difference between the local equilibrium vapor pressure around the large and small islands. An adatom, in addition to meeting another to form a nucleus, meeting an existing island (growth), or traveling between existing islands along a concentration gradient (coarsening), may also meet one of these fates: walking into a special sink site like a substrate step, diffusing into the bulk of the substrate, or re-evaporating from the surface. Fig. 3 schematically illustrates all these processes during growth from the vapor. The major part of this review will concentrate on kinetic aspects of each individual process and identify whenever possible microscopic parameters controlling the process. Despite extensive experimental and theoretical studies that have been carried out to explore various aspects of the growth of Si on Si(001), a number of fundamental issues concerning adsorption, nucleation, and
262 diffusion remain unclear. We hope this review will provide a guideline for future studies of this challenging field.
s'e~
deposition 0 re-evaporation
incorporation
l
(~ nucleation interdiffusion
T
deposition C)
island coarsening surface incorporation migration
Figure 3. Schematic illustration of major processes occurring during growth from the vapor. 3. ADATOM ADSORPTION: theoretical predictions In a semiconductor surface, in addition to the presence of dangling bonds, the directional bonding often introduces surface anisotropy and nonuniformity. For Si(001), the (2xl) reconstruction further complicates the situation, producing multiple adatom adsorption sites as well as complex diffusion pathways. STM has allowed us to observe directly the formation of Si islands at the initial stage of MBE growth with atomic resolution [15-19], but it is much more difficult, because of its rapid motion, to image directly the individual adatom, especially to record its exact location and its motion. On the other hand, the adsorption sites of an adatom can be easily calculated theoretically, assuming the existence of a reliable interatomic potential. The STM experiments [15-19] stimulated extensive theoretical investigations of Si adatom adsorption and diffusion on Si(001) [20-27]. The potential-energy surface of a Si adatom on Si(001) has been mapped out by both ab initio [20-22] and empirical calculations [22-27], but the empirical calculations, using either Tersoff [28] or Stillinger-Weber(SW) [29] potentials, are all in disagreement with ab initio calculations in predicting the most stable adsorption site. In Fig. 4 local minima in the potential-energy surface for an adatom sitting at various sites in the (2x l) unit cell are marked for two representative calculations: one [20] based on density functional theory (Fig. 4a), the other [24] using the SW potential (Fig. 4b). Besides the difference in total number of local minima, in Fig 4a the absolute minimum is at the M site, while in Fig. 4b it is at F.
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0
(c)
Figure 4. (a) and (b) Potential-energy minima (solid squares) for a Si adatom adsorbed at various sites in the Si(001) (2x l) unit cell calculated by ab initio (a) and SW (b) potentials. The global minima are at M and F in (a) and (b), respectively. Arrows mark the proposed diffusion pathways. (c) Four possible high-symmetry ad-dimer configurations. In principle, ab initio calculations are capable of giving reliable predictions. At the present time, however, the limited computational resource might prevent ab initio calculations from achieving their full potential. Approximations are often made in model system size, basis function expansion, and Brillouin zone sampling (integration) [11]. Empirical calculations are quantitatively less reliable, especially when they are applied to surfaces, because the empirical potentials are usually developed by fitting to bulk properties. Also, a short-range cutoff employed in the empirical potentials introduces additional errors in treating a dynamic process like surface adsorption or diffusion, in which bond breaking and bond formation processes are involved. Despite these shortcomings, the computational efficiency gives empirical potentials the advantage that they can be easily implemented into molecular dynamics and Monte Carlo algorithms to simulate the adsorption and diffusion in real time so that more insightful information of growth dynamics can be obtained. Two such studies by Zhang et al. [24] and Srivastava and Garrison [25] reveal that as atoms are deposited onto the surface, the most preferable adsorption sites at the initial stage are not necessarily the energetically most stable sites. Because the system is far from equilibrium, the population at a given local minimum site is not determined by its energy relative to other sites but rather determined by the escape rate of an adatom at this site. The kinetic barriers calculated from empirical potentials suggest that the Si adatoms are preferentially adsorbed on top of the dimer rows rather than in more stable places between dimer rows,
264 leading to a so-called 'population inversion' [24]. Such a population inversion may have an impact on nucleation process (see section 5). Although the population inversion results from kinetic barriers calculated from classical potentials [24], this process is likely to occur also if the kinetic barriers from a recent ab initio calculation [21] are adopted. According to this calculation, if an adatom lands on top of a dimer row, the kinetic barrier to migrate along the dimer row is 0.55 eV and the barrier to escape from the dimer row by jumping into the trough between dimer rows is 0.60 eV, so the adatom spends a long time on top of the dimer row before jumping into the trough. If an adatom lands in the trough between dimer rows, the kinetic barrier to migrate along the trough is at least 0.75 eV and the barrier to leave the trough is 0.70 eV, so the adatom stays a short time in the trough before jumping onto the top of a dimer row. Consequently, more adatoms will end up diffusing on top of the dimer rows at the initial stage of growth. At low enough temperature, a single adatom (bound only to the atoms in a lower plane) can be observed by STM. Two recent low-temperature STM experiments by Wolkow [30] and Wu [31] have identified multiple adsorption sites for an adatom, but the most probable position for an adatom to sit is just off the end of two adjacent dimers (M site in Fig. 4a), in agreement with the absolute minimum predicted by ab initio theories [20-22]. These studies also indicate that the location of an adatom can be influenced by substrate-mediated long-range adatom-adatom interactions, making the scenario of Si adatom adsorption more complicated. Besides the complexities in adsorption sites, the dynamics of the adsorption process of Si on Si(001) is expected to be strongly temperature-dependent, an interesting subject for future experimental and theoretical studies. 4. D I R E C T M E A S U R E M E N T OF Si SELF-DIFFUSION W I T H STM Surface diffusion is the most important kinetic process during growth. Technologically, understanding surface diffusion will lead to better control of the growth parameters necessary to achieve atomically smooth interfaces. For layer-by-layer growth, in general, surface migration helps to smooth the growth front, hence a low diffusion coefficient will result in a rough surface. In the extreme case, if the surface diffusion coefficient is zero and all adatoms stay where they land, the roughness of the growth front will diverge following the Poisson distribution as the thickness increases. The diffusion of adatoms on a solid material is one the most fundamental problems in surface science, one that has attracted attention for
265 many years. Despite its importance, however, reliable measurements of surface diffusion coefficients are rare, especially for semiconductor surfaces. In particular, the diffusion coefficient at zero coverage, i.e., the pure migration of adatoms on the surface, is difficult to determine. Macroscopic methods based on the observation of the spreading of an initially well-defined distribution of adatoms [32] or the decay of intensity oscillations in reflection high-energy electron diffraction with increasing temperature [33] may be ambiguous because of the influence of surface defects such as steps and because of interactions between adatoms themselves. Field-ion microscopy [34] can measure the pure migration of single adatom in an elegant manner. However, it is limited in the materials that can be studied because of the high field necessary for imaging, and has seen little application to semiconductors. Two STM-based methods for measuring diffusion coefficients have been developed on the Si surface: one by directly recording the motion of diffusive species and the other by counting island number density. For the first approach to work, the motion of diffusive species must be tractable by STM within the experimental temperature window. This is sometimes true for diffusive clusters at ambient temperature. For example, two such studies [35,36] have been done to measure the diffusion of Sb and Si dimers on Si(001). However, the motion of a monomer, such as a Si adatom on Si(001), is often too fast to record at ambient temperature, it is more convenient to apply the second approach, which we discuss below.
4.1 Dependence of island number density and denuded-zone width on the diffusion coefficient Mo et al [37-41] performed the seminal work to determine the surface diffusion coefficient of Si on Si(001). Based on STM analysis of the number density of islands far from steps and the width of denuded zones at the steps, the activation energy for diffusion is determined to be Ea - 0.67+0.08 eV with a prefactor of Do - 1 0 -3 cm2/sec. The diffusion is highly anisotropic: the surface migration is at least 1000 times faster along the dimer rows than perpendicular to them. The method has since been widely applied to other systems [42]. In this section, we review the major details of their work. As adatoms are deposited on a surface at sufficiently low temperatures, they either form islands or walk into steps. The competition between island formation and step incorporation results in a spatial distribution of stable islands with denuded zones around those steps that are good sinks for the adatom and a uniform distribution far from the steps. By establishing the dependence of island number density and denuded-zone width on the
266 diffusion coefficient, it is possible to determine the diffusion coefficient by measuring the island number density or denuded-zone width without observing the individual adatom. At the center region of a wide terrace (hence a negligible influence of steps), an arriving adatom will either form a new island with another free adatom (nucleation) or walk into an existing island (growth). The surface diffusion coefficient determines how large an area an adatom interrogates in unit time. Therefore, the diffusion coefficient controls the outcome of the competition between nucleation and growth, and hence determines the number density of stable islands after deposition to a certain dose at a given deposition rate. A large diffusion coefficient, for instance, means a high probability for an arriving adatom to find an existing island before another adatom is deposited in its vicinity to provide a chance for nucleation. As a result, a large diffusion coefficient yields a lower number density of stable islands. Quantitatively, the relationship between island number density and diffusion coefficient has been established through a simple dimensional argument [38,41]. The deposited adatoms make a random walk on the surface. The diffusion coefficient for a random walk process is D = J a 2,
(3.1)
where J is the number of hops made in unit time and a is the step size, here taken to be the lattice spacing. The lifetime XAof an adatom is controlled by two different collision rates, WAg (adatom-adatom collision) and wAi (adatomisland collision), in such a way that the "death rate" of adatoms is n/'~A 2 WAg + WAX, "
-
(3.2)
where n is the number density of free adatoms deposited at a rate of R, n=R'~a. According to the theory of random walks [43,44], the number of sites visited by the adatoms after J = D'ca/a2 hops (for large J's) during their lifetime is approximately C(D'~A/a2)~v2, where d is the dimension of the random walk and C is a constant that depends on the dimensionality and the capture number of the single adatoms or islands. On the average, an area of 1/nB is associated with each adatom (nB = n) or island (na = N) enclosing 1/( nBa2) lattice sites. Hence the probability of an arriving adatom to collide with
267 an existing adatom or island is CnBa2(D'~A/a2)d/2. Multiplying this by n/'i~ A yields the collision rates WAg and WA~, WAB = CnnB a2-d(D'l;A)d/2/'l;A .
(3.3)
The nucleation rate or the rate of increase of the island number density is dN/dt = WAA= Cn 2 a2-d(D'l;A)d/2/a;A 9
(3.4)
At the very beginning of the deposition, the island density is negligible, so the decay of adatom density is mainly caused by nucleation, i.e., n/'~A = 2 WAg. For a large enough diffusion coefficient, the island density catches up rapidly and collision with islands becomes the dominant factor in limiting the adatom lifetime, "cA, which should be much shorter than the deposition time, t (in order for this analysis to hold). Now n/'~A ----WAI, SO that C N a2-d(D'l;A)d/2= 1
(3.5)
Substituting Eq. (3.5) into (3.4) yields N 2/d+ldN =
C-2/d(R2a2"4/d[D)dt.
(3.6)
By integration, we have N(2+2/d)_
C-2/d(2+2/d)(RO[D)a(2-4/d),
(3.7)
where 0 = Rt is the total dose deposited up to time t. So we have a general form of dependence of the island number density on diffusion coefficient as N - (RfD)X; Z = 1/(2+2/d).
(3.8)
For isotropic diffusion, d = 2, Z = 1/3; for highly anisotropic diffusion, d= 1, Z = 1/4 [41]. Similar arguments can be applied to the denuded-zone width at those steps that are good adatom sinks. Qualitatively, the larger the diffusion coefficient, the larger the denuded zone. We have just shown that on the average an adatom needs to m a k e - 1 / ( N a 2) hops to find an island. For an adatom to reach a step from a random site, it will also on the average take
268 -1/(Na 2) hops, because this is simply a 1D random walk problem. This means that the probability for an adatom to find the island is of the same order as that for it to walk into the step even though there are many more sites available on the step. This seemingly counter-intuitive conclusion can be understood by considering the fact that sites on the step are correlated on a line and that the sum of all the possible paths to reach the line is not (Na) ~/2 times that to reach a single random point because many paths are shared by the points on the line. This conclusion indicates that when the diffusion coefficient is changed, the denuded-zone width should scale with the mean island separation, i.e., W D Z cx: N "1/2 '
(3.9)
where WDZ is the denuded-zone width and N "1/2 is the mean island separation. From Eq. (3.8), we have WDZ ~: D 1/6 for isotropic diffusion and WDZ o~ D 1/8 for highly anisotropic diffusion. Several assumptions and approximations have been made in the above dimensional argument. Therefore the analysis can only be applied under appropriate conditions. For Eq. (3.4) to be valid, the dimer must be the stable nucleus (critical nucleus i=l atom). Generally speaking, this assumption is correct for strongly bonded materials (metals, semiconductors) [45] at not too high temperature. For Si/Si(001), single dimers are observed to be stable up to 600 K by STM[37-39]; a recent low-energy electron microscopy (LEEM) experiment [46] shows that the stable nucleus remains a single dimer up to -770 K, but then increases rapidly with increasing temperature to as large as 650 dimers at 970 K. Another assumption is that there is no coarsening and coalescence of islands during deposition, which requires that deposition be carried out at low temperatures and the total coverage be small. Experiments [37-39] show that the deposition of Si on Si(001) below 500 K up to a total dose of--0.1 ML will satisfy the condition. One more implicit assumption used in the dimensional argument is that all the islands are point targets. The actual island shape and how the adatoms stick to the islands are not considered. In reality, the growth shape of the islands is highly anisotropic. The aspect ratio can be as large as 20:1 [15-18], with the long side along the dimer row direction perpendicular to the substrate dimer rows. One can view the long edges of the islands as SA steps and short edges as SB steps. It has been shown that the SA step acts like a mirror and the SB step is nearly a perfect sink for adatoms (see section 6). The lateral sticking coefficient for adatoms to bond to SB and SA edges of the islands differs by an order of
269 magnitude [18]. Taking these effects into account, Wu [31] shows that the power-law exponent for the R/D dependence of N becomes Z = 1/5 (see Eq. (3.8)). The power-law dependence of island number density and of denudedzone width on the diffusion coefficient that is derived from the dimensional argument has also been confirmed by computer simulations and rate equation calculations [38,40].
4.2 Diffusional anisotropy Because Si(001) has two-fold symmetry, it is natural to assume the surface migration to be anisotropic. All theoretical studies based on totalenergy calculations [20-27] predict that surface diffusion is faster along the dimer rows. Mo and Lagally showed direct experimental evidence of anisotropy in the surface diffusion of Si and Ge on Si(001) [37], based on STM analysis of the width of denuded zones at substrate steps. The denuded-zone width around a step depends, in addition to the diffusion coefficient, also on how good a sink the step is for the adatom. Therefore, it is desirable to study the diffusional anisotropy by analyzing denuded zones around those steps that are good sinks for the adatoms. From the study of the anisotropic growth shape of 2D Si islands [18] and the adatom-step interaction [37,39] (see section 6), SB steps are identified as good symmetric sinks for adatoms, hence, the diffusional anisotropy can be determined by analyzing denuded zones around them. As shown in Fig. 5, on the down terrace of an SB step, dimer rows are parallel to the step [(lx2) domain], while on the up terrace of an SB step, dimer rows are perpendicular to the step [(2xl) domain]. Thus, the mechanisms of diffusion toward the step on these two neighboring terraces are different: either along or perpendicular to the dimer rows. Because SB steps are symmetric sinks, adsorbing adatoms equally well from up and down terraces [37,39], an anisotropy in the diffusion rate will result in an asymmetry in the two denuded zones around an SB step. Figure 5 shows two examples of STM scans after Si deposition at substrate temperatures of 563 and 593 K, respectively. Clearly there is an asymmetry: the denuded zones on the (2x l) domain are much larger than those on the (lx2) domain. At 593 K, the denuded zone on the (2xl) terraces appears free of islands, indicating that diffusion is faster along the surface dimer row direction. The adatoms on the (2x l) terraces reach SB steps and get adsorbed before having a chance to collide with each other, while the adatoms on the (lx2) terraces run fast parallel to steps and stay on the terraces much longer, and are therefore more likely to meet other adatoms to
270 form islands. By measuring the distance of each island from the SB step near it, the island density profiles across (2xl) and (lx2) terraces are obtained. The denuded-zone width can be defined as, for instance, the distance from the SB step at which the island density is 70% of that far from the step [37]. However, the rough shape of SB steps results in a very poor accuracy in the measurements of the denuded-zone width on (lx2) domains, on which the dimer rows run parallel to the terrace edges. As shown in Fig. 5a, adatoms landing in the "bay" areas on the (lx2) terrace (downstairs of SB steps) can diffuse rapidly parallel to the mean step direction and thus reach and stick to the "capes". The denuded zone thus generated will not reflect the adatom migration across the dimer rows. As a consequence, only an upper limit of the denuded-zone width on the (lx2) domains is obtained.
SB SB SA
SA
Figure 5. STM images, 5000/~ x 5000 ,i,, showing the asymmetry of denuded zones around SB steps, as the result of the diffusional anisotropy of adatoms. 0.1 ML of Si is deposited at a rate of 1/400 ML/sec at two growth temperatures; (a) 563 K, (b) 593 K. The surface steps down from upper right to lower left. The white bars correspond to the directions of the dimer rows on the terrace [40]. In conclusion, for temperatures between 300 and 600 K, the denuded zone on the terrace on which the dimer rows run perpendicular to the SB step is at least 3 times larger than that on the terrace on which the dimer rows run parallel to the step. Using the relation of WDZ o~ D ~/6 in their original analysis, Mo and Lagally [37] concluded that the diffusion along the dimer rows is at least 103 times faster than perpendicular to them. An anisotropy of this magnitude means that diffusion is essentially one-dimensional. Therefore, it is more appropriate to use the relation of WDZ ~: D ~/s (see section 4.1),
271 which gives rise to an even larger diffusional anisotropy. The ratio of diffusion coefficients in orthogonal directions must be of the order of at least 10 4. In a recent analysis of island number density, taking into account the actual anisotropic island shape (instead of assuming point targets) and adatom accommodation, Wu [31] also shows that the magnitude of diffusion anisotropy is more likely to be 10 4. Theoretically, total-energy calculations [20-27] all show that the kinetic barriers for diffusion along the dimer rows are different from those perpendicular to them, consistent with the diffusion anisotropy observed experimentally. 4.3 Diffusion coefficient and activation energy In section 4.1 we showed that the surface diffusion coefficient of adatoms can be determined by measuring the island number density after deposition at a given rate and to a certain dose. One such measurement for Si diffusion on Si(001) has been done by Mo et al. [38]. The outline of their experiments is as follows: a sub-ML dose (e.g. 0.07 ML) of Si adatoms is deposited onto Si(001) held at different temperatures; when the deposition is shut off, the sample temperature is simultaneously quenched to near room temperature by turning off the heating power; the sample is then transferred to the STM for scanning; scans are made near the centers of the large terraces to avoid the interference of steps; many scans are obtained to achieve good statistics; and the number of islands in each scan is counted to obtain an average number density. Figure 6 shows examples of islands formed after deposition at four different temperatures ranging from 348 to 653 K. The smallest islands are identified as single dimers; they are stable at room temperature. Data for T < 348 K are not included because the quench rate after deposition is too slow and it can not be assured that all islands are formed only during the deposition, a necessary condition of the model relating island number density to diffusion coefficient. For T > 573 K, the island number density drops drastically. This effect is caused by island coarsening, an additional ordering mechanism that becomes important at higher temperatures (or lower deposition rate) (see section 7). Also, the critical size appears to start to go up a t - 700K [46]. Although Eq. (3.7) provides a physical rationalization of the relationship between island number density and diffusion, a quantitative determination of the diffusion coefficient has to be done with the aid of computer simulations. Using a solid-on-solid model [38], simulated island densities are compared to the experiments for the same total deposited dose.
272 Figure 7(a) is a plot of calculated number density of islands versus the jump rate incorporating different diffusional and sticking anisotropies. For a sufficiently high jump rate, the island number density is proportional to j-~/3 for isotropic diffusion and j-1/4 for anisotropic diffusion [41], in agreement with the dimensional argument. For a very small jump rate, the lifetime of adatoms to find an existing island is longer than the total deposition time and most islands are formed after deposition, resulting in a constant island number density [39].
,~
~:'
i ~ 84 ~
Figure 6. STM images of islands formed after deposition at different substrate temperatures at a rate of 1/600 ML/sec to a dose of 0.07 ML. Top left panel: T=348 K, 250 ~ x 250 A,; top right: T=400 K, 300 ,~ x 300 A; lower left: T= 443 K, 300 ~ x 300/~; lower right: T=500 K, 400 ,~ x 400/~. The islands formed at higher deposition temperatures are larger than those at lower temperatures, with lower number densities, because of the larger diffusion coefficients
at higher temperatures. The islands in each image are counted to obtain an average number density for each temperature [38]. Figure 7(b) shows Arrhenius plots of the diffusion coefficients obtained from the three models determined by choosing the data in Fig. 7(a) that
273
correspond to the measured island density at several temperatures. Using the curve that incorporates a 1000:1 diffusional anisotropy, Mo et al. obtain an activation energy for surface diffusion of adatoms of 0.67 eV, and a preexponential factor of -- 10 .3 cm2/s[38] (a higher anisotropy like 104:1 will give a virtually identical activation energy). Assuming the diffusional anisotropy is all ascribed to a difference in activation energy, the activation energy for diffusion across dimer rows becomes --1 eV. Although essentially all calculations [20-27] predict the anisotropic diffusion, the ab initio kinetic barriers[20-22] agree quantitatively better with these experimental values. 1
O"
- e=t/ooo (~/s,=)-
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-
e=o.o7 (m.)
~" o I01=
555
476
417
370
333
z.4
2.7
3.0
_
10-t t ~9, lOt= la~JJo Bo,,. Z:IO00 gff. b o . Bo,u. I : ! Diff.
.P.~L~ equmUon =u'n=~
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lO-i=
t .... a=,~ .... , ~ , ..... ,a . . . . ,a ..... .~ ..... .~ ...... ,J . . . . . .
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a
,L o 0
10 = 10 = 10 ~ 10 6 10 e
Jump rate (sec -l)
10 7
10 e
10-"
b
1.5
~.8
e.~
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( 1 0 -= K - t )
Figure 7. (a) Relationship between the island number density and the jump rates of adatoms. Three of the curves are from computer simulations with different diffusional anisotropy assumptions while the fourth curve is from rate equation calculations. Circles: both isotropic sticking and diffusion. Diamonds: rate equation, isotropic sticking and diffusion. Squares: anisotropic sticking and isotropic diffusion. Triangles: both anisotropic sticking and diffusion. The anisotropic diffusion assumes a jump rate along the dimer rows of 1000 times that perpendicular to the dimer rows. The anisotropic sticking assumes a probability of one for sticking at the ends and zero at the sides of islands. Simulations are for the same deposition condition as in experiments (Fig. 6) [40]. (b) Diffusion coefficients obtained from comparison of the measured island number density with those from computer simulations using three different models. Notations are the same as in (a) [40].
The experimentally derived barriers for diffusion should be considered as average values because only a single adsorption site and two orthogonal diffusional directions are used in the computer simulations of experimental analysis, while on a real surface, multiple adsorption sites and complex diffusion pathways are involved. From the measured diffusion coefficient, one would expect that the motion of a monomer will be slow enough to be
274 observable at -200 K. However, in reality monomers can be observed only at much lower temperatures [7,31], suggesting that there exists on top of the dimer rows a fast diffusion pathway with lower barrier than the average, leading to a faster motion of monomers than what one would have expected. Several different models have been proposed theoretically: Brocks et al. [20] proposed a zigzag path connecting two most stable adsorption sites (Fig. 4a); Zhang et al. [24] and Srivastava and Garrison [25] proposed that the diffusion predominantly occurs on top of dimer rows (Fig. 4b); Roland and Gilmer [27] suggested exchange events between adatoms and substrate atoms during diffusion.
5. NUCLEATION: energetics and dynamics of Si ad-dimers For Si growth on Si(001), dimers are identified as the stable nuclei, at least up to substrate temperatures as high as 600 K [18,39,40]. Total-energy calculations [47-51] have been done to determine the most stable site for an ad-dimer. Similar to the situation for adatoms, empirical potentials disagree qualitatively with ab initio calculations. Recently, the stability and dynamics of ad-dimers have been studied directly in real space, using variabletemperature STM [49,52] and the newly developed atom-tracking technique [36,53]. These experiments provide direct information on ad-dimer stability and confirm a rotational motion of ad-dimers on top of a dimer row predicted by theory. Fig. 4c shows four possible high-symmetry positions for an ad-dimer adsorbed on Si(001). Their relative stabilities, determined by an ab initio calculation, [50] were ED-D: EB-B: ED-D*: EF-F = 0.00 : 0.01 : 0.31 : 1.11 eV. Similar calculations with two empirical potentials [48,49] give a very different order of stability. For example, with the SW potential [49], ED-D: EB-B" ED-D* " EF-F = 0.92 " 0.86 " 0.78 " 0.0 eV. The major difference between ab initio and empirical calculations is that the former predicts on-top dimers to be more stable while the latter predicts the in-trough dimers to be more stable. While empirical potentials are less reliable, ab initio calculations suffer from the fact that only limited system size can be employed. So far, the controversy of site stability has not been completely resolved, as we discuss below. Images of ad-dimers have been taken by STM [31,49]. When 0.01 ML of Si is deposited at room temperature, it is found that most adatoms form addimers, with an average separation of--50,1,. Two kinds of images are taken to identify the ad-dimer configurations" Images over a large area (300 ,~. x 300
275 A) provide overall quantitative, statistical information about the configurations of the as-grown ad-dimers, including the populations of different orientations at different sites; repeated images of a particular addimer with higher magnification (80 ~ x 80 A) facilitates the study of the dynamics of an individual ad-dimer. Also, post-growth annealing has been performed to observe changes in the configurations.
Figure 8. STM images of Si dimers, taken after 0.01 ML deposition at room temperature, with high magnification to show the rotation of a on-top ad-dimer of Si on Si (001). (a)(c) are each separated by 40 sec. The ad-dimer indicated by the arrows rotates. In (a), its axis is perpendicular to the substrate dimers. In (b), it has rotated by 90~ with its axis parallel to the substrate dimers. In (c), it has rotated back. Shown at the lower-left corner are substrate orientations [49]. Large-area images [31] show that most of the dimers reside on top of the dimer rows. Although ab initio calculations [50,51] do predict the addimer to be more stable on top of the dimer row than inside the trough, it has been argued [49] that the as-grown ad-dimer configurations may not be determined solely by their energetics but also by kinetics, because the adatoms are more likely to diffuse and meet each other on top of the dimer rows (see sections 3 and 4). The on-top ad-dimers (Fig. 4c) are oriented either parallel (D-D) or perpendicular (B-B) to the substrate dimers. The high-magnification images [31,49] reveal that the on-top ad-dimers can oscillate between the two orientations, as shown in Fig. 8, confirming the theoretical prediction [47,48]. However, their relative population is observed in the large images to remain approximately constant at a ratio of n D - D ] n B - B " 1/(10_+2) for hours at room temperature. Assuming local thermal equilibrium
276 has been reached between these two configurations, this ratio indicates that the D-D dimer is about 0.06 eV less stable than the B-B dimer. The rotational motion and the relative populations have also been observed in two other experiments [52,53]; all three measurements give the same results. Theoretically, two ab initio calculations [51,53] agree well with experiment, showing the D-D dimer to be --0.07 eV less stable than the B-B dimer, while the other [50] can not resolve the difference in stability of these two configurations; two empirical potentials [48,49] also give the fight relative stabilities for these two ad-dimer positions. Experiments [31,49] indicate that upon annealing ad-dimers appear half-way between two dimer rows (i.e., the in-trough position), at the expense of dimers on top of the dimer rows. Because annealing helps ad-dimers to find more stable positions, this would indicate that the in-trough ad-dimers are more stable than the on-top ones, in contradiction with ab initio calculations but in agreement with empirical potentials. To resolve this puzzle, apparently more experiments and larger-scale ab initio calculations are needed. It has been suggested [50,51] that the observed in-trough addimers might be stabilized by their interaction with other adatoms or addimers or by defects. What appears to be an in-trough dimer in the filledstate STM image [49] may actually be a cluster containing more than two atoms. An ab initio calculations [50] shows that the isolated ad-dimer is more stable on top of the dimer row but an infinite row of in-trough D-D* dimers is more stable than an infinite row of any other possible dimers. Similarly, the D-D* dimer can attract an adatom to form a "dilute" ad-dimer row in the direction perpendicular to the substrate dimer rows, as observed experimentally [52], while the on-top B-B and D-D dimers don't bind an adatom. Although ad-dimers are stable against dissociation up to 600 K, not all of them are stationary above room temperature. The in-trough dimers (if that is what they are) are observed to be immobile [31,49] but the on-top dimers show a highly anisotropic diffusion along the substrate dimer rows [36,57]. Using his newly developed atom-tracking STM, Swartzentruber [36] directly measured the diffusion barrier for on-top dimers to be 0.94 + 0.09 eV. This value is much smaller than the 1.45 eV predicted by a recent ab initio calculation [51], suggesting that the atomistic mechanism of ad-dimer migration differs from the one used in the calculation [51 ].
277
6. GROWTH: adatom-step interaction One of the remaining challenging questions concerning growth of Si on Si(001) is how ad-dimers (stable nuclei) transform into epitaxial dimer-row islands. Although a single ad-dimer is most frequently observed at the epitaxial position on top of a dimer row, it does not bind an adatom [50]; theory [50] predicts that only in-rough dimers can attract adatoms, but they form "dilute" ad-dimer rows rather than epitaxial dimer rows [50,52] (see section 5). It has been speculated that the "dilute" ad-dimer rows are transient structures mediating the formation of anisotropic epitaxial dimerwide islands from single ad-dimer nuclei [18,50,52]. Several molecular dynamics [55,56] and Monte Carlo simulations [57] have been carried out to explore the microscopic mechanism of the formation and growth of epitaxial islands, but none of them has observed the "dilute" ad-dimer row structure. Other mechanisms (e.g., substrate dimer opening [55,56] due to adatom insertion) have been proposed. But these have also not been confh'med experimentally. There thus remains a large gap in understanding the very initial stage of island formation from the stable nucleus. We have obtained a much better understanding of epitaxial dimer-row island growth, once past the initial formation stage, and of step-flow growth. At typical experimental deposition rates of-0.001 ML/sec to --0.01 ML/sec, between room temperature and -500 K, the growth proceeds via 2D islands [15-18]; above 500 K, the growth proceeds via step-flow [19]. Annealing experiments [18] clearly show that the shape of the as-grown islands is controlled by kinetics, because it differs from the equilibrium shape. The islands consist of a few dimer rows with an aspect ratio as high as 20:1 [1518]. Analyses show that the highly anisotropic shape is caused by the large difference of lateral accommodation coefficient in two orthogonal directions rather than by anisotropic diffusion [18]. Arriving adatoms stick to the ends of dimer rows (SB steps) at least one order of magnitude better than to the sides of the rows (SA steps). For the same reason, in the higher-temperature step-flow growth mode, SB steps advance to catch up with SA steps, resulting in a single-domain surface [19]. The anisotropic accommodation has also been shown to play a key role in the 2-D kinetic roughening of the step growth front during step flow or near step-flow conditions [58]. In the following we discuss a few elegantly-designed experiments [37,39] that allow us to investigate in detail the nature of the adatom-step interaction. The interaction between adatoms and surface steps is one of the most important microscopic aspects of the growth kinetics. The nature of this
278 interaction determines the growth rate and shape of islands, the mode of stepflow growth, and the width and asymmetry of the denuded zone around steps. The width of a denuded zone is, in addition to surface diffusion and its anisotropy (discussed in section 4), also controlled by the adatom sticking coefficient at the step and the energy barrier for adatoms to cross the step. It is possible to address each individual effect separately [37,39].
~ ~~i~"~
~
Figure 9. The spatial distribution of 2D Si islands on a large terrace (-7000/~ wide), showing a large anisotropy in the denuded zones that reflects the anisotropy of the lateral sticking coefficients of adatoms at SA and SB steps. The scan range is 1.0 x 0.9 ].tm. - 0.1 ML deposited at 563 K and at a rate of 1/4000 ML/sec. The surface steps down from lower fight to upper left [37]. The relative magnitudes of the lateral sticking coefficients of adatoms at the SA and SB steps can be studied by analyzing denuded zones on any single terrace that is bounded by the two types of steps. Fig. 9 is an STM image of a large single terrace about 7000 A wide, created by applying a small external stress to the wafer [59] (the effect of the external strain on growth kinetics is negligible [60]). The terrace is bounded by an SB step at the downstairs side (the upper left) and an SA step at the upstairs side (the lower fight). On each side are much smaller minor-domain terraces. The bright strings on the terrace are 2D islands. An obvious asymmetry exists in the spatial distribution of the islands: the denuded zone near the SB step is much larger than that near the SA step. Because the diffusion toward the two steps must be same everywhere, this asymmetry is clear evidence for the anisotropy in the lateral sticking coefficients of adatoms at the two types of
279 monatomic steps: SB steps are good sinks for adatoms while SA steps are not. Both Mo [18,39] and Wu[31] show quantitatively, from the analysis of the highly anisotropic shape of growth islands, that the ratio of sticking coefficient of a monomer at SB and SA steps is at least 10:1. Mo [39] also pointed out that for a dimer-wide island to grow preferentially at its ends, a monomer must have some residence time at the end of the row, waiting for another monomer to come to form the next dimer. Indeed, monomers trapped at the end of dimer rows have been observed [31,61 ]. 1 /
~:~'~ ~:!?~,~!ik .o.. ~.~!~z.~:,~.~-~:~.-~.~:~.~,:~.~.~.~.i~:~-~..~@...~.~:%-~i~ ~.~:
-
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jr162
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- " .
Figure 10. STM images, 5000 A x 5000 .~, showing symmetric denuded zones around steps. -- 0.1 ML deposited at a rate of 1/400 ML/sec, at (a) 563 K, and (b) 593 K, respectively. The surface steps down from top to bottom. The underlying dimer rows run 45 ~ to the steps and form a chevron pattern orthogonal to the directions of the long axes of the deposited islands [37]. SB steps are not only good sinks but also symmetric sinks: i.e., they adsorb adatoms coming from either up or down terraces equally well [37]. This conclusion is reached by analyzing the denuded zones around steps in directions, which are at 45 ~ to the dimer rows of both domains. In this configuration, all the terraces are equivalent and the diffusion toward any step on both the up and the down terraces is identical. Fig. 10 shows STM images of the island distributions around steps. In Fig. 10a, the four denuded zones shown have the same widths. The middle terrace is so narrow that the two denuded zones from the bounding steps nearly overlap. For the conditions in Fig. 10b, the denuded zones are wider than the terrace. Although 45 ~ steps are not pure SB steps, microscopically the SB step
280 segments are adsorbing the adatoms with at least one order of magnitude greater sticking coefficient [18,31]. Thus one can conclude that SB steps are symmetric sinks for adatoms either from up or down terraces. The existence of a large denuded zone on the up-terrace side of SB steps (Fig. 9) suggests that, in addition to SB steps being good sinks, there must be no significant barrier for adatoms to cross downward over SB steps, because a barrier would act to keep atoms on the terrace and thus reduce the denuded zone even if the sticking coefficient at the SB step is large. The absence of a denuded zone on the down-terrace side of SA steps indicates that SA steps are poor sinks as well as, at least to a certain degree, mirrors for adatoms from the down terrace. In Fig. 9, the SA step at the lower-fight comer is very close to the next SB step. If adatoms could easily cross an SA step from the down (2xl) terrace, they would climb over to the up (lx2) terrace and get adsorbed by the next SB step or by the kinks in the SA step. This would result in a large denuded zone on the down (2xl) terrace of the SA steps even though SA steps themselves are poor sinks. No such denuded zone is observed; hence the SA steps must have a significant step crossing barrier. The adatom-step interaction has also been studied extensively by theory [21,62-64]. The results of an ab initio calculation [21] are in very good agreement with the above experimental conclusions, showing that SA steps are poor sinks for adatoms both because the binding energy of an adatom at the SA step edge is comparable to that on the terrace and because the barrier for adatoms approaching the SA step from the lower terrace to escape the SA step again is low. Rebonded SB steps are good sinks for adatoms because the binding energy to the SB step is large and because adatoms approaching the SB step from the upper terrace encounter only small barriers to cross the step edge. All empirical calculations [62-64] have reached the conclusion that SB steps are much better sinks for adatoms than SA steps, but they wrongly predict that only non-rebonded SB steps bind adatoms strongly. Experiments [6,31] show that most SB steps appearing on the surface are rebonded and hence for growth to occur they must bind adatoms also. 7. COARSENING If deposition is interrupted, the average supersaturation of free adatoms on the surface continues to reduce through nucleation and growth until it is eliminated. At this stage, islands of different sizes exist in equilibrium with their local vapor pressures. The local equilibrium vapor pressure, i.e., the
281 concentration of free adatoms around an island, is inversely proportional to the radius of the island [39,65]. Hence there will be locally different concentration of free adatoms on the surface. As a consequence of Fick's law of diffusion, there will be net fluxes of adatoms flowing from small islands to large ones. Following nucleation and growth, therefore, the system is further organized by the coarsening process: large islands grow at the expense of small ones. The driving force decreases as the islands become more uniform in size, leading to the phenomenon of Ostwald ripening [66] in which a distribution of islands with uniform size results. The kinetics of coarsening have been intensively studied theoretically. It has been established [67-69] that the growth rate of the average radius of islands follows a long-time asymptotic power law with a growth exponent of 1/3, i.e., 3 - 3 + K(T) (t-to),
(3.10)
where ro is the radius at an arbitrary initial time to, K(T) is the rate constant for the coarsening process, which can be expressed as a pre-exponential factor and an activation energy. This equation is valid after an early-time "transient" regime and before growth slows due to Oswald ripening. Some experiments [65] and computer simulations [70] show that the growth exponent is often less than 1/3. In general, when the average island radius is smaller than a critical length [71] of microscopic scale, the exponent gradually increases as the average island size grows, and eventually reaches 1/3. For Si islands on Si(001), because of the limited terrace size and the incorporation at steps the average island size may never reach the macroscopic scale for the exponent to reach 1/3. This has been directly tested by experiments [16,39]. Fig. 11 shows STM images taken after four annealing periods at 513 K after a deposition of-0.1 ML of Si on Si(001) at -323 K. The islands grow in size while the number density decays as the annealing time increases. By plotting the average island radius vs. the annealing time at three different anneal temperatures (513, 573, and 623 K), an average growth exponent of 0.18 is obtained [39]. Using this exponent, the rate constant K(T) is extracted to yield a value of 2.5 + 0.9 eV for the activation energy for the growth of average island radius in this regime [37]. It is also found [39] that long-time anneals increase the island coverage in addition to the initial dose of deposition, with a concurrent rise in the concentration of dimer vacancies (see Fig. 11). This observation indicates
282 that during annealing some Si atoms in the surface pop up onto the terrace where they can migrate to form islands. The origin of this phenomenon is not yet clear. However, most of the adatoms generated by this effect will likely merge into the existing islands rather than forming new islands because of the high density of existing islands. So, this effect will not cause much error in the derived activation energy for coarsening because it is the island number density and not the total coverage that has been used in the analysis.
Figure 11. STM images, all 600/~ x 600/~, after 4 annealing cycles at 573 K, showing the increases of both the island coverage and the defect density. Top left, annealed for 6 sec. Top right, 30 sec. Lower left, 90 sec. Lower right, 270 sec. Apparently, some top layer atoms are "pulled" up to merge into islands formed by deposition [39]. Although the exact meaning of a coarsening activation energy obtained in the above manner is not fully understood, the derived value seems to be consistent with the activation energies obtained for step motions induced by external stress [60]. Also, assuming the activation energy for coarsening is the sum of diffusion activation energy and the desorption energy of mobile species from island boundaries ( S A and/or SB steps), the resultant desorption energy agrees reasonably well with the step fluctuation activation energy (see
283 section 8.1). Theis, Bartelt, and Tromp [72] also conclude, from a recent LEEM study, that the ripening of 2D islands on Si(001) can be understood in a common framework with step fluctuations. In addition, they demonstrate that the ripening process is strongly influenced by the nearest-neighbor correlations between islands. 8. R E A L - T I M E MEASUREMENTS OF KINETICS OF SURFACE DEFECTS Many surface properties are affected by defects, such as steps and vacancies. In general, defects are the most active sites on the surface. The chemical reactivity of the surface, as well as the sticking and diffusion of adsorbed species, can be altered by the presence of defects. For example, we have demonstrated how steps dominate the growth through adatom-step interaction. To elucidate further the role that defects play in the growth process it is important to understand some of the fundamental kinetic parameters that control the behavior of surface defects themselves. In order to do real-time measurements, the rate of the dynamic processes of interest must occur on a similar time scale as that of the STM data acquisition. Only a limited number of processes (e.g., the rotation of Si ad-dimers on Si(001) [49]) can be observed in real time at ambient temperature, where STM is most easily accomplished. As a result, room temperature STM is most often applied to the study of static surface structures. Nevertheless, many high-temperature processes can still be studied by room temperature STM through quenching experiments. The observed after-the-fact surface structures, reflecting a distribution at some higher "freeze-out" temperature, are compared with kinetic models to extract the relevant kinetic parameters. For example, in sections 4.3 and 7 we presented two such studies: a quantitative determination of the activation energies for diffusion and for coarsening from the analysis of quenched island distributions. The development of variable-temperature STM [6,7,73-75] allows us to observe in real time a much wider range of kinetic processes on the surface. Those processes that are too slow at room temperature will be observed at higher temperature (quantitatively, processes that must surmount activation barrier greater than-0.75 eV require temperatures above room temperature in order to proceed at an appreciable rate); while those processes that are too fast at room temperature will be observed at lower temperature. In the following, we discuss the applications of high-temperature STM to
284 study the kinetics of surface defects on Si(001). By elevating the substrate temperature to an appropriate range, step fluctuation and dimer vacancy migration are observed directly in real time.
8.1 Activation energy for step fluctuation and step motion Below 500 K, both SA and SB steps appear stable; at -500 K, the rough SB steps start to fluctuate, with the step fronts becoming rough[6,75,76]; at temperatures above -1300 K, both steps fluctuate and all the step fronts become very rough, consisting of mixtures of SA and SB segments [77]. The dynamics of SB step fluctuation has been studied between 500 K and 620 K [6,76], using variable-temperature STM. Figure 12 shows four sequential STM images taken by Kitamura et al. [6], illustrating the atomic rearrangement events that occur at 518 K. By digitizing the atomic configuration of steps in each image frame [6,76], one can extract quantitative data on step dynamics from the images. The fluctuation always proceeds via attachment and detachment of four atoms (two dimers) at a time at the ends of dimer rows (columns) [6,75,76]. In doing so, SB steps preserve the rebonded edge structure as well as the periodicity of 2 perpendicular to the step of the lower terrace [78], consistent with energetics calculations [4,79]. The average position of the steps remains constant [6,75,76]. 9.r162 !'~:
.
.
.
.
.
~
a) l
I
Figure 12. Four sequential 300 A x 300 ~, STM images of the Si(001) surface taken at 573 K showing step rearrangement events occurring between images. Each image was acquired in about 15 sec [6]. The activation energy of this fluctuation process is obtained [6,76] from the measured distribution of probability of a column changing by certain
285 number of units (two dimers per unit). Using an "independent-event" model in which each column performs a 1D random walk, an effective activation energy of 1.4-1.7 eV is derived by Kitamura [6]. However, step fluctuations exhibit significant correlations in both the nearest-neighbor column event rate and in the configuration-dependent event rate. The probability that two neighboring columns move together, either into or out of the terrace, is about a factor of 3 times the probability that neighboring columns move in opposite directions at 500 K [6]. The probability of observing an event at a kinked column is a few times higher than that at a kinkless column between 500 K and 620 K [6,76]. While the absolute rate of the fluctuations is controlled by the activation barriers, the relative rate at which the step fluctuates between step configuration states is controlled by thermodynamic detailed balance, i.e., configurational free energies. Step rearrangement events are relatively more likely to change the step configuration into one of lower free energy than into one of higher free energy. Based on the measured ratio of relative rates, an effective activation barrier difference of a few hundred meV is estimated [6,76] for events occurring at the kinked and kinkless columns, of the same order as the difference in configurational energy between kinked and kinkless columns [78,80]. Swartzentruber and Schacht [76] have incorporated the configurafional energies [78] into a potential-energy model in order to derive a more accurate effective activation barrier for step fluctuation. Numerical solution of the model produces a value of 1.3 + 0.3 eV [76], which is slightly lower than that of "independent-even" model [6]. A 1.2 eV activation barrier has been obtained from LEEM experiments [77] at temperatures between 1130 K and 1480 K, in good agreement with the STM results. The activation barrier for step fluctuation measured by STM is considered as an "effective" value [6,76] because it is an average over the various step configurations and the atomistic details of the atomic rearrangement process are unknown. Experiments [6,75,76] cannot tell where the atoms go or from where they come. The events can occur either by exchange with the 2D monomer "gas" on the terraces or through rapid long-range edge diffusion along the steps. It is also uncertain whether a fouratom unit detaches from the step all at once or whether there is a rate-limiting step whereby one or two atoms leave, after which the rest become unstable. Furore theoretical studies will be helpful to understanding the atomisfic mechanism of step fluctuations. When an external uniaxial strain is applied to the Si(001) surface, steps propagate in order to reduce the surface strain energy by changing the relative
286 populations of (2xl) and (lx2) domains [59,60]. By measuring the rate of step motion as a function of temperature, the activation energy for the step motion is determined to be 2.2 eV [60]. As for the coarsening process, the total activation energy for step motion is the sum of diffusion activation energy and the desorption energy of mobile species, if the adsorption is considered to be not activated. Assuming the mobile species is an adatom (monomer), a desorption energy of 1.5 eV is obtained, using a value of 0.67 eV for the diffusion activation energy (See section 4.3). This activation energy for desorption of an atom from a step is in good agreement with the activation energy for step fluctuations [6,76].
8.2 Dimer-Vacancy Migration Dimer vacancies, vacancy clusters, and complexes form a second class of intrinsic surface defects on Si(001), recognized since the first time the Si(001) surface was observed with STM [3]. Pandey [8] suggested from a theoretical analysis that vacancy formation on Si(001) is mediated by strain relaxation and the reduction of dangling bonds. These mechanisms are confirmed by other ab initio calculations [10,79]. The single-rimer vacancy (SDV) can have either a non-rebonded, metastable configuration or a rebonded, stable configuration. The rebonding of the exposed second-layer atoms reduces the number of dangling bonds on the surface by 2, making the formation energy of SDVs as low as -0.2-0.3 eV/dimer [10,81]. The structure of dimer vacancies has been investigated in several STM experiments [82-84]. The measured current-voltage (I-V) curve [83] appears to be consistent with the calculated electronic structure of the rebonded configuration [81]. Through an extensive ab initio calculation [81], Wang et al. showed that the dimer vacancies prefer to form vacancy clusters and complexes. Using a nonequilibrium statistical-mechanical model, they calculated the distribution of dimer vacancies, clusters and complexes, in good agreement with experimental observations [85]. Their study also ruled out the dimer interstitial model for missing dimers proposed by Ihara et al. [861. The appearance of dimer vacancies seems to be unavoidable during Si(001) surface preparation but the kinetic barriers for their creation are still unknown. Long-time anneals can increase the dimer vacancy concentration [39]. Additional or excess vacancies and vacancy clusters can be created by ion bombardment [84,87,88] or by oxygen exposure [89]; these methods are used to investigate vacancy kinetic behavior. Indirect evidence of the anisotropic diffusion of vacancies is provided by a reflection high-energy
287 electron microscopy study [89], in which the nucleation of large elongated "vacancy islands" is observed during oxygen exposure of Si(001) at temperatures above 773 K. Vacancies created by Xe sputtering are mobile at -723 K [87], as demonstrated by oscillations in the reflection high-energy electron diffraction intensity as they are created. STM studies show that excess vacancies preferentially annihilate at the ends of dimer rows if they are close to steps [88], or coalesce to form line defects perpendicular to the dimer rows on terraces [84]. These experiments have provided qualitative features of vacancy kinetics, but do not give any detail about the vacancy diffusion pathways, nor can they determine quantitatively kinetic parameters controlling the diffusion. Recently, real-time observations of vacancy diffusion on Si(001) were achieved by Kitamura through the application of a novel STM measurement method [90,91 ]. The method allows the direct measurement of the activation energy for the diffusion of SDVs on Si(001). High-temperature STM is used to observe the vacancy migration. In order to improve the time resolution of the dynamic observations, single-line scans are repeatedly taken along the same path and the time evolution of the scans is displayed in the form of a time-versus-position pseudoimage. The individual jumps of dimer vacancies, as well as their creation and annihilation, are clearly resolved with this new technique [90], which also confirms that vacancy motion is virtually restricted to occur along the dimer rows, thus following the trajectory of a onedimensional random walk. By measuring the jump rate as a function of temperature, an activation energy of 1.7 + 0.4 eV is extracted for SDV diffusion [90]. This activation energy is considerably lower than the theoretical values from two earlier calculations [81,92]. Assuming a simple lateral displacement of the surface dimer next to the single-dimer vacancy (a motion that may, however, involve complex diffusion pathways [81]), an ab initio calculation [81] estimated an activation barrier of about 2.5 eV and a calculation employing the SW potential produced an activation barrier of at least 2.2 eV [92,93]. The discrepancy between the experiment and theories is resolved by a more recent theoretical study [93], which proposed a vacancy migration mechanism involving a wavelike concerted motion of four atoms" two rebonded atoms in the second layer move up to the top layer, while two dimerized atoms in the top layer simultaneously descend into the second layer. Because there is no bond breaking involved in this migration process, the resultant activation energy, which is calculated to be about 1.4-1.6 eV [93], is not only much lower than the earlier value obtained with the same SW potential [92] but is also in very good agreement with the experimental value
288 [90]. Although this interesting vacancy diffusion mechanism has not been directly checked with an ab initio calculation, a recent ab initio calculation [51] of ad-dimer diffusion involving the similar concerted motion of four atoms does produce a kinetic barrier similar to the barrier for vacancy migration. 9. THERMODYNAMIC SURFACE M O R P H O L O G Y
PROPERTIES
AND
EQUILIBRIUM
While it is essential to understand growth kinetics to achieve controlled ftim growth, manipulating kinetic processes requires also a good understanding of the thermodynamic properties of the surface. As we discussed for step fluctuation in section 8.1, the relative rate of a kinetic process dependent on thermodynamic balances among different configurational states. By choosing properly the initial configuration of states, it is possible to alter the kinetic route for subsequent growth. For example, the growth of III-V semiconductors on vicinal Si(001) templates is largely controlled by the initial step configurations [94]. In this section, we discuss the thermodynamic properties of equilibrium surface structures and morphologies on Si(001).
9.1 Equilibrium shape of Si islands and energetics of steps It has been shown that the highly anisotropic shape of as-grown Si islands, with an aspect ratio as large as 15 to 20, is determined by growth kinetics rather than being an equilibrium property [18]. Upon annealing at --600K, the islands become more rounded, with a much smaller aspect ratio of about 2 to 3 [18]. This has also been confLrmed by two LEEM experiments in the same temperature range [72,95]. At equilibrium, the shape of islands is controlled by their boundary free energies. For Si(001), the island boundary is comprised of SA and SB steps, so the difference in these two step free energies determines the island anisotropy. At low temperature, when the entropy contribution to the free energy is small, the aspect ratio of the equilibrium island shape reflects the ratio of SA and SB step energies. The observed aspect ratio of islands of 2 to 3 at 600 K is in very good accordance with the measured step energies [78,96], once entropy has been taken into account. Swartzentruber et al. [78] have performed an STM analysis of the equilibrium distribution of steps and kinks on Si(001). For steps bounding wide terraces, the kink excitations at the individual step sites are shown to be statistically independent and each excitation obeys a simple Boltzmann distribution. From the analysis, Swartzentruber et al. derived SA and SB step
289 energies to be 0.028 eV/atom and 0.09 eV/atom, respectively. A similar analysis by Zandvliet et al., involving a somewhat more complicated model [80], gives SA and SB step energies of 0.026 eV/atom and 0.06 eV/atom, respectively. The SA and SB step energies have also been determined from LEEM measurements of island shape and step fluctuations [72,77]. The results from two different techniques (STM and LEEM) are in very good agreement [77]. As temperature increases, the entropy component of the free energy becomes dominant and the difference between SA and SB step free energies becomes smaller, leading to a more isotropic shape of islands. The LEEM images [71] show that the equilibrium aspect ratio of island decreases from 2.6 at 970 K to 1.5 at 1370 K. The higher-temperature ratio is consistent with values of 1.25 to 1.43 observed for single-atom deep sublimation holes (trenches) by reflection electron microscopy at 1200-1400 K [97,98]. This agreement is no surprise, as these trenches are also bounded by SA and SB steps. Trench structures have also been formed by STM atom manipulation, transferring atoms from the surface to the STM tip [99]. Similar to as-grown islands, the shape of trenches for this situation is kinetically limited and differs drastically from the equilibrium shape. The step edge structures in these artificial trenches are also very different from those occurring at natural steps because of geometry constraints and kinetic limitations [ 100].
9.2 Equilibrium step configurations 9.2.1 Nominal surface Step configurations on vicinal Si(001) surfaces have been a subject of intensive study, because, in practice, vicinal surfaces are used in device fabrication as the growth template, utilizing the steps to facilitate smooth growth by step flow. On vicinal Si(001) with a small miscut ( 4/3 T'~) ML) than in the commensurate phase) are formed on Ge(111), light walls (lower density) are (lxl) formed on S i ( l l l ) , reflecting the 300 smaller lattice parameter of Si. By carefully desorbing Pb from SlCmax+3D Islands 180 the fully compressed R3i phase, a ~- phase SICv ' HIC' S i ( l l l ) lxl-Pb phase was observed | at RT by STM [12] ; the topographs show protusions located in T1 site. Again this structure was interpreted (b) as resulting from a slightly compressed, 30 ~ rotated, Pb layer T("C) (lxl) located above an ideally terminated 280 substrate surface. The information obtained by Seehofer et al. [12] by LEED, RHEED and RT-STM on the SICv SICma+3D Islands 20 various dense structures of Pb on Ge(lll) and Si(lll) are i --! co co o ~ | (ML) summarized in the schematic phase diagrams shown in fig.16. :
....
. . . . .
,
, ....
_
~!tz3
.
0 P-.
Figure 16. Schematic phase diagrams of the closely packed phases of Pb on Ge(111) (a) and Si(111) (b). The HIC of Pb on Ge is metastable while the commensurate R3 phase on Si(111) was not observed ; it is only indicated in the diagram for comparison. (from ref. 12).
315
In these diagrams, the temperatures have been taken respectively from measurements by Ichikawa [13] and by Yaguchi et al. [72] and the coverages calculated from the domain walls using the structural models of fig.17. Interestingly these phase diagrams have been compared with theoretical predictions within the framework of domain-waU theory [69-71]. (a)
Co)
(c)
(d)
% % % % % %,
9 Ge top layer 9Ge second Lwer
./
!1
i If~':"/
!
I
4::~,/'~l,A
15!
0
~
i(:
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-!fi
-
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Figure 17. Schematic models for the closely packed structures of Pb on Ge(111) and Si(111). The Pb atoms are labeled with numbers while adsorption sites are labeled with small letters. The three high symmetry adsorption sites T1, "1"4and 1-13are also shown. The shift of the individual unit cells introduced by a domain wall of Pb on Ge(111) is illustrated in (b-d) : (b) on the left-hand side of the domain wall, (c) in the middle of the domain wall, and (d) on the right-hand side of the domain wall. The arrows indicate the direction of the compression and the dashed line indicates the direction of the domain wall. The high resolution STM image of the Ge(111)SIC-Pb phase shown in (e) corresponds to (b-d) as highlighted by the three R3 unit cells, assuming that the protusions are located at the positions of Pb atoms on high symmetry sites. (from ref. 12).
316 We note that by examining by STM at RT, at very low tunneling currents (50 pA), the Pb/Si(lll) IC phase, and the l x l phase, Hwang et al. [68, 73] observed images similar to those of ref.12, in particular, the local coexistence of two types of Pb trimer protusions and quasi-lxl regions. However, at variance, with the saturation coverages close to 4/3 ML, implying closepacked structural models, they determined a completion at 1ML, supported by RBS measurements [3] and thus proposed instead a structural model with two kinds of Pb tfirners, located either on H3 or T4 sites, and single Pb atoms on T1 sites (see fig. 18).
H3 @0~1
Pbadatom
o 1st layer Si atom
T1 [Tlo] [112]
Figure 18. a) 70/~ x 60/k RT STM image of the Pb/Si(111) IC phase on a surface prepared by two-stage deposition, taken at sample bias + 2.0 V and tunneling current 50 pA. Parallel lines are drawn to indicate the structure of two domain boundaries ; b) corresponding atomic model. (from ref. 71a). In this case the interpretation is that the protusions truly reflect the Pb atom positions, while Seehofer et al. on the contrary stress the fact that none of the observed patterns of protusions in their STM topograms correspond directly to the positions of the Pb atoms [63]. Here we are faced again with the question of the ideal completion of the 2D adlayer, either 1 ML or 4/3 ML. Since previous experimental determinations are in conflict we might expect gaining some help from theoretical considerations. In fact the ab initio molecular dynamics study performed for P b / G e ( l l l ) [20] retains an atomic model where the Pb atoms form chains with three atoms
317 per unit cell in OC T1 sites, whereas the fourth Pb atom is in an OC T4 position. Thus a 4/3 ML completion is favored but on the basis of a model which has gained no experimental support for germanium 9the last XSW experiments gave a preference to either the model derived by SXRD (OC T1, H3 [55]) or the model derived from a LEED study (OC T1, H3) where the Pb atoms form a bilayer [74], while the STM results of Seehofer et al. rather indicated an OC T4, H3 bilayer arrangement [8]. Indeed, in the case of Si, two types of domains centered either on 113 or T4 sites have been visualized with equal probability [12, 68, 73], but on Ge the H3 site appears undoubtedly to correspond to a lower energy. This fact rises some questions as to the validity of the 4/3 ML theoretical derivation... We would like to add a new piece of experimental work that might well start the dispute again. In a very careful experiment, we studied the growth of Pb on G e ( l l l ) at RT by ellipsometry at fixed wavelength (600 nm) and s i m u l t a n e o u s l y by Auger intensity measurements, while recording also the crystal current to ground [75]. The variations of the three independent quantities (ellipsometric angle W, Pb N00 peak to peak intensity, crystal current) measured in concert as a function of the evaporation time (the Pb flux evaporating from a temperature stabilized Kundsen cell being perfectly stable) are displayed in fig.19. PolGe(1TI} RT
Pb/Ge(1111RT ,,
tz
(b) ~
m2-
000%0oo00000 O0
.0..0.0..0~
(c)
8
=.,,
2~t- ,~e
o..
9
t)
o.
0oo0~ O0
evaporationtime (min)
oOO
I
I
I ~ ~ -
- --~- ~----'i --"
---
evaporation time (min)
Figure 19. Variations versus Pb deposition time at a constant flux of a) the ellipsometric angle 9, b) the crystal current to ground, c) the Auger intensity (Pb N00 94eV) upon growth of lead onto Ge(111) at RT. We note that W measures the changes in the optical properties of the system upon Pb adsorption, while the crystal current to ground reflects the energy and angular integrated total secondary electron yield, and the Auger intensity
318 measures the adsorbed Pb amount. The Auger intensity and crystal current variations show a behaviour which is typical of the layer plus islands growth mode (Stranski-Krastanov growth mode). The break, followed by a plateau where the curves reach their saturation level corresponds to the completion of the 2D Pb adlayer at t s - 30 minutes. Beyond ts, 3D islands start to grow. The break at ts in the W(t) curve is less pronounced than in the case of the electronic signals. This is due to the difference in information depth of the optical probe as compared to the electronic probes. The ellipsometric signal is composed of contribution from the surface as well as the bulk up to the penetretion depth of 600 nm light into the semiconductor, which is typically several tens of nanometers. The electronic probes, especially the Pb Auger signal at 94 eV kinetic energy, are sensitive only to the first few A. The impinging flux, calibrated with a quartz crystal microbalance replacing the sample at its very position, gave at ts a saturation coverage of Os = 1ML with an accuracy estimated to be 5%. However, using the same quartz crystal calibration, other groups found a saturation coverage at 4/3 ML (see e.g. ref 7). Of course this has raised some questions about the relevance of the method... Nevertheless, we note that even if we ignore the microbalance calibration, we can directly extract some relevant information from the variations of the signals themselves. Very clearly an initial rapid decrease (increase) of the crystal current (the Auger intensity) up to a time tl = 10 minutes is noticed. In between t l and ts, the current to ground (the Auger intensity) varies more slowly (rapidly) with fairly linear variations. The time ts corresponds to the completion of the R313 phase. If we assume, as most authors do, that it corresponds to 4/3 ML, then the time t l corresponds to -- 0.444 ML, a coverage which has no peculiar significance. If otherwise we assume that ts corresponds to 1 ML, then t l corresponds just to 1/3 ML, the completion of the R3tx structure. In this context the variations of the current and Auger signals are easily understood : the initial rapid (slow) variations occur during the formation of the R3ct phase, the linear variations which follow reflect the growth in 2D islands of the R313 phase, as seen in STM topographs, where domains of R3ct and R313 phases are seen to coexist beyond 1/3 ML, up to saturation (see e.g. fig.1 in paper [63]). The variations of the ellipsometric angle ~ , not only confirm this point of view but in addition reveal another break at t2 - 2 t l which indicates that a change in the optical properties takes place at about 2/3 ML, in between the completion of the R3t~ and R313 phases. This probably indicates the existence of an intermediate R3 phase completed at 2/3 ML, previously unnoticed. As a matter of fact we had pointed out in Marseille the existence of such a 2/3 ML R3 phase several years ago in the course of a comparative study of P b / S i ( l l l ) by LEED, AES isothermal thermal desorption spectroscopy
319 (ITDS) and ellipsometry [76-78]. To summarize, if the 1 ML saturation coverage determination is correct, the interpretation of the STM topographs acquired at very low current is straightforward, but the incommensurate phases remain a puzzle. In any case, a new thorough detailed SXRD study, including rod scans, is strongly needed, to clarify the situation. 4.2. T h e R313 # l x l
phase
transition
Another matter of dispute is the question of the nature of the reversible Ri/R313 # l x l phase transitions which take place at-- 300 ~ C/-- 180 ~ C on S i ( l l l ) / G e ( l l l ) . Years ago, Ichikawa, from the observation of halos of diffuse scattering in RHEED, suggested that the transition R3~ # l x l on germanium was a 2D melting transition [13]. Later, SXRD experiments by Grey et al. [14] revealed an azimuthally anisotropic ring of diffuse scattering. In a recent RHEED study Weitering et al. [79] observed also diffuse streaks on Si(111). Because of this diffuse scattering, these investigators supported the concept of 2D melting of the (assumed) close-packed Pb layers in the solid R3i~313 phases.
.:.:..
....::
9, , -
:.:.i:::?ii:
~ :., . ....:..
:. :.:!:?
....:.:::
9 ~ ~~.~.~
.:~ .-:..::,,: i:::~ ~:
,, ~
.......
..'.:..'.~ ".:~!~i:::.::.~::.'. ~'~!i!~iii~::~iiii:'::~:::::" ~i.~ .e:.'.::::N
i:iz! ~~::::i:i:~,~i.-.'.!::'.:.~:::::::~,~.".~ii::::ii~x.:.'i~~ 9 ~:':':':,~".~:-:-:-":'~"'.,~R::i':':':':" ~'~:~"::':':':':'. ~":::" :':':':':': .'.'.': .::::.~.i::.~z...````~:.~::!:::::!~!~:~::...`..`.:~:i:i:i...:.``.:::.~i:;.......!::::::~~i~i::.. ~:...',.,.: ~.:!"?'~~ :"'~ ~ ,~
9
..~ ..:.::::;.~
:!:!:~i.
:i!i:i:i Figure 20. a) 55/~ x 50/~ image of the R3~ phase of Pb/Ge(111) at RT acquired at - 0.57 V sample bias and 30 pA tunneling current ; b) 45 A x 40 A image of the high temperature lxl phase acquired at 200~ C, taken at a sample bias of- 0.4 V and tunneling current of 50 pA. (from ref.79). However a first high temperature structural study on the R313 #-- l x l transition on G e ( l l l ) by XSW gave evidence that the l x l phase was not produced by a true 2D liquid, but rather appeared to be composed of small islands of the original crystalline layer [15]. As a matter of fact the ab-initio molecular dynamics study of Ancilotto et al.
320 [20] confirmed that a strong correlation with the Ge substrate was present in the high temperature l x l phase. Recently, Hwang et al. have used a high temperature STM to examine this phase transition [79]. They could resolve both the R313 and the l x l phase below and above the transition temperature. With sharp tips they obtained consistently, at both polarities a trimer structure (which indicates that this trimer structure is not merely an electronic effect) of the R313 phase, while the tunneling images of the l x l phase taken at 200~ determined the Pb atoms to be located on T1 sites and thus the transition is order-order (see fig.20). Fluctuations associated with the phase transition (formation of instantaneous trimers and dimers in the l xl phase) have been observed, which can explain the diffuse halo seen using x-ray diffraction and RHEED. The transition is described as due to a loss of long range order of the ~/3x~/3 periodicity resulting from large lateral vibrations of the Pb adatoms single bonded to the Ge atoms in the [111] direction. Since a Pb atom can be displaced in any one the three possible directions to form a trimer with neighboring Pb atoms, this system may be related to the three state Potts model [80]. As the temperature increases the average size of an ordered patch decreases and fluctuations become faster : the lxl ordered structure seen in STM at 200 ~ C stems from the fact that on average, each Pb atom is then centered over the Ge atom underneath. In the case of the R3i ~- l x l phase transition on S i ( l l l ) , I had also argued that it is an order-orded solid transition some years ago, because of the persistence of a sharp LEED pattern and of a pronounced surface state in valence band photoemission above the transition temperature [11,43] and because the lead 5d shalow core-levels in SXPS showed practically no increase in their FWHM past the phase transition. A corresponding surface state of the R313 phase on germanium on the contrary, reversibly disappeared and reappeared past the transition upon heating and cooling again. This may reveal larger fluctuations in the Pb/Ge system than the Pb/Si one, a point which differentiates the two, otherwise similar R31]/R3i ~ l x l phase transitions and which ought to be clarified.
4.3. Equilibrium formation of 2D-adlayers The controversial debate on the 2D melting of the lead layer could have come to an end after our study of the high temperature growth of Pb on Ge(111). We could trace (by AES intensity measurements, under a controlled varying Pb impinging flux, onto heated samples at different constant temperatures) equilibrium adsorption isotherms [21], from which we could directly extract the thermodynamic properties of the 2D Pb adlayer. As seen in fig. 21, the isotherms show a sygmo~'d shape which characterizes a supercritical phase [81].
321 0 - --r..-
--tr
*--~-
-0
~-A
---B-
-o-
....
I:::: =9 0.5 LLI
v
1
10" ~
10"
,
,
,
1 .
.
10"
.
.
.
P
(~orr)
Figure 21. Equilibrium adsorption isotherms of Pb/Ge(111) at various temperatures beyond the R313 ~ lxl phase transition. The solid lines are the best fit obtained with a Fowler equation. In the temperature range studied (633-693 K) a good fit of the experimental data was obtained with the Fowler isotherm : P = K[0/1-0]exp(nV0/2kT). In this equation, P is the equivalent pressure of the impinging flux J, measured accurately by a quartz oscillator : P = J(2~mkT)~r2 (m is the mass of the lead atoms, k the Boltzman constant and T the substrate temperature) and K is the constant of the Langmuir equation: K = [fv/fad]exp(-E/kT). Here S is the lead-germanium binding energy, V the lateral pair-wise adatom-adatom interaction potential, n the coordination number and fv and fad the partition functions of the monoatomic perfect gas and of the adsorbate. The calculated isotherms, with n = 6 nearest neighors, led to the following equilibrium quantities 9a strong Pb-Ge binding energy E -- 2.0 + 0.1 eV and weak lateral attractive interactions : V -- - 0.06 + 0.006 eV. These results perfectly match with the strong correlation with the underlying Ge substrate deduced from the molecular dynamics [20] and XSW [15,42] studies mentioned above. We stress further that the supercritical state of the l x l phase agrees with the experimental observations of large spatial and temporal fluctuations in the HT STM images. The 1 ML saturation coverage, the same as that of the R313 phase, leads support to the trimer structural model [68] against the closepacked one [17]. Recently, adsorption isotherms were also measured (this time by mass
322 spectrometry) for Ag/Si(111) by MUller et al. [22]. They could determine that the ~/3x~/3-Ag structure is completed at 1 ML and that it undergoes also a transition to a surpercriticalphase at 873 + 5 K. Furthermore they showed that the formation of the ~/3x~/3-Ag phase is entropically driven. This demonstrate that 2D layers of unreactive metals on elemental semiconductor, which represent examples of rather strongly chemisorbed systems, still behave in many respects as physisorbed layers at low temperatures, (typically like rare gases adsorbed on graphite) which have given rise to a considerable amount of litterature on phase transitions and critical phenomena in two-dimensions. 5. THIN METAL FILMS Smooth thin silver and lead films (few atomic layers thick) grown on Si(ll 1) exhibit unusual quantum size effects (QSE). The growth morphology can be drastically changed by the mediation of an hydrogen intra-layer. The structure of the buried interfaces has been recently determined by x-ray diffraction, giving clues to the important issues on structural dependent Schottky barrier heights (SBHs). These different questions will be successively addressed now.
5.1. Quantum size effects in thin Ag and Pb films While QSEs in semiconductors are already used in applications, less progress has been made in metals. It is thus particularly striking to measure such effects during growth of Ag at RT, or lead at LT, on Si(lll). The quantized Ag states upon growth of Ag thin films (0-17 ML) on the Si(lll)7x7 surface were detected by angle-resolved photoemission by Wachs et al. [23]. Since any thickness distribution wider than about + 2 ML would smear out the weak features observed in the EDCs, these films states indicate a fairly smooth overgrowth confirming many previous studies on this system [82]. A perfectly laminar growth of lead films a t - 80-110 K onto Si(111) surfaces precovered with a gold monolayer (Si(ll 1)6x6-Au structure) was achieved by Jalokowski et al. [24,25]. Besides RHEED and classical resistivity oscillations with a 1 ML periodicity (here defined in terms of a dense metal plane) caused by the periodic variation of the surface roughness during monolayer by monolayer growth, they could measure QSE oscillations with a 2 ML period. This 2 ML period results from quantization of the energy band structure due to the fact that the matching condition (QSE condition) 9m~F/2 = nd0 (~,F de Broglie wave length at the Fermi level, do ML thickness, m and n integers) is fullfilled for Pb every 2 ML, with m = 3 and n = 2, since ~,F = 3.9118/~ and do = 2.8435/~ for (111) growing planes at 110 K. For such P b ( l l l ) films, Saalfrank [83], on the basis of Hartree-Fock band calculations has found oscillations of the electronic density of states (DOS) at the Fermi level EF. Measurements of the integrated photoemission intensity I
323 at photon energies hv close to the work function surely sample this DOS. Results of such measurements [24] are presented in fig. 22 a, while the slope of I(hv) within the energy range from 4.5 to 5.0 eV is compared to the theoretical data for the DOS at EF [83] in fig. 22 b. Although the experimental data rather represent the joint density of states for which the DOS at EF is only one component, the agreement of the two curves in fig.22 b is fairly nice, at least up to 4 ML. 10 Pb/Si(111)-(6x6)Au
0.4 -
~5 o
,•
DOS(E,)
Co)
", \\ ~ .,,, INTENSITYSLOPE
0.3
s
0.2
0.1
i
o
4
8
12
~8
THICKNESS (ML)
20
24
0.0
o
~
~
~
~
~
~
NUMBER OF MONOLAYERS
Figure 22. a) Integrated photoemission intensity of Pb(111) films as a function of thickness. The parameter is the photon energy hv in eV ; b) slope of the photoemission intensity vs photon energy dependence (solid line) and theoretical DOS at the Fermi level (dashed line). (from ref. 24).
5.2. Hydrogen-termination effects Although the growth Ag on Si(ll 1)7x7 at RT appears fairly smooth, still the quality of the thin film can be improved by first saturating the S i dangling bonds by atomic hydrogen, prior to Ag condensation. A comparative study of the Ag growth on the bare 7x7 surface and on the hydrogenated saturated (1.5 ML) surface displaying the so-called 67x7-H LEED pattern, both at RT and 300~ was performed by the group of K. Oura in Osaka [26,27], on the basis of impact-collision ion-scatterring spectroscopy (ICISS) with time-of-flight (TOF) detection, using 1.0-2.5 keV He + beams, together with LEED observations. Fig. 23 a, shows the variation of the ICISS Ag peak intensity versus Ag coverage for three different deposition conditions, while fig.23 b illustrates the growth models derived in this study.
324 i--i m
I,,, ~d I ~
, I He+12"5keV)
A-domain
Ag(111)/Si(111) 300"C
f
RT
4/3xCr3[layer ~ /
Ag
_
< (/) ()-
~)
-;--:-::= - " " 5 --....
10
15
20
Ag COVERAGE [ML]
,ID .a.
>" I--
J.,,~.,~.'300*C:H
,.,z I-- . . , a ~ . . ~ ; . _z _1 ,< z i~" ~0
>,
Ni 3d
Ooooe ~ : " o O%.o~~o~o~Ooo o
9
'~'.... oo ~
.c_ 6 IZl
0
a.) NiO(100) cleaved in vacuo
t-
~36-
o~ o q ~
0 2p,
rn
&
8
X
A
k~
F
3d
~ ~ O~oo eoOo~ 9 9 9
9
c-
~~176176176 o o 080
~,,,.***,,, 9 Ni
*'" " * " % ~
A
k,
O 2Px.y eelle
,..~, O 2p, X
Fig. 17: Bandstructures of cleaved NiO(100) (left panel) and NiO(100)/Ni(100) (right panel).
somewhat lower energy, which is due to defects contained in the film. The upper two non dispersing bands are due to Ni 2+ ionizations whereas the other bands which show strong dispersions have to be attributed to the 2p levels of the O z. ions. Ni 2p
Ols
.',. ,
NiO(100)
;,~~
cleaved in vacuo
~,/'"%J
9
.et'.'~.~
'.,j
;~~
uq. ,~. o co
l'-coco
~o 9 u')
v.-
Ni(100)
9
0
-t...."..
~/~
NIO(111)/ Ni(100) /
C(2x2)O/ Ni(100)
if)
0 b,.
,n:
880
dc ~
/"i A
.:"
870
860
850
....
Binding energy [eV]
Fig. 18:Ni 2p and O ls core level spectra of clean Ni(100), oxygen covered Ni(100), NiO( 100)/Ni(100), and NiO(100) cleaved in vacuo.
354
From this observation one may conclude that the Ni 2+ electronic states are localized (small dispersion) whereas the O 2-bands are delocalized (dispersion of some electron volts). This is what is expected from chemical intuition for an oxide like NiO since the charge transfer from Ni to O in the oxide leads to an occupation of spatially extended states of the oxygen ions whereas the outer valence states of the Ni ions are unoccupied in the oxide. This has certain consequences for the photoelectron spectra of the Ni 2+ ions. Due to the localized nature of the electronic states correlation effects and, in particular hole localization have to be taken into account. For NiO this leads to complicated photoionization spectra with intense shake up lines which are partly under discussion even today [43]. The satellite lines are found in the valence level region as well as in the energetic regime of the core levels [ 34, 48, 50]. As an example a set of core level spectra is shown in Fig. 18 [34]. The Clustermodel of NiO NiO(100) surface; (NiOs)8-
NiO EEL S, specular detection
Bulk NiO; (NiO6)l~
NOOH NiO( 100)/N i (100) Ep= 13eV .overtone(OH)
NO+OH covered
>., "i7I
t-"
OH covered
t-
dehydroxylated
I
NIO(100) single crystal E e = 100 eV b.)
Fig. 20: Arrangement of ions used to model NiO in the bulk (left panel) and the (100) surface (right panel).
N O covered
clean
0.0
0.5
1.0
1.5
2.0
2.5
Energy loss (eV)
Fig. 19: ELS spectra of a dehydroxylated, an OH covered and a NO+OH covered film of NiO(100) on Ni(100). At the bottom spectra of a clean and a NO covered NiO(100) single crystal surface are shown.
355 spectra shall not be discussed in detail, but it is obvious that the ones of the Ni 2p levels are more complex for NiO than for Ni which is to be attributed to the localization of the Ni 2+ electronic states in NiO. Similar to the case of the valence bands we observe a shift to higher binding energy in the core level regime of NiO(100)/Ni(100) as compared to NiO(100). However, the general structure of the spectra is the same.
3.1.2.2 Electronic excitations The study of electronic excitations with ELS turns out to be very fruitful for oxides with a sufficiently large bandgap and a partially filled valence band of the metal ions [23, 55, 56, 58, 63-66]. If these conditions are fulfilled one may detect energy losses in the region of the optical gap which are due to electronic transitions within the valence band of the metal ions. Since such transitions are optically forbidden or only weakly allowed they tend to be not very intense but, due to the resulting long lifetime their halfwidth is usually small so that even complicated systems with complicated excitation functions may be studied. The small intensity turns out to be unproblematic since the background intensity in the optical gap is very small. A set of ELS spectra of NiO(100)/Ni(100) is shown in the upper part of Fig. 19 [58]. One observes intense and sharp losses due to vibronic excitations at energies below 0.6 eV and somewhat broader features at higher energies due to electronic transitions within the 3d manifold of the Ni 2+ ions. Two of the latter losses are due to surface excitations as concluded from their sensitivity towards NO adsorption and spin resolved ELS experiments [ 55]. These losses are marked (SS) in Fig. 19. OH ions on the surface do not modify these excitations which indicates that the hydroxyl groups must be coordinated to non regular sites on the surface. The spectra of the NiO(100) crystal cleaved in vacuo look similar. However, the effect of NO adsorption is not as pronounced as in the case of the NiO(100) film. This is most likely due to an incompleteness of the NO layer which we attribute to insufficient cooling or to desorption due to the electron beam. Cooling is always a problem for massive single crystals like the one used for these experiments. The electronic surface excitations are local sensors for the electronic and geometric structure of the surface as well as for the geometry of adsorbates and their interaction with the surface since their energy depends strongly on the local surrounding. Therefore the electronic excitation spectrum of the NiO(100) surface and NiO in the bulk has been theoretically modelled using ab initio calculations. For these calculations clusters as shown in Fig. 20 have been used.
356
In order to model the electric fields correctly these clusters were surrounded by an infinite array of point charges (bulk) or a semi infinite array (surface). Additionally, calculations have been performed for a NO molecule bound to a nickel ion at the surface using a (NiO 5-NO)8 cluster with the NO molecule tilted by different angles with respect to the surface normal. Since we were only interested in the excitations of the Ni 2+ ions it was sufficient to explicitly model the first coordination shell of this ion and to replace the other ions by point charges. The results of the calculations (MC-CEPA formalism; except for (NONiOs) 8 (VCI(d))) are presented in Fig. 21 in comparison with the experimental 2.0 3E
3E
1.5
/
3E ,.,..i~ ;S - 3A2/ 3B2 ~
1.0
3E
3T
3E " /k ':~:i:;.~:i; / , .."i 3A2 382
3T1g
3T 3T2g
LU
Cr charge transfer excitation is 6.2 eV which is also the energy of the optical gap. These excitations are clearly visible in Fig. 32 at energies above the optical gap. However, there is a intense feature between 4 and 5 eV in the optical gap which might also be a charge transfer excitation as indicated by its intensity and peak form. ELS spectra of adsorbate covered chromium oxide surfaces clearly show that this feature is a surface transition [ 64, 70]. Therefore one may infer that this feature is due to a charge transfer excitation occuring at the surface of the oxide which would mean that the optical gap at the surface is smaller than that in the bulk. This excitation has also been treated theoretically in ref. [ 72] using the CASSCF formalism. It could be shown that the energy of the first charge transfer excitation at the surface should be, depending on the nature of the state, between 3.22 and 4.5 eV. As this state would be one in the low energy onset of the loss peak this result fits well to the experimental data thereby pointing towards a reduced width of the optical gap at the surface.
3.3 AI203(lll)/NiAI(110) A thin film of A1203 may be formed on NiAI(110) by thermal oxidation [ 11, 79-93]. This is achieved by annealing in 2.5"10 6 mbar of oxygen at T=500 K for 10 minutes with subsequent flashing to 1100 K. As revealed by Auger data the film thickness is only about 5 A [92]. A valence photoelectron spectrum of the oxide is presented in Fig. 29 in comparison with spectra of NiO(100) and NiAI(110) [ 11 ]. The spectrum of the oxide is dominated by the intense emission of the O2p levels. Besides this only a weak emission near to the Fermi edge shows up which may be attributed to emission from the substrate as revealed by a comparison with the spectrum at the bottom. The emission of Ni 2+ ions is located in the binding energy range from 1 eV to 3 eV (see spectrum at the top). In the spectrum of the oxide film on NiAI(110) no emission is found in this energy range which could be
365
Tan=1200K
8~,o 1I
~600
Al. o
,67o
9o9 1,000
"~2 "a %
658 ,
0
0
500
1000 1500 Energy loss [crn "1]
2000
I
J ,
0
400
,
500
,
i
1000 1500 Energy Loss [crn"~]
2000
Fig. 31: Left panel: HREELS spectrum of A1203/NiAl(110). Right panel: calculated HREELS spectrum of y-A1203/NiAI(110). attributed to Ni 2+ ions so that one may conclude that the oxide film grown on NiAI(110) consists of aluminum oxide. This result is not too surprising since the formation of aluminum oxide is thermodynamically favorable due to its much higher energy of formation. A similar conclusion may be drawn from the data shown in Fig. 30. A comparison of the HREELS spectra shows that the oxide formed on NiAI(110) is not NiO(100) nor c~-A1203(0001). However, the spectrum of the oxide film is rather similar to that of oxidized aluminum. More detailed information may be derived from Fig. 31 where a HREELS spectrum of A1203/NiAI(110) is compared to a spectrum calculated for y-A1203/NiAI(ll0) using dielectric theory. The similarity is striking which means that the structure of the oxide film is at least
~r
,i
9
r
-lip
m-
Fig. 34" Left panel: photograph of a LEED pattem of AlzO3/NiAI(110). Right panel" SPALEED pattern of ~/-A1203 on NiAI(110). The Brillouin zone of the substrate and those of the two domains of the oxide are indicated. Due to aberrations of the SPA-LEED systems the Brillouin zone of the oxide appears is somewhat distorted.
366 near to that of 7-A1203. There are some differences between the energetic positions of the losses which is mainly due to the fact that the oxide film was prepared using ~SO2instead of ~602. At this point details of the structure still have to discussed. One hint towards this topic comes from the LEED pattern of the film as shown in Fig. 34. The pattern of the oxide exhibits numerous sharp reflexes. As may be seen from Fig. 34 the Brillouin zone of the film is small and approximately rectangular. Two domains of the oxide which are rotated with respect to each other contribute to the LEED pattern. The unit cell as calculated from the LEED pattern has a size of 10.6 A x 17.9 A and is commensurate with the substrate only along [001 ]. In the photograph of the LEED pattern (Fig. 34 left panel) the distribution of intensities of the LEED spots resembles a hexagonal pattern. This is a first sign that the base structure of the oxide is hexagonal. However, the lattice structure
a~
bl
NiAI(110)
a 4.1'
AI203 domain A / ~ .
.....
a~
10,6A ~ ~ ~ ' * ~ 7
.9A
.17A-1
[110]
T
b'~
domainAI203B ~" 0"350 " A'I
Fig. 35: Schematic diagram exhibiting the Bri]]ouin zones and unit cells of A]zO3/NiA](]00)
and NiAI(I l 0). must be somewhat distorted since otherwise one would observe a purely hexagonal pattern for the oxide film instead of the numerous reflexes. In order to elucidate the structure of the oxide film further studies with electron microscopy have been undertaken [ 93]. For these studies a crystal with a conical hole as depicted in Fig. 36 has been used. This sample allowed to investigate the supported oxide film as well as unsupported oxide near to the boundary of the hole in the crystal surface. Thicker layers on NiA1 with different structure have been studied by Rfihle and Coworkers [ 94]. Before oxidation the hole was drilled into the sample in a system that contained a strong ion gun. The sample was oxidized in a standard UHV chamber where the quality of the oxide film could be judged with LEED. From there the sample was transferred into the electron microscope which was operated at pressures in the 10 v mbar range. During these transfers the sample
367 had contact with air. However, the oxide film survived the transfers as will be discussed in the following. Two electron micrographs are shown in Fig. 37; one of the supported oxide and another one of the unsupported film. The micrograph of the unsupported film exhibits several line patterns which are due to planes in the oxide lattice. In table 2 the experimentally determined periods of the line patterns are compared Cut through a NiAI(11 O) sample used for studies with electron microscopy A1203film
Conical hole drilled with an ion beam
Fig. 36: Schematic diagram of a cut through a NiAI(110) single crystal with oxide film used for the experiments with electron microscopy.
Fig. 37:Left panel: electron micrograph of unsupported A1203 grown on NiAI(ll0) (33.6x22.0 nm) In the upper right part of the image aluminium oxide with NiAI(110) support is visible. Right panel (bottom): electron micrograph of supported A1203/NiAI(110) (84.8x83.5 nm). Right panel (top): section of the micrograph below. (21.9x 17.3 nm) to distances in the lattice of A1203/NiAI(110) as calculated from the LEED pattern in Fig. 34. This comparison strongly indicates that the structure of the unsupported oxide film is the same than that of the supported film. The same conclusion may be drawn from a fourier transform of part of electron
368
LEED reflex (1,7) m
(0,5) (1,3) (2,2)
Distances in A1203/NiAI(110) as calculated from the LEED pattem in Fig, 34 [A] 2.49 3.57 5.24 4.59
Distances between lines in the electron micrograph [ A ] 2.45 3.59 5.28 4.57
Table 2: Comparison of lattice spacings in 7-A1203 with line spacings in the electron micrograph of the unsupported aluminum oxide film. micrograph (see Fig. 38) as shown in Fig. 37 (left panel) which compares well to the reciprocal space pattern of the oxide film. The observation that the unsupported film has the same structure than the supported one is interesting by itself. A structure like that of A1 203/NiAI(110) is unique among the numerous modifications of aluminum oxide indicating that the structure of the film is stabilized by the substrate-oxide interaction. Therefore one would expect that the film changes its structure upon removal of the substrate. This is obviously not the case, so that one is led to the conclusion that the structural transformation of the oxide structure into a more stable one is thermodynamically hindered. In the micrograph of the supported film (Fig. 37, fight panel) the lines due to the lattice of the oxide are not observed although the lattice of the substrate is well resolved (top of the fight hand side of Fig. 37) However, one observes
Fig. 38: Fourier transform of part of the electron micrograph shown in Fig. 37 (left panel). The assignment of two maxima to LEED reflexes of A1203/NiAI(110) is given in the figure.
369
'~. ~ ~
[0Ol] ~ ~
~,:~,
:~
~,~
Fig. 39: STM image of A1203/NiAI(ll0). Fig. 40: STM image of A1203/NiAI(110). CCT, 4 V, 0.5 nA, ~300x300 A2. CCT,- 1 V, 1.5 nA, ~90x90 A 2. broad lines in the micrograph which are oriented in different directions (bottom of the fight hand side of Fig. 37). These lines are not due to the lattice of the oxide or the substrate but to both of them. They result from electrons which are scattered first by the substrate and then by the oxide film so that the wave vector change of these electrons corresponds to the sum of a substrate and an oxide lattice vector. When the lengths of the vectors are similar and when they are oriented in nearly opposite directions then the sum of these vectors may be small which corresponds to a large period in real space. This is what is observed in the micrograph of the supported oxide. The experimentally observed lines may be traced back to sums of k-vectors ofNiAl(110) and the oxide film. The directions of the lines are indicated in the fight hand side of Fig. 37 (bottom). One finds two types of line systems; i.e. one with a larger spacing (marked with thick black lines) and another one with a smaller spacing (marked with thin black lines). Whereas the first system is due to a (2,0) type beam of the NiAI(110) substrate which is subsequently scattering by the oxide layer the other one is due to a (1,1) type reflex of the substrate, also with subsequent scattering by the oxide. As expected from the symmetry of the system, the [1 10] and [001] directions of the substrate act as mirrors lines for the line patterns in that for every line pattern another one is found with a mirrorlike direction. It was not possible yet to achieve atomic resolution in STM pictures of this oxide. This is at least partly due to the electronic structure of aluminum oxide. Since the bandgap of aluminum oxide is large, voltages of several electron have to be applied to extract electrons from or to put electrons into the oxide. This
370
Fig. 41: STM image of A1203/NiAI(110). Fig. 42: STM image of A1203/NiAI(110). CCT, -8 V, 0.5 nA, ~2400x2400 A2. CCT, 4 V, 0.5 nA, ~500x500 A2. corresponds to large tip-surface distances and therefore to a decreased resolution. In Fig. 39 a STM scan taken with a voltage of 4 eV is shown which exhibits a boundary between two oxide domains [ 83]. At this voltage the oxide seems to be already visible since the oxide unit cells are readily observable (denoted A and B). At low tunneling voltage (1 V) the STM pattern looks different (Fig. 40). Since the oxide has no electronic levels at 1 eV or below the visible structures must be due to the substrate. In this context Fig. 40 shows the first layer of the substrate below the oxide with atomic resolution. A more detailed evaluation of the scan shows that the structure of this layer is distorted due to the interaction with the oxide film. The structure of the oxide film on a larger scale is depicted in Fig. 41. In this figure antiphase domain boundaries between oxide islands are visible as white lines. Fig. 42 depicts these domains on a larger scale. The reasons for these domains is most likely stress within the oxide film which breaks it into anntiphase domains with an approximate size of 120 A along [1-10]. The domain structure can also be observed with SPA-LEED where a splitting of some of the oxide reflexes is observed [ 83]. 4. SUMMARY In this chapter we have reviewed the properties of some oxide films focusing on preparation, structure and electronic properties. We have shown that the study of oxidic film may be an alternative to single crystal oxides, especially
371 when electron spectroscopic investigations are concerned. One main topic was the stabilization of polar surfaces which has been discussed for Cr203(0001)/Cr(110) and NiO(111)/Ni(111) where different stabilization mechanism, including reconstruction and stabilization by a charged adsorbate layer occur. Also, structural investigations using different methods have been discussed for several oxide films. Another topic was the electronic structure of the films with a strong focus on electronic excitations within the valence band of the metal ions. We have shown that these excitations may serve as sensors for the local environment of the ions thereby giving access to informations like the site of the metal ions and their interaction with adsorbates.
ACKNOWLEDGEMENTS We are grateful to the large number of coworkers who contributed to the results presented here and to the funding institutions which made our work possible. Specifically we name the Deutsche Forschungsgemeinschaft (DFG), the Bundesministerium ~ r Bildung und Forschung (BMBF), the Fonds der Chemischen Industrie (FCI) as well as the European Community (EC). REFERENCES
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
375
Chapter 10 Chemical and spectroscopic studies of ultrathin oxide films S.C. Street and D.W. Goodman Department of Chemistry, Texas A&M University, College Station, TX 77843, USA
1. INTRODUCTION The surfaces of metal oxides are of obvious importance not only as chemically active catalysts or catalyst supports but also as chemical sensors, corrosion inhibitors, ceramics, and electronic and dielectric materials. The high melting points, low density, hardness, and selective chemical resistivity of metal oxides are well-suited to a range of technological applications. Nevertheless, in spite of years of study our knowledge of important surface characteristics on the atomic scale is still lacking [1 ]. In part this deficiency arises because the surfaces of metal oxides are complex in terms of physical and electronic structure, composition, oxidation states, etc. Furthermore, there are the problems related to the of characterization of surface rather than bulk properties. One way to circumvent these problems is the use of surface science techniques employing surface sensitive charge particle probes under the requisite ultra-high vacuum (UHV) conditions. The number of such modem spectroscopies and the information they can provide is impressive [2,3]: however, application of these tools to understanding the chemical reactivity of well-characterized oxide surfaces is limited [4,5]. This approach to studying oxide surfaces has a particularly difficult set of problems in that many of the metal oxides are wide bandgap semiconductors or insulators with poor electronic and thermal conductivities. The use of electron- or ion-based spectroscopies induces a charging problem limiting the effectiveness of these probes on bulk (or even powder) oxide surfaces. A related problem is the imaging of oxide surfaces with scanning tunneling microscopy (STM) since this requires the flow of current between the probe tip and a conducting medium. The thermal conductivity problem involves difficulties with inhomogeneous sample heating and cooling, and the inability to control heating rates as needed for temperature programmed desorption (TPD) studies.
376 A way around these problems is the heteroepitaxial growth of ultrathin oxide films on refractory metal substrates chosen to limit lattice mismatch with the oxide overlayer. The oxide films are formed by depositing the metal from a hot-filament or other suitable source onto the clean substrate in the presence of "high" oxygen pressures (-- lx10-6). The layers range from less than a monolayer to a few tens of monolayers thick (< 100 A). The results of extensive characterization have demonstrated that the ultrathin films have bulk-terminated-like surfaces. This method has been used to prepare highly ordered films of NiO, MgO, A1203, TiO2, and SiO2 for surface science studies of electronic and physical structures and the adsorption properties of probe molecules such as CO, alcohols, and acids, as well as supported metal particles. The so-called "pressure gap" has been bridged by kinetic measurements at elevated pressures (up to 100 Torr) coupled with in-situ reflectance IR measurements. Certain case studies are given below. Other methods to grow epitaxial oxide films, e.g. the controlled oxidation of single crystal metal surfaces, have been excluded from the scope of this chapter. 2. MAGNESIUM OXIDE MgO has the simplest of oxide structures, rocksalt, with a bulk structure that consists of layers with equal numbers of Mg 2§ cations and 02. anions. The ions are arranged in a lattice of two intersecting face-centered cubes such that each cation is surrounded by six anions in an octahedral array, and vice versa. The optical bulk bandgap is 7.8 eV. Mineral MgO (periclase) cleaves easily to expose the cubic (100) face, which is by far the most stable [1 ]. Low-energy electron diffraction (LEED) dynamical studies have shown that the (100) surface has essentially the truncated bulk crystal structure with very little relaxation or rumpling [6,7]. MgO is a basic catalyst active for the H2/D 2 exchange reaction [8], the dehydration of formic acid and methanol [9], and isomerization of alkenes. Li-doped MgO catalysts are reported to promote the oxidative coupling of methane to ethane and ethylene [10].
2.1 Synthesis and characterisation of MgO(100) ultrathin films Ultrathin films of varying thicknesses and one-to-one stoichiometry have been prepared on the Mo(100) surface [11-14]. The oxide films were synthesized by exposure of the clean (lxl) Mo(100) substrate to evaporated Mg in a background pressure of oxygen. The Mg source was a high-purity Mg ribbon tightly wrapped around a tungsten filament and degassed extensively prior to use. The flux of Mg was calibrated by line-of-sight mass spectrometry during Mg
377 (metal) deposition and subsequent thermal desorption of Mg from the metal substrate. The growth of the MgO film has been followed by X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) as a function of the background oxygen pressure. Analysis of MgO synthesized at pressures below l xl 0 .7 Torr oxygen showed the presence of the Mg ~ (L23VV) Auger transition at 44.0 eV in AES and the Mg(2p) XPS peak at 49.6 eV indicative of metallic Mg (no suboxide Mg § features). This is confirmed by the lower temperature (< 1000 K) features in TPD which indicate metallic Mg desorpfion. MgO synthesized at lxl 0.7 oxygen pressure or above showed only the Mg 2§features in Auger (at 32.0 eV) and XPS (50.8 eV) spectra, and no metallic Mg desorpfion features in the TPD spectra. The epitaxial growth of MgO was also monitored by LEED in the temperature range 200-600 K under the optimum oxidation conditions. The results showed that MgO(100) formed in layered planes parallel to the Mo(100) substrate with similar square (lxl) spots, evidence of long-range order, across the temperature range (see Fig. 1). Neither subsequent annealing nor growth in pressures higher than l xl 0 .7 Ton: oxygen visibly improved the LEED patterns. High resolution electron energy loss spectra (HREELS) of the phonon mode fundamental and overtones were characteristic of single-crystal MgO [15]. Along with the AES and LEED pattern data this confirmed the one-to-one stoichiometry of the overlayer with the substrate, in spite of the 5.4% lattice mismatch between MgO(100) and Mo(100). Figure 1. A ball model of epitaxial MgO overlayers grown on Mo(100). [On..
i Mo
102. Mg 2"
378
2.1.1 Adsorption of CO on MgO (100) ultrathin films Ab initio method theoretical calculations predict that CO should bind to a defect-free MgO(100) surface molecularly on top of or near Mg 2+ sites, with the molecular axis perpendicular to the surface plane [16]. The calculated binding energy difference between bonding through the O or C atom is small, but the Mg z+CO configuration is slightly preferred with a binding energy of-- 9 kcal/mol. The calculations predict a small charge transfer (0.007 e-) between CO and the surface, involving transfer of electrons from the CO 50 orbitals to the oxide surface. Experimentally, while IR spectroscopy has identified CO adsorbed on MgO powder [17], no CO adsorption has been found on stoichiometric Mg(100) surfaces at room temperature. He et. al have studied the adsorption of CO on 7 ML MgO(100) using XPS, TPD, and infrared reflection adsorption spectroscopy (IRAS) [18,19]. The IRAS spectra obtained upon exposure of CO in UHV (low coverage) exhibit a CO stretch frequency at 2178 cm -1, which is a 35 cm -1 blue-shift with respect to the gas phase absorption (2143 cm-1). This is in contrast to the red-shift commonly observed with CO adsorbed on transition metals where n* backdonation from the metal to the adsorbed CO weakens the C-O bond. The forward donation from the slightly antibonding 50 orbital of CO to the oxide strengthens the C-O bond leading to the observed blue-shift and indicating charge transfer as predicted by calculations. This explanation is further supported by XPS measurements which show a 0.4 eV shift in both Mg(2p) and O(ls) core levels of the MgO(100) film to lower binding energies upon CO adsorption. As the CO coverage increases with ambient background CO pressure (up to 5xl 0 .6 Torr) the CO stretch frequency red-shifts back towards the gas phase value. This arises from lateral electrostatic interactions whereby an increase in the number of electron donors results in decreased charge donation from each CO molecule. Isothermal adsorption measurements indicate a heat of adsorption for CO of 9.9 kcal/mol. TPD spectra exhibit a CO desorption peak temperature at 180 K (7 K/s heating rate) corresponding to a desorption activation energy of 10.6 kcal/mol-- both experimental measures of the binding energy of CO to MgO(100) agree well with the theoretical result of-- 9 kcal/mol related above. 2.1.2 Acid~base and Li-doped properties of MgO(lO0) ultrathin films The catalytic activity of MgO powders is linked to their acid/base properties. Surface spectroscopic studies have had only limited success investigating these
379 properties, however. For instance, the thermal decomposition of alcohols to alkenes and water via surface alkoxides has been found to occur on MgO powders [20], but was not observed on single-crystal MgO [21] or on MgO thin films [22]. The reason for this chemical difference among forms of MgO may relate to the heterogeneity of the surface sites. The active sites have been ascribed to surface Mg-O pairs which have varying coordination numbers: sites with lower coordination show greater basicity and react with increasingly weaker acids. The interaction of BrCnsted acids adsorbed on well-defined ultrathin MgO(100) films has been investigated by Wu, et. al, using HREELS and TPD [13,23,24]. The acidity of the adsorbates used decreased in the order: carboxylic acid, methanol and water, alkenes, alkanes. HREELS results were interpreted to indicate the formation of hydroxyl groups from the acids, methanol, and water. Hydroxyl v(OH) stretching modes were observed with higher frequencies than the v(OH) modes of multilayers of the hydrogen bonded parent molecule. This indicated dissociative adsorption of at least some fraction of the molecules and the formation of bound methoxy in the case of methanol. The hydroxyl features were not thermally stable, however, and largely disappeared by ~ 400 K. TPD showed only recombinative desorption of the parent molecules, with no dehydration or HREELS CHaOH/MgO(100)/Mo(100)
x2oo v \ .
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WAVENUMBER (cm "t)
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i 4000
Figure 2. HREELS spectra of methanol adsorbed on a -- 30 ML MgO(100) film at 90 K. (a) 180 L CH3OH at 90 K; (b) flash to 160 K; (c) flash to 273 K; (d) flash to 498 K; (e) 5 L CH3OH at 90 K. Spectra collected at Eo ~ 46 eV and a 8.5~off-specular reflected beam direction.
380 decomposition. The recombinative desorption was complete below -- 400 K. Thus it is not clear that HREELS is actually identifying independent hydroxyl groups at the surface, even for formic and acetic acid which should dissociate, since the TPD spectl:a indicate no dehydration products. Recent IRAS studies of water on MgO [25] found no evidence for hydroxyl groups, and concurrent TPD spectra showed complete molecular desorption below room temperature. Nevertheless, the sensitivity of HREELS is such that it is possible that hydroxyl groups are formed at the very small minority of defect sites present on the MgO(100) ultrathin film as synthesized. Defect sites, particularly point defects, are very likely related to the activity of the MgO(100) surface to ethane. Ethane (C2H6) and ethylene (C2H4)adsorb associatively and desorb molecularly a b o v e - 400 K. No v(OH) features were observed [24] in the HREELS spectra. However, upon annealing to 1300 K the adsorption of ethane (but not ethylene) led to a v(OH) feature in the HREELS spectra which was stable up to 600 K. The annealed MgO(100) surfaces also exhibited a new feature in the band gap region as monitored by energy loss spectroscopy (ELS). This feature, centered around 0.9 eV, has been attributed to surface defect states [26] with lower coordination numbers. These sites are apparently capable of dissociating ethane. The defect centers (color centers) generated thermally and by Li doping of MgO(100) have been investigated using ELS and kinetic measurements at elevated 6OO
.io
I
~" 360
Figure 3. ELS spectra of Li/MgO/Mo(100). (a) pure MgO(100); (b-d) Li-doped MgO(100) with increasing annealing temperature.
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HREELS Li/MgO/Mo(100)
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, .x,,oo.ff
Z
, 200 K [43]. Based on the HREELS data a monodentate bonding configuration for formate is proposed with bonding through the oxygen atom to a Ni cation site. Upon fimher heating formic acid desorbs from the surface between 300-400 K by recombination of formate with surface hydrogen. Further study found a minor dehydrogenation/dehydration pathway for formic acid decomposition on Ni(100) [53]. This chemistry is similar to that found for adsorption of carboxylic acid on MgO(100) (Sect. 2.2.3), with the exception of the temperature dependence of O-H bond breaking. It appears that the NiO is basic enough to accommodate proton donation from moderately strong acids, but neither NiO(100) nor the MgO(100) is highly active for formate decomposition in competition with the recombination and desorption of the parent molecules under UHV conditions.
3.2 Synthesis and characterisation of NiO(lll) ultrathin films NiO(111 ) ultrathin films are prepared on the Mo(110) surface in much the same way NiO(100) surfaces are prepared on Mo(100) (Sect. 3.2.1 ). Films -~ 30 ML thick are stable up to 850 K. By 950 K AES spectra begin to show Mo signal and weaker NiO features indicating interdiffusion of the substrate metal with the oxide. An interfacial reaction leading to the oxidation of Mo to MOOx and reduction of NiO to Ni metal is assumed since no desorption occurs in this temperature range. The NiO(111) films were characterized using AES, LEED, and HREELS [39]. The LEED patterns show that the quasi-hexagonal pattern of Mo(110) is replaced by a regular hexagonal (lxl) pattern upon growth of the NiO film. The relative sharpness of the pattern indicates well-defined, epitaxial growth of Ni(111). The LEED spots are elliptical rather than circular, possibly a result of the 8% lattice mismatch between NiO(100) and Mo(110). Auger spectra of the NiO(111 ) ultrathin film are essentially identical to that reported for single crystal Ni(100) [47], and the Auger Ni(LMM)/O(KLL) ratio is consistent with epitaxial growth. The ELS spectra of the electronic transitions region of NiO(111) show a sharp feature at 0.46 eV which disappears upon heating to 850 K. This is assigned to O-H stretching from hydroxyl groups present on the surface upon formation of the film, in agreement with other ELS results for the hydroxylated NiO(111 ) surface [54]. Of the other features observed in the ELS spectrum, peaks at 0.60 eV and 1.63 eV are assigned to surfaces states in accordance with other experimental and theoretical results [55]. They arise from reduced coordination number and hence symmetry of the crystal field at the surface, and are described as modified d-d
388 transitions. The HREELS spectra of the vibrational structure show losses (and a gain) indicative of single crystal NiO [56].
3.2.1 Adsorption on NiO(lll) ultrathin films The adsorption of CO [53] and formic acid [39,53] on NiO(111) has been studied by TPD on HREELS. The electrostatic nature of the CO/NiO interaction seems to dominate bonding on the polar (111) surface. Both the low coverage blueshift of the v(CO) mode measured by HREELS and the heat of adsorption measured by TPD are greater for CO adsorption on NiO(111) than on NiO(100). These observations are consistent with the interaction of CO with a stronger electric field at the polar NiO(111) surface than the corresponding field above NiO(100), even for a relaxed or reconstructed face [34]. There are marked differences in the reactivity of adsorbed formic acid on NiO(111) and NiO(100) (Sect. 3.2.3). The breaking of the O-H bond and formation of formate on NiO(100) occurred above -- 200 K, but on NiO(111) formic acid adsorbs dissociatively at 100 K. Desorption of formate from NiO(100) is almost completely by recombination to formic acid. But on NiO(111) the desorption pathway is through decomposition, with a branching ratio between dehydrogenation
_
--•.X
NiO(100)
NiO(111 )
I0
555 K
~ r
r
4.1
c 1/)
200
400
200 600 Temperature (K)
400
600
Figure 8. TPD spectra following adsorption of a saturation coverage of formic acid on the NiO(111) and NiO(100) surfaces.
389 and dehydration near unity [39] indicating very similar energies for C-H and C-O bond breaking. Furthermore the reaction temperature for these decomposition pathways is lower on NiO(111 ) than the minority decomposition route on NiO(100) (Fig. 8). [It should be noted vis Sect. 2.3.2 that the NiO(111) films were completely dehydroxylated by annealing to 850 K]. These differences in reactivity are attributed to enhanced activity of the polar NiO(111 ) for surface-stabilizing products and the presence of neighboring Ni 2+reaction sites on Ni(111 ) not available on the Ni(100) surface. 4. ALUMINA Alumina, one of the most technologically useful metal oxides, finds applications in ceramics, catalyst supports, and electronics. Like MgO, A1203 is an insulator that cannot be made to conduct by doping. Bulk alumina has a bandgap of-- 9.5 eV. A1203 occurs naturally as the mineral corundum, 0c-A1203, which has the most thermodynamically stable structure over a wide temperature range. It has a rhombohedral crystal structure with a hcp array of oxygen ions with aluminum ions ordered in one-third of the interstices [57]. The non-cleavage, reduced symmetry (0001) surface of corundum is non-polar, but its cations are coordinated to only three oxygen anions which is half the bulk coordination number, and thus the surface is almost certain to reconstruct in some way [1]. Qualitative LEED studies have shown that below -- 1300 K the most stable pattern is (lxl). The catalytically more interesting alumina y-A1203 is the activated alumina formed by dehydration of the minerals boehmite (y-A10(OH)) or gibbsite (yAI(OH3) ). It is less compact than ~-A1203, having a defect spinel-type structure with a fcc array of oxygen ions and random distribution of cations at -- 90% of the available octahedral and tetrahedral sites [57]. Conversion of bulk y-A1203 to czA1203 is irreversible upon heating in air to above -- 1300 K (AHtran s -20 kJ/mol [57]). The surface of y-A1203 has not been characterized, so the only speculation as to its structure is based on bulk termination of the cubic spinel.
4.1 Synthesis and characterisation of AI203 ultrathin films Highly ordered ultrathin films of A1203have been grown heteroepitaxially on Ta(110) [58] and Mo(110) [59] and studied by AES, LEED, HREELS, and ISS. The LEED and AES results show formation of epitaxial A1203 films with long-range order and a slightly distorted hexagonal lattice characteristic of close-packed O zplanes. There was no indication of metallic A1 after high temperature oxygen
390 annealing. Initial film growth was found to be essentially two-dimensional. In this initial growth regime lattice and symmetry mismatch with the bcc Ta and Mo substrates leads to a strain relief mechanism evidenced by a superstructure of complex diffraction patterns in LEED [58,60]. These are most likely due to formation of domain walls and/or misfit dislocations which govern the strain relief and might control film growth mode. Film growth a b o v e - 15 A leaves only the hexagonal overlayer spots with increasing background intensity in LEED, indicating three-dimensional film growth. The LEED structures reveal only the ordering of the 0 2. anions; there is no evidence regarding ordering of the A13+cations. Since both bulk forms of alumina-the cubic spinel y-Al203 and rhombohedral 0c-A1203-- have close-packed O 2- planes (they differ in the stacking sequence of the oxygen planes: ABCABC for y-A1203, and ABAB for t~-A1203) definitive surface structure determination in terms of the bulk structures cannot be made from the LEED data alone. The observed hexagonal pattern can be interpreted as arising from either the (111) face of y-Al203 or the (0001) face of ct-A1203. Chemically, the as-synthesized alumina film is inert to a variety of probe molecules indicating the absence of dangling or unsaturated surface bonds.
4.2 Interaction of benzene with AL203 and MgO ultrathin films The adsorption and electronic structure of benzene (C6H6) on the thin film MgO(100)/Mo(100) and AIzO3]Mo(110) substrates were studied using TPD and HREELS [61]. Three desorption states were found for both surfaces. The first corresponds to adsorption of the ring plane parallel to the surface at low coverages (_ 1 ML) give rise to a desorption at a slightly lower temperature, corresponding to the metastable, uptight (end-on) adsorption of benzene on the monolayer covered surface. Large exposures of benzene yield the multilayer with an anomalous higher temperature desorption sequence in the TPD. Both surfaces reveal spectroscopic windows by ELS between the phonon modes and optical band gap transitions which allow identification of benzene electronic and vibronic transitions. This window is between 2.5 eV and 5.5 eV in MgO/Mo(100) and 2.5 eV and 6.7 eV in AlzO3]Mo(110). The low temperatures of these desorption states for both substrates (150-175 K) indicated weak interaction between benzene and the thin metal oxide films (AH~ds = -10-12 kcal/mol). The TPD results were similar to the results for benzene desorption from noble metals [62,63], which also found only weakly adsorbed benzene with similar multilayer desorption temperatures and behavior as a function of coverage. The differences are in the temperature of desorption of the low
391 coverage (-- 1 ML) state, indicating stronger interaction of the benzene g-system with the metal d- orbitals than with the metal oxides. The electronic spectra of benzene adsorbed on alumina and magnesia show the allowed transition from the ground state to 1Elu as well as the weaker "forbidden" transitions to 3Blu, 1B2u,and 1Blu, present because of symmetry breaking interactions with molecular vibrations. Approaching multilayer coverages the vibronic fine structure bands with 110 meV spacing are observed. The energies of the observed transitions are only slightly less than their counterparts for benzene in the gas phase, which indicates a weak interaction between the molecular n-system and the oxide substrate, in accord with the TPD results. These results differ from the ELS spectra of benzene on Ag(111) [63], where it was found that interaction with the metal d-orbitals shifted the benzene n-g* transitions to slightly higher energies. The transitions on metals surfaces were also significantly broader, with no observable fine vibronic structure, indicating short excited lifetimes and a stronger interaction than found for the weakly interacting magnesia and alumina surfaces. The observation of the vibronic fine structure of benzene at monolayer coverage on the metal oxides supports the conclusion of Freund and co-workers [64], working on the CO/alumina system, as to the shorter lifetimes of electronically excited states of molecules on oxide versus metal surfaces.
IB1,~ IElu 3
1
C
=i
b
4.75
I
.~"
I
....
| .... 2
, ....
! .... 4
, ....
| .... 6
Energy Loss
, ....
(eV)
! .... 8
,
Energy Loss
(eV)
Figure 9. ELS spectra of benzene on AI203[Mo(110). Left: clean A1203 (a) and benzene adsorbed at 90 K, up to slightly more than 1 ML (c). Right: -1 ML benzene on AlzO3 surface showing the vibronic fine structure. Both spectra Eo = 25 eV, - 20 meV resolution
392
5. LAYERED AND MIXED OXIDE ULTRATHIN FILMS There is current interest in various disciplines of physics and chemistry in the thin films of mixed and layered oxides. The influence of one oxide on the structural or electronic properties of another or the interface between two oxides may lead to significant alterations of their individual characteristics, perhaps leading to novel catalytic activity, for instance. Layered oxide films can also be models for naturally occumng materials such as silicate clays. These are composed of layered sheets of oxides and are of great importance in soil science [65]. Having shown that ultrathin films of single component metal oxides can be studied to advantage, this work has been extended to layered mixed oxides.
5.1 The MgO/NiO mixed oxide system The epitaxial growth of MgO on NiO(100) [66,67] and NiO on MgO(100) [67] have been studied using LEED, AES, ELS, and ISS. The initial, substrate layer oxides were prepared on a Mo(100) single crystal as described in the Sections above. (lxl) square LEED patterns were obtained for both the NiO on MgO(100) and MgO on NiO(100) films grown up to -- 30 ML thick. Indeed, the close lattice match between these rocksalt oxides is such that the LEED patterns of the layered NiO/MgO oxides (regardless of order) are of higher quality than the corresponding oxide prepared directly on the Mo(100) metal surface. [Lattice constants: NiO(100), 2.947 A; MgO(100), 2.978 A; Mo(100), 3.147 A]. Relative ISS intensifies from spectra taken as a function of overlayer coverage indicate that NiO on MgO and MgO on NiO behave identically, with overlayer coverage of 1 equivalent monolayer masking -- 90% of the underlayer, and essentially complete masking of the substrate layer by 2 equivalent ML. TPD spectra using NO as a probe molecule give the same results. The well-resolved desorption features corresponding to NO on MgO ( Tp = 120 K) and NiO (Tp = 200 K) provide a straightforward method for titrating the exposed sites. ISS and NO-TPD interrogation of the interfacial and thermal stability of the mixed oxide layers determined that the systems NiO/MgO(100) and MgO/NiO(100) are equally stable. Annealing to 700 K induces a slight overlayer morphology change, judged by ISS relative intensity changes, and heating above 800 K leads to significant interdiffusion. ELS spectra for the MgO on NiO(100) system show no evidence for true interfacial states since all of the features can be accounted for by comparison to spectra of pure MgO or pure NiO [66]. But it is clear that twodimensional band structure growth determines the features of the ELS spectra as a
393
function of MgO coverage in the very low coverage regime. The features at 11.3 eV and 14.0 eV associated with the O 2p -- Mg transitions at the Brillouin zone edge [68] are shifted or missing until two-dimensional growth is nearly complete at -- 2 equivalent ML MgO on NiO(100). Thick films of MgO on NiO have electronic spectra essentially identical to pure MgO fihns. Increasing MgO coverage does influence the XPS spectra. The Ni (2p3/2) binding energy is shifted upwards 1.0 eV at 7.5 ML coverage of MgO/NiO(100), interpreted as negative charge transfer from MgO to NiO [66]. But recent ab initio calculations [69] have suggested that the shift is consistent with an ionic-like model with small surface relaxations, and that such small surface geometry changes have a large impact on the initial states of ions in the oxides. These effects discount the role of charge transfer in the observed XPS shifts.
100-
1.0
0.8
n o
,~
9 NiO_MgO 9 MgO_NiO NiO_CaO c,ao NiO
MgOI.L/NIO(100) NiOmLIMgO(100)~ -41-- NiOmLICaO(100) CaOI.dNIO(100)
80m
,j,.,..4r" r re
== 0.6 "E
O3 ,=.,
>
~0.4
60-
/
40-
n" 0.2
0.0
I
0
I
I
-
I
I
- -
;
I
1 2 3 4 5 Overlayer Coverages (ML)
Figure 10. ISS substrate oxide relative intensities as a function of coverage for the CaO/NiO/MgO mixed oxides.
1 ,
, 400
600 Temperature
o
(K)
, 800
Figure 11. Stabilities of the various oxide/oxide interfaces as probed by ISS.
394 Films of NiO on MgO(100) [67] which are thicker than 2.8 ML have electronic structure as measured by ELS identical to single crystal NiO(100) [55,70]. A weak feature at 2.2 eV is apparent in films < 2 ML NiO on MgO(100). This peak has tentatively been assigned to a surface state. The ability to identify such a feature is a measure of the usefulness of the ultrathin film technique: for the thicker film or bulk-terminated oxide this feature would be lost among the bulk electronic transitions. The slight shifts of NiO features at low coverages on the MgO substrate from their bulk values is taken to be a manifestation of the small distortions of the octahedral symmetry about the Ni cation sites as the initial NiO layer accommodates to the MgO lattice template. This results in small energy differences that split the degeneracies of the d-levels and alter the electronic excitation energy levels.
5.2 The CaO/NiO mixed oxide system and comparison to the NiO/MgO system Like NiO and MgO, CaO crystallizes in the simple rocksalt structure. But its lattice parameter is considerably larger [lattice constant: CaO(100), 3.402 ,~]. In order to determine the influence of this lattice mismatch on the mixed oxide layers' growth and stability the CaO/NiO system was studied [67] and the results compared to the MgO/NiO results (Sect. 5.2). CaO(100) was prepared on the Mo(100) surface in much the same way as the other surfaces, as described in preceding sections. The Ca metal source was a tantalum foil "boat" open at one end and heated resistively. Monolayer and multilayer Ca metal coverages are easily defined by features apparent in TPD, allowing a convenient estimate of metal dosing. As on MgO(100), NiO grows epitaxially on CaO(100) exhibiting a square (lxl) LEED pattern. The quality of this pattern, however, is much poorer than that found for NiO on MgO. CaO(100) ultrathin films on Mo(100) show a fairly good quality (lxl) LEED pattern, only slightly more diffuse than that of MgO(100). NiO on CaO and CaO on NiO show identical growth mode behavior, but this behavior differs from that found for the NiO/MgO system. Relative ISS intensity measurements show that at 1 equivalent monolayer of either overlayer oxide (CaO or NiO) only -~ 65% of the underlayer is masked, compared to ~ 90% for the NiO/MgO system. Complete masking of one oxide by the other in the NiO/CaO system only occurs after 4-5 ML of the overlayer oxide have been deposited. These data indicate that while the NiO/MgO system shows excellent wetting of one oxide by the other and essentially layer-by-layer growth, there is significant threedimensional clustering within the first layers of CaO on NiO(100) and NiO on CaO(100). The NiO/CaO system also shows very different thermal stability. Interdiffusion occurs for NiO on CaO(100) at 400 K. A slight overlayer
395 morphology change appears for the CaO on NiO(100) system at 550 K, but further heating to 900 K causes virtually no change in the relative ISS intensifies-- no significant interdiffusion is found for CaO/NiO(100). The four systems studied can thus be ordered in terms of their interfacial stability: CaO/NiO(100) > MgO/NiO(100) - NiO/MgO(100) > NiO/CaO(100).
5.3 NiO ultrathin film supported on Al203 Supported transition metal oxides have been shown to have catalytic behavior which differs from that of their bulk counterparts, and as such are used in technologically important processes [71,72]. The highly ordered A1203 ultrathin films (Section 4) prepared on Mo(110) and Re(0001 ) substrates have been used as model supports for NiO [73]. The NiO in NiO/A1203 powder systems is thought to form a "spontaneous" monolayer, and the resulting catalyst is active for a number of reactions [74,75]. The electronic structure of NiO of various thicknesses supported on -- 30 ML A1203 was investigated by ELS. As reported above (Sect 4.3) alumina ultrathin films present a featureless loss spectrum between the phonon modes and the optical bandgap (--2-7 eV) which in this case allows the study of the electronic structure of the overlayer NiO film. The results show that by 1 equivalent ML coverage of NiO all the features associated with bulk NiO (e.g., a 28 ML film) are present, with no observable shifts or absences. This indicates that the electronic structure of thin NiO films is very similar to that of the thick films and that the support alumina does not influence this electronic structure in any gross manner. The chemical properties of the thin NiO films are very different from the properties of the thick film. TPD and IRAS measurements using CO as a probe molecule were made to determine the nature of the films. The peak temperature of CO desorption from NiO on A1203 converges with that for desorption from NiO bulk at -- 10 ML coverage of NiO. Annealing the films to 800 K uncovered another difference in the CO-TPD spectra. After annealing, films < 10 ML thick showed a high temperature feature on the TPD spectra characteristic of CO desorption from metallic Ni. Even thinner NiO films (1 ML) exhibit, after annealing to 800 K, a broad high -temperaure CO desorption feature different than desorption from either NiO or Ni. The presence of three adsorption sites on these very thin, thermally treated NiO/A1203 films was corroborated by IRAS of adsorbed CO. The IR absorption due to CO adsorbed on NiO is found at 2182 c m -1. Another due to CO on metallic Ni atop sites is observed near 2100 cm -a. The third feature at 2124 cm -a has been assigned to adsorption at Ni 1+sites at the interface, in agreement with other IR studies of NiO supported on powdered A1203 [76] and Ni supported on powdered
396
A1203 [77]. The reactivity of the 1 ML films of NiO on AlzO 3 towards CO was investigated by monitoring COz production from the surface in pressures of CO as high as l x l 0 -7 Torr. A desorption feature indicative of the reaction between lattice oxygen and CO appears a t - 500 K, and attenuates in subsequent temperature programmed reactions runs, leaving metallic Ni on the surface. Neither A1203 nor bulk-like NiO films react with CO towards oxidation at temperatures up to 800 K.
i~
~/
^•
5 min. annealed at 800 K
after oxidation at4OOK, lXlO"TorrO,
before CO adsorption
C e" A
E 0
200
400
600
200
400
600
Temperature (K)
Figure 12. CO TPD on various NiO films supported on AlzO 3. The film was freshly
prepared (left) and annealed to 800 K in vacuum for 5 min. (fight).
The properties of very thin supported NiO films are substantially different than those of thick NiO films or the bulk NiO. Alumina is a useful support for these films because its interaction with monolayer NiO is not strong, while its affinity for Ni metal, in the presence of the oxide, is high. This keeps the dimensionality of the NiO thin film low, with tittle three-dimensional clustering, allowing a high concentration of very active sites at the NiO/AlzO 3 interface, and dispersing the reduced Ni metal (no bridging CO; only CO on atop sites are found in CO-IRAS). It is important to note that the electronic structure of these films as determined by ELS is insensitive to the changes obvious in the chemical properties. This may often be the case: the chemistry itself may be the most sensitive probe of the properties of a material.
397
5.4 Mixed AI203/SiO 2 ultrathin films Layered oxides prepared in the surface science fashion can be models for classes of environmentally important materials such as the silicate clays and aluminosilicates [65,78], and of course the mixed oxides such as A l 2 0 3 / S i O 2 with three-dimensional structure (zeolites) are useful catalysts for cracking and isomerization of hydrocarbons [79]. Using gas-phase precursors should allow a wide composition range (Si/A1 ratio, for instance) of ultrathin films to be prepared for surface science study. A l 2 0 3 / S i O 2 mixed oxide prepared on substrate Mo(100) has been studied using TPD, AES, XPS, and ISS [80]. The mixed oxide was formed by evaporation of metallic A1 onto an ultrathin film of S i O 2. The S i O 2 films have been shown to grow a complete first layer before three-dimensional bulk film growth begins [81 ]. The gas phase precursor for S i O 2 film growth is SiO, produced by the oxidative etching of the doped silicon source in lxl 0 .5 Torr oxygen background. Annealing the as-synthesized S i O 2 film to 1350 K caused the formation of fused networks of [SiO4] which have the electronic and bonding structures of vitreous silica. Subsequent to the deposition of A1 on this surface the following oxidation steps are observed as a function of annealing temperature:
SiO2/Mo + A1 ~ A1/SiO2/Mo A1/SiO2/Mo ~ A1203/Si/SiO2]Mo AlzO3/Si/SiOz/Mo ~ AlxOySiz/Mo + SiO
100-300 K 300-800 K 800-1200 K
SiO desorbs between 1000-1100 K, leaving a homogeneous A1203/SiO 2 mixed oxide film as determined by ISS/sputtered depth profiling. The important step for the formation of Si-O-A1 linkages is the concerted diffusion of A1203 into the bulk of the SiO 2 film, with the coincident desorption of volatile SiO as a result of the solid state reaction between Si and S i O 2. XPS core-level shifts indicate that these mixed oxide films have electronic properties similar to the aluminosilicate glasses and zeolites. For example, the same general trend as to variation in the binding energies of the Si and O transitions with changing A1 concentration are observed for these ultrathin films and powdered aluminosilicates [82] and zeolites [83-84] (Fig. 13). The major difference, of course, is that the AI203/SiO 2 mixed oxide films prepared for surface science study do not have acidic surface hydroxyl groups since they are formed in the absence of water.
398
Figure 13. XPS core level shifts of mixed A1203/SiO 2 films as a function of the film composition.
533.0/
oOs) n
>
1:3
o
532.5
I"1
I"1
El
El
>-
O
103.5,
Sil2p)
ILl Z ILl (:3 Z r~
9
9
~k
I03.0 -
&
al
Ail2P) 75.5
75.
o'.1
o'.,,
o'.3
o14
o.s
AI/(AI+Si) RATIO
6. STM I M A G I N G OF OXIDE SURFACES
Very recent work in our laboratory has used STM imaging to investigate the morphology of the ultrathin metal oxides and metal particles supported on the ultrathin oxide films (see Sect. 7). The imaging of the oxide ultrathin films is a balance between sufficient conduction through the oxide and direct tunneling to the metal. Films which are too thick are difficult to image because of the poor conduction, and films too thin yield unreliable scanning tunneling spectroscopy (STS) results due to the interference of substrate metal electronic states. Nevertheless, our results show considerable detail with regard to oxide surface morphology and electronic structure. STM images of the A1203 surface prepared on Re(0001) show relatively small domain sizes. Even for the very thin A1203 films which exhibit bright and sharp LEED spots the domain sizes do not appear to exceed-- 60 A. The image in Figure 14 of 12.5 ML alumina shows these domains. The domains are essentially atomically fiat with defects limited to the domain edges. The defect density is low (-- 10%) and of very regular type. The STS for 3.6 ML alumina (A/V curve, Figure 15) shows a band gap of 6.25 eV and no apparent defect surface states in the flat region. Ultrathin films of MgO(100) as shown in the STM image in Figure 16 also
399 display very small domain sizes, and for this 8 ML sample a substrate step is apparent from the rumpling of the oxide overlayer. A representative STS spectrum (A/V vs. V, Figure 17) shows the band gap of 4.0 eV with no interband surface states exhibited. The STM image of a relatively thick (30 ML) TiO2 film on Mo(100) is presented in Figure 18. The surface is rough but completely covered by titania (including the "low" points, dark areas in the image). The crystalline-like domains of titania are large-- several hundred angstroms across. The top of one of these crystallites is shown with atomic resolution in Figure 19. It presents a very fiat surface. At very low oxide coverage (2 ML titania, Figure 20) the substrate metal surface is imaged (it is probably oxided; dark areas in image, Fig. 20). The titania islands are very sharp, regularly featured rectangles obviously growing in an oriented manner with respect to the metal[85].
tim
3.394 3.182 2.970 2.758 2.546 2.334 2.121 1.909 1.697 1.485 1.273 1.061 O.849
Figure 14. STM image of 12.5 ML A1203 on Re(0001) showing the domain boundaries. Surface +5 bias voltage; 0.2 nAmp
0.636 0.424 0.212 0
0.000 0
20
40
13A
60
.
80
100
w
o.01
o.0o
..O.Ol
-,.~:2.~' 1--2
.... 3-
o.oo -
~.oo
Figure 15. Representative A vs. V curve STS of 3.6 ML alumina showing the apparent band gap of 6.25 eV.
400
nm
0.427 0.401
Figure 16. STM image of 8 ML MgO showing the very small domain sizes of the oxide. Surface +4 bias voltage; 0.2 nA feedback current.
0.374 0.347
150
0.321 0.294 0.267 0.240 0.214 0.187 0.160 o.134 O.lO7 0.080 0.053 0.027 0.000 0
5o
100 nm
150
200
nA/V
.......................
2.00
Figure 17. Representative A/V vs. V curve STS of 8 ML MgO showing the apparent band gap of 4.0 eV.
1.50
o+f
....... -4.00
1--2
300
nm
3.570 3.315 3.060 2.805 2.550 2.295 2.040 1.785 1.530 1.275 1.020 0.765 0.510 0.255 0.000 15o nm
200
250
300
3-
0.00
2.00
4.0~/
-
4.080 3.825
loo
.....
-2.00
Figure 18. STM image 30 ML TiO2 on Mo(100) showing the large, rough domains. Surface +2 bias voltage; 0.5 nA feedback current.
401
nm
Figure 19. STM image of the top of
1.267 1.188 1.109
one of the crystallites depicted in Fig. 18.
1.029 0.950 0.871 0.792 0.713 0.633 0.554 0.475 0.396 0.317 0.238 0.158 0.079 0.000 0
10
20
30
nm
40
nm
1.1 1.1 1.0 0.9 0.8 0.8 0.7 0.6
Figure 20. STM image of 2 ML TiOz with atomic resolution, showing the growth of the oxide on the
substrate metal surface.
0.6 0.5 0.4 0.4 0.3 0.2 0.1 0.1 0.0 0
10
20
30 nm
40
50
60
7. OXIDE S U P P O R T E D M E T A L P A R T I C L E S A considerable amount of work in this laboratory has focused on the use of well characterized ultrathin oxide films as supports for metal particles which serve as models for practical catalysts [59, 86-99]. For instance, the study of model silica
402 supported copper and palladium catalysts has shown that the preparation conditions define the corresponding metal particle dispersions or average size. The adsorption and reaction of CO on the silica supported Pd particles has been investigated over a range of temperatures and pressures, using kinetics measurements, reflectance IR spectroscopy, and STM to demonstrate the continuity between catalysis on Pd single crystals and small Pd particles. As indicated in Section 6 the imaging of surfaces prepared on refractory metal substrates has been a recent area of interest. The ability to determine the morphology of metal particles supported on oxide surfaces and to monitor the changes undergone as a function of coverage or temperature is important for understanding the sintering process and the stability of small structures. STM images of Ni particles on A1203 are shown below. The A1203 films were prepared on Re(0001) and are 3.6 ML thick (- 10 ,~). Second layer alumina features appear as the lighter background areas of Figure 21. The Ni particles were deposited at room temperature, and the images were obtained also at room temperature. They appear as the circlular white areas in the images. At both 0.5 ML (Fig. 21) and 0.1 ML (Fig. 22) Ni coverages the particles formed are similar in that they are fairly monodisperse, with apparent diameters of 20-30 ,~. Annealing the 0.5 ML Ni/A1203 system to 900 K causes the Ni particles to aggregate. The resulting particles are -50 A in diameter (Fig. 23). Only partial wetting of the alumina by nickel is apparent. This reflects on the work presented in Sect. 5.4, indicating that the tendency for alumina to accommodate metallic Ni is mediated by the presence of the nickel oxide [ 100]. 8. CONCLUSION The epitaxial growth of ultrathin metal oxides on refractory metals allows the surface science study of technologically important wide bandgap semiconductors and insulators. Some of these surfaces are themselves catalytically active or support catalytically active materials, and the use of charged particle probes without attendant charging problems previously encountered greatly expands our ability to investigate their chemical properties on the microscopic scale. In combination with such techniques as reflectance IR this approach to model surfaces can bridge the pressure and material "gaps" in surface science simultaneously: the direct connection of well-defined model system studies to "real world" processes. The scanning microscopies can be applied to these surfaces, both in and out of UHV, to investigate supported metal particle size and morphology. These kinds of investigations offer unprecedented opportunities to address the molecular details of the chemistry at oxide surfaces.
403
Figure 21. STM image of 0.5 ML Ni on 3.6 ML alumina showing the fairly monodisperse particles. Surface +5 bias voltage; 0.2 nA feedback current.
rtm
0.116
....
I
i
0 tO9
0 ~ot
9
o.o8r
..-
oor2
.:
0 065
G
o 080
0 058 00St 0O43 0 036 0 029 0 022 0.014 O.O07 0.000 5O rlflP'
Figure 22. STM image of 1.0 ML Ni on 3.6 ML alumina. Note the change in scale from Fig. 21.
100 1307 1.225 1.144
1 O62 0.980 0.898 0.817 0 735 0.653 0.572 0.490 0.408 0.327 0.245 0.163 0.082 0.000 0
20
40
60
Figure 23. STM image of 0.5 ML Ni on 3.6 ML alumina annealed to 900 K, showing the aggregation of the particles.
nm
t 046 O98O 091S 0 850 0 7114 0 ?tg 0.65.4
6o
0.S~8 01~ 3 0 4s~
40
0 39? 0 321 026t otg6 0.131 0.06s o(x)o ~0
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60
80
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404
REFERENCES 1. V. E. Henrich and P. A. Cox, The Surface Science of Metal Oxides, Cambridge University Press, Cambridge, 1994. 2. G. A. Somorjai, Introduction to Surface Chemistry. and Catalysis, J. Wiley & Sons, New York, 1994. 3. D. P. Woodruff and T. A. Delchar, Modern Techniques of Surface Science, Cambridge University Press, Cambridge, 1986. 4. V. E. Henrich, Rep. Prog. Phys. 48 (1985) 1481. 5. H.-J. Freund and E. Umbach, eds., Adsorotion on Ordered Surfaces of Ionic Solids and Thin Films, Springer Verlag, Berlin, 1993. 6. M. Prutton, J. A. Walker, M. R. Welton-Cook, and R. C. Felton, Surf. Sci. 89 (1979) 95. 7. T. Urano, T. Kanaji, and M. Kaburagi, Surf. Sci. 134 (1983) 109. 8. M. Boudart, A. Delbouile, E. G. Derouane, V. Indovina, and A. B. Waiters, J. Am. Chem. Soc. 94 (1973) 6622. 9. P. Mars, J. J. F. Scholten, and P. Zweitering, Advan. Catalysis 14 (1963) 35. 10. J. H. Lunsford, Catal. Today 6 (1990) 235. 11. M.-C. Wu, J. S. Corneille, C. A. Estrada, J.-W. He, and D. W. Goodman, Chem. Phys. Lett. 182 (1991) 472. 12. M.-C. Wu, J. S. Corneille, J.-W. He, C. A. Estrada, and D. W. Goodman, J. Vac. Sci. Technol. A 10 (1992) 1467. 13. M.-C. Wu, C. A. Estrada, J. S. Corneille, and D. W. Goodman, J. Chem. Phys. 96 (1992) 3892. 14. J. S. Corneille, J.-W. He, and D. W. Goodman, Surf. Sci. 306 (1994) 269. 15. P. A. Thiry, M. Liehr, J. J. Pireaux, and R. Caudano, Phys. Rev. B 29 (1984) 4824. 16. E. A. Colburn and W. C. MacKrodt, Surf. Sci. 143 (1984) 391. 17. E. Guglielminotti, S. Coluccia, E. Garrone, S. Cerruti, and A. Zecchina, J. Chem. Soc. Faraday Trans. 175 (1979) 96. 18. J.-W. He, C. A. Estrada, J. S. Corneille, M.-C. Wu, and D. W. Goodman, Surf. Sci. 261 (1992) 164. 19. J.-W. He, C. A. Estrada, J. S. Corneille, M.-C. Wu, and D. W. Goodman, J. Vac. Sci. Technol. A 10 (1992) 2248. 20. S. L. Parrott, J. W. Rogers Jr., and J. M. White, Appl. Surf. Sci. 1 (1978) 443. 21. H. Onishi, C. Egawa, T. Aruga, and Y. Iwasawa, Surf. Sci. 191 (1987) 479. 22. X. D. Peng and M A. Barteau, Surf. Sci. 224 (1989) 327. 23. M.-C. Wu, C. A. Estrada, and D. W. Goodman, Phys. Rev. Lett. 67 (1991) 2910. 24. M.-C. Wu and D. W. Goodman, Catal. Lett. 15 (1992) 1. 25. C. Xu and D. W. Goodman, unpublished results. 26. V. E. Henrich, G. Dresselhaus, and H. J. Zeiger, Phys. Rev. B 22 (1980) 4764. 27. M.-C. Wu, C. M. Truong, K. Coulter, and D. W. Goodman, J. Am. Chem. Soc. 114 (1992) 7565. 28. M.-C. Wu, C. M. Truong, and D. W. Goodman, Phys. Rev. B 46 (1992) 12688. 29. M.-C. Wu, C. M. Truong, and D. W. Goodman, J. Vac. Sci. Technol. A 11 (1993) 2174. 30. M.-C. Wu, C. M. Truong, K. Coulter, and D. W. Goodman, J. Catal. 140 (1993) 344.
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K. Coulter and D. W. Goodman, Catal. Lett. 16 (1992) 191. S. K. Pumell, X. Xu, D. W. Goodman, and B. C. Gates, J. Phys. Chem. 98 (1994) 4076. S. K. Pumell, X. Xu, D. W. Goodman, and B. C. Gates, Langmuir 10 (1994) 3057. D. Wolf, Phys. Rev. Lett. 68 (1992) 3315. F. Rohr, K. Wirth, J. Libuda, D. Cappus, M. B~iumer, and H.-J. Freund, Surf. Sci. 315 (1994) L977. C. Xu and D. W. Goodman, manuscript in preparation. C. J. Papile and B. C. Gates, Langmuir 8 (1992) 74. S. Radajurai, Catal. Rev.-Sci. Eng. 36 (1994) 385. C. Xu and D. W. Goodman, J. Chem. Soc. Faraday Trans. 91 (1995) 3709. X. D. Peng and M. A. Barteau, Catal. Lett. 7 (1990) 395. T. Shido, K. Asakura, and Y. Iwasawa, J. Catal. 122 (1990) 55. H.-J. Freund, H. Kuhlenbeck, and V. Staemmler, Rep. Prog. Phys. 59 (1996) 283. C. M. Truong, M.-C. Wu, and D. W. Goodman, J. Chem. Phys. 97 (1993) 9447. C. M. Truong, M.-C. Wu, and D. W. Goodman, J. Am. Chem. Soc. 115 (1993) 3647. M.-C. Wu, C. M. Truong, and D. W. Goodman, J. Phys. Chem. 97 (1993) 9425. M.-C. Wu, C. M. Truong, and D. W. Goodman, J. Phys. Chem. 97 (1993) 4182. R. P. Furstenau, G. McDougall, and G. Langell, Surf. Sci. 150 (1985) 55. M. W. Roberts and R. St C. Smart, J. Chem. Soc. Faraday Trans 1 80 (1984) 2957. C. M. Truong, Ph. D. thesis, Texas A&M University, 1993. G. Pacchioni, G. Cogliandro, and P. S. Bagus, Surf. Sci. 255 (1991) 344. S. M. Vesecky, X. Xu, and D. W. Goodman, J. Vac. Sci. Technol. A 12 (1994) 2114. G. Pacchioni, G. Cogliandro, and P. S. Bagus, Intern. J. Quantum Chem. 42 (1992) 1115. C. Xu and D. W. Goodman, Catal. Today, in press. D. Cappus, C. Xu, D. Ehrlich, B. Dillmann, C. A. Ventrice, K. A1-Shamery, H. Kuhlenbeck, and H.-J. Freund, Chem. Phys. 177 (1993) 533. A. Freitag, V. St~iemmler, D. Cappus, C. A. Ventrice, K. A1-Shamery, H. Kuhlenbeck, and H.-J. Freund, Chem. Phys. Lett. 210 (1993) 10. K. W. Wulser and M. A. Langell, Catal. Lett. 15 (1992) 39. N. N. Greenwood and A. Earnshaw, Chemistry_of the Elements, Pergamon Press, New York, 1984. P. J. Chen and D. W. Goodman, Surf. Sci. 312 (1994) L767. M.-C. Wu and D. W. Goodman, J. Phys. Chem. 98 (1994) 9874. D. W. Goodman, submitted to J. Vac. Sci. Technol. Q. Guo, S. C. Street, C. Xu, and D. W. Goodman, manuscript submitted to J. Phys. Chem. M. Xi, M. X. Yang, S. K. Jo, and B. E. Bent, J. Chem. Phys. 101 (1994) 9122. P. Avouris and J. E. Demuth, J. Chem. Phys. 75 (1981) 4783. R. M. J~iger, K. Homann, H. Kuhlenbeck, and H.-J. Freund, Chem. Phys. Lett. 203 (1993) 41. G. Sposito, Th~ Surface Chemistry. of Soils, Springer Verlag, Berlin, 1985. M. L. Burke and D. W. Goodman, Surf. Sci. 311 (1994) 17. C. Xu, W. S. Oh, Q. Guo, and D. W. Goodman, submitted to J. Va. Sci. Technol. M. L. Bortz, R. H. French, D. J. Jones, R. V. Kasowski, and F. S. Ohuchi, Phys. Scr. 41 (1990) 537. M. D. Towler, N. M. Harrison, and M. I. McCarthy, Phys. Rev. B 52 (1995) 5375.
406 70. P. A. Cox and A. A. Williams, Surf. Sci. 152/153 (1985) 791. 71. H. H. Kung, Transition Metal Oxides: Surface Chemistry. and Catalysis, Elsevier, Amsterdam, 1989. 72. D. S. Kim, M. Ostromecki, I. E. Wachs, D. Kohler, and J. G. Ekerdt, Catal. Lett. 33 (1995) 209. 73. C. Xu, Q. Guo, and D. W. Goodman, manuscript submitted to Catal. Lett. 74. Y.-C. Xie and Y.-Q. Tang, Adv. Catal. 37 (1990) 1. 75. H. Pines, Adv. Catal. 35 (1987) 323. 76. J. S. Raschko, R. J. Willey, and J. B. Peri, Chem. Eng. Comm. 104 (1991) 167. 77. J. B. Peri, J. Catal. 86 (1984) 84. 78. F. Liebau, Structural Chemistry of Silicates, Springer Verlag, Berlin, 1985. 79. B. C. Gates, J. R. Katzer, and C. C. A. Schuit, Chemistrv of Catalytic Processes, McGrawHill, New York, 1979. 80. C. Grtindling, J. A. Lercher, and D. W. Goodman, Surf. Sci. 318 (1994) 97. 81. X. Xu and D. W. Goodman, Surf. Sci. 282 (1993) 323. 82. J. A. Kovacich and D. Lichtman, J. Electron. Spectrosc. Relat. Phenom. 35 (1985) 7. 83. T.L. Barr and M. A. Lishka, J. Am. Chem. Soc. 108 (1986) 3178. 84. J. Stoch, J. A. Lercher, and S. Ceckiewicz, Zeolites 12 (1992) 81. 85. W. S. Oh, C. Xu, D. Y. Kim, and D. W. Goodman, in preparation. 86. X. Xu, J.-W. He, and D. W. Goodman, Surf. Sci. 284 (1993) 103. 87. X. Xu, S. M. Vesecky, N. Loganathan, and D. W. Goodman, Science 258 (1992) 788. 88. X. Xu and D. W. Goodman, J. Phys. Chem. 97 (1993) 683. 89. X. Xu and D. W. Goodman, J. Phys. Chem. 97 (1993) 9425. 90. X. Xu, S. M. Vesecky, J.-W. He, and D. W. Goodman, J. Vac. Sci. Technol. A 11 (1993) 1930. 91. X. Xu, J. Szanyi, Q. Xu, and D. W. Goodman, Catal. Today 21 (1994) 57. 92. X. Xu, P. Chen, and D. W. Goodman, J. Phys. Chem. 98 (1994) 9242. 93. J. Szanyi, X. Xu, and D. W. Goodman, Proc.of Symposium on Chemistry. and Characterization of Supported Metal Catalysts, American Chemical Society, Chicago, IL, 1993. 94. X. Xu and D. W. Goodman, "Metal Clusters on Oxides," in Handbook of Surface Ima~in~ and Visualization, A. T. Hubbard, ed., CRC Press, Inc. 1994. 95. K. Coulter, X. Xu, and D. W. Goodman, J. Phys. Chem. 98 (1994) 1245. 96. D. W. Goodman, Surf. Rev. and Letts 1 (1994) 449. 97. D. W. Goodman, Surf. Rev. and Letts 2 (1995) 9. 98. D. W. Goodman, Chem. Rev. 95 (1995) 523. 99. S. M. Vesecky, D. R. Rainer, and D. W. Goodman, J. Vac. Sci. Technol. A, in press. 100. C. Xu, X. F. Lai, and D. W. Goodman, accepted for Faraday Disc. 105. w
91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
407
Chapter 11 Growth, structure and reactivity of ultrathin metal films on TiO 2 surfaces Rajendra Persaud and Theodore E. Madeyr Laboratory for Surface Modification and Department of Physics and Astronomy, Rutgers, The State University of New Jersey PO Box 849 Piscataway, NJ 08855, USA 1.
INTRODUCTION
There are many applications where ultrathin layers of metals deposited onto oxide surfaces are of importance, including catalysis, chemical sensors, fiber optics, microelectronic devices, and metal-ceramic bonding. Many of the interesting properties of metal-on-oxide systems are determined by phenomena occuring at the interface between metal and oxide. An important issue in studies and applications of metals-on-oxides is the relationship between the structure and reactivity of the metal oxide interface, and the growth modes of the ultrathin metal layers. That is, how does the interface chemistry affect the film morphology in the initial stages of growth. We address this matter in the present review. Papers by Goodman and by Freund in this volume contain discussions of metals interacting with surfaces of wide bandgap insulators, SiO2 and A1203. Our focus in the present paper is on the systematics of the interactions of a range of metals with surfaces of rutile TiO2, a medium bandgap (--3.1eV) reducible oxide at which surface oxygen vacancies can be readily generated. We emphasize the use of surface science methods in studies of metals on crystalline TiO2 substrates. The most extensive studies have been made on TiO2(110) surfaces; TiO2(110) is the charge neutral surface of rutile TiO2, is thermally stable, and is believed to have a relaxed bulk truncation structure. To the best of the authors' knowledge, there have been no reported studies of metals on crystalline surfaces of anatase or brookite TiO2 using surface science methods. ~: Author for correspondence: madey@physics'rutgers'edu
408 Metals on TiO2 have been and are being used for many applications. TiO2 is an excellent catalyst for the photolytic decomposition of water, and the presence of Pt at the TiO2 surface is known to enhance the photocatalytic activity [1]. Metal-coated TiO2 is also used in chemical sensing applications [2, 3]. Oxygen vacancies in TiO2 play a key role in these sensors: gas sensing is based on changes in surface and near-surface conductivity caused by a space charge region induced by gas adsorption or the formation of surface oxygen vacancies. Ultrathin metallic overlayers on TiO2 can affect the adsorption and sensing properties dramatically. Metals on TiO2 have interesting properties as heterogenous catalysts in reducing atmospheres, largely because of the so-called Strong Metal-Support Interaction (SMSI) effect. Reduced TiOx species can diffuse over and "encapsulate" supported metal particles [4], thereby affecting their adsorption properties and catalytic activity. There are a number of useful articles and books that provide an excellent introduction to the electronic, structural and chemical properties of metal/oxide systems. Of particular note are review articles by Lad [5], Goodman [6], Freund [7], and Campbell [8, 9] as well as books by Henrich and Cox [10], Noguera [11], and several conference proceedings [12, 13]. The purpose of the present review is to build upon previous summaries by Madey et al. [14], Diebold et al. [15], and Campbell [9] to provide a guide to the many studies of metals on TiO2 surfaces, and to draw some generalizations about trends. In section 2, we present the main issues concerning metal/TiO2 interactions, i.e., film growth modes, interfacial reactivity, film structure, and thermal stability. Also in section 2, we introduce the main experimental methods used in the published studies. We occasionally discuss reactions of gases with metals on TiO2, but this is a secondary focus. In section 3, we provide an element-by-element survey of published data and conclusions for metals on TiO2, with emphasis on the (110) surface. A summary and outlook are given in section 4.
2.
OVERVIEW OF METALS ON TiO2(ll0)
2.1
Stoichiometric TiO2(110)
Rutile TiO2 has the tetragonal structure. Although rutile TiO2 does not cleave well, cleavage occurs preferentially along the (110) face, the most stable
409 of the low index faces of rutile [10]. A model of the surface of a single crystal TiO2(110) is shown along with the corresponding unit cell in figure 1.
[OOl]
[110] In-plane Oxygen anions
....
....
o..
Bridging Oxygen anions 0
Ti cations Below surface
plane Oxygen
Figure 1:
l; ..... 0 ~"
6.48 A
..... ; "1
(a) Schematic of the TiO2(110) surface with (b) the corresponding unit cell. The arrows in (a) point to two types of defects corresponding to missing oxygen anions. Small solid circles represent Ti cations. The large (lighter) shaded circles represent in-plane oxygen anions while the hollow circles represent bridging oxygen anions. The darker shaded circles in (b) represent oxygen anions below the surface plane.
The surface consists of alternating rows of oxygen anions (shaded circles) and Ti cations (solid circles) running along [001]. Every other row of Ti cations is covered up by a bridging row of oxygen anions (hollow circles) which protrudes above the surface. It is now well established that defects can be created on the surface through Ar + bombardment [16], high temperature annealing [10, 16] and from exposure to electron beam irradiation [17]. Two types of defects corresponding to missing oxygen anions are shown in figure 1. The creation of oxygen vacancies is the predominant form of point defects which result from the above
410 treatment [10]. These are the most important form of defects in that they can affect the electronic structure and/or the chemisorptive and catalytic properties of the surface [10]. The bulk truncation model of the stoichiometric surface presented in Figure l(a) is consistent with Medium Energy Electron Diffraction (MEED) data [18] and with scanning tunneling microscope (STM) measurements [19-28]; theory indicates that the structure is a relaxed bulk truncation [29]. In several of the STM studies, atomic scale resolution images have been obtained [22-28]. One such image, taken from reference [28], is displayed in Figure 2.
Figure 2:
Atomicallyresolved STM image of the TiO2(110) surface. The bright rows run along the [001] direction. The image was scanned over 140A x 140A. Sample bias +1.6V and tunneling current 0.3nA. From Ref. [28].
There has been some controversy regarding whether the bright rows shown in the figure represent rows of oxygen anions [24, 30] or Ti cations [23, 26, 27]. In an attempt to resolve this issue, Diebold et al. [28] performed a first principles plane-wave pseudopotential calculation based on the methods of reference [29]. They reported that the bright rows are related to the exposed Ti cations and the dark rows to the oxygen anions; in essence, electronic structure effects dominate over topological features in STM images [28]. The stoichiometric TiO2(110) surface can be easily prepared and regenerated under UHV conditions followed by annealing and cooling produces a sharp (1 x 1) LEED although under certain conditions a
through a sequence of Ar+ bombardment in ambient oxygen [16]. The clean surface (low energy electron diffraction) pattern, (1 x 2) can be obtained [31].
411 Whereas TiO2(110) has received the most attention in the literature, a number of studies on (100) and (001) surfaces have been reported; models of these surfaces are shown by Henrich and Cox [10]. Fractured (100) surfaces exhibit fair (1 x 1) LEED patterns, but polished and annealed surfaces reconstruct upon annealing to display (1 x 3), (1 x 5) and (1 x 7) LEED patterns. The (1 x 3) reconstructed surface has been identified as displaying facets with the (110) orientation [32-36]. The (001) surface is the least stable of the low index surfaces [10]; poor (1 x 1) LEED patterns are seen on fractured surfaces, and the surface develops facets upon annealing. At temperatures below 1000K, (011) facets are formed in which the Ti cations have 5-fold O coordination. Annealing above 1300K produces (114) facets for which most cations have 4-fold O coordination. A complex faceting structure was reported using AFM after annealing to 1573K [36]. Rutile TiO2 has a bulk bandgap of 3.05 eV [37] and could therefore be regarded as a wide band gap semiconductor or insulator. It is usually reduced through vacuum annealing to make it sufficiently conductive to reduce charging effects in electron spectroscopy and permit tunneling measurements. Extensive reduction can lead to the formation of bulk Magneli phases, characterized by an array of shear planes [38]. The reduced TiO2 is an n-type semiconductor with its Fermi level pinned just below the bottom of the Ti 3d conduction band.
2.2
Thermodynamics of Metal/TiO2 Interactions
Discussions of the thermodynamics [5, 9-11, 14, 15] and kinetics [9, 39] of the growth of metals on oxides have appeared in the literature, and salient features are summarized briefly here. The majority of the examples discussed in this review involve deposition of metal atoms from a vapor source onto atomically clean TiO2 surfaces. The first stages of the interaction between metal and oxide involve adsorption of metal atoms, diffusion, and nucleation and growth of islands. Under equilibrium conditions, the nature of the growth of metal layers on oxides and other substrates is governed by energetic and thermodynamic parameters, and several different growth modes are observed. 9 Volmer-Weber (VW) or island growth, in which three-dimensional islands or clusters of metal coexist with patches of clean oxide surfaces.
412 9
9
Frank-van der Merwe (FM) or layer-by-layer growth; in which metal layers are formed one after the other, covering the oxide substrate. Stranski-Krastanov (SK), or layer + island growth: Initially, one or two monolayers cover the oxide substrate, and subsequent deposition leads to metal cluster formation.
A simple thermodynamic relation involving the following surface and interface energies (expressed in J/m 2) determines the growth modes: Ymv: specific surface free energy of metal in vacuum Yov" specific surface free energy of oxide in vacuum 7m/o: interfacial energy between metal and oxide For Yov < Ymv + Ym/o, VW growth occurs; for 7ov > Ymv + 7m/o, either SK or FM growth occurs. The occurrence of FM growth under equilibrium conditions also requires good lattice match between metal overlayer and oxide substrate. A fourth growth mode can also be considered, in which a new interphase is formed between metal and oxide as a consequence of chemical reaction and diffusion at the interface [5, 11]. Although the growth modes described above refer to equilibrium conditions (which are not often achieved), they are useful descriptors of experimentally observed growth forms. In some cases (e.g., deposition at cryogenic temperatures) kinetic limitations can lead to metastable layer-bylayer growth, which relaxes to clusters (VW) upon annealing at higher temperatures. For transition metals, surface free energies 7my range from --1 J/m 2 (Au) to 2.7 J/m2 (Pd) and higher; for alkali metals, surface energies are considerably less than 1 J/m2 [40]. The surface energy of TiO2 (Yov) is reported to be --0.35 J/m2 [41], substantially lower than most values of Ymv, so that VW or cluster growth might be expected to be the dominant growth mode for metals on TiO2. Indeed, VW growth is observed for the mid to late transition metals including Cu, Pd, Pt, and Au on TiO2(ll0). For early transition metals and alkalis, layer forms of growth are observed in the initial stages; in some cases this occurs because of large negative interfacial energies, Ym/o [42].
413 The term "wetting" is often used to describe the case of two dimensional or layer growth (SK or FM) in the initial growth stages. Wetting corresponds to a contact angle of 0 ~ between a three-dimensional particle and the oxide substrate, i.e., the lateral dimension greatly exceeds the thickness [9]. The "nonwetting" condition (VW growth) can be viewed as a case where the cohesive energy of the metal is considerably less than the adhesive energy between metal and oxide. The adhesion energy, or work of adhesion Wadh, is the work required to pull apart a unit area of metal/oxide interface, thus creating one oxide/vacuum surface and one metal/vacuum surface, Wadh = ]tOv + ]tmv]tm/O [11]. For an indication of whether or not an interfacial reaction is expected to occur when depositing a metal on TiO2, it is useful to consider the thermodynamic stabilities of the oxides [5, 9-11, 14, 15, 43]. If metal M is deposited onto TiO2, then M should reduce the TiO2 surface and itself become oxidized if the reaction M + TiO2 ~ MOx + TiO(2-x)
(1)
is thermodynamically favorable. In the case of bulk compound formation, this occurs when the free energy of formation of the oxide M is more negative than that of TiO(2-x) (Note that free energies of formation are here referenced per mole of 02 [5, 43]; other authors [9, 10] reference per mole of O). Bulk TiO2 can be reduced to lower oxides (Ti203, TiO), e.g., 4TiO2(s) ---) 2Ti203(s) + O2(g) (AG o = 728 kJ/mole at OK) f
(2)
2Ti203(s) ---) 4TiO (s) + O2(g)
(3)
(AG of = 966 U/mole at OK) Thus, reactions of the type (1) can occur when AG o of the oxide of M is more f negative than -AG ~ for the reduction of TiO2 to a lower oxide, when compared per mole of oxygen [5, 43]. Several examples of metal overlayer oxidation and TiO2 substrate reduction [e.g., for Hf, Ti, V, Cr [15, 44-47]] are discussed below. Note that this discussion focuses on stable bulk compounds, whose formation may be precluded by kinetic factors (diffusion, etc.). The fact that surface oxygen atoms have reduced coordination means that they may be more
414 reactive than "bulk" oxygen, so that a reaction can occur in the first monolayer even if it is not thermodynamically favorable in the bulk (e.g., for monolayer films of Fe [42]).
2.3. Experimental Procedures Most of the metal-on-TiO2 experiments reported here have been carried out under ultrahigh vacuum (UHV) conditions, with base pressure --1 to 2 x 10 -10 Torr. The TiO2 substrates used most often are bulk rutile TiO2 crystals with polished surfaces [(110), (100) etc.]. They are annealed in UHV for hours so that the bulk is reduced enough to become conductive; this ensures that the oxide samples are free from charging problems. The stoichiometric surface region is restored by annealing the sample in oxygen (--2 x 10 -6 Torr) followed by cooling in oxygen. Other surface preparations include sputtered thin films, MBE-grown TiO2 films [48], anodically grown TiO2 films [49], films grown by atomic layer epitaxy (ALE) [50] and epitaxial films of Ti suboxides [51]. Anatase TiO2 crystals have been grown [52], but no studies of metallic overlayers have been reported. The metal overlayer films studied in most of this work are deposited from metal evaporation sources at a rate of 1 to 3 A/min; at Rutgers, we use a liquid nitrogen cooled thermal evaporator source. Accurate determination of deposited film thicknesses is essential for meaningful measurements of growth modes. For our studies, film thicknesses are measured using a quartz crystal monitor (QCM) [15]. The QCMs are calibrated using Rutherford backscattering (RBS), which gives the true thickness. The reported thicknesses are generally average values in angstroms (A), for which uniformly thick films with the appropriate bulk density are assumed. o
The various electron-, ion- and optical- spectroscopic methods used for characterizing the metal-TiO2 interactions are discussed in the following paragraphs.
2.4
Growth Modes for Metals/TiO2
The majority of studies of metal films deposited onto TiO2 have focused on the initial stages of growth, i.e., for average metal coverages ranging from fractional monolayer coverages to tens of monolayers. Details of specific
415 metallic overlayers on TiO2 are given in Section 3, below. In the present section, and in the remainder of Section 2, we provide a broad overview and intercomparison between the different systems studied. The most extensive measurements have involved the growth of a series of transition metals on TiO2(ll0) surfaces, studied using Low Energy Ion Scattering (LEIS) together with X-ray Photoelectron Spectroscopy (XPS). This is a powerful combination for studying ultrathin film growth: because of the high sensitivity of LEIS to the atomic composition in the topmost layer [14, 15, 53], one can separate 3-D island (VW growth) from the layer + island (SK growth) and layer-by-layer (FM growth) modes by identifying the coverage necessary to complete the first monolayer. Figure 3 illustrates the use of LEIS (He +, 1 KeV incident energy) for characterizing the initial growth [15]. The attenuation of the substrate Ti (LEIS) signal is shown for increasing coverages of Cu, Fe, Cr or Hf deposited onto TiO2(110) at 300K. The intensities are normalized to the value for the clean TiO2 surface. The attenuation of the substrate signal is an upper limit for the covering of the surface by overlayer atoms. For complete covering (wetting) of the substrate by the metal overlayer one would expect a linear decrease, with the signal approaching zero at monolayer coverage (--2-3 ,~). Such behavior is observed for Hf on TiO2 and in the initial stages of Cr depoCu 1.0
rG)
A
-"
0.8-
Fe
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_
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-9 0 . 2 0 Z 0,0
Hf --
I
0
I
2 Overlayer
Figure 3:
I
4
I
I
6
Thickness
8
I
1(
(ML)
A comparison of the wetting trends of Hf [15], Cr [15], Fe [15], and Cu [54] on TiO2(110). Depositionwas carried out at room temperature. From [15].
416 sition in Fig. 3, but is very different from the behavior for Fe and Cu shown in Fig. 3. In the case of Cu, the fact that a LEIS substrate signal isvisible up to high average coverages is clear evidence for Volmer-Weber (3-dimensional islands) growth [54]. In the case of Cr, the LEIS signal initially is attenuated linearly up to a point where -80% of the substrate is covered [47]. It appears that Cr grows in a quasi-two-dimensional fashion, where the first monolayer covers -80% of the substrate. For higher Cr coverages, the growth of the Cr film deviates from 2-D growth and becomes 3-dimensional. The growth behavior of Cr/TiO2 is similar to that reported for Cu/ZnO [55]. In the case of Fe at 300K, the film grows clearly in 3-D islands initially, and its wetting ability is intermediate between that of Cr and Cu. Schematics of the initial growth modes are shown at the side of Fig. 3. Direct microscopic evidence for the formation of Cu, Au and Pd nanoclusters (VW growth) on TiO2 has been obtained using STM and high resolution scanning electron microscopy (HRSEM) [56-58]. Cu and Au clusters appear to nucleate on TiO2(ll0) terraces, whereas Pd clusters are formed preferentially near atomic steps [58]. In recent papers [59-61], there is evidence that 2D growth may occur at very low coverages ( 1ML, The Ti 4+ cations are reduced to lower oxidation states; charge transfer is from the Na oveflayer to the substrate. The work function is observed to decrease with coverage reaching a minimum after the deposition of 0.5ML Na. This is consistent with charge transfer from Na to the substrate due to a strong interaction between Na and O. The large dipole - dipole repulsion expected to be present in this coverage regime may explain the lack of order below this coverage. Using resonant photoemission, Nerlov et al. [84] report states at the Fermi level which show the resonant behavior expected for Ti 3+ states due to the alkali-metal-to-substrate charge transfer (seen also by Prabhakaran et al. [68]). In a low energy D + study of alkali-metal (Na, K and Cs) adsorption on T i O 2 ( l l 0 ) , Souda et al. [77] suggested that the alkali metals (AM) are "perfectly" ionized for lower coverages with an ionic-neutral transition of the AM overlayer taking place after -0.5 ML coverage, the point where the work function is minimum. It has been shown that the Na promoted surface can lead to the dissociation of NO and the formation of a carbonate after exposure to CO2 [76]. Since neither NO nor CO2 adsorbs on the clean surface, this is a clear indication of how an alkali metal can enhance the catalytic activity of TiO2(110). Murray et al. [26] showed recently (in an STM study of reduced (1 x 2) surfaces of TiO2(110)) that Na adsorbs in three-fold coordinated sites adjacent to the bridging-O row, forming a p(4 x 2) overlayer. Adsorption on areas of the surface containing a 2 x 2 superlattice suggest that Na adsorbs in a site with a four-fold coordination to oxygen; this is accompanied by Na-induced substrate restructuring.
3.1.1.2
K/Ti 0 2
TPD studies indicate that multilayers of K can be grown on TiO2(110) at 140K [69]. The saturation coverage at room temperature was reported to be 1ML although unstable multilayers can be grown using high fluxes [78, 85]. This is consistent with temperature programmed desorption (TPD) results which show that the multilayers are desorbed around room temperature [69].
424 LEED studies [69, 70, 77, 85] show no evidence of any ordered structures for K deposited at 140K or RT. A c(2 x 2) structure was reported when multilayers of K deposited on TiO2(110) at 140K are annealed between 650 and 750K [69], however no ordered structures were observed in LEED and RHEED when K was deposited on TiO2(110) at RT and annealed up to 900K [70]. On TiO2(100), based on SEXAFS measurements, the preferred adsorption site for K at fractional monolayer coverages is identified as a bridge-site bonded to two oxygen atoms [68]. UPS and XPS studies show that K interacts strongly with the (110) substrate causing a reduction in the Ti 4+ cations for fractional monolayer coverages [70, 78, 85]. The bonding for coverages below 1/2ML is reported to be predominantly ionic with charge transferred from K to the substrate [77, 78]. At coverages > 0.5ML the bonding becomes increasingly covalent in nature with a smaller ionic contribution [77, 78]. Hayden and Nicholson [69] reported the presence of metallic potassium on TiO2(110) for coverages > 1ML as evidenced by the appearance of a 2.7 eV surface plasmon in their ellipsometric measurement. Heise and Courths [78] also reported the presence of potassium (2p) plasmon losses which disappeared with the desorption of the multilayers. These two studies indicate that the first K layer is non-metallic in nature but that the thicker layers are metallic. These results are in contrast to those of Lad and Dake [70] who reported the absence of metallic potassium even at higher coverages. They [70] also reported that the multilayers of K20 formed at room temperature were stable under annealing up to 900K. Further work is needed to sort out the relative roles of lattice oxygen, and oxygen from other sources, in oxidation of multilayers of K. TPD results [69] show that the K multilayers are completely desorbed at -370K and the single monolayer at -- 750K. Heise and Courths [78] reported that 0.27ML K starts to desorb at 650K and is completely desorbed at 1000K. They also suggested that the desorption species are most likely KOx rather than K ions.
3.1.1.3
Cs/Ti02(llO)
TPD results [8] indicate that multilayers of Cs can be grown on T i O 2 ( l l 0 ) at 170K. The multilayers desorb at temperatures around 300K,
425 leaving behind one layer of Cs. At least 0.5ML of Cs is stable under annealing up to 800K. Low energy D + scattering studies [77] and work function and bandbending changes as a function of Cs coverage [8] indicate that the bonding is ionic at low coverages. As for Na and K, charge is transferred from Cs to the substrate. As in the case of K/TiO2(110), there is a transition from an ionic to covalent bonding at a coverage > 0.5ML.
3.1.2
Al/Ti02
XPS and AES studies show that for coverages up to 1ML, A1 is completely oxidized and wets the TiO2(ll0) surface [63, 86]. Concomitantly, the Ti4+ cations in the near surface region are reduced. For thicker coverages (> 6ML A1), a mixture of metallic and oxidized aluminum is observed. LEED [86] and RHEED studies show no evidence of ordering of the overlayers. The LEED pattern from the substrate is completely obscured for A1 coverages as low as 0.5ML, indicating that A1 disorders the substrate. XPS shows that metallic aluminum films are oxidized after flash heating of samples containing both metallic and oxidized A1 to 500~ The oxidation involves the diffusion of oxygen from the bulk which also re-oxidizes the reduced TiO2(ll0) [63]. These results all indicate that charge transfer is from A1 to the substrate. Experiments conducted on the reduced (oxygen deficient) substrate show similar behavior. In spite of the oxygen deficiency and although valence states lower than Ti4+ are present initially, the A1 is still oxidized. Surprisingly, Carroll et al. [87] report that A1 deposited at 300K onto faceted TiO2(100) surfaces grows in island form, and appears to remain metallic; the conclusions are based on STM observations.
3.2
3.2.1
Transition Metals on TIO2(110)
Ti/Ti02(110)
The deposition of 4A Ti on TiO2(ll0) results in the formation of an interface -12A thick composed of reduced titanium oxides [44]. Beyond this coverage, Ti grows on top of the reduced region with the LEIS intensity of oxygen being completely attenuated after the deposition of-~ 22.~ of Ti. XPS
426 spectra taken at these coverages indicate the presence of metallic Ti overlayers. The reduction in Ti cations and transition to metallic overlayers are observed at equivalent coverages for growth at both 150K [44] and 300K [88]. XPS reveals the onset of oxidation of the metallic Ti overlayer after a short anneal at 800K. This oxidation occurs presumably through the diffusion of oxygen from the substrate [44]. It has been found that the stoichiometric surface can be restored by annealing to 900K for greater than 30 minutes in an oxygen background (P > 1 x 10 -6 mbar) irrespective of the initial Ti concentration [88].
3.2.2
Hf/Ti02(11 O)
At room temperature, the Ti LEIS intensity shown in Figure 3 decreases linearly and is completely attenuated after the deposition of 1 ML H f . At the same time, the Hf LEIS signal increases linearly before reaching a plateau at 1 ML Hf [15]. Since LEIS is sensitive to the topmost layer, these results indicate that Hf grows two-dimensionally and completely wets the TiO2(110) surface after deposition of 1ML Hf. XPS spectra taken of the Ti 2p peak before and after the deposition of 7 ML Hf are shown in Figure 4. The sharp Ti 4+ feature of the stoichiometric surface is altered substantially with the appearance of low-binding energy features in the spectrum. These features are due to the formation of lower oxidation states (Ti x+, x < 4). The first monolayer of Hf deposited onto the 300K surface is fully oxidized to HfO2. Further deposition of Hf results in formation of lower oxidation states of Hf; for Hf coverages >10.~, metallic Hf appears at the surface [15]. The total thickness of the disturbed layer formed by deposition of Hf (i.e., from TiO2 through reduced Ti oxides, to reduced Hf oxides, to metallic Hf) is of order 20A.
3.2.3
V/Ti02(11 O)
Sambi et al. [45] studied the growth mode for 5ML V on TiO2(110) using XPD. They reported that V grows as 3-dimensional islands. The sharp LEED (1 x 1) pattern from the stoichiometric surface is reported to become dimmer and the background intensity increases after deposition of 0.15 ML V, indicating rapid disordering of the substrate [46].
427 However, from their XPD studies, Sambi et al. [45] reported that the islands formed after deposition of a few monolayers of V have a bcc(100) structure. From an analysis of their XPS azimuthal intensity data for V 2p and Ti 3p, they inferred that the [001] azimuth of the overlayer is aligned with [110] of the substrate. The absence of a LEED pattern was interpreted to mean that there was no long range order in the V overlayer, although the XPD data indicated short range local order. UPS and XPS studies show that there is a vigorous interaction between V and the substrate immediately after V deposition [46]. The O 2p valence band is observed to shift away from the Fermi level after adsorption. The valence band motion is similar to that observed for a reduced TiO2(110) substrate. This indicates that charge is transferred from V atoms to Ti cations in the substrate, an interpretation supported by work function measurements which show similar trends as for the alkali-metals. UPS spectra show that the densityof-states at the Fermi edge increases with V coverage, becoming more metallic like at monolayer coverage, while XPS shows that the V 2p core levels are close to the value for metallic vanadium. The work function curve also approaches the value for metallic V at--2ML. Combining the results of references [45] and [46] reveals that after V deposition, there is a formation of a thin layer of mixed Ti-O-V composition upon which metallic V islands grow. The valences of the oxidized V are inferred from thermodynamic arguments to be 2+ and 3+; the TiO2 is reduced to Ti3+ at the interface [46]. LEED studies show that after annealing the 2ML V/TiO2 substrate, the surface is still disordered. However, both the Ti-O-V oxide monolayer and the metallic V layer formed on top of it are unstable upon annealing. At 573K (5 min. anneal), the V AES peak is reduced by 50%. This peak continues to decrease and eventually disappears with time. Since the vapor pressure of V is 10 -18 torr at this temperature, desorption is ruled out. Since clustering of the V atoms will not lead to complete attenuation of the V AES signal, the conclusion is that the V atoms diffuse into the bulk at this temperature [46]. Experiments performed on previously reduced TiO2 show that there is only a weak interaction between the substrate and V [46]. UPS and XPS show no oxidation nor reduction of the substrate; only metallic V particles are
428 formed at the interface. No work function changes are observed (work function of reduced TiO2 is the same as for V). Annealing also does not order the surface, but bulk diffusion is observed. These results can be understood as follows. Reduced Ti cations in Ti203 and TiO have stronger affinity for oxygen than Ti 4+ in TiO2; further reduction by V is thermodynamically unfavorable.
3.2.4
Cr/Ti02(110)
At room temperature, Cr initially grows two dimensionally on TiO2(110), covering about 80% of the substrate after deposition of an average thickness of 2,~; cf. Fig. 3. The growth proceeds three dimensionally beyond this thickness [47]. A structural study carried out using LEED, MEED and ARXPS shows that Cr grows in a bcc[100] orientation on the TiO2(110) surface with the bcc [001 ] of the overlayer parallel to [001] of the substrate [65]. The Ti scattering peak in LEIS experiments is completely attenuated after the deposition of ~9,~ of Cr on the TiO2(110) surface. However the oxygen peak is still present at this coverage. In order to identify the mechanism by which oxygen appeared on top of the Cr overlayers, Cr was also evaporated on a specially prepared 180_enriched stoichiometric TiO2(110) surface. The LEIS spectrum recorded after deposition of the same amount of Cr showed the presence of 180. This is clear evidence that the deposited Cr atoms are not being oxidized by the ambient oxygen but are rather in dynamic exchange with the O atoms from the substrate. XPS studies show that the Ti cations are reduced upon Cr adsorption with the Cr 2p peak showing evidence for oxidation at fractional monolayer coverages [47]. This oxidation may be due to charge transfer at the interface which also explains the reduction of the Ti; however, the exchange process between O and Cr could also contribute to this effect. The work function of the Cr/TiO2(110) system exhibits similar trends as for the other elements discussed; it decreases with Cr coverage reaching a minimum before increasing to a plateau value consistent with the bulk value for Cr [47]. This observation is consistent with charge transfer from the Cr atoms to the substrate at low coverages.
429 No changes were observed in the XPS intensities of Ti, O or Cr during annealing up to 300~ This suggests that the films are stable up to this temperature. Upon annealing at 500~ surface diffusion and growth of metallic Cr clusters compete with oxidation and dissolution of Cr in the bulk TiO2. At 600~ the overlayer Cr becomes fully oxidized; upon prolonged annealing, the Cr appears to dissolve into the bulk TiO2 [47]. Growth studies performed on the heavily argon-ion-sputtered surface (oxygen deficient) show that the wetting of the surface is less effective for the sputtered surface as compared to the stoichiometric surface. This was correlated (using XPS) to less strong chemical interaction at the Cr-TiO2(110) interface [47].
3.2.5
Mn/Ti 0 2 ( l l O)
There have been no detailed studies of the growth mode for Mn on TiO2(ll0). However, based on the reactivity between Mn and T i O 2 ( l l 0 ) observed in their soft X-ray photoelectron spectroscopy (SXPS) and X-ray absorption (XAS) studies, Diebold and Shinn [73] suggested that Mn may initially wet the substrate. For fractional monolayer coverages deposited at room temperature, the Ti 3p peak in the SXPS spectrum is broadened, indicating that the Ti cations are reduced from +4 to lower oxidation states. At thicker average Mn coverages (>17.~) the Ti 3p peak is almost fully attenuated in the SXPS spectrum and the binding energies of the Mn 3p and valence states at the Fermi level are characteristic of a metallic Mn overlayer. XAS data obtained from films of similar thickness are consistent with this interpretation. Evidence for the partial reduction of the Ti cations seen at low coverages in SXPS are also observed for thicker films using XAS. The Mn films are unstable at 650~ After annealing at this temperature, the Ti 3p peak re-emerges in the SXPS spectrum and becomes narrower suggesting that the Ti cations are being re-oxidized. The electron excited LMM Auger transition of Mn, monitored as a function of temperature, remains constant up to 500~ and then drops sharply and remains at a non-zero value between 550 and 600~ This drop is related to the thermal evaporation of metallic Mn. Analyses of XAS spectra indicate that local order is increased at the interface and that oxidized Mn2+ ions remain on the surface after the
430 thermal desorption of metallic Mn. The authors of this study relate the chemical and structural changes to the formation of a crystalline ternary surface oxide MnTiOx(x < 4) [73].
3.2.6
Fe/Ti02(110)
LEIS data obtained from Fe deposited onto TiO2(l10) at room temperature are shown in Figure 3. It is clear from the figure that the substrate is still exposed even after 8,~ Fe has been deposited [42]. This indicates that in the initial stages, Fe islands grow on TiO2(ll0). This is different from the reports of a layer-by-layer growth mode for this system based on AES measurements [89]. For growth at 160K, the mobility of the Fe atoms is reduced sufficiently so that Fe forms a complete layer on the substrate [42]. Weak long range order is seen in LEED, for several monolayers of Fe deposited onto TiO2(l10) at 300K; moreover, ARXPS data shown in Figure 6(a), and 2-D medium energy backscattered electron diffraction (MEED) show clear evidence for a locally ordered bcc(100) structures on both stoichiometric and Ar+ sputtered TiO2(ll0) surfaces [65]. The arrangement is that Fe(001)II (001) of the substrate. Although the LEIS signal from Ti is completely attenuated after the deposition of--16,~ Fe on TiO2(110), an oxygen signal is still present in the LEIS spectra for much thicker average coverages [42, 89]. As in the case of Cr discussed earlier, it has been shown that the presence of the oxygen is partly due to diffusion of oxygen from the substrate [42]. XPS [42], UPS [89, 90], inverse photoemission [90], and SXPS [91] studies show that interfacial Fe adatoms are oxidized, with electrons transferred from Fe to the substrate, causing the reduction of Ti cations. UPS [89] studies indicate that Fe 3+ and Fe2+ are formed in the early stages of deposition along with Ti3+. SXPS from shallow core levels and the valence band show that Fe starts to exhibit metallic character at an average coverage of--0.7 ML. Two well-separated defect states appear in the bandgap of TiO2 at Fe coverages well below 1 ML. Based on the use of resonant photoemission to study the partial density of states, the defect states are identified as Fe-derived and Ti-derived, located at the Fe and Ti sites, respectively. It is suggested that a position change of surface oxygen is involved in bonding of Fe to TiO2(110) [91].
431
/
I
.c
V
v
along [001]
X
20
10
0
10
20
30
40
50
t
I
60
70
angle (degree from normal)
0~
26 ~
45 ~
A
| |
t
9
@
bee (100)
Figure 6:
(a) ARXPS spectra obtained from Fe/TiO2(110), (b) Schematic of "forward focussing" of XPS from bcc(001).
XPS and LEIS (using He and subsequently Ne as the probe ions) show that the Fe islands are encapsulated by TiOx suboxides after annealing at 500~ for--2 hours, [92]. The interaction of Fe with reduced substrates (produced by Ar+ bombardment) is somewhat complicated [42]. Fe wets a partially reduced substrate better than it does the stoichiometric surface; Fe wets a more fully reduced substrate less well than it does the stoichiometric surface. XPS shows that Fe oxidation still occurs. The wetting appears to be controlled by a competition between surface diffusion on the roughened substrate, and interface reactivity.
432
3.2.7
Rh/Ti02(11 O)
Rhodium forms three dimensional islands on TiO2(110) [71]. The metal is only weakly bound to the oxide surface [93]. Using AES in combination with Ar+ ion sputtering, Sadeghi and Henrich [94] showed that the rhodium islands (formed by deposition of 1.5 to 4 ML of Rh onto TiO2(ll0)) are encapsulated by TiOx suboxides after annealing at 673K. Linsmeier, Kn/Szinger and Taglauer [49] have verified using LEIS that Rh particles supported on an amorphous TiO2 film are encapsulated upon heating to 750K, regardless of the presence or absence of hydrogen. They also report that encapsulation cannot be reversed by an oxidation/reduction cycle. EELS, AES and UPS studies of Rh deposited on stoichiometric TiO2 at 300K indicate no evidence for an interfacial reaction. The results are different for a TiO2(ll0) substrate that has been reduced by ion bombardment to remove oxygen preferentially. For Rh on reduced TiO2(110) surfaces, there is a net oxidation of the surface Ti3+ cations [93]. Electrons are transferred from the reduced Ti cations in the substrate to the rhodium overlayer. The Rh-Ti bond is partially ionic with Rh being negatively charged. Other aspects of Rh/TiO2 are discussed in [95, 96].
3.2.8
Ni/Ti02(llO)
There have been two independent reports [97, 98] of a Stranski-Krastanov growth mode for this system; Ni islands are reported to grow on top of one complete Ni layer which forms on the TiO2(110) substrate. However, the techniques used in both cases (XPS [97] and AES [98]) cannot be used to determine unambiguously the growth mode of a particular system. In fact, it appears surprising that Ni would form a complete monolayer on this substrate in the absence of a strong interaction between Ni and the substrate; none of the elements neighboring Ni (Fe, Cu, Pd) exhibit SK growth [15, 42, 99]. From LEED studies, Wu and Moller [98] determined that the Ni islands are oriented in two ways, and that both have the fcc (111) orientation. One is oriented with (lll)N i II (ll0)TiO~, [10T]Ni II [001]T~O~and the other is tilted with respect with the surface plane with (131)N i II (ll0)TiO: II [101]N i II [001]TiO .
433 Based on an AES study of Ni deposited onto an oxidized Ti substrate, evidence for encapsulation of Ni following annealing in H2 was reported [100].
3.2.9
Pd~i02(110)
LEIS studies indicate that Pd grows as three dimensional clusters on TiO2. LEED, MEED and ARXPS studies conducted on 20 ,~ Pd/TiO2(110) show that the overlayers are oriented with the fcc(111) plane parallel to the (110) substrate [99]. An STM image showing Pd clusters on TiO2(110), from the lab of D. W. Goodman [58], is presented in Fig. 7. No evidence for any interfacial reaction between Pd and the substrate was obtained from XPS studies, similar to data for Cu shown in Fig. 4. The clusters grow larger with annealing in the temperature range 300 to 475K. After annealing up to 775 975K in UHV, Pd clusters are encapsulated by TiOx sub-oxides [99]. 50
nn~.135 2.002 1.869 1.735 1.602 1.468 1.335 1.201 1.068 0.934 0.801 0.667 0.534 0.400 0.267 0.133 0.000
40 3O 20 10
0
10
20
30
40
50
nm
Figure 7:
STM image of 0.2 ML Pd/TiO2(110), from C. Xu and D. W. Goodman [58].
Evans, Hayden and Lu have used LEED, XPS and FT-RAIRS of adsorbed CO to study Pd layers on TiO2(ll0) [101]. Measurements of the intensities of CO stretching vibrations provide insights into the local structure of Pd particles as a function of Pd coverage, deposition temperature, and annealing temperature. Low coverages of Pd (32.~), the fcc(111) overlayer consists of two equivalent domains rotated by 180 ~ with respect to each other. XPS studies of Pt deposited onto the substrate at 300K show no evidence of any interfacial reaction between Pt and the substrate [67, 74]. Schierbaum et al. [102] report that metallic Pt exhibits electron acceptor properties and causes Schottky barrier formation at the Pt/TiO2 interface, at temperatures below 700K. Evidence for quasi-2D growth of Pt at fractional monolayer coverages at 300K, prior to the appearance of 3D growth, has also been reported [74]. Pt clusters on TiO2 substrates are prototypical systems for the so called Strong Metal-Support Interaction (SMSI) effect, in which the Pt clusters are coated with a reduced Ti oxide, TiOx, after annealing in a reducing at atmosphere [4, 103, 104]. After depositing Pt onto TiO2(ll0), annealing to temperatures above 450K in vacuum results in the encapsulation of the Pt clusters by TiOx suboxides [72]. LEIS spectra recorded by Pesty et al. [72] after annealing a 8.8 .~ deposit of Pt on TiO2(110) to 800K are shown as a function of cumulative annealing time in figure 8a. It is clear that the Pt signal decreases with anneal time and that for sufficiently long times, the stoichiometric surface is recovered. XPS shows that metallic Pt is still present (Pt does not desorb at this temperature) and it is inferred from the absence of significant changes in the Pt 4f line shape that Pt clusters remain intact and that interdiffusion at the interface does not occur [72]. Figure 8b shows the effect of replacing the He + probe ions with Ne + ions that are massive enough to sputter off the suboxides and still retain a sensitivity to Pt. Initially, the suboxides are sputtered off and the Pt intensity increases to a maximum. Increasing exposure to the Ne ions beyond this point results in the
435 removal of Pt from the substrate. A schematic of the encapsulation process is shown in figure 8c.
I
i
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i
30 m
"
3
20
I
7.1 A
.&
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-
30 min.@ 800 K. l-keY Ne+ .
kA
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15
|
I
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I
1
2
3
4
5
6
7
Fluenee (10!6 ions/em2) 300 400 500
600 700 800 900 1000 1100 Energy (eV)
(a)
(b)
WiOx Gxxx.x,.,x\ x~TiO 2 T > 450 K
(c) Figure
8:
Encapsulation of Pt by TiOx suboxides; (a) LEIS of 8.8A Pt/TiO2(110) annealed
to 800K, (b) Pt signal is recovered after Ne sputtering of the suboxides, (c) schematic of the encapsulationprocess. Taken from reference [72]. Schierbaum et al. [74] have reported that encapsulation of the Pt clusters by TiO2 suboxides does n o t occur upon annealing. Their evidence is based on LEIS studies of Pt deposited onto a TiO2(l10) substrate that has not been previously reduced extensively by heating in vacuum. In addition, Gao et al. [48] have reported that Pt deposited onto stoichiometric, MBE-grown defectfree TiO2(100) is much more thermally stable than Pt deposited onto vacuumreduced TiO2: no evidence for encapsulation by suboxides of TiO2 is found using XPS. These results suggest that diffusion of oxygen vacancies from the bulk to surface may play a critical and (to this time) unappreciated role in promoting reduction to TiOx(x10 on clean vacancy-free TiO2(110) surfaces, to 10 in the presence of oxygen vacancies, to 1 in the presence of carbonaceous impurities. 3.2.13
Au/Ti02(110)
The LEIS Ti signals recorded as a function of average Au thickness for deposition at 160, 300 and 450K are shown in Figure 9 [61]. During the initial stages of growth for a fractional monolayer of Au (thicknesses < 1 ' ) , the substrate Ti signal follows a slope close to that expected for 2D growth
438 (dashed line). At higher coverages, the growth exhibits 3D behavior. This conclusion is similar to that reported for Ag [59, 60], and similar results have been seen also by Campbell et al. [108] for Au/TiO2. For deposition at 475K, the slope of the LEIS data (Fig. 9) indicates that 3D growth occurs at all cov-
1.2 . ~
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, ~-- 475K D 300K
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~
.~
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I
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,
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,
15
Average Figure 9:
I
30
,
I
45
,
60
Au Thickness(~)
Low energy ion scattering (LEIS) data for Au deposited on TiO2(110) at (a) 160K (b) 300K and (c) 475K. The data provide evidence for 3D growth at high coverages [61].
erages. The 2D growth seen at low temperatures and very low coverages is due to kinetic effects rather than thermodynamic effects. It is clear in Fig. 9 that at all temperatures studied, the substrate is still exposed well after 10,~ of Au has been deposited. This indicates that the growth is three dimensional under these conditions. The LEIS results [61] have been corroborated by our STM and SEM studies of this system [57]. A HRSEM image corresponding to 10,~ of Au deposited onto TiO2(110) at 300K is presented in Fig. 10, where evidence for 3-dimensional Au clusters is seen clearly [109]. From Figure 9, it should be noted that the substrate is more effectively covered by Au at lower than at higher temperatures. This indicates that diffusion is slower at 160K as compared to 300 or 450K. As mentioned in
439 section 3.2.11, this behavior is quite different from that reported for Cu/TiO2(110) [54]. Weak hexagonal LEED patterns are reported for thicker films (>20/k) grown on TiO2(110). These results along with ARXPS [57] indicate that Au grows in the fcc(111) orientation on the substrate with [111] of Au parallel with [110] of TiO2(ll0). This conclusion is further supported by recent electron backscattering measurements on single Au clusters in a HRSEM instrument [109]. XPS studies [61] show no evidence of any interfacial reaction between Au and the substrate. After annealing the substrate to 500~ the Au islands grow larger and no encapsulation is observed. It is interesting to note that Au/TiO2 is an active catalyst for CO oxidation at low-temperatures [110], and is also an active sensor for detection of CO in air [3].
440
Figure 10:
HRSEM images of 10A Au/TiO2(110) obtained after deposition at 300K [109].
441 Table 2"
Metal Overlayers on TiO2(110)
Metal
Interfacial Reaction
Growth Morphology (Technique)
Structure
Na
Reduced TiOx Na20 units
Atomic layer formed
c(4x2) at 0.5ML
K
Reduced TiOx
Layer Growth (TPD)
c(2x2) 650-750K
,
Cs
(XAES)
Thermal Stability
26, 66, 76, 77, 84 Desorbs as KOx
Layer Growth (TPD)
Ai
Reduced TiOx OxidizedA1
Ti
Reduced TiOx Metallic Ti at high coverage
1-If
Refs
1/2ML stable up to 800K
69, 70, 77, 78, 85 8, 77
Disorder
A1203 formed 63, 86 at 800K
Metallic clusters on oxide interface (LEIS)
Disorder
stoichiometric TiO2 at 900K
44, 88
Reduced TiOx
HfO layer covers substrate (LEIS)
Disorder
Hf completely oxidized
15
Reduced TiOx V 2+ or V3+
3D islands (XPD)
V(IO0)
Diffusion into substrate
45, 46
i
Cr
Reduced TiOx
Mn
Reduced TiOx Formation of Mn2+
Fe
Reduced TiOx
Rh
Metallic Rh
Ni
No Reduction Metallic Ni
Pd
No Reduction Metallic Pd
3D islands (LEIS)
Pd(lll)
Encapsulation 58, 99, 101
Pt
No Reduction Metallic Pt
3D islands (LEIS)
Pt(lll) 2 domains
Encapsulation 67, 72, 74, 102, 105
Cu
No Reduction
3D islands (LEIS, STM)
Cu(lll) 2 domains
Clusters grow
2D islands (LEIS)
Cr(100)
i
Metallic Cu
3D flat islands (LEIS)
Fe(100)
3D islands
Oxidized at 873K
47, 65
Formation of MnTiOx; desorption of metallic Mn
73
Encapsulation 42, 65, 89, 90, 91, 92 Encapsulation 49, 71, 93, 94, 95, 96
Ni(111) and Encapsulation 97, 98, tilted Ni( 11 I) 100
|
Ag
No Reduction Metallic AI~
3D islands (AFM, optical scattering)
Au
No Reduction Metallic Au
3D islands (LEIS, STM, SEM)
Au( 111 )
31, 54, 56, 64, 65, 90, 106, 107
Clusters grow
59, 60
Clusters grow
57, 61
442 Table 3"
Metal Overlayers on TiO2(100) and (001).
Metai/Ti02(lO0) Interracial reaction
K/TiO2(100) AI/TiO2(100) Ni/TiO2(100)
Rh/TiO2(001)
4.
Reduced TiOx Metallic A1 at low coverages
Growth morphology (technique)
Structure
SK (AES)
C(2 x 2) at 0.5ML
VolmerWeber (STM) SK (3 layers + Islands) (SEM and SIMS) VW (STM)
Thermal Stability
Refs 68, 83, 109,
110 Film oxidized 87 after heating to 1000C 114
115, 116
S U M M A R Y AND O U T L O O K
Summaries of al! of the elements discussed in this review are given in Figure 5, and Tables 2 and 3. The data indicate clearly that interfacial chemistry strongly affects film morphology in the initial stages of growth. Metals that are highly reactive towards oxygen wet and cover stoichiometric TiO2 substrates in the initial growth stages; these include alkali metals (Na, K, Cs), A1, and early transition metals. Metals that are relatively unreactive to oxygen (Cu, Pd, Pt, Au) mainly form three-dimensional clusters and do not wet the substrate effectively. Mid-transition metal elements (Fe) also grow as clusters, with flattened islands. Whereas much is known about metal/TiO2 interactions, there are many issues that remain as challenges for future studies. These include *the role of steps and point defects in metal nucleation and growth, *flux and temperature-dependent microscopic studies of nucleation and growth, *details of island shapes, sizes, and thicknesses, *atomic beam studies of metals on oxides, to measure residence times and binding energies, *the relative roles of cation and anion diffusion on thermal stability [111]. *the stability of faceted TiO2 surfaces when covered by metals,
443
*the role of impurity atoms (e.g. W or Mo) on growth of metals such as Fe or Au: can a high density of nuclei and better wetting be achieved by predosing with certain impurities? *electron spectroscopy of non-metal to metal transition in ultrathin films,
*correlation of film growth with electrical conductivity; percolation, *theory of metal bonding to TiO2 surfaces. There are multiple challenges for the coming years! ACKNOWLEDGEMENTS
The authors acknowledge valuable discussions with C. T. Campbell, F. Cosandey, U. Diebold, D. W. Goodman, and Lei Zhang. This work has been supported in part by the U. S. Department of Energy, Office of Basic Energy Sciences. REFERENCES
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448
9 1997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
Chapter 12 Intrinsic stress of epitaxial thin films and surface layers
R. Koch Institut for Experimentalphysik, Freie Universit~it Berlin, Arnimallee 14, D- 14195 Berlin, Germany
1. INTRODUCTION Future application of thin films in nanoscale technology substantially tightens the demands on stability as well as on structural and compositional integrity and ultimately necessitates the fabrication of high quality single crystalline films. A preparation technique, that in the past definitely has proven its capability to meet these high standards, is molecular beam epitaxy (MBE). Here the single crystalline films are deposited at well-defined UHV conditions by directing an atomic or molecular beam onto single-crystalline substrates, which determine the epitaxial orientation of the films. A major obstacle arises from the fact that usually the equilibrium lattice dimensions of the films differ by a few percent from that of the substrates, so that the films have to be strained to grow in complete registry. Frequently an intermediate layer grows pseudomorphically, i.e. with the lateral lattice constants of the substrate, which introduces huge intrinsic stress into the films. As a rule of thumb, misfit of 1% gives rise to misfit stress in the GPa range, which exceeds the tensile strength of common metals (= 0.2 GPa) by at least a factor of ten. Therefore misfit stress may have crucial impact on the reliable performance of technological thin film devices, namely by reducing their life-time and altering their physical properties. The majority of intrinsic stress investigations reported so far in literature deals with polycrystalline films. Meanwhile a detailed understanding of the relevant stress mechanisms has been achieved that relate the intrinsic stress to microstructural features characteristic of the growth of polycrystalline films. For reviews on that topic the reader is referred to recent articles by Abermann [1], Doerner and Nix [2] or myself [3].
449 The intrinsic stress of epitaxial thin films, on the other hand, is a rather new and still growing field of research. Therefore considerably less experimental data hitherto are available on the stress behaviour of epitaxial thin films. The main source of stress upon epitaxial growth certainly arises from the misfit between the lattices of film and substrate. Recent experiments disclose already a number of different possibilities for the films to respond to the misfit. Moreover the results clearly indicate that the mechanisms for relaxation of the misfit strain are strongly dependent on the particular mode, in which the epitaxial films are grown (VolmerWeber, Stranski-Krastanov, Frank-Van der Merwe modes, non-equilibrium growth, etc.). When speaking of stress of a few monolayers, however, it is not justified to generally apply the concept of misfit, which besides usually is calculated with the lattice constants of the respective bulk phases. Particularly for some examples of Stranski-Krastanov growth it appears more appropriate to think in terms of surface stress or changes of surface stress. In the following a survey is given on the stress of epitaxial systems available at present in the literature. Emphasis is laid on a thorough discussion of the underlying atomistic mechanisms responsible for the occurrence of stress as well as their relation to growth mode features. Section 4 and 5 deal with epitaxial films grown in equilibrium and in the presence of Ehrlich-Schwoebel-barriers, respectively. Section 6 summarises present results on the stress of surfaces as well as changes of surface stress due to adsorption from the gas phase. To facilitate the entire discussion a short introduction to the calculation of the tensor components of film and surface stress is given in section 2, whereas section 3 describes the main experimental techniques used to measure stress and strain of ordered films and surface layers. The review is concluded by summarising remarks in section 7.
2. N O M E N C L A T U R E , D E F I N I T I O N S OF STRESS 2.1. Intrinsic stress of thin films in one dimension
When thin films are in a state of stress, their actual dimensions ~ length 1F, width w F and thickness t F ~ deviate from the respective equilibrium dimensions IF,0, wF,0 and tF,0. Consequently the films alter their dimensions parallel as well as perpendicular to the film plane when they are removed from the substrate. This is illustrated in Fig. 1 for uniaxial stress in direction of the long substrate axis. Quantitatively, stress in thin films is defined analogous to stress externally applied to bulk materials. It is equal to the forces acting on the film divided by its crosssection wFtF. The film stress ~ is related to the film strain ~ = (1F--1F,0)/1F,0 by Hooke's law, which in one dimension is
450 I
I
I
11o
I
iiiiiii!iii!iiii~ili!ill~i~iiii i ilii~ii ~iiiiiiii!iiill i iiiliiiiiii!iiiii i!!iiiiiiiiiii 0
I
compressive
stress
tensile stress
(-)
(+)
Figure 1. Schematic illustration of the definition of tensile and compressive stress.
O=
1F- 1~'~ = E I s - 1F'~ E e = E ~ 1F.o 1F,o
(1)
For uniaxial stress the elastic constant E is equal to Young's modulus Y. As the actual film dimensions are identical with that of the coated substrate, 1F = 1s and w F = w s. For pseudomorphic epitaxial growth e therefore is equal to the misfit: f
l s - 1F,o
(2)
. . - -
1F,O When the film laterally contracts (expands) upon detachment from the substrate it was under tensile (compressive) stress before, which according to equation (1) is positive (negative) in sign.
2.2. I n t r i n s i c s t r e s s of thin films in t h r e e d i m e n s i o n s
In three dimensions, characterised by an orthogonal set of axes x~, x 2, X3, stress is described by the second-rank tensor ~. As illustrated in Fig. 2 by means of the forces exerted on a cube, its components oij correspond to forces in xi-direction on planes normal to xj; the (~ii are the normal components of stress and the oil (i # j)
451
x3
0"33
~~1~(~2] ||O"31
,'GI 1
0'22 X2
//
x1
Figure 2. Schematic illustration of the components t~ij of the stress tensor due to forces acting on a unit cube with edges parallel to the axes x l, x 2 and x 3.
are the shear components. The t~ij are obtained by differentiating the elastic energy with respect to the corresponding tensor components eij of the film strain. For the cubic system, which all examples treated in this article belong to, the elastic energy of a unit volume F~l is given by
FeI(E) =
1
2 2 1 2 2 --~-CII(E~ q- E 2 + E3) + CI2(EIE 2 + E2E 3 + E3EI) + ~ C 4 4 ( E 2 + E 5 + E6) z z
(3)
In equation the strain components Ei and the elastic stiffness components C o are written in the shorter matrix notation, where two suffixes are abbreviated into a single one running f r o m 1 to 6: 11=1, 22-2, 33=3, 23=4, 31=5, 12-6. This substitution accounts for the fact that tensors ~ and g are symmetric, i.e. ~ij = l~ji and eij = eji but introduces a factor of 2 (I) upon converting the shear components of strain: E 1 = 1~11
E 4 = 2E23 = 2E32
E 2 = E22
E 5 = 2E31 = 2E13
E 3 = E33
E 6 = 2E12 = 2E21
(4)
452 The stress components 0.i for the cubic system are calculated to: 0.1 = Clll~l "1- C12(1~2 d- ~3)
0"4 "- C44~4
0.2 = CI1E2 -F Cl2(~ 1 -I- E3)
0.5 = C44E5
0.3 = CllE3 + Cl2(El +
E2)
(5)
0.6 = C441~6
Equations (5) represent Hooke's law in three dimensions. Notice, however, that is referred to a coordinate system generated by the axes of the cubic crystal and therefore yields the film stress only, when the axes of the crystal system and the film system are identical. The film system conveniently is expressed by axes parallel and perpendicular to the film plane. In the following example of an epitaxial cubic(001) film crystal and film axes coincide. Biaxial misfit-stress of cubic (001) films: For pseudomorphic growth of cubic(001) films on substrates with square lattices the strain is biaxial in [100] and [010] directions, el = e2 = e = (ls--IF,0)/1F,0 = f and 1~4 = I~5 -- I~6 -- 0. Since the substrate cannot exert forces perpendicular to the film plane 0.3 = 0; e3 therefore is related to e by e3 = --(C12/Cll)(el+ e2) = -2(Cl2/Cll)e. Inserting into equation (5) then yields the misfit-stress: (Cll-
C12)(C11 d- 2C12)
0.1--" 0.2 =
(6)
Cl I
In general, film and crystal axes are not identical. For uniaxial as well as
isotropic biaxial strain it is useful to calculate the misfit stress by means of generalized expressions of Young's modulus Y and Poisson' s ratio v. Young's modulus in arbitrary directions 1 = (11, 12, 13) of the cubic system is given by [4]" 1
-~ = S l l - 2 ( S l l - Sl2 --
s
22
22
22
544 ) (1112+ 1213+ 1311)
(7)
The 1i are the direction cosines of 1 and the Sij are the three independent elastic compliances referred to the cubic (100) axes. The corresponding Poisson' ratio in direction of the unit vector (m~, m 2, m3) lying in the film plane perpendicular to 1 is calculated by [5]: 512 +
(Sll - Sl2 -
1/ 2/ 8 4 4 )
V ~
Sll-
2 (Sll-
812-
2 12m2+ 2 2 13m3) 2 2 (112ml+
22 1/2 844 ) (1~122-1- 1221~+131' )
(8)
453 The elastic stiffness constants and compliances are related by Sll -]- Sl2 Cll =
(Sll_
C12 =
(811-S12)(S11--b
CII
S l 2 ) ( S l l + 2S12) -
-
Sll = (Cll
S12
2S12)
1
C44- $44
S12-
"l-
(9)
C12
C12)(C11 +
-- C12 ( C l l -- C12)(C11 -I.-
2C12) 2C12)
1
$44- C44
Young's modulus of a cubic(001) film in [100] direction, i.e. 1 = (1,0,0), is 1/Sll, the corresponding in-plane Poisson's ratio with lia = (010) is -(SI2/S~ ). In connection with equations (9) the biaxial modulus of a cubic(001) plane is calculated to Y / ( 1 - v ) = 1/(Sll + Sl2) = ( C t l - Cl2)(Cll + 2C12)/C1~, which is identical with the previous result [compare equation (6)]. Further analysis reveals that the biaxial modulus of a cubic(001) plane is isotropic, i.e. independent of the direction within the (001) plane. The uniaxial modulus, on the other hand, depends on the direction of the strain, e.g. Ytll0~ = 4/(2S11+2S12+$44) compared to Yt~001 = 1/Sl~. Misfit-stress of cubic (111) films: For a cubic(l 1 l) plane irrespective of direction (1~1~+1~1]+1]1~)= 1/4 and 2 2 2 2 2 2 (llm~ + 12m2 + 13m3) = 1/6. Therefore both uniaxial and biaxial moduli are isotropic with Y = 4/(2511+2Si2+S44 ) and Y / ( 1 - v ) = 6/(4S11+8S12+S44 ). For more complex stress problems as well as for film materials crystallising in other crystal classes, where respective expressions particularly for v are not yet available, the tensor equations (5) of the crystal system have to be transformed to the axes x~, x~, x~ of the film system. For this purpose, however, it is necessary to return to the tensor notation: oij = CO~ e~
~j - C~j~ e h
(1 O)
For simplicity equation (10) utilises Einstein's summation convention, which implies summation with respect to a suffix that occurs twice in the same term. If the p p p film axes xj, x 2, x 3 are related to the crystal axes x~, x 2, x 3 by P
Xl=
a t l x I + a l 2 x 2 + al3x 3
P
X 2 = a21x I -I- a22x 2 -I- a23x 3 I
X 3 = a31x1-I- a32x 2 -t- a33x 3
P
P
P
x I = a l l x I + a21x 2 + a31x 3 P
g
g
I
g
9
x 2 = a l 2 x I -t- a22x 2 -t- a32x 3 x 3 = al3x I + a23x 2 -t- a33x 3
(11)
454 then the transformation law for the fourth-rank tensor of the elastic stiffness constants is
C~ki=aimajnakoalpCmnop
(12)
Misfit-stress of cubic (011) films: On substrates with rectangular unit cells cubic (011) films may be obtained by m epitaxial growth that are strained along [100] and [ 01 1 ]. Useful film coordinates g for that geometry arex~ = x~ and x 2 = (x2-x3)/~f2, which both lie in the film plane, and x~= (x2+x3)/,fi, which is perpendicular to it. Tensor transformation by equation (12) yields the elastic stiffness constants in the new coordinates; some of them are given below (13)
C~lll = Cllll-" El i
' = C3333 ' -- 21 1 2-,l- C4444 1 -C2222 -Cllll + 2 C1122 ] C~!22-. C1133-- C1122-- C12
C11 "~'LCI2 "[" C44
2
C;233-" 2C1 Ill +1C!122- C4444-" 2C1 1 +let2 C 4 4 2For arbitrary strains Ell and E22 the in plane misfit-stress ( ~ = 0!) can be calculated by: 9 Cll(Cll + Cl2 + 2C44)- 2C~2 , 4C,2C44 , SII = Ell + E22 Cl I + C n + 2C44 Cll "1" C12 -]- 2C44
(14)
9_ 4CNC44 , 4(Cll + Cn)C44 , $22 -- CII "~" C12 "~" 2C44 ell + C~l + Cn + 2C44 e22
In a recent review article [6] Jona and Marcus suggested an alternate method to calculate misfit-strain in arbitrary directions, which is based on minimisation of the respective elastic energy. This method can be applied for the calculation of misfitstress as well and occasionally might be simpler than the tedious transformation of the fourth-rank tensors of elastic stiffness constants. The idea is to replace the strain components e~ appearing in the standard formulas of the elastic energy [e.g. equation (3)] by the respective expressions e~ in coordinates of the film system. Differentiation with respect to e~ yields the corresponding stress components o~ in the film coordinates, which then can be calculated by inserting the appropriate values of the e~. Some of the e~ are already fixed by the epitaxial geometry, all
455 others (usually e~) can be determined by minimisation of the elastic energy. Notice, however, that in order to transform the strain components e~, which appear e.g. equation (3) in matrix notation, to the film coordinates one has to return to tensor notation l~ii (compare equations (4)!) before applying the transformation laws for second-rank tensors: p
13ij= akialjl3kl
p
13ij:
aikajlEkl
(15)
2.3. Surface tension and surface stress
In the last years an increasing number of theoretical and experimental studies deals with stress and stress changes located in the surface layers of single crystals, at the interface to vacuum [78-9]. Due to the reduced number of chemical bonds the interatomic distances at surfaces usually differ from that of the bulk. Consequently, when the surface atoms are arranged coherently with the atoms of the crystal planes beneath, they experience stress. The stress of surface layers is defined analogous to that in thin films: A surface is in a state of stress when it would change its dimensions upon detachment from the rest of the crystal, as illustrated in Fig. 1 for thin films. But in this case it is a true Gedankenexperiment because the surface atoms need the electronic environment of the adjacent bulk to establish their inherent surface properties. For our Gedankenexperiment we therefore have to remove the surface together with the electronic contributions of the bulk, so that its atoms still remain the original surface atoms, but we have to leave behind the bulk's capability to clamp the surface in lateral registry with the (bulk) crystal lattice. In analogy to the thin film experiment described in section 2.1. the surface experiences tensile (compressive) stress, when it contracts (expands) upon detachment (though still remaining flat!). In order to derive a quantitative expression for the surface stress let us start from the conceptually simpler situation provided by liquid surfaces. Contrary to solids, free liquid surfaces cannot be elastically deformed by external forces. Molecules have to emerge from or to dissolve in the volume when surface is created or removed, respectively. The free energy 1s of a liquid surface of area A 0 is"
Is= Ao~
(16)
is the free surface energy per unit area [J/m 2 = N/m], which is independent of A 0 as long as the atomic density of liquid surfaces does not change. As is well known, to create infinitesimal new surface area dA 0 = Ao(del~ + de22) the work dW = ~,dA0 has to be done against the surface tension ?; it represents the force per unit length (or width) of liquid [N/m] which opposes the formation of new surface. (Notice that the dEii are not necessarily referred to elastic distortion, but serve here to de-
456 note normalised displacement dxJxi). On the other hand, dW increases the total energy by dls = OdA 0. The surface tension "7 of liquids therefore is equal to the free surface energy ~; moreover it is a scalar, because it is independent of the direction in which the new surface area dA 0 is added. An analogous situation is obtained when solid surface is generated at constant atomic density. In this case the surface energy 9 is constant and dF s is solely proportional to the change of area. As mentioned already by Gibbs [10] elastic deformation of solids offers an alternate possibility to create new surface area, namely by stretching pre-existing solid surfaces. As in this case the atomic density is changed, 9 no longer has to be constant. From equation (16) we obtain: (17)
dt s = OdA o + Aod~
A 0 denotes the unstrained surface area where all atoms are positioned at interatomic distances, which correspond to elastic 'surface-equilibrium'. Creation of new unstrained surface area dA 0 - - analogous to the liquid case ~ is done against the surface tension 7:
r:
1r
/
jo
l (3ls]
=~
(18)
As partial differentiation is performed at constant ~, dl3ii again denote normalised displacement dxi/x i. If the surface is elastically deformed, work has to be done el which is obtained by partial difagainst the elastic part of the surface stress gij, ferentiation of the free surface energy with respect to the strain d~ij at constant Ao: (19)
The resulting surface s t r e s s g~! is a tensor because elastic forces of crystals, in general, depend on direction. It contains the normal components g~l and g2e~2 as well as the shear component g~"2.The total stress of a solid surface gij is the sum of el.
and gij
~, b7 gij = cI~iij+ ~ = ~'fiij + beij
(20)
~Sij is the Kronecker delta function. Equation (20) for the total surface stress has been derived previously by Shuttleworth [11] and Herring [12]. Whereas the surface tension ~ is always positive, (~//~eij) may be positive or negative as well depending on whether the elastic part of the surface stress is tensile or compressive,
457 respectively. Therefore gij, too, may be positive or negative as well. Unfortunately, in literature both expressions g~j and gijel are referred to as 'surface stress' so that one has to be careful when comparing results! For treating surface elasticity by means of elastic stiffness constants the reader is referred to an article by Schmid et al. [13].
3. MEASUREMENT OF MISFIT STRAIN AND STRESS Epitaxial films and surface layers, which are arranged coherently with a mismatched support, i.e. the substrate or bulk crystal, respectively, are elastically strained and therefore ~ as discussed in the preceding section ~ are in a state of stress. In the literature so far two complementary approaches can be found to investigate the response to misfit" (i) Techniques which determine the strain by measuring interatomic distances and (ii) techniques which determine the stress from the bending of the support. 3.1. Techniques to determine misfit strain Diffraction of electrons [14], atomic beams [15] and x-rays [16] has been successfully employed in the past to investigate the structure of numerous single crystal surfaces as well as ordered adsorbate overlayers. The most prominent method certainly is LEED (quantitative low energy electron diffraction), which meanwhile belongs to the standard equipment of every UHV chamber for surface science studies. In the last years LEED more and more is used also for growth studies of ordered thin films. Particularly in the case of layer-by-layer growth the absence or presence of superstructure spots is indicative of pseudomorphic or commensurate [e.g. 17] overlayers, respectively. When evaluating the ( l x l ) LEED patterns characteristic of pseudomorphic growth by visual inspection, one should be aware that only misfits larger than about 2 % can be resolved unambiguously. The accuracy can be significantly improved by registering the energy dependence of the spot intensities e.g. with a video technique and quantitatively analysing the I(V) curves by means of multiple scattering theory. As quantitative (Q) LEED provides both the atomic positions within the unit cell and the vertical distance between topmost layers, in-plane and perpendicular strain can be calculated. The ratio of the two strain values reflects the elastic film properties that can be compared with respective bulk behaviour. A recent review on the application of QLEED to the study of ultrathin epitaxial films is provided by Ref. 6. Another method based on the diffraction of electrons is SPA-LEED (spot profile analysis-LEED), where the shapes of single LEED spots are analysed in greater detail. As from the peak fine structure important information on surface geometry
458 and surface defects can be deduced, this method is well-suited to study epitaxial growth [ 18]. Due to the high instrumental resolution the changes of the lateral unit cell dimensions of 0.5 % can easily be detected, which allows investigation of strain and changes of strain during growth. Additional information on step heights is obtained from the beam energies, at which in-phase and out-of-phase interference of vertically displaced terraces occurs. More recently STM (scanning tunneling microscopy) has also contributed successfully to the investigation of the transmittance of misfit strain during epitaxial growth. Atomic resolution of the film lattice as function of film thickness reveals the critical thickness at which the strain is relieved [e.g. 19, 20]. As discussed in the preceding chapters of this volume insertion of misfit dislocations gives rise to Moir6-patterns due to the different dimensions of substrate and relaxed film unit cells. It should be emphasised, however, that all these techniques measure strain which, in general, is referred to the equilibrium dimensions of the bulk phase. As indicated by theoretical calculations, however, for monolayer thin films and surface layers the equilibrium dimensions may deviate significantly from the respective bulk spacings, which introduces a uncertainty into the determined strain values. The corresponding film stress is then calculated via the formalism discussed in section 2.2. and requires additional knowledge of the elastic constants, which again usually are not available for thin films and surface layers. 3.2. Techniques to determine misfit stress Techniques, that measure stress directly, rely commonly on detection of the bending of the substrates, onto which the thin films are deposited, or the samples itself, in the case of surface stress changes. Complete characterisation of the stress behaviour of epitaxial systems actually requires knowledge of the three in-plane tensor components of stress. An experimental set-up to determine the two dimensional bending of disk-like samples by a multiple point capacitance technique has been reported by R~ll [21]. The in situ UHV experiments performed so far, however, utilise only the one dimensional bending of cantilever beam substrates. A schematic drawing is depicted Fig. 3. The cantilever beam substrate S is clamped on its left side, the other end is free to move when the deposited film or surface layer develops stress. As long as the film thickness tF is small compared with the thickness of the substrate t s, the respective film forces F F (normalised to unit substrate width w - w s = wF) are indirectly proportional to the radius of curvature R of the substrate and can be calculated via Stoney's well known formula [22, 23]:
459
'~
Z
j
Y "X
Figure 3. Schematic illustration of the cantilever beam technique for measurement of the intrinsic stress of thin films: The cantilever beam substrate (S) is clamped on its left side, the right end is free to move. One possibility to determine the radius of the substrate curvature (R) is by measuring the respective substrate displacement (A) by means of a differential capacitance technique (C).
For large R, i.e. small substrate deflections Az, the approximation 1/R = 2Az/12 can be used ( 1 - 1s -1F). E s is the appropriate elastic constant of the substrate. For polycrystalline or amorphous [24] films deposited onto amorphous substrates such as glass the stress within the film plane usually is isotropic. In this case the elastic constant of equation (21) then is equal to the biaxial modulus E s = Ys/(1-Vs), with Ys being Young's modulus and v s Poisson's ratio of the substrate [25, 26]. In the case of epitaxial films growing on single-crystalline substrates the evaluation of the film forces from the substrate deflection is more sophisticated. In a first approximation the film forces can be estimated by taking Young's modulus Ys in the crystallographic direction of the long substrate axis (l). For substrates of the cubic crystal class, e.g., Young's modulus in direction of the unit vector l = (11, 12, 13) is given by equation (7). Calculation of the exact value of the film forces as well as their correlation with respective film strain eij, however, requires detailed knowledge of the epitaxial film structure to solve the tensor equations oij = Cijkll~kl of both film and substrate. For uniaxial film stress in the direction of the bending beam axis one obtains E s = Ys, for isotropic biaxial stress E s = Ys/(1-Vs) with Ys and v s given in the proper orientations by equations (7) and (8). Notice that the normalised film forces Fv-/w of equation (21) are the total forces acting in a unit width of film at a certain thickness t F. In analogy to surface stress, which denotes the forces of a unit width of surface (compare section 2.3.), the film forces are measured in units of N/m. Because of their finite thickness, however, stress in thin films usually is defined analogous to stress in bulk materials, namely as the total forces F F divided by the respective cross-section: t~F = FF/WFtF [N/m2]. In all diagrams presented in this article dealing with stress in thin films the normalised film forces are plotted; the film stress is obtained after division by t F, respective slopes of the force curve correspond to the stress increment. .,.#
460 normalised film forces are plotted; the film stress is obtained after division by t F, respective slopes of the force curve correspond to the stress increment. The radius of the substrate curvature R usually is determined optically by detecting the change of the reflection angle of a laser beam [e.g. 27, 28] or ~ as illustrated in Fig. 3 ~ by measuring the substrate displacement Az with capacitance methods [e.g. 29, 30, 31]. In both cases lock-in assisted phase sensitive signal detection guarantees a high sensitivity. The smallest detectable deflection of the capacitance technique is approximately 1 nm, which corresponds to minimum detectable torques and forces of about 5 x 10l~ Nm and 0.003 N/m, respectively, for 0.1 mm thick substrates. Therefore the misfit stress of submonolayer films (1% of misfit yields film forces of about 0.2 N/m) [32] as well as adsorbate induced surface stress [31] are readily resolved. Recently Haiss and Sass demonstrated that the sensitivity can be further improved by measuring the substrate bending by means of an STM tip [33]. Cantilever beam magnetometer (CBM): Recently we have shown that the cantilever beam device can easily be modified to operate as sensitive UHV-magnetometer for quantitative measurements of magnetostriction and magnetic moments of thin films as well [34]. To that end the cantilever beam substrate is mounted in the centre of three orthogonal pairs of Helmholtz-like coils in order to apply homogenous magnetic fields in any direction of space. As is well known, the equilibrium dimensions of magnetic materials depend on their state of magnetisation, a phenomenon called magnetostriction. In the case of magnetic thin films the lateral dimensions are held fixed by the substrate. Consequently magnetostrictive stress develops upon magnetisation, which analogous to intrinsic stress ~ can be measured from the corresponding substrate bending. In order to determine the film magnetisation, it is made use of the fact that magnetic dipoles rfi experience a torque T = rfix B in homogeneous magnetic fields /~; the y-component Ty gives rise to a respective bending of the substrate. Due to the magnetic anisotropy of most magnetic thin films two simple situations frequently can be arranged, where the substrate deflection directly reflects the total film magnetisation: (i) in the very common case of a strong in-plane anisotropy (due to the demagnetising field), by magnetising the films in x-direction (i.e. along the length of the cantilever beam, compare Fig. 3) and applying a small vertical field B z and (ii) in the case of an out-of-plane anisotropy by magnetising the films in z-direction and applying a magnetic field in x-direction. The appropriate equations for evaluation are given in Ref. [34]. The sensitivity of the CBM allows magnetisation measurements of films with thicknesses of 1 - 2 monolayers. For the magnetostrictive investigations the limit of resolution is reached at film thicknesses of 1 - 2 nm depending on the magnitude of the magnetostrictive ....
....
461
constant (10 - 4 - 10-6). As discussed in Ref. [35] the sensitivity of the cantilever beam device can be further improved by performing the magnetic measurements in a dynamic mode. Upon using magnetic fields that rotate within the film plane for the magnetostrictive measurements and oscillating perpendicular fields for the magnetisation measurements the cantilever beam substrate starts to vibrate. The amplitude o f vibration depends on the frequency of the driving field and is the largest, when the substrate vibrates in resonance. Because of the amplification effect the substrate deflection no longer corresponds to absolute quantities; it can be calibrated, however, by depositing a thicker film, where both static and dynamic measurements are possible.
4. INTRINSIC STRESS UPON EQUILIBRIUM EPITAXY In this section examples of the intrinsic stress of epitaxial films grown by the three well known equilibrium modes of film growth ~ Volmer-Weber or island mode, Frank-Van der Merwe or layer-by-layer mode and Stranski-Krastanov or layer/ island mode ~ are presented. Since in all cases the stress behaviour is directly related to typical structural or microstructural features of the three growth modes the main aspects of equilibrium growth are recalled beforehand.
4.1. Film growth in thermodynamic equilibrium For film growth which proceeds at or near equilibrium valuable insights may be obtained by applying the familiar concept of equilibrium thermodynamics. As a phenomenological theory thermodynamics is valid precisely only for macroscopic systems. In the case of thin films, however, it is particularly the microscopic stage of nucleation, where application of thermodynamics is still useful, because only at small film thicknesses does the mass-transport proceed sufficiently fast to guarantee arrival at the state of equilibrium. For nuclei formed at the very beginning of film growth the ratio between the number of surface and/or interface atoms to atoms of the bulk is rather high. Consequently their equilibrium shape will be influenced strongly by the magnitudes of the free surface energies I ~ i of respective crystal facets as well as the corresponding interface energies ~ s . In principle, the size of the crystal facets that contribute to the equilibrium polyhedron can be calculated by extending the ideas, that originally led to Wulff"s theorem, to heterogeneous nucleation [36]. As a result one obtains a relation between the chemical potential Ag of isolated nuclei and the ratio of the free surface energies ~ (compare section 2.3.) and the central distance h i of individual crystal facets (see Fig. 4a):
462 ~
~
I~
d~, _
hi
It
~s
m
d~s = ~=d~e- '6
hes
(22)
kT,,,ln P
AN= 2v
hn
2v
P
Here k, T and v are Boltzmann's constant, substrate temperature and the volume of a single film atom, respectively; P and P** are the respective vapour pressureS of the nuclei and the bulk phase. As illustrated in Fig. 4a the interface is created between the facet F at the bottom of the nucleus and the substrate surface S. Notice that facet F also forms the nucleus top and on further growth will turn into the film surface. The specific interface free energy ~rs is calculated to ~FS = ~F + ~s -- 13 with 13being the corresponding free energy of adhesion, which is released when the It surfaces F and S are brought into contact. As pointed out by Bauer ~Fs is assumed to be independent of size and shape of the interface [37]. An instructive derivation of equation 22 can be found in Ref. [38].
a) hr S
N~
I
/
,,
iiiiiiii!iiiiiiiiiiiiiiRii 'iiiiiiiiiiiii(iiil b
c)
.....
.............. i . . . . . . .
Volmer-Weber
Frank-Van der Merwe
Stranski-Krastanov
Figure 4: a) Equilibrium shape of a single nucleus on a substrate surface S; (I) i and h i are the free surface energies and central distances of the crystal facets i formed at equilibrium; Ors and hFs are the respective values of the interface FS. b-d) Schematic illustration of the three modes of film growth: b) Volmer-Weber or 3D island mode, c) Frank-Van der Merwe or layer-by-layer mode and d) Stranski-Krastanov mode, where 3D islands nucleate on top of one or a few monolayers.
463 What can we learn from equation 22 with respect to the growth of thin films? The primary information on the three-dimensional shape of the initially formed nuclei comes from the value of the central distance hFs of the interface. Whereas the h i, and thus h F, are always positive, hFs may be positive or negative. Its actual value is determined by the relative magnitude of the free energy of adhesion B with respect to ~F ~ the free energy of the crystal facet forming the top of the equilibrium nuclei, and ultimately of the film surface. Depending on the magnitude and sign of hFs three different modes of film growth are distinguished: Volmer-Weber mode: In the common case of supersaturation during film deposition (AIx > 0) it follows that hFs > - h F as long as {3 < 2tI)F. Because the particle thickness t perpendicular to the substrate plane is t = h F + hFs, (compare Fig. 4a), 3D islands grow (Volmer-Weber mode: Fig. 4b). On subsequent growth individual islands coalesce into larger islands that still exhibit equilibrium shapes. For kinetic reasons, however, at some critical island size coalescence into equilibrium shapes is no longer possible [39]. At this stage the first grain boundaries are formed and elongated islands are observed. At percolation (network stage), when the films become electrically conducting, the majority of islands grows together. Upon increasing coverage most of the deposited film material is consumed tO fill the remaining open channels (channel stage), i.e. there is no noticeable increase of the average film thickness until eventually the stage of the continuous film is reached. It is noteworthy that continuous Volmer-Weber films, in general, are rough, because individual grains have different heights and moreover are separated from each other by grooves that may be several nanometers deep. As growth proceeds, depending on the self diffusion of the film material, the average grain size is preserved (columnar grain growth) or increases laterally due to recrystallisation processes. Frank-Van der Merwe mode: When the free energy of adhesion 13 approaches a value of 2tI)F the particle thickness vanishes (hFs ~ - hF). The films then wet the substrate completely and film growth proceeds via the formation of 2D islands in a layer-by-layer like fashion (Frank-Van der Merwe mode: Fig. 4c). This is particularly the case for homoepitaxial systems where ~l = 2tI)F. Notice, however, that basically the same growth stages as for the 3D Volmer-Weber mode ~ network stage, channel stage, continuous layer ~ are passed, although in 2D. Ideally this sequence is repeated layer-by-layer, on real Frank-Van der Merwe films at least 2 - 4 terraces are exposed. Stranski-Krastanov mode: Frequently a third growth mode is observed in thin film studies, where 3D islands start to grow on top of one or a few monolayers (Stranski-Krastanov mode: Fig. 4d). The reason for this more complex growth behaviour lies in the specific nature of the interfaces formed. Obviously the free surface energy of the first deposited monolayers still deviates significantly from
464 the value 9 F of a surface terminating an extended crystal. Possible reasons are intrinsic stress (e.g. misfit stress [40]) or the formation of interface alloys or compounds. The interface layer therefore has to be regarded as a new substrate, to which the thermodynamic considerations from above have to be applied again. It should be emphasised, however, that the described growth features represent ideal versions of the three growth modes. The thermodynamic picture discussed above relies on the assumption of a homogeneous substrate surface, which is characterised by uniform O~s over large distances. In practice, however, such surfaces are hardly available. Real substrate surfaces usually exhibit many different defects such as vacancies, adatoms, step and kink sites [41], stacking faults [42], dislocations [43], domain boundaries if the substrate surface reconstructs [44], impurity atoms or molecules, which have either diffused out of the bulk or adsorbed from the residual gas, etc. As a consequence of the inhomogenous ~Fs, nuclei of various equilibrium shapes may be formed at the initial stages of film growth. In addition, most of these defects can be regarded as energetic sinks for diffusing atoms, as they provide adsorption sites, where the number of nearest neighbour atoms is increased compared with sites on flat terraces. Due to the resulting stronger bonding the mean residence time of diffusing atoms at such defect sites is significantly increased and thus the chance to combine with other atoms to form supercritical nuclei. The presence of defects on surfaces therefore may considerably increase the nucleation rate (e.g. decoration of steps [45]). As discussed in section 5 defects may also affect diffusion controlled processes in the growing films itself. Unfortunately one more major obstacle is encountered upon applying the rather plausible thermodynamic theory to real film/substrate systems" To date there is still an enormous lack of experimental data on the free surface and interface energies for the numerous possible combinations of metal and substrate surfaces, so that the predictive value of thermodynamics for the growth of thin films remains poor.
4.2. Volmer-Weber epitaxy The intrinsic stress developing upon Volmer-Weber epitaxy is introduced by means of film growth on quasi-hexagonal mica(001) substrates. As is well established by many TEM (transmission electron microscope) studies mica(001) constitutes a typical Volmer-Weber substrate for the noble metals Ag, Cu and Au. At elevated substrate temperatures film growth proceeds epitaxially with (111) planes parallel to the substrate; the epitaxial temperatures reported in literature are 5 2 0 - 570 K for Ag [ 4 6 - 4748], about 670 K for Cu [49, 50] and Au [47, 51]. In the case of the stress experiments presented here [52, 30] the epitaxial nature of the films was verified with LEED (Fig. 5). The respective azimuthal orientations are
465
Figure 5. LEED patterns of a) clean mica(001) and of 100 nm thick films of b) Ag, c) Cu (primary energy Ep = 130 eV) and d) Au (Ep = 110 eV), (from Ref. [30]). exhibit sharp, single domain LEED patterns, in the case of Au the degree of epitaxy is less perfect as can be concluded from the faint ring due to randomly oriented (111) facets (Fig. 5d).
Z,O
|
!
i
-
i
30
~
! ........ I
,,~176
.t4"s: ":I I O K ~..."
-
"~ 10
~ ~
.-/ O
I-Iigh-mob~ Voimer-Weber growth
300 K
.......,'"
\
-10 0
4 O O K .....
% %. ~.~. 570 K
Epitaxial ........ Volmer-Weber growth I
20
I
z,O
I
60
.....
I
80
Thickness / nm
I
100 0 5
I
10 15
Time/rnin
Figure 6. Film forces per unit width vs. mean thickness (left side) and time (right side) of Ag films UHV-deposited onto mica(001) at various substrate temperatures. By convention positive and negative values denote tensile and compressive forces, respectively (from Ref. [52]).
466 Figure 6 displays the development of the film forces (normalised to unit width, compare discussion in section 3.2.) of Ag films deposited at temperatures between 110 K and 570 K as function of the average film thickness. As evidenced by the different shapes of the force curves displayed in Fig. 6, Volmer-Weber growth of Ag on mica(001) is strongly influenced by the substrate temperature. As verified by structural investigation with x-ray-diffraction and STM [53] polycrystalline Ag films grow at temperatures lower than about 450 K. Due to the low-mobility at 110 K the Ag films exhibit a morphology characterised by columnar grains. Above room temperature, on the other hand, recrystallisation processes proceed sufficiently fast for grains to grow also laterally in size and the films exhibit a predominant (111) texture. An STM image of a 100 nm thick Ag film prepared at room temperature is shown in Fig. 7a, where the grainy microstructure due to polycrystalline Volmer-Weber growth is clearly visible. The grain size varies between 30 and 70 nm, the vertical corrugation is in the range of 10 nm. As shown in Fig. 6 both types of Volmer-Weber growth ~ low-mobility and high-mobility VolmerWeber growth ~ are clearly distinguished by their stress behaviour. For an in depth discussion of the underlying stress mechanisms the reader is referred to Ref. [1] or [3].
..
Figure 7. STM topview images, 250 x 250 nm2, of 100 nm thick metal films UHV-deposited onto single-crystalline mica(001)" a) polycrystalline Ag film deposited at 300 K; b-d) respective epitaxial films of b) Ag, c) Cu and d) Au (from Ref. [53]).
467 At temperatures higher than 450 K film growth gradually becomes epitaxial, whereby at 570 K sharp LEED patterns of Ag(111) are observed (Fig. 5b). STM investigation reveals a morphology characterised by grains with dimensions of several hundred nanometers (Fig. 7b). Contrary to the polycrystalline room temperature films (Fig. 7a) individual grains exhibit atomically flat (111) terraces separated by steps, which are only a few monolayers high. The transition from polycrystalline to epitaxial growth again is accompanied by a dramatic change of the intrinsic stress (Fig. 6). Large compressive forces appear in the thickness range from 20 nm to 60 nm. The contribution of the compressive force increases with substrate temperature until it saturates at about 570 K. In situ conductance measurements revealed that the epitaxial films percolate at film thicknesses, at which the respective compressive force arrives at its maximum value (--60 nm for the 570 K film). The appearance of the compressive stress therefore coincides with the network stage of the Ag films. Obviously it is connected with the formation of domain walls separating coalescing islands, which is the prevailing growth process of epitaxial Volmer-Weber films close to percolation. As will be discussed in more detail below, in Volmer-Weber epitaxy isolated islands grow with their equilibrium lattice parameter, i.e. free of stress. However, when two islands meet, most likely there is a mismatch at the boundary because each of the islands has nucleated at positions determined by the substrate lattice. The experiments performed so far agree that the strain developing at boundaries separating epitaxially oriented grains is predominantly compressive rather than tensile as in the case of low-angle grain boundaries of polycrystalline films [25, 54]. As illustrated in Fig. 8 the gain in bond energy by compressing neighbouring islands obviously exceeds the resulting elastic energy.
Figure 8. Schematic illustration of the process of domain wall formation in Volmer-Weber epitaxy. Additional atoms (dark circles), which complete coalescence, tend to compress neighbouring islands (see text).
468 At the end of the network stage part of the compressive strain is released by the sudden formation of misfit dislocations. This interpretation is supported by a previous TEM investigation of Matthews [46], who observed 1014- 1015 dislocations per m 2 in continuous Ag(111) films on mica(001). The tensile stress contribution observed on further film growth and after the film deposition is caused by recrystallisation processes (see below). At the end of the network stage part of the compressive strain is released by the sudden formation of misfit dislocations. This interpretation is supported by a previous TEM investigation of Matthews [46], who observed 1014- 1015 dislocations per m 2 in continuous Ag(111) films on mica(001). The tensile stress contribution observed on further film growth and after the film deposition is caused by recrystallization processes (see below).
0
-
a)
-10
d, 9
-20
-30 ~
gh
0
40 Thickness / n m
80
0
10
Time/min
Figure 9. Film forces per unit width vs. mean film thickness (left) and time (right) of thin metal films growing by epitaxial Volmer-Weber mode: a) Au(111), b) Ag(111) and e) Cu(111) UHV-deposited onto mica(001) at 570 K and 715 K, respectively; (from Ref. [30]); d) Ag(001) UHV-deposited at 530 K onto p-doped Si(001)(2xl) (from Ref. [32]).
Fig. 9 collects the intrinsic stress results available so far for epitaxial VolmerWeber systems: A g ( l l l ) [30] and C u ( l l l ) [30] on mica(001) and Ag(001) on Si(001)(lx2) [32]; the corresponding LEED patterns are depicted in Figs. 5 and 10. Qualitatively all films are characterized by a similar dependence of the film forces
469 on film thickness. In all cases the compressive stress due to domain wall formation dominates the film stress in the respective network stages, whereas tensile stress contributions at higher film thicknesses indicate ongoing recrystallization [55]. STM investigation of the epitaxial Ag(001) film impressively supports this interpretation. At mean thickness of 5 nm islands with mainly square and rectangular shapes are imaged (Fig. 10a). Individual islands have lengths between 60 nm and 130 nm and are atomically fiat over distances of several 10 nm on their upper termination. The many open channels still visible in Fig. 10b confirm the film thickness of 5 nm lying close to the percolation point of the Ag(001) film. Upon increasing the mean film thickness to 100 nm a remarkable transformation of a film microstructure to an average grain size of about 1 ~m has taken place (Fig. 10c), which is in agreement with the observed tensile stress contribution indicating considerable recrystallization. To be fair it should be mentioned that the degree of epitaxial growth on mica(001) usually is subject to some irreproducibility (particularly in the case of Au) due to contaminants always present on air-cleaved surfaces [56] and depending on its thermal pretreatment [57]. Nevertheless, for the experiments described above there is always full agreement beween the structural information derived from ISM and LEED, i.e. if the force curves exhibit shapes characteristic of epitaxial growth, also sharp LEED patterns are obtained. It is worth discussing the stress behaviour of Volmer-Weber films during deposition of the first few monolayers in more detail. The metal films on mica(001) have grown with orientations causing the smallest the lattice misfit (Ag: 4 %, Cu: 2 %), which nevertheless would give rise to huge tensile stress in the GPa-range corresponding to film forces of several N/m in 1 nm thick films. In the case of Ag(001)/Si(001)(2xl) an epitaxial Ag overlayer with four Ag atoms within three Si lattice spacings constitutes a low-stress surface configuration though demanding film forces of 0.3 N/m per nm, again a value easily detected with cantilever beam devices. Up to film thicknesses of several monolayers ( 2 - 15 nm), however, no film stress is detected at all. Obviously the substrates impose the epitaxial orientation on the growing metal films, but do not strain them in the island stage due to lattice misfit. Matthews arrived at the same conclusion for the system Ag(111)/mica(001) upon interpreting the Moir6 fringes of Ag islands imaged with TEM [58]. It seems that the absence of film stress at low film thicknesses is a general property of epitaxial Volmer-Weber growth, which can be understood in terms of the limited adhesion due to the weak film/substrate interaction, which is the necessary pre-requisite for Volmer-Weber growth (section 4.1.).
470
100
C
10
0
1500
Figure 10. Ag(001)/Si(001)(2xl) grown at 530 K by epitaxial Volmer-Weber mode: a) 744 x 744 nm 2 and b) 175 x 175 nm 2 STM images of 5 nm thick epitaxial Ag(001) films; single scan is along dashed line in b). c) 1500 x 310 nm 2 STM topview images of a 100 nm thick Ag(001) film. U r = - 5 0 0 mV, I T = 10 nA; units in nm. LEED patterns of d) Si(001)(2xl) and e) 100 nm thick Ag(001) films, Ep = 137 eV (from Ref. [32]).
471
4.3. Stranski-Krastanov Epitaxy A Stranski-Krastanov system that is well established in the literature is provided by Ag(111)/Si(001)(2xl). According to a LEED study by Hanbticken and Neddermeyer flat epitaxial A g ( l l l ) islands grow at 300 K on top of the Si(001)(2xl) dimers [59] without lifting the (2xl) reconstruction. STM revealed that film growth actually proceeds by Stranski-Krastanov mode with the initial adsorption of Ag occurring at the twofold bridge sites between adjacent dimer rows [60, 61]. A sphere model showing a single A g ( l l l ) island adsorbed on the Si(001)(2xl) substrate is shown in Fig. 11 a. Fig. 1 l b and c depict LEED pattern and film forces of a Ag(111) film deposited at room temperature onto Si(001)(2xl). As illustrated in Fig. l l b the LEED patterns reveal two A g ( l l l ) domains rotated by 90 ~ due to the two possible Si(001) terminations. Contrary to the epitaxial Volmer-Weber films with negligible film forces in the initial stages of film growth (Fig. 9) a huge tensile stress contribution is observed during adsorption of the first three Ag monolayers. The maximum stress of 1.1 GPa develops immediately after starting the deposition up to 0.7 monolayers of Ag. The observed stress value is in good agreement with the misfit stress of 2/2 GPa calculated for an epitaxial Ag overlayer consisting of three close-packed Ag rows within two Si lattice spacings (Fig. 1 l a) as suggested in Ref. [59]. The factor 1/2 is due to the fact that only one of the two A g ( l l l ) domains gives rise to a bending of the cantilever beam along its long axis. At Ag coverages higher than three monolayers the film forces remain nearly constant indicating the beginning of 3D islanding of the films. Notice that the misfit strain built up at the interface region of the first monolayers is stored upon further film growth and thus is not affected by the process of 3D islanding. All in all the stress results also strongly support the Stranski-Krastanov mode as the mechanism for film growth. The room temperature growth of Ag on Si(001) described above provides an example of a Stranski-Krastanov system, where the stress is mainly determined by the misfit between the lattices of film and substrate. Nevertheless the good agreement between experimental and calculated misfit stress is surprising as it suggests that the elastic constants of thin films even in the monolayer range are already close to the respective bulk values. Similar results were reported by Schell-Sorokin and Tromp on the semiconductor Stranski-Krastanov system Ge/Si(001)(2xl) [27]. Here the experimental stress determined during deposition of 2 - 4 monolayers of Ge is compressive; its value o f - 5 . 7 GPa again agrees well with the misfit stress of -6.0 GPa calculated for a Ge sample compressed by 4.3% as demanded by the lattice mismatch. Obviously for both systems surface tension or surface stress effects play minor roles (compare section 2.3.). In the case of Ag(111)/Si(001) this
472
a) @
Si(O01)(lx2) second layer third layer
~
b)
s
m
c)
Ag(lll)
S
~
EE z
0.4f
3: ~
:~ L-
0.2
U L_ U--
0.0
0
1
Thickness (Nm)
2
5 ~0 15
Time {mini
Figure 11. Ag(1 ll)/Si(001)(2xl) grown at 300 K by Stranski-Krastanov mode: a) Structural model according to Ref. [59]; b) LEED pattern (Ep = 134 eV) of the two possible Ag(111) domains (from Ref. [32]) and c) film forces per unit width vs. mean film thickness (left) and time (right) (from Ref. [32]).
473 may be due to the fact that the film/substrate interaction is weak [59]; as the (2xl) reconstruction of Si(001) is preserved upon Ag deposition no corresponding change of stress should be expected. In the case of Ge/Si(001), on the other hand, the Si reconstruction is lifted by the Ge deposition; but as an analogous (2xl) structure is formed by the topmost Ge layer, surface stress effects again should be small. The following example dealing with the growth of Ag on Si(111)(7x7) at elevated temperatures represents a Stranski-Krastanov system, where the observed film stress cannot straighforwardly be attributed to misfit. It is generally agreed that at temperatures above 520 K the famous Ag(~f3 x .~f3)R30~ superstructure (see e.g. [62] and references therein) is formed atop of which 3D Ag(111) islands are growing [63]. Though studied intensively in the past its structure was not solved until recently. Fig. 12a displays a sphere model of the honeycomb-chained trimer of the Ag(.~/3 x 4"3)R30 ~ phase which has meanwhile been established (redrawn from Ref. [62]): The Ag atoms replace the topmost Si layer at slightly displaced positions, whereas the Si atoms of the layer below are arranged in trimers. Because of the considerably larger interatomic distances of the Si lattice, the Ag layer is expanded by about 20 % compared with the spacings of a Ag(111) plane. Therefore the physical and chemical properties of the Ag layer of the Ag(.J-3 x ,f3)R30 ~ phase certainly differ from that of an ideal Ag(111) layer. Fig. 12d shows the film forces of Ag deposited at about 550 K and two different deposition rates (0.1 and 0.01 nm/s) onto Si(lll)(7x7) [64]. The formation of the Ag(.~-3 x 4r3)R30 ~ structure was monitored by LEED (e.g. Figs. 12b and c). It should be added that in 100 nm thick films weak LEED spots (not shown in Fig. 12) due to the presence of Ag(111) islands are also observed. The film stress obviously is compressive and not tensile as expected from simple misfit considerations. Moreover, as indicated by the two force curves measured at two different deposition rates, the film forces seem to be mainly a function of the deposition time rather than the actual amount of deposited Ag. In both cases the compressive forces exhibit a similar time dependence, though differing somewhat with respect to their absolute magnitude. In several previous investigations of the deposition of Ag onto Si(lll)(7x7) at elevated temperatures it was found that the Ag(~f3 x 4r3)R30 ~ domains preferentially nucleate and grow along the step edges of the substrate [65, 66]. From evaluation of STM height profiles Ohnishe et al. [67] concluded that the Ag(~-3 x 4r3)R30 ~ domains extend to both sides of a step, i.e. to the lower and the upper terrace as well, with Si atoms diffusing from the respective adjacent terraces. It seems that the film forces plotted in Fig. 12d reflect the time dependence of the diffusion process involved with the compressive stress being mainly due to the formation of the Ag(.f3x ,f3)R30 ~ interface. The A g ( l l l ) i s l a n d s , analogous to isolated 3D islands of Volmer-Weber growth (section 4.2.), most likely grow free of stress. This interpretation is confirmed by monitoring the film forces during and
474
a) '.
Ag 9 si
@ooo 0
2
4
6
8
10
10
o
-5 t-i tD 0
0.1 nm/s
o -10
g~
0
20
40
60
Thickness/rim
80
100
10
Time/rain
Figure 12. a) Schematic illustration of the honeycomb-chained trimer of the Ag(x/-3 x 4~)R30 ~ phase on Si(111) (redrawn from Ref. [62]). LEED patterns of b) Si(lll)(7x7) (Ep =97 eV) and c) Ag(x/~ x ~f3)R30 ~ (Ep = 85 eV). d) Film forces per unit width vs. mean film thickness (left) and time (right) developing during growth of Ag on Si(111)(7x7) at two different deposition rates and about 550 K (from Ref. [64]).
475 after deposition of only one monolayer of Ag. Depending on the substrate temperature compressive forces up to -4 N/m develop within a period of about five minutes after finishing deposition, whereby no noticeable change of the slope is observed in the force curves when the Ag deposition is stopped. The above examples certainly demonstrate the more complex nature of StranskiKrastanov growth that by now is still far from being understood in full detail. At least the first monolayers of Ge/Si(001) and Ag(111)/Si(001) are elastically strained due to the misfit. The transition from 2D to 3D growth therefore seems to be driven by the misfit stress (compare also discussion in Ref. [68]). In the case of Ag(111)/Si(001) 3D islanding may be additionally favoured by the buckling of the interface as a result of the different geometries of the hexagonal Ag(111) layer growing on the square Si(001) lattice. The Ag(,~/-3x x/-3)R30~ phase on S i ( l l l ) , on the other hand, resembles more an interface alloy rather than a strained metal layer. The compressive stress developing during formation of this interface alloy therefore is better regarded as a change of surface stress (see also section 6.2.). Martinez et al. [69], who formerly investigated the surface stress of another 'surface alloy', Ga(~r3 x-~/-3) R30 ~ on Si(lll)(7x7), observed a similar stress behaviour. Here the stress change is tensile with a value of 1.3 N/m.
4.4. Frank-Van der Merwe Epitaxy Although layer-by-layer or FM growth is found frequently for metals growing on metals [e.g. 70], hardly any results on corresponding film stress have been reported by now. The main reason certainly originates in the difficulty of preparing metallic single-crystals with dimensions of cantilever beam substrates. Winau [71] investigated the homoepitaxial thin film system Si/Si(001), where ~ as should be expected [72] ~ no film stress is observed; however, the residual gas pressure during deposition has to be better than 5 x 10 -~~ mbar. At higher deposition pressures considerable compressive stress develops due to incorporation of gas contaminants into the growing S i films. A heteroepitaxial system that at substrate temperatures of about 500 K most likely exhibits Frank-Van der Merwe growth is Fe/MgO(001). By now it is generally agreed [73, 74] that epitaxial bcc Fe(001) films grow on the fcc substrate with Fe[100] parallel to MgO[1 10]. Compared to bcc Fe(001) lattice spacings the unit mesh of MgO(001) is slightly expanded yielding a misfit of 3.5 %. According to a LEED intensity analysis by Urano and Kanaji [75] the Fe atoms of the first rnonolayer sit on top of the oxygen ions of the substrate. Probably it is the strong interaction between Fe and oxygen that favours layer-by-layer growth from a thermodynamic point of view. Thtirmer et al. [76] recently reported that at temperatures about 500 K film growth is kinetically controlled by Ehrlich-Schwoebel barriers [ 7 7 - 80], i.e. diffusion barriers at step edges, which suppress the step-
476 down diffusion of Fe atoms to the next terrace. Depending on the substrate temperature a rough surface characterised by mounds or regular pyramidal structures is obtained. These findings are supported by recent studies on homoepitaxial growth of Fe on Fe(001) by Stroscio et al., who found perfect layer-by-layer growth only at temperatures higher than 500 K [81] as well as a mounded surface at room temperature [82].
a
Figure 13. LEED patterns of a) clean MgO(001) (Ep =142 eV) and of epitaxial Fe(001) films at b) 500 K (tF = 100 nm, Ep =159 eV), from Ref [85] and c) 455 K (tF = 300 nm, Ep = 101 eV); right pattern is calculated by means of kinematic LEED theory using a unit cell consisting of 600 atoms for each of the four {012} facets (see text), from Ref. [76].
The discussion here concentrates on films deposited at temperatures at which the Ehrlich-Schwoebel barriers are overcome. The intrinsic stress accompanied with pyramidal growth is described in more detail in the next section. At substrate temperatures of 500 K film growth proceeds layer-by-layer as indicated by atomically flat terraces extending over several hundred nm which are observed with STM. The respective LEED patterns (Fig. 13b) are characterised by sharp spots of Fe(001) t h a t ~ analogous to other bcc metals such as W [83] and Mo [84] has undergone a c(2x2) reconstruction. Fig. 14 presents the film forces of the respective Fe(001) films [85]. The experimental film stress at low film thicknesses is 6 GPa. Due to the better quality of the MgO(001) substrates [86] the agreement with misfit stress calculated by elastic constants of the bulk (6 GPa) is even better than in previous experiments [87]. Although the film forces at first sight appear to be similar to those of misfitcontrolled Stranski-Krastanov films ~ huge misfit stress developing during the initial stages of film growth (Fig. 11 c ) ~ a remarkable difference becomes evident on closer inspection. Contrary to the Stranski-Krastanov films, where the film forces become constant upon islanding after deposition of a few monolayers (section 4.3.), in the case of Fe(001)/Mg(001) misfit stress is observed up to about
477
60
40 20
0
20
40
60
80
100
Thickness / I n Figure 14. Film forces per unit width vs. mean film thickness of epitaxial Fe(001) films UHV-deposited at 500 K onto MgO(001) substrates (from Ref. [85]).
60 monolayers. Obviously then the strain energy is high enough to relieve the misfit. Part of the misfit certainly is relieved by the formation of misfit dislocations. Cracks imaged by STM, in addition, indicate local rupture of the Fe films [88]. Analogous to the Stranski-Krastanov film of Fig. 1 l c a strained layer is preserved at the film/substrate interface, that in the case Fe(001)/Mg(001) has an average thickness of 8 - 9 nm. The entire stress behaviour of Fe(001)/Mg(001) therefore certainly supports the Frank-Van der Merwe mode as the underlying mechanism of film growth.
5. INTRINSIC STRESS UPON P Y R A M I D A L G R O W T H 5.1. Film growth at presence of Ehrlich-Schwoebel barriers
In the last few years there has been increasing experimental and theoretical interest in film growth proceeding at non-equilibrium conditions, particularly where Ehrlich-Schwoebel barriers at step edges [ 7 7 - 80] suppress the downwarddiffusion of impinging atoms to the next terrace (Fig. 15). As discussed by Villain [89] Ehrlich-Schwoebel barriers destabilise extended densely packed terraces and are ultimately responsible for the transition from 2D to 3D growth in homoepitaxy [90], where layer-by-layer growth definitely is favoured by thermodynamics (see
478 section 4.2.). Both the formation of 2D islands on terraces that are wider than the average diffusion length and the uphill current due to the preferred diffusion to step ledges lead to an increase of the local slope and ultimately to the formation of rough surfaces.
"7
...........
Figure 15. Schematic illustration of Ehrlich-Schwoebel barriers (EEs), which suppress the step-down diffusion of atoms to underlying terraces (ET). Johnson et al. [91] as well as Siegert and Plischke [92] recently suggested analytic expressions, which relate the surface diffusion current j to the respective substrate inclination m(r,t)= IVh(r,t)l and can be inserted into the Langevin equation for MBE growth: 0h(r, t) / Ot = - V j [Vh(r, t)] + f(r, t)
(23)
h(r, t) is the local height at position r as function of the deposition time t, f(r,t) represents the local deposition rate and its temporal fluctuations. Numerical solution of equation (23) yields surface profiles characterised respectively by mounds [91] as well as regular pyramids [92]. The formation of pyramid structures upon epitaxial growth has been investigated also by means of Monte-Carlo simulations of several solid-on-solid models [ 9 3 - 95]. So far, however, only few experimental studies report on pyramidal growth; examples are GaAs/GaAs(001) [91 ], Pt/Pt(111) [96], Cu/Cu(001) [97] Ge/Ge(001) [98] and Fe/MgO(001) [76]. In the latter study involving STM of epitaxial Fe(001) films with thicknesses up to 2000 ML (monolayers) the main features predicted by Ref.[92] have been experimentally verified in real space, namely the growth of square pyramids as well as their temporal evolution according to a power law t TM. As shown in the STM image of Fig. 16 the surface of 300 nm thick Fe(001) films is decorated by a dense array of pyramid-like structures, which are 2 - 4 nm high and exhibit lateral dimensions of about 20 nm. Evaluation of single STM scans (e.g. Fig. 16) reveals that the pyramid side planes eventually converge into a steady state slope, that corresponds to that of {012} facets. This is confirmed by the facet reflections observed in the respective LEED patterns (Fig. 13c), which are in good agreement with LEED patterns calculated by means of kinematic theory (Fig. 13c) [76].
479
T lnm :
/\
A
.,
,
.",i-;,,,
,,
"J
~
t
q
',,N
/ "., !.,
;
v ',,7
"
J '-'-".-,
l
v
v
o
2o0
Figure 16. Large area STM topview image of a 300 nm thick epitaxial Fe(001) film exhibiting paramidlike surface structures (UT = - 7 V, I T = 0,5 nA); single scan is along the straight line marked in the topview (from Ref. [76]).
Fig. 17 displays the film forces of epitaxial Fe(001) films deposited between 350 K and 500 K onto MgO(001). Compared to the layer-by-layer films (curve a or Fig. 14) striking differences of the stress behaviour are observed. Obviously, when the Ehrlich-Schwoebel barriers become effective, the main source of stress, namely the misfit of 3.5 % between the lattices of Fe and MgO, is released at lower and lower film thicknesses. The pyramidal films of Fig. 16 develop small tensile forces only up to a mean thickness of 3 - 4 nm, at which value the films percolate (curve c in Fig. 17) as revealed by the onset of long range ferromagnetic order [85]. As discussed in section 4.4. Fe films that grow via layer-by-layer mode transmit the misfit strain up to a critical thickness tMD at which among others misfit dislocations are inserted. It is well known that, because nucleation of misfit dislocations is an activated process, tMD is not determined by energetic parameters alone [58, 99]. It seems that the transition to 3D growth due to the presence of
480
i9
:
i
~ 80 i
.................. t ...................... ......................t..................1
"~
i
~9 40--
~ 0
i
i
i ::::'............. ~
..... 20
i 40
i 60
i .... I 80 100
Thickness / nm Figure 17. Film forces per unit width vs. mean film thickness of epitaxial Fe(001) films UHV-deposited onto single-crystalline Mg(001) substrates at a) 500 K, b) 465 K, c) 440 K and d) 360 K (from Ref. [85]).
Ehrlich-Schwoebel barriers provides an alternate, energetically more favourable path for dislocations to nucleate. Since misfit stress at the film/substrate interface introduces shear forces into adjacent layers, part of the misfit strain of isolated 3D islands can be relaxed. This situation is illustrated in Fig. 18 by means of islands with pyramidal shapes, which are slightly expanded at the interface to the substrate and gradually approach the respective equilibrium spacings in upper layers. This me-
O
Figure 18. Schematic illustration of a) the relaxation of misfit stress in isolated 3D islands growing at presence of Ehrlich-Schwoebel barriers (to simplify cubic shapes are assumed!) and of b) the preferred nucleation of misfit dislocations at the boundary separating two 'relaxed' islands; dashed contour indicates pseudomorphic shape.
481 chanism allows for stress relief as long as the films are discontinuous (Fig. 18a). When two 'relaxed' islands touch each other, the boundary region separating the two islands constitutes a natural line to insert an additional Fe row (Fig. 18b). Coalescence of 'relaxed' 3D islands therefore favours nucleation of misfit dislocations, which in the case of Fe(001) films deposited at 4 0 0 - 450 K (Fig. 17, curve c) leads to a complete release of the misfit stress at percolation ( 3 - 4 nm). The small tensile stress contribution observed at higher film thicknesses probably is the result of a vertical strain component introduced by substrate steps. Due to the different step heights of film and substrate vertical and corresponding lateral strain develops when Fe layers from different substrate terraces meet. At 360 K the film forces (curve d of Fig. 17) increase nearly linearly with film thickness giving rise to a constant film stress of about 1.4 GPa, which lies well below the maximum misfit stress of 6 GPa. Fig. 19 displays an STM topview image
t 0
I o.sm
50
Figure 19. 70 x 62 nm2 STM topview image of a 5 nm thick epitaxial Fe(001) deposited at 360 K onto MgO(001) exhibiting a mounded surface morphology (U T = - 7 V, I T = 0,5 nA); single scan is along the straight line marked in the topview (from Ref. [100]).
482 of a 5 nm thick Fe(001) film. Due to the reduced mobility the island density near percolation is significantly increased. The low ledge diffusion furthermore generates a surface consisting predominantly of irregular mounds, which are about 5 nm wide and less than 1 nm high. Despite the structural similarity to Volmer-Weber films (e.g. Fig. 7a) at 5 nm, the fundamental difference between the two growth modes becomes clear after deposition of 100 nm of Fe, as still only the five topmost Fe layers are exposed. Both irregular shapes and smaller sizes of the islands at percolation certainly impede the formation of misfit dislocations according to the mechanism proposed above for regularly shaped pyramids and ultimately they are responsible for incomplete stress relaxation at 360 K. The combined results of Fe(001)/MgO(001) therefore definitely underline the decisive role of the pre-percolation stage for relaxation of misfit stress.
6. INTRINSIC STRESS OF SURFACE LAYERS 6.1. Stress of clean surfaces
As discussed in section 2.3. due to the changed bonding geometry at surfaces, the equilibrium interatomic distances may differ significantly from that of the bulk. Coherent arrangement with the bulk therefore may generate considerable stress in surface layers. In recent years an increasing number of theoretical studies has been concerned with the issue of surface stress [101] and have explicitly calculated the contribution of ~7/~eij to the total energy (compare equation 20) originating in the elastic distortion of the surface atoms. First principle calculations by Needs and Godfrey [102, 7] on AI(111) and AI(110) underline the importance of considering both terms 7 and O7/Oeij to correctly judge the stability of surfaces. Usually O7/Oeij is of the same order of magnitude as 7 itself, namely about 1 N/m (e.g. Ref. [103]), and may be positive or negative as well. In the case of AI(111) and AI(110) the surface stress is tensile with values of 1 . 0 - 2.5 N/m and nearly independent of direction as should be expected for a free electron metal. More recently Fiorentini et al. [ 104] compared the surface stress calculated for the (001) planes of 4d metals Rh, Pd and Ag and 5d metals Ir, Pt and Au. For unreconstructed Ir(001), Pt(001) and Au(001) large tensile stress of 3 - 6 N/m (corresponding to misfit strains of about 15% !) was identified as the driving mechanism for the formation of the well known quasi hexagonal overlayers [ 105 - 106107]. The authors, however, point out that high surface stress values alone are not sufficient to induce reconstructions as the resistance of the substrate bondings to reconstruction has to be overcome as well. Vanderbilt and co-workers investigated the surface stress of Si(111) [108] and respective contributions of adatoms [109], dimers and stacking fault [110],
483 which are structural elements of the (7x7) superstructure. The weak compressive stress o f - 0 . 6 N/m found for unreconstructed S i ( l l l ) indicates that the (7x7) reconstruction is not induced by surface stress. In addition, relaxation of the interlayer distances near the surface may effect the elastic surface properties. On basis of effective-medium theory Schmidt et al. [13] concluded that the elastic constants of more close-packed surfaces of Pd [Pd(111), Pd(100)] are nearly bulk-like, but are significantly weaker in the more open Pd(110) surface. High values of surface stress can even influence the elastic constants of thin films itself, when they lead to a considerable change of interatomic distances [ 111 ]. At the end of this section it should be emphasised that all the results presented here were exclusively obtained by theoretical methods. Due to the lack of proper experimental techniques so far no absolute measurements of surface stress are available in literature [112]. Stress investigations employing cantilever beam techniques (section 3.2.) actually measure changes of stress. When assuming ideal, i.e. defect-free substrates, the curvature of the cantilever beam reflects the difference in stress between its front and rear sides. For this reason cantilever beam techniques are not suited to measure the stress of clean surfaces in absolute values. Moreover it should be pointed out that only surface stress effects due to elastic distortion (c)7/~)s compare equation 20) give rise to bending.
6.2. Changes of surface stress induced by adsorbates Examples of surface stress changes induced by metallic adsorbates have been discussed in detail in the two preceding sections. Although the general topic there was the stress in thin films, particularly in some cases of Stranski-Krastanov growth, e.g. of Ga/Si(111) [69] or Ag/Si(111) [64], it was difficult to decide whether the stress of the resulting (~/3 x ~f3)R30 ~ ovcrlayers would not better be regarded as surface stress. That adsorption of small molecules such as CO or O z can also lead to substantial stress changes has been demonstrated previously by Thurnor and Abermann on polycrystalline Cr films [113]. Meanwhile similar experiments were performed on various single crystal surfaces. Sander and Ibach [114] investigated the adsorption of oxygen on Si(lll)(7x7) and Si(001)(lx2). Whereas one monolayer of oxygen causes a large compressive stress change o f - 7 . 2 N/m on Si(111), a small tensile stress change of +0.26 N/m was observed on Si(001), both values in decent agreement with cluster calculations based on a valence-bond model. High compressive stress changes were also found upon adsorption of oxygen, carbon and sulphur on Ni(001) [115] and Ni(111) [116], which in the latter case could directly be related to the occurrence of ordered phases. A recent review on the gas adsorption experiments can be found in Rcf. [8].
484 7. S U M M A R I S I N G DISCUSSION Systematic investigations of polycrystalline thin films grown in UHV on amorphous substrates established the close relation between intrinsic stress and microstructure on an atomistic level. Obviously the dominant parameter, which determines both growth and stress of polycrystalline films, is the mobility of the film atoms. It ultimately manifests itself in two different types of Volmer-Weber modes proceeding either with or without lateral grain growth in the continuous films; the latter version is also known as columnar grain growth. The proposed mechanisms responsible for the film stress mainly originate in the films. For instance stress arises at grain boundaries [25], from annealing of grain boundaries [117] or via surface tension effects in small particles [118]. For details the reader is referred to Refs. [ 1] or [3]. When summarising the presently available results on intrinsic stress of epitaxial growth this preliminary picture certainly needs to be extended. Firstly, the studies involve all three modes of film growth described in the literature, which differ significantly with respect to the film/substrate interaction (section 4.1.). Whereas it is weak in the case of Volmer-Weber mode, strong film/substrate interaction is typical of Frank-Van der Merwe mode. Secondly and contrary to polycrystalline films the origin of stress is located at the film/substrate interface and arises due to misfit or due to surface stress effects. Although up to now still rather few stress investigations deal with epitaxial films, from the results at hand several general aspects can be deduced already: 9 Heteroepitaxial Frank-Van der Merwe films generally are dominated by large misfit stress during growth of the first monolayers. The actual thickness of the strained, pseudomorphic intermediate layer strongly depends on the activation barrier to introduce misfit dislocations. When the strain energy exceeds a critical value the film forces become constant, i.e. a strained layer remains at the film/substrate interface, thus reflecting the strong bonding between film and substrate. 9 Nucleation of misfit dislocations is strongly influenced by growth processes at the initial stages of film growth. Coalescence of 'relaxed' 3D islands upon pyramidal growth, for example, decisively facilitates nucleation of misfit dislocations and thus favours relaxation of misfit stress. 9 Stranski-Krastanov films develop stress as long as film growth proceeds layerby-layer. The film forces become constant when 3D islands nucleate. As in the case of Frank-Van der Merwe growth a strained layer remains at the film/ substrate interface. The origin of the stress, however, is not as clear as in the case of Frank-Van der Merwe growth. Depending on the actual structure of the interface layer/s the stress may be related either to misfit or to surface stress effects.
485 9 Volmer-Weber mode is characterised by the absence of misfit stress during nucleation and island stages due to the low film/substrate interaction. In the network stage, however, when individual islands coalesce, huge compressive stress develops due to mismatch of the domain boundaries. Since nucleation of islands occurs at locations determined by the substrate lattice, it is again the misfit, which here indirectly gives rise to stress. 9 The surface stress of both thin films and substrates may substantially be altered by adsorption of small molecules such as 0 2 and CO or small amounts of impurities, e.g. carbon or sulphur. Although the general validity of the proposed stress mechanisms certainly needs to be tested by future stress experiments using different film/substrate combinations, several of the above issues already today are relevant for application of epitaxial films in high-tech devices. Misfit dislocations, for instance, have crucial impact on electron mobility and thus on the performance high speed transistors based on GeSi alloy films [119]. Multilayer thin films of magnetoelectronics require high-quality layer-by-layer growth, which might be suppressed by misfit stress. Small amounts of adsorbates (e.g. O [120] or Sb [121]) that recently were employed as surfactants to enhance the degree of epitaxy of thin films, may also effect the surface stress. High magnitudes of misfit stress may even alter the
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Figure 20. Effective magnetoelastic coupling constants B~ee of epitaxial Fe(001) films plotted as function of the average intrinsic stress (~}. The linear dependence of B~ff on (~} indicates the dominating influence of second order terms on the magnetoelastic energy for stress values (~} > 0.1 GPa (from [85]).
486 physical properties of thin films. An example is provided by Fig. 20, which shows the magnetoelastic coupling constant B~ of epitaxial Fe(001) films measured together with the intrinsic stress by means of a cantilever beam magnetometer described in section 3.2. (from [85]). At average film stress exceeding 0.1 GPa B 1 deviates significantly from the respective bulk value (-3.44 MJ/m 3) and even changes sign above 0.7 GPa. Obviously at stress values quite characteristic of ordinary thin films second order terms of the magnetoelastic coupling constants no longer can be neglected. The above examples therefore definitely emphasise the importance of measurements of intrinsic stress and hopefully will stimulate future experiments and theoretical studies on stress and stress relaxation of epitaxial thin films. ACKNOWLEDGEMENTS I wish to thank K. H. Rieder for his permanent scientific and moral support. I also thank G. Meyer, P. Marcus and S. F61sch for fruitful discussions as well as the former students D. Winau, M. Weber, K. Thtirmer, A. Ftihrmann, E. Henze and V. Hoffmann. The work was partly supported by the Bundesministerium ftir Forschung und Technologie (Projekt 15N5739) and the Deutsche Forschungsgemeinschaft (Projekt Ko 1313 and Sonderforschungsbereich 290).
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
Chapter 13 Density-functional theory of epitaxial growth of metals
R Ruggerone, C. Ratsch and M. Scheffler Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D- 14195 Berlin-Dahlem, Germany
This chapter starts with a summary of the atomistic processes that occur during epitaxy. We then introduce density functional theory (DFT) and describe its implementation into state-of-the-art computations of complex processes in condensed matter physics and materials science. In particular we discuss how DFT can be used to calculate parameters of microscopic processes such as adsorption and surface diffusion, and how they can be used to study the macroscopic time and length scales of realistic growth conditions. This meso- and macroscopic regime is described by the ab initio kinetic Monte Carlo approach. We discuss several specific theoretical studies that highlight the importance of the different diffusion mechanisms at step edges, the role of surfactants, and the influence of surface stress. The presented results are for specific materials (namely silver and aluminum), but they are explained in simple physical pictures suggesting that they also hold for other systems.
1. I N T R O D U C T I O N Many basic concepts for surface diffusion and crystal growth have been developed already more than 40 years ago (see e.g. [1-3]). In recent years the subject has attracted significant attention that is largely due to new experimental advancements, progress in theoretical methods, and the importance of crystal growth for technological applications. A thorough knowledge of the motion of atoms at surfaces is a key factor to the understanding of chemical reactions at surfaces, of crystal growth, and to the question under which conditions thermal equilibrium can be achieved (at least locally) at crystal surfaces. In typical growth experiments deposition rates are of the order of a monolayer (ML) per minute, and the
491
Frank-van der Merwe
m Volmer-Weber
m
A
Stranski-Krastanov
Figure
1.
Three different growth modes of heteroepitaxial growth.
diffusion of atoms at the surface is too slow (at least for some processes) so that thermal equilibrium is often not reached. As a consequence, the structures which occur at surfaces are usually a result of the kinetics. Nevertheless, under certain conditions the resulting structures are ruled by thermal equilibrium, i.e., they correspond to the minimum of the free energy. This may occur when the adatom mobility is very high, the deposition rate is low, or when growth is interrupted and the sample annealed. Concerning the acquired surface morphology one then distinguishes the following three different growth modes (cf. Fig. 1): Frank-van der Merwe or layer-by-layer growth, Volmer-Weber growth, where three-dimensional islands are formed and the overlayer does not completely cover the exposed substrate surface, and Stranski-Krastanov growth with layer-by-layer growth supplanted by island growth. Bauer [4] had discussed the conditions for these growth modes and pointed out that the actually realized surface morphology (under thermal equilibrium conditions) is controlled by the competition of the surface energy of the substrate, the surface energy of the film, and the interface energy of the film and substrate.
492 The modern treatment of growth under non-equilibrium conditions starts with the seminal paper by Burton, Cabrera, and Frank (BCF) [3], who realized that a surface usually is not perfectly flat but has imperfections such as steps. Steps are the boundary between regions that correspond to upper terraces and regions that correspond to lower terraces. They might occur at random or can be created in a controlled manner by cutting the surface in an orientation close to a low index plane. In the latter case the surface is called a vicinal surface. At steps and particularly at kink sites adatoms are bound most favorable and BCF assumed that on a stepped surface growth occurs by attachment of deposited adatoms to steps that subsequently advance. This growth mode is called step flow and is indeed easily achieved experimentally at higher temperatures. It results in flat films. The step-flow growth mode requires a high mobility of the deposited atoms, so that they reach the existing steps before meeting other adatoms. Thus this situation is close to thermal equilibrium. Usually it is desirable to grow crystals at not too high temperatures. Then the adatom mobility is lower, and deposited atoms might not reach an intrinsic step edge. Instead, they will wander around on the surface and meet other atoms, eventually nucleating a new small island. Further atoms will be caught at the edges of these islands (or create new ones), so that growth proceeds via two-dimensional growth of the islands. Additionally, during the initial stage of film growth the chance that newly deposited atoms land on an island is small. Nucleation and growth of islands can be described by phenomenological rate equations [5,6] and we will discuss this approach briefly in the following Section. The competition between step flow growth and growth via nucleation, spread, and eventual coalescence of islands on the terraces of a vicinal surface can be captured if one incorporates the rate equation formalism into the BCF equations [7]. Using rate equations one usually describes diffusion by effective parameters but unfortunately lacks a detailed understanding of the microscopic mechanism behind them. For example, it has been discussed by several authors [8-14] that surface diffusion can occur via two different mechanisms: i) An adatom may simply hop from one low-energy site to another one, while the substrate reacts only modestly by local relaxations, or
ii) an adatom may diffuse by atomic exchange where it changes place with a substrate atom and the ejected substrate atom moves further. These two mechanisms are operative at the flat regions of the surface, but also for diffusion across steps or parallel to step edges. The interplay of
493 those different diffusion processes significantly affects the shape of growing islands. We will also see an interesting dependence of these two mechanisms on surface stress, that exists at free surfaces and also results from lattice mismatch during heteroepitaxy. Kinetic limitations might lead to either two-dimensional growth or threedimensional growth. The former is achieved when atoms that land on islands can easily move down. However, when atoms which land on an island are hindered to move down, islands nucleate on top of islands, and a three-dimensional structure results (see also Ref. [15]). As in the above discussion of thermal equilibrium one also often labels the kinetic growth modes according to the surface morphologies of Fig. 1, although the kinetic and the thermodynamic limit represent totally different physics. In order to gain insight into growth phenomena it is necessary to examine all possibly relevant microscopic processes on the atomic scale. In Section 2.1 these processes will be identified. Section 2.2 then summarizes some aspects of the description of growth by rate equations, and Section 2.3 analyses the conditions at which two-dimensional growth is attained. Theoretical methods that are promising for a reliable description of surface diffusion and growth are described in Section 3. In particular we give a brief review of density functional theory in Section 3.2. Then, in Section 3.3 we sketch how DFT is implemented in actual computational schemes and utilized to identify microscopic processes and to obtain growth-relevant parameters. Section 3.4 describes how these ab initio parameters can be used to predict or analyze the temporal and spatial evolution of epitaxial growth on macroscopic scales. A b initio kinetic Monte Carlo simulations make the connection between the atomic scale and time and length scales of realistic growth conditions. Section 4 then presents some recent results of close-packed fcc surfaces. We start with an analysis (but all these results are still predictions) of the aluminum and silver (111) surfaces (Sections 4.1 and 4.2). Sections 4.3 and 4.4 discuss results for aluminum and silver (100). In particular, we consider the effects of stress for the two silver surfaces (Sections 4.2.1 and 4.4.2), possibly modified by strain due to heteroepitaxy. For the Ag (111) surface we discuss in Section 4.2.2 how adatom motion, the island density, and consequently the growth mode can be influenced by surface active contaminants, so-called surfactants.
494 2. A T O M I S T I C P R O C E S S E S A N D R A T E E Q U A T I O N S 2.1. A t o m i s t i c p r o c e s s e s The conceptually simplest growth technique is molecular beam epitaxy where an atom that has landed at the surface may either stay on the surface and wander around, or evaporate back into the gas phase. The latter happens at a rate F ev - F~v exp(-Ead/ksT), where F~v is the effective attempt frequency (in some works this term is approximated by the vibrational frequency of the isolated adatom on the surface), Ead is the adsorption energy of the adatom, ks the Boltzmann constant, and T the substrate temperature (for simplicity we assume here a situation of atomic desorption, i.e., no formation of molecules). Typically Ead is larger than the activation barriers for other processes that occur on a surface so that regardless of the exact magnitude of F~v (typically of the order of 1013s-1) evaporation can be neglected during growth. The different atomistic processes encountered by adatoms are illustrated in Fig. 2. After deposition (a) atoms can diffuse across the surface (b) and will eventually meet another adatom to form a small nucleus (c) or get captured by an already existing island or a step edge (d). Once an adatom has been captured by an island, it may either break away from the island (reversible aggregation) (e) or remain bonded to the island (irreversible aggregation). An atom that is bonded to an island may diffuse along its edge (f) until it finds a favorable site. As long as the coverage of adsorbed material is low (say (9 _ 10 %), deposition on top of islands is insignificant and nucleation of islands on top of existing islands practically does not occur. However, if the step down motion (g) is hindered by an additional energy barrier, nucleation of island on top of islands becomes likely (h). In principle it is possible that not just single adatoms but also dimers and bigger islands migrate (i). For example, a dimer might diffuse by the two atoms rotating around each other. Moreover, compared to a single adatom, a dimer may be less bounded to the substrate since the electrons of the two adatoms participate to the adatom-adatom bond and not only to the adatom-substrate bonds. Therefore, it may be expected a low activation barrier for the diffusion of dimers, but there is no clear evidence yet available. Finally, it is sometimes believed that a large island is completely immobile. However, results of Wen et al. [16] for Ag/Ag (100)show that even large scale clusters with 10 2 to 10 3 atoms can diffuse at room temperature. Diffusion of a cluster can either happen by consecutive edge diffusion of single atoms from one side of the cluster to the other, or by some concerted motion of all atoms in the cluster. The importance of the
495
i~a)
(l~a)
F i g u r e 2. The different atomistic processes for adatoms on a surface: (a) deposition, (b) diffusion at flat regions, (c) nucleation of an island, (d) diffusion towards and capture by a step edge, (e) detachment from an island, (f) diffusion parallel to a step edge, (g) diffusion down from an upper to a lower terrace, (h) nucleation of an island on top of an already existing island, and (i) diffusion of a dimer (or a bigger island). For the processes (a), (c), (g) and (h) also the reverse direction is possible, but typically less likely.
diffusion of dimers or large islands during growth is an issue that deserves more attention in future research but will not be addressed any further in this chapter. Processes such as attachment to and detachment from step edges depend quite sensitively on the local environment, because chemical bonding is a rather local phenomenon and largely determined by the coordination of nearest neighbor atoms. Figure 3 displays three important geometries of step-edge atoms. In a bond cutting model of metallic bonding the energy of an atom scales as the square root of the local coordination (see Section 3.1 for more details). In this approach it follows that the binding energy of an atom at a kink site (atom 1 in Fig. 3) equals the cohesive energy. This is indeed a general results and implies that kink sites help to establish thermal equilibrium of the surface with the bulk (note that a kink atom which detaches from a step creates a new kink in the step edge). Compared to an isolated adatom on the surface, the binding energy of an atom in the step edge (atom 2 in Fig. 3) is about 30 % and 60 % larger than the binding energy of atom 1 and atom 3, respectively. The above discussion refers to metallic bonding and is not necessarily valid for systems which can form covalent bonds and therefore prefer a certain low coordination.
496
Figure 3. Three important geometries of atoms at step edges at an island on a fcc (100) surface.
At not too high temperatures atoms will usually not detach from an island but diffuse along the edge. Eventually they will reach a higher coordinated site such as kink site 1. In general, fast edge diffusion leads to rather compact island shapes, but when the edge diffusion is strongly hindered, adatoms remain at the edge site where they reach the island and islands acquire a fractal or dendritic form ("hit and stick mechanism" [17]). At a f c c ( l l l ) there are two close-packed steps (see Fig. 4), and because more open steps typically have a higher step formation energy, these close-packed steps are expected to dominate the periphery of islands. The steps are labeled as {100} and {111} facets, referring to the plane passing through the atoms of the step and the atom of the substrate (often these steps are labeled A and B). Because of the microscopic difference of the two types of steps the diffusion along them will be different as well. It has been observed for growth of Pt on Pt (111) [18] that at a certain temperature the shape of the islands observed is triangular. At a higher temperature, triangular islands are observed again, but the triangles are rotated by 60 ~. More precisely, the islands are bounded only by {100}-faceted steps at a lower temperature while at a higher temperature the islands are bounded by {lll}-faceted steps. It was proposed [18] that this is a consequence of the different diffusion constants for migration along the two steps and particularly their different temperature dependences. The key idea behind the kinetic description of the growth phenomena is that processes occurring during growth, such as diffusion or desorption, are described by rates. The rate of a microscopic process j that occurs during
497
t
A
Q
v
-
F i g u r e 4. T h e two different t y p e s of close-packed steps on a fcc (111) surface.
growth usually has the form [19-21] F(j) = kBT
---if-- e x p ( - AF(J) / kBT)
,
(1)
where AF(J) is the difference in the Helmholtz free energy between the maximum (saddle point) and the minimum (equilibrium site) of the potential curve along the reaction path of the process j. T is the temperature, kB the Boltzmann constant, and h the Planck constant. The free energy of activation A F (j) needed by the system to move from the initial position to the saddle point is given by
A F(J) __ E(J)
~ ^ o(J)
-- ~t..~Ovi b
(2)
.
Here E(dj) is the sum of the differences in the static total and vibrational energy of the system with the particle at the minimum and at the saddle ~_a~vib is the analogous difference in the vibrational entropy. The point, and ^c(j) rate of the process j can be cast as follows"
- r J) exp(-E(dJ) /ksT)
,
(a)
498 where V~j) - (kBT/h)exp(AS(~)b/kB)is the effective attempt frequency. In the case of isotropic motion of an adatom on the surface it follows from Eq. (3) that the diffusion constant is D - Do exp(-E(dJ)/kBT) [22]. The prefactor Do - 1/(2a)F~J)l 2 where / i s the jump length and c~ the dimensionality of the motion (a - 2 for the surface). The two basic quantities in Eq. (3) are the attempt frequency F~j) and the activation energy E(dj). Transition state theory (TST) [20,21] allows an evaluation of F~j) within the harmonic approximation:
r0
--
1-I3N j-1 .j 1-Ij=l /]j 3N-I
(4)
,
where vj and u] are the normal mode frequencies of the system with the adatom at the equilibrium site and at the saddle point, respectively, and 3N is the number of degrees of freedom. The denominator in Eq. (4) contains the product of only 3 N - 1 normal frequencies, because for the adatom at the saddle point one of the mode describes the motion of the particle toward the final site and has an imaginary frequency. TST is only valid when Ed is larger than ksT. The attempt frequency F d shows a much weaker temperature dependence than the exponential and for typical growth temperatures it is of the order 1012- 1013s-1. When the barriers for two different diffusion events are different a compensation effect [23] may occur, i.e., F d is larger for processes with a higher energy barrier. Indeed, a higher energy barrier usually implies a larger curvature of the potential well around the equilibrium site of the adatom. The corresponding vibrational frequencies of the adatom in such a potential are larger as well, which implies [see Eq. (4)] that the attempt frequency increases. To define and determine Ed(j) (and other quantities important for the description of growth such as adsorption energies) we need to calculate the ground-state total energy of the adsorbate system for a dense mesh of adatom positions. This yields the so-called potential-energy surface (PES) which is the potential energy experienced by the diffusing adatom, EPES(Xad, Yad) --
min Et~
z~d,{l~,}
Yad, Zad, {aI})
,
(5)
where Et~ Yad, Zad, {RI}) is the ground-state energy of the manyelectron system (also referred as the total energy) at the atomic configuration (Xad, }Tad,Zad, {RI}). According to Eq. (5) the PES is the minimum of the total energy with respect to the z-coordinate of the adatom gad and all
499
initial geometry
(a)
transition state
final geometry [011-]
[011]
(b)
(c)
llzii
[110]
[112-] Figure 5. Diffusion via hopping (a) and exchange (b) on a fcc (100) surface and diffusion along a { 111 } step on a fcc (111) surface via exchange (c).
coordinates of the substrate atoms {Rz}. Assuming that vibrational effects can be neglected, the minima of the PES represent stable and metastable sites of the adatom. Note that this PES refers to slow motion of nuclei and assumes that for any atomic configuration the electrons are in their respective ground state. Thus, it is assumed that the dynamics of the electrons and of the nuclei are decoupled. This is the Born-Oppenheimer approximation that for not too high temperatures is usually well justified. Now consider all possible paths 1 to get from one stable or metastable adsorption site, Rad, to an adjacent one, Rad ~. The energy difference Edl between the energy at the saddle point along I and the energy of the initial geometry is the barrier for this particular path. If the vibrational energy is negligible compared to Edl, the diffusion barrier then is the minimum value of all Edl of the possible paths that connect Rad and Rad ~, and the lowest energy saddle point is called the transition state. Although often only the path with the most favorable energy barrier is important, it may happen that several paths exist with comparable barriers or that the PES consists
500 of more than one sheet (e.g. Ref. [24]). Then the effective barrier measured in an experiment or a molecular dynamics (MD) simulation represents a proper average over all possible pathways. In the previous description it was assumed that an adatom moves from one binding site to the nearest neighbor one. However, at higher temperatures diffusing adatoms may from time to time jump over long distances, spanning several lattice spacing [25]. Only little is known about this process. In a recent experimental work on the diffusion of Pd on W (211) Senff and Ehrlich [26] have extracted from their field ion microscopy (FIM) measurements an activation barrier for long jumps roughly twice that for single jumps. From the analysis of their experimental data they have determined the temperature dependent probability for the occurrence of very long jump (at least three nearest neighbor distances). These values differ of at least one order of magnitude from the theoretical ones [27] and the reason for this discrepancy are still unknown. More effort has to be put into a better understanding of the influence of such long jumps on the intralayer transport. But diffusion might also occur with a completely different mechanism, the so-called diffusion by atomic exchange (or exchange mechanism). The adatom can replace a surface atom and the replaced atom then assumes an adsorption site. This was first discussed by Bassett and Webber [8] and Wrigley and Ehrlich [9]. Even for the crystal bulk, namely Si, exchange diffusion has been discussed [28]. This mechanism is activated by the desire of the system to keep the number of cut bonds low along the diffusion pathway. On fcc (100) surfaces diffusion by atomic exchange was observed and analyzed for Pt [11] and Ir [12]. For AI(100)it was predicted by Feibelman [13] and for Au (100) by Yu and Scheffier [14]. The geometries for hopping and exchange diffusion at a fcc (100) surface are shown in Figs. 5(a) and (b). Diffusion along a step edge can also occur via the exchange mechanism as illustrated in Fig. 5(c) for a {111} step on the (111) surface. An adatom at this step edge experiences a rather high diffusion barrier, if the mechanism would be hopping: Either it has to move ontop of a substrate atom or to leave the step edge to reach an adjacent step edge position. However, if an in-step atom would move out of the step and the adatom fill the opened site, the coordination of all the particles would not decrease appreciably during the whole process. Thus, the corresponding energy barrier may be lower than that of the hopping process. It is also plausible that in general the attempt frequency is different for a hopping and an exchange process.
501
N) t-i
i~iiii!J~,
Figure 6. Schematic representation of the potential energy close to a step: E~- is the step-edge barrier, whereas E~ and E~ are the diffusion barriers at the upper and lower terrace. The additional step-edge barrier is E~- - E~.
So far we have only discussed growth processes in the submonolayer regime. But except when coverage is sufficiently low atoms might also land on top of an existing island. Several questions arise at this point. If the island is large enough and the adatom is far enough away from the edge of the island, diffusion of this adatom usually will not differ from diffusion on the flat terrace. However, this assumption is not always valid. The strain present on the island may affect the self-diffusion barrier. Moreover, the atomic structure ontop of the island may differ from the structure of the flat surface. An example is given by Pt islands on Pt (111)" at T = 640 K STM images show reconstructed and unreconstructed terraces in coexistence with different island densities [29]. Furthermore, what happens if the adatom is close to the island edge? Is the atom attracted by the edge? Does it stay on top of the island or is it hopping down? It has been found first by Ehrlich and Hudda [30] and Schwoebel and Shipsey [31] and afterwards by a number of other studies that metallic systems often exhibit an additional barrier hindering the diffusion over a step edge as it is illustrated in Fig. 6. This step-edge barrier is often referred to as Ehrlich-Schwoebel barrier. Intuitively its occurrence can be understood if hopping is the relevant mechanism by employing simple bond counting arguments" The atom that diffuses over the step edge is weaker bound right over the step edge because at this position the number of bonds is reduced.
502
F i g u r e 7. The motion of an atom from the upper terrace to the lower terrace down by the exchange mechanism.
This argument is valid for a step down process by hopping. The situation may be different in the case of the exchange mechanism (cf. Fig. 7) because here the number of cut bonds remains low along the diffusion pathway. For some metallic systems [for example, A1 on A1 (111) and Ag on Ag (100)] calculations have shown that this is the favored situation (see Sections 4.1 and 4.4). Note that the description of the process in terms of a PES [see Eq. (5)] valid for simple jumps of an adatom (i.e., diffusion by hopping) holds for the diffusion by atomic exchange as well [see Fig. 5(5) and (c)]. The step-edge barrier determines in homoepitaxy whether the growth mode is three-dimensional island growth or two-dimensional layer-by-layer growth. From experiments this barrier has been estimated by analyzing STM images [32,33]. The idea is to measure the size of an island just when nucleation on top of an island starts and to utilize nucleation theory to estimate the step-edge barrier. Similar, indirect studies that interpret Monte Carlo simulations [34] will give an estimate of the step-edge barrier. However, these approaches do not distinguish between different step types and are unable to identify the microscopic mechanism for interlayer mass transport.
2.2. Rate equations Processes (a), (b), (c), (d), and (e) of Fig. 2 form the basis of phenomenological rate equations of the form dN1 _ dt
dt
_
- N1 E j>l
jNj +
+ E j>2
"-- N I ( t~j_ I N j _ 1 - I~j N j ) - ~/j N j -+- ,)/j + I N j + 1
jNj
(6) (7)
503 These equations describe the time evolution of the adatom density, N1, and the density of islands of size j, Nj, for growth on a flat surface in the submonolayer regime. Adatoms are deposited onto the substrate at a rate - F A r adatom/s where F is the flux in ML/s and N the number of atoms pro ML. The second and third term in Eq. (6) account for isolated adatoms being "lost" because two adatoms can meet at a rate nl to form a new nucleus, or adatoms get captured at a rate ~j by an island of size j. The last two terms in Eq. (6) describe further supply sources of adatoms and are gain terms because dimers may dissociate and adatoms detach from an island of size j at a rate "),j. Equation (7) reflects the fact that the number of islands of size j increases because islands of size j - 1 grow and islands of size j 4- 1 shrink. The number of islands of size j decreases when islands of size j either shrink or grow. Note that no evaporation into the gas phase is included in Eqs. (6) and (7) (that means that the description in terms of Eqs. (6) and (7) is appropriate only at not too high temperatures). One could assume that the rate coefficients ~j c< D and -),j are independent on the island size and surface coverage (point island models). Another plausible choice is that the rates depend on the length of the perimeter of the island so that a first approximation is ~j oc 3'j c< V~ for compact islands. It has been shown [35] that the dependence on size and coverage is more complex but this will not be discussed here. The rate coefficients ~ and % are only effective parameters and the physics behind them remains unclear. For example, we will see below that the different processes shown in Fig. 2 may have different energy barriers and different pre-exponential factors, and/or they may proceed by different microscopic mechanisms (see Section 4). In principle, all these features can be taken into account in Eqs. (6) and (7) by introducing different coefficients ~j and "yj but they become less tractable and their clarity gets lost. A rate equation analysis may help to gain some qualitative understanding of growth processes but one can not expect insight into the microscopic mechanisms governing growth. With the assumption that agglomerates of i* 4- 1 and more adatoms are stable against break-up (-),j - 0 for j > i*) one derives the scaling relation [36] i*
Nis cx:
(8)
where N is - Ej>i, Nj is the island density and D the diffusion coefficient of an adatom on the flat surface. The number i* is called the size of the critical nucleus. Relation (8) can be used to extract microscopic parameters
504 from experimental (in particular STM) measurements: If one measures the island density as a function of F, one can determine the critical nucleus size i*. With a known value for i* (assuming that it does not change with temperature) one can determine the diffusion barrier Ed and the prefactor Do if one measures the temperature dependence of N is. It is not the purpose of this article to review scaling theory; however, we would like to point out that this method is not as straightforward as often believed. For example, as pointed out by Ratsch et al. [37,38] the size of the critical nucleus i* is not always well defined unless the temperature is sufficiently low and i* = 1. 2.3. C r i t i c a l i s l a n d a r e a a n d t h e a c t i o n of s u r f a c t a n t s The definition of layer-by-layer growth mentioned at the beginning of Section 1 trivially translates into the following equation [39-41], A~ >_ 1 / g is
,
(9)
where A~ is the island area at which nucleation sets in on top of an already existing island, and N is is the island density [cf. also Eq. (8)]. As before and in all what follows we assume that we are in a regime of island growth rather than step flow. If Eq. (9) is fulfilled, the islands will coalesce before a second layer has started to grow. The island density, N is, and the critical island area, Aics are controlled by the growth conditions (deposition rate and temperature) as well as by the different energy barriers and interactions of the deposited adatoms on the surface and by the minimal size of an island nucleus. Ales is determined by the probability that a number of i* + 1 adatoms meet on the same island and form a stable nucleus. Without a step-edge barrier the adatoms that land on an island are not hindered to move down and bind at the favorable sites. Thus, the formation of a nucleus on top of an island becomes unlikely, and layer-by-layer growth is expected. However, the situation is different when atoms that land on top of an island are hindered by a step-edge barrier to move downwards. In this case it is more likely that i* + 1 adatoms meet to form a stable cluster that subsequently will grow into a bigger and bigger island. Thus, Aics is smaller (compared to 1 / g is) and it is more likely that islands on the surface reach the area Aics before the layer is completed. In other words, when a noticeable step-edge barrier exists Eq. (9) may not be fulfilled and the system will grow three-dimensionally. Eq. (9) can be also rewritten in the following form
ec-
Ai~N is _ 1
,
(10)
505 where ~ is the critical coverage for which, when it is exceeded, islands will grow on top of already existing islands. Looking at experimental situations it appears that the conditions set by Eqs. (9) and (10) are slightly too strong and it is probably sufficient to request Oc _ 0.9 for good layer-bylayer growth. The importance of the above equations is that they show that the growth mode can be influenced in two independent ways: One can modify the island density (which is controlled by the adsorbate mobility at fiat regions) or one can modify the critical island area Aics which is largely determined by the physics at step edges. Thus, it follows that the growth mode can be changed from three-dimensional to layer-by-layer in the following ways:
1)
It has been shown by Kunkel et al. [42] that on Pt (111) at very low temperatures the island shape is fractal. This implies that the island perimeter is particularly long, that the islands have rough edges, and many rather thin branches. As a consequence the step-edge barrier might be reduced substantially. But even if the step-edge barrier remained unchanged, the probability for an adatom which lands on such an island to move down to the lower terrace is high, because the adatom will visit the edge very frequently. This makes it likely that a possibly existing energy barrier can be overcome. Moreover, a large number of kink sites or weakly bound atoms is present along the edges of the fractally shaped islands. Thus, an exchange downward diffusion of an adatom on the upper terrace at these sites may be more likely than the same mechanism involving an atom of a compact step edge. Furthermore, we note that the island density N is is high at low temperature [cf. Eq. (8)] which reduces the probability that more than one atom land in a reasonable time interval on the same island. Altogether these properties give rise to layer-by-layer growth.
2)
A second possibility was demonstrated by Rosenfeld et al. [43]. These authors have shown that increasing the island density N is is in fact sufficient to achieve layer-by-layer growth. A high island density can be obtained for example by lowering the temperature or increasing the deposition rate in the very beginning of growth. Once the island density is increased, the growth is continued at normal (higher T and lower F) conditions. Thus, the island density N is is set large (to low T and high F parameters) but A~ is not reduced and remains at the value determined by the "normal" T and F parameters. Indeed, threedimensional growth did not start before the layer was completed.
506 3) For completeness we mention the possibility to enhance the mobility of deposited adatoms by photo-stimulation. However, we will not elaborate on this mechanism.
)
A very interesting way to achieve layer-by-layer growth uses surface contaminants, so called surfactants. There is one necessary condition these species should fulfill: They should stay on the surface during growth, thus they should not become buried during the growth process. While a good probability of surface segregation is necessary it alone would not affect the growth mode. There are the following possible mechanisms that, when active, provide that a surface segregating contaminant increases the inter-layer mass transport: i) The simplest idea that comes to mind is that the surfactant decorates edges of steps and islands and reduces the step-edge barrier, since the atom-surfactant interaction is usually weaker than the atom-atom interaction. Figure 7 demonstrates how this could be achieved. Lowering the step edge barrier facilitates the interlayer transport and e~ ~ i. Oxygen for Pt (IIi) [44] and indium for Cu (i00) seem to have this effect [45] and enhance the 2D character of the growth mode. Recently another picture has been proposed [46]" A repelling action of In at steps hampers the attachment of Cu atoms approaching the step edge from the lower terrace and gives rise to an enhancement of the island density. However, the experimental data of Ref. [45] seems to rule out this scenario.
ii)
iii)
It is also possible that surface impurities induce a potential energy gradient that attracts deposited atoms towards the step; for deposited atoms that land on an island the number of visits at the edge is thus increased, and as a consequence the probability to move down is increased as well.
Surfactants may act as nucleation centers, thus increasing the island density N is, while Aics remains unchanged (of course, an increase would be even better). This will induce layer-by-layer growth, provided that the probability that atoms which land on an island and move to the lower terrace is not reduced as well. Moreover, if the surfactant increases the diffusion barriers E/d and E~ but leaves E~- (cf. Fig. 6)essentially unaffected, it follows that E~ - E~ is reduced and the wanted effect may result. This mechanism was recently discussed by Zhang and Lagally [47].
507
iv) A forth possibility was discussed in the context of the surfactant action of Sb on Ag (111). The basic mechanism here is that Sb impurity atoms on the surface are practically immobile and act repulsively to deposited Ag adatoms. This will also increase the island density N is and thus further two-dimensional growth. This mechanism will be discussed in Section 4.2.2. Tersoff et al. [40] have recently discussed Eq. (9) by assuming a circular island shape and various sizes for the island nucleus. They demonstrated that the critical island area is indeed a useful concept. However, we hesitate to give an explicit formula for it in terms of diffusivities and deposition rate because in reality Aics will depend sensitively on the longand medium-range adatom-adatom and adatom-step interactions (see the attractive gradient towards the step on the upper and lower terraces in Fig. 6), as well as on the diffusion barriers of adatoms parallel to step edges, as these determine the actual shape of an island. A study of Memmel and Bertel [48] has raised an interesting point. They propose a simple model which connects the diffusion behavior on metal surfaces to the charge density supplied by occupied two-dimensional fleeelectron surface states. The argument is very appealing: A decrease in the difference between the step edge barrier and the activation energy for diffusion on the flat terraces could enhance the interlayer mass transport. The barrier for the diffusion on the flat terrace is mainly determined by the corrugation of the electron density to which both bulk Bloch states as well as surface states contribute. The surface states are particularly interesting, since they can strongly be influenced. A depopulation of these states induced by confinement onto small islands or by the presence of an appropriate surfactant increases the diffusion barrier on the flat surface with a consequent reduction of the additional step edge barrier at the step edge. Thus, an increased interlayer transport is expected with the related layer-by-layer growth. This picture seems to be appropriate for the effects of oxygen on the growth mode of Pt on Pt (111) [44]. 3. T O T A L E N E R G Y A N D T H E D E S C R I P T I O N O F G R O W T H In Section 2.1 we defined the potential energy surface (PES) of a diffusing adatom. Obviously, the PES is governed by the breaking and making of chemical bonds, and we also noted the need to take atomic relaxations into account [cf. Eq. (5)]. Thus, the evaluation of the PES requires an accurate, quantum-mechanical description of the many-electron system. This can be achieved by modern density functional theory calculations
508 that combine electronic self-consistency and efficient geometry optimization. Approximate methods, based on the concepts of DFT but employing empirical parameter instead of elaborate calculations have been developed as well. Such approximate methods are widely used by several groups to investigate surface properties and to perform MD investigations of adatom diffusion. We will sketch their main characteristics in Section 3.1. A description of the basic concepts of DFT is then given in Section 3.2, and Section 3.3 describes how DFT is implemented into accurate self-consistent calculation methods. Finally, in Section 3.4 we describe briefly the kinetic Monte Carlo (KMC) technique that is capable to tackle the realistic time and length scale of growth.
3.1. B o n d - c u t t i n g m e t h o d s Several methods have been developed based on the idea that the energy of a many-electron, poly-atomic system can be written in terms of contributions from the individual atoms: Et~
-- Z E1
(11)
9
I
The sum goes over all atoms, and Es is the contribution of the I-th atom. Es depends sensitively on the local geometry of atom I (its embedding). The different bond-cutting methods differ in the treatment of the actual form of the "embedding function" and in the way to determine the necessary materials parameters. The differences are not very significant and the most popular names of these methods are: embedded atom method (EAM)[49,50], effective medium theory (EMT) [51-54], FinnisSinclair N-body potentials [55], second-moment approximation [56], and glue-model [57]. In the simplest version of a bond-cutting approach it is assumed that the energy per atom Es varies linearly with the atom's coordination number. Thus, it is assumed that the strength of a bond is invariant of the number of bonds the atom does form. This approach clearly neglects the quantummechanical properties of bonding, namely that the bond strength saturates at a certain number of neighbors [56,58,59]. In fact, detailed DFT studies have shown [58,59] that the dependence of Es on the local coordination is very similar to Es ~ -Av/-C//+ BC/
,
with Cs the coordination number of the I-th atom.
(12)
509
A more general approach gives 1
E1 - F (pI) + ~ E r j#I
- RII)
9
(13)
Here r describes the pair-wise, repulsive interaction between atoms, and F is called the embedding function, that depends on the electron density created at site I. For the effective medium theory Christensen and Jacobsen [60] have shown that Eq. (13) resembles the behavior of the simple function noted in Eq. (12), but also contains some refinements. Indeed, is has been shown that Eqs. (11) and (13) represent an approximation of the total-energy expression of density functional theory [53,54]. The main problem in actual calculations is to determine the necessary parameters to define the embedding function. Typically the parameters are obtained by fitting results from a treatment based on Eq. (13) to some experimental or D FT results of "related systems". The results depend on what systems and what properties are chosen. The predictive power of these methods has to be questioned (see e.g. [61,62]). We note, however, that bond-cutting methods hold a significant share of the quantummechanical description and thus are most valuable to summarize and to explain trends of results obtained by DFT calculations. 3.2. Density functional t h e o r y The total energy of an Ne-electron, poly-atomic system is given by the expectation value of the many-particle Hamiltonian, using the many-body wave-function of the electronic ground state. For a solid or a surface the calculation of such expectation value is impossible when using a wave-function approach. However, as has been shown by Hohenberg and Kohn [63], the ground-state total energy can also be obtained without explicit knowledge of the many-electron wave-function, but from minimizing an energy functional E[n]. This is the essence of density functional theory (DFT), which is primarily (though in principle not exclusively) a theory of the electronic ground state, couched in terms of the electron density n(r) instead of the many-electron wave function ~({ri}) with ri the coordinates of the i-th electron. The important theorem of nohenberg and Kohn [63] (see also Levy [64]) tells: The specification of a ground state density n(r) determines the manybody wave function. In other words, Hohenberg and Kohn realized that for the ground state the known functional n(r) - n[~] - (~1Ei 5 ( r - ri)l~ ) can be inverted, i.e., ~ - ~[n(r)]. Although it was shown that ~[n] exists, its explicit form remains unknown.
510 With the help of this theorem the variational problem of the manyparticle Schrhdinger equation transforms into a variational problem of an energy functional:
Eo __1/4 ML). The DFT calculations also predict a long-range attraction of adatoms towards step edges for approach from the upper as well as from the lower terrace. It appears that this attraction is actuated by electronic surface
522 states. The attraction is weak at long distances but close to the step it becomes so strong that particularly at the lower terrace an adatom will be funneled toward the step. This is clearly visible in Fig. 12 (lower curve) where the total energy along the adatom diffusion path involving the migration toward and over a step and on the flat surface is displayed for the hopping (upper curve) and the exchange (lower curve) mechanism. The attraction is present with and without relaxation of the system and thus cannot be elastic. An electrostatic origin can also be discarded, since the dipoles located at the step and of the isolated adatom have the same sign. Thus, the resulting dipole-dipole interaction is repulsive. However, the adatom and step induce localized electronic states that interact and it was concluded [91,116] that they are responsible for the long-range attractive interaction. Figure 12 also shows the difference between the hopping and the exchange mechanism for the diffusion across the step from the higher to the lower terrace. The upper curve is calculated for the hopping process, and the presence of an energy barrier that hinders the roll over of the adatom from the upper to the lower terrace is clearly seen. On the other hand, practically
2.7 3.0 3.3 >
(1) >,
3.0
L
," 3 . 3
o ..~ e--
3.6
o 3.9
t,t) "10
-10
-5
0
5
10
15
Q (bohr)
Figure 12. Total energy along the diffusion path of an A1 adatom over a {111}-faceted step on Al(lll). The upper curve is evaluated for a hopping process, while the lower one refers to an exchange process. The generalized coordinate is Q = X1 + X2 with Xx = x-coordinate of the adatom I. The x axis is parallel to the surface and perpendicular to the step orientation. For the undistorted step X2 = 0.
523 no hindrance exists for diffusion by exchange (cf. Fig. 7). The activation barrier for the exchange process for the step-down motion is very low and comparable to the diffusion barrier on the flat surface: 0.08 eV and 0.06 eV for {100}- and {lll}-faceted steps, respectively, whereas it is 0.04 eV for diffusion on the flat surface. Thus, we predict layer-by-layer growth for A1 on A1 (111) for a wide range of substrate temperatures. The barriers for the exchange might hamper 2D growth only at T ~ 25 K. However, at such a low temperature the island edges are frayed which may reduce the barriers resulting in layer-by-layer growth. One origin for the preference of the exchange process at step edges might be the bonding character of A1. Although A1 is often considered as a jellium-like metal, it is a rather covalent atom with its sp valence electrons (we remind that A1 and As form the AlAs compound, a covalent, zincblende semiconductor). Thus, similarly as discussed by Pandey [28] for the exchange diffusion in Si bulk, and by Feibelman [13] for exchange diffusion at A1 (100), we believe that this mechanism is favored by the tendency of the system to keep a low number of cut bonds along the diffusion pathway. We expect that exchange diffusion is a rather common mechanism for down movement of adatoms at step edges. We now address the diffusion of adatoms parallel to the two close-packed steps. As will be shown in Section 4.1.2, this is of particular importance for the shapes of islands which develop during growth. The migration along the steps may take place via a hopping or an exchange mechanism. The calculations predict that along the {100}-faceted step an adatom preferentially jumps to an adjacent site with an activation barrier of 0.32 eV, whereas along the {111} facet diffusion by atomic exchange is preferred with activation barrier of 0.42 eV. To understand this difference we consider the Table 1
Energy barriers Ed for different self-diffusion processes on A1(111). process mechanism flat AI(lll) hopping I11} step exchange hopping 1111 step 100 step hopping 100} step exchange exchange 1111 step _ descent 111 step descent hopping 100} step descent exchange 100} step descent hopping
I
Ed (eV) 0.04 0.42 0.48 0.32 0.44 0.06 0.33 0.08 0.45
524
TS.
TS{lll}
Figure 13. The transition sites for the hopping diffusion along the two close-packedsteps on A1(111).
positions labeled TS{100} and TS{111} in Fig. 13 that are the lowest-energy transition state of a hop along both steps. Along the {lll}-faceted step the adatom in the transition state has three neighbors, whereas in the same position along the {100}-faceted step the adatom has four neighbors [91]. The higher coordination suggests a lower barrier for hopping along the { 100}-faceted step. Indeed, the calculations yield a value of 0.32 eV, smaller than the value of 0.48 eV obtained for the hopping along the {lll}-faceted step. The calculated barrier for the exchange mechanism is about the same for both steps (0.42 and 0.44 eV).
4.1.2 Ab initio KMC study of growth We now analyze typical growth conditions where kinetic processes are dominant. The detailed characterization of the energetics of diffusion processes carried out by Stumpf and Scheffier [91,116] for A1/AI(lll) and presented in the previous Section has provided several parameters for realistic KMC simulations. Among the processes listed in Table 1 we have considered the following diffusion mechanisms: (i) diffusion of a single adatom on the flat surface: Ed -- 0.04 eV;
(ii) exchange diffusion from upper to lower terraces: Ed -- 0.06 eV at the {100}-faceted step and Ed -- 0.08 eV at the {111}-faceted step;
(iii) diffusion parallel to the {100}-faceted step via hopping: Ed -- 0.32 eV;
(iv) diffusion parallel to the {lll}-faceted step via exchange: Ed = 0.42 eV.
525 The DFT calculations give that the binding energy of a dimer is 0.58 eV [91], and we therefore assume that dimers, once they are formed, are stable (i* - 1). Moreover, in the lack of reliable information we assume that dimers are immobile. We note that the reported value for the selfdiffusion energy barrier is rather low (0.04 eV) [91,116] and comparable to the energy of optical phonons of A1 (111) ( 0 . 0 3 - 0.04 eV [117]). Thus, simulations at room temperature may not be reliable because the concept of single jumps between nearest neighbor sites is no more valid. A single optical phonon can furnish enough energy to an adatom for leaving its adsorption site and diffusing on the flat surface. At room temperature the level population of optical phonon is high and the adatoms have practically no saddle point and migrate freely on the flat surface. We therefore limited our study to substrate temperatures T _ 250 K. We adopt periodic boundary conditions, and our rectangular simulation area is compatible with the geometry of an fcc (111) surface. The dimensions of the simulation area are 1718 x 2976/~2. These dimensions are a critical parameter and it is important to ensure that the simulation area is large enough so that artificial correlations of neighboring cells do not affect the growth patterns. The mean free path A of a diffusing adatom before it meets another adatom with possible formation of a nucleation center or is captured by existing islands should be much smaller than the linear dimension of the simulation cell [118]. Since A is proportional to (D/F) 1/6 [36], we find that (with F - 0.08 ML/s) A ~ 50/~ for T - 50 and gets as large as ~ 103/~ for T - 250 K. We see that our cell is large enough (for the imposed deposition rate) for T ___ 150K, whereas at higher temperatures the dimensions of the cell are too small, i.e., for T > 150K the island density is influenced by the sizes of the simulation area. Nevertheless, the island shape is determined by local processes (edge diffusions) and is still meaningful. In the KMC program two additional insights extracted from the DFT calculations are included: (i) the attractive interaction between steps and single adatoms, and (ii) the fact that diffusion processes take place via different mechanisms (hopping or exchange). Particularly the second point plays an important role in our investigation. In several KMC simulations of epitaxial growth the attempt frequency of the diffusion rate has the same value for all the processes, and this value lies usually in the range of a typical optical phonon vibration or the Debye frequency. However, this assumption may not be right. First, processes with larger activation barriers may have a larger attempt frequency than processes with smaller
526
A
W~
T=50K
@
A
@ w
T = 200 K
l
T = 150 K
i
W;
9
1A
A
T = 250 K 100 A
F i g u r e 14. A surface area of (1718 • 1488) /~2 (half of the simulation area) at four different substrate temperatures. The deposition rate was 0.08 ML/s and the coverage in each picture is O - 0.04 ML.
energy barriers. This is a consequence of the compensation effect briefly described in Section 2.1. Moreover, processes as hopping and exchange that involve a different number of particles and different bonding configurations may also be characterized by different attempt frequencies. This has been observed [8,119-121] for several systems (Rh, Ir, Pt) and implies that the attempt frequency for exchange diffusion can be larger by up to two orders of magnitude than that for hopping. For A1 surfaces calculations with the embedded atom method [122] showed a difference of prefactors of one order of magnitude. The results of the ab initio KMC simulations shown in Fig. 14 are for a coverage of O = 0.04 ML. When the growth temperature is 50 K the
527 shape of the islands is highly irregular and indeed fractal. Adatoms which reach a step cannot leave it anymore and they cannot even diffuse along the step. Thus, at this temperature ramification takes place into random directions, and island formation can be understood in terms of the hit and stick model [17]. At T - 150 K the island shapes are triangular with their sides being {100}-faceted steps. Increasing the temperature to T - 200 K a transition from triangular to hexagonal shape occurs and for T = 250 K the islands become triangular again. However, at this temperature they are mainly bounded by { 111 }-faceted steps. To understand the island shapes in the temperature regime between 150 and 250 K we consider the mobility of the adatoms along the steps (at such temperatures the adatoms at the step edges cannot leave the steps)" The lower the migration probability along a given step edge, the higher is the step roughness and the faster is the speed of advancement of this step edge. As a consequence, this step edge shortens and eventually it may even disappears. Since diffusion along the densely packed steps on the (111) surface (the {100} and {111} facets) is faster than along steps with any other orientation this criterion explains the presence of islands which are mainly bounded by {100}- or {lll}-faceted steps. The same argument can be extended to the diffusion along the two close-packed steps and applied to the triangular islands at T = 150 K, where the energy barrier
.~
101~
"4% 4% 4 %
'.% 4%
,._ C 0 0,,=
"0 0 O) "0 ,,,
10 s 10 0 10-5
'.%
!
|
11250 1/T
1/;25
(l/K)
Figure 15. Temperature dependence of the edge diffusion rates for atom diffusion along the {100}-faceted step by hopping with F0 - 2.5 x 1012 s-1 (solid line), and along the {lll}-faceted step by exchange with Fo = 2.5 x 1014 s-1 (dash-dotted line).
528
0 = 0.006 ML
e = 0.02 ML
0
e
=
0.025 ML
e = 0.03 ML
F i g u r e 16. Shape of the islands at T = 250 K as they develop with time (or coverage). The snapshots refer to e = 0.006 ML, O = 0.02 ML, O - 0.025 ML, and O = 0.03 ML. The section of the simulation cell t h a t is shown is 1718 • 1488 .~2 and the deposition rate is 0.08 ML/s.
for the diffusion along the {111} facet is larger and thus the {100}-faceted steps survive so that triangular islands with {100} sides are obtained. By considering the energy barriers we would expect only these islands, until the temperature regime for the thermal equilibrium is reached. However, as noted in Section 2.1, the diffusion rates of adatoms are not only governed by the energy barrier but also by the effective attempt frequency. For A1/A1 (111) the effective attempt frequencies have not been calculated, but the analysis of Ref. [91] proposes that the exchange process should have a larger attempt frequency than the hopping process. The results displayed in Fig. 14 are obtained with 1.0 • 1012 s -1 for the diffusion on
529 the fiat surface, 2.5 x 1012 S - 1 for the jump along the { 100}-faceted step, and 2.5 x 1014 s -1 for the exchange along the {lll}-faceted step. These effective attempt frequencies are the only input of the KMC not calculated explicitly by DFT, but were estimated from the theoretical PES as well as from experimental data for other systems. In Fig. 15 the edge diffusion rates along the two steps are plotted as a function of the reciprocal temperature. At lower temperatures the energy barrier dominates the diffusion rate but at T - 250 K the attempt frequencies start to play a role and lead to faster diffusion along the {111} facet than along the {100} one. Thus, the latter steps disappear and only triangles with {lll}-faceted sides are present. The roughly hexagonally shaped islands at T - 200 K are a consequence of the equal advancement speed for the two steps at that temperature. Obviously, the temperature dependence of the growth shapes found in Fig. 14 is crucially determined by the ratio of the two diffusivities and in particular by the temperature at which the two lines of Fig. 15 cross. If the difference were only one order of magnitude, the crossing would be at a temperature that is too high (500 K). The formation of fractals (Fig. 14, upper left) and of {100}-faceted step triangles would still occur. Obviously, the importance of the attempt frequencies should receive a better assessment through accurate calculations, and work in this direction is in progress. A peculiarity of the triangular islands in Fig. 14 is that they exhibit concave sides. In order to understand this behavior we examine the evolution of the island shape for the deposition at T - 250 K. The results are collected in Fig. 16. At very low coverage the islands are roughly hexagonal and upon successive deposition they evolve into a nearly triangular shape. The longer sides are formed by straight { l ll}-faceted step edges but short {100}-faceted edges can still be identified, at least for (9 < 0.01 ML. The latter edges become rougher and progressively disappear. For (9 - 0.025 ML the sides are still nearly straight, but at (9 - 0.03 ML the concavities appear. The corners of the triangles seem to increase their rate of advancement during deposition. The effect can be understood on the basis of competition between adatom supply from the flat surface and mass transport along the sides. The adatom concentration field around an island exhibits the steepest gradient close to the corners, and the corners of the islands receive an increased flux of adatoms. When the sides of the islands are not too long, this additional supply of adatoms is compensated by the mass transport along the steps, i.e., the adatoms have a high probability to leave the region around the corners before the arrival of the successive
530 adatom. For 8 = 0.025 ML this scenario still seems to be true, while at 8 = 0.03 ML the island edges are longer and the mass transport along the sides is not able to compensate the additional supply of particles at the corners. That means that the probability for a particle to leave the corner region and to move along the island edge before being reached by another particle decreases considerably, and the corners start to grow faster than the sides of the triangles so that the concave shape develops.
4.2 Ag(111) 4.2.1 The influence of strain on surface diffusion Growth of one material on a different material is of particular interest for a number of technological applications. In such a heteroepitaxial system with usually different lattice constants the material to be deposited is under the influence of epitaxial strain. Growth of Ag on Pt (111) and Ag on a thin Ag film on Pt (111) has been the focus of a number of recent studies [113,123,124], and with a lattice mismatch of 4.2 % it serves as an ideal system that can provide important information about the effects of strain during growth. We will particularly discuss how strain affects the surface diffusion barrier. Only few theoretical studies of the effect of lattice mismatch on the diffusion barrier are present in the literature. For a metallic system we are only aware of results for Ag on Ag (111) where the authors of Ref. [113] find in an EMT calculation that the diffusion barrier increases under tensile strain and decreases under compressive strain. Here, we present first principle calculations (more details are given in Ref. [62]) where we study systematically the dependence of the diffusion barrier on the lattice constant for Ag on Ag (111) [113]. In the range of • % strain the DFT results exhibit a linear dependence with a slope of 0.7 eV as it is illustrated in Fig. 17. The calculated diffusion barrier for the unstrained system, E~ g-Ag- 81 meV, is in good agreement (within the error margins of the experiment and the calculations) with the scanning tunneling microscopy (STM) results of E~ g-Ag- 97 meV. The accordance between experiment and theory extends to the system A g / P t (111) and Ag/1ML Ag/Pt (111). These results are summarized in Table 2. In Fig. 17 the DFT-LDA results are compared to those of an EMT study [113]. The EMT results exhibit a linear dependence only for very small values of strain (4-2 %) and the diffusion barrier starts to decrease for values of misfit larger than 3 %. Indeed, it is plausible that a decrease of the diffusion barrier occurs when the atoms are separated far enough that eventually bonds are broken. However, as our DFT-LDA results show, for Ag/Ag (111) this
531 120
. . . . .
ODFT-LDA []EMT
N' ioo ID
i
. . . .
i
0
i i S
'O
f
L
~
o,~ L
II1 c
80
o
60
a
40
om
20
S-
0.95 I
I
I
i ! I
I
I
1.00 I
"
'
Relative Lattice Constant
'
,
1.05 I
F i g u r e 17. Diffusion barrier (in meV) for Ag on Ag (111) as a function of strain. The circles are DFT-LDA results from Ref. [62] and the squares are EMT results from Ref. [1131.
happens at values for the misfit that are larger than 5 %. Additionally, when comparison with experiment is possible [i.e., Ag on Ag (111), and Ag on a monolayer Ag on Pt (111)] the EMT results are off by a factor that varies from 1.2 to 2. The DFT results in Fig. 17 were obtained with the LDA for the exchangecorrelation functional and test calculations show that GGA increases the diffusion barrier by no more than 5 - 10 %. The (lll)-surface is a closed packed surface with a very small surface corrugation and since LDA and GGA results on this surface do not show significant differences for the diffusion barrier (as long as the mechanism is hopping and not exchange) it is plausible to assume that both the LDA and the GGA are good approximations for the exact exchange-correlation functional. This is also true for P t / P t (111) [125] and Ag on Ag (100) [87]. The general trend of an
Table 2 Diffusion barriers (i n meV) for Ag on Pt (111), Ag on one monolayer (ML) Ag on Pt (111), and Ag on Ag (11 1).
System Ag/Pt (111) Ag/1ML Ag/Pt (111) Ag/Ag (111)
Experiment [113] 157 60 97
EMT [113] 81 50 67
DFT [62] 150 65 81
532 increasing energy barrier for hopping diffusion with increasing lattice constant is quite plausible (for exchange diffusion see Section 4.4.2). Smaller lattice constants correspond to a reduced corrugation of the surface, and as result the atom is not bonded much stronger at the adsorption sites than at the bridge site. In contrast, when the surface is stretched the corrugation increases and the adsorption energy at the three-fold coordinated hollow sites increases. This picture will change when the strain is so large that bonds are broken and then it is expected that the hopping diffusion barrier will start to decrease again at very large tensile strain. It is worth noting that the diffusion barrier for Ag on top of a pseudomorphic layer of Ag on Pt (111) is substantially lower than it is for Ag on Ag (111). A question that arises is whether this reduced diffusion barrier is a result of the compressive strain or should be ascribed to electronic rearrangements induced by the Pt substrate. The diffusion barrier for Ag on Ag (111) with a lattice constant that is compressed to the value of the lattice constant for Pt is E~ g-Ag = 60 meV while that for Ag on Pt (111) (also with the Pt lattice constant of 3.92 A obtained from DFT) is ]~-TAg-Ag/Pt ~-Jd -65 meV. The agreement of these two values suggests that the reduction of the diffusion barrier for Ag on a layer of Ag on Pt (111) is mainly a strain effect and that the diffusion barrier on top of a layer of Ag is essentially independent of the substrate underneath. Brune et al. [113] also measured the island densities of Ag on two monolayers (ML) of Ag on Pt (Iii) and found that the island density is much larger than it is for Ag on just one M L of Ag on Pt (111). But the reason for this increased island density is not a larger barrier for surface diffusion. The second layer of Ag on Pt (i 11) reconstructs in a trigonal network where domains with atoms in the fcc and hcp site alternate [126]. This reconstruction occurs either during growth with high enough adatom mobility or upon annealing and it can be concluded that this trigonal network is the equilibrium structure. The periodicity of these domains is approximately two domain boundaries for every 24 atoms. This can be understood very well with purely geometrical arguments because the lattice mismatch is 4.2 % and every domain boundary implies that there is half of an Ag atom less so that the domain network provides an efficientmechanism to relief epitaxial strain. The barrier to diffuse across such a domain wall appears to be rather high and domain walls act as repulsive walls so that the island density is determined by the defect density and not the barrier for self diffusion. It is not clear however why this domain network is formed only after 2 M L Ag have been deposited and not already upon completion of
533 Table 3
Energy difference AE = -(Efcc - Ehcp) between the total energies of the two adsorption sites for Ag on Pt (111) and Ag on Ag (111). System A E (in meV) A E (in meV) 1 x 1 cell 2 x 2 cell Ag/Pt(lll) 30 50 Ag/1ML A g / P t ( l l l ) ~ 0
1.0
~
(D v
r
v
0.5
(D e-
uJ
s~
1.0
>', 0.5
E
t,.= (D r
ILl
o.o ' , 0.0
' , 1.0
' . 2.0
'.. 30
Distance(a,)
'. 40
0.0 M I
-1.0
,
I
0.0
.
I
1.0
,
I
2.0
Distance(a,) Figure 20. Diffusion path (upper panel) and total energy (lower panel) of an Ag adatom diffusing across a descending step by hopping (left side) and exchange process (right side). The values of the energy have been calculated within the LDA. For the exchange mechanism the total energy is plotted as function of the distance of the step edge atom 2 from the undistorted step edge.
540 relativistic effects give rise to a contraction and energy lowering of s-states, and as a consequence, the d-band moves closer to a Fermi energy [132]. Indeed, a relativistic treatment is most important in order to attain a good description of structural and elastic properties of 5d metals, while it is not important for the 4d metals. Thus, while the significant tensile surface stress of Au (100) pulls the dimer of the exchange transition state "into" the surface, it lowers the energy of the transition state, and enables exchange diffusion. The surface stress at Ag (100) is too weak to have a significant effect. With respect to the stress a stretched silver film gets more gold-like, and therefore the two diffusion mechanisms for a strained silver slab were analyzed in detail. When the system is under tensile strain the energy barrier for the exchange diffusion increases, while the barrier for the hopping diffusion decreases. For hopping diffusion the trend can be understood as follows: Smaller lattice constants correspond to a reduced corrugation of the surface potential, and thus diffusion energy barriers are reduced [62,113]. In contrast, for a stretched surface the corrugation increases and the adsorption energy at the four-fold coordinated hollow sites increases. The latter reflects the wish to reduce (at least locally) the strain induced surface stress. The hopping-diffusion transition state is less affected by the strain than the adsorption site. For exchange diffusion this is just the opposite. Here the transition-state geometry reacts particularly strongly to the tensile stress, and locally the tensile stress is reduced by the very close approach of the dimer [Fig. 5(b)]. Thus, it is predicted that for pseudomorphic Ag films (with increased parallel lattice constant) self-diffusion should get noticeably affected by the exchange mechanism. The results of this study strongly suggest that tensile surface stress (to be precize, the e x c e s s surface stress, i.e. the strain derivative of the surface energy) is the main actuator for the exchange diffusion on fcc (100) surfaces [14]. REFERENCES M. Volmer and J. Estermann, Z. Phys. 7, 13 (1921). I. Langmuir and J.B. Taylor, Phys. Rev. 40, 463 (1932). W.K. Burton, N. Cabrera, and F.C. Frank, Philos. Trans. R. Soc. London Ser. a 243, 299 (1951). E. Bauer, Z. Kristallogr. 110, 372 (1958). 5. J.A. Venables, G.D.T. Spiller, and M. Hanbiicken, Rep. Prog. Phys. 47, 399 (1984). 6. J.A. Venables, Chapter 1 of this book. 7. A.K. Myers-Beaghton and D.D. Vvedensky, Phys. Rev. A 44, 2457 (1991). 8. D.W. Bassett and P.R. Webber, Surf. Sci. 70, 520 (1978). . 9. J.D. Wrigley and G. Ehrlich, Phys. Rev. Lett. 44, 661 (1978). 10. R.T. Tung and W.R. Graham, Surf. Sci. 97, 73 (1980). .
541 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45.
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxial Layers D.A. King and D.P. Woodruff, editors.
545
Chapter 14 Electronic structure of ultrathin magnetic films
Peter D. Johnson Physics Department, Brookhaven National Laboratory, NY 11973, USA
1. INTRODUCTION Over the past decade the increasing demands for new information storage capabilities have lead to an enormous increase in the amount of research devoted to the study of the magnetic properties of surfaces and thin films.[ 1] A number of technological developments allow these new magnetic materials to be routinely fabricated and investigated on the atomic scale. Further, studies of thin films have been extended into studies of magnetic multilayers which, with their unique property of giant magneto-resistance [2], are already showing promise for a number of new technological applications. In the present chapter we review the different studies, both theoretical and experimental, of the properties of magnetic thin films with a particular emphasis on the electronic structure and studies of the latter using various electron spectroscopies. Itinerant magnetism involves spins that are not highly localized. We therefore chose to examine the properties of these systems within the framework of band theory and the Stoner model. Whilst acknowledging that such an approach does not provide an adequate description of the high temperature phenomena in the vicinity of the Curie temperature,[3] the Stoner model does provide considerable insight into the mechanism by which these systems acquire their magnetic characteristics. We investigate the spin polarization effects that are induced in an interface when one element of the interface is ferromagnetic. In particular we examine the unique magnetic structures that are produced when ultrathin 3d, 4d, and 5d transition metal films are deposited on both the ferromagnetic Fe(001) surface and on other surfaces. Itinerant magnetism is normally confined to elements at the center of the 3d row in the periodic table. With their increased bandwidths the 4d and 5d transition metals do not exhibit magnetic ground states within the bulk. However the reduced dimensionality of thin films does
546 allow the possibility of long range order particularly as an interracial phenomena.[4] Finally we examine the properties of noble metal films deposited on ferromagnetic substrates. With filled d-bands the noble metals are not expected to show significant magnetic structures. However several studies have demonstrated the existence of spin-polarized quantum well states within the noble metal thin film.[5-7] We discuss in detail the characteristics of these states and examinethe relationship between them and the oscillatory exchange coupling observed in the associated magnetic multilayers.[8]
2. ITINERANT MAGNETISM AND THE STONER MODEL The itinerant magnetic state reflects the competition between the kinetic and potential energies of the system. The kinetic energy is represented by the bandwidth or the ability of the electrons to move from one site to another. The potential energy on the other hand reflects the on-site coulomb or exchange terms. In the Stoner model of itinerant magnetism the system will become spin polarized as a means of reducing the total energy of the system. The relative shift of either one of the two spin components o is given by [9] Eo = E0 + tin o'
(1)
where E0 is the binding energy in the unpolarized band, U is the coulomb or exchange potential and ng is the number of electrons of the opposite spin. From equation (1) the solitting between the two spin components A is given by a = Eo
-
E,~, = Um
(2)
where we have now introduced a magnetic moment m =n o -no,. Equation (2) has been successfully used as a self-consistency condition in several fight binding calculations of magnetic systems. [ 10-12] The Stoner parameter U represents an effective exchange potential. It is related to the susceptibility of the material X such that z =
Zo
I-!UN(EF) 2
(3)
547 where N(EF) is the density of states at the Fermi level and X0 is the freeelectron Pauli susceptibility. The denominator in equation (3) introduces the localized properties into the susceptibility via the site-specific U tenn. The Stoner criterion for ferromagnetism is of course IUN(EF) > I.
(4)
Such a model provides us with considerable physical insight into the properties of magnetic thin films. By growing the film on different substrates it is possible to vary the bandwidth of the overlayer and the density of states at the Fermi level. Providing equation (4) is satisfied the system will polarize to achieve a local moment according to the condition defined by equation (2). In fact the density of states at the Fermi level is approximately the density of dstates. The latter is inversely related to the d:.bandwidth Wd which within the tight binding framework may be written [13] Wd =2~N,,.h d.
(5)
Here Nnn represents the number of nearest neighbors or coordination number and h d is the hopping matrix element for the d-electrons. That such a dependence of the magnetic properties on the coordination number exists has been demonstrated in a number of first-principles calculations.[4] As an example, the magnetic moment at the surface of an Fe crystal cut in the (001) plane is predicted to be 2.96#B as opposed to the 2.2#13 characteristic of the bulk. On the (110) surface, where the coordination number is six rather than the four of the (001) surface the moment is predicted to be 2.6#B. Moving to the linear chain the magnetic moment is calculated to be 3.3/zB and that of the free atom, 4.0#13. The relationship between exchange splitting and magnetic moment as expressed in equation 2 has been the basis for the suggestion that an experimental measurement of the splitting may be used to directly determine the magnitude of the local magnetic moment. This idea with a ratio of leW#B has been used both in photoemission [14] and in electron energy loss studies.[15] In the former case the photoelectrons are emitted directly from the exchange split bands; in the latter case spin flip transitions result in structure in the loss specman at energies corresponding to the exchange splitting between the two spin components. It is important however to remember that the ratio leV/#B is
548
not a universal relationship. Indeed it applies only approximately to the elements in the center of the 3d row. For the 4d and 5d elements the Stoner parameter U in equation (2) takes smaller and smaller values.[16] Whilst the Stoner model provides physical insight, the major advances in our understanding of the magnetic properties of surfaces and thin films have come from first-principles electronic structure calculations based on the local density functional theory (LSDF) [17,18] and formulated within the slab geometry. In particular the f ~ potential linearized augmented plane wave (FLAPW) and the linearized muffan-tin orbital (LMTO) methods have been very successful.[19] In the local spin density approximation the total energy of the system E(n) is written as E(n) = T(n) + V(n) + Exc(n,m)
(6)
where the kinetic energy T and the coulomb energy V reflect the local charge density n(~)= n T(~)+ n~ (~) and the exchange correlation potential Exc is a function of both the charge density and the magnetization or spin density m(?) = n l , ( ? ) - n~ (~). The density functional method represents a mean field approach in that each electron experiences the average field of the other electrons. The approximations made for the exchange correlation potential in these calculations do not adequately account for non-local effects and fitaher, as with the mean field Stoner model, the first-principles FLAPW calculation is strictly only applicable at temperatures well below the Curie temperature. However even with such restrictions the approach has been extremely successful.
3. TRANSITION METAL FILMS. 3.1 Theoretical Studies
A nice example of the information that may be-obtained from spinpolarized electronic structure calculations of the FLAPW type is shown in figure 1 where the magnetic moments calculated for the 3d, 4d and 5d transition metal overlayers on a Ag(001) substrate are presented.[20] Ferromagnetism does not exist in the bulk form of the 4d and 5d transition metals simply because the bandwidth is too large. However from the figure we see that thin films of these same materials do offer the potential for supporting long range magnetic order.
549 I
I
I
I
I
I
I
4 tn :1. f.. r
E O E
3
,,...,,
2
m
o O
--
1
Ti
Zr Hf
V
Nb Ta
Cr
Mo W
Mn
Tc Re
Fe
Ru Os
Co
Rh Ir
Ni
Pd Pt
Fig. 1. Calculatedlocal magnetic moments for 3d, 4d and 5d transition metal monolayerson a Ag(001) surface. The magnitude of the magnetic moment for the 3d transition metals peaks in the center of the row where the d-bands in the overlayer are half-filled. This represents the residue of Hund's rule for the isolated atoms. As one moves from the 3d row through the 4d to the 5d row the calculated moments steadily decrease. This reflects the observation that the bandwidth is steadily increasing through this progression as the in-plane d-d overlap increases. However as one moves through the 4d and 5d rows the peak in the moment moves to the right. This reflects the observation that within a row the bandwidth decreases as one moves from left to right. Hence the Stoner criterion of equation (4) is more likely to be satisfied to the right of the row. The Ag(001) substrate represents a non-magnetic substrate. Although not shown here similar trends are found in calculations of the magnetic structure of the same overlayers on a ferromagnetic Fe(001) substrate.[21] The nearest neighbor distance within the overlayer film is in fact nearly identical on both substrates. However as a result of the increased d-d hybridization with the substrate bands, the calculated moments tend to be smaller on the left side of the row for the Fe substrate than the silver substrate. Another observation is that in
550
the case of Fe the possibility exists for spin-polarization effects being induced in the overlayer by direct hybridization with the spin-dependent substrate bands. Ferromagnetic alignment of the moments in the overlayer with the moments in the substrate may not in fact represent the lowest energy configuration. Indeed more detailed 5indies indicate that ferromagnetic alignment is favored only on the right hand side of, for instance, the 3d row and that to the left of the row antiferrome,gnetic alignment within the overlayer is favored for the Ag(001) substrate and antiferromagnetie alignment between overlayer and substrate is favored for an Fe(001) substrate.[22] In the latter ease the moments are still aligned ferromagnetically within the overlayer. The switch from antiferromagnetic to ferromagnetic alignment for the overlayers on an Fe(001) substrate is also found in calculations of impurity atoms embedded in an Fe lattice.[23] In the latter ease the calculated moments may have a different magnitude reflecting the different level of hybridization or coordination number but the overall trend is the same. Sitting between Cr and Fe in the periodic table, Mn represents an interesting crossover point and several calculations indicate that the lowest energy configuration for a Mn monolayer on an Fe substrate is an antiferromagnetic alignment within the overlayer itself.[21,24] The overall behavior is even more complex. Indeed the calculations indicate that for submonolayer coverages, antiferromagnetie alignment between overlayer and substrate is favored. As the coverage approaches one monolayer antiferromagnetism within the Mn layer itself becomes the lowest energy eonfigm'ation and this antiferromagnetie structure is predicted to drive a c(2x2) buckling reconstruction within the overlayer. With the formation of a Mn bilayer the moments on the Mn layer closest to the interface now align parallel to those of the substrate. The two Mn layers are coupled antiferromagneticaUy as found for adjacent layers in Cr films. The parallel alignment in the interface has also been predicted in calculations of the magnetic configuration in related FeMn multilayers. [ 12] The calculations represent studies of the "perfect" monolayer. In reality complications may arise in any comparison with experiment for a number of reasons. For instance it is possible that the ovedayer growth proceeds via island formation rather than layer by layer. Another possibility is that interdiffusion may occur at the interface. However even with such complexity considerable progress in the verification of the general ideas has been achieved.
551 9
I
V
9
~
9
k% 0
!
o _=
O O
,
t~
I
-2 0 2
State
4 6 -2 0 2 Energy (eV)
4
6
Fig. 2 Inverse photoemnission spectra recorded from 3d transition metal overlayers deposited on a Ag(001) substrate. The left panel recorded with incident electron energies of 14.5 eV highlights contributions from the s,p states; the fight panel recorded at the higher incident energy of 19.5 eV highlights contributions from the 3d states.
3.2 Experimental Studies. There has been no direct confirmation of the predicted magnetic structures for the 3d overlayer films on Ag(001). An inverse photoemission study of the unoccupied electronic structure for these overlayers identified, as shown in figure 2, the correct trend in that on moving across the 3d row an unoccupied d-band of A 5 symmetry moved closer to the Fermi level.[25] The importance of such a study is that it does appear to provide an indication of the presence of a magnetic moment in the overlayer. However it is not possible on the basis of such a non spin-polarized study to determine whether the magnetic structure in the overlayer is ferromagnetic or antiferromagnetic, an observation
552 that stems from the fact that the calculated moments in the overlayer are nearly identical for both the ferromagnetic and antiferromagnetie configurations.[13] The general trend of the d-band moving closer to the Fermi level is therefore predicted for both magnetic configurations. Many of the theoretical predictions for the 3d overlayers on Fe(001) have however been confirmed by experiment. Chromium films in particular have been extensively studied. The interest largely stems from the oscillatory exchange coupling [8,26] that has been observed in the related Fe/Cr multilayers. Here the moments in two adjacent Fe films in the multilayer will align either parallel or anti-paralld depending on the thickness of the intervening Cr film. The multilayer has also been shown to exhibit giant magneto-resistivity at Cr thicknesses corresponding to the anti-parallel or antiferromagnetic alignment of the adjacent Fe layers.[2] Chromium has an identical lattice structure to Fe but it's half filled d-band results in the antiferromagnetic state rather than the ferromagnetic state representing the ground state. In the bulk crystal each atom is antiferromagnetically coupled to its nearest neighbor so that every (001) plane is ferromagnetically aligned within the plane but antiferromagnetically aligned to neighboring (001) planes. As noted above calculations indicate that a Cr monolayer deposited on an Fe(001) substrate will also be ferromagnetically aligned within the plane but antiferromagnetically aligned to the substrate [11,27,28]. The calculations predict an enhanced moment of the order of 3.1# B on the Cr site which is to be compared with 0.6#13 characteristic of bulk Cr. Spin-polarized photoemission (SPPES) studies have in part confirmed these predictions. A valence band study was unable to conclude anything about the size of the moments, but, through its coverage dependence, did confirm the prediction of a Cr related interfacial electronic state at a binding energy close to the Fermi level for the monolayer coverage. [l l ] The authors' tight-binding calculation suggested that this state of dz2 character has its charge density split equally between the Cr layer and the surface Fe layer, an observation that has recently been suggested elsewhere [29] as the appropriate criterion for identifying a true interface state. A later spin polarized core level photoemission study of the Cr and Fe 3p levels demonstrated that the initial monolayer is indeed ferromagneticaUy aligned within the layer and fia'ther, as predicted, that the moments of this Cr layer are antiferromagnetically aligned with those of the substrate.[30] On the basis of the spin polarization observed in the core level Hillebrecht et al concluded that the magnetic moment on the initial layers was in the range 0.61.0/zB. A similar result was obtained in a study using Magnetic Circular
553 Dichroism (MCD) in which the authors concluded that in the sub-monolayer range the magnetic moment on the Cr site was identical to that. for bulk Cr, 0.6#B.[31] Unfortunately structural studies indicate that at room temperature the growth of Cr on Fe(001) does not proceed in a simple layer by layer fashion. Rather in a recent scanning tunneling microscopy (STM) study, Pierce et al [32] were able to demonstrate that the initial growth proceeded with the formation of islands. By increasing the substrate temperature the size of the islands or platelets increased but at temperatures above 300~ interdiffusion of Cr and Fe occurs at the interface.
I
l
I
I
I
I
I
Fe
A
Cr
::)
>, (n C aP .r
c
I
65
!
60
I
55
I
50
|
45
I
40
I
35
Binding Energy (eV)
Fig. 3. Spin integrated (upper panel) and spin polarized photoemission spectra (lower panel) from ref. 33 showing the Fe 3p and Cr 3p core levels recorded from 0.6 ML of Cr on Fe(O01). In the lower panel the solid up triangles represent the majority spin and the open down triangles represent the minority spin. The incident photon energy for these spectra was 250 eV.
554 In a second spin-p01arized core level photoemission study of the 3p levels Xu et al [33] compared their experimental observations with a fight binding simulation of the development of thicker Cr films. Their model indicated that the growth of chromium proceeded with each new Cr layer aligning antiferromagnetically with respect to the preceding one a result consistent with experimental studies that had previously demonstrated the antiferromagnetic layer by layer growth. [34] The fight-binding study found that throughout the growth of the films the surface layer of Cr always supports an enhanced moment of the order of 2.1 #B and that as the films become thicker the inner layers have a moment that slowly relaxes towards a value characteristic of bulk Cr. A similar result was found in a second fight-binding study of layer by layer growth by Stoeffler and Gautier.[35] The latter authors also examined the role of mono-atomic steps in the Fe substrate. They found that these lead to magnetic frustration in the Cr antiferromagnetic ordering and a reduction in the average magnetic moment on the Cr sites. Shown in figure 3, with their increased sensitivity, Xu et al. [33] were able to obtain a measure of the Cr 3p spin polarization at a coverage corresponding to 0.6 ML, i.e. lower than that of the earlier core level study. The reversal of the net spin in the Fe and Cr core levels is a clear indication that the moments on the two sites are reversed with respect to each other. On the basis of their modeling Xu et al concluded that at this coverage, the magnetic moment on the Cr site was at least 1.8 #B a result in good agreement with the findings of a study of this system using spin polarized electron energy-loss spectroscopy.[15] Whilst the findings of the experimental studies are coming closer to the theoretical predictions it is clear that the growth of Cr on Fe represents a complex system and that more studies will be helpful. Several predictions for the Mn overlayers have also been confirmed experimentally. A SPEELS study [36] found that initially the Mn aligns antiferromagnetically with respect to the substrate and beyond 5 ML each Mn layer is antiferromagnetically coupled to the previous layer. For thicknesses less than 5ML the authors concluded that the outer Mn layer was antiferromagneticaUy aligned with respect to the substrate. In a spin-polarized core level photoemission study of the Mn 3p core level at sub monolayer coverages Roth et al. [37] found evidence for the Mn aligning antiferromagneticaUy with respect to the substrate. Further at a film thickness close to one monolayer the authors claimed, on the basis of a local minimum in the measured spin,polarization, to have found evidence for the predicted antiferromagnetic ordering within the Mn layer. Measuring the spin polarization in the Fe 3p level Roth et al. concluded that the Fe interracial
555
>
~-2 L._
" -4 iii
-6 -8 F
X
F
X n
Fig. 4. Band structure of majority and minority spin even symmetry states along I' -X for a 49-layer Fe film in the left and fight panels respectively. States with high localization in the surface region are marked with circles. moment decreased as found in the calculations for the monolayer coverage but they did not observe the anticipated increase in the Fe moment with the formation of the Mn bilayer. Moving across the 3d row it is clearly not easy to study an Fe oveflayer on an Fe substrate. However first principles calculations indicate that the Fe(001) surface layer will have an enhanced moment of 2.9#B.[38] Although experimentally it is difficult to determine the magnitude of the surface moment directly it is possible using angle resolved photoemission studies to verify many other aspects of the calculation. In particular it has been possible to identify and characterize the surface electron states that are responsible in part for the surface magnetic structure. A surface state represents an electronic state that is localized within the surface region. Surface states of d-character which are the more highly spinpolarized tend to be more localized in the outer surface layers than the s-p derived states which may have wavefunctions decaying over several layers away from the surface. A true surface state must lie within a gap that is formed when the bulk bands are projected onto the two-dimensional surface Brillouin zone. However outside of these bulk band-gaps there may also exist states, referred to as surface resonances, which resonate in the surface region and have many characteristics in common with surface states. Figure 4 shows the results
556 of a spin-polarized electronic structure calculation for a 49 layer Fe(001) slab.[39] The figure shows both majority and minority spin surface states of even symmetry as defined by the minor plane in the r x azimuth. Using spin-resolved angle-resolved photoemission Brookes et al. [40] were able to identify the minority spin surface state with binding energy 2.4 eV at the center of the Brillouin zone. By measuring the binding energy as a function of emission angle they followed its dispersion out along the r x azimuth to the zone boundary at x . At this point in the Brillouin zone the state falls within, a projected bulk band gap and becomes a true surface state localized in the surface layers. The experimentally determined dispersion was in excellent agreement with the results of the calculation shown in fig. 4. Further experimental support for this calculated electronic structure was provided in the accompanying tunneling spectroscopy study. [39] Examining the unoccupied electronic states, Stroscio et al observed an intense sharp feature in their spectra in agreement with a minority spin surface state predicted to lie 0.2 eV above the Fermi level. Ni grown epitaxially on Fe(001) has been studied using Low-Energy Electron-Diffraction (LEED) [41]; reflection high-energy electron-diffraction (RHEED) [42]; polarized neutron reflection (PNR) [43] and spin polarized photoemission [44]. The structural studies indicate that films less than six layers thick grow in a bee manner. Above this thickness it is thought that the strained overlayer relaxes by forming misfit dislocations [45]. Calculations predict that at the Fe(001) lattice spacing the bee phase of nickel should be ferromagnetic with a magnetic moment of 0.5 ~tB.[46] In the PNR study of a Au/3ML bee Ni/5ML bee Fe/Ag(001) sandwich at 4~ Bland et al. [43] reported a nickel magnetic moment of 0.55-0.801xB and a moment of 2.2-2.4~tB for the Fe substrate. Spin-polarized photoemission studies of Ni films deposited on Fe are difficult because both the overlayer and the substrate have a high density of states near the Fermi level. However recording spectra from a thick bee Ni film Brookes et al. [40] were dearly able to demonstrate the presence of ferromagnetism within the Ni layer itself by showing that a characteristic satellite at a binding energy of 6 eV was spin polarized. They further measured the background spin polarization as a function of the Ni thickness. With the assumption that this polarization P scales with the magnetic moment m such that p _m na
(7)
557 where n d represents the number of localized d electrons they concluded that the magnetic moment on the Ni sites was of the order of 0.4PB in agreement with the calculations. In the same study Brookes et al examined the evolution of the electronic structure from the ultrathin regime through to the thicker films. They reported that in the thinnest films (< 4ML) the photoemission spectra reproduced in figure 5 showed distinct characteristics suggestive of unique interfacial properties. Indeed a first principles FLAPW calculation for one- and two-layer Ni films on Fe(001) [47] shows that there are strong hybridization effects between the iron and nickel d-bands which lead to an interfacial iron moment that is enhanced slightly with respect to the bulk but lower than that characteristic of the clean Fe(001) surface. The authors report interfacial moments of 2.65PB on the iron site and 0.86#B on the nickel site for the one monolayer film and 2.59PB on the iron site and 0.69PB on the nickel sites for I
I
I
I
I
I
I
I
I
"
i.A ~
i
I 9
I 1
(e)
4t '=-lld)
,4
~llk (c)
,(b)
m
q
I
I
I
I
I
I
2.5 2.O 1.5 1.0 0.5 E F
I
Blndlng Energy (eV)
t !,,
2,5 21) 1.5 1.0 0.5
~k,~(a) EF
Binding Energy(eV)
Fig. 5. Spin-resolvedphotoemission spectra taken at normal emission for nickel overlayers grown on Fe(001). The majority and minority spectra are shown in the left and fight panels respectively and correspond to the following coverages: (a) --2.0 ML, (b) --4.1 ML, (b) -5.1 ML, (b) --6.2 ML, (b) -7.5 ML.
558 the two monolayer film. Interestingly both the experiment and calculation place even symmetry states exchange split by approximately 0.5 eV immediately below the Fermi level for the two monolayer film. Whilst no study has demonstrated ferromagnetism in 4d thin films on a Ag substrate it has been demonstrated in Rh and Pd thin films on an Fe(001) substrate. Kaehel et al have reported the results of a spin-polarized photoemission study of the valence bands of the Rh/Fe(001) system.[48] Here because of the atomic size mismatch between Rh and Fe (7.7%), the growth mode is layer by layer but not epitaxial. However from the observation of spin polarization it was concluded that the Rh was ferromagnetic as predicted in the authors' first principles calculation, which indicated a moment of 0.82#13 on the Rh site. Kachel et al. concluded that the spin polarization reflected the strong hybridization between the Rh 4d bands and the substrate 3d bands. The Pd/Fe interface has been the subject of a number of different studies. Weber et al [49] studied the deposition of Pd on the Fe(110) surface. On this surface Pd grows epitaxially until at coverages close to one monolayer a phase transition results in the ovedayer adopting the (111)structure. Subsequent growth proceeds epitaxially in (111) planes. Thus the study of Weber et al represents a study of the Pd(111)/Fe(110) interface. The authors identified an interface state at a binding energy of 1.5 eV with respect to the Fermi level, El. The interfacial character was confirmed by its lack of dispersion with k~ as the incident photon energy was varied and the observation that its intensity saturated at 1.5 ML. The authors interpreted the spin-resolved spectra shown in figure 6 for the one and two monolayer coverage as an inverted exchange split pair an indication of possible antiferromagnetie coupling. However, the complete identification of an exchange split pair requires the demonstration that the two spin components, majority and minority, have the same symmetry. Weber, et al. did not report such an observation. In a study of a Pd monolayer deposited on Fe(001) Rader et al. were again able to show that spin polarized features characterizing the Pd overlayer were evident in the photoemission spectra.[50] By examining the spin polarization as a function of coverage, these authors were able to confirm the observation made in the earlier study [49] that the polarization of the Pd was confined to the interfacial layer. Through comparison with calculation, it was confirmed that the magnetization induced in the Pd reflected, as in the case of Rh, a strong Pd-Fe interaction rather than a lateral Pd-Pd interaction. Indeed, as indicated in figure 1, a monolayer of Pd on Ag(001) is predicted tO be essentially non-magnetic even though the expansion of the Pd lattice is slightly larger than that associated with Pd on Fe(001).[20] Because of the large
559
9
,r
X
,,
$I
~--"
2 1
.=
r,' z,; o
-5
-4
-3
-2
-1
0
1
Binding Energy (e~r) Fig. 6. Spin-resolved spectra recorded from different thicknesses (x atomic layers) of Pd deposited on an Fe(110) surface. The majority and minority spin spectra are indicated by the solid up triangles and empty down triangles respectively. The incident photon energy is 21.2 eV.
exchange splitting in the Fe substrate, the interaction of the Pd is found to be stronger in the majority spin channel than the minority spin channel. As the calculation in figure 7 shows this results in the majority spin states in the oveflayer being distributed over a larger range in binding energy than those states of minority spin character. The Pd/Fe interface has also been studied from the reverse direction with Fe deposited on Pd(001) [51,52] rather than Pd on Fe(001) [50]. In both cases calculations predict that the Pd atoms in the interface will have a local moment of the order of 0.3gB.[50,53,54] LEED studies indicate that the Fe films grow pseudomorphically on the Pd(001) substrate in a tetragonally distorted bodycentered cubic structure.[55] Liu and Bader [51] have studied the temperature
560
..
-
A
1
V
§
~0, 0
v
0 .._1._. 1
.
i
-2!
6
1
I
4
I
I
2
J
I
I
I
i
" 0
Energy (eV)
Fig. 7. FLAPW calculation for a Pd/7Fe(001)/Pd slab. Layer resolved majority spin (1") and minority spin (,1,) density of states of the Pd overlayer on Fe(001) (solid line) and of the topmost Fe layer underneath the Pd (dotted line). dependence of the magnetization in the Fe films using the SMOKE technique. Samples grown at 100~ have a vertical easy axis. Samples grown at 300~ have an in-plane easy axis. However the thickness dependence of the Curie Temperature T e is independent of the spin orientation of the sample. Liu and Bader found that both the thickness dependence of T e and the critical exponent /9 of the magnetization M defined as
(8) followed a 2-d Ising like behavior with 19approximately equal to 0.125. Shown in fig. 8, a study of Fe films deposited on Pd(001) at room temperature by Rader et al. [52] revealed that a non-magnetic surface state associated with the Pd surface evolved into a magnetic interface state localized in the interface between the Fe and Pd. As a working definition the authors chose to defne an interface state as a state with approximately 50% of its charge density located either side of the interface. The Pd surface state of even
561
symmetry had previously been investigated in a separate spin integrated photoemission study.[56] Rader et al reported that a first-principles FLAPW calculation indicated this state to be more than 50% localized in the surface layer.[52] However, with the deposition of Fe the state does not disappear, a behavior characteristic of surface states as discussed earlier, but rather evolves into the interface state at slightly higher binding energy. The spin-polarized calculations show this new interface state, which has majority spin character, results from the hybridization between Pd 4d and Fe 3d states. In fact the presence of a band gap in the substrate helps to localize the state in the
~'1.15 , 0 UJ
o
o
8
Copper Thickness (ML)
Fig. 16. Plot of the effective masses of the quantum-well states as a function of the copper film thickness in atomic layers. The solid circles indicate the fits to the experimental data; the open circles indicate the results of tight-binding calculations of the effective masses. The dashed lines represents the flee-electron mass. that the effective mass increased from 2.2m e to 3. l rne on going from the one to two monolayer coverage. Examination of the hybridization band gap in the vanadium substrate shows that at the center of the zone it has a similar alignment with the Fermi level as the gap found within the Fe minority spin band structure.[93] Li .et al [94] have studied the confinement of quantum well states by a ferromagnetic barrier of varying thickness. Here the authors measured the intensity of different quantum well states, a measure of the confinement, in a two monolayer thick copper film deposited on a Co wedge. Two states representing the spz derived state at a binding energy of 1.7 eV and a more tightly bound dxz quantum well state at the higher binding energy of 3.0 eV were examined. The study found that as a function of Co thickness, the intensity of the more localized dxz state saturated more quickly than the Spz state. Fitting the increase in intensity I of the Spz quantum well state with a function of the form I =(1 , e x p ( -t / ~,) where t is the thickness of the film, the authors found a scaling parameter X = 2.3 A.
576 An identical scaling parameter has been found in a study of the magneto-resistance of eopper/permalloy multilayers with varying thicknesses of Co deposited in the interface.[95] The dependence of the measured magnetoresistance on the Co thickness was taken as evidence of the important role played by the interface. Li et al concluded that their study supported this idea although a note of caution should be added into the discussion at this point. A recent STM study of ion beam sputtered copper films grown on Co(001) and Co films grown on Cu(001) has shown that some degree of surface roughness exists in both systems.[96] However the authors noted that in general the copper tends to act as a "smoothing agent" when deposited on the pre-grown "rough" Co films. Whilst such studies suggest that the observation of Li et al [94] could be influenced by the presence of Co islands it is clear that the presence of quantmn well states down to the very thinnest Co layer is an indication that some form of barrier exists. Quantization of the d-bands has also been observed in a number of thin films. The ability to resolve discrete quantum well states can depend on a number of different factors. Obviously if the experimental energy resolution is comparable to the energy separation their observation is more difficult. The energy separation AE is related to both the number of layers in the film N and the rate of dispersion of the bulk band from which the quantum well states are derived such that [97] 2naE AE = ~ ~ Na c~
(17)
where a is the separation between layers. One might anticipate therefore that quantization of the more localized d-bands will be seen more easily in thinner films. This is indeed the case. Systems that have been studied include Cu, Au, Pd and Pt overlayers on Fe(ll0) and Co(0001).[98,99] In general these systems all show a similar behavior. Two peaks appear in the coverage dependent spectra which saturate in intensity at coverages of 1.5A1 and 2AI respectively. As an example we show in fig. 17 the photoemission spectra obtained from Pd films deposited on an Fe(110) substrate. A peak at a binding energy of-1.5 eV appears in the 0.5A1 Pd coverage spectrum, saturates at 1.0AI and then reduces in intensity. With fiu'ther coverage a second peak appears at -0.7 eV binding energy saturating at a coverage of 2AL. By 4AI the photoemission spectra resemble those characteristic of a Pd(111) surface. Similar quantization effects in the d-
577 I
I
i
I
i
I
i
F(
h~ Nc
X=
5.0 4.0 3.0 2.0 1.5 1.0 0.5 0.0
_>,
~
e.. m
-6
I
I
1
I
-5
-4
-3
-2
I
t
-1
-
t
t
0
1
2
Binding Energy (eV) Fig. 17. Spin-integrated photoemission spectra recorded from various Pd coverages (in atomic layers = AL) on Fe(110). The spectra are plotted on the same absolute intensity
scale. bands have also been observed in studies of the noble metals Cu and Ag deposited on Co(001) [94,100] and Fe(001) [80] respectively.
5. SUMMARY In our discussion of the magnetic properties of thin films we have shown that many of the details produced in the theoretical studies have been continued experimentally. Many of the discrepancies may be traced to structural problems relating to the growth procedure. Thus island formation or interdiffusion often adds complexity to the problem. Indeed the interplay between magnetic properties and interface structure represents an important growth area for future research. For both transition and noble metal overlayers the polarization induced in the overlayer reflects the interaction in the interface. In the former case the dbands in the oveflayer become polarized. In the case of noble metal overlayers the s-p and d-bands can all become polarized with the largest effect for the latter being particularly pronounced at the interface. The means by which spin polarization effects are induced in the noble metals are largely understood. The reflectivities in the vicinity of the hybridization gaps in the substrate determine
578
the level of confinement of the quantum well states and the associated spin polarization. This raises the question as to whether or not the properties of the interface can be modified to tune the strength of the oscillatory coupling in the magnetic multilayers. Indeed can the refleetivities at the interface be modified by s ~ g the hybridization gaps to higher or lower binding energies through the use of alloys in the ferromagnetic layer. Such questions are now being investigated. Finally we note that we have restricted our discussion to the electronic structure of the thin films. We have chosen not to discuss the film thickness dependence of the magnetic anisotropy observed in these films. This is an active area of research [101, 102]. However to date, because of the small energy scales involved, there has been tittle experimental study of the relationship between the microscopic electronic structure and the anisotropy.
ACKNOWLEDGEMENTS
The author is pleased to acknowledge stimulating conversations with N. Brookes, N.V. Smith, M. Weinert, E. Vescovo, S. Blugel, D. Li and S.D. Bader. Support for this work is provided by the Department of Energy under contract number DOE-AC02-76CH00016.
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91997 Elsevier Science B.V. All rights reserved. Growth and Properties of Ultrathin Epitaxiat Layers D.A. King and D.P. Woodruff, editors.
583
Chapter 15 Ultrathin magnetic structures - magnetism and electronic properties
J.A.C. Bland Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE In this article, the magnetic properties of ultrathin transition metal films and multilayers are discussed. Specific emphasis is given to the ground state magnetic moments, magnetic anisotropies, the magnetic reversal process in epitaxial structures and to the connections between these properties. Experimental tools for probing the basic magnetic properties of ultrathin magnetic films and multilayers are first introduced, specifically the magnetooptic Kerr effect for vector magnetometry measurements and polarised neutron reflection as an absolute magnetometry technique. Measurements of the thickness dependent ground state magnetic moments for bcc Fe epitaxial films are reviewed and compared with the results of ab-initio calculations. It is shown that quantitative agreement between the measured and predicted values requires that the interface structure atomic roughness is known and accounted for. The magnetic anisotropy behaviour as a function of thickness and orientation are described for transition metal epitaxial structures grown on single crystal substrates, including semiconductors, and discussed in the context of computational studies and phenomenological models of interface anisotropies, including strain effects. Atomic scale structures (e.g. steps) are shown to create additional symmetry breaking local anisotropies which can have a marked influence on the global magnetic hysteresis behaviour. Finally the vector spin switching processes which occur in anisotropic ultrathin films are described with particular reference to epitaxial Fe films. 1. INTRODUCTION The subject of ultrathin film magnetism is now very rapidly growing, stimulated by discoveries of a steadily increasing range of phenomena and by the increasing contribution it is making to our fundamental understanding of the physics of magnetism [ 1]. For example, studies of the 2D phase transition, magnetic interactions, magnetic moments, surface anisotropies, 2D domain
584 structures and 2D magnetic ordering phenomena have all yielded important new fundamental insights. Particularly important findings from an applied viewpoint include the discovery of perpendicular anisotropy, the giant magnetoresistance effect, interlayer exchange coupling and room temperature spin dependent tunnelling. The lively and continuing interplay between applications-oriented and basic research has generated much excitement and is characteristic of this field. Many key issues central to device or materials performance remain poorly or incompletely understood and hence applications and fundamental science go hand in hand. The realisation of the huge potential for magnetic structures in advanced device and information storage applications is now starting a revolution in condensed matter science and technology. The subject of magnetoelectronics in which magnetic film structures and semiconductors are combined to create new electronic devices which rely on the electron spin is now beginning in the centennial year of the electron's discovery [2]. As these new initiatives gain momentum, the drive to better understand the magnetism of interfaces becomes ever stronger. In the early 80s, the magnetic moment of sufficiently thin (few monolayer) epitaxial Fe/Ag(001) films was predicted [3] and experimentally confirmed [4] to lie perpendicular to the plane of the film. This occurs because a surface magnetic anisotropy term favouring a perpendicular spin orientation overwhelms the volume dependent dipolar energy. Perpendicular anisotropy has now been identified in a wide range of ultrathin ferromagnetic film structures and has already been exploited in perpendicular recording media based on Co/Pt multilayers [5]. In such media, the field perpendicular to the film plane generated by the magnetic domains which store the information is sensed and external perpendicular fields are applied during the magnetic recording process. The giant magnetoresistance (GMR) effect, first identified in Fe/Cr trilayers [6] and multilayers in 1988 [7], describes the large reduction in electrical resistance which occurs when the relative alignment of the Fe layers is changed from an antiparallel to parallel configuration by the application of an external field. Originally this effect was identified in structures with fixed Cr thickness, for which an antiparallel alignment of the Fe layers is favoured due to the interlayer exchange coupling across the Cr spacer layer. The coupling strength was since found [8] to oscillate with thickness in a wide range of spacer materials (so called oscillatory coupling) and this behaviour has since been theoretically described in terms of RKKY interactions in the 2d geometry and magnetic quantum well effects within the spacer layer [9] [10]. New applications based on these discoveries have fuelled much excitement in this field. For example IBM demonstrated in 1994 that a magnetoresistive read head based on the giant magnetoresistance behaviour of a so-called 'spin valve' multilayer structure can be used to read a 1Gb/in2 disc [11] and miniature read heads based on spin valves are now a reality. Read heads for higher density discs (3-5 Gb/in2)have been recently demonstrated.
585 This progress is remarkable, given that less than 10 years have passed from the discovery of the effect to the realisation of the first commercial devices. Very recently, the demonstration of a large room temperature spin dependent tunnelling resistance for transport across thin oxide layers has generated great excitement, both for the basic physics involved but also because of possible applications in magnetic random access memory cells and other devices [12] [13]. The subject of thin film magnetism owes much to the stimulus created by the theoretical predictions during the mid 80's of strongly enhanced magnetic moments for monolayers of the 3d ferromagnetic transition metals supported by noble metal single crystal substrates. It is only recently that methods of sample growth, structural characterisation and magnetic measurement have been refined to the point that accurate tests of these predictions have become possible. Moreover, with the increasing sophistication of our understanding of such phenomena as interface anisotropy, GMR and interlayer coupling, the role of the interface magnetic moments in controlling and giving rise to this behaviour is becoming recognised as increasingly important. For this reason, in this article, particular emphasis will be given to the measurements of the absolute magnetic moment in ultrathin epitaxial films and to a discussion of the techniques equal to this task. New impetus to this field has been recently been given by the application of scanning tunnelling microscopy (STM) studies to the structural characterisation of ultrathin magnetic films, new magnetic microscopy techniques for the study of magnetic microstructure (notably magnetic force microscopy, spin-sensitive STM and near optical MOKE techniques) and the application of advanced lithography and pattern transfer techniques to the fabrication of nanoscale magnetic elements based on ultrathin magnetic films. While the latter subject does not fall within the scope of this article, the insights that STM studies have provided will be highlighted. 2. ULTRATHIN MAGNETIC FILM MAGNETOMETRY Measurements of the magnetic properties of ultrathin structures are highly demanding in view of the small amount of magnetic material involved. A monolayer of Fe in a sample of area 1cm 2 has a total magnetic moment of .-105 emu for example, which corresponds to a signal close to the detection limit of a conventional vibrating sample magnetometer. It is therefore necessary to find methods which can probe such small signals routinely. While good commercial SQUID magnetometers do provide the sensitivity required, the relatively long acquisition time makes the use of other techniques important, while the difficulty of accurately subtracting the comparatively large response of a typically thick diamagnetic substrate remains a challenge. The advent of
586 commercial alternating gradient magnetometry [14] provides an alternative technique, offering the sensitivity of SQUID magnetometry with much more rapid data acquisition. However, the requirement that an alternating field is applied at the sample position in addition to the dc applied field makes it unsuitable for accurate determinations of small switching fields, while high sensitivity temperature dependent measurements are difficult. In this section we will review the use of just two techniques relevant to the detailed studies to be discussed later: magneto-optic Kerr effect magnetometry which has made a very considerable impact in this field as a probe of the M-H loop and magnetic reversal process and polarised neutron reflection which, alongside X-ray circular dichroism, is becoming recognised as a powerful absolute magnetometry technique particularly appropriate to ultrathin films. In addition to magnetometry techniques, RF techniques using ferromagnetic resonance and Brillouin light scattering (BLS) have provided an important role in the quantitative determination of magnetic anisotropies. For excellent reviews of these techniques, the reader is referred to the articles by Heinrich [ 15], Cochran [ 16] and by Hillebrands and Guntherodt [ 17]. 2.1 The magneto-optic Kerr effect: an introduction The magneto-optic Kerr effect (MOKE) was first reported by the Rev. John Kerr in 1877, following a suggestion from Faraday to search for an optical polarisation change induced by a magnetic field [18]. However it was not until relatively recently that the extraordinary sensitivity of the effect in probing the magnetic properties of magnetic films was fully appreciated. In 1985 Moog and Bader [19] demonstrated that the magnetic hysteresis loop of submonolayer Fe/Au films could be detected in UHV. A particular advantage is that a polarised light beam can be readily passed through the windows of a UHV chamber and the reflected beam can also be easily analysed using an external polariser. Thus, in contrast with the relative complexity of polarised electron beam techniques the magneto-optic Kerr effect can be readily adapted to the sensitive probing of the magnetic properties of ultrathin (typically 1-30 monolayer thickness for the case of Fe) films in-situ. In such studies, the saturation and coercive fields can be accurately obtained as a function of the applied field orientation but the loop amplitude is frequently not analysed. Many of these studies are made at fixed wave-length using a laser source, although a number of groups have now carried out spectroscopic measurements in which the Kerr rotation and ellipticity are studied as a function of wavelength. Many exciting new advances in the field of ultrathin magnetic structures have been provided by Kerr effect studies, of which the observation of a 2D Ising behaviour in the magnetic phase transition of Fe/Pd films [20] and the reorientation transition in Fe/Ag films [21] are just two important examples. The development of metallic multilayer materials with perpendicular anisotropy for magneto-optic recording is an important area of
587 applied research. For example rare-earth (RE) - transition metal (TM) alloy films are used commercially for erasable magnetic recording [22] and recently, Co/Pt multilayers [5] have become available for this application. Co/Pt multilayers offer the advantage of a large Kerr rotation at the short wavelengths needed for high bit-packing densities. These important aspects lie outside the scope of the current article although they have stimulated a large research effort addressing the magneto-optic properties of magnetic multilayers. We refer thereader here to previous reviews which focus particularly on MOKE applied to in-situ studies of magnetic films [23] [24] [25]. An excellent introduction to the physical description of magneto-optical effects was given by Freiser. [26] We shall not describe experimental arrangements for measuring the Kerr effect since it is possible to obtain high quality measurements using extremely simple arrangements. The most straightforward of these is based on dc detection using a high quality photodiode and an intensity stabilised laser source. Either the Kerr rotation can be measured by setting an analysing polariser close to extinction or the ellipticity can be measured by inserting a quarter wave plate between the sample and analyser [23]. Conventional ellipsometry techniques can be adapted to allow the determination of the rotation and ellipticity either at fixed wavelength or as a function of wavelength using a spectrometer and a Xe source [27].
2.2 The Magneto-optic Kerr Effect The magneto-optic Kerr effect can be described as the magnetisation-induced change in polarisation state and/or intensity of light upon reflection from a magnetised medium. The Kerr effects are proportional to the magnetisation, thus distinguishing them from other magneto-optical effects. At normal incidence the plane of polarisation is rotated (polar Kerr effect) by a sizeable fraction of a degree [28] for perpendicularly saturated ferromagnetic transition metals and is therefore easily measurable. Indeed, using a relatively simple arrangement, the effect was first demonstrated by reflecting light from the polished poles of an electromagnet. Since light penetrates metals only the short distance determined by the optical skin depth (typically 15-20nm in metals [29]) the Kerr rotation is determined by the surface vicinity of the medium on this lengthscale. For this reason ultrathin films can yield a measurable Kerr rotation and ellipticity. The origin of magneto-optical effects in ferromagnetic metals lies in the spin-orbit interaction between the electron spin and the orbital angular momentum [30]. The electric field of the light couples to the electron dipoles via the orbital wavefunctions which are in turn influenced by the electron spin via the spin-orbit interaction. [31] In ferromagnets a net electron spin polarisation leads to an overall rotation of the polarisation of the light.
588 Calculation of the magneto-optic response of metals requires that the spinresolved bandstructure is known. Spin dependent optical transitions are calculated for the appropriate photon energy for right and left circularly polarised light. For the ferromagnetic transition metals, for example, the magneto-optic contribution to the conductivity (off-diagonal components of the conductivity tensor) has been computed in the visible range [32] [33]. Since the electronic structure of films beneath typically 5ML thickness departs from the bulk structure, the magneto-optic response is modified accordingly. Surprisingly, bulk constants do appear to describe well experimental measurements of Kerr spectra obtained for Fe/Ag [34] films of few monolayers thickness, but recent studies for Co/Au films [35] show that an interface induced Kerr rotation exists. Following recent advances in computational and measurement techniques, obtaining accurate agreement between the measured and calculated magneto-optic constants is now in prospect and thus magneto-optical studies of ultrathin films may soon be placed on a quantitative footing. Magnetic circular dichroism (MCD) in the X-ray region is now being widely applied to the study of ultrathin magnetic layers and interfaces. MCD can be used to probe spin split atomic levels thus providing element specificity together with magnetic information [36] [37] [38]. It is also possible to separate the spin and orbital contributions to the magnetic moment while high sensitivity can be achieved by exploiting an absorption edge and using a synchrotron source. In the following treatment we shall not be concerned with calculation of the appropriate magneto-optic constants but rather with a phenomenological description based on the dielectric tensor. We will also restrict our attention to the visible range.
2.3 A macroscopic description of the Kerr effect The macroscopic description of magneto-optical effects is based on the dielectric tensor in which off-diagonal terms arise due to the magneto-optical transitions [39] [40] [41]. Such off-diagonal terms can easily be understood to arise from the Lorentz force on the electrons giving rise to a component of the dielectric tensor proportional to B • E. For a crystal with cubic symmetry the dielectric tensor is given by: 1 iQz-iQy) [E] = EoEr -iQz 1 iQx iQy -iQx 1
(1)
Y where Q = :--B (B is the magnetic induction and y is a constant), the y axis is the intersec~iron of the scattering plane with the sample surface and z is the
589 normal to the interface, e0 is the permittivity of free space, s is the relative permittivity of the material. For ferromagnetic transition metals, Q is of the order of 10-2 and has been tabulated in the literature for various metals [42]. When the off-diagonal terms are absent, the electromagnetic modes of the light which propagate without change through the medium (the eigenmodes) are pand s-plane polarised waves. Both of these modes have the same velocity. By diagonalization and suitable transformation of the Maxwell equations it is possible to show that the eigenmodes correspond to left-circularly and rightcircularly polarized waves, where each propagates with a different velocity. Thus as the two circularly polarized modes propagate through the magnetic medium a phase difference builds up between them resulting in a change of the observed polarization state of transmitted light. Since the magnetic induction inside a ferromagnetic medium is approximately equal to the magnetisation M, to a very good approximation the off-diagonal terms of the matrix are proportional to the appropriate components of M. The wave equation can be written down using (1) and the resulting eigenvalue equation used to yield the eigenmodes of the medium. Wave solutions can then be written in terms of the forward and backward propagating eigenmodes. This requires a 4 component vector since each mode in general has to be defined by 2 components of electric field. By satisfying the boundary conditions on the electric field components it is possible to obtain the reflectivity matrix. This approach can be extended for an arbitrary number of layers: Yeh [43, 44] has described a matrix approach to the problem and a similar approach appropriate for ultrathin film multilayers has been described by Zak et al. [45] The reflectivity matrix can be written as:
[ R ] = / r )prpprssrss p
(2)
where p,s refer as usual to the components of the light polarisation in the scattering plane and perpendicular to it. The components of the matrix depend upon the appropriate component of Q according to the orientation of M with respect to the scattering plane. The orientation of the magnetisation with respect to the scattering plane defines each of the three principal geometries for the Kerr effect. For the polar and longitudinal geometries (magnetisation M in the scattering plane, normal and parallel to the sample surface respectively) the off-diagonal terms are proportional to Q and the diagonal terms are unchanged. For the transverse (or equatorial) geometry (M perpendicular to the scattering plane but in the plane of the sample surface) no off-diagonal term arises and the diagonal reflectivities contain a Q dependent term.
590 2.4 Vector M O K E The distinction between the orientation of the applied field and the component of the magnetisation being observed is of key importance. For the applied field the terms PF, LF and TF are used for the polar, longitudinal and transverse geometries respectively. For the magnetisation components the terms PM, LM and TM are used to describe the orientation of the component being detected. Thus it is possible to have the magnet in the transverse geometry while detecting the longitudinal component of the magnetisation (TF/LM), for example. Since the longitudinal magnetisation component produces a change in rps only, while the transverse magnetisation component produces a change in r only, it is possible to measure components independently of each oP~er, allowing a determination of components these parallel and perpendicular to the applied field. At normal incidence the longitudinal effect vanishes allowing the perpendicular magnetisation component to be separated. Vector MOKE magnetometry is an extremely powerful probe of the magnetisation process in epitaxial magnetic films in the presence of competing energy terms [46] [47]. In the absence of large positive interface anisotropies, the dipolar interaction forces the magnetisation into the plane and the process is characterised by a 2d vector. Typically, the Zeeman and anisotropy energies compete in single layers, while an additional exchange coupling energy can arise in trilayer and multilayer structures. 2.5 Polarised Neutron Reflection: an introduction While MOKE provides measurements of the magnetisation vector (to within a scaling factor) it does not provide measurements of the total sample moment since the origin of the Kerr effect is the spin-orbit interaction, not the magnetic induction. In contrast, PNR provides an absolute measure of precisely this quantity. Interest is now rapidly growing in the application of polarised radiation techniques such as X-ray Magnetic Circular Dichroism (XMCD) [37] [38], second harmonic generation [48] and polarised neutron reflection (PNR) [49] which give access to the magnetic structure at interfaces. The development of sum rules in XMCD permits element selective quantitative estimates of the spin and orbital moments from measurements of the X-ray absorption spectrum and dichroism spectrum. However these sum rules were derived from an atomic picture of moment formation and so their application to the transition metal magnets remains controversial. For strongly itinerant ferromagnets such as Ni they are unlikely to be appropriate. Wu, Wang and Freeman [50] used local density energy band calculations to show that the sum rule for the orbital moment was accurate to within 10% if the effects of band hybridisation could be accounted for experimentally. Additional difficulties arise from accounting for effects associated with the magnetic dipole term (which can affect the spin sum rule for <Sz> for solids which lack cubic symmetry) and for the effects of diffuse scattering [51].
591 Moreoever, the sum rules have not been fully tested for low symmetry structures. In addition to the theoretical difficulties, experimental difficulties exist such as the precise relation between the photo-absorption cross section and the detected signal. The current consensus is that XMCD is reliable for measuring trends or differences in the quantities <Sz>, and the ratio /<Sz>. For this reason the availability of an alternative reliable, absolute magnetometry technique remains important. The specific problem of interface induced moments demands that the layer dependent magnetic moment distribution is known. In general a variation in the magnetisation as a function of layer position can arise in chemically homogeneous layers, due to interface strain effects or interface anisotropies for example. PNR is particularly important in this context since it is able to provide layer selective measurements of the vector magnetic moment in ultrathin structures. An important advantage in ultrathin film magnetometry is that no substrate induced signal arises in PNR. SQUID magnetometry, while widely used and offering the advantage of very high sensitivity, suffers from the disadvantage that the magnetic signal which arises from a diamagnetic substrate such as Ag or Cu is often comparable with that of the magnetic layer, thus making an absolute measurement extremely difficult and requiring, ideally, in-situ measurements during growth. Since a stronger temperature dependence of the magnetisation occurs in ultrathin films in comparison with the bulk it is also necessary to carry out magnetisation measurements at liquid helium temperatures, a requirement easily met using PNR. Although to date PNR has been regarded as a relatively specialised technique, the number of reflectometers throughout the world is rapidly growing and the technique is being increasingly used.
2.6 Polarised neutron reflection
In PNR the partially reflected neutron intensity is measured as a function of the incident spin state and incident wave vector. The incident wave vector ki is varied either by rotating the sample with fixed incident wavelength )~i or by employing a time of flight method with a fixed incidence angle 0 [49]. The ideal reflecting (ferromagnetic) medium can be represented by a onedimensional (1D) optical potential V(y) where the direction normal to the surface of the film defines the y axis. A multilayer can be described by a sequence of layers (i.e. a stratified medium) each with a constant interaction potential. For the ith layer, the in-plane spatially averaged optical potential Vi, may be approximated by: 2rth2 Vi = mn p i b i - [tn.Bi
(3)
592 where mn is the neutron mass, 9i is the atomic density, bi is the bound coherent neutron scattering length of the material [49], ~tn is the neutron magnetic moment, Bi is the total magnetic induction in the medium (arising from the magnetically aligned atomic moments) and the suffix i labels the medium. In this simple description each ferromagnetic medium is assumed to be uniformly magnetised with the spins in-plane and held parallel to the z direction by the external field. The case of non-aligned spins is discussed elsewhere [49] [52] [53] [54]. Non-magnetic media have no magnetic term. The critical wavevector qci for the ith medium in a multilayer structure is obtained from (3) using Schr6dinger's equation. The critical angle is typically of the order of lo for many solids using cold neutrons (12,~). The flipping ratio F = R+/R - where the superscripts correspond to the incident spin parallel (+) or antiparallel (-) to the applied field or the spin asymmetry S given by ( F - 1)/(F + 1) is determined as a function of wavevector so yielding magnetometric information. Matrix methods for calculating these reflectivity coefficients have been described elsewhere [52] [53]. It is also straightforward to follow an approach frequently used in multilayer optics in which the amplitude of successively reflected beams is added in a geometric series [55]. To a first approximation, in the case of an ultrathin ferromagnetic film of thickness t supported by a non-magnetic substrate and covered with a non-magnetic overlayer of thickness d2 the spin asymmetry is given by" S -- qmt sin(2q2d2)
(4)
where q is the incident wavevector defined above, q2 is the wavevector in the 2nd medium (non-magnetic overlayer) rn is the magnetisation of the layer given by rn = psg~tB where p is the density of the magnetic layer, s is the spin per atom, g = 2 (since in ferromagnetic transition metals the contribution of the orbital moment is very small) and ~B is the Bohr magneton. Thus the size of the spin asymmetry is directly proportional to the total moment ~t of the sample, mt. In the case of an ultrathin magnetic film an independent determination of the thickness of the film (using for example RHEED oscillations or X-ray diffraction) needs to be made in order to extract the moment per atom ~t = sg~tB. In Fig. 1 we show the observed spin asymmetry obtained at He temperatures corrected for partial incident beam polarisation, background intensity and diffuse scattering for Ag/10.9 Fe/Ag(001) and Ag/5.5 Fe/Ag(001) sandwich structures described in section 3 [56]. Since the spin asymmetry is insensitive to small roughness amplitudes it can be fitted with the magnetic moment the only adjustable parameter. In each case the spin asymmetry was therefore calculated assuming uniformly magnetised ferromagnetic layers and a moment per atom adjusted to best fit the data. For
593 comparison the calculated spin asymmetry assuming the bulk moment per Fe atom is also shown (dashed line in Fig. 4). It is clear that a strong enhancement of the magnetic moment occurs, as we shall discuss further in section 3, but the spin asymmetry follows well the form of the behaviour expected from eqn. 4. For nm thickness ferromagnetic films the wavevector dependence of the spin dependent reflectivities can be used to obtain very accurate values for the film thickness. Thus the technique is self calibrating in so far as it independently provides a measurement of the film thickness and the magnetic moment. For an ultrathin film, in principle the same information can be extracted from measurements of the reflectivity but the smaller magnetic layer
Ag/Fe(O01)structures '
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Figure 1. The observed spin asymmetry obtained at He temperatures corrected for partial incident beam polarisation, background intensity and diffuse scattering for Ag/10.9 Fe/Ag(001) andAg/5.5 Fe/Ag(001) sandwich structures. From reference [56].
594 thickness requires that measurements are made to very large values of wavevector (typically of the order of q = 2rc/t ) and in this limit the reflectivity is impractically low. In all cases the measured value of S is modified by the beam polarisation. Macroscopic surface waviness gives rise to long-range fluctuations in the surface flatness, i.e. the fluctuations are correlated over a distance much longer than the effective coherence length of the neutron in-plane (typically 100 ktm [57]). Such waviness can be described by an increase in the effective wavevector resolution of the experiment, equivalent to an increase in the angular spread of the incident beam. Following Nevot and Croce [58] for an interface exhibiting a random gaussian roughness distribution, the specular reflectivity rij is modified to become rij exp(-Wij) where Wij = 2qiqj~ij and where ~ij = defines the variance of the local fluctuation in interface position. In practice roughness correlations occur and diffuse reflection results [59]. The diffuse scattering intensity accepted by the detector scales with the solid angle accepted and for measurements on single crystal substrates its contribution must be accounted for at large wavevector [60]. For the case of non-spin aligned layers it is necessary to use a 4 component vector of the neutron wave within each medium of the form (Ai+,Bi+Ai-,Bi -) where the superscripts refer to the spin component with respect to the applied field [52] [61] [54]. The + a n d - reflectivities are both dependent on both of the in-plane components of the magnetisation vector as described by a 4 component reflectivity matrix (vector PNR). In the case of two fully antiparallel ferromagnetic layers PNR is able to determine the orientation of each layer and not only the antiparallel ordering seen in diffraction experiments [49].
3 ABSOLUTE M A G N E T I C MOMENTS The magnetic moment per atom is a fundamental quantity and therefore knowledge of its value is essential in relating the magnetic properties of an ultrathin film to the electronic structure. Relatively few accurate measurements of interface magnetic moments are available due to the technical difficulties involved. Excellent introductions to the electronic structure and magnetic properties of magnetic thin films are to be found in the review articles by Gay and Richter and by Daalderop et al. in ref. [ 1] 3 . 1 3-d metal magnetic m o m e n t s - an overview In the bulk ferromagnetic transition metals Fe, Co and Ni the moment arises principally from the unfilled 3d band with a small 4s contribution. The familiar Slater-Pauling curve for the bulk elements demonstrates a clear trend in the magnetic moment as a function of the band filling. Initially, the moment
595 increases in going from Cr to Fe but as the bandfilling further increases the moment reduces, with the maximum moment occurring for Fe with g= 2.2 gB. The itinerant electrons are sensitive to changes in the environment of the atom but in going from the bulk element to an ultrathin film the effect of reduced dimensions differs according to the bandfilling. In all cases the coordination Z of the atoms at the surface of a ferromagnetic layer is reduced in comparison with that of the bulk. As a result the bandwidth of the 3d electrons is reduced which scales as_ -,72. For Fe, in which both the majority (1") and minority ($) bands are both partially filled, the effect of narrowing the majority band is to dramatically increase the magnetic moment which is given by:
= I(~ 1"-~$)dE
(5)
In the case of ultrathin bcc Fe(001) slabs for example, for a 5 monolayer (ML) slab the moment predicted by Ohnishi et al [62] at the surface is almost 3gB, strongly enhanced with respect to the value of 2.2gB found in the bulk (see Table 1). For comparison the moment of a l d chain is calculated to be 3.3gB [63] whereas the moment for the isolated atom is 4gB. For the case of an uncoated 5 layer Fe slab an oscillation in the magnetic moment is clearly seen. This is also supported by the results of calculations by Alden et al [64] using a tight-binding linear muffin-tin orbital (LMTO) approach within the atomic sphere approximation. In fig. 2 we show the majority spin densities of states for the surface (S) and centre (S-3) layers for a 7ML Fe(001 slab. It is clear that the bandwidth is indeed reduced for the surface layer. For the clean Fe(001) surface there are surface states within the valley between the bonding and antibonding bulk peaks. Since these increase the density of states, the presence of the surface states is a further mechanism for increasing the magnetic moment in Fe. These calculations were based on spin density functional theory using the full-potential linearized augmented-plane-wave (FLAPW) method. The calculations indicate that the moment falls as the layer position is moved away from the surface, eventually reaching a value close to that of the bulk within the interior of the slab in the case of thick layers. This clearly demonstrates that the origin of the enhanced moment is the interface. For the (001) surface the moment is more strongly enhanced (32%) than at the (110) surface (19%) according to Freeman and Fu [65] and this finding is also corroborated in the results of Alden et al. The more open (001) surface is expected to have the higher moment given the mechanism for the moment enhancement. Several authors have made ab-initio calculations of the magnetic moments of Fe monolayers, both as unsupported structures and supported on noble metal substrates with and without an overlayer. There is a good degree of consensus concerning the magnitude of the enhancement in Fe. The effect of strain is small in this case
596 and in the calculations by Ohnishi et al. for example, the effect of surface relaxation is ignored. MINORITY S I
M A J O R I T Y SPIN S 1 !
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Figure 2. Majority local partial density of states (in states/eV) in the surface S and centre (S3) atomic spheres of a 7ML Fe(001) slab. Energies are measured with respect to the Fermi energy. The d (s-p) partial densities of states are given by the solid (dotted lines). After Ohnishi et al. [62] Table 1 Predicted moments (gB) in Fe(001) and F e ( l l 0 ) films with and without non-magnetic overlayers and at the surfaces of semi-infinite slabs (cols. 3-4). a: [62]; b: [64]. Layer S S-1 S-2 S-3 Aver. Bulk
Ag/5 Fe/A~(001) 0.08 a 2.52a 2.37 a 2.27a 2.4a
5 Fe(001)
Fe(110)
Fe(100)
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The induced polarisation in X/Fe/Ag structures with X=Pd, Cu, Ag and Au has been studied by the Strasbourg group in parallel with the experimental studies described below. The aim of these studies was (i) to identify the relative contributions of the X layer (via an induced polarisation) and the Fe
597 layer to the total moment of the sample and (ii) to simulate the effects of nonabrupt interfaces. The computational method used is based on the ab-initio augmented spherical wave (ASW) technique within the local spin density approximation (LSDA). An elementary cell is required which is reproduced in 3 spatial directions for the determination of the band structure in reciprocal space. The advantage of this reciprocal space approach is that interface roughness can be modelled within the cell. In these calculations the lattice parameter of Ag and the interplanar
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Fe thickness (monolayer)
F i g u r e 3. The total m o m e n t per Fe atom as a function of the Fe thickness for X/n F e / A g structures in the (001) orientation [66].
separations are determined assuming that the atomic volumes of Fe and X remain constant. The Fe is then bct (body centred tetragonal), the Cu and Au layers are fct (face centred tetragonal) and the stacking as an AB stacking of (001) planes. For the case of Pd oveflayers on Fe(001) the lattice parameter is expanded in-plane by 4.2% in order for lattice matching with the Fe to occur. The ASW calculations show that the stablest configuration corresponds to a structure in which the vertical lattice parameter is contracted by 7.2% in order
598 to conserve the total volume per atom. High resolution X-ray diffraction experiments confirm that this indeed occurs for the case of a Ag/6.9MLPd/5.7ML Fe/Ag(001) epitaxial structure. The calculations again confirm that most of the enhancement originates in the interface region. The polarisation induced in the Cu, Ag and Au overlayers is small and nearly negligible, in agreement with the FLAPW calculations, but for Pd a sizeable polarisation is predicted. Fig. 3 shows the total moment per Fe atom as a function of the Fe thickness. The Fe/Pd is the most strongly polarized, then Fe/Au, Fe/Ag and finally Fe/Cu is the least strongly polarized. This trend is seen in the moment values for the structures given in table 3. A weak oscillation in the moment with thickness occurs at around 4ML Fe and the fall off in moment with increasing thickness is clearly seen. For a 10ML Fe film a substantial enhancement of the average moment per Fe atom is still seen. For a Pd/5ML Fe/Ag(001) structure an average moment per Fe atom of 2.64 Bohr magnetons is calculated assuming 25% intermixing within 1 monolayer (ML) of the Fe/Pd interface. The corresponding value for the sharp interface is 2.59 Bohr magnetons. In table 2 we show the calculated values for 5ML Fe films covered with various materials. In table 3 we show the moments in Fe monolayers supported by different substrates calculated by B lugel et al using spin density functional theory in the LSDA and also by Stoeffler et al for various sandwiched configurations. The largest moment is obtained for the Pd(001) surface and the Pd/1Fe/Ag(001) structure. The smallest moment is obtained on the Cu substrate and for the Cu overlayer where hybridization effects are strongest. For Co and Ni the surface/interface enhancement effect is much weaker than in Fe since the majority band is almost saturated. As a result a large enhancement occurs for Fe/Ag, less for Co/Cu while for Ni/Ag the moment is approximately the same as in the bulk (see tables 3 and 4). This trend is confirmed by the calculations of Stepanyuk et al for the moments per atom of 3d metal monolayers supported by Pd substrates [70]. Table 2 Predicted layer averaged moments (gB) for Ag/5Fe/Ag (001) oriented slabs [66]. The calculations assume sharp interfaces. Interplanar relaxation effects are included. These calculations form the basis for comparison with detailed experiments using PNR described below. Structure Pd/5 Fe/Ag(001) Ag/5Fe/Ag(001) Au/5Fe/Ag(001) Cu/5Fe/Ag(001)
Moment(gB) 2.59 2.51 2.50 2.50
Reference [66] [66] [66] [66]
599
Table 3 Calculated moments in ~tB for Fe monolayers supported by different substrates for the FM and AFM configurations and for the unsupported case and for the coated case. System
FM
AFM
1Fe 1Fe/Pd(001) 1Fe/Ag(001) 1Fe/Cu(001) 6Pd/1Fe/5Ag(001) 6Au/1Fe/5Ag(001 ) 6Ag/1Fe/5Ag(001 ) 6Cu/1Fe/5Ag(001)
3.18 (free) 3.19 3.20 3.01 3.06 2.61 2.35 3.19 2.77 2.73 2.70
Reference [62] [67] [68] [69] [66] [66] [66] [66]
These calculations were based on density functional theory and the KorringaKohn-Rostoker (KKR) Green's function method. The moment of Ni is very close to the bulk value whether the Ni is an overlayer or an impurity whereas for Fe the moment as an overlayer or as an impurity is strongly enhanced in comparison with the bulk value (see fig. 4). Due to the hybridization with the substrate and with the adatoms in the clusters, the maximum of the moment is shifted to large valencies with respect to the bulk case. The magnetic moments follow Hund's rule and so are largest at the centre of the transition metal series. Except for V and Cr, the moments are well saturated and the maximum magnetic moment is found for Mn corresponding to half band filling. The impurity and adatom moments of Fe and Co are predicted to be slightly larger than the corresponding monolayer ones. It is important to consider the case of adatoms as well as the monolayer case for the insight they bring into the question of how the structure of the system affects the magnetic moment. For Cu and Ag the electronic d bands are located well below the Fermi energy and the influence on adatoms and overlayers is principally via the sp electrons. In contrast, for Pd and Pt the d bands cross the Fermi level and are not completely filled. The d band of Pd is close to the ferromagnetic instability and bulk Pd has the largest Stoner enhanced susceptibility amongst the 4d metals. Hence the main difference between the magnetic properties of adatoms, clusters and monolayers on Pd(Pt) and Ag, Au and Cu is the increased d-d hybridization between the electronic states of the adsorbates and the substrates. The semi-empirical tight binding method has been widely used by the Strasbourg group to calculate atoms at steps for example [71]. In the case of Fe/Cr interfaces the effect of roughness is seen to lead to strong frustration
600 5 m
4
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3
0
2
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1
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l ..... .'~ol,,ye, .S:7~u,
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:-
Sc
Ti
4
i
i
I
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I
V
Cr
Mn
Fe
Co
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Figure 4. Comparison between the magnetic moments per atom of 3d transition metals as adatoms on Pd(001), 3d monolayers on Pd(001) and 3d impurities in bulk Pd [70]. effects in the Cr which strongly modify the magnetic moments [72]. The advantage of the method is that it is applicable to modelling real space structure and consideration of such effects is particularly important in comparing theory and experiment quantitatively. 3.2 Strain and volume dependence of the magnetic moment The issue of strain is extremely important in considering the magnetic properties of epitaxial films. It is well known that the lattice matching of an epitaxial overlayer onto a single crystal substrate introduces a sizeable strain which can affect strongly the magnetic anisotropy. An important example is the fct Ni/Cu system in which the tetragonal distortion of the cubic fcc Ni cell (which occurs via a 2.5% in plane tensile strain of the Ni lattice parameter (3.52A) to match that of the Cu(001) substrate (3.61A)) introduces a strong perpendicular anisotropy within a restricted thickness range [73][74][75]. While the effect of strain on magnetic moment formation has not been widely studied, theoretical studies for bulk phases show that this is an important issue. Tests of ab-initio calculations of magnetic moments have so far been largely restricted to epitaxial systems where the strain, and hence the change in WiSher Seitz sphere volume is small or negligible. Moruzzi and Marcus [76] have used first principles total energy band theory in the local spin density approximation to study the onset and the large volume limit of magnetic behaviour for the 3d transition metals. They find that all 3d transition metals undergo transitions from non magnetic to magnetic behaviour with increasing volume. As a function of volume the magnetic moment increases, tending toward the Hund's rule limit. In general the equilibrium (zero pressure) state is not one of maximum spin, i.e. Hund's rule is not satisfied. As the volume increases, the bands become narrow and eventually approach the discrete levels of a free atom and so Hund's rule for the ground-state is satisfied. This
601 effect can be understood to arise from the competition between exchange energy which favours high spin states and the kinetic energy of the 3d electrons. At large volumes it becomes energetically favourable to increase the spin by populating high kinetic energy states. Bulk total energy calculations indicate that both ferromagnetic and antiferromagnetic states exist for fcc Fe close to the lattice parameter of Cu on which Fe(001) can be grown epitaxially [76]. For smaller lattice constants a non magnetic state dominates whereas at expanded values the ferromagnetic state is stabilized.
3.3 Magnetic moments and surface stability It should be mentioned that the size of the magnetic moment and consequent exchange energy is important in determining the total surface free energy of a magnetic overlayer/substrate structure. It is well known that magnetism plays an important role in the stability of bulk metals and alloys, the case of Fe being an important example. Broadly speaking, there is a competition between the exchange energy, which scales as the square of the magnetic moment, and therefore which is largest for lowest coordination and the cohesive energy which is lowest for the largest coordination. As a result the stability of various overlayer structures actually depends on the magnetic configuration of the overlayer and the value of the magnetic moment. This has been demonstrated explicitly by Blugel et al. [68] [67] [69] who have calculated the total energy of various 3d magnetic monolayer structures as a function of the magnetic order. They find strong differences between the p(1 x 1) ferromagnetic and the c(2 x 2) antiferromagnetic structures. For Mn the difference between the wetting energies for the ferromagnetic and c(2 • 2) state is largest, corresponding to an energy gain of 0.15eV and 0.32 eV respectively. For V, Cr and Mn monolayer films on noble metal substrates the c(2 x 2) state is the most stable whereas for Fe, Co and Ni, the p(1 • 1) is favoured. The energy difference is of the order of 300 meV which is a sizeable energy in the formation of alloys. A consequence is that magnetism tends to stabilise ultrathin films on noble metal substrates and to prevent transition metal films from interdiffusion. In Table 4 the moments of the stable configurations of various 3d overlayers is given. As in the bulk, AF structures are favoured by transition metals at the middle of the series. An important conclusion is that considerations of the surface energies of the deposited atoms made without including the effect of magnetism will not be reliable in predicting the stable structure. The total energies of monolayers as buried layers and as overlayers have been compared by Blugel et al. [69] using spin density functional theory in the local spin density approximation (LSDA). The resulting energies in all cases favour the formation of buried layers for Cu(001) substrates. Thus the monolayer film on Cu(001) is a metastable state. This finding is supported by the observations of several
602 Table 4 Calculated average moments in ~B for various epitaxial transition metal monolayer structures for the FM and AFM configurations. System 1V/Ag(001) 1V/Pd(001) 1Cr/Ag(001) 1Cr/Au(001) 1Cr/Pd(001) 1Mn/Ag(001) 1Fe/Cu(001) Cu/1Fe/Cu(001) Co/Cu(001) Co/Cu(111) Co/Ag(001) Co/Pd(001) Co/Pd(111) Co/Pt(111) Ni/Cu(001) Ni/Cu(111) Ni/Ag (001) Ni/Pd(001)
FM
2.85 2.60 1.79 1.63 2.03 2.12 1.88 1.84 0.39 0.34 0.58-0.65 0.89
AFM
Reference
2.08 1.39 3.57 3.48 3.46 4.11
[77] [78] [77] [79] [78] [77] [80] [80] [81] [82] [77] [77] [83] [83] [84] [85] [77] [78]
groups that for fcc Co films deposited at room temperature on Cu(001) a surface segregation of Cu occurs. With increasing temperature the coverage of the Cu overlayer increases. This has an important effect on the magnetic properties as we shall discuss later. Relaxation of the overlayer is in general important in determining magnetic stability. Wuttig et al. [86] have investigated the structure and magnetism of a new class of magnetic structure, the two dimensional ordered surface alloy c(2 x 2)Mn/Cu(001). They find that this system can support ferromagnetism due to the gain in energy associated with the outward buckling of the Mn atoms. 3.4 Measurements of absolute magnetic moments in ultrathin transition metal films Our discussion of experimental tests of the ab-initio calculations will be restricted to ultrathin bcr Fe films which provide a sufficiently well
603 characterised epitaxial structure to enable accurate tests to be made. Fcc Fe on the other hand, is complicated by the fact that FM or AF phases can be stabilised according to the growth temperature and preparation conditions, and complex internal spin structures have been reported for ultrathin films in which the surface magnetic order differs from that of the interior of the film. We note that although the fcc Co/Cu(001) system has been widely studied in magnetism since the fcc Co phase can be stabilised up to very large thicknesses, Co on Cu(001) forms complicated interdiffusion structures in the monolayer regime making few monolayer thickness films unsuitable for magnetometry studies [87]. Beyond 2ML the Co grows in an almost layer by layer mode. An early PNR study revealed that the magnetic moment for a thick (10ML) Co film sandwiched by Cu had a moment close to the bulk value [88]. Highly strained fct Co films can be grown on Ag(001). Angle resolved Auger studies indicate that the film grows as an fct structure and beyond around 3ML it is not possible to stabilise a single crystal film due to the very strong in-plane strain. For a 2ML film, sandwiched by Ag, a moment close to 2gB was determined by PNR, close to the theoretically predicted value given in Table 4 [89]. While some of the theoretical predictions for bcc Fe films have been indirectly confirmed by experiments such as photoemission [90] and Mossbauer studies of the hyperfine fields [91], at present very few direct magnetometric studies have been carried out on films supported by noble metals with sufficient accuracy to yield absolute values of the magnetic moment per atom and which distinguish between the degree of enhancement obtained for different overlayer materials. In many cases the presence of islands and defects in the films in the monolayer range makes magnetometry measurements impossible, the Fe/W(110) system being an exception [92] [93] as we discuss below. SQUID magnetometry studies of relative moments have been reported by Wooten et al. [94] for Fe ultrathin ( 2 . 9 - 4.4 ML) Fe films incorporated into sandwich structures on Ag(001) system, the results of which we discuss later.
3.5 X/Fe(001) films on Ag(001) substrates Epitaxial bcc films stabilised by Ag(001) substrates have provided an important opportunity for accurately testing the theoretical predictions of modified magnetic moments using PNR [95]. The epitaxial growth of bcc Fe(001) layers on Ag(001) has been described by Heinrich et. al. [96] [97]. Fe grows in the 45 degree rotated bcc phase on Ag(001) substrates with the inplane lattice parameter of the Fe expanded by 0.8% to match the Ag lattice parameter, and fcc phase Ag and Au overlayers can be stabilised on such Fe(001) epitaxial layers. Ultrathin epitaxial Pd(001) layers grow in a metastable cubic phase on Fe(001) with the in-plane lattice constant expanded as noted previously [21], closely corresponding to the critical value at which
604 the onset of ferromagnetism occurs according to the non-relativistic calculations of Chen et al. [98]. The epitaxial growth of metastable bcc Cu(001) on Fe(001) occurs with the in-plane Cu lattice parameter 1.2% smaller than that of the Fe substrate. In the PNR studies by Bland and co-workers [99], sandwich structures of the form Au/X/Fe/Ag(001) were grown by the Simon Fraser Group on singular Ag(001) substrates held at room temperature. A parallel FMR study of the relative values of the magnetic moments was carried out as a check on the PNR measurements [100]. For films above 5ML thickness prepared in this way, the samples have an in-plane easy axis, as required for the PNR measurements. Moreover, the vertical mismatch between the bcc Fe and fcc Ag lattice parameters makes the growth very sensitive to the presence of steps on the surface, making the use of singular substrates important [97]. The inplane lattice parameter and Fe film thickness was determined from RHEED intensity oscillation measurements during growth. RHEED patterns and RHEED intensity oscillations indicate that the interface roughness is limited to a maximum of two monolayers [ 101] [96] [97]. The observed spin asymmetry obtained at He temperatures was corrected for partial incident beam polarisation, background intensity and diffuse scattering. In each case the spin asymmetry was calculated assuming uniformly magnetised ferromagnetic layers and a moment per atom adjusted to best fit the data. Representative data was shown earlier in section 2. In Fig. 5 we show the measured layer averaged moments for each thickness of Fe compared with the values predicted by Ohnishi et al. (a dashed line is drawn to connect the values predicted by Ohnishsi et al.; for the 1 ML case, the value for the 1 Fe/Ag structure is used). The only variable parameters are therefore the layerdependent magnetisation and the roughness amplitude. However the spin asymmetry is insensitive to small roughness amplitudes and so the spin asymmetry can be fitted with the magnetic moment the only adjustable parameter. These results confirm that the moments are enhanced with respect to the bulk and that the interface is the origin of the enhancement. A summary of the results and a comparison with the FMR measurements of the relative moment is given in Table 5. For a Pd/5.6Fe/Ag(001) sample an effective layer averaged moment of 2 . 6 6 _ 0 . 0 5 g B (including the contribution from spin polarised Pd) was determined. The ASW calculations yield a moment for the Pd/Fe sample of 2.59gB for an ideal interface, in disagreement with the measured value. However the calculated value increases to 2.64gB when 25% intermixing is included across a 1ML region at the interface (see Fig. 5). This value agrees within errors with the moment determined by PNR. XRD measurements show that the interface has a local roughness amplitude of--2ML so supporting this model. The average value of the layer averaged moments for Cu/Fe, Ag/Fe
605 3.1 .~
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It is known from several independent studies of this system that the strength of the anisotropies depends strongly on the method of surface preparation and can differ significantly from substrate to substrate. Hence studies of the strength of the anisotropies based on samples measured ex-situ show large scatter. In-situ magneto-optic Kerr effect (MOKE) measurements [141] allow an evaluation of the complete thickness dependence of the magnetic anisotropy of a film on a single surface, avoiding any uncertainties due to different substrate morphologies. On both the (001) and (110) substrates Fe initially grows in a paramagnetic phase up to a thickness of---15 A. On the (001) substrate, beyond the paramagnetic region a uniaxial anisotropy with the
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616 decreases monotonically with thickness, falling to zero at around 500,~. This range over which the uniaxial anisotropy varies for the (001) surface, although large could be consistent with an anisotropic strain mechanism since strain effects can persist over such large thicknesses. The cubic anisotropy increases from zero to the bulk value over a thickness range of approximately 250A. The magnetisation shows a similar variation suggesting a common origin for the thickness dependence. For the (-110) surface, both the MOKE and B LS results are consistent with a change of sign in Ku with increasing thickness. At 200/k thickness, Ku is positive and still increasing. This behaviour is consistent with previous ex-situ measurements [142]. Such a behaviour cannot be explained as arising from a single mechanism only and suggests that competing mechanisms arise, e.g. strain-induced, step-induced or surface anisotropy. At a critical thickness around 100,~, the exact value depending sensitively on the substrate and the growth conditions, a purely 4 fold symmetry develops due to the interface anisotropy balancing the intrinsic 2-fold anisotropy. The bcc Fe/W(-110) system shows similar behaviour to that seen for the GaAs(-110) surface with the difference that the uniaxial anisotropy decays purely as d-1 and so does not exhibit the change of sign seen on the GaAs surface. From the thickness at which the effective anisotropy is purely 4 fold the uniaxial anisotropy strength can be accurately determined assuming that the cubic anisotropy is independent of thickness for the Fe/W case [143]. A strongly thickness dependent uniaxial anisotropy arises which has been attributed to the 2 fold symmetry of the unsatisfied Ga or As bonds at the Garich or As-rich surface terminations. If when Fe is first deposited these bonds are first satisfied, an atomic scale anisotropic structure resulting in equivalent strains along the two in-plane directions could be imagined. Alternatively, atomic steps at the GaAs surface, possibly associated with the surface reconstructions, could give rise to step-induced magnetic anisotropies. Experimental studies show that the sign of the uniaxial anisotropy is almost always the same for a give substrate suggesting that atomic steps due to miscuts are not the origin. However, as we shall discuss below, it is possible that structures associated with the reconstructed GaAs surface give rise to step-like anisotropies. In the case of the Ga rich (001) surface the Ga dangling bonds extend along the [110] direction whereas for the As rich (001) surface the dangling bonds extend along the [-110] direction. Thus differing uniaxial anisotropy behaviour can be expected for these two cases. Gester et al. find that the easy uniaxial axis lies along the [-110] direction on Ga rich substrates prepared by sputter annealing whereas on As rich reconstructed (001) surfaces the uniaxial anisotropy indeed has an easy axis along the [110] direction. Gester et al. also found the magnetic anisotropy behaviour to be essentially the same for Fe grown on sputter annealed substrates and annealed-only substrates, the latter showing no LEED pattern o
617 prior to Fe growth. It is assumed that crystallographically ordered areas exist on the annealed-only substrate but that they extend over a length scale too small to be detected by LEED. This result indicates that short range atomic ordering is primarily responsible for the anisotropy behaviour. Recent studies by Jonker et al. [ 144] have also addressed the issue of the possible dependence of the magnetic properties on the atomic scale structure of the Fe film revealed by STM studies. They find that on As rich reconstructed (001) surfaces the uniaxial anisotropy indeed has an easy axis along the [110] direction for both the (2 • 4) and c (4 • 4) surfaces. However, the (2 • 4) and c(4 • 4) surfaces show very different As dimer configurations and STM studies during the initial growth of the Fe confirm that the morphology of the Fe clusters differ in the early stages of Fe growth. For the c(4 x 4) surface no atomic ridges occur in contrast to the (2 • 4) surface which has ridges of As directed long the [110] axis. In the latter case, the STM studies show that the Fe initially forms elongated structures along the As ridges and that subsequently deposited Fe fills the areas between the ridges. However, for thicker films no detectable difference in the uniaxial magnetic anisotropy behaviour is seen suggesting that the ridge structure associated with the original GaAs surface reconstruction is not important. The STM studies also confirm that after 1ML Fe growth the surface reconstruction has completely disappeared, so arguing against the step anisotropy model. The change in the sign of the uniaxial anisotropy for the Fe films prepared on As rich surfaces compared with those prepared on Ga rich surfaces is however consistent with the anisotropic strain mechanism originating in the directionality of the dangling bonds. However vector Kerr microscopy studies on Fe structures similar to those investigated by Gester et al. [ 145] confirm that the direction of the uniaxial anisotropy axis does not lie precisely along the directions, lending support to the local atomic step model. Thus the origin of the uniaxial anisotropy remains unclear and it would be desirable to be able to probe the Fe in-plane strain variation with high precision as a test of the anisotropic strain model.
5.2 Vector switching processes in Fe/GaAs(001) The vector magnetometric technique has been applied to the study of switching processes in epitaxial Fe/GaAs(001) films [ 146] [ 147] [ 148]. The combination of the uniaxial and cubic anisotropies results in the two hard cubic directions being inequivalent and it is found that the interplay of these two terms strongly affects the magnetisation reversal process. Remarkably, it is found that except for fields applied close to the easy axis, the magnitude of the magnetisation vector remains virtually constant during the reversal process except very close to the switching field at which abrupt reorientation of the magnetisation vector in plane occurs [ 149].
618 Figs. 9 and 10 show vector M - H loops and corresponding vector spin maps obtained by M O K E for an Fe film with a significant anisotropy ratio r = Ku/K 1- 0.42 as a function of the angle ~ between the applied field and the hard uniaxial anisotropy axis. For large ~, 1 jump switching occurs. For ~ = 20 ~ two jumps can be seen as shown in Fig. 10. These two jumps occur when the magnetisation traverses each of the two hard axis directions that exist in a sample with Irl < 1. The jumps correspond to the magnetisation vector making an abrupt transition from an orientation corresponding to a local energy m i n i m u m to another orientation corresponding to a deeper minimum. In a model of this process which assumes coherent rotation, the jump occurs when the first energy minimum completely disappears, but in practice domains form
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