Surface Phonons

309 Pages·1991·17.64 MB·English

by  W. Kress, F. W. de Wette (auth.), Dr. Winfried Kress, Professor Dr. Frederik W. de Wette (eds.)

Springer Series in
Surface Sciences
21
Editor: Gerhard Ertl
Springer Series in Surface Sciences
Editors: G. Ertl and R. Gomer Managing Editor: H. K. V. Lotsch
Volume 1: Physisorption Kinetics By H. J. Kreuzer, Z. W Gortel
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Volume 5: Chemistry and Physics of Solid Surfaces VI
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Experiment, Theory and Surface Structure Determination
By M. A. Van Hove, W H. Weinberg, C.-M. Chan
Volume 7: Electronic Phenomena in Adsorption and Catalysis
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Editors: R. Vanselow, R. Howe
Volume 11: The Structure of Surfaces II
Editors: J. F. van der Veen, M. A. Van Hove
Volume 12: Diffusion at Interfaces: Microscopic Concepts
Editors: M. Grunze, H.J. Kreuzer,J.J. Weimer
Volume 13: Desorption Induced by ElectronicTransitions, DIET III
Editors: R. H. Stulen, M. L. Knotek
Volume 14: Solvay Conference on Surface Science Editor: F. W. de Wette
Volume 15: Surfaces and Interfaces of Solids By H. Liith
Volume 16: Theory of the Atomic and Electronic Structure of Surfaces
By M. Lannoo, P. Friedel
Volume 17: Adhesion and Friction Editors: M. GrunzeandH.J. Kreuzer
Volume 18: Auger Spectroscopy and Electronic Structure
Editors: G. Cubiotti, G. Mondio, K. WandeIt
Volume 19: Desorption Induced by ElectronicTransitions, DIET IV
Editors: G. Betz, P. Varga
Volume 20: Semiconductor Surfaces ByW. Monch
Volume 21: Surface Phonons Editors: W Kress, F. W de Wette
Volume 22: Chemistry and Physics of Solid Surfaces VIII
Editors: R. Vanselow, R. Howe
W Kress RW de Wette (Eds.)
Surface Phonons
With.Contributions by
G. Benedek J.E. Black V. Celli
W. Kress A. A. Maradudin L. Miglio
D.L. Mills G.!. Stegeman J.P. Toennies
S. Y Tong R W. de Wette
With 160 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Dr. Winfried Kress
Max-Planck-Institut fUr Festkorperforschung, Heisenbergstrasse 1,
W-7000 Stuttgart 80, Fed. Rep. of Germany
Professor Dr. Frederik W. de Wette
Department of Physics, The University of Texas at Austin,
Austin, TX 78712, USA
Series Editors
Professor Dr. Gerhard Ertl
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6,
1000 Berlin 33, Fed. Rep. of Germany
Professor Robert Gomer, Ph. D.
The James Franck Institute, The University of Chicago, 5640 Ellis Avenue,
Chicago, IL 60637, USA
Managing Editor: Dr. Helmut K. V. Lotsch
Springer-Verlag, Tiergartenstrasse 17,
W-6900 Heidelberg, Fed. Rep. of Germany
ISBN-13: 978-3-642-75787-7 e-ISBN-13: 978-3-642-75785-3
DOl: 10.1007/978-3-642-75785-3
Library of Congress Cataloging-in-Publication Data. Surface phonons 1 W. Kress, F. W. de Wette (eds.).
p. cm.-(Springer series in surface sciences; v. 21) Includes bibliographical references and index. ISBN
0-387-52721-4 (alk. paper) 1. Phonons. 2. Surfaces (Physics) I. Kress, W. (Winfried), 1941-. II. Wette, F. W.
de (Frederick w.) III. Series: Springer series in surface sciences; 21. QCI76.8.P5S87 1991 530.4'16-
dc20 90-10345
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Preface
In recent years substantial progress has been made in the detection of surface
phonons owing to considerable improvements in inelastic rare gas scattering tech
niques and electron energy loss spectroscopy. With these methods it has become
possible to measure surface vibrations in a wide energy range for all wave vectors
in the two-dimensional Brillouin zone and thus to deduce the complete surface
phonon dispersion curves. Inelastic atomic beam scattering and electron energy
loss spectroscopy have started to play a role in the study of surface phonons
similar to the one played by inelastic neutron scattering in the investigation of
bulk phonons in the last thirty years. Detailed comparison between experimen
tal results and theoretical studies of inelastic surface scattering and of surface
phonons has now become feasible. It is therefore possible to test and to improve
the details of interaction models which have been worked out theoretically in the
last few decades. At this point we felt that a concise, coherent and self-contained
guide to the rapidly growing field of surface phonons was needed.
The present book contains a series of contributions by experts in the field
of surface phonons which review the fundamental concepts of surface waves,
describe the most successful methods of calculating the dynamics of crystal
surfaces (the slab and the Green's function methods), outline the experimental
techniques of atomic beam spectroscopy and electron energy loss spectroscopy,
together with the recent developments of the appropriate scattering theory, and
give a survey of the measured and calculated surface phonon dispersion curves.
We dedicate this volume to the memory of Heinz Bilz, who made essential
contributions to the better understanding of solid state physics, in particular in
the fields of lattice dynamics, infrared absorption, light scattering and displacive
phase transitions. To the authors of this volume he was more than just an open
minded partner for very many fruitful, encouraging, and extremely stimulating
discussions; he was a wonderful human being and a very dear friend.
Stuttgart and Austin Winfried Kress, Frederik W. de Wette
November 1990
v
Heinz Bilz
(18 May 1926 - 26 June 1986)
VI
Contents
1. Introduction
By W. Kress and F.W. de Wette 1
2. Surface Acoustic Waves
By A.A. Maradudin and G.l. Stegeman (With 10 Figures) . . . . . . . 5
2.1 Surface Acoustic Waves on Various Media ............... 6
2.1.1 Elastic Media ................................ 6
2.1.2 Piezoelectric Media ........................... 16
2.2 Generation and Detection of Surface Acoustic Waves 24
2.2.1 Electrical Generation and Detection
in Piezoelectric Media ......................... 25
2.2.2 Generation on Non-piezoelectric Media ........... 27
2.2.3 Acousto-optic Detection
of Generated Surface Acoustic Waves .......... . . 28
2.2.4 Brillouin Scattering from Surface Waves ......... . 28
2.3 Some Applications of Surface Acoustic Waves ........... . 30
2.3.1 Applications to Electronic Signal Processing ...... . 30
2.3.2 Measurements of Intrinsic Material Properties ..... . 32
References 34
3. The Green's Function Method
in the Surface Lattice Dynamics of Ionic Crystals
By G. Benedek and L. Miglio (With 10 Figures) .............. . 37
3.1 Outline of the Time-Independent Green's Function Method .. 37
3.2 The Green's Function Method in Surface Dynamics ....... . 42
3.3 The Intrinsic Perturbation for a Semi-Infinite Lattice ...... . 46
3.4 The Electronic Contribution to Surface Dynamics
in the Framework of Shell Models ...................... 50
3.5 Surface Phonon Polaritons ............................. 53
3.6 Surface Vibrations in Alkali Halides .... . . . . . . . . . . . . . . . . 55
3.7 Further Developments:
The Study of Surface Phonon Anomalies ................. 62
References ............................ . . . . . . . . . . . . . . . . . . 65
VII
4. Study of Surface Phonons by the Slab Method
By F.W. de Wette (With 20 Figures) . . . . . . . . .. . ... . . . . . . .. . . . 67
4.1 Fonnalism .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.1 Slab Dynamics ............................... 69
4.1.2 Use of Symmetry ............................. 73
4.1.3 Slab Vibrational Modes
and Their Dispersion Curves .................... 74
4.1.4 Macroscopic and Microscopic Surface Modes ...... 78
4.1.5 Attenuation Curves ............................ 78
4.1.6 Systematic Features of Surface Modes ............ 80
4.2 Computational Considerations .......................... 81
4.2.1 Diagonalization Techniques ..................... 81
4.2.2 Surface Brillouin Zone Sampling ................ 82
4.3 Interaction Models ................................... 85
4.3.1 Simple Pair Potentials (Molecular Crystals) ........ 85
4.3.2 Shell Models (Ionic Crystals) .. . . . . . . . . . . . . . . . . . 86
4.3.3 Force Constant Models (Semiconductors, Metals) ... 88
4.4 Results ............................................ 89
4.4.1 Relaxation and Dynamics
of the (001) Surfaces of Alkali Halides ........... 89
4.4.2 Results for fcc and bec Metals .. . . . . . . . . . . . . . . . . 92
4.4.3 Layered Structure - Graphite .................... 95
4.5 Derived Physical Quantities .............. . . . . . . . . . . . . . 97
4.5.1 Mean-Square Amplitudes of Vibration
and Vibrational Correlation Functions ............. 97
4.5.2 Surface Debye Temperature ..................... 103
4.5.3 Surface Thennodynamic Quantities ............... 104
4.6 Concluding Remarks ................................. 107
References .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5. Experimental Determination of Surface Phonons
by Helium Atom and Electron Energy Loss Spectroscopy
By J.P. Toennies (With 30 Figures) .... ..... ........... .. ... 111
5.1 Theoretical Background ............................... 112
5.2 Kinematics ......................................... 116
5.3 Helium Scattering ................................... 123
5.3.1 General Considerations ......................... 123
5.3.2 Helium Nozzle Beam Source .................... 126
5.3.3 Target Chamber .............................. 131
5.3.4 Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.5 Typical Measurements and Resolution ............ 133
5.4 Electron Scattering ................................... 140
5.4.1 Apparatus ................................... 140
5.4.2 Typical Measurements ......................... 142
VIII
5.5 Intensities ......................................... . 142
5.5.1 Helium Atom Scattering ....................... . 144
5.5.2 Electron Scattering ........................... . 150
5.5.3 Comparison of Experimental Intensities .......... . 153
5.6 Discussion of Experimental Results and Summary ........ . 154
References ............................................. . 162
6. Theory of Helium Scattering from Surface Phonons
By V. Celli (With 5 Figures) .............................. . 167
6.1 Kinematics ........................................ . 167
6.1.1 Kinematic Focusing .......................... . 170
6.2 Dynamical Theory: General Considerations .............. . 171
6.2.1 Box Normalization and Scattering Geometry ...... . 171
6.2.2 Cross Sections and Reflection Coefficients ........ . 172
6.2.3 State-to-State Cross Sections
vs Differential Cross Sections .................. . 173
6.3 One-Phonon Exchange Processes ...................... . 173
6.3.1 The Distorted Wave Born Approximation ......... . 174
6.3.2 The Phonon Matrix Elements '" ............... . 176
6.3.3 The Atom-Surface Matrix Elements ............. . 177
6.3.4 The Differential Reflection Coefficient ........... . 178
6.3.5 Relation to Phonon Density of States
and Correlation Functions ..................... . 179
6.4 The Inelastic Atom-Surface Interaction ................. . 180
6.4.1 The Static Repulsive Potential .................. . 181
6.4.2 The Static Attractive Potential .................. . 183
6.4.3 The Total Static Potential ...................... . 185
6.4.4 The Dynamic Repulsion and the Cutoff Factor .... . 186
6.4.5 Dynamical Effects of the Attractive Potential ...... . 187
References 189
7. The Study of Surface Phonons
by Electron Energy Loss Spectroscopy:
Theoretical and Experimental Considerations
By D.L. Mills, S.Y. Tong and J.E. Black (With 2 Figures) ....... . 193
7.1 A Brief Review .................................... . 194
7.2 The Surface Phonon Excitation Mechanism
in the Impact Regime ............................... . 197
7.3 The Green's Function Approach
to Spectral Density Calculations ....................... . 200
7.4 Calculations of the Cross Section
for Surface Phonon Excitation ........................ . 204
7.5 Concluding Remarks ................................ . 206
References ............................................. . 206
IX