Topics in Applied Physics Volume 54

Topics in Applied Physics Founded by Helmut K.V. Lotsch

1 Dye Lasers 2rid Ed. Editor: F. P. Schiifer

2 Laser Spectroscopy of Atoms and Molecules. Editor: H. Walther

3 Numerical and Asymptotic Techniques in Electromagneties Editor: R. Mittra

4 Interactions on Metal Surfaces Editor: R. Gomer

5 Miisshauer Spectroscopy Editor: U. Gooser

6 Picture Processing and Digital Filtering 2nd Edition. Editor: T. S. Huang

7 Integrated Optics 2nd Ed. Editor: T. Tamir

8 I,ight Scattering in Solids 2nd Edition Editor: M. Cardona

9 Laser Speckle and Related Phenomena 2nd Ed, Editor: J. C. Dainty

10 Transient Electromagnetic Fields Editor: L. B. Felsen

11 Digital Picture Analysis Editor: A. Rosenfeld 12 Turbulence 2nd Ed. Editor: P. Bradshaw 13 High-Resolution Laser Spectroscopy

Editor: K. Shimoda 14 Laser Monitoring of the Atmosphere

Editor: E. D. Hinkley 15 Radiationless Processes in Molecules

and Condensed Phases. Editor: F. K. Fong 16 Nonlinear Infrared Generation

Editor: Y.-R. Shen 17 Electrolumlnescenee Editor: J. 1. Pankovc 18 Ultrashort Lighl Pulses

Picosecond Techniques and Applications Editor: S. L. Shapiro

19 Optical and Infrared Detectors 2rid Ed. Editor: R.J . Keyes

20 Holographic Recording Materials Editor: H. M. Smith

21 Solid Electrolytes Editor: S. Geller 22 X-Ray Optics. Applications to Solids

Editor: H,-J. Queisser 23 Optical Data Processing. Applications

Editor: D. Casasent 24 Acoustic Surface Waves Editor: A.A. Oliner 25 Laser Beam Propagation in the Atmosphere

Editor: J. W. Slrohbehn 26 Photoemission in Solids I. General Principles

Editors: M, Cardona and L. Ley

27 Phutoemission in Solids II. Case Studies Editors: L. Ley and M. Cardona

28 Hydrogen in Metals 1. Basic Properties Editors: G. Alefeld and J. V61kl

29 Hydrogen in Metals If Application-Oriented Properties Editors: G. Alefeld and J, V61kl

30 Excimer Lasers 2rid Ed. Editor: Ch. K. Rhodes

31 Solar Energy Conversion. Solid State Physics Aspects. Edilm': B.O. Seraphin

32 Image Reconstruction from Projections Implementation and Applications Editor: G. T. Herman

33 Electrets Editor: G. M. Scssler 34 Nonlinear Methods of Spectral Analysis

2nd Edition. Editm': S. Haykin 35 Uranium Enrichment Editor: S. Villani 36 Amorphous Semiconductors

Editor: M. H. Brodsky 37 Thermally Stimulated Relaxation in Solids

Editor: P. Br/iunlich 38 Charge-Coupled Devices Editor: D. F, Barbe 39 Semiconductor Devices for Optical

Communication. 2nd Ed. Editor: H. Kressel 40 Display Devices Editor: J. I. Pankove 41 The Computer in Optical Research

Methods and Applications. Editor: B. R. Frieden 42 Two-Dimensional Digital Signal Processing I

Linear Filters. Editor: T. S, Huang 43 Two-Dimensional Digital Signal Processing II

Transforms and Median Filters. Editm': T. S. Huang

44 Turbulent Reacting Flows Editors: P. A. Libby and F. A, Williams

45 Hydrodynamic Instabilities and the Transition to Turbulence Editors: I], L. Swinncy and J. P. Gollub

46 Glassy Metals I Editors: H.-J. Gfintherodt and H. Beck

47 Sputtering by Particle Bombardment 1 Editor: R. Behrisch

48 Optical Information Processing Fundamentals. Editor: S. H. Lee

49 Laser Spectroscopy of Solids Editors: W. M. Yen and P. M. Seizer

50 Light Scattering in Solids It. Basic Concepts and Instrumentation Editors: M. Cardona and G. Gfintlmrodt

5I Light Scattering in Solids Ill. Recent Results Editors: M. Cardona and G. G~ntherodt

52 Sputtering by Particle Bombardment II Sputtering of Alloys and Compounds, Electron and Neutron Sputtering, Surface Topography Editor: R. Behrisch

53 Glassy Metals II. Atomic Structure and Dynamics, Electronic Structure, Magnetic Properties Editors: H. Beck and H.-J. Gfintherodt

54 Light Scattering in Solids IV. Electronic Scattering, Spin Effects, SERS, and Morphic Effects Editors: M. Cardona and G. Gfintherodt

55 The Physics of Hydrogenated Amorphous Silicon I Structure, Preparation, and Devices Editors: J .D. Joannopoulos and G. Lucovsky

56 The Physics of Hydrogenated Amorphous Silicon ll Electronic and Vibrational Properties Editors: J .D. Joannopoulos and G. Lncovsky

Light Scattering in Solids IV Electronic Scattering, Spin Effects, SERS, and Morphic Effects

Edited by M. Cardona and G. Gi in therodt

With Contributions by G. Abstreiter K. Arya M. Cardona S. Geschwind G. Giintherodt R. Merlin A. Otto A. Pinczuk R. Romestain B.A. Weinstein R. Zallen R. Zeyher

With 322 Figures

Springer-Verlag Berlin Heidelberg NewYork Tokyo 1984

Professor Dr. Manuel Cardona

Max-Planck-Institut fiir Festk6rperforschung, Heisenbergstral3e 1, D-7000 Stuttgart 80, Fed. Rep. of Germany

Professor Dr. Gernot Gi~ntherodt

Universit~it zu K61n, II. Physikalisches Institut, Ziilpicher StraBe 77, D-5000 K61n 41, Fed. Rep. of Germany

ISBN 3-540-11942-6 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-11942-6 Springer-Verlag New York Heidelberg Berlin Tokyo

Library of Congress Cataloging in Publication Data. (Revised for volume 54) Main entry under title: Lig scattering in solids. (Topics in apptied physics; v. 8, 50) (Series traced differently) Vols. edited by M. Cardo~ and G. Giintherodt. Includes bibliographies and indexes. 1. Light-Scattering. 2. Raman effect. 3. Sen conductors-Optical properties. 4. Solids-Optical properties. I. Cardona, Manuel, 1934-. I1. Giintherodt, (Gernot), 1943-. Ill . Series: Topics in applied physics; v. 8, etc. QC427.4.L53 530.4'1 75-20237

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerto specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopyi machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law, where cop are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.

(c~ by Springer-Verlag Berlin Heidelberg 19~4 Printed in Germany

The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a speci statement, that such names are exempt from the relevant protective laws and regulations and therefore free t general use.

Monophoto typesetting, offset printing and bookbinding: Briihlsche Universitiitsdruckerei, Giessen 2153/3130-5432 I0

Preface

This volume is the fourth of a series* devoted to light scattering in solids and related phenomena. The first and second volumes (TAP 8 and 50) emphasize general concepts and basic theory, the third one (TAP 51), investigations of specific materials and also Brillouin scattering, while the present one (TAP 54) discusses light scattering by electronic excitations (including magnetic effects), surface-enhanced Raman scattering (SERS), and effects of pressure on phonon spectra. A detailed list of the contents of the whole series can be found in the second edition (paperback) of Vol. l (TAP 8).

The reader may be struck by the imbalance in the size of the various contributions in this volume. Two of them (Chaps. 2 and 6) are exceptionally long. They grew to the present size because the fields they cover exploded while they were being written up. The reader may notice this in the structure of these chapters. While Chap. 2 was being written, the quantum Hall effect and modulation doping were discovered. This gave new impetus to light scattering by two-dimensional electron gases which had been early recognized as an ideal technique for the study of technologically important MOS structures, hetero- structures, superlattices, and Schottky barriers. Chapter 6 discusses SERS from an experimental point of view, with particular emphasis on the effects of adatoms and other chemisorption phenomena versus the electromagnetic resonance mechanism, a rather controversial subject which is still the object of considerable current research. Chapter 6 is complemented in Chap. 7 by the theory ofchemisorption-induced SERS. Chapters 3-5 discuss various aspects of light scattering by electrons and by phonons in which magnetic interactions are of the essence, including the important family of the rare-earth chalcogenides. Finally, Chap. 8 concerns itself with the dependence of scattering by phonons on hydrostatic pressure. It discusses data obtained mainly with the powerful and elegant diamond-anvil-cell technique.

The editors would like to thank all the authors for their cooperation in bringing this volume together and for the patience of those who complied with the original deadline. One half of the contributions are the fruit of transatlantic collaboration, with all the problems of logistics this involves. In the course of solving them, the editors have come to the realization that in this age, in which hundreds of jetliners cross the Atlantic Ocean daily, there is a lot of room for

* Topics in Applied Physics (TAP) Vols. 8, 50, 51, 54

VI Preface

improvement in the postal service within the Atlantic community. Thank goodness for the telephone and telex!

In view of the impossibility of mentioning explicitly the large number of scientists who directly or indirectly have influenced these volumes, we shall mention a few institutions:

AT & T Bell Laboratories in Murray Hill and Holmdel, N J, Brown Uni- versity, the IBM T. J. Watson Research Center in Yorktown Heights, NY, the Ioffe Institute in Leningrad, the Institut ffir Festk6rperforschung der Kern- forschungsanlage Jfilich, the Max-Planck-Institut ffir Festk6rperforschung in Stuttgart, the University of Pennsylvania in Philadelphia, PA, the Universitfit zu K61n, the University of Michigan in Ann Arbor, MI, and the Xerox Research Laboratories in Rochester, NY and Palo Alto, CA. Last but not least thanks are due to our secretaries Kerstin Weissenrieder and Suzanne Wood for patient organizational work and skillful typing of large parts of these volumes, and to Mr. B. Hillebrands for text editing and help with the keywords index.

Stuttgart and K61n, Manuel Cardona December 1983 Gernot Gi~ntherodt

Contents

1. Introduction. By M. Cardona and G. Giintherodt . . . . . . . . . 1 1.1 Contents of Previous Volumes . . . . . . . . . . . . . . . 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. Light Scattering by Free Carrier Excitations in Semiconductors By G. Abstreiter, M. Cardona, and A. Pinczuk (With 99 Figures) . 5 2.1 Introduction and Historical Survey . . . . . . . . . . . . . 6 2.2 Light Scattering by Electron Plasmas in Semiconductors . . . . 10

2.2.1 Electron-Photon Coupling in Semiconductors . . . . . . 10 2.2.2 Single-Component Plasmas . . . . . . . . . . . . . . il 2.2.3 Fluctuation-Dissipation Analysis . . . . . . . . . . . . 14 2.2.4 Single-Component Plasmas: Highly Diluted Case . . . . 16 2.2.5 Single-Component Plasmas: The High Density Case 18 2.2.6 Multicomponent Plasmas . . . . . . . . . . . . . . . 21 2.2.7 The Simple Two-Component Plasma: Acoustic and Optic

Plasmons . . . . . . . . . . . . . . . . . . . . . . 23 2.2.8 The Simple Two-Component Plasma: Neutral Density

Excitations . . . . . . . . . . . . . . . . . . . . . 26 2.3 Resonant Light Scattering by Free Electron Excitations . . . . 27

2.3.1 General Considerations for Light Scattering Cross Sections 28 a) Electron-Density Fluctuations . . . . . . . . . . . 28 b) Charge-Density Fluctuations . . . . . . . . . . . . 32 c) Spin-Density Excitations . . . . . . . . . . . . . . 34 d) Coupled Plasmons LO-Phonons . . . . . . . . . . 36

2.3.2 Experimental Results . . . . . . . . . . . . . . . . . 41 a) Eo+Ao Gap: Single-Particle Excitations . . . . . . . 43 b) Eo+A o Gap: Collective Modes . . . . . . . . . . . 48 c) E1 a n d E l + A 1 Gaps . . . . . . . . . . . . . . . 51

2.4 Scattering by Free Carriers: The Wavevector- and Frequency- Dependent Dielectric Function . . . . . . . . . . . . . . . 53 2.4.1 Background . . . . . . . . . . . . . . . . . . . . 53 2.4.2 Light Scattering Response Functions . . . . . . . . . . 55 2.4.3 Doped Semiconductors . . . . . . . . . . . . . . . . 60

a) n-Type GaAs . . . . . . . . . . . . . . . . . . 60 b) n-Type GaAs Under High Hydrostatic Pressure . . . . 64 c) n-Type GaSb . . . . . . . . . . . . . . . . . . . 65 d) p-Type GaAs . . . . . . . . . . . . . . . . . . 66

VIII Contents

2.4.4 Photoexcited Plasmas . . . . . . . . . . . . . . . . 69 2.5 Light Scattering by Two-Dimensional Electron Systems . . . . 74

2.5.1 Resonant Light Scattering . . . . . . . . . . . . . . 74 2.5.2 GaAs-(AlxGa l_x)As Heterostructures . . . . . . . . . 77

a) Intersubband Spectroscopy . . . . . . . . . . . . . 79 b) Intersubband Spectroscopy: Collective Electron LO-

Phonon Modes . . . . . . . . . . . . . . . . . . 81 c) Intersubband Spectroscopy: Correlation with

Transport Properties . . . . . . . . . . . . . . . 83 d) Intersubband Spectroscopy: Resonant Enhancements 85 e) Intersubband Spectroscopy: Photoexcited P l a s m a s . . 87 f) Spectroscopy of In-Plane Motion: Landau Level

Excitations . . . . . . . . . . . . . . . . . . . . 89 g) Spectroscopy of In-Plane Motion: Plasma Oscillations 90

2.5.3 Ge-GaAs Heterostructures . . . . . . . . . . . . . . 92 2.5.4 Periodic GaAs Doping Multilayer Structures . . . . . . 94

a) Description of the System . . . . . . . . . . . . . 94 b) Tunable Effective Energy Gap Pho to luminescence . . 97 c) Single-Particle and Collective Excitations . . . . . . . 98

2.5.5 Metal-Insulator-Semiconductor Structures . . . . . . . . 100 a) Electrons at InAs Surfaces . . . . . . . . . . . . . 101 b) Hole Accumulation Layers in Si . . . . . . . . . . 103 c) Electron Accumulation Layers in InP . . . . . . . . 106

2.6 Barriers on Semiconductor Surfaces . . . . . . . . . . . . . 107 2.6.1 Electric-Field-Induced Raman Scattering . . . . . . . . 108 2.6.2 Unscreened LO Phonons and Coupled Modes . . . . . . 114 2.6.3 Resonance Effects in InAs . . . . . . . . . . . . . . 116

2.7 Light Scattering in Heavily Doped Silicon and Germanium. 117 2.7.1 Scattering by Intervalley Density Fluctuations . . . . . . 119

a) n-Type Si . . . . . . . . . . . . . . . . . . . . 122 b) p-Type Si . . . . . . . . . . . . . . . . . . . . 125

2.7.2 Interaction Between Raman Phonons and Electronic Continua . . . . . . . . . . . . . . . . . . . . . . 127 a) n-Type Si . . . . . . . . . ' . . . . . . . . . . . 131 b) p-Type Si . . . . . . . . . . . . . . . . . . . . 133 c) Local Vibrational Modes of B in Si . . . . . . . . . 140 d) p-Type Ge, p-Type GaAs . . . . . . . . . . . . . 142

References . . . . . . . . . . . . . . . . . . . . . . . . . . 145

3. High Resolution Spin-Flip Raman Scattering in CdS By S. Geschwind and R. Romestain (With 28 Figures) . . . . . . . 151 3.1 Introductory Comments . . . . . . . . . . . . . . . . . . 151

3.1.1 Historical Background . . . . . . . . . . . . . . . . 151 3.1.2 Role of High Resolution Fabry-Perot Spectroscopy

in SERS . . . . . . . . . . . . . . . . . . . . . . 151 3.1.3 Experimental Procedure . . . . . . . . . . . . . . . 152

Contents IX

3.2 Review of Spin-Flip Raman Scattering . . . . . . . . . . . 153 3.2.1 Classical Picture and Role of Spin-Orbit Coupling . . . . 153 3.2.2 Cross Section by Semiclassical Treatment:

Raman Dipole D (2) . . . . . . . . . . . . . . . . . 154 3.2.3 Momentum Representation for Delocalized Electrons. 156 3.2.4 SFRS in Terms of Quantization of Radiation Field 156 3.2.5 SFRS as Measuring the Transverse Spin Susceptibility

x+(q, rn) . . . . . . . . . . . . . . . . . . . . . . 157 3.2.6 Multiple Spin-Flip Raman Scattering . . . . . . . . . . 158

3.3 Excited States Contributing to SFRS in CdS . . . . . . . . . 159 3.3.1 SFRS Selection Rules for C3v Symmetry . . . . . . . . 159 3.3.2 Role of Bound Excitons in SFRS from Bound Donors 160 3.3.3 Excited States for Scattering from Delocalized Electrons 163 3.3.4 Polariton Effects in CdS . . . . . . . . . . . . . . . 164

3.4 The Insulator-Metal (IM) Transition in CdS Studied by SFRS 165 3.4.1 The Insulator-Metal Transition . . . . . . . . . . . . 165 3.4.2 Charge Diffusion in Terms of a Collisionally-Narrowed

Doppler Width . . . . . . . . . . . . . . . . . . . 166 3.4.3 Distinction Between Spin and Charge Diffusion . . . . . 167 3.4.4 Experimental Results on Diffusive Linewidths . . . . . . 168

3.5 Relationship Between Spin Faraday Rotation and SFRS . . . . 170 3.5.1 Spin Faraday Rotation and Raman Dipole . . . . . . . 170 3.5.2 Wavelength Dependence of SFRS Cross Section in CdS

Determined from Spin Faraday Rotation . . . . . . . . 171 3.5.3 Measurement of Donor Susceptibility by Faraday Rotation 173 3.5.4 Measurement of Donor Relaxation T a by Faraday

Rotation . . . . . . . . . . . . . . . . . . . . . . 174 3.6 Determination of the k-Linear Term in the Conduction Band of

CdS by SFRS . . . . . . . . . . . . . . . . . . . . . . 174 3.6.1 Origin of the k-Linear Term . . . . . . . . . . . . . 174 3.6.2 Appearance of the k-Linear Term in Diffusional SFRS

Linewidth . . . . . . . . . . . . . . . . . . . . . 176 3.6.3 Comparison of 2 in Conduction and Valence Bands 178 3.6.4 Generalization to Bound Donors with Spin Diffusion. 179

3.7 Bound Donors as Model Amorphous Antiferromagnets . . . . 181 3.7.1 Static Properties Studied by Faraday Rotation . . . . . . 181 3.7.2 Dynamics of the Amorphous Antifcrromagnet . . . . . . 184

a) Low-Field Regime: Pure Spin Diffusion . . . . . . . 184 b) High-Field Case: Field-Induced Exchange Stiffness

and Dispersion . . . . . . . . . . . . . . . . . . 186 3.8 Coherence Effects in SFRS and Stimulated SFRS . . . . . . . 188

3.8.1 Scattering from Coherent States in CdS . . . . . . . . . 188 3.8.2 Experimental Observation of SFRS from Coherent States

and Phase Matching . . . . . . . . . . . . . . . . . 190 3.8.3 SFRS fi'om Coherent States Viewed as Modulation of

Faraday Rotation . . . . . . . . . . . . . . . . . . 192

x Contents

3.8.4 Stimulated S F R S . . . . . . . . . . . . . . . . . . 194 3.8.5 R a m a n Echo . . . . . . . . : . . . . . . . . . . . 197

References . . . . . . . . . . . . . . . . . . . . . . . . . . 199

4. Spin-Dependent Raman Scattering in Magnetic Semiconductors By G. Gi in therodt and R. Zeyher (With 19 Figures) . . . . . . . . 203 4.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . 203 4.2 Phenomenologica l Theory . . . . . . . . . . . . . . . . . 205 4.3 Microscopic Theory . . . . . . . . . . . . . . . . . . . . 212 4.4 Scattering in the Paramagnet ic Phase o f EuX ( X = O , S, Se, Te) 216

4.4.1 Selection Rules and Scattering Intensity . . . . . . . . 216 4.4.2 Coupl ing Constants and Resonance Enhancement . . . . 220 4.4.3 Second-Order R a m a n Scattering . . . . . . . . . . . . 221

4.5 R a m a n Scattering in the Magnet ical ly-Ordered Phases o f EuX (X = O, S, Se, Te) . . . . . . . . . . . . . . . . . . 223 4.5.1 Fer romagnet ic Phase . . . . . . . . . . . . . . . . . 223 4.5.2 Magnet ic "Bragg" Scattering f rom Spin Superstructures 225 4.5.3 Resonan t R a m a n Scattering . . . . . . . . . . . . . . 227

4.6 Spin Fluctuat ions near Magnet ic Phase Transit ions . . . . . . 230 4.7 C a d m i u m - C h r o m i u m (Cd-Cr) Spinels (CdCrzX4, X = S , Se) . 232 4.8 Vanad ium Dihalides . . . . . . . . . . . . . . . . . . . 236 4.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 238 No te Added in P roo f . . . . . . . . . . . . . . . . . . . . . 239 References . . . . . . . . . . . . . . . . . . . . . . . . . . 240

5. Raman Scattering in Rare-Earth Chalcogenides By G. Gi in therodt and R. Merlin (With 25 Figures) . . . . . . . . 243 5.1 An Overview of the Properties o f Rare-Ear th Monochalcogenides 244 5.2 Semiconductors . . . . . . . . . . . . . . . . . . . . . 249

5.2.1 Magnet ic-Phase Dependent Scattering by Phonons in EuX (X = O, S, Se, Te) . . . . . . . . . . . . . . . 249

5.2.2 Multiple Scattering by LO(F) Phonons in YbX (X = S, Se, To) . . . . . . . . . . . . . . . . 256

5.3 Metals . . . . . . . . . . . . . . . . . . . . . . . . . 258 5.3.1 Defect- Induced Scattering . . . . . . . . . . . . . . 259 5.3.2 Superconductors . The Model o f Local Cluster

Deformabili t ies . . . . . . . . . . . . . . . . . . . 260 5.4 Semiconductor-Meta l Transit ions . . . . . . . . . . . . . . 262

5.4.1 Phonon Anomalies . . . . . . . . . . . . . . . . . 263 5.4.2 Electronic R a m a n Scattering near Configurat ion

Crossover . . . . . . . . . . . . . . . . . . . . . 264 5.5 Intermediate Valence Materials . . . . . . . . . . . . . . . 268

5.5.1 Phonon Anomalies and R a m a n Intensities . . . . . . . 269 5.5.2 Metallic SmS . . . . . . . . . . . . . . . . . . . . 274 5.5.3 Bound Polaronic Charge Fluctuat ion M o d e . . . . . . . 275

Conlents xI

5.6 Higher Rare -Ear th Chalcogenides . . . . . . . . . . . . . . 277 5.6.1 Inhomogeneous Intermediate-Valence Materials . . . . . 277 5.6.2 Miscellaneous Materials . . . . . . . . . . . . . . . 280

5.7 Conclus ions . . . . . . . . . . . . . . . . . . . . . . . 281 References . . . . . . . . . . . . . . . . . . . . . . . . . . 282

6. Surface-Enhanced Raman Scattering: "Classical" and "Chemical" Origins. By A. Otto (With 91 Figures) . . . . . . . . . . . . . . 289 6.1 Background . . . . . . . . . . . . . . . . . . . . . . . 289 6.2 The P h e n o m e n o n of Surface-Enhanced R a m a n Scattering (SERS),

"Roughness" and Electromagnet ic Resonance Effects . . . . . 291 6.3 Classical Enhancemen t . . . . . . . . . . . . . . . . . . 299

6.3.1 Single-Particle Resonances . . . . . . . . . . . . . . 300 6.3.2 Collective Resonances . . . . . . . . . . . . . . . . 312 6.3.3 Resonances on Grat ings, Rough Surfaces, and by

At tenua ted Total Reflection . . . . . . . . . . . . . 317 6.3.4 Commen t s . . . . . . . . . . . . . . . . . . . . . 323

6.4 Adsorbate-Surface P lasmon Polar i ton In terac t ion Compared to Adsorbate-Mcta l Electron In terac t ion . . . . . . . . . . . . 326

6.5 Is SERS Only an Electromagnet ic Resonance Effect? Selected Relevant Experiments . . . . . . . . . . . . . . . . . . 332 6.5.1 Spacer Exper iments . . . . . . . . . . . . . . . . . 332 6.5.2 SERS from Regular Arrays of Silver Particles . . . . . 335 6.5.3 Optical Properties and "Classical E n h a n c e m e n t " of

Silver-Island Fi lms . . . . . . . . . . . . . . . . . 337 6.5.4 Optical Properties o f " C o l d - D e p o s i t e d " Silver F i l m s . . 347 6.5.5 Second Harmon ic Genera t ion from "SERS-Act ive"

Surfaces . . . . . . . . . . . . . . . . . . . . . . 357 6.5.6 SERS from Colloids . . . . . . . . . . . . . . . . 360 6.5.7 Shor t -Range Effects in SERS . . . . . . . . . . . . . 367 6.5.8 SERS on Metals of Low Reflectivity . . . . . . . . . 373 6.5.9 Chemical Specificity of SERS . . . . . . . . . . . . 377

6.6 Indicat ions for the In terac t ion of Metal Electrons with Adsorbates in SERS . . . . . . . . . . . . . . . . . . . . . . . . 383

6.7 Conclus ion on "Classical E n h a n c e m e n t " . . . . . . . . . . 387 6.8 Charge-Transfer Excitat ions and SERS . . . . . . . . . . . 389 6.9 Evidence for "SERS-Act ive Sites" . . . . . . . . . . . . . 399 6.10 Relevance for Catalysis . . . . . . . . . . . . . . . . . . 409 Note Added in Proof . . . . . . . . . . . . . . . . . . . . . 410 References . . . . . . . . . . . . . . . . . . . . . . . . . . 411

7. Theory of Surface-Enhanced Raman Scattering By K. Arya and R. Zeyher (With 15 Figures) . . . . . . . . . . . 419 7.1 Background . . . . . . . . . . . . . . . . . . . . . , . 419 7.2 Hami l ton i an . . . . . . . . . . . . . . . . . . . . . . . 422 7.3 Scattering Cross Section . . . . . . . . . . . . . . . . . . 424

XII Contents

7.3.1 General Expression . . . . . . . . . . . . . . . . . 424 7.3.2 Scattering Cross Section in the Case of a Molecule with

Two Electronic States . . . . . . . . . . . . . . . . 428 7.4 Local Field Effects Caused by a Bounded Metal . . . . . . . 430

7.4.1 Plane Metal Surface with Roughness . . . . . . . . . . 432 a) Weak Sinusoidal Gra t ing . . . . . . . . . . . . . 435 b) R a n d o m l y Rough Surface . . . . . . . . . . . . . 438

7.4.2 Sphere and Other Substrate Geometr ies . . . . . . . . 443 7.5 Local Field Effects Due to the Presence of a Molecule . . . . . 450 7.6 Chemisorp t ion Effects . . . . . . . . . . . . . . . . . . . 456 7.7 Conclus ions . . . . . . . . . . . . . . . . . . . . . . . 460 References . . . . . . . . . . . . . . . . . . . . . . . . . . 461

8. Pressure-Raman Effects in Covalent and Molecular Solids By B. A. Weinste in and R. Zal len (With 45 Figures) . . . . . . . . 463 8.1 The R a m a n Effect . . . . . . . . . . . . . . . . . . . . 464

8.1.1 How Pressure Enters . . . . . . . . . . . . . . . . . 464 8.1.2 Gr/ ineisen Parameters and Scaling . . . . . . . . . . . 467

8.2 Exper imental Aspects . . . . . . . . . . . . . . . . . . . 468 8.3 P h o n o n Frequencies U n d e r Pressure in Tetrahedral

Semiconductors . . . . . . . . . . . . . . . . . . . . . 471 8 . 3 . 1 0 n e - P h o n o n Spectra and the Transverse Effective C h a r g e . 471 8.3.2 P h o n o n Dispers ion at High Pressure - Two-Phonon Results 479 8.3.3 Thermal Expans ion . . . . . . . . . . . . . . . . . 485 8.3.4 Impl icat ions for Lattice Dynamics Theory . . . . . . . 486

8.4 Changes in P h o n o n Line Shape with Pressure . . . . . . . . . 489 8.4.1 P h o n o n - P h o n o n Interact ions . . . . . . . . . . . . . 489

8.5 Phase Changes . . . . . . . . . . . . . . . . . . . . . . 492 8.5.1 Trans i t ions in CuI . . . . . . . . . . . . . . . . . . 492 8.5.2 Pressure-Induced Metal l iza t ion - Possible Antecedent

Behavior . . . . . . . . . . . . . . . . . . . . . . 495 8.6 Pressure-Tuned Resonan t R a m a n Scattering . . . . . . . . . 498 8.7 Molecular Solids . . . . . . . . . . . . . . . . . . . . . 499

8.7.1 Rat iona le for Pressure -Raman Studies of Molecular

Crystals . . . . . . . . . . . . . . . . . . . . . . 499 8.7.2 Pressure-Induced R a m a n Line Shifts in Simple Organic

and Inorgan ic Molecular Solids . . . . . . . . . . . . 505 8.7.3 Vibra t ional Scaling and the Systematics of the Response

to Pressure . . . . . . . . . . . . . . . . . . . . . 511 8.7.4 The Connec t ion "Between the Effects of Pressure and

Tempera ture . . . . . . . . . . . . . . . . . . . . 514 8.7.5 Molecu la r -Nonmolecu la r Trans i t ions at High Pressure . . 518

References . . . . . . . . . . . . . . . . . . . . . . . . . . 521 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 525

Errata for Light Scattering in Solids II (TAP 50) . . . . . . . . . . 529

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Contributors

Abstreiter, Gerhard Technische Universit/it Mfinchen, Physik Department D-8046 Garching, Fed. Rep. of Germany

Arya, Karamjeet Physics Department, The City College of the City University of New York New York, NY 10031, USA

Cardona, Manuel Max-Planck-Institut ffir Festk6rperforschung, Heisenbergstral3e 1 D-7000 Stuttgart 80, Fed. Rep. of Germany

Geschwind, Stanley AT & T Bell Laboratories, 600 Mountain Avenue Murray Hill, NJ 07974, USA

Gfintherodt, Gernot Universit~it zu K61n, II. Physikalisches Institut, Z/ilpicher Strage 77 D-5000 K61n 41, Fed. Rep. of Germany

Merlin, Roberto Department of Physics, University of Michigan Ann Arbor, MI 48109, USA

Otto, Andreas Universit/it Dtisseldorf, Physikalisches Institut III Universitfitsstral3e 1, D-4000 Diisseldorf 1, Fed. Rep. of Gcrmany

Pinczuk, Aron AT & T Bell Laboratories, 4B-437, Holmdel, NJ 07733, USA

Romestain, Robert Laboratoire de Spectrometrie Physique, B.P. 68 F-38402 St. Martin d'H6res, France

XIV Contributors

Weinstein, Bernard A. Xerox Corporation, Joseph C. Wilson Center for Technology-114 Rochester, NY 14644, USA

Zallen, Richard Virginia Polytechnic Institute, Blacksburg, VA 24061, USA

Zeyher, Roland Max-Planck-Institut ffir Festk6rperforschung, HeisenbergstraBe 1 D-7000 Stuttgart 80, Fed. Rep. of Germany