1 Overview of Phonon Raman Scattering in Solids
R. Merlin, A. Pinczuk, W.H. Weber ............................ 1
1.1 Light Scattering Mechanisms and Selection Rules ......... 3
1.1.1 Conservation Laws ................................ 3
1.1.2 Kinematics: Wave Vector Conservation ............. 4
1.1.3 Kinematics: Breakdown of Wave Vector
Conservation ..................................... 5
1.1.4 Light Scattering Susceptibilities ................ 6
1.1.5 Enumeration of Raman Active Modes ................ 9
1.1.6 Stokes and Anti-Stokes Scattering Intensities ... 11
1.2 Resonant Light Scattering and Forbidden Effects ........ 12
1.3 Two-Phonon Scattering .................................. 15
1.4 Phonons in Semiconductor Alloys ........................ 17
1.5 Impurity Centers and Other Defects ..................... 19
1.6 Phonons in Amorphous Materials ......................... 22
1.7 Structural Phase Transitions: Effects of Temperature,
Pressure and Composition ............................... 23
1.8 Conclusions ............................................ 26
References ............................................. 26
I The Effect of a Surface Space-Charge Electric Field on
Raman Scattering by Optical Phonons
Elias Burstein ............................................. 30
References ................................................. 33
2 Raman Instrumentation
Sanford A. Asher, Richard Bormett ........................... 35
2.1 Raman Measurement Regime ............................... 36
2.1.1 Spontaneous, Non-resonance Raman Spectral
Measurements .................................... 36
2.1.2 Spontaneous, Resonance Raman Spectral
Measurements .................................... 37
2.1.3 Nonlinear Raman Measurements .................... 38
2.2 Choice of Raman Excitation Wavelength .................. 38
2.2.1 CW Lasers ....................................... 38
2.2.2 Pulsed Lasers ................................... 39
2.3 Optical Methods for Rayleigh Rejection ................. 40
2.3.1 Holographic Notch Filter ........................ 41
2.3.2 Dielectric Edge Filters ......................... 41
2.3.3 Pre-monochromator Rayleigh Rejection ............ 42
2.4 Raman Spectrometers .................................... 42
2.4.1 Dispersive Raman Spectrometers .................. 42
2.4.2 FT-Raman Spectrometers .......................... 44
2.4.3 Detectors ....................................... 44
2.4.4 Imaging Raman Spectrometers ..................... 45
2.5 Examples of New Raman Instruments for Materials
Characterization ....................................... 46
2.5.1 UV Raman Microspectrometer for CVD Diamond
Studies ......................................... 47
2.5.2 UV Raman Instrument for in situ Studies of CVD
Diamond Growth .................................. 50
2.6 Conclusions ............................................ 52
References .................................................. 53
3 Characterization of Bulk Semiconductors Using Raman
Spectroscopy
J. Menéndez ................................................. 55
3.1 Inelastic Light Scattering by Phonons in
Semiconductors ......................................... 56
3.1.1 Phonons in Semiconductors ....................... 58
3.1.2 Anharmonic Effects .............................. 63
3.1.3 Raman Scattering by Phonons ..................... 64
3.2 Semiconductor Characterization ......................... 76
3.2.1 Crystal Orientation ............................. 76
3.2.2 Temperature Monitoring .......................... 77
3.2.3 Stress Measurements ............................. 80
3.2.4 Impurities ...................................... 85
3.2.5 Alloying ........................................ 90
3.3 Conclusion ............................................. 99
References ............................................. 99
II Finding the Stress from the Raman Shifts: A Case Study
Ingrid de Wolf ............................................ 104
References ................................................ 106
III Brillouin Scattering from Semiconductors
M. Grimsditch ............................................. 107
References ................................................ 108
4 Raman Scattering in Semiconductor Heterostructures
Daniel Gammon .............................................. 109
4.1 Electrons in Semiconductor Heterostructures ........... 111
4.2 Resonant Raman Scattering ............................. 114
4.3 Kinematics ............................................ 117
4.4 Vibrational Raman Scattering in Semiconductor
Heterostructures ...................................... 118
4.4.1 Phonons in Semiconductor Quantum Wells ......... 118
4.4.2 Phonons as a Probe of Interface Roughness
in a Quantum Well .............................. 124
4.5 Electronic Raman Scattering in Semiconductor
Heterostructures ...................................... 132
4.5.1 Shallow Impurities ............................. 133
4.5.2 Quasi-Two-Dimensional Electron Gas ............. 137
4.6 Conclusion ............................................ 144
References ................................................. 144
IV Raman Scattering Enhancement by Optical Confinement in
Semiconductor Planar Microcavities
B. Jusserand, A. Fainstein ................................ 148
References ................................................ 150
5 Raman Scattering in High-Tc Superconductors: Phonons,
Electrons, and Magnons
M. Cardona ................................................. 151
5.1 High-Tc Superconductors: Chemical Composition
and Crystal Structure ................................. 154
5.2 Raman Scattering by Phonons in High-Tc
Superconductors ....................................... 161
5.2.1 Vibrational Frequencies and Eigenvectors ....... 161
5.2.2 Raman Intensities, Raman Tensors ............... 173
5.2.3 The Phases of the Raman Tensors ................ 173
5.3 Scattering by Intraband Electronic Excitations ........ 176
5.3.1 Normal Metals .................................. 176
5.3.2 Scattering in the Superconducting State ........ 184
5.4 Electron-Phonon Interaction ........................... 193
5.5 Crystal Field Transitions Between ƒ-Electron Levels ... 199
5.6 Light Scattering by Magnons in HTSC and Their
Antiferromagnetic Parent Compounds .................... 204
5.6.1 Antiferromagnetic Structures in the
Underdoped Parent Compounds .................... 204
5.6.2 Introduction to Light Scattering by Magnons
in Antiferromagnets ............................ 208
5.6.3 Electronic Structure of the СuО2
Antiferromagnetic Insulator and the Mechanism
of Scattering by Two Magnons ................... 210
5.6.4 Lineshape of Two-Magnon Raman Scattering
in the Insulating HTSC Phases .................. 214
5.6.5 Resonant Raman Scattering by Magnons ........... 216
5.6.6 Scattering by Magnetic Fluctuations in Doped
(Superconducting) Cuprates ..................... 217
References ............................................ 219
V Thoughts About Raman Scattering from Superconductors
Miles V. Klein ............................................ 226
References ................................................ 228
VI Two-Magnon Inelastic Light Scattering
David J. Lockwood ......................................... 230
References ................................................ 232
6 Raman Applications in Catalysts for Exhaust-Gas Treatment
Willes H. Weber ............................................ 233
6.1 Supports and Substrates ............................... 235
6.2 Oxides of the Pt-Group Metals ......................... 239
6.2.1 Platinum Oxides ................................ 239
6.2.2 Iridium and Osmium Oxides ...................... 243
6.2.3 Palladium Oxide ................................ 243
6.2.4 Rhodium Oxides ................................. 246
6.2.5 Ruthenium Oxide ................................ 246
6.2.6 Mixed Oxides ................................... 248
6.3 Oxygen Storage Materials .............................. 249
6.4 Adsorbed Species ...................................... 252
6.4.1 Oxides of Nitrogen ............................. 253
6.4.2 Oxides of Sulfur ............................... 257
6.5 Particle-Size Effects ................................. 259
6.6 Quantitative Analyses ................................. 261
6.7 Summary and Outlook ................................... 265
References ................................................. 266
VII Historical Perspective of Raman Spectroscopy in
Catalysis
Israel E. Wachs ........................................... 271
References ................................................ 272
7 Raman Scattering Spectroscopy and Analyses of III-V
Nitride-Based Materials
Leah Bergman, Mitra Dutta, Robert J. Nemanich .............. 273
7.1 Experimental Considerations for Raman Scattering
of Wide Band-Gap Semiconductors ....................... 274
7.2 Raman Scattering of GaN, AlN, and InN Films and
Crystallites .......................................... 275
7.2.1 Raman Tensors and Structure Identification of
GaN, A1N, and InN .............................. 275
7.2.2 Wurtzite and Zincblende Phases of GaN .......... 279
7.2.3 Wurtzite and Zincblende Structure of AlN and
InN ............................................ 284
7.3 Stress Analysis and Substrate Issues for Epitaxial
Growth ................................................ 287
7.3.1 Stress Analysis of GaN Films ................... 287
7.3.2 Stress Analysis in WZ-AlN ...................... 290
7.4 Raman Analysis of the Quasi-Modes in AlN .............. 292
7.5 Phonon-Plasmon Interaction in GaN Films and
Crystallites .......................................... 296
7.6 Isotopic Effects and Phonon Lifetimes in the
Wurtzite Materials .................................... 301
7.7 Wide Band-Gap Alloys .................................. 303
7.8 Concluding Remarks .................................... 309
References ............................................ 310
8 Raman Scattering in Fullerenes and Related Carbon-Based
Materials
M.S. Dresselhaus, M.A. Pimenta, P.C. Eklund,
G. Dresselhaus ............................................. 314
8.1 Graphite Related Materials ............................ 316
8.1.1 Single Crystal Graphite and 2D Graphene
Layers ......................................... 317
8.1.2 Raman Spectra of Disordered sp2 Carbons ........ 319
8.2 Introduction to Fullerene Materials ................... 326
8.2.1 Mode Classification in Fullerene Molecules ..... 327
8.2.2 C60 Intra-Molecular Modes ...................... 329
8.2.3 Higher-Order Raman Modes in C60 ................ 332
8.2.4 Perturbations to the Raman Spectra ............. 333
8.2.5 Vibrational Spectra for Phototransformed
Fullerenes ..................................... 333
8.2.6 Inter-Molecular Modes .......................... 335
8.2.7 Vibrational Modes in Doped Ceo-based Solids .... 335
8.2.8 Vibrational Spectra for C70 and Higher
Fullerenes ..................................... 337
8.3 Raman Scattering in Carbon Nanotubes .................. 337
8.3.1 Structure of Carbon Nanotubes .................. 338
8.3.2 Nanotube Phonon Modes .......................... 340
8.3.3 Raman Spectra of Single-Walled Carbon
Nanotubes ...................................... 343
8.3.4 Raman Scattering Studies at High Pressure ...... 352
8.3.5 Charge Transfer Effects in Single-Wall Carbon
Nanotubes ...................................... 354
8.4 Summary ............................................... 358
References ............................................
VIII A Case History in Raman and Brillouin Scattering:
Lattice Vibrations and Electronic Excitations in Diamond
A.K. Ramdas ............................................... 365
References ................................................ 368
9 Raman Spectroscopic Studies of Polymer Structure
Shaw Ling Hsu .............................................. 369
9.1 Overview of Structural Characterization ............... 375
9.1.1 Amorphous Polymers: Low Frequency
Observations ................................... 379
9.1.2 Solid State Properties ......................... 382
9.2 Polymer Anisotropy .................................... 385
9.2.1 Motivation ..................................... 385
9.2.2 Partially Oriented Systems ..................... 389
9.2.3 Definition of Orientation Function ............. 394
9.3 Long-Range Order and Disorder in Polymers ............. 396
9.3.1 Initial Observations Made for Models and
Polymers ....................................... 396
9.3.2 Other LAM Observations ......................... 397
9.3.3 Applications of LAM to Polymer Structural
Characterization ............................... 400
9.4 Fermi Resonance Interaction and Its Application
to Structural Analysis ................................ 411
9.5 Disordered States ..................................... 418
9.5.1 Normal Coordinate Approach ..................... 419
9.5.2 Molecular Dynamics Approach .................... 421
9.5.3 Examples ....................................... 423
References ................................................. 438
IX C.V. Raman: A Personal Note
Samuel Krimm .............................................. 446
References ................................................ 447
10 Raman Scattering in Perovskite Manganites
V.B. Podobedov, A. Weber ................................... 448
10.1 Manganite Structure and Selection Rules for Optical
Vibrational Modes ..................................... 451
10.2 Doped Crystals (x > 0) ................................ 453
10.3 Undoped Crystals (x = 0) .............................. 463
10.4 Films ................................................. 467
10.5 Summary ............................................... 475
References ............................................ 476
X Raman Scattering from Perovskite Ferroelectrics
R.S. Katiyar .............................................. 479
References ................................................ 481
Index ......................................................... 483
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