1 Introduction ................................................. 1
1.1 A Survey of Semiconductors .............................. 2
1.1.1 Elemental Semiconductors ......................... 2
1.1.2 Binary Compounds ................................. 2
1.1.3 Oxides ........................................... 3
1.1.4 Layered Semiconductors ........................... 3
1.1.5 Organic Semiconductors ........................... 4
1.1.6 Magnetic Semiconductors .......................... 4
1.1.7 Other Miscellaneous Semiconductors ............... 4
1.2 Growth Techniques ....................................... 5
1.2.1 Czochralski Method ............................... 5
1.2.2 Bridgman Method .................................. 6
1.2.3 Chemical Vapor Deposition ........................ 7
1.2.4 Molecular Beam Epitaxy ........................... 8
1.2.5 Fabrication of Self-Organized Quantum Dots
by the Stranski-Krastanow Growth Method ......... 11
1.2.6 Liquid Phase Epitaxy ............................ 13
Summary ..................................................... 14
Periodic Table of "Semiconductor-Forming" Elements .......... 15
2 Electronic Band Structures .................................. 17
2.1 Quantum Mechanics ...................................... 18
2.2 Translational Symmetry and Brillouin Zones ............. 20
2.3 A Pedestrian's Guide to Group Theory ................... 25
2.3.1 Definitions and Notations ....................... 25
2.3.2 Symmetry Operations of the Diamond and Zinc-
Blende Structures ............................... 30
2.3.3 Representations and Character Tables ............ 32
2.3.4 Some Applications of Character Tables ........... 40
2.4 Empty Lattice or Nearly Free Electron Energy Bands ..... 48
2.4.1 Nearly Free Electron Band Structure in a Zinc-
Blende Crystal .................................. 48
2.4.2 Nearly Free Electron Energy Bands in Diamond
Crystals ........................................ 52
2.5 Band Structure Calculations by Pseudopotential
Methods ................................................ 58
2.5.1 Pseudopotential Form Factors in Zinc-Blende-
and Diamond-Type Semiconductors ................. 61
2.5.2 Empirical and Self-Consistent Pseudopotential
Methods ......................................... 66
2.6 The hp Method of Band-Structure Calculations ........... 68
2.6.1 Effective Mass of a Nondegenerate Band Using
the hp Method ................................... 69
2.6.2 Band Dispersion near a Degenerate Extremum:
Top Valence Bands in Diamond- and Zinc-Blende-
Type Semiconductors ............................. 71
2.7 Tight-Binding or LCAO Approach to the Band Structure
of Semiconductors ...................................... 83
2.7.1 Molecular Orbitals and Overlap Parameters ....... 83
2.7.2 Band Structure of Group-IV Elements by the
Tight-Binding Method ............................ 87
2.7.3 Overlap Parameters and Nearest-Neighbor
Distances ....................................... 94
Problems .................................................... 96
Summary .................................................... 105
3 Vibrational Properties of Semiconductors, and Electron-
Phonon Interactions ........................................ 107
3.1 Phonon Dispersion Curves of Semiconductors ............ 110
3.2 Models for Calculating Phonon Dispersion Curves
of Semiconductors ..................................... 114
3.2.1 Force Constant Models .......................... 114
3.2.2 Shell Model .................................... 114
3.2.3 Bond Models .................................... 115
3.2.4 Bond Charge Models ............................. 117
3.3 Electron-Phonon Interactions .......................... 121
3.3.1 Strain Tensor and Deformation Potentials ....... 122
3.3.2 Electron-Acoustic-Phonon Interaction
at Degenerate Bands ............................ 127
3.3.3 Piezoelectric Electron-Acoustic-Phonon
Interaction .................................... 130
3.3.4 Electron-Optical-Phonon Deformation Potential
Interactions ................................... 131
3.3.5 Frohlich Interaction ........................... 133
3.3.6 Interaction Between Electrons and Large-Wave
vector Phonons: Intervalley Electron-Phonon
Interaction .................................... 135
Problems ................................................... 137
Summary .................................................... 158
4 Electronic Properties of Defects ........................... 159
4.1 Classification of Defects ............................. 160
4.2 Shallow or Hydrogenic Impurities ...................... 161
4.2.1 Effective Mass Approximation ................... 162
4.2.2 Hydrogenic or Shallow Donors ................... 166
4.2.3 Donors Associated with Anisotropic Conduction
Bands .......................................... 171
4.2.4 Acceptor Levels in Diamond- and Zinc-Blende-
Type Semiconductors ............................ 174
4.3 Deep Centers .......................................... 180
4.3.1 Green's Function Method for Calculating
Defect Energy Levels ........................... 183
4.3.2 An Application of the Green's Function Method:
Linear Combination of Atomic Orbitals .......... 188
4.3.3 Another Application of the Green's Function
Method: Nitrogen in GaP and GaAsP Alloys ....... 192
4.3.4 Final Note on Deep Centers ..................... 197
Problems ................................................... 198
Summary .................................................... 202
5 Electrical Transport ....................................... 203
5.1 Quasi-Classical Approach .............................. 203
5.2 Carrier Mobility for a Nondegenerate Electron Gas ..... 206
5.2.1 Relaxation Time Approximation .................. 206
5.2.2 Nondegenerate Electron Gas in a Parabolic
Band ........................................... 207
5.2.3 Dependence of Scattering and Relaxation Times
on Electron Energy ............................. 208
5.2.4 Momentum Relaxation Times ...................... 209
5.2.5 Temperature Dependence of Mobilities ........... 220
5.3 Modulation Doping ..................................... 223
5.4 High-Field Transport and Hot Carrier Effects .......... 225
5.4.1 Velocity Saturation ............................ 227
5.4.2 Negative Differential Resistance ............... 228
5.4.3 Gunn Effect .................................... 230
5.5 Magneto-Transport and the Hall Effect ................. 232
5.5.1 Magneto-Conductivity Tensor .................... 232
5.5.2 Hall Effect .................................... 234
5.5.3 Hall Coefficient for Thin Film Samples (van
der Pauw Method) ............................... 235
5.5.4 Hall Effect for a Distribution of Electron
Energies ....................................... 236
Problems .............................................. 237
Summary ............................................... 241
6 Optical Properties I ....................................... 243
6.1 Macroscopic Electrodynamics ........................... 244
6.1.1 Digression: Units for the Frequency of
Electromagnetic Waves .......................... 247
6.1.2 Experimental Determination of Optical
Functions ...................................... 247
6.1.3 Kramers-Kronig Relations ....................... 250
6.2 The Dielectric Function ............................... 253
6.2.1 Experimental Results ........................... 253
6.2.2 Microscopic Theory of the Dielectric
Function ....................................... 254
6.2.3 Joint Density of States and Van Hove
Singularities .................................. 261
6.2.4 Van Hove Singularities in εi ................... 262
6.2.5 Direct Absorption Edges ........................ 268
6.2.6 Indirect Absorption Edges ...................... 269
6.2.7 "Forbidden" Direct Absorption Edges ............ 273
6.3 Excitons .............................................. 276
6.3.1 Exciton Effect at M0 Critical Points ........... 279
6.3.2 Absorption Spectra of Excitons ................. 282
6.3.3 Exciton Effect at Mx Critical Points or
Hyperbolic Excitons ............................ 288
6.3.4 Exciton Effect at M3 Critical Points ........... 291
6.4 Phonon-Polaritons and Lattice Absorption .............. 292
6.4.1 Phonon-Polaritons .............................. 295
6.4.2 Lattice Absorption and Reflection .............. 298
6.4.3 Multiphonon Lattice Absorption ................. 299
6.4.4 Dynamic Effective Ionic Charges in
Heteropolar Semiconductors ..................... 303
6.5 Absorption Associated with Extrinsic Electrons ........ 305
6.5.1 Free-Carrier Absorption in Doped
Semiconductors ................................. 306
6.5.2 Absorption by Carriers Bound to Shallow
Donors and Acceptors ........................... 311
6.6 Modulation Spectroscopy ............................... 315
6.6.1 Frequency Modulated Reflectance and
Thermoreflectance .............................. 319
6.6.2 Piezoreflectance ............................... 321
6.6.3 Electroreflectance (Franz-Keldysh Effect) ...... 322
6.6.4 Photoreflectance ............................... 329
6.6.5 Reflectance Difference Spectroscopy ............ 332
6.7 Addendum (Third Edition): Dielectric Function ......... 333
Problems .............................................. 334
Summary ............................................... 343
7 Optical Properties II ...................................... 345
7.1 Emission Spectroscopies ............................... 345
7.1.1 Band-to-Band Transitions ....................... 351
7.1.2 Free-to-Bound Transitions ...................... 354
7.1.3 Donor-Acceptor Pair Transitions ................ 356
7.1.4 Excitons and Bound Excitons .................... 362
7.1.5 Luminescence Excitation Spectroscopy ........... 369
7.2 Light Scattering Spectroscopies ....................... 375
7.2.1 Macroscopic Theory of Inelastic Light
Scattering by Phonons .......................... 375
7.2.2 Raman Tensor and Selection Rules ............... 378
7.2.3 Experimental Determination of Raman Spectra .... 385
7.2.4 Microscopic Theory of Raman Scattering ......... 394
7.2.5 A Detour into the World of Feynman Diagrams .... 395
7.2.6 Brillouin Scattering ........................... 398
7.2.7 Experimental Determination of Brillouin
Spectra ........................................ 400
7.2.8 Resonant Raman and Brillouin Scattering ........ 401
Problems .............................................. 422
Summary ............................................... 426
8 Photoelectron Spectroscopy ................................. 4ll
8.1 Photoemission ......................................... 431
8.1.1 Angle-Integrated Photoelectron Spectra of the
Valence Bands .................................. 440
8.1.2 Angle-Resolved Photoelectron Spectra of the
Valence Bands .................................. 443
8.1.3 Core Levels .................................... 451
8.2 Inverse Photoemission ................................. 456
8.3 Surface Effects ....................................... 457
8.3.1 Surface States and Surface Reconstruction ...... 457
8.3.2 Surface Energy Bands ........................... 458
8.3.3 Fermi Level Pinning and Space Charge Layers .... 460
Problems ................................................... 465
Summary .................................................... 468
9 Effect of Quantum Confinement on Electrons and Phonons in
Semiconductors ............................................. 469
9.1 Quantum Confinement and Density of States ............. 470
9.2 Quantum Confinement of Electrons and Holes ............ 473
9.2.1 Semiconductor Materials for Quantum Wells and
Superlattices .................................. 474
9.2.2 Classification of Multiple Quantum Wells
and Superlattices .............................. 478
9.2.3 Confinement of Energy Levels of Electrons and
Holes .......................................... 479
9.2.4 Some Experimental Results ...................... 489
9.3 Phonons in Superlattices .............................. 494
9.3.1 Phonons in Superlattices: Folded Acoustic and
Confined Optic Modes ........................... 494
9.3.2 Folded Acoustic Modes: Macroscopic Treatment ... 499
9.3.3 Confined Optical Modes: Macroscopic
Treatment ...................................... 500
9.3.4 Electrostatic Effects in Polar Crystals:
Interface Modes ................................ 502
9.4 Raman Spectra of Phonons in Semiconductor
Superlattices ......................................... 511
9.4.1 Raman Scattering by Folded Acoustic Phonons .... 511
9.4.2 Raman Scattering by Confined Optical Phonons ... 516
9.4.3 Raman Scattering by Interface Modes ............ 518
9.4.4 Macroscopic Models of Electron-LO Phonon
(Frohlich) Interaction in Multiple Quantum
Wells .......................................... 521
9.5 Electrical Transport: Resonant Tunneling .............. 525
9.5.1 Resonant Tunneling Through a Double-Barrier
Quantum Well ................................... 526
9.5.2 I-V Characteristics of Resonant Tunneling
Devices ........................................ 529
9.6 Quantum Hall Effects in Two-Dimensional Electron
Gases ................................................. 533
9.6.1 Landau Theory of Diamagnetism in a Three-
Dimensional Free Electron Gas .................. 534
9.6.2 Magneto-Conductivity of a Two-Dimensional
Electron Gas: Filling Factor ................... 537
9.6.3 The Experiment of von Klitzing, Pepper and
Dorda .......................................... 538
9.6.4 Explanation of the Hall Plateaus in the
Integral Quantum Hall Effect ................... 541
9.7 Concluding Remarks .................................... 545
Problems ................................................... 546
Summary .................................................... 551
Appendix A: Pioneers of Semiconductor Physics Remember ........ 553
Ultra-Pure Germanium: From Applied to Basic Research
or an Old Semiconductor Offering New Opportunities
By Eugene E. Haller ................................... 555
Two Pseudopotential Methods: Empirical and Ab Initio
By Marvin L. Cohen .................................... 558
The Early Stages of Band-Structures Physics and Its
Struggles for a Place in the Sun By Conyers Herring ... 560
Cyclotron Resonance and Structure of Conduction and
Valence Band Edges in Silicon and Germanium By
Charles Kittel ........................................ 563
Optical Properties of Amorphous Semiconductors and
Solar Cells By Jan Tauc ............................... 566
Optical Spectroscopy of Shallow Impurity Centers By
Elias Burstein ........................................ 569
On the Prehistory of Angular Resolved Photoemission
By Neville V. Smith ................................... 574
The Discovery and Very Basics of the Quantum Hall
Effect By Klaus von Klitzing .......................... 576
The Birth of the Semiconductor Superlattice
By Leo Esaki .......................................... 578
Appendix B: Solutions to Some of the Problems ................. 583
Appendix C: Recent Development ................................ 673
Appendix D: Recent Developments and References ................ 687
References .................................................... 755
Physical Parameters of Tetrahedral Semiconductors (Inside Front
Cover)
Table of Fundamental Physical Constants (Inside Back Cover)
Table of Units (Inside Back Cover)
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