About the book

Experience has shown that the rather high standards employed in formulating the material do not present undue difficulties to the students. The understanding is substantially facilitated by the presence of practically all of the intermediate calculations. The results of the calculations are sometimes illustrated by experimental data.

The use of the methods of the theory of groups simplifies the handling of many of the problems involved. However, the author bearing in mind that the theory of groups is as a rule not studied in technical colleges felt he had no right to use the theory of groups approach in formulating the material contained in the book limiting himself to an Appendix containing the fundamentals of this theory.

Treating Semiconductor Physics as a separate discipline the author shied away from anything that dealt with the operation of concrete semiconductor devices

CONTENTS
Preface 9

Chapter I. Introduction. Electron Theory of Conductivity 11

1. Electron Theory of Conductivity. Ohm's Law 11
2. Mean-Free Time and Free-Path Distribution Functions 16
3. Electron Distribution Function. Mean Values of Physical Quantities 20
4. Semiconductors. The Classification of Materials According to Their Conductivity 31
5. Semiconductor Conductivity Models. The Concept of a Hole 35
6. Intrinsic and Extrinsic Conductivities 39

Chapter II. The Fundamentals of the Band Theory of Semiconductors 42
7. The Schrödinger Equation for the Crystal 42
8. The Adiabatic Approximation 45
9. Single Electron Approximation 50
10. Periodic Field of the Crystal Lattice. Translational Operator 54
11. Quasimomentum 59
12. The Effective Mass of the Electron 64
13. Relation Between Velocity and Quasimomentum 70
14. Acceleration Operator 73
15. Brillouin Zones 80
16. Normalising Inside a Potential Box and the Discrete Nature of Quasimomentum 85
17. Theory of the Quasifree Electron 90
18. Theory of the Quasibound Electron 105
19. Effective Mass Method. Influence of External Fields on Energy Spectrum of a Crystal 119
20. Localised States 125
21. Elementary Theory of Impurity States 130
22. Surface States 138
23. Quantisation of Electron Energy in a Magnetic Field. Landau Levels 141
24. Pauli Principle. Concept of Metal, Semiconductor, and Dielectric 146
25. Main Features of the Hole 153
26. Band Structure of Some Semiconductors. Calculation Methods 158
27. Quasiparticle Concept 175

Chapter III. Electron and Hole Statistics in Semiconductors 180
28. Density of States 180
29. Electron and Hole Concentrations 189
30. Electric Neutrality Equation 197
31. Intrinsic Semiconductor 200
32. Extrinsic Semiconductor. Impurity of One Type 205
33. Semiconductor Doped with Both Acceptor and Donor Impurities 215
34. Degenerate Semiconductor 221
35. Density of States in a Magnetic Field 225

Chapter IV. Kinetic Phenomena in Semiconductors 234
36. Boltzmann's Kinetic Equation 234
37. Relaxation Time 241
38. Electric Current Density and Energy Flux Density 249
39. Kinetic Coefficients 253
40. Conductivity of Semiconductors 261
41. Galvanomagnetic Effects 270
42. Hall Effect in Extrinsic Conductivity Range 280
43. Hall Effect in a Substance with Several Types of Charge Carriers 288
44. Magnetic Field Dependence of Hall Coefficient 294
45. Magnetoresistive Effect 302
46. Heat Conductivity of Semiconductors 311
47. Thermoelectric Phenomena 318
48. Thermomagnetic Phenomena 334
49. General Analysis of Kinetic Phenomena 338
50. On Kinetic Phenomena in Semiconductors with Tensor Effective Masses 348
51. Tensorsensitive Effect. Tensorsensitivity 352
52. Piezoresistive Effect. Piezoresistance Coefficients 359

Chapter V. The Theory of Charge Carrier Scattering 369
53. Effective Scattering Cross Section 369
54. Relationship Between Relaxation Time and Effective Cross Section 378
55. Elements of Quantum Transition Theory 383
56. Impurity Ion Scattering 390
57. Scattering by Neutral Impurity Atoms 398
58. Lattice Vibrations. Normal Coordinates, Phonons 401
59. Acoustical and Optical Lattice Vibrations 409
60. Lattice Specific Heat. Phonon Statistics 422
61. Scattering by Thermal Lattice Vibrations. Method of Deformation Potential 432
62. Temperature Dependence of Charge Carrier Mobility 441
63. Dependence of Relaxation Time on External Fields. Deviations from Ohm's Law 452

Chapter VI. Charge Carrier Recombination 461
64. Continuity Equation. Lifetime 461
65. Recombination Mechanism. Linear Recombination 472
66. Diffusion and Drift of Nonequilibrium Charge Carriers 484
67. Surface Recombination 492

Chapter VII. Contact Phenomena in Semiconductors 497
68. Debye Length 497
69. Work Function 510
70. Contact Potential Difference. Metal-Metal Contact 515
71. Metal-Semiconductor Contact 519
72. Inhomogeneous Semiconductor, p-n Junction 525

Chapter VIII. Optical and Photoelectrical Phenomena in Semiconductors 532
73. Light-Absorption Spectrum 532
74. Light Absorption by Free Charge Carriers 536
75. Cyclotron Resonance 546
76. Intrinsic Light Absorption 555
77. Absorption of Light by the Lattice 573
78. Light Absorption by Electrons in Localised States 579
79. Influence of the Ambient on Absorption Spectrum 586
80. Photoresistive Effect 590
81. Dember Effect. Photovoltaic Effect 599
82. Photomagnetoelectric Effect 608
83. Faraday Effect 613
84. Spin-Orbital Splitting of Energy Bands 623

Appendix. Introduction to the Theory of Groups 633

Recommended Literature 694