Fundamentals of the Physics of Solids (eBook)

Preface 7
Contents 10
Contents Volume 1: Structure and Dynamics 18
16 Free-Electron Model of Metals 21
16.1 Classical Drude Model 22
16.2 Quantum Mechanical Sommerfeld Model 44
16.3 Electric and Heat Currents in an Electron Gas 67
16.4 Scattering of Free Electrons by Impurities 84
16.5 Inadequacies of the Free-Electron Model 94
Further Reading 96
17 Electrons in the Periodic Potential of a Crystal 97
17.1 Band Structure of Electronic States 98
17.2 Representation of the Band Structure 104
17.3 Metals, Insulators, Semiconductors 109
17.4 Bloch Electrons as Quasiparticles 112
17.5 Wannier States 120
17.6 Electron States Around Impurities 124
Further Reading 128
18 Simple Models of the Band Structure 129
18.1 Nearly-Free-Electron Approximation 129
18.2 Tight-Binding Approximation 159
Further Reading 169
19 Methods for Calculating and Measuring the Band Structure 170
19.1 Matrix Methods 171
19.2 Variational Methods and Methods Based on Scattering Theory 183
19.3 Band Structure and Fermi Surface of Simple Metals 197
19.4 Experimental Study of the Band Structure 206
Further Reading 213
20 Electronic Structure of Semiconductors 214
20.1 Semiconductor Materials 215
20.2 Band Structure of Pure Semiconductors 220
20.3 Electrons and Holes in Intrinsic Semiconductors 231
20.4 Electronic Structure of Doped Semiconductors 238
20.5 Doped Semiconductors at Finite Temperatures 243
Further Reading 256
21 Semiclassical Dynamics of Electrons 258
21.1 Basics of Semiclassical Dynamics 258
21.2 Bloch Electrons in Uniform Magnetic Fields 267
21.3 Size Effects 287
21.4 Limitations of the Semiclassical Description 290
Further Reading 295
22 Electrons in Strong Magnetic Fields 296
22.1 Free Electrons in a Magnetic Field 296
22.2 Landau Diamagnetism 314
22.3 Bloch Electrons in Strong Magnetic Fields 316
22.4 Quantum Oscillations in Magnetic Fields 325
Further Reading 346
23 Electrons in Thermally Vibrating Lattices 347
23.1 Adiabatic Decoupling 348
23.2 Hamiltonian of the Electron–Phonon Interaction 351
23.3 Consequences of the Electron–Phonon Interaction 361
Further Reading 374
24 Transport Phenomena 375
24.1 General Formulation of Transport Phenomena 376
24.2 Boltzmann Equation 379
24.3 Relaxation-Time Approximation 388
24.4 Transport Coefficients in Metals and Semiconductors 405
24.5 Quantum Hall Effect 423
Further Reading 428
25 Optical Properties of Solids 429
25.1 Interaction of Solids with the Classical Radiation Field 430
25.2 Quantum Mechanical Treatment 453
Further Reading 465
26 Superconductivity 466
26.1 Superconductivity: The Phenomenon 468
26.2 Superconducting Materials 478
26.3 Phenomenological Description of Superconductivity 486
26.4 Ginzburg–Landau Theory 499
26.5 Josephson Effect 518
Further Reading 532
27 Transport of Carriers in Semiconductor Devices 533
27.1 Interfaces and Junctions 534
27.2 Generation, Motion, and Recombination of Carriers 549
27.3 Biased Semiconductor Junctions 557
27.4 Simple Semiconductor Devices 574
27.5 Semiconductor Quantum Devices 580
27.6 Basics of Spintronics 589
Further Reading 593
G Quantum Mechanical Perturbation Theory 594
G.1 Time-Independent Perturbation Theory 594
G.2 Time-Dependent Perturbation Theory 599
Reference 603
H Second Quantization 604
H.1 Occupation-Number Representation 604
H.2 Second-Quantized Form of Operators 608
References 617
I Canonical Transformation 618
I.1 Derivation of an Effective Hamiltonian 618
I.2 Diagonalization of the Hamiltonian 627
Figure Credits 631
Subject Index 638