Quantum theory of the optical and electronic properties of semiconductors

This invaluable textbook presents the basic elements needed to understand and research into semiconductor physics. It deals with elementary excitations in bulk and low-dimensional semiconductors, including quantum wells, quantum wires and quantum dots. The basic principles underlying optical nonlinearities are developed, including excitonic and many-body plasma effects. Fundamentals of optical bistability, semiconductor lasers, femtosecond excitation, the optical Stark effect, the semiconductor photon echo, magneto-optic effects, as well as bulk and quantum-confined Franz-Keldysh effects, are covered. The material is presented in sufficient detail for graduate students and researchers with a general background in quantum mechanics.

Author Notes

Hartmut Haug joined the Institute of Theoretical Physics of the University of Frankfurt, where he was a full professor from 1975 to 2001 and currently is an emeritus
Stephan W. Koch in the fall of 1993, he joined the Philipps-University of Marburg where he is a full professor of Theoretical Physics

Preface	p. v
1. Oscillator Model	p. 1
1.1 Optical Susceptibility	p. 2
1.2 Absorption and Refraction	p. 6
1.3 Retarded Green's Function	p. 12
2. Atoms in a Classical Light Field	p. 17
2.1 Atomic Optical Susceptibility	p. 17
2.2 Oscillator Strength	p. 21
2.3 Optical Stark Shift	p. 23
3. Periodic Lattice of Atoms	p. 29
3.1 Reciprocal Lattice, Bloch Theorem	p. 29
3.2 Tight-Binding Approximation	p. 36
3.3 k-p Theory	p. 41
3.4 Degenerate Valence Bands	p. 45
4. Mesoscopic Semiconductor Structures	p. 53
4.1 Envelope Function Approximation	p. 54
4.2 Conduction Band Electrons in Quantum Wells	p. 56
4.3 Degenerate Hole Bands in Quantum Wells	p. 60
5. Free Carrier Transitions	p. 65
5.1 Optical Dipole Transitions	p. 65
5.2 Kinetics of Optical Interband Transitions	p. 69
5.2.1 Quasi-D-Dimensional Semiconductors	p. 70
5.2.2 Quantum Confined Semiconductors with Subband Structure	p. 72
5.3 Coherent Regime: Optical Bloch Equations	p. 74
5.4 Quasi-Equilibrium Regime: Free Carrier Absorption	p. 78
6. Ideal Quantum Gases	p. 89
6.1 Ideal Fermi Gas	p. 90
6.1.1 Ideal Fermi Gas in Three Dimensions	p. 93
6.1.2 Ideal Fermi Gas in Two Dimensions	p. 97
6.2 Ideal Bose Gas	p. 97
6.2.1 Ideal Bose Gas in Three Dimensions	p. 99
6.2.2 Ideal Bose Gas in Two Dimensions	p. 101
6.3 Ideal Quantum Gases in D Dimensions	p. 101
7. Interacting Electron Gas	p. 107
7.1 The Electron Gas Hamiltonian	p. 107
7.2 Three-Dimensional Electron Gas	p. 113
7.3 Two-Dimensional Electron Gas	p. 119
7.4 Multi-Subband Quantum Wells	p. 122
7.5 Quasi-One-Dimensional Electron Gas	p. 123
8. Plasmons and Plasma Screening	p. 129
8.1 Plasmons and Pair Excitations	p. 129
8.2 Plasma Screening	p. 137
8.3 Analysis of the Lindhard Formula	p. 140
8.3.1 Three Dimensions	p. 140
8.3.2 Two Dimensions	p. 143
8.3.3 One Dimension	p. 145
8.4 Plasmon-Pole Approximation	p. 146
9. Retarded Green's Function for Electrons	p. 149
9.1 Definitions	p. 149
9.2 Interacting Electron Gas	p. 152
9.3 Screened Hartree-Fock Approximation	p. 156
10. Excitons	p. 163
10.1 The Interband Polarization	p. 164
10.2 Wannier Equation	p. 169
10.3 Excitons	p. 173
10.3.1 Three- and Two-Dimensional Cases	p. 174
10.3.2 Quasi-One-Dimensional Case	p. 179
10.4 The Ionization Continuum	p. 181
10.4.1 Three- and Two-Dimensional Cases	p. 181
10.4.2 Quasi-One-Dimensional Case	p. 183
10.5 Optical Spectra	p. 184
10.5.1 Three- and Two-Dimensional Cases	p. 186
10.5.2 Quasi-One-Dimensional Case	p. 189
11. Polaritons	p. 193
11.1 Dielectric Theory of Polaritons	p. 193
11.1.1 Polaritons without Spatial Dispersion and Damping	p. 195
11.1.2 Polaritons with Spatial Dispersion and Damping	p. 197
11.2 Hamiltonian Theory of Polaritons	p. 199
11.3 Microcavity Polaritons	p. 206
12. Semiconductor Bloch Equations	p. 211
12.1 Hamiltonian Equations	p. 211
12.2 Multi-Subband Microstructures	p. 219
12.3 Scattering Terms	p. 221
12.3.1 Intraband Relaxation	p. 226
12.3.2 Dephasing of the Interband Polarization	p. 230
12.3.3 Full Mean-Field Evolution of the Phonon-Assisted Density Matrices	p. 231
13. Excitonic Optical Stark Effect	p. 235
13.1 Quasi-Stationary Results	p. 237
13.2 Dynamic Results	p. 246
13.3 Correlation Effects	p. 255
14. Wave-Mixing Spectroscopy	p. 269
14.1 Thin Samples	p. 271
14.2 Semiconductor Photon Echo	p. 275
15. Optical Properties of a Quasi-Equilibrium Electron-Hole Plasma	p. 283
15.1 Numerical Matrix Inversion	p. 287
15.2 High-Density Approximations	p. 293
15.3 Effective Pair-Equation Approximation	p. 296
15.3.1 Bound States	p. 299
15.3.2 Continuum States	p. 300
15.3.3 Optical Spectra	p. 300
16. Optical Bistability	p. 305
16.1 The Light Field Equation	p. 306
16.2 The Carrier Equation	p. 309
16.3 Bistability in Semiconductor Resonators	p. 311
16.4 Intrinsic Optical Bistability	p. 316
17. Semiconductor Laser	p. 321
17.1 Material Equations	p. 322
17.2 Field Equations	p. 324
17.3 Quantum Mechanical Langevin Equations	p. 328
17.4 Stochastic Laser Theory	p. 335
17.5 Nonlinear Dynamics with Delayed Feedback	p. 340
18. Electroabsorption	p. 349
18.1 Bulk Semiconductors	p. 349
18.2 Quantum Wells	p. 355
18.3 Exciton Electroabsorption	p. 360
18.3.1 Bulk Semiconductors	p. 360
18.3.2 Quantum Wells	p. 368
19. Magneto-Optics	p. 371
19.1 Single Electron in a Magnetic Field	p. 372
19.2 Bloch Equations for a Magneto-Plasma	p. 375
19.3 Magneto-Luminescence of Quantum Wires	p. 378
20. Quantum Dots	p. 383
20.1 Effective Mass Approximation	p. 383
20.2 Single Particle Properties	p. 386
20.3 Pair States	p. 388
20.4 Dipole Transitions	p. 392
20.5 Bloch Equations	p. 395
20.6 Optical Spectra	p. 396
21. Coulomb Quantum Kinetics	p. 401
21.1 General Formulation	p. 402
21.2 Second Born Approximation	p. 408
21.3 Build-Up of Screening	p. 413
Appendix A Field Quantization	p. 421
A.1 Lagrange Functional	p. 421
A.2 Canonical Momentum and Hamilton Function	p. 426
A.3 Quantization of the Fields	p. 428
Appendix B Contour-Ordered Green's Functions	p. 435
B.1 Interaction Representation	p. 436
B.2 Langreth Theorem	p. 439
B.3 Equilibrium Electron-Phonon Self-Energy	p. 442
Index	p. 445

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