Semiconductor Optics and Transport Phenomena

by Schafer, Wilfried; Wegener, Martin

• ISBN13: 9783540616146
• ISBN10: 3540616144
• Format: Hardcover
• Copyright: 2002-06-30
• Publisher: Springer Verlag

Summary

This introduction to the field of semiconductor optics, including transport phenomena in semiconductors, has its origin in an advanced course jointly given by a theoretician and an experimentalist. Starting with the theoretical fundamentals of this field the book develops, assuming a basic knowledge of solid-state physics. The text is suitable for graduates and scientists alike who need a well-balanced and up-to-date introduction to this area. The application areas of the theory covered include semiconductor lasers, detectors, electro-optic modulators, single-electron transistors, microcavities and double-barrier resonant tunneling diodes. One hundred problems with hints for solution help the readers to deepen their knowledge.

Table of Contents

Some Basic Facts on Semiconductors	1	(6)
Semiconductor Heterostructures	2	(2)
Doped and Modulation-Doped Semiconductors	4	(3)
Interaction of Matter and Electromagnetic Fields	7	(44)
Microscopic Maxwell Equations	8	(2)
The Many-Particle Hamiltonian	10	(2)
Second Quantization for Particles	12	(7)
Quantization of Electromagnetic Fields	19	(5)
Coherent States	22	(2)
The Interaction Hamiltonian of Fields and Particles	24	(5)
Macroscopic Maxwell Equations and Response Functions	29	(14)
Direct Calculation of Induced Charges and Currents	30	(2)
Phenomenological Theory of Linear Response	32	(2)
Time-Dependent Perturbation Theory	34	(1)
Longitudinal Response Functions	35	(5)
Transverse Response Functions	40	(3)
Measurable Quantities in Optics	43	(5)
Linear Optical Susceptibility and Macroscopic Polarization	46	(1)
Absorption Coefficient	47	(1)
Problems	48	(3)
One Particle Properties	51	(34)
Hartree-Fock Theory for Zero Temperature	52	(3)
Hartree-Fock Theory for Finite Temperature	55	(5)
Band Structure and Ground-State Properties	60	(9)
The Local-Density Approximation	60	(5)
Lattice Periodicity	65	(4)
The Effective-Mass Approximation	69	(4)
kp Perturbation Theory for Degenerate Bands	73	(4)
Transition Matrix Elements	77	(3)
Density of States	80	(1)
Position of the Chemical Potential	81	(2)
Problems	83	(2)
Uncorrelated Optical Transitions	85	(30)
The Optical Bloch Equations	86	(5)
Linear Optical Properties	91	(3)
Nonlinear Optical Properties	94	(15)
Perturbation Analysis in the Frequency Domain	95	(2)
Introducing the Bloch Vector	97	(6)
Perturbation Analysis in the Time Domain	103	(4)
Alternative Approaches	107	(2)
Semiconductor Photodetectors	109	(4)
The Field-Field Correlation Function and its Relation to Coherence	110	(3)
Problems	113	(2)
Correlated Transitions of Bloch Electrons	115	(20)
Equations of Motion in the Hartree-Fock Approximation	115	(4)
Linear Optical Properties: The Continuum of Interband Transitions	119	(8)
The Bethe-Salpeter Equation	122	(2)
The Dielectric Function	124	(3)
Solution by Continued Fractions	127	(4)
Problems	131	(4)
Correlated Transitions near the Band Edge	135	(40)
The Semiconductor Bloch Equations	135	(3)
Linear Optical Properties: Bound Electron-Hole Pairs	138	(21)
The Coulomb Green's Function	140	(4)
Optical Properties due to Bound Electron-Hole Pairs	144	(5)
Numerical Methods	149	(1)
Excitons in Quantum Wells	150	(4)
Propagation of Light: Polaritons and Cavity Polaritons	154	(5)
Nonlinear Optical Properties	159	(13)
The Local-Field Approximation	159	(7)
Numerical Solutions	166	(6)
Problems	172	(3)
Influence of Static Magnetic Fields	175	(32)
One-Particle Properties	176	(12)
Effective Mass Theory for Isolated Bands	178	(3)
Degenerate Bloch Electrons in a Magnetic Field	181	(5)
One-Particle States in Quantum Wells	186	(2)
Optical Properties of Magneto-Excitons	188	(16)
Evaluation of the Coulomb Matrix Element	189	(2)
Linear Optical Properties	191	(5)
Semiconductor Bloch Equations in Two and Three Dimensions	196	(2)
Boise Condensation of Magnetoexcitons in Two Dimensions	198	(3)
Nonlinear Absorption of Magnetoexcitons in Quantum Wells	201	(3)
Problems	204	(3)
Influence of Static Electric Fields	207	(30)
Introduction	207	(2)
Uncorrelated Optical Transitions in Uniform Electric Fields	209	(4)
Optical Absorption	211	(2)
Correlated Optical Transitions in Uniform Electric Fields	213	(5)
An Analytical Model	214	(3)
Representation in Parabolic Coordinates	217	(1)
Quantum Wells in Electric Fields	218	(4)
Superlattices in Electric Fields	222	(13)
One-Particle States in Superlattices	222	(9)
Semiconductor Bloch Equations	231	(4)
Problems	235	(2)
Biexcitons	237	(28)
Truncation of the Many-Particle Problem in Coherently Driven Systems	240	(4)
Decomposition of Expectation Values	241	(3)
Equations of Motion in the Coherent Limit	244	(8)
Variational Methods	245	(2)
Eigenfunction Expansion	247	(5)
Bound-State and Scattering Contributions	252	(4)
Separation of Bound States	252	(2)
Biexcitonic Scattering Contributions	254	(2)
Signatures of Biexcitonic Bound States	256	(8)
Nonlinear Absorption	257	(2)
Four-Wave Mixing	259	(5)
Problems	264	(1)
Nonequilibrium Green's Functions	265	(48)
Time Evolution under the Action of External Fields	266	(3)
Definitions of One-Particle Green's Functions	269	(4)
Equations of Motion of One-Particle Green's Functions	273	(5)
Screened Interaction, Polarization, and Vertex Function	278	(3)
Quantum Kinetic Equations	281	(10)
The Two-Time Formalism	284	(4)
Reduction of Propagators to Single Time Functions	288	(3)
The Self-Energy in Different Approximations	291	(5)
Ground-State Energy	293	(1)
The Screened Hartree-Fock Approximation	294	(2)
The Screened Interaction	296	(8)
Separation of the Intraband and the Interband Susceptibility	297	(1)
The Screened Interaction in Random Phase Approximation	298	(6)
The Second-Order Born Approximation	304	(6)
Problems	310	(3)
The Electron-Phonon Interaction	313	(46)
The Phonon-Induced Interaction	314	(3)
The Phonon Green's Function	317	(6)
Eigenmodes of Lattice Vibrations	317	(4)
Green's Function Representation of the Density-Density Correlation Function	321	(2)
Electron-Phonon Coupling in the Long-Wavelength Limit	323	(7)
Coupling to Longitudinal Optical Phonons	325	(3)
Coupling to Acoustic Phonons	328	(2)
The Phonon Self-Energy	330	(17)
The Polaron	331	(5)
Dephasing Induced by Phonons	336	(11)
Nonequilibrium Phonons	347	(9)
Renormalization of Phonons	347	(2)
Kinetic Equation for the Phonon Green's Function	349	(7)
Problems	356	(3)
Scattering and Screening Processes	359	(28)
Carrier-Phonon Scattering	360	(9)
Luminescence Spectra	361	(4)
Four-Wave-Mixing Experiments	365	(3)
Nonequilibrium Phonons	368	(1)
Carrier-Carrier Scattering	369	(13)
The Limit of Quasi-Equilibrium	378	(4)
Scattering in the Presence of Bound States	382	(3)
Exciton-Phonon Scattering	382	(1)
Exciton-Exciton versus Exciton-Electron Scattering	383	(2)
Problems	385	(2)
The Semiconductor Laser	387	(28)
Introduction	387	(2)
Semiclassical Approach	389	(15)
The Semiconductor Bloch Equations in a Cavity	389	(4)
The Standard Rate Equations	393	(3)
Extended Rate Equations	396	(6)
Spectral Hole-Burning	402	(2)
Quantum Theory	404	(9)
The Photon Kinetics	404	(3)
The Carrier Kinetics	407	(2)
The Semiconductor Laser Linewidth	409	(4)
Problems	413	(2)
Classical Transport	415	(14)
Transport Coefficients (Without Magnetic Field)	417	(3)
Electrical Conductivity	419	(1)
Peltier Coefficient	419	(1)
Thermal Conductivity	420	(1)
Transport Coefficients (with Magnetic Field)	420	(4)
Hall Effect and Hall Resistance	422	(2)
Towards Ballistic Electrons: The Hot-Electron Transistor	424	(2)
Problems	426	(3)
Electric Fields in Mesoscopic Systems	429	(24)
Elementary Approach	429	(14)
Resonant Tunneling	431	(4)
Quantized Conductance	435	(4)
Coulomb Blockade and the SET Transistor	439	(4)
Resonant Tunneling II	443	(7)
Boundary Conditions and Discretization	445	(2)
Scattering Contributions	447	(1)
Numerical Results	448	(1)
Time-Dependent Phenomena	449	(1)
Problems	450	(3)
Electric and Magnetic Fields in Mesoscopic Systems	453	(24)
The Integer Quantum Hall Effect	453	(2)
Edge Channels and the Landauer-Buttiker Multiprobe Formula	455	(7)
Edge Channels	456	(6)
Microscopic Derivation of the Landauer-Buttiker Formula	462	(6)
Linear Response Theory	462	(4)
The Multiprobe Landauer-Buttiker Formula	466	(2)
The Fractional Quantum Hall Effect	468	(2)
Magnetotransport Through Dot or Antidot-Lattices	470	(5)
Problems	475	(2)
References	477	(14)
Index	491