Quantum Processes in Semiconductors

by Ridley, B. K.

• ISBN13: 9780198505792
• ISBN10: 0198505795
• Edition: 4th
• Format: Paperback
• Copyright: 2000-03-09
• Publisher: Oxford University Press

Summary

This book presents the fundamental quantum processes involved in the physics and technology of semiconductors. Its relatively informal style makes it an ideal introduction for graduate courses as well as a reliable reference for researchers in the field. This edition has been expanded to include new chapters on quantum transport, semi-classical transport and space-charge waves, extending the discussion to statistical, many-particle behavior in transport phenomena. The author has also taken the opportunity to update other sections. As with previous editions the text restricts its attention to bulk semiconductors. It traces the path from quantum processes describable by density matrices, through the semi-classical Boltzmann equation and its solutions, to the drift-diffusion description of space-charge waves, the latter appearing in the contexts of negative differential resistance, acoustoelectric and recombination instabilities.

Author Biography

Brian K. Ridley FRS is Professor of Physics at the University of Essex

Table of Contents

Band Structure of Semiconductors	1	(43)
The crystal Hamiltonian	1	(1)
Adiabatic approximation	1	(1)
Phonons	2	(1)
The one-electron approximation	3	(1)
Bloch functions	4	(2)
Nearly-free-electron model	6	(4)
Group theory notation	9	(1)
Energy gaps	10	(3)
Spin-orbit coupling and orbital characteristics	13	(3)
Band structures	16	(5)
Chemical trends	21	(7)
k.p Perturbation and effective mass	28	(7)
Oscillator strengths	34	(1)
Temperature dependence of energy gaps	35	(3)
Deformation potentials	38	(3)
Alloys	41	(3)
Energy Levels	44	(38)
The effective-mass approximation	44	(3)
Electron dynamics	47	(3)
Zener-Bloch oscillations	50	(3)
Landau levels	53	(5)
Plasma oscillations	58	(1)
Excitons	59	(2)
Hydrogenic impurities	61	(6)
Hydrogen molecule centres	67	(2)
Core effects	69	(2)
Deep-level impurities	71	(4)
Scattering states	75	(1)
Impurity bands	75	(7)
Lattice Scattering	82	(56)
General features	82	(4)
Energy and momentum conservation	86	(8)
Spherical parabolic band	86	(6)
Spherical non-parabolic band	92	(1)
Ellipsoidal parabolic band	93	(1)
Equivalent valleys	93	(1)
Non-equivalent valleys	94	(1)
Acoustic phonon scattering	94	(12)
Spherical bands: equipartition	97	(2)
Spherical band: zero-point scattering	99	(1)
Spheroidal parabolic bands	100	(3)
Momentum and energy relaxation	103	(3)
Optical phonon scattering	106	(7)
Inter-valley scattering	110	(1)
First-order processes	110	(3)
Polar optical mode scattering	113	(6)
The effective charge	116	(1)
Energy and momentum relaxation	117	(2)
Piezoelectric scattering	119	(6)
Scattering-induced electron mass	125	(3)
Mobilities	128	(2)
Appendix: Acoustic waves in the diamond lattice	130	(8)
Impurity Scattering	138	(46)
General features	138	(3)
Charged-impurity scattering	141	(11)
Conwell-Weisskopf approximation	142	(1)
Brooks-Herring approach	143	(4)
Uncertainty broadening	147	(2)
Statistical screening	149	(3)
Neutral-impurity scattering	152	(9)
Hydrogenic models	152	(2)
Square-well models	154	(2)
Sclar's formula	156	(1)
Resonance scattering	156	(3)
Statistical screening	159	(2)
Central-cell contribution to charged-impurity scattering	161	(7)
Dipole scattering	168	(3)
Electron-hole scattering	171	(2)
Electron-electron scattering	173	(3)
Mobilities	176	(3)
Appendix: Debye screening length	179	(2)
Appendix: Average separation of impurities	181	(1)
Appendix: Alloy scattering	181	(3)
Radiative Transitions	184	(51)
Transition rate	184	(4)
Local field correction	187	(1)
Photon drag	188	(1)
Photo-ionization and radiative capture cross-section	188	(2)
Wavefunctions	190	(3)
Direct interband transitions	193	(5)
Excitonic absorption	197	(1)
Photo-deionization of a hydrogenic acceptor	198	(2)
Photo-ionization of a hydrogenic donor	200	(2)
Photo-ionization of quantum-defect impurities	202	(6)
Photo-ionization of deep-level impurities	208	(2)
Summary of photo-ionization cross-sections	210	(1)
Indirect transitions	210	(4)
Indirect interband transitions	214	(4)
Free-carrier absorption	218	(9)
Energy and momentum	220	(1)
Scattering matrix elements	221	(1)
Electron scattering by photons	222	(2)
Absorption coefficients	224	(3)
Free-carrier scattering of light	227	(6)
Scattering of laser light	231	(2)
Appendix: Justification of effective-mass approximation in light scattering	233	(2)
Non-Radiative Processes	235	(47)
Electron-lattice coupling	235	(3)
The configuration co-ordinate diagram	238	(3)
Semi-classical thermal broadening	240	(1)
Semi-classical thermal generation rate	241	(3)
Thermal broadening of radiative transitions	244	(8)
Thermal generation and capture rates	252	(4)
Electron-lattice coupling strength	256	(7)
Selection rules for phonon-impurity coupling	263	(2)
Phonon-cascade capture	265	(4)
The Auger effect	269	(7)
Impact ionization	276	(2)
Appendix: The multiphonon matrix element	278	(4)
Quantum Processes in a Magnetic Field	282	(36)
Introduction	282	(1)
Collision-free situation	283	(6)
Quantum states in a magnetic field	283	(2)
Magnitudes	285	(1)
Density of states	286	(1)
Spin	287	(1)
Phenomenological quantities	288	(1)
Collision-induced current	289	(7)
Expression for the scattering rate in the extreme quantum limit	289	(1)
Energy and momentum conservation	290	(2)
Integrations	292	(1)
General expression for the drift velocity	293	(3)
Diffusion	296	(1)
Scattering mechanisms	296	(8)
Acoustic phonon scattering	296	(3)
Piezoelectric scattering	299	(1)
Charged-impurity scattering	300	(4)
Transverse Shubnikov-de Haas oscillations	304	(6)
Magnetoconductivity in the presence of many Landau levels	304	(3)
The oscillatory component	307	(1)
Collision broadening	308	(1)
Thermal broadening	308	(1)
Spin-splitting	309	(1)
Shubnikov-de Haas formula	309	(1)
Longitudinal Shubnikov-de Haas oscillations	310	(3)
Magnetophonon oscillations	313	(5)
Scattering in a Degenerate Gas	318	(10)
General equations	318	(2)
Elastic collisions	320	(1)
Acoustic phonon scattering	321	(6)
Low-temperature limit	323	(1)
High-temperature limit	324	(1)
Strong screening	325	(2)
Energy relaxation time	327	(1)
Dynamic Screening	328	(19)
Introduction	328	(1)
Polar optical modes	329	(2)
Plasma modes	331	(1)
Coupled modes	332	(7)
The Lindhard dielectric function	339	(3)
Fluctuations	342	(4)
Screening regimes	346	(1)
Phonon Processes	347	(35)
Introduction	347	(2)
Three-phonon processes	349	(11)
Coupling constants	349	(1)
Selection rules for acoustic phonons	350	(2)
Rates for LA modes via normal processes	352	(3)
Rates for TA modes via normal processes	355	(1)
Rates for umklapp processes	356	(2)
Higher-order processes	358	(1)
Lifetime of optical phonons	358	(2)
Scattering by imperfections	360	(2)
Scattering by charged impurities	362	(2)
Scattering by electrons	364	(2)
Other scattering mechanisms	366	(3)
Quantum Transport
The density matrix	369	(3)
Screening	372	(3)
The two-level system	375	(2)
Fermi's Golden Rule	377	(1)
Wannier-Stark states	378	(2)
The intracollisional field effect	380	(1)
The semi-classical approximation	381	(1)
Semi-Classical Transport	382	(27)
The Boltzmann equation	382	(5)
Weak electric fields	387	(4)
Electron-electron scattering	391	(3)
Hot electrons	394	(4)
Hot-electron distribution functions	398	(11)
Scattering by non-polar acoustic phonons	400	(2)
Scattering by non-polar optical modes	402	(1)
The drifted Maxwellian	403	(6)
Space-Charge Waves	409	(18)
Phenomenological equations	409	(3)
Space-charge and acoustoelectric waves	412	(4)
Parametric processes	416	(1)
Domains and filaments	417	(4)
Recombination waves	421	(6)
Author Index	427	(4)
Subject Index	431