ELECTRONS AND PHONONS IN SEMICONDUCTOR MULTILAYERS

Transcription

1 ELECTRONS AND PHONONS IN SEMICONDUCTOR MULTILAYERS В. К. RIDLEY University of Essex CAMBRIDGE UNIVERSITY PRESS

2 Contents Introduction 1 Simple Models of the Electron-Phonon Interaction 1.1 General remarks 1.2 Early models of optical-phonon confinement The dielectric-continuum (DC) model The hydrodynamic (HD) model The reformulated mode (RM) model Hybrid modes 1.3 The interaction of electrons with bulk phonons The scattering rate The coupling coefficients The overlap integral in 2D The 2D rates The ID rates 1.4 The interaction with model confined phonons 2 Quantum Confinement of Carriers 2.1 The effective-mass equation Introduction The envelope-function equation The local approximation The effective-mass approximation 2.2 The confinement of electrons 2.3 The confinement of holes 2.4 Angular dependence of matrix elements 2.5 Non-parabolicity 2.6 Band-mixing Vll

3 viii Contents 3 Quasi-Continuum Theory of Lattice Vibrations Introduction ^ Linear-chain models Bulk solutions Interface between nearly matched media Interface between mismatched media Free surface Summary The envelope function Non-local operators Acoustic and optical modes Boundary conditions Interface model Summary Appendix: The local approximation 4 Bulk Vibrational Modes in an Isotropic Continuum 4.1 Elasticity theory 4.2 Polar material 4.3 Polar optical waves 4.4 Energy density 4.5 Two-mode alloys 5 Optical Modes in a Quantum Well 5.1 Non-polar material 5.2 Polar material 5.3 Barrier modes: optical phonon tunnelling 5.4 The effect of dispersion 5.5 Quantization of hybrid modes 6 Superlattice Modes 6.1 Superlattice hybrids 6.2 Superlattice dispersion 6.3 General features 6.4 Interface polaritons in a superlattice 6.5 The role of LO and TO dispersion 6.6 Acoustic phonons 7 Optical Modes in Various Structures 7.1 Introduction 7.2 Monolayers Single monolayer Double monolayer

4 Contents ix 7.3 Metal-semiconductor structures Slab modes Quantum wires Quantum dots Electron-Optical Phonon Interaction in a Quantum Well Introduction Scattering rate Scattering potentials for hybrids Matrix elements for an infinitely deep well Scattering rates for hybrids Threshold rates Scattering by barrier LO modes Scattering by interface polaritons Summary of threshold rates in an infinitely deep well Intrasubband rates Intersubband rates Comparison with simple models The interaction in a superlattice The interaction in an alloy Phonon resonances Quantum wire The sum-rule 214 Appendix: Scalar and vector potentials Other Scattering Mechanisms Charged-impurity scattering Introduction The Coulomb scattering rate Scattering by single charges Scattering by fluctuations in a donor array An example Interface-roughness scattering Alloy scattering Electron-electron scattering Basic formulae for the 2D case Discussion Electron-hole scattering Phonon scattering Phonon-phonon processes Charged-impurity scattering 243

5 X Contents Alloy fluctuations and neutral impurities Interface-roughness scattering Quantum Screening 10.1 Introduction 10.2 The density matrix 10.3 The dielectric function 10.4 The 3D dielectric function 10.5 The quasi-2d dielectric function 10.6 The quasi-id dielectric function 10.7 Lattice screening 10.8 Image charges 10.9 The electron-plasma/coupled-mode interaction Discussion The Electron Distribution Function The Boltzmann equation Net scattering rate by bulk polar optical phonons Optical excitation Transport The 3D case The 2D case The ID case Discussion Acoustic-phonon scattering The 3D case The 2D case The ID case Piezoelectric scattering Discussion Acoustic-phonon scattering in a degenerate gas Introduction Energy- and momentum-relaxation rates Low-temperature approximation The electron temperature The high-temperature approximation 316 Appendix: The Polar-Optical Momentum-Relaxation Time in a 2D Degenerate Gas 321 References 323 Index 329