Problems of Linear Electron (Polaron) Transport Theory in Semiconductors

Preface

Key to Abbreviations

Chapter I Basic Relations in the Quantum Theory of Linear Transport Phenomena (Kubo Formula)


1. General Relations in Quantum Statistical Mechanics


1.1 Formulation of the Problem. Macroscopic Systems


1.2 Dynamical and Statistical (Thermal) Forces


1.3 Mean Values and the Density Matrix


1.4 Density of States (Spectral Density) and Green Functions


2. Kubo Formula for the Transport Coefficients


2.1 Linear Reaction of a System to Dynamical Forces


2.2 Linear Reaction of a System to Dynamical and Statistical Forces


3. General Properties and Modifications of Kubo Formula


3.1 Basic (Symmetry) Properties


3.2 Modifications of the General Kubo Formula


4. Phenomenological Transport Coefficients


4.1 Basic Relations


4.2 Thermoelectric, Galvanomagnetic and Thermomagnetic Coefficients

Chapter II Elementary Excitations in a Crystalline Semiconductor


1. The Energy Spectrum


1.1 Introduction


1.2 Basic Problems of Semiconductor Crystal Dynamics


1.3 Elementary Excitations (Quasi-Particles)


2. Phonons


3. Conduction Electrons and Holes


3.1 The Hartree-Fock Approximation. Bloch and Wannier States


3.2 Some Effects of Electron-Electron Interactions


4. Dynamical and Thermodynamic Properties of Electrons and Holes in an almost Ideal Semiconductor


4.1 The Effective Hamiltonian


4.2 Point Defects. Localized and Quasi-Localized States


4.3 Some Remarks on the Thermodynamics of Charge Carriers in Semiconductors


4.4 Current-Carriers in a Strong Magnetic Field

Chapter III Polarons and Polaron Scattering in an Ideal Semiconductor


1. The Problem of Polarons


2. Electron-Phonon Interaction in an Ideal Semiconductor


2.1 General Description


2.2 Polarization Phonons


2.3 Acoustic Phonons


3. Qualitative Analysis of the Dynamical Properties of a Phonon Polaron in an Ideal Crystal


3.1 Classifications of Polarons


3.2 The Polaron Binding Energy δp and Radius Rp


3.3 Effective Mass of the Polaron


3.4 Some Other Aspects of Polaron Properties


4. The Weak-Coupling Phonon Polaron in the Fröhlich Model


4.1 Formulation of the Problem. General Relations


4.2 Polarization and Acoustic Polarons


4.3 Resonance Scattering by Polarization Phonons


5. Polarization Continuum Polarons in an Ionic Crystal


5.1 Weak and Intermediate Coupling


5.2 Strong Coupling. Adiabatic Approximation


5.3 The Feynman Polaron

Chapter IV Linear Transport of Wide-Band Polarons in an Almost Ideal Semiconductor


1. The Transport Equation and Its Parameters


1.1 Introduction


1.2 The Boltzmann-Bloch Transport Equation


1.3 Criteria of the Boltzmann-Bloch Transport Equation


2. Transport Coefficients and Relaxation Transport Times


2.1 Elastic Scattering


2.2 Isotropic Elastic Scattering


3. Transport Coefficients (Continued)


3.1 Elastic Scattering in Anisotropic Bands


3.2 Inelastic and Anisotropic Scattering. The Variational Method for Calculating Transport Coefficients


3.3 The Matthiessen Rule


4. Basic Relations for the Transport Coefficients in Simple Specific Cases


4.1 The Simplest Relations for the Transport Coefficients


4.2 Frequency-Dependent Electrical Conductivity of Wide-Band Feynman Polarons


5. Non-Boltzmann Conductivity. Conductivity in the Quantum Range of Strong Magnetic Fields


5.1 Introduction


5.2 Conductivity in Strong Quantizing Magnetic Fields


5.3 Quantum Transport Equation in Strong Quantizing Magnetic Fields

Chapter V Basic Theory of the Dynamical and Transport Properties of Small Polarons in an Almost Ideal Crystal


1. Low Mobility in an Ideal Crystal: Qualitative Survey


1.1 Introduction


1.2 The Holstein and Yamashita-Kurosawa Models


1.3 Introductory Remarks on the General Theory of Transport of Non-adiabatic Small Polarons


2. Spectrum and Transitions of a Non-adiabatic Small Polaron


2.1 The General Model


2.2 Properties of the States and Transitions


3. Decay of the Small Polaron as a Quasi-particle


3.1 General Considerations


3.2 Estimates of Transition Properties


3.3 Comments on Scattering in Very Narrow Bands and on the Correlations of Small Polarons and the Adiabatic Motion of Small-Polaron-Like Carriers


4. Basic Theory of Transport Coefficients for (Non-adiabatic) Small Polarons


4.1 Introduction


4.2 Charge and Energy Currents


4.3 Perturbation-Theory Calculation of the Transport Coefficients

Chapter VI Transport Coefficients of Small Polarons in an Almost Ideal Crystal


1. The Stationary Longitudinal Mobility


1.1 General Relations


1.2 Hopping Mobility


1.3 Coherent Mobility


1.4 The Mobility Mechanism at Intermediate Temperatures


2. Galvanomagnetic Effects


2.1 Introduction


2.2 Hopping Magnetoconductivity and Transverse Mobility


2.3 Coherent and 'Mixed' Transverse and Longitudinal Mobility


2.4 Hopping versus Non-hopping Conduction. The Hall Effect for Adiabatic Motion


3. Energy Transport. Thermoelectric and Thermomagnetic Effects. Thermal Conductivity


3.1 Basic Expressions


3.2 Discussion of Results


3.3 Other Effects in Energy Transport


4. Non-steady Conduction of Small Polarons and of Polarons in Small-Radius Impurity Centers. The Theorem of Frequency-Field Correspondence for Hopping Conduction of Small Polarons in the Non-ohmic Region


4.1 Introduction


4.2 Frequency-Dependent Electrical Conductivity


4.3 Electromagnetic-Wave Absorption in Polaron Impurity Centers of Small Radius


4.4 Effect of a Strong Electric Field on the Hopping Conductility of Small Polarons in a Lattice (Frequencyfield Correspondence) and on the Conductivity of Polarons in Local Small-Radius Centers (Paraelectric Resonance and Relaxation)


5. Some Problems of the Theory of Transport of Small-Polaron-Type Carriers and the Experimental Observation of Small Polarons


5.1 Non-Boltzmann Features of Transport of Small Polarons


5.2 Small-Polaron Carriers in a Magnetic Crystal


5.3 Some Problems in the Experimental Detection of Small Polarons


5.4 Some Further Theoretical Problems


6. The 'Quasi-classical Limit' of Weak Tunneling. Microscopic Theory of Conductivity and Diffusion of 'Light' Ions or Atoms (Defectons) in the Crystal and in Local (Paraelectric) Centers


6.1 Introduction


6.2 Steady Diffusion and Conduction


6.3 Conduction and Diffusion in Variable Fields


6.4 Concluding Remarks

Chapter VII Electron Conduction in Disordered Semiconductors. Spectral Density. Conduction in Heavily Doped Semiconductors without Strong Compensation


1. General Concepts


1.1 Introduction


1.2 The Electron Hamiltonian and Random, Mean and Self-averaging Characteristics


1.3 SDS Models


1.4 Approximate Methods of Averaging the Electron Characteristics in SDS (Green Functions)


2. The Single-Electron Spectral Density


2.1 General Discussion


2.2 Structure of the Spectrum in the BSW


2.3 Structure of the Impurity Band


2.4 Structure of the Single-Electron Spectrum Band tail


2.5 Final Remarks


3. Electron Transport in a Band of Weakly Scattered Waves. Heavily Doped Semiconductors without Strong Compensation


3.1 Introduction


3.2 Heavily Doped Semiconductors without Strong Compensation

Chapter VIII Electron Conduction in Disordered Semiconductors: Low-Mobility Mechanisms


1. Introduction


2. Electron Localization in a Three-dimensional Disordered System (the Anderson Model)


2.1 General Considerations


2.2 The Condition for Anderson Localization


2.3 Mobility Edges in the Anderson Model


3. Electron Localization and the Localization-Delocalization Transition in a Random Potential


3.1 Electron Localization-Delocalization and Conductivity


3.2 Electron Mobility and Percolation


3.3 Comments on Other Aspects of the Localization Problem


4. Application to Actual Disordered Systems


4.1 Introduction


4.2 Lightly Doped Crystalline Semiconductors with Impurity Band


4.3 Covalent Amorphous Semiconductors (Glasses)


5. Polaron Transport in the Spectral Band of Localized Carrier States


5.1 Stationary Conduction (without Magnetic Field)


5.1a Introduction. Electron Conduction in a Random Network of Sites. The Mott Approach


5.1b Stationary Polaron Conduction. General Description. Optimal Paths for T > Tc


5.1c Stationary Polaron Conduction at Low Temperatures (T < Tc). The Role of Percolation. Mitt's Law


5.2 High-frequency Conduction (without Magnetic Field)


5.3 Some Comments on Other Transport Coefficients


5.4 Effect of Interaction of Localized Carriers with the Spin System on the Hopping Conduction in a Magnetic Semiconductor


6. Conduction in the Band of Non-localized States with Strong Scattering


6.1 Introduction. The Random-Phase Model


6.2 The Mobility u, Thermoelectric Power η, Thermal Conductivity Λ, and Hall Effect


6.3 Discussion


7. Effects of Spin-Density and Charge-Density Disorder on the Conductivity of Some Systems with Electron-Electron Correlation


7.1 Mott Semiconductors in the Hubbard Model


7.2 Solids with a Low-temperature (T < TV) Dielectric Charge-Ordered Phase

Appendices I - VI

References

Notes Added in Proof

Additional References

Index

Other Titles in the Series