Solid state physics has grown rapidly in the past two decades. Unprecedented developments in technology have been accompanied by a substantial refinement and extension of the fundamental theory. New phenomena have been discovered and interpreted, and old puzzles clarified. The one-electron theory has come to maturity with the development of powerful methods of calculation and successful applications to real crystals. It is now possible to describe the results of numerous experiments concerning both semiconductors and metals in the language of band theory in a consistent fashion with the use of a small number of parameters. Calculations from first principles are able to reproduce most of the important qualitative features and some quantitative characteristics of the energy levels of actual materials.
This book contains a discussion of the principles and methods of the calculation of the energy levels of electrons in crystals. In Chapter I, the language of band theory is developed with attention to the general features of band structures which may be deduced from considerations of crystal symmetry. Chapter 2 includes a description of the principal methods for the solution of the Schrodinger equation in a periodic potential together with a survey of the problems encountered in the construction of the potential function in the Hartree-Fock approximation. Some of the results of experimental investigations of the band structures of materials, including the alkali metals, the noble metals, and common semiconductors, are surveyed in Chapter 3, and compared with theoretical calculations. The effects of external perturbations, including electric and magnetic fields, on band structures are considered in Chapter 4, together with a discussion of the energy levels of electrons bound to point impurities. A calculation of optical constants is also included.
Author(s): Joseph Callaway
Series: Pure and Applied Physics - Vol. 16
Publisher: Academic Press
Year: 1964
Language: English
Pages: X; 357
City: New York & London
Title Page
Preface
Table of Contents
Chapter 1 - The Language of Band Theory
1.1 Bloch's Theorem
1.2 The Reciprocal Lattice
1.3 The Brillouin Zone
1.4 Energy Bands in the Free Electron Limit
1.5 Space Groups
1.6 Irreducible Representations
1.7 The Effective Mass
1.8 The Density of States
1.9 The Fermi Surface in the Free Electron Approximation
1.10 Spin Orbit Coupling
1.11 Time Reversal Symmetry
Chapter 2 - Methods of Calculation
2.1 General Discussion
2.2 Plane Wave Expansions
2.3 Plane Wave Expansions: An Example
2.4 Orthogonalized Plane Waves
2.5 The Pseudopotential
2.6 The Cellular Method
2.7 The Effective Mass
2.8 Variational Methods
2.9 The Augmented Plane Wave Method
2.10 The Tight Binding Approximation
2.11 Wannier Functions
2.12 The Hartree-Fock Equations
2.13 Determination of the Crystal Potential
2.14 The Quantum Defect Method
2.15 The Pseudopotential in Relation to the Quantum Defect Method
Chapter 3 - Band Structure of Materials
3.1 The Alkali Metals: Cohesive Energy
3.2 Cohesive Energies of the Alkali Metals: Results: Lattice Constant and Compressibility
3.3 Band Calculations in the Alkali Metals
3.4 Wave Functions for the Alkali Metals
3.5 Valence Crystals: Diamond, Germanium, and Silic
3.6 Valence Crystals: Results of Calculations
3.7 Zinc Blende Structures
3.8 Aluminum
3.9 The Noble Metals
3.10 d Bands and Transition Metals
3.11 Bismuth
3.12 Graphite
3.13 Summary
Chapter 4 - Point Impurities and External Fields
4.1 General Discussion
4.2 Point Impurities
4.3 The Effective Mass Equation
4.4 The Steady Magnetic Field
4.5 The Magnetic Susceptibility of Free Electrons
4.6 The Cyclotron Frequency for an Arbitrary Fermi Surface
4.7 The Steady Diamagnetic Susceptibility: Arbitrary Band Structure
4.8 The Steady Electric Field
4.9 Optical Properties of Semiconductors
4.10 Optical Absorption by Free Carriers
4.11 Optical Properties in a Magnetic Field
Appendices
Appendix 1. Some Symmetrized Linear Combinations of Plane Waves
Appendix 2. Summation Relations
Appendix 3. The Effective Mass Equation in the Many Body Problem
Appendix 4. Evaluation of a Tunneling Integral
Appendix 5. Spin Density Waves
Bibliography
Author Index
Subject Index
