16:332:599 Solid State

Copyright 1997-2004 M. A. Parker
Marcel-Dekker Publishing

Important Note: The page below contains an initial version (Draft 0) of the 581 book "Solid State and Quantum Theory" as first transcribed from raw notes without correction of significant errors in Chs 6. The corrected version will be added to the 581 class pages.

Corrections to Chapters, Last Updated: 01 Sept 04

Course Outline

Contents

1.0 Introduction to the Solid State

1.1 A Brief Preview
1.2 Introduction to Matter and Bonds
1.3 Introduction to Bands and Transitions
1.4 Introduction to the pn Junction
1.5 Device Trends
1.6 Vacuum Tubes and Transistors
1.7 Brief Summary of Some Nanometer Scale Devices

2.0 Linear Algebra - Hilbert Space

2.1 Vector and Hilbert Spaces
2.2 Dirac Notation and Euclidean Vector Spaces
2.3 Intro to Coordinate and Vector Repres. of Functions
2.4 Function Space with Discrete Basis Sets
2.5 Function Spaces with Continuous Basis Sets
2.5b Summary Table
2.6 The Grahm-Schmidt Orthonormalization Procedure
2.7 Fourier Basis Sets
2.8 Closure Relations, Kronecker Delta and Dirac Delta Functions
2.9 Introduction to Direct Product Spaces
2.10 Minkowski Space
2.11 Review Problems

3.0 Linear Operators

3.1 Introduction to Linear Transformations
3.2 Matrix Representations
3.3 Operator Space
3.4 Operators and Matrices in Direct Product Space
3.5 Operator-Matix Facts and Operations
3.7 An Algebra of Operators and Commutators
3.8 Unitary Operators and Similarity Transformations
3.9 Hermitian Operators and the Eigenvector Equation
3.10 A Relation Between Unitary and Hermitian Operators
3.11 Eigenvectors and Eigenvalues for Hermitian Operators
3.12 Eigenvectors, Eigenvalues and Diagonal Matrices
3.13 Theorems for Hermitian Operators
3.14 Raising-Lowering and Creation-Annihilation Operators
3.15 Translation Operators
3.16 Rotation Operators
3.17 Dyads
3.18 Introduction to Groups
3.19 Review Problems

4.0 Fundamentals of Classical Mechanics

4.1 Brief Summary of the Structure of Space-Time
4.2 Constraints and Generalized Coordinates
4.3 The Action, the Lagrangian, and Lagranges Equation
4.4 The Hamiltonian
4.5 Poisson Brackets
4.6 Classical Field Theory
4.7 The Lagrangian and the Schrodinger Equation
4.8 Review Exercises

5.0 Quantum Mechanics

5.1 The Relation Between Quantum Mechanics and Linear Algebra
5.2 Basic Operators of Quantum Mechanics
5.3 Examples for Schrodinger's Wave Equation
5.4 The Harmonic Oscillator
5.5 Introduction to Angular Momentum
5.6 Introduction to Spin and Spinors
5.7 Angular Momentum for Multiple Systems
5.8 Quantum Mechanical Representations
5.9 Time Independent Perturbation Theory
5.10 Time-Dependent Perturbation Theory
5.11 Introduction to Optical Transitions
5.12 Fermi's Golden Rule
5.13 Density Operator
5.14 Introduction to Multi-Particle Systems
5.15 Introduction to Second Quantization
5.16 The Propagator
5.17 The Feynman Path Integral
5.18 Review Exercises

6.0 Solid State: Structure and Phonons

6.1 Origin of Crystals
6.2 The Crystal, Lattice, Atomic Basis and Miller Notation
6.3 Special Unit Cells
6.4 The Reciprocal Lattice
6.5 Introduction to Symmetries
6.6 Phonon Dispersion Curves for the Monatomic Crystal
6.7 Classical Phonons in the Diatomic Linear Crystal
6.8 Phonon Modes
6.9 The Phonon Density of States
6.10 Phonon Crystal Momentum
6.11 Phonons and Material Properties
6.12 Quantum Mechanical Development of Phonon Fields
6.13 Phonons and Continuous Media
6.14 Chapter Review Exercises

7.0 Solid State Conduction, States and Bands

7.1 Classical Currents and the Equation of Continuity
7.2 The Equation of Continuity for Quantum Particles
7.3 Scattering Matrices
7.4 The Transfer Matrix
7.5 Introduction to the Free and Nearly-Free Quantum Model
7.6 The Bloch Function
7.7 Introduction to Effective Mass and Band Current
7.8 3-D Band Diagrams and Tensor Effective Mass
7.9 The Kronig-Penney Model for the Nearly-Free Electron
7.10 Tight Binding Approximation
7.11 Introduction to the Effective Mass Equation
7.12 Introduction to kp Band Theory
7.13 Introduction to the kp Theory for Degenerate Bands
7.14 The Infinitely Deep Quantum Well in a Semiconductor
7.15 Finitely deep well
7.16 Introduction to Density of States
7.17 DOS for Reduced Dimensional Structures with Infinite Barriers

8.0 Statistical Mechanics

8.1 Introduction to Reservoirs
8.2 Statistical Ensembles and Introduction to Statistical Mechanics
8.3 The Boltzmann Distribution
8.4 Introduction to the Fermi-Dirac Distribution
8.5 Derivation of the Fermi-Dirac Distribution
8.6 Effective Density of States, Doping and Mass Action
8.7 Dopant Ionization Statistics
8.8 The pn-Junction at Equilibrium
8.9 Electronic Model for the Basic Laser Diode
8.10 The Bose-Einstein Distribution
8.11 The Density Operator and the Boltzmann Distribution
8.12 Review Problems

9.0 Applications

9.1 Self Electro-optic Effect Devices (SEEDs)
9.2 Introduction to Quantum Computing
9.3 Quantum Cryptography
9.4 Introduction to Quantum Teleportation
9.5 Introduction to Single Electron Transistors
9.6 NanoLasers
9.7 Resonant Tunnel Diodes
9.8 Aranov-Bohm Effect Devices

Appendices

1 The Dirac Delta Function
2 Review of Probability Theory and Statistics
3 Review of Integrating Factors
4 Integrals with Two Time Scales
5 The Group Velocity
6 Combinatorials
7 Lagrange Multipliers
8 Dynamics of Carrier Equilibrium