Quantum Wells, Wires and Dots

Preface
Acknowledgements

About the author(s)

About the book

Introduction

1 Semiconductors and heterostructures

1.1 The mechanics of waves

1.2 Crystal structure

1.3 The effective mass approximation

1.4 Band theory

1.5 Heterojunctions

1.6 Heterostructures

1.7 The envelope function approximation

1.8 The reciprocal lattice

2 Solutions to Schrödinger's equation

2.1 The infinite well

2.2 In-plane dispersion

2.3 Density of states

2.4 Subband populations

2.5 Finite well with constant mass

2.6 Effective mass mismatch at heterojunctions

2.7 The infinite barrier height and mass limits

2.8 Hermiticity and the kinetic energy operator

2.9 Alternative kinetic energy operators

2.10 Extension to multiple-well systems

2.11 The asymmetric single quantum well

2.12 Addition of an electric field

2.13 The infinite superlattice

2.14 The single barrier

2.15 The double barrier

2.16 Extension to include electric field

2.17 Magnetic fields and Landau quantisation

2.18 In summary

3 Numerical solutions

3.1 Shooting method

3.2 Generalised initial conditions

3.3 Practical implementation of the shooting method

3.4 Heterojunction boundary conditions

3.5 The parabolic potential well

3.6 The Pöschl-Teller potential hole

3.7 Convergence tests

3.8 Extension to variable effective mass

3.9 The double quantum well

3.10 Multiple quantum wells and finite superlattices

3.11 Addition of electric field

3.12 Quantum confined Stark effect

3.13 Field-induced anti-crossings

3.14 Symmetry and selection rules

3.15 The Heisenberg uncertainty principle

3.16 Extension to include band non-parabolicity

3.17 Poisson's equation

3.18 Self-consistent Schrödinger-Poisson solution

3.19 Computational implementation

3.20 Modulation doping

3.21 The high-electron-mobility transistor

3.22 Band filling

4 Diffusion

4.1 Introduction

4.2 Theory

4.3 Boundary