1 - FOUNDATIONS

Summary

This book is about low-dimensional semiconductors, structures in which electrons behave as though they are free to move in only two or fewer free dimensions. Most of these structures are really heterostructures, meaning that they comprise more than one kind of material. Before we can investigate the properties of a heterostructure, we need to understand the behaviour of electrons in a uniform semiconductor. This in turn rests on the foundations of quantum mechanics, statistical mechanics, and the band theory of crystalline solids. The first two chapters of this book provide a review of these foundations. Unfortunately it is impossible to provide a full tutorial within the space available, so the reader should consult one of the books suggested at the end of the appropriate chapter if much of the material is unfamiliar.

This first chapter covers quantum mechanics and statistical physics. Some topics, such as the theory of angular momentum, are not included although they are vital to a thorough course on quantum mechanics. The historical background, treated at length in most textbooks on quantum mechanics, is also omitted. There is little attempt to justify quantum mechanics, although the rest of the book could be said to provide support because we are able to explain numerous experimental observations using the basic theory developed in this chapter.