Basic Electronics for Scientists and Engineers

The band theory of solids

Introduction

A fundamental result from basic modern physics is that atoms are characterized by discrete energy levels. Each of these energy levels can accept up to two electrons. When “building” an atom, we start from the lowest level, fill in two electrons, and then move up to the next energy level and fill it with electrons. This continues until we have placed all the atom's electrons in energy levels. We also know that if an atom absorbs energy from the outside (for example, by absorbing a photon), an electron can be promoted to a higher energy level. Conversely, an electron that falls from a higher to a lower energy level emits a photon.

What happens to this energy level model when we assemble many atoms together into a solid? As the atoms get closer together, we must start to talk about the energy levels of the solid as a whole rather than those of the individual atoms. Rather than doing quantum mechanics for an isolated potential (the atom), we do it for a periodic array of atoms that exhibits a periodic potential. The net result of this is that, during the assembly of N atoms, the individual atomic levels split into N levels. This is shown schematically in Fig. 3.1. Thus when the solid is assembled and the atoms are at their final equilibrium spacing, the solid is characterized by a series of energy bands consisting of a large number of closely spaced allowed energy levels.