ABSTRACT
In Chapter 12, we treated the electrons in a metal as if they were free, except for the conhning potential which keeps them within the metal. This is a drastic assumption, which is valid as a rough approximation in most metals, but is not valid, even qualitatively, for an insulator or semiconductor. In a real solid, the electrons move in the rapidly varying potential of the atoms, and the density of states g(E) is more complicated than the free electron value given by Equation (6.20). In general, there are regions of energy, called bandgaps or energy gaps (or gaps), where there are no states.1 The regions of energy where g(E) W= 0 are called energy bands, which are separated by gaps where g(E) = 0. A density of states with such a gap is illustrated schematically in Figure 13.1. The width of the gap is denoted Eg.
