Insulators and Semiconductors

The origin of the strange band gaps that arise in the electron density of states in real materials is that the regular arrangement of the nuclei in a crystal lattice creates a periodic potential. This affects the energy levels of the electrons and gives rise to gaps in the energy spectrum. The properties of insulators and semiconductors are very important in modern technology. They are largely due to the Fermi–Dirac statistics obeyed by electrons. Following the discussion of the behavior of free electrons in the previous chapter, this one turns to the properties that emerge when electrons are subject to a periodic potential, as they are in a crystal. The periodic potential leads to Bloch's theorem, band theory, and the prediction of band gaps, which are responsible for the differences in the properties of metals, insulators, and semiconductors. Dopants and their basic effects are discussed.