The concentration of neutral impurities, ionized impurities, and free carriers in a doped semiconductor depends on a large number of parameters such as the impurity atom concentration, the free carrier mass, the bandgap energy, and the dielectric constant. The interdependences of the free majority and minority carrier concentration, the impurity concentration, impurity ionization energy as well as some other constants and materials parameters are given by semiconductor statistics. Semiconductor statistics describes the probabilities that a set of electronic states are either vacant or populated.

Electronic states include localized impurity states as well as delocalized conduction and valence band states. In the simplest case, an impurity has a single state with no degeneracy (g0 = 1). However, an impurity may have a degenerate ground state (g0 > 1) as well as excited levels which may need to be considered. The states in the bands and their dependence on energy are described by the density of states. In semiconductor heterostructures, the free motion of carriers is restricted to two, one, or zero spatial dimensions. In order to apply semiconductor statistics to such systems of reduced dimensions, the density of states in quantum wells (two dimensions), quantum wires (one dimension), and quantum dots (zero dimensions), must be known. The density of states in such systems will also be calculated in this chapter.