The random distribution of impurities in a semiconductor host lattice introduces potential fluctuations that allow energy levels within the forbidden energy gap. This statistical effect distorts the unperturbed density of states of the pure semiconductor, and, at high doping concentrations, substantial band tails appear. The changes in the density-of-states function are particularly important in determining the number of free carriers in a heavily doped semiconductor. Together with many-particle interactions, band tailing constitutes one of the most significant heavy-doping effects. Although the band-tailing phenomenon has been studied for many years, only a one-dimensional analytical model, which assumes a Gaussian whitenoise probability distribution of the potential fluctuation, exists. In this paper the different classes of theories that describe this band tailing of the density of states in heavily doped semiconductors are reviewed in detail.

DOI:https://doi.org/10.1103/RevModPhys.64.755