Theory of Electron Band Tails and the Urbach Optical-Absorption Edge

The density of states (E) in the tail for an electron in a correlated Gaussian random potential in three dimensions is constructed from first principles by means of a simple physical argument. This yields a linear exponential dependence of on E which, for reasonable values of the rms potential fluctuation and correlation length, spans many decades, and occupies most of the experimentally observable energy range. This is suggested as the origin of the fundamental Urbach optical-absorption edge.