Band tails in disordered systems

Abstract

The density of electron states, ρ(E), in disordered systems in the band-tail region near band edges is investigated. We show that the ρ(E) of the Halperin and Lax type derived by Sa-yakanit predicts, in three dimensions, an exponential (Urbach) band tail for the correlation lengths found in amorphous Si and within the energy range observed in optical absorption near band edges. The simple exponential behavior is not universal and may not, for example, be observed in heavily doped semiconductors.