First-Principles Calculations of the Urbach Tail in the Optical Absorption Spectra of Silica Glass

We present density-functional theory calculations of the optical absorption spectra of silica glass for temperatures up to 2400K. The calculated spectra exhibit exponential tails near the fundamental absorption edge that follow the Urbach rule, in quantitative agreement with experiments. We discuss the accuracy of our results by comparing to hybrid exchange correlation functionals. We derive a simple relationship between the exponential tails of the absorption coefficient and the electronic density-of-states, and thereby establish a direct link between the photoemission and the absorption spectra near the absorption edge. We use this relationship to determine the lower bound to the Urbach frequency regime. We show that in this frequency interval, the optical absorption is Poisson distributed with very large statistical fluctuations. We determine the upper bound to the Urbach frequency regime by identifying the frequency at which transition to Poisson distribution takes place.