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 2400 K. The calculated spectra exhibit exponential tails near the fundamental absorption edge that follow the Urbach rule in good agreement with experiments. We discuss the accuracy of our results by comparing to hybrid exchange correlation functionals. We show that the Urbach rule holds in a frequency interval where optical absorption is Poisson distributed with very large statistical fluctuations. In this regime, a direct relation between the optical absorption coefficient and electronic density of states is derived, which provides a link between photoemission and absorption spectra and is used to determine the lower bound to the Urbach frequency regime.