INTERBAND OPTICAL ABSORPTION IN AMORPHOUS SEMICONDUCTORS.

A simple, analytic derivation is presented of the exponential tails universally observed in the optical absorption of three-dimensional disordered systems based on recent analysis of exponential band tails. These tails contain states localized inside relatively large regions within which the local average of the potential falls below its overall average. The physical extent of a tail state is governed by the fluctuation size and not the localization length. Strong anticorrelation in the fluctuations of the valence and conduction band edges implies that the Urbach tail arises from valence tail to conduction tail transitions. Otherwise, the urbach tail arises from a superposition of valence tail to conduction extended and valence extended to conduction tail state transitions. The wider band tail then dominates the Urbach tail, as inthe case, e. g. , for a-Si:H, where the valence band tail dominates.