# Band-tail model for optical absorption and for the mobility edge in amorphous silicon

## Abstract

The potential in amorphous Si is assumed to be the crystalline potential perturbed by a fluctuating potential with a root-mean-square amplitude Vrms and a correlation length L. The density of states for such a perturbing potential is taken from the work of Halperin and Lax. The optical absorption is calculated using effective-mass-approximation envelope wave functions whose degree of localization depends on energy. A good fit to optical-absorption data for amorphous Si films annealed at room temperature is obtained using Vrms=0.89 eV and L=6, provided the wave-vector separation between the conduction- and valence-band edges is reduced from 9.5 × 107 to 6 × 107 cm-1. The mobility edge is found from an extension to the model which gives an effective bandwidth W and a spacing parameter rs, each as a function of energy. The mobility edge Em lies approximately where W(Em)=23Vrms. The mobility near the mobility edge is estimated from a diffusion model to be 5 cm2/V sec, and the density of states at the edge is 1021 cm-3 ev-1. © 1971 The American Physical Society.