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 $V_{\mathrm{rms}}$ 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 $V_{\mathrm{rms}}=0.89\mathrm{}$ eV and $L=6\mathrm{}$ Å, provided the wave-vector separation between the conduction- and valence-band edges is reduced from 9.5 × ${10}^7$ to 6 × ${10}^7$ ${\mathrm{cm}}^{-1\mathrm{}}$. The mobility edge is found from an extension to the model which gives an effective bandwidth $W$ and a spacing parameter $r_s$, each as a function of energy. The mobility edge $E_m$ lies approximately where $W\left(E_m\right)=\frac{2}{3}{V}_{\mathrm{rms}}$. The mobility near the mobility edge is estimated from a diffusion model to be 5 ${\mathrm{cm}}^2$/V sec, and the density of states at the edge is ${10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$ ${\mathrm{ev}}^{-1\mathrm{}}$.