Fluctuation tail of valence bands in hydrogenated amorphous silicon.

Abstract

A theoretical approach to the problem of the valence-band tail of hydrogenated amorphous silicon is developed. A quantitative description of experimental data on the density of states (DOS) in the region of the valence-band tail is attempted. A single-band three-dimensional version of the Brodsky model complemented by an assumption of the random size distribution of potential wells and barriers was used in the calculation. This model corresponds to a solid solution where the regions of amorphous silicon and those saturated by hydrogen play the role of constituents. The Brodsky model restricts the depth of potential wells for holes by the difference between the valence-band tops of the crystal and hydrogenated amorphous silicon. The experimental total-yield photoemission data on the DOS of hydrogenated amorphous silicon for various samples were compared with theoretical calculations. The results show that a good quantitative agreement can be achieved with the DOS for both undoped and doped samples. The random potential characteristics, deduced from a comparison with experimental data mainly on undoped and B-doped samples, show no dependence on the level of doping, and, in fact, describe well the DOS of P-doped samples as well. Earlier, a similar conclusion was drawn from the data on hole drift mobility. However, we obtain the best coincidence with experimental data when the depth of the fluctuation wells is approximately two times that assumed in the simplest version of the model. The possible reasons for this divergence seem to be an addional fluctuation potential obeying the Gaussian statistics and (or) the shallow B-acceptor states neglected in our calculations. We obtain also general and simplified expressions for the D-center band contour due to the interaction with a fluctuation potential. It is shown that the band contour of these centers is a source of supplementary information about the fluctuation potential, which is in qualitative agreement with data derived from comparison with the DOS of the host band tail.