Non-Gaussian Transport Measurements and the Einstein Relation in Amorphous Silicon

Abstract

We propose an experimental procedure for testing the Einstein relation for carrier drift and diffusion in semiconductors exhibiting non-Gaussian or dispersive transport. We present corresponding hole time-of-flight and steady-state photocarrier grating measurements in hydrogenated amorphous silicon ( $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$). For a range of mobilities ${10}^{\ensuremath{-}5}--{10}^{\ensuremath{-}2}\mathrm{cm}{}^{2}/\mathrm{V}\mathrm{s}$ we find that our estimates of hole diffusion are approximately twice as large as predicted by the Einstein relation and the mobility measurements. We consider the deviation to represent an upper bound to any true failure of the Einstein relation for hole transport in $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$.