Diffusion coefficient of charge carriers in disordered semiconductors retaining a combination of exponential and Gaussian mobility-gap states: Application to amorphous selenium

Abstract

Charge carrier transport in disordered semiconductors is highly influenced by the defect states near the mobility edges. A theoretical model for the generalized Einstein relation, namely, the diffusivity-mobility ratio, for disordered semiconductors retaining a combination of exponential and Gaussian mobility-gap states with square-root distribution of extended states, is presented in this article. The conditions for determining the diffusion coefficient of charge carriers in disordered semiconductors from the Einstein relation are described in the article. The effects of various parameters constituting the density of states (DOS) distribution on the Einstein relation are examined. The results show that the diffusivity-mobility ratio for such DOS distribution substantially deviates from the traditional constant value for carrier concentration larger than 1010 cm−3. The value of diffusivity-mobility ratio strongly depends on the amount, energy position, and the shape of the Gaussian peaks. The additional diffusion coefficient due to multiple trapping in disordered semiconductors (namely, field diffusion) under quasi-equilibrium transport is also examined as a function of electric field and carrier concentration.