Transport Characteristics of Amorphous Semiconductors in the Dilute Carrier Regime: A Variable Range Hopping Treatment

Abstract

We survey the analytical methods which are used to find the conductivity of amorphous solids as a function of temperature, specifically the work done by N. F. Mott and Apsley et al. and we point out the problems with deriving such a relationship. We then develop a self consistent numerical system for calculating the charge occupancy factors, and apply it to a specific case of amorphous boron carbide, where positional disorder is introduced by incorporating random shifts in the positions and orientations of icosahedral clusters of boron and carbon atoms in an initially pristine rhombohedral arrangement of icosahedra. We find the transport characteristics to be most sensitive to the size of the icosahedral clusters relative to their mean separation, while it is robust with respect to disorder. In particular, the transport characteristics are only mildly affected (i.e. slightly diminished) by random displacements in the icosahedral positions, while they do not appear to be discernibly changed in the presence of even significant orientational disorder.