Activated transport in amorphous semiconductors. I. The theoretical approach

Abstract

A transport theory based on a tight-binding model that generalises conventional hopping theory is presented. The conductivity may be expressed in terms of a density-relaxation matrix which, if evaluated to the lower order in the electronic transfer, is given by the binary hopping rates. By going beyond this approximation and calculating the density-relaxation matrix in the framework of Gotze's self-consistent current-relaxation approach, the resulting conductivity interpolates between a pure hopping behaviour for transport far below a mobility edge and a coherent behaviour above it. The theory is formulated in a site representation and, using approximation appropriate for the tight-binding model, a set of simple equations follows that makes possible the calculation of the conductivity for the density-of-states functions envisaged for amorphous semiconductors. In the first part of this work the results are illustrated for a box-shaped band.