Theory of hopping and multiple-trapping transport in disordered systems

We present a general theory to describe equilibrium as well as nonequilibrium transport properties of systems in which the carriers perform an incoherent motion that can be described by means of a set of master equations. This includes hopping as well as trapping in the localized energy region of amorphous or perturbed crystalline semiconductors. Employing the mathematical analogy between the master equations and the tight binding problem we develop approximation schemes using methods of many-particle physics to derive expressions for the averaged propagator of the carriers and the conductivity tensor. The calculated conductivity and Hall conductivity of hopping systems compare extremely well to computer simulations over the whole range of frequency, density, and temperature. We are able to derive expressions for dispersive transport in hopping as well as trapping systems that contain the results of earlier theories of Scher, Montroll and Noolandi, Schmidlin as special cases and establish criteria for the occurrence of dispersive transport in such systems. We find that in principle hopping can lead to dispersive transport if the times and densities are very low, but actual experimental data are more easily explained in terms of multiple trapping.