Stochastic Models of Charge Transport in Disordered Media

Charge transport in disordered materials, such as organic and amorphous inorganic semiconductors, is often modeled in a stochastic framework. The microstructure of the disordered material is interpreted as a realization of a stochastic model and, given a realization of this model, the charge transport process itself is treated as a random process. In this paper, we give an introduction to this combined stochastic modeling approach. We first describe the basic physics underlying charge transport in disordered materials. Then, we discuss stochastic models of the material and the charge transport process. In organic semiconductors, charge transport is modeled either by a continuous-time random walk in a random environment or an interacting particle system in a random environment. In amorphous inorganic semiconductors, charge transport is modeled by a continuous-time random walk in a deterministic environment. In the organic semiconductor case, the resulting stochastic models need to be solved using numerical methods. As such, we discuss Monte Carlo methods for estimating charge transport properties. In particular, we discuss a recently developed method, Aggregate Monte Carlo, which can be used to significantly speed up Monte Carlo simulations. Finally, we discuss the problem of modeling recombination in organic semiconductors.