This paper introduces a new approach to Monte Carlo estimation of the velocity of charge carriers drift-diffusing in a random medium. The random medium is modeled by a 1-dimensional lattice and the position of the charge carrier is modeled by a Markov jump process, whose state space is the set of lattice points. The transition rates of the Markov jump process are determined by the underlying energy landscape of the random medium. This energy landscape is modeled by a Gaussian process and contains regions of relatively low energy, in which charge carriers quickly become stuck. As a result, the state space is not adequately explored by the standard algorithms and the velocity of the charge carrier is poorly estimated. In addition, the conventional Monte Carlo estimators have very high variances. Our approach aims to reduce the number of simulation steps that are spent in the low energy problem regions. We do this by identifying the problem regions via a stochastic watershed algorithm. We then use a coarsened state space model, where the problem regions are treated as single states. In this way, we are able to simulate a semi-Markov process on the coarsened state space. This results in estimators that are unbiased and have considerably lower variance than the crude Monte Carlo alternatives.
['Tim Brereton', 'Dirk P. Kroese', 'Ole Stenzel', 'Volker Schmidt', 'Björn Baumeier']
Efficient simulation of charge transport in deep-trap media