Drift-Diffusion Transport in a Randomly Inhomogeneous One-Dimensional Medium

Organic semiconductors are intrinsic randomly inhomogeneous materials where charge transport occurs by hopping of the carriers between localized sites having a distribution of energy levels. However, the average carrier density seems to be accurately described by a simple drift-diffusion equation. We investigate the reasons for the effectiveness of the drift-diffusion model in a random material and show that the key assumption for its validity is that the correlation lengths of the randomly perturbed coefficients are much smaller than any other characteristic length of the problem. As a byproduct, we find how the effective drift and diffusion coefficients depend on the randomness.