ON THE EINSTEIN RELATION FOR HOPPING ELECTRONS

Transport properties of disordered semiconductors at low temperatures are determined by hopping of electrons via localized band tail states. Much attention has been paid recently in both experimental and theore tical studies to the relation between the diffusion coefficient of car riers, D, and their mobility, mu, in the hopping regime. Rather contro versial results have been reported. In particular, some computer simul ations have been claimed to show that the conventional Einstein relati on mu = eD/kT is violated in the hopping regime even in the case of th ermal equilibrium. We study the relation between mu and D by a compute r simulation and show that such statements were based on a wrong inter pretation of the simulation results. In thermal equilibrium, the Einst ein relation between mu and D must hold, although in a nonequilibrium system this relation can be violated. (C) 1998 Elsevier Science B.V. A ll rights reserved.