ON THE EINSTEIN RELATION FOR HOPPING ELECTRONS

Diffusion coefficient of carriers, D, and their mobility, mu, in disor dered semiconductors at very low temperatures are temperature-independ ent, being determined by the energy-loss hopping of carriers through l ocalized band-tail states. In such a hopping relaxation in a system wi th exponential density of tail states, the relation between mu and D h as the form mu similar to eD/epsilon(0), where epsilon(0) is the energ y scale of the exponential band tail. With rising temperature, thermal ly-activated hopping transitions increase their contribution to transp ort processes and the model of the energy-loss hopping is not applicab le. We study by a Monte Carlo computer simulation how the relation bet ween mu and D evolves with increasing temperature from its temperature -independent form at T = 0 to the conventional Einstein relation mu = eD/kT.