A general theory was developed to describe diffusion phenomena in biased semiconductors and semiconductor superlattices. It was shown that the Einstein relation was not applicable for all field strengths so that the calculation of the field-mediated diffusion coefficient represents a separate task. Two quite different diffusion contributions were identified. The first one disappears when the dipole operator commutes with the Hamiltonian. It plays an essential role in the theory of small polarons. The second contribution was obtained from a quantity that was the solution of a kinetic equation but that could not be identified with the carrier distribution function. This was in contrast to the drift velocity, which was closely related to the distribution function. A general expression was derived for the quantum diffusion regime, which allows a clear physical interpretation within the hopping picture.

Theory of Quantum Diffusion in Biased Semiconductors. V.V.Bryksin, P.Kleinert: Journal of Physics - Condensed Matter, 2003, 15[9], 1415-25