A general theory was developed in order to describe diffusion phenomena in biased semiconductors and semiconductor superlattices. It was shown that the Einstein relationship was not applicable at all field strengths, so that calculation of the field-mediated diffusion coefficient was a separate problem. Two very different diffusion contributions were identified. The first one disappeared when the dipole operator commuted with the Hamiltonian. It played an essential role in the theory of small polarons. The second contribution was obtained from a quantity that was the solution to a kinetic equation, but which could not be identified with the carrier distribution function. This contrasted with the drift velocity, which was closely related to the distribution function. A general expression was derived for the quantum diffusion regime, which permitted 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