A microscopic model for electrotransport in semiconducting ionic crystals was described. This was based upon the movement of electrostatically interacting hopping charge carriers (cation vacancies and electron holes). The rate equations for the thermally activated motion of electronic and ionic defects in external fields allowed for the calculation of stationary charge distributions. In the case of large differences in the mobilities of the defects, an adiabatic approximation could be introduced which permitted the separation of the motion of electron holes and vacancies. The formal problem was identical to the solution of the Poisson-Boltzmann equation for large defect concentrations. An expression was derived, for charge transport, which was equivalent to the Debye-Hückel expression for the relaxation effect but which included distinct geometrical positions around a central point charge.

J.Janek, M.Martin: Berichte der Bunsengesellschaft für Physikalische Chemie, 1994, 98[5], 665-73