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Low-temperature relaxations of charge carriers in disordered hopping systems

Energetic relaxation, drift, diffusion and recombination of charge carriers are considered at low temperatures in disordered hopping systems. It is shown that, due to its scaling form, an exponential energetic distribution of the density of localized states (DOS) generates very specific transport characteristics which cannot be obtained for other types of DOS functions. In contrast with other distributions, only an exponential DOS function allows (i) the introduction of a low-temperature analogue of the Einstein relation between carrier mobility and diffusivity for some initial time domain of relaxation and (ii) the description of carrier drift in strong electric fields in terms of a field-dependent effective temperature.