Diffusion and drift of charge carriers in a random potential: Deviation from Einstein’s law

Employing Monte Carlo techniques, the diffusion and drift of charge carriers within an array of hopping states subject to a Gaussian distribution of site energies of width {σ} has been studied as a function of {σ}/kT and electric field. With increasing disorder and field, significant deviations from Einstein's law are noted. They are shown to be the consequence of anomalous, field-assisted diffusion while the mobility remains constant. The effect can account for anomalous transit-time dispersion observed in polymeric photoconductors exhibiting time independent transport.