Deviation from the Einstein relation: mobility of unrelaxed carriers

The relation between the drift mobility and the diffusion coefficient of charge carriers in one-dimensional systems with energy disorder is investigated. By using the effective medium approximation, we derived expressions for these transport coefficients. The analytical results verified by computer simulations demonstrate that the Einstein relation is invalid during the energy relaxation of the charge carriers. Our findings suggest that under typical experimental conditions, the time-of-flight mobility of charge carriers is independent of the field strength and decreases with the sample thickness according to the power law.