Dispersive energy transport and relaxation in the hopping regime

A method for investigating relaxation phenomena for charge-carrier hopping between localized tail states is developed. It allows us to consider both c harge and energy dispersive transport. The method is based on the idea of q uasielasticity: the typical energy loss during a hop is much less than all other characteristic energies. We investigate two models with different den sity-of-state energy dependencies with our method. In general, we find that the motion of a packet in energy space is affected by two competing tenden cies. First, there is a packet broadening, i.e., dispersive energy transpor t. Second, there is a narrowing of the packet if the density of states is d epleting with decreasing energy. It is the interplay of these two tendencie s that determines the overall evolution. If the density of states is consta nt, only broadening exists. In this case a packet in energy space evolves i nto a Gaussian one, moving with a constant drift velocity and mean-square d eviation increasing linearly in time. If the density of states depletes exp onentially with decreasing energy, the motion of the packet slows down trem endously with time. For large times the mean-square deviation of the packet becomes constant, so that the motion of the packet is "solitonlike."