Drift and diffusion in materials with traps

The multiple-trapping model is used in order to analyse the propagation and broadening of a carrier packet. The traps are considered to be distributed over rather a wide energy region in the gap. We assume that at the initial moment traps are empty and all the carriers occupy mobile states. Under these conditions the thermal equilibrium between mobile and localized carrier fractions cannot be established immediately and within rather a long time interval the energy distribution of localized carriers remains in non-equilibrium. In the present paper a non-equilibrium transport equation is obtained. The energy dependences of trap density and carrier capture probability are incorporated into the coefficients of this equation. The solution of the non-equilibrium transport equation for a delta-function initial condition presents an extremely dispersive non-Gaussian packet whose mean position moves with a velocity that decreases with time.