Coupled-Langevin-equation analysis of hot-carrier transport in semiconductors

Using the results of a Monte Carlo simulation, a set of coupled Langevin equations for the relevant variables: the fraction of free carriers, the velocity, and energy, is constructed and applied to the case of p-type Si at 77 K under the influence of an electric field of arbitrary strength. The properties of the Langevin equations, by separating the terms associated with dissipation from those associated with fluctuations, is found to help the physical understanding of the results. The relaxation and generalized-diffusion matrices describing dissipation and fluctuations, respectively, are evaluated for different free-carrier concentrations. Their physical interpretation is shown to describe the cross correlation among different variables, which is present at equilibrium or is induced by the field.