Determination of diffusion coefficients in degenerate electron gas using Monte Carlo simulation

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Abstract
We propose a method for determining diffusion coefficients in degenerate semiconductors from an ensemble Monte Carlo simulation. The basic idea is that what is relevant for this problem is not the whole electron distribution function, but its perturbation in response to an addition of “excess carriers.” Starting from the Boltzmann transport equation, we derive the equation of evolution for this “excess electron distribution function.” We propose an interpretation in terms of scattering events suffered by particles, allowing one to solve the problem by Monte Carlo simulation. We simulate two sets of carriers, coupled by an “exchange scattering” mechanism which is properly defined. The first set represents the uniform background density in the semiconductor, whereas the second one represents the excess carriers. Only the latter is used for calculating diffusion coefficients. This method is applied to a highly degenerate two-dimensional electron gas in a doped GaAs quantum well. The diffusivity-field characteristics are calculated and discussed.