Monte Carlo method for the investigation of electron diffusion in degenerate semiconductors

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Abstract
We propose an efficient Monte Carlo method for calculating diffusion coefficients in degenerate semiconductors by simulating two populations of particles: one obeying the nonlinear Boltzmann equation and the other obeying the linearized Boltzmann equation. The required numbers of particles and observation times are very different for the two populations. With the aim of improving computing efficiency, we have developed a rejection technique in order to account for the coupling between the two populations. We apply this method to the study of highly degenerate GaAs. We compare diffusivity and noise spectral density in order to investigate the noise reduction induced by degeneracy. We find that the magnitude of this effect is strongly sensitive to the applied field. We also suggest a possible application of our method to the accurate determination of low-field mobility.