We compare two approaches of incorporating the long‐range Coulomb electron‐electron interaction into Monte Carlo simulations of bulk, degenerate GaAs, i.e., the semi‐classical approach of solving the Poisson equation self‐consistently, and the first order quantum mechanical treatment in which the electron‐plasmon interaction is included as an additional scattering mechanism. The critical issues involved in the semi‐classical, direct approach are the mesh size, charge assignment to the mesh nodes, and interpolation of the field at the particle location. All of these factors determine the stability of the system, the accuracy and computational time required in the calculation. The steady‐state electron drift velocity in bulk GaAs calculated using the direct, semi‐classical approach for the electron‐plasmon interaction is significantly less than the corresponding bulk drift velocity in the absence of the electron‐plasmon interaction. The alternative approach of treating the electron‐plasmon interaction as a scattering mechanism is attractive since it is computationally easier to include and is, at least to first order, quantum mechanically based. It is found that the calculated steady‐state electron drift velocity in bulk GaAs based on this model is affected in the opposite way, i.e., the velocity is greater than in the absence of the electron‐plasmon interaction. The cause of the discrepancy in the calculated results of the two approaches is not too surprising since they attack the problem from very different directions. Neither model can at present be considered complete. Further detailed investigations are required to achieve a better model for the electron‐plasmon interaction.
Mansour, N.S. and Brennan, K.F. (1992), "INCLUSION OF ELECTRON‐PLASMON SCATTERING IN ENSEMBLE MONTE CARLO SIMULATIONS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 11 No. 4, pp. 471-479. https://doi.org/10.1108/eb010107
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