Theory of the electron-plasmon interaction in Monte Carlo calculations through the direct solution of the Poisson equation

Abstract

Ensemble Monte Carlo calculations of the steady-state electron drift velocity in degenerate bulk GaAs using a self-consistent algorithm specially tailored to directly include the electron-plasmon interaction are presented. The critical issues implicit in the direct approach are the mesh size, charge assignment to the mesh nodes, interpolation of the field at the particle location, and the frequency with which the solution of the Poisson equation is updated. All of these factors determine the stability of the system, the accuracy, and the computational time required in the calculation. Comparison is made to quantum mechanically based techniques in which the electron-plasmon interaction is treated as an additional scattering mechanism. It is found that the steady-state electron drift velocity in bulk degenerate GaAs calculated using the semi-classical approach for the electron-plasmon interaction is significantly less than that calculated assuming no electron-plasmon interaction is present. The steady-state drift velocity calculated using the quantum mechanical approach, wherein the electron-plasmon interaction is treated as a separate scattering mechanism, is affected in the opposite way, i.e., the velocity is greater than in the absence of the electron-plasmon interaction. Neither model can at present be considered complete and caution should be exercised in adopting either approach in device simulation until a more satisfactory model has been developed.