Discontinuous Galerkin Deterministic Solvers for a Boltzmann-Poisson Model of Hot Electron Transport by Averaged Empirical Pseudopotential Band Structures

摘要

The purpose of this work is to incorporate numerically, in a discontinuousGalerkin (DG) solver of a Boltzmann-Poisson model for hot electron transport,an electronic conduction band whose values are obtained by the sphericalaveraging of the full band structure given by a local empirical pseudopotentialmethod (EPM) around a local minimum of the conduction band for silicon, as amidpoint between a radial band model and an anisotropic full band, in order toprovide a more accurate physical description of the electron group velocity andconduction energy band structure in a semiconductor. This gives a betterquantitative description of the transport and collision phenomena thatfundamentally define the behaviour of the Boltzmann - Poisson model forelectron transport used in this work. The numerical values of the derivativesof this conduction energy band, needed for the description of the electrongroup velocity, are obtained by means of a cubic spline interpolation. TheEPM-Boltzmann-Poisson transport with this spherically averaged EPM calculatedenergy surface is numerically simulated and compared to the output oftraditional analytic band models such as the parabolic and Kane bands,numerically implemented too, for the case of 1D $n^+-n-n^+$ silicon diodes with400nm and 50nm channels. Quantitative differences are observed in the kineticmoments related to the conduction energy band used, such as mean velocity,average energy, and electric current (momentum).