Fully Numerical Monte Carlo Simulator for Noncubic Symmetry Semiconductors

In this paper, we present the workings of a fully numerical Monte Carlo simulator that can be employed to study transport in materials with noncubic symmetry. All of the principal ingredients of the Monte Carlo model, i.e., the energy band structure, phonon scattering rates, and impact ionization transition rate are used in numerical form. Various considerations such as k-space mesh size, numerical integration convergence, etc. that impact numerical accuracy will be discussed. The workings of the simulator are illustrated using example calculations of the bulk transport properties of GaAs and GaN. The simulation of bulk GaAs in particular challenges the numerics since the low electron effective mass within the gamma valley requires a high degree of numerical refinement to correctly capture the dynamics in this region. We calculate the steady-state drift velocity, impact ionization coefficients, valley occupations, and average carrier energy in bulk GaAs and GaN.