Parallel implementation of cellular automata model of electron-hole transport in a semiconductor

Abstract

A parallel implementation of a three-dimensional cellular automaton (CA) model of electron — hole transport in a semiconductor is presented. Carriers transport is described by a nonlinear system of drift-diffusion-Poisson equations. This system includes the drift-diffusion equations in divergence form for electrons and holes and the Poisson equation for the potential, the gradient of which enters the drift-diffusion equations as the drift velocity. We solve the drift-diffusion-Poisson system for the three-dimensional case using the CA approach. A regular mesh is introduced in the three-dimensional domain, and the solution is calculated in all lattice cells. The drift-diffusion-Poisson system is solved by an iterative algorithm consisting of two alternating steps. In the first step, the electron and hole concentrations are calculated. In the second step, the drift velocity is calculated as the gradient of the solution to the Poisson equation with the right-hand side depending on the electron and hole concentrations. The correctness of both CA models is tested against the exact solutions of the drift-diffusion and Poisson equations for some special cases. A parallel implementation of the iterative CA algorithm using the domain decomposition method is presented. The efficiency of the parallel code is analyzed. The simulation results are obtained for the model parameters specific to GaN semiconductors.