Numerical solution of the nonlinear Poisson equation for semiconductor devices by application of a diffusion-equation finite difference scheme

Abstract

An effective iterative finite difference method for solving a nonlinear Poisson equation for semiconductor device theory is presented. The nonlinear Poisson equation is replaced by an equivalent diffusion equation. As a result, a stable and fully controlled iterative method was found to solve this equation, regardless of the level of heterostructure complexity and the type of electrical contacts, passivating dielectric layers or environment. Selected numerical results obtained using this method for a gated HgCdTe photodiode with metal contacts are reported.