Improved diffusion-equation finite difference schema in numerical solution of the nonlinear Poisson equation

Abstract

In this work a numerical iterative method for solving the nonlinear Poisson equation has been developed with the use of the diffusion-equation (parabolic) finite difference schema, to describe semiconductor hetero-structures. Procedures to control the convergence and stability of the method are presented. The approach enables us to solve the nonlinear Poisson equation in a small number of iterations, regardless of the level of hetero-structure complexity, type of electrical contacts and passive dielectric layers. Some numerical results obtained by this method for nBn Hg1-xCdxTe hetero-structure infrared detectors with metal contacts are reported.