Computer solution of one-dimensional Poisson's equation

Abstract

The one-dimensional Poisson's equation for semiconductors doped with an ion-implanted profile (or any profile) is solved numerically using the mesh method of solution. The original equation is replaced by a set of finite difference equations. Solutions using a uniform mesh distribution together with the Störmer or the Cowell method are described. A variable mesh formulation of both the Störmer and the Cowell method is derived and is shown to give better accuracy for much smaller amounts of computation than the corresponding uniform mesh formulation.