Solution of a nonlinear Poissons equation for the potential of impurity ions in semiconductors with a spatially variable dielectric constant by an equivalent variational method

Abstract

A correct knowledge of the screening potential in heavily doped semiconductors is highly desirable for analyzing various electronic engineering problems. In this paper a method for the solution of a nonlinear Poissons equation in the framework of an equivalent variational approach is presented. Strengths and weaknesses of the earlier methods, including those of Csavinszky and co-workers, have been discussed in some detail. On the basis of a comparison of the present method with the earlier ones, it is felt that the present one is very promising, and perhaps more general and unified than most, if not all, other methods available in the literature. © 1992 The American Physical Society.