VARIATIONAL PRINCIPLES FOR SOLVING NON-LINEAR POISSON EQUATIONS FOR THE POTENTIAL OF IMPURITY IONS IN SEMICONDUCTORS WITH SPATIALLY VARIABLE DIELECTRIC-CONSTANTS

In the above-named paper, a simplified form of the nonlinear Poisson equation for the impurity-ion potential has been solved approximately by making use of an equivalent variational principle. The difference between the exact and the simplified nonlinear Poisson equations is a term involving the derivative of the potential and the derivative of the spatially variable dielectric constant. The purpose of the present paper is the presentation of a more general variational principle, by which one might obtain an approximate solution of the exact nonlinear Poisson equation. © 1979 The American Physical Society.