Semiconductor heterostructure nonlinear Poisson equation

Abstract

A nonlinear Poisson partial differential equation descriptive of heterostructure physics is presented for two-dimensional device cross sections. The equation is solved using a hybrid nonlinear Jacobi–Newton iteration method. The approach has the characteristic of giving explicit numerical relationships which are amenable to the development of elegant proofs of numerical behavior based on local physical properties and boundary conditions. These proofs are provided in complete detail for nonequilibrium conditions.