ON THE NUMERICAL SOLUTION OF NONLINEAR ELLIPTIC PDEs ARISING FROM SEMICONDUCTOR DEVICE MODELING

Abstract

This chapter discusses the numerical solution of nonlinear elliptic partial differential equations arising from semiconductor device modeling. The coupled nonlinear elliptic partial differential equations that model the intrinsic behavior of semiconductor devices provide a significant challenge for the scientific computing community. The chapter discusses various formulations of the basic semiconductor equations and presents several numerical algorithms for solving them efficiently. It provides some computational results to indicate the relative merits of different solution schemes. This formulation of the semiconductor equations has proved preferable if the Einstein relation holds mainly because the triple u, v, w are smoother than u, n, p, and therefore, there is less sensitivity to the mesh and to the initial guess for the discrete solution. In some special cases, it is convenient to reduce the nonlinearity and introduce a further change of variables.