A Finite Difference Method for the Basic Stationary Semiconductor Device Equations

Abstract

In this paper we analyse a special-purpose finite difference scheme for the basic stationary semiconductor device equations in one space dimension. These equations model potential distribution, carrier concentration and current flow in an arbitrary one-dimensional semiconductor device and they consist of three second order ordinary differential equations subject to boundary conditions. A small parameter appears as multiplier of the second derivative of the potential, thus the problem is singularly perturbed. We demonstrate the occurence of internal layers at so called device-junctions, which are jump-discontinuities of the data, and present a finite difference scheme which allows for the resolution of these internal layers without employing an exceedingly large number of grid-points. We establish the relation of this scheme to exponentially fitted schemes and give a convergence proof. Moreover the construction of efficient grids is discussed.KeywordsFinite Difference MethodFinite Difference SchemeInternal LayerDoping ProfileOrder Ordinary Differential EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.