Implications of Analytical Investigations About the Semiconductor Equations on Device Modeling Programs

This paper gives guidelines for the development of computer programs for the numerical simulation of semiconductor devices. For this purpose, the basic mathematical results on the corresponding elliptic boundary value problem are reviewed. Particularly, existence, smoothness, and structure of the solutions of the fundamental semiconductor equations are discussed. Various feasible approaches to the numerical solution of the semiconductor equations are described. Much emphasis is placed on constructive remarks to help authors of device simulation programs make decisions on their code design problems. Thus criteria for an optimal mesh generation strategy are given. The iterative solution of the systems of nonlinear and linear equations obtained by discretizing the semiconductor equations is discussed. An example shows the power of these concepts combined with modern numerical methods in comparison to classical approaches.