EQUATION FORMULATION CONSIDERATIONS FOR EFFICIENT NUMERICAL MODELING OF SEMICONDUCTOR PHENOMENA*

Abstract-This paper highlights he importance ofequation formulation and associated programming efficiency with respect o modeling of semiconductor phenomena via numerical methods. Two numerical modeling efforts are developed inthis paper for one-space dimension device modeling. It is shown on a per iteration basis that he ratio of the computational effort between the two methods i a factor of sixteen. The reduction in the computational effort between the two methods was realized by reformulating the mathematical equations and by reconsidering the effect of programming efficiency. A by-product of the reformulation was a factor of two to three improvement i the convergence rate of the nonlinear iteration. With all considerations, the overall improvement i the solution times for one-space dimension device numerical modeling was determined tobe a factor of 30-50. When considering equation formulation alone, the per iteration improvement is a factor of 1.43. Coupled with the two to three convergence rate imorovement the overall improvement due to equation formulation was approximatel