Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

In this article we concisely present severalmodern strategiesthat are applicable to drift-dominated carriertransport in higher-orderdeterministicmodels such as the driftdiffusion,hydrodynamic, and quantumhydrodynamic systems. The approachesinclude extensions of “upwind” and artificialdksipation schemes, generalizationof the tradltional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwindPetrov Galerkin (SUPG), “entropy” variables, transformations, least-squaresmixed methods and other stabilized Galerkinschemessuch as Galerklnleast squaresand dkcontinuous Galerkin schemes. The treatment is representativerather than an exhaustive review and several schemesare mentioned only briefly with appropriatereferenceto the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examplesfrom our recent researchtests with some of the methods. A second aspect of the work deals with algorithmsthat employ unstructured grids in conjunction with adaptive refinementstrategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dialan-operator approaches such as that used in the industrial simulatorPROPHET, and object-oriented software support such as those in the SANDIA National Laboratory frameworkSIERRA.