Advanced numerical methods and software approaches for semiconductor device simulation

In this article we concisely present several modern strategies that are app licable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of "upwind" and artificial dissi pation schemes, generalization of the traditional Scharfetter-Gummel approa ch, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), "entropy" variables, transformations, least-squares mixed methods and other stabiliz ed Galerkin schemes such as Galerkin least squares and discontinuous Galerk in schemes. The treatment is representative rather than an exhaustive revie w and several schemes are mentioned only briefly with appropriate reference to the literature, Some of the methods have been applied to the semiconduc tor device problem while others are still in the early stages of developmen t for this class of applications, We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction wi th adaptive refinement strategies. The full benefits of such approaches hav e not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adap tivity. Finally, we briefly consider some aspects of software frameworks, T hese include dial-an-operator approaches such as that used in the industria l simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.