Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

In this article we concisely present several modern strategies that are applicable to driftdominatedcarrier transport in higher-order deterministic models such as the driftdiffusion,hydrodynamic, and quantum hydrodynamic systems. The approaches includeextensions of “upwind” and artificial dissipation schemes, generalization of the traditionalScharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind PetrovGalerkin (SUPG), “entropy” variables, transformations, least-squares mixed methodsand other stabilized Galerkin schemes such as Galerkin least squares and discontinuousGalerkin schemes. The treatment is representative rather than an exhaustivereview and several schemes are mentioned only briefly with appropriate referenceto the literature. Some of the methods have been applied to the semiconductor deviceproblem while others are still in the early stages of development for this class of applications.We have included numerical examples from our recent research tests withsome of the methods. A second aspect of the work deals with algorithms that employunstructured grids in conjunction with adaptive refinement strategies. The full benefitsof such approaches have not yet been developed in this application area and weemphasize the need for further work on analysis, data structures and software tosupport adaptivity. Finally, we briefly consider some aspects of software frameworks.These include dial-an-operator approaches such as that used in the industrial simulatorPROPHET, and object-oriented software support such as those in the SANDIANational Laboratory framework SIERRA