ABSTRACT
In 1950, van Roosbroeck introduced the fundamental semiconductor device equations as a system of three nonlinearly coupled partial differential equations (PDEs). They describe the semiclassical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation. This chapter introduces a method for discretizing the van Roosbroeck system which is close to the physicist's approach to derive PDEs based on a subdivision of the computational domain into representative elementary volumes or control volumes. The method has two main ingredients: a geometry-based approach to obtain a system describing communicating control volumes; and a consistent description of the fluxes between two adjacent control volumes. When applied to the drift-diffusion formulation, compared to various variants of the stabilized finite element method, the two-point flux finite volume scheme is outstanding in the sense that it guarantees positivity of densities and absense of unphysical oscillations. Spin-polarized drift-diffusion models have been proposed for the description of spintronic devices.
