Discretization schemes for high-frequency semiconductor device models

This paper provides an overview on the numerical issues involved in the spatial and time-domain discretization of the coupled transport-electromagnetic models used in the simulation of high-frequency semiconductor devices. The physical transport models derived from the Boltzmann transport equation (BTE) are reviewed in order of decreasing complexity, from the full hydrodynamic model to the drift-diffusion approach. Spatial discretization is introduced starting from ad hoc approaches developed in the field of semiconductor modeling, like the Scharfetter-Gummel (1969) scheme; a critical comparison is then provided with the upwind finite-element schemes. Finally, time-domain discretization issues are reviewed, with particular stress on innovative developments in the area of hydrodynamic and of coupled transport-full-wave EM models.