Redheffer products and numerical approximation of currents in one-dimensional semiconductor kinetic models
Résumé
When numerically simulating a kinetic model of $n^+nn^+$ semiconductor device, obtaining a constant macroscopic current at steady-state is still a challenging task. Part of the difficulty comes from the multiscale, discontinuous nature of both $p|n$ junctions which create spikes of electric field and enclose a channel where corresponding depletion layers glue together. The kinetic formalism furnishes a model holding inside the whole domain, but at the price of strongly-varying parameters. By concentrating both the electric acceleration and the linear collision terms at each interface of a Cartesian computational grid, we can treat them by means of a Godunov scheme involving 2 types of scattering matrices. Combining both these mechanisms into a global S-matrix can be achieved thanks to ''Redheffer's star-product''. Assuming that the resulting S-matrix is stochastic permits to prove maximum principles under a mild CFL restriction. Numerical illustrations of collisional Landau damping and various $n^+nn^+$ devices are provided on coarse grids.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...