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Article Dans Une Revue Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Année : 2014

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.
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Dates et versions

hal-00962242 , version 1 (20-03-2014)

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Laurent Gosse. Redheffer products and numerical approximation of currents in one-dimensional semiconductor kinetic models. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2014, pp.???-???. ⟨10.1137/130939584⟩. ⟨hal-00962242⟩

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