A finite-volume scheme for a spinorial ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors
Author(s) :
Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Jüngel, Ansgar [Auteur]
Institute for Analysis and Scientific Computing [Wien]
Shpartko, Polina [Auteur]
Institute for Analysis and Scientific Computing [Wien]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Jüngel, Ansgar [Auteur]
Institute for Analysis and Scientific Computing [Wien]
Shpartko, Polina [Auteur]
Institute for Analysis and Scientific Computing [Wien]
Journal title :
Numerical Methods for Partial Differential Equations
Pages :
819-846
Publisher :
Wiley
Publication date :
2016
ISSN :
0749-159X
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, ...
Show more >An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly coupled equations for the charge and spin-vector densities, coupled to the Poisson equation for the elec-tric potential. The equations are solved in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The charge and spin-vector fluxes are approximated by a Scharfetter-Gummel discretization. The main features of the numerical scheme are the preservation of positivity and L ∞ bounds and the dissipation of the discrete free energy. The existence of a bounded discrete solution and the monotonicity of the discrete free energy are proved. For undoped semiconductor materials, the numerical scheme is uncon-ditionally stable. The fundamental ideas are reformulations using spin-up and spin-down densities and certain projections of the spin-vector density, free energy estimates, and a discrete Moser iteration. Furthermore, numerical simulations of a simple ferromagnetic-layer field-effect transistor in two space dimensions are presented.Show less >
Show more >An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly coupled equations for the charge and spin-vector densities, coupled to the Poisson equation for the elec-tric potential. The equations are solved in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The charge and spin-vector fluxes are approximated by a Scharfetter-Gummel discretization. The main features of the numerical scheme are the preservation of positivity and L ∞ bounds and the dissipation of the discrete free energy. The existence of a bounded discrete solution and the monotonicity of the discrete free energy are proved. For undoped semiconductor materials, the numerical scheme is uncon-ditionally stable. The fundamental ideas are reformulations using spin-up and spin-down densities and certain projections of the spin-vector density, free energy estimates, and a discrete Moser iteration. Furthermore, numerical simulations of a simple ferromagnetic-layer field-effect transistor in two space dimensions are presented.Show less >
Language :
Anglais
Popular science :
Non
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