A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors

Claire Chainais-Hillairet (1, 2) , Ansgar Jüngel (3) , Polina Shpartko (3)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Institute for Analysis and Scientific Computing [Wien]

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.

Domaines: Analyse numérique [math.NA]

Claire Chainais-Hillairet, Ansgar Jüngel, Polina Shpartko. A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors. Numerical Methods for Partial Differential Equations, 2016, 32 (3), pp.819-846. ⟨10.1002/num.22030⟩. ⟨hal-01115858v3⟩