[Zurück]

C. Chainais-Hillairet, M. Gisclon, A. Jüngel:
"A finite-volume scheme for the multidimensional quantum drift-diffusion model for semiconductors";
in: "ASC Report 16/2009", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

A nite-volume scheme for the stationary unipolar quantum drift-di usion equations
for semiconductors in several space dimensions is analyzed. The model consists of a
fourth-order elliptic equation for the electron density, coupled to the Poisson equation for
the electrostatic potential, with mixed Dirichlet-Neumann boundary conditions. The numerical
scheme is based on a Scharfetter-Gummel type reformulation of the equations. The
existence of a sequence of solutions to the discrete problem and its numerical convergence to
a solution to the continuous model are shown. Moreover, some numerical examples in two
space dimensions are presented.

Quantum Bohm potential, density-gradient model, nite-volume method, discrete Sobolev

http://www.asc.tuwien.ac.at/preprint/2009/asc16x2009.pdf