A finite‐volume scheme for the multidimensional quantum drift‐diffusion model for semiconductors |
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| Authors: | Claire Chainais‐Hillairet Marguerite Gisclon Ansgar Jüngel |
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| Affiliation: | 1. Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal, Aubière 63177, France;2. Laboratoire de Mathématiques, CNRS UMR 5127, Université de Savoie, Le Bourget‐du‐Lac 73376, France;3. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien 1040, Austria |
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| Abstract: | A finite‐volume scheme for the stationary unipolar quantum drift‐diffusion 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. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1483–1510, 2011 |
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| Keywords: | density‐gradient model discrete Sobolev inequality existence of solutions finite‐volume method numerical convergence quantum Bohm potential quantum semiconductor devices |
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