A Finite-Volume Scheme for the Multidimensional Quantum Drift-Diffusion Model for Semiconductors

被引：9
|
作者：
Chainais-Hillairet, Claire [2 ]
Gisclon, Marguerite [3 ]
Juengel, Ansgar [1 ]
机构：
[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria
[2] Univ Clermont Ferrand, Math Lab, CNRS, UMR 6620, F-63177 Aubiere, France
[3] Univ Savoie, Math Lab, CNRS, UMR 5127, F-73376 Le Bourget Du Lac, France
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 27卷 / 06期
基金：
奥地利科学基金会;
关键词：
density-gradient model; discrete Sobolev inequality; existence of solutions; finite-volume method; numerical convergence; quantum Bohm potential; quantum semiconductor devices; HYDRODYNAMIC EQUATIONS; DEVICE; CONVERGENCE; SIMULATION; TRANSPORT; ELECTRON; SYSTEM; STATE; LIMIT;
D O I：
10.1002/num.20592
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1483-1510, 2011
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页码：1483 / 1510
页数：28
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