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

引用

页码：1483 / 1510

页数：28

共 50 条

[41] Monte Carlo simulation of bulk semiconductors for accurate calculation of drift velocity as a parameter for drift-diffusion, hydrodynamic models
Donnarumma, Gesualdo
Wozny, Janusz
Lisik, Zbigniew
MATERIALS SCIENCE AND ENGINEERING B-ADVANCED FUNCTIONAL SOLID-STATE MATERIALS, 2009, 165 (1-2): : 47 - 49
[42] FINITE-VOLUME METHODS FOR ANISOTROPIC DIFFUSION PROBLEMS ON SKEWED MESHES
Liu, Xiaogang
Ming, Pingjian
Zhang, Wenping
Fu, Lirong
Jing, Lilong
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, 2015, 68 (03) : 239 - 256
[43] A scheme using finite-volume method for local horizontal derivatives in spectral model: Hydrostatic case
Yang, Jinhui
Wu, Jianping
Song, Junqiang
Peng, Jun
Yin, Fukang
Leng, Hongze
Ren, Kaijun
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 2023, 149 (753) : 1263 - 1270
[44] Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation
Sugiyama, Yuusuke
Yamamoto, Masakazu
JOURNAL OF EVOLUTION EQUATIONS, 2021, 21 (02) : 1383 - 1417
[45] Relaxation Limit from the Quantum Navier-Stokes Equations to the Quantum Drift-Diffusion Equation
Antonelli, Paolo
Carnevale, Giada Cianfarani
Lattanzio, Corrado
Spirito, Stefano
JOURNAL OF NONLINEAR SCIENCE, 2021, 31 (05)
[46] Learning Quantum Drift-Diffusion Phenomenon by Physics-Constraint Machine Learning
Li, Chun
Yang, Yunyun
Liang, Hui
Wu, Boying
IEEE-ACM TRANSACTIONS ON NETWORKING, 2022, 30 (05) : 2090 - 2101
[47] A finite-volume diffusion-limited aggregation model for predicting the effective thermal conductivity of frost
Negrelli, Silvia
Cardoso, Rodrigo P.
Hermes, Christian J. L.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2016, 101 : 1263 - 1272
[48] On the uniqueness and stability of solutions to the control problems for the electron drift-diffusion model
Brizitskii, R. V.
Maksimova, N. N.
VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2025, 35 (01): : 27 - 46
[49] ASYMPTOTIC STABILITY OF STATIONARY SOLUTIONS TO THE DRIFT-DIFFUSION MODEL IN THE WHOLE SPACE
Kobayashi, Ryo
Yamamoto, Masakazu
Kawashima, Shuichi
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2012, 18 (04) : 1097 - 1121
[50] FORMAL DERIVATION OF QUANTUM DRIFT-DIFFUSION EQUATIONS WITH SPIN-ORBIT INTERACTION
Barletti, Luigi
Holzinger, Philipp
Juengel, Ansgar
KINETIC AND RELATED MODELS, 2022, 15 (02) : 257 - 282

← 1 2 3 4 5 →