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Title: On steady-state carrier distributions in semiconductor devices (English)
Author: Gröger, Konrad
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 32
Issue: 1
Year: 1987
Pages: 49-56
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: The author proves the existence of solution of Van Roosbroeck's system of partial differential equations from the theory of semiconductors. His results generalize those of Mock, Gajewski and Seidman. (English)
Keyword: van Roosbroeck's equation
Keyword: steady-state carrier distribution
Keyword: semiconductor devices
Keyword: existence
Keyword: van Roosbroeck's system
Keyword: transport of mobile charge carriers
Keyword: spatially homogeneous semiconductor devices
Keyword: Fermi-Dirac statistics
Keyword: Schauder's fixed point theorem
Keyword: unique steady- state
MSC: 35J65
MSC: 35Q20
MSC: 35Q99
MSC: 78A35
MSC: 78A55
MSC: 82C70
idZBL: Zbl 0621.35047
idMR: MR0879329
DOI: 10.21136/AM.1987.104235
Date available: 2008-05-20T18:31:36Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. L. Blue C. L. Wilson: Two-dimensional analysis of semiconductor devices using general-purpose interactive PDE software.IEEE Trans. Electron Devices ED-30 (1983), 1056-1070. 10.1109/T-ED.1983.21260
Reference: [2] V. L. Bonč-Bruevich S. G. Kalašnikov: Halbleiterphysik.Berlin 1982.
Reference: [3] V. L. Bonč-Bruevich I. P. Zvjagin A. G. Mironov: Spatial electrical instability in semiconductors.(Russian). Moscow 1972.
Reference: [4] H. Gajewski: On the existence of steady-state carrier distributions in semiconductors.In: Probleme und Methoden der Mathematischen Physik. Teubner-Texte zur Mathematik 63 (1984), 76-82. Zbl 0562.35022, MR 0781760
Reference: [5] H. Gajewski K. Gröger K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Berlin 1974. MR 0636412
Reference: [6] D. Gilbarg N. S. Trudinger: Elliptic partial differential equations of second order.Berlin- Heidelberg-New York 1977. MR 0473443
Reference: [7] P. Grisvard: Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain.In: Numerical solution of partial differential equations III (1976), 207-274. Zbl 0361.35022, MR 0466912
Reference: [8] M. S. Mock: On equations describing steady-state carrier distributions in semiconductor devices.Comm. Pure Appl. Math. 25 (1972), 781-792. MR 0323233, 10.1002/cpa.3160250606
Reference: [9] M. S. Mock: Analysis of mathematical models of semiconductor devices.Dublin 1983. Zbl 0532.65081, MR 0697094
Reference: [10] T. I. Seidman: Steady state solutions of diffusion-reaction systems with electrostatic convection.Nonlinear Analysis 4 (1980), 623-637. Zbl 0438.35030, MR 0574378, 10.1016/0362-546X(80)90097-8
Reference: [11] S. Selberherr: Analysis and simulation of semiconductor devices.Wien-New York 1984.
Reference: [12] W. Van Roosbroeck: Theory of the flow of electrons and holes in Germanium and other semiconductors.Bell Syst. Tech. J. 29 (1950), 560-607. 10.1002/j.1538-7305.1950.tb03653.x


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