Article
MSC:
35J65,
35Q20,
35Q99,
78A35,
78A55,
82C70 | MR 0879329 | Zbl 0621.35047 | DOI: 10.21136/AM.1987.104235
Full entry |
PDF
(1.0 MB)
Feedback
PDF
(1.0 MB)
Feedback
Keywords:
van Roosbroeck's equation; steady-state carrier distribution; semiconductor devices; existence; van Roosbroeck's system; transport of mobile charge carriers; spatially homogeneous semiconductor devices; Fermi-Dirac statistics; Schauder's fixed point theorem; unique steady- state
van Roosbroeck's equation; steady-state carrier distribution; semiconductor devices; existence; van Roosbroeck's system; transport of mobile charge carriers; spatially homogeneous semiconductor devices; Fermi-Dirac statistics; Schauder's fixed point theorem; unique steady- state
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.
References:
[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. DOI 10.1109/T-ED.1983.21260
[2] V. L. Bonč-Bruevich S. G. Kalašnikov: Halbleiterphysik. Berlin 1982.
[3] V. L. Bonč-Bruevich I. P. Zvjagin A. G. Mironov: Spatial electrical instability in semiconductors. (Russian). Moscow 1972.
[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. MR 0781760 | Zbl 0562.35022
[5] H. Gajewski K. Gröger K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Berlin 1974. MR 0636412
[6] D. Gilbarg N. S. Trudinger: Elliptic partial differential equations of second order. Berlin- Heidelberg-New York 1977. MR 0473443
[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. MR 0466912 | Zbl 0361.35022
[8] M. S. Mock: On equations describing steady-state carrier distributions in semiconductor devices. Comm. Pure Appl. Math. 25 (1972), 781-792. DOI 10.1002/cpa.3160250606 | MR 0323233
[9] M. S. Mock: Analysis of mathematical models of semiconductor devices. Dublin 1983. MR 0697094 | Zbl 0532.65081
[10] T. I. Seidman: Steady state solutions of diffusion-reaction systems with electrostatic convection. Nonlinear Analysis 4 (1980), 623-637. DOI 10.1016/0362-546X(80)90097-8 | MR 0574378 | Zbl 0438.35030
[11] S. Selberherr: Analysis and simulation of semiconductor devices. Wien-New York 1984.
[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. DOI 10.1002/j.1538-7305.1950.tb03653.x
Search
Partner of
