Abstract
We consider a modified time-dependent van Roosbroeck system with saturating velocities and a source term subject to assumptions designed to permit a standard generation term corresponding to impact ionization. This is then a nonlinear parabolic system with a right hand side of the form S = S(., u, Δu, ɛ), coupled with the map L : u ⇔ ɛ defined by the Poisson equation at each t. The analysis leads to existence of solutions for all time as well as uniqueness (and continuous dependence on data) under stronger conditions.
This research was partially supported by the Air Force Office of Scientific Research under grants #AFOSR-82-0271 and #AFOSR-87-0190.
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References
J. P. Aubin, Un théorème de compacité, CRAS de Paris 265, pp. 5042–5045 (1963).
S. Belbas and T. I. Seidman, Periodic solutions of a parabolic quasi-variational inequality from stochastic optimal control, Applicable Anal. (to appear).
H. Gajewski and K. Gröger, On the basic equations for carrier transport in semiconductors, J. Math. Anal. Appl. 113, pp. 12–35 (1986).
P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman APP, Boston (1985).
J. Jerome Consistency of semiconductor modeling: an existence/stability analysis for the stationary van Roosbroeck system, SIAM J. Appl. Math. 45, pp. 565–590 (1985).
M. Mock An initial value problem from semiconductor device theory, SIAM J. Math. Anal. 5, pp. 597–612 (1974).
C. B. Morrey, Jr. Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York (1966).
T. I. Seidman Steady state solutions of a nonlinear diffusion-reaction system with electrostatic convection, Nonlinear Anal.-TMA 4, pp. 623–637 (1980).
T. I. Seidman Time-dependent solutions of a nonlinear system arising in semi-conductor theory, II: boundedness and periodicity, Nonlinear Anal.-TMA 10, pp. 491–502 (1986).
T. I. Seidman The transient semiconductor problem with generation terms, in Computational Aspects of VLSI Design and Semiconductor Device Simulation, Amer. Math. Soc., Providence (1988).
T. I. Seidman Time-dependent solutions of a diffusion-reaction system with with electrostatic convection, in preparation
T. I. Seidman and G. M. Troianniello Time-dependent solutions of a nonlinear system arising in semiconductor theory, Nonlinear Anal-TMA 9, pp. 1137–1157 (1985).
S. Selberherr Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Wien (1984).
J. Simon Compact sets in the space L p(0, T; B), Ann. Mat. pura appl. CXLVI, pp. 65–96 (1987).
W. van Roosbroeck Theory of flow of electrons and holes in germanium and other semiconductors, Bell System Tech. J. 29, pp. 560–607 (1950).
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Seidman, T.I. (1989). The transient semiconductor problem with generation terms, II. In: Gill, T.L., Zachary, W.W. (eds) Nonlinear Semigroups, Partial Differential Equations and Attractors. Lecture Notes in Mathematics, vol 1394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086760
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DOI: https://doi.org/10.1007/BFb0086760
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