Abstract
In submicron devices the transport of carriers are govern by the Boltzmann transport equation coupled with electromagnetics. The aim of this paper is to prove the existence of stationary solutions for the corresponding boundary value problems with arbitrary large data. The techniques are those developed by the author for the mathematical analysis of the stationary Vlasov Maxwell system. They are based on the use of upper solutions of the Boltzmann transport equation that give enough a-priori estimates to apply the Schauder fixed-point theorem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Bardos, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d’approximations; application à l’équation de transport, Ann. Sci de l’Ec. Norm. Sup., 4e série, 3 (1970), pp. 185–233.
J.S. Blakemore, Semiconductor statistics, Dover, New York, 1987.
P. Degond, F. Poupaud, B. Niclot and F. Guyot, Semiconductor modelling via the Boltzmann equation, Lectures in Appl. Math., 25, AMS, Providence, Rhode Island, (1990), pp. 51–73.
P. Degond and P.-A. Raviart, An asymptotic analysis of the Darwin model of approximation to Maxwell’s equations, Forum Math. (to appear).
R.J. Diperna and P.L. Lions, On the Cauchy problem for the Boltzmann equation: global existence and weak stability, Ann. of Math., 130 (1989), pp. 321–366.
R.J. Diperna and P.L. Lions, Global weak solutions of Vlasov-Maxwell systems, Com. on Pure and Appl. Math., XLII (1989), pp. 729–757.
R.J. Diperna and P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), pp. 511–547.
F. Golse, P.L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., 88 (1988), pp. 110–125.
C. Greencard and P.A. Raviart, A boundary value problem for the stationary Vlasov-Poisson system: the plane diode, Com. on Pure and Appl. Math., XLII (1990), pp. 473–507.
P.A. Markowich, C. Ringhofer and C. Schmeiser, Semiconductor equations, Springer, Vienna, 1990.
M. Mock, An initial value problem from semiconductor device theory, SIAM J. of Math. Anal., 5 (1974), pp. 597–612.
F.J. Mustieles, Global existence of solution for a system of nonlinear Boltzmann equations of semiconductor physics, Math. Meth. in the Appl. Sci., 14 (1991), pp. 107–121.
F. Poupaud, On a system of nonlinear Boltzmann equations of semiconductor physics, SIAM J. on Appl. Math., 50 (1990), pp. 1593–1606.
F. Poupaud, Solutions stationnaires des equations de Vlasov-Poisson, C.R. Acad. Sci. Paris, série I, 311 (1990), pp. 307–312.
F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system, Forum Math. (to appear).
F. Poupaud and C. Schmeiser, Charge transport in semiconductors with degeneracy effects, Math. Meth. in the Appl. Sci., 14 (1991), pp. 301–318.
L. Reggiani (ed.), Hot-electron transport in semiconductors, Topics in Appl. Phys., 58, Springer-Verlag, Berlin, Heidelberg, 1985.
T.I. Seidman, The transient semiconductor problem with generation terms, Lectures in Appl. Math., 25, AMS, Providence, Rhode Island (1990), pp. 75–87.
S.M. Sze, Physics of semiconductor devices, J. Wiley and sons, New York, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Poupaud, F. (1994). Boundary Value Problems in Semiconductors for the Stationary Vlasov-Maxwell-Boltzmann Equations. In: Coughran, W.M., Cole, J., Lloyd, P., White, J.K. (eds) Semiconductors. The IMA Volumes in Mathematics and its Applications, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8410-6_17
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8410-6_17
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8412-0
Online ISBN: 978-1-4613-8410-6
eBook Packages: Springer Book Archive