Abstract
During the last decade the simulation of semiconductor devices became a valuable and indispensable tool for the design of new devices. In this paper we present and analyze new simulation models which also account for quantum effects.
The authors acknowledge support from the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” under Grant No. P6771.
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References
V.I. Tatarskii, The Wigner representation of quantum mechanics, Sov. Phys. Usp. 26, 311–327 (1983).
P.A. Markowich, On the equivalence of the Schrödinger and the quantum Liouville equation, Math. Meth. Appl. Sci. 11, 459–469 (1989).
P.A. Markowich and C. Ringhofer, An analysis of the quantum Liouville equation, ZAMM 69, 121–127 (1989).
A. Arnold and H. Steinrück, The ‘electromagnetic’ Wigner equation for an electron with spin, ZAMP 40, No. 6, 793–815 (1989).
H. Steinrück, The one dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem, to appear in SIAM (1990).
A. Arnold and F. Nier, The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case, manuscript (1990).
F. Brezzi and P.A. Markowich, The three-dimensional Wigner-Poisson problem: Existence, uniqueness and approximation, submitted (1989).
A. Arnold, P. Degond, P.A. Markowich and H. Steinrück, The Wigner-Poisson problem in a crystal, Appl. Math. Lett. 2, No. 2, 187–191 (1989).
H. Steinrück, The Wigner-Poisson problem in a crystal: Existence, uniqueness, semiclassical limit in the one dimensional case, to appear in ZAMM (1990).
P. Degond and P.A. Markowich, A mathematical analysis of quantum transport in three dimensional crystals, to appear in Annali di Mat. Pura ed Appl. (1990).
P. Degond and P. A. Markowich, A quantum-transport model for semiconductors: the Wigner-Poisson problem on a bounded Brillouin zone, to appear in M2AN (1990).
U. Ravaioli, M.A. Osman, W. Pötz, N. Kluksdahl and D.K. Ferry, Investigation of ballistic transport through resonant-tunneling quantum wells using Wigner function approach, Physica 134B, 36–40 (1985).
W.R. Frensley, Wigner function model of a resonant-tunneling semiconductor device, Phys. Rev. B 36, 1570–1580 (1987).
C. Ringhofer, A spectral method for the numerical simulation of quantum tunneling phenomena, Technical Report No. 115, Arizona State University (1988).
N. D. SUH, L’étude des structures coherentes dans l’éspace des phases du plasma unidimensionnel électrostatique: aspect classique et quantique, thesis at University of Orleans (1989).
A. Arnold and F. Nier, Numerical analysis of the deterministic particle method applied to the Wigner equation, manuscript (1990).
G. Grimvall, The electron-phonon interaction in metals, North Holland, Amsterdam - New York - Oxford (1981).
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© 1991 Kluwer Academic Publishers
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Arnold, A., Markowich, P.A. (1991). Quantum Transport Models for Semiconductors. In: Spigler, R. (eds) Applied and Industrial Mathematics. Mathematics and Its Applications, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1908-2_24
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DOI: https://doi.org/10.1007/978-94-009-1908-2_24
Publisher Name: Springer, Dordrecht
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