Strong discontinuities for the 2-D MEP hydrodynamical model of charge transport in semiconductors
Author:
A. M. Blokhin
Journal:
Quart. Appl. Math. 66 (2008), 359-377
MSC (2000):
Primary 76X05; Secondary 35B35, 35Q35, 82D37
DOI:
https://doi.org/10.1090/S0033-569X-08-01081-3
Published electronically:
February 29, 2008
MathSciNet review:
2416778
Full-text PDF Free Access
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Abstract: For the balance equations of charge transport in semiconductors based on the maximum entropy principle (see Anile and Romano (1999) and Romano (2000)), we derive and study the Rankine-Hugoniot jump conditions.
References
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References
- A. M. Anile and V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Cont. Mech. Thermodyn., 11 (1999), pp. 307–325. MR 1723705 (2000j:82044)
- V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Cont. Mech. Thermodyn., 12 (2000), pp. 31–51. MR 1753005 (2001g:82117)
- S. Selberherr, Analysis and simulation of semiconductor devices, Wien - New York, Springer-Verlag, 1984.
- W. Hänsch, The drift-diffusion equation and its applications in MOSFET modeling, Wien, Springer-Verlag, 1991.
- P. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor equations, Wien, Springer-Verlag, 1990. MR 1063852 (91j:78011)
- D. Chen, E. C. Kan, U. Ravaioli, C-W. Shu and R. Dutton, An improved energy-transport model including nonparabolicity and non-maxwellian distribution effects, IEEE on Electron Device Letters, 13 (1992), pp. 26–28.
- E. Lyumkis, B. Polsky, A. Shir and P. Visocky, Transient semiconductor device simulation including energy balance equation, COMPEL, 11 (1992), pp. 311–325.
- N. B. Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys., 37 (1996), pp. 3308–3333. MR 1401227 (98b:82091)
- A. M. Anile and V. Romano, Hydrodynamical modeling of charge carrier transport in semiconductors, MECCANICA, 35 (2000), pp. 249–296.
- A. M. Anile, G. Mascali, V. Romano, Recent developments in hydrodynamical modeling of semiconductors, pp. 1-54 in Mathematical Problems in Semiconductor Physics, Lecture Notes in Mathematics, 1832, Springer, 2003. MR 2073497
- I. Müller and T. Ruggeri, Rational Extended Thermodynamics, Berlin, Springer-Verlag, 1998. MR 1632151 (99h:80001)
- D. Jou, J. Casas-Vazquez and G. Lebon, Extended irreversible thermodynamics, Berlin, Springer-Verlag, 1993. MR 1271780 (95a:80004)
- C. D. Levermore, Moment closure hierarchies for kinetic theories, J. Stat. Phys., 83 (1996), pp. 331–407. MR 1392419 (97e:82041)
- A. M. Anile, O. Muscato, V. Romano, Moment equations with maximum entropy closure for carrier transport in semiconductor devices: validation in bulk silicon, VLSI Design, 10 (2000), pp. 335–354.
- O. Muscato, V. Romano, Simulation of submicron silicon diode with a non-parabolic hydrodynamical model based on the maximum entropy principle, VLSI Design, 13 (2001), pp. 273–279.
- V. Romano, Nonparabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices, Math. Meth. Appl. Sci., 24 (2001), pp. 439–471. MR 1829038 (2002c:82083)
- V. Romano, 2D simulation of a silicon MESFET with a non-parabolic hydrodynamical model based on the maximum entropy principle, J. Comp. Phys., 176 (2002), pp. 70–92.
- A. M. Blokhin, R. S. Bushmanov, A. S. Rudometova, V. Romano, Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors, Nonlinear Analysis, 65 (2006), pp. 1018–1038. MR 2232491 (2006m:76153)
- L. C. Woods, Principles of Magnetoplasma Dynamics, Clarendon Press - Oxford, 1987. MR 957923 (89i:76099)
- L. V. Ovsyannikov, Lectures on the fundamentals of gas dynamics, Moscow, Nauka, 1981 (Russian). MR 665918 (84f:76041)
- L. I. Sedov, Continuum mechanics, Vol. 1, River Edge, NJ, World Scientific, 1997.
- A. M. Blokhin, R. S. Bushmanov, V. Romano, Asymptotic stability of the equilibrium state for the hydrodynamical model of charge transport in semiconductors based on the maximum entropy principle, Int. J. Eng. Sci., 42(8-9) (2004), pp. 915–934. MR 2054625 (2005c:82093)
- A. M. Blokhin, R. S. Bushmanov, V. Romano, Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors, Nonlinear Analysis, 65 (2006), pp. 2169-2191. MR 2266431 (2007i:35225)
- A. M. Blokhin, R. S. Bushmanov, V. Romano, Global existence for the system of the macroscopic balance equations of charge transport in semiconductors, J. Math. Anal. Appl. 305 (2005), pp. 72-90. MR 2128112 (2005k:35392)
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Additional Information
A. M. Blokhin
Affiliation:
Institute of Mathematics, Novosibirsk 630090, Russia
Received by editor(s):
November 11, 2006
Published electronically:
February 29, 2008
Article copyright:
© Copyright 2008
Brown University