Strong discontinuities for the 2-D MEP hydrodynamical model of charge transport in semiconductors

Blokhin, A.

doi:10.1090/S0033-569X-08-01081-3

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
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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

Angelo Marcello Anile and Vittorio Romano, Non-parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. 11 (1999), no. 5, 307–325. MR 1723705, DOI https://doi.org/10.1007/s001610050126
Vittorio Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12 (2000), no. 1, 31–51. MR 1753005, DOI https://doi.org/10.1007/s001610050121

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. A. Markowich, C. A. Ringhofer, and C. Schmeiser, Semiconductor equations, Springer-Verlag, Vienna, 1990. MR 1063852

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. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys. 37 (1996), no. 7, 3306–3333. MR 1401227, DOI https://doi.org/10.1063/1.531567

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, and V. Romano, Recent developments in hydrodynamical modeling of semiconductors, Mathematical problems in semiconductor physics, Lecture Notes in Math., vol. 1823, Springer, Berlin, 2003, pp. 1–56. MR 2073497, DOI https://doi.org/10.1007/978-3-540-45222-5_1

Ingo Müller and Tommaso Ruggeri, Rational extended thermodynamics, 2nd ed., Springer Tracts in Natural Philosophy, vol. 37, Springer-Verlag, New York, 1998. With supplementary chapters by H. Struchtrup and Wolf Weiss. MR 1632151

D. Jou, J. Casas-Vázquez, and G. Lebon, Extended irreversible thermodynamics, Springer-Verlag, Berlin, 1993. MR 1271780

C. David Levermore, Moment closure hierarchies for kinetic theories, J. Statist. Phys. 83 (1996), no. 5-6, 1021–1065. MR 1392419, DOI https://doi.org/10.1007/BF02179552

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.

Vittorio Romano, Non-parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices, Math. Methods Appl. Sci. 24 (2001), no. 7, 439–471. MR 1829038, DOI https://doi.org/10.1002/mma.220

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, and V. Romano, Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors, Nonlinear Anal. 65 (2006), no. 5, 1018–1038. MR 2232491, DOI https://doi.org/10.1016/j.na.2005.09.045

L. C. Woods, Principles of magnetoplasma dynamics, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1987. MR 957923

L. V. Ovsyannikov, Lektsii po osnovam gazovoĭ dinamiki, “Nauka”, Moscow, 1981 (Russian). MR 665918

L. I. Sedov, Continuum mechanics, Vol. 1, River Edge, NJ, World Scientific, 1997.

A. M. Blokhin, R. S. Bushmanov, and V. Romano, Asymptotic stability of the equilibrium state for the hydrodynamical model of charge transport in semiconductors based on the maximum entropy principle, Internat. J. Engrg. Sci. 42 (2004), no. 8-9, 915–934. MR 2054625, DOI https://doi.org/10.1016/j.ijengsci.2003.09.007

A. M. Blokhin, R. S. Bushmanov, and V. Romano, Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors, Nonlinear Anal. 65 (2006), no. 11, 2169–2191. MR 2266431, DOI https://doi.org/10.1016/j.na.2006.01.030

A. M. Blokhin, R. S. Bushmanov, and V. Romano, Global existence for the system of the macroscopic balance equations of charge transport in semiconductors, J. Math. Anal. Appl. 305 (2005), no. 1, 72–90. MR 2128112, DOI https://doi.org/10.1016/j.jmaa.2004.10.024