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A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation

Published online by Cambridge University Press:  31 January 2014

GIUSEPPE ALÌ ,
GIOVANNI MASCALI ,
VITTORIO ROMANO  and
ROSA CLAUDIA TORCASIO
GIUSEPPE ALÌ
Affiliation:
Dipartimento di Matematica, Università della Calabria and INFN-Gruppo c. Cosenza, 87036 Cosenza, Italy emails: [email protected]; [email protected]; [email protected]
GIOVANNI MASCALI
Affiliation:
Dipartimento di Matematica, Università della Calabria and INFN-Gruppo c. Cosenza, 87036 Cosenza, Italy emails: [email protected]; [email protected]; [email protected]
VITTORIO ROMANO
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, viale A. Doria 6, 95125 Catania, Italy email: [email protected]
ROSA CLAUDIA TORCASIO
Affiliation:
Dipartimento di Matematica, Università della Calabria and INFN-Gruppo c. Cosenza, 87036 Cosenza, Italy emails: [email protected]; [email protected]; [email protected]
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Abstract

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We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC.

Keywords

Compound semiconductorsHydrodynamical modelsMaximum entropy principle
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 2 , April 2014 , pp. 255 - 276
Copyright
Copyright © Cambridge University Press 2014 

References

[1]Alì, G., Mascali, G., Romano, V. & Torcasio, R. C. (2012) A hydrodynamic model for covalent semiconductors with applications to GaN and SiC. Acta Appl. Mat. 103 (1), 335–348, DOI:10.1007/s10440-012-9747-6.Google Scholar
[2]Anile, A. M. & Romano, V. (1999) Non-parabolic band transport in semiconductors: Closure of the moment equations. Contin. Mech. Thermodyn. 11, 307Google Scholar
[3]Dreyer, W. (1987) Maximisation of the entropy in non-equilibrium. J. Phys. A: Math. Gen. 20, 6505.Google Scholar
[4]Fawcett, W., Boardman, A. D. & Swain, S. (1970) Monte Carlo determination of electron transport properties in gallium arsenide. J. Phys. Chem. Solids 31 (9), 1963.Google Scholar
[5]Hjelm, M., Nilsson, H.-E., Martinez, A., Brennan, K. F. & Bellotti, E. (2003) Monte Carlo study of high-field carrier transport in 4H-SiC, including band-to-band tunneling. J. Appl. Phys. 93 (2), 1099.Google Scholar
[6]Jacoboni, C. & Lugli, P. (1989) The Monte Carlo Method for Semiconductor Device Simulation, Springer-Verlag, Wien, New York, NY.CrossRefGoogle Scholar
[7]Jaynes, E. T. (1957) Information theory and statistical mechanics. Phys. Rev. 106, 620.Google Scholar
[8]La Rosa, S., Mascali, G. & Romano, V. (2009) Exact maximum entropy closure of the hydrodynamical model for Si semiconductors: The 8-moment case. SIAM J. Appl. Math. 70, 710.Google Scholar
[9]Majorana, A. (1993) Equilibrium solutions of the non-linear Boltzmann equation for an electron gas in a semiconductor. IL Nuovo Cimento B 108 (8), 871–877.Google Scholar
[10]Mascali, G. (2002) Maximum entropy principle in relativistic radiation hydrodynamics II: Compton and double Compton scattering. Contin. Mech. Thermodyn. 14 (6), 549.Google Scholar
[11]Mascali, G. & Romano, V. (2005) Si and GaAs mobility derived from a hydrodynamical model for semiconductors based on the maximum entropy principle. Physica A 352 (2–4), 459.Google Scholar
[12]Mascali, G. & Romano, V. (2010) Hydrodynamic subband model for semiconductors based on the maximum entropy principle. IL Nuovo Cimento C 33 (1), 155–163.Google Scholar
[13]Mascali, G. & Romano, V. (2011) A hydrodynamical model for holes in silicon semiconductors: The case of non-parabolic warped bands. Math. Comp. Modelling 53 (1–2), 213.Google Scholar
[14]Mascali, G., Romano, V. & Sellier, J. M. (2005) MEP parabolic hydrodynamical model for holes in silicon semiconductors. IL Nuovo Cimento B 120 (2), 197.Google Scholar
[15]Mickevicius, R. & Zhao, J. H. (1998) Monte Carlo study of electron transport in SiC. J. Appl. Phys. 83 (6), 3161.Google Scholar
[16]Muscato, O. (2001) The Onsager reciprocity principle as a check of consistency for semiconductor carrier transport models. Physica A 289 (3–4), 422.Google Scholar
[17]Muscato, O. & Di Stefano, V. (2008) Modeling heat generation in a sub-micrometric n+-n-n+ silicon diode. J. Appl. Phys. 104 (12), 124501.Google Scholar
[18]Muscato, O. & Di Stefano, V. (2011) Local equilibrium and off-equilibrium thermoelectric effects in silicon semiconductors. J. Appl. Phys. 110 (9), 093706.Google Scholar
[19]Muscato, O., Pidatella, R. M. & Fischetti, M. V. (1998) Monte Carlo and hydrodynamic simulation of a one dimensional n+-n-n+ silicon diode. VLSI Design 6 (1–4), 247.CrossRefGoogle Scholar
[20]Nilsson, H. E., Hjelm, M., Fröjdh, C., Persson, C., Sannemo, U. & Petersson, C. S. (1999) Full band Monte Carlo simulation of electron transport in 6H-SiC. J. Appl. Phys. 86, 965.Google Scholar
[21]Pennington, G. & Goldsman, N. (2004) Consistent calculations for n-type hexagonal SiC inversion layers. J. Appl. Phys. 95 (8), 4223–4234.Google Scholar
[22]Romano, V. (2000) Non-parabolic band transport in semiconductors: Closure of the production terms in the moment equations. Cont. Mech. Thermodyn. 12, 31.Google Scholar
[23]Tomizawa, K. (1993) Numerical Simulation of Submicron Semiconductor Devices. Artech House, Boston, MA.Google Scholar
[24]von Muench, W. & Pettenpaul, J. (1977) Saturated electron drift velocity in 6H silicon carbide. J. Appl. Phys. 48, 4823.Google Scholar
[25]Zhao, J. H., Gruzinskis, V., Luo, Y., Weiner, M., Pan, M., Shiktorov, P. & Starikov, E. (2000) Monte Carlo simulation of 4H-SiC IMPATT diodes. Semicond. Sci. Technol. 15, 1093.Google Scholar