Abstract
A mixed finite element scheme is used to simulate a consistent energy-transport model for electron transport in semiconductor devices, free of any fitting parameters, formulated on the basis of the maximum entropy principle.
Simulations of silicon n+-n-n+ diodes, 2D-MESFET and 2D-MOSFET and comparisons with the results obtained with Monte Carlo direct simulation and with other energy-transport models, known in literature, show the validity of the model and the robustness of the numerical scheme.
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References
A. Schenk, Advanced Physical Models for Silicon Device Simulation (Springer, Wien, New York)
A.M. Anile and V. Romano, “Non parabolic band transport in semiconductors: Closure of themoment equations,” Continuum Mech. Thermodyn. 11, 307 (1999) Springer-Verlag.
V. Romano, “Non parabolic band transport in semiconductors: Closure of theproduction terms in the moment equations,” Continuum Mech. Thermodyn. 12, 31 (2000) Springer-Verlag.
V. Romano, “Non-parabolic band hydrodynamical model for silicon semiconductorsand simulation of electron devices,” Math. Meth. Appl. Sci. 24, 439 (2001),John Wiley and Sons, Ltd.
V. Romano, “2D simulation of a silicon MESFET witha nonparabolic hydrodynamical model based on the maximum entropyprinciple,” J. Comp. Phys. 176, 70 (2002).
P.A. Raviart and J.M. Thomas, “A mixed finite element method for 2nd orderelliptic problems,” In Mathematical Aspecys of Finite Elementmethods, edited by I. Galligani and E. Magenes, Lecture Notes 606 (Springer-Verlag, 1977), pp. 292.
Marr A. Marrocco and Ph. Montarnal, “Simulation des modèles energy-transport à'aide des éléments finis mixtes,” C.R. Acad. Sci. Paris, 323, series I, 535, 1996.
Ph. Montarnal, “Modèles de transport d'ènergie des semi-conducteurs,ètudes asymptotiques et rèsolution par èlèments finis mixtes,” Thèse de doctorat,Universitè Paris VI(Oct. 1997).
N. Ben Abdallah, P. Degond, and S. Genieys, “Anenergy-transport model for semiconductors derived from the Boltzmannequation,” J. Stat. Phys., 84, 205 (1996).
N. Ben Abdallah and P. Degond, “On a hierarchy ofmacroscopic models for semiconductors,” J. Math. Phys. 37, 3306 (1996).
R. Stratton, “Diffusion of hot and cold electrons insemiconductor barriers,” Phys. Rev. 126, 2002 (1962).
D. Chen, E.C. Kan, U. Ravaioli, C.-W. Shu, and R. Dutton,“An improved energy-transport model including nonparabolicity andnon-maxwelliandistribution effects,” IEEE on Electron Device Letters 13, 26 (1992).
E. Lyumkis, B. Polsky, A. Shir, and P. Visocky, “Transientsemiconductor device simulation including energy balance equation,” Compel 11, 311 (1992).
S. Selberherr, Analysis and Simulation of Semiconductor Devices (Wien, New York, Springer-Verlag, 1984).
K. Blotekjaer, “Transport equations forelectron in two-valley semiconductors,” IEEE Trans. on Electron Devices 17, 38 (1970).
G. Baccarani and M.R.Wordeman, “An investigation on steady-state velocity overshootin silicon,” Solid-state Electronics, 29, 970 (1982).
I. Müller and T. Ruggeri, Rational Extended Thermodynamics (Springer, New York, 1998).
D. Jou, J. Casas-Vazquez and G. Lebon, Extended Irreversible Thermodynamics, (Springer-Verlag, Berlin, 1993).
A.M. Anile, G. Mascali, and V. Romano, “Recent developments in hydrodynamical modelingof semiconductors,” in Mathematical Problems in Semiconductor Physics, 1, 54 (2003) Lecture Notes in Mathematics, Springer, (2003), vol. 1832.
S.R. de Groot and P. Mazur, Non Equilibrium Thermodynamics (Dover Publications Inc., New York, 1985).
G. Mascali and V. Romano, “Si and Ga As mobility derived fromthe hydrodynamic model of semiconductors based on the maximum entropy principle,” Physica A 352, 459 (2005).
Bre F. Brezzi and M. Fortin, “Mixed and Hybrid Finite Element Methods.Springer Series in Computational Mathematics 15,” Springer-Verlag, (1991).
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics, (SIAM, Studies in Applied Mathematics, Philadelphia, 1989).
Ch. Faure and Y. Papegay. Odyssèe user's guide, version 1.7. Rap. Tech., R.T.0224., (Sept. 1998).
GNU/Archimedes-website: http://www.gnu.org/software/archimedes
J.W. Jerome and C.-W. Shu, “Energy models for one-carrier transportin semiconductor devices,” in Semiconductors Part II, The IMA Volumes in Mathematics and its Applications, edited by N.M. Coughran,J. Cole, P. Lloyd, J. K. White (1994), pp. 185.
C. Jacoboni and L. Reggiani, “The Monte Carlo method forthe solution of charge transport in semiconductors withapplication to covalent materials,” Rev. Mod. Physics, 55, 645 (1983).
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Anile, A.M., Marrocco, A., Romano, V. et al. 2D Numerical Simulation of the MEP Energy-Transport Model with a Mixed Finite Elements Scheme. J Comput Electron 4, 231–259 (2005). https://doi.org/10.1007/s10825-005-5039-y
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DOI: https://doi.org/10.1007/s10825-005-5039-y