Particle simulation and asymptotic analysis of kinetic equations for modeling a Schottky diode

Degond, P. ; Poupaud, F. ; Yamnahakki, A.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996), p. 763-795 / Harvested from Numdam

Détail

Publié le : 1996-01-01

MR 1419938 | Zbl 0866.65096

Bibliographie

[1] E. M. Azoff, 1987 Generalized energy moment equation in the relaxation time approximation, Solid Stat. Electr. 30, pp. 913-917.

[2] G. Baccarani and M. R. Wordeman, 1982, An investigation of steady-state velocity overshoot effects in Si and GaAs devices, Solid-State Electron, 29, pp. 970-977.

[3] N. Ben Abdallah, Convergence of the Child Langmuir asymptotics of the Boltzmann equation of semiconductors, SIAM. J. on Math. Anal., to appear. | MR 1373149 | Zbl 0847.35009

[4] N. Ben Abdallah and P. Degond, 1995, The Child-Langmuir for the Boltzmann equation ot semiconductors, SIAM. J. Math. Anal. 26, pp. 364 398. | MR 1320225 | Zbl 0828.35131

[5] N. Ben Abdallah, P. Degond and A. Yamnahakki, 1996. The Child-Langmir low as a model for election transport in semiconductors , Solid State electronics, 39, pp. 737-744.

[6] Birdsall and Langdon, 1985, Plasma Physics via Computer Simulations, McGrawHill, New-York.

[7] J. U. Brackbill and D. W. Forslund, 1982, J. Comput. Phys., 46, p. 271. | MR 672909 | Zbl 0489.76127

[8] A. Brincer and G. Schön, 1988, Extended moment equations for electron transport in semiconducting submicron structures. J. Appl. Phys., 61, pp. 2445-2455.

[9] G. H. Cottet, 1987, Analyse numérique des méthodes particulaires pour certains problèmes non linéaires, Thèse d'état, Université Paris 6.

[10] P. Degond, 1994, The Child-Langmuir law in the kinetic theory of charges particles Part I electron flows in vacuum in Advances in Kinetic Theory and Computing B. Perthame (ed.), World Scientific, Singapore. | MR 1323180 | Zbl 0863.76091

[11] P. Degond, F. Delaurens and F. J. Mustieles, 1991, in Computer Methods in Applied Sciences and Engineering, R. Glowinski and A. Lichnewsky (eds), SIAM, Philadelphia.

[12] P. Degond and F. J. Mustieles, 1991, Solid State Electron, 34, pp. 1335-1345.

[13] P. Degond, B. Niclot and F. Poupaud, 1988, J. Comput. Phys., 78,pp. 313. | Zbl 0662.65126

[14] P. Degond and P.-A. Raviart, 1991, An asymptotic analysis of the one-dimensional Vlasov-Poisson system the Child-Langmuir law, Asymptotic Analysis 4, pp. 187-214. | MR 1115929 | Zbl 0840.35082

[15] P. Degond, S. Jaifard, F. Poupaud and P.-A. Raviart, 1996, The Child-Langmuir asymptotics of the Vlasov-Poisson equation for cylindrically or Spherically symmetric diodes, Part I statement of the problem and basic estimates, Part II Analysis of the reduced problem and determination of the Child Langmuir current. Math. Meth. Appl. Sci. 19, pp. 287-340. | MR 1375208 | Zbl 0844.35087

[16] P Degond, C. Schmeiser and A. Yamnahakki, A mathematical analysis of a multidimensional Shottky diode, Asymptotic Analysis to appear.

[17] F. Delaurens and F. J. Mustieles 1992 A deterministic particle method for solving kinetic transport equations the semiconductor Boltzmann equation case, SIAM. J. Appl. Math. 52, pp. 973-988. | MR 1174041 | Zbl 0755.65132

[18] C. L. Gardner, J. W. Jerome, D. J. Rose 1989, Numerical methods for the hydrodynamic device model: Subsonic flow, ILEE Trans. Comp. Design. 8, pp. 501-507.

[19] C. Greengard and P. A. Raviart 1993 A Boundary value problem for the stationary Vlasov-Poisson equations the plane diode, Comm. Pure. Appl. Math. 43, pp. 473-507. | MR 1047333 | Zbl 0721.35084

[20] F. Guyot-Delaurens, 1990, Ph. D. thesis, Ecole Polytechnique, Palaiseau.

[21] P. Hesto, 1984, Simulation Monte-Carlo du transport non stationnaire dans les dispositifs submicroniques importance du phénomène balistique dans GaAs à 77 K, Ph-D thesis Paris-sud, Orsay.

[22] R. W. Hockney and J. W. Eastwood 1981, Computer Simulation using Particles, McGrawHill, New York. | Zbl 0662.76002

[23] J. W. Jerome and Chi-Wang Shu , Energy Models tor One-Carrier Transport in Semiconductor Devices, Preprint.

[24] S. Mas-Galuc, 1987, Transp. Theory Stat. Physics, 16, pp. 855. | Zbl 0658.76075

[25] P. A. Markowich, 1986 The stationary semiconductor device equations, Springer, Wien, New York. | MR 821965

[26] P. A. Markowich, 1990, C. Ringhofer and C. Schmeiser, Semiconductor equations, Springer, Wien, New York. | MR 1063852 | Zbl 0765.35001

[27] H. Neuzert and J. Wick, 1980, in Mathematical Methods of Plasma Physics, R. Kress and J. Wick (eds), Verlag Peter D. Lang, Frankfurt. | MR 713641 | Zbl 0508.00012

[28] F. Poupaud, 1991, Derivation of a hydrodynamic Systems hierarchy from the Boltzmann equation, Appl. Math. Letters 4, pp. 75-79. | MR 1088041 | Zbl 0733.35102

[29] F. Poupaud 1992, Boundary value problems for the stationary Vlasov-Maxwell System, Forum Math. 4, pp. 499-527. | MR 1176884 | Zbl 0785.35020

[30] A. Yamnahakki 1995, Second order boundary conditions for Drilt Diffusion equations of semi conductor , Math. Mod. Meth. Appl. Sci. 5, pp. 429-455. | MR 1335827 | Zbl 0830.65117

[31] P. A. Raviart, 1985 An Analysis of particle methods in Fluid Dynamics, F. Brezzi ed., L. N. in Math. 1127, Springer-Verlag, Berlin. | MR 802214 | Zbl 0598.76003

[32] L. Reggiani (ed), 1985, Hot electron transport in semiconductors, Springer, Berlin.

[33] S. Selberherr, 1985, Analysis and simulation of semiconductor devices, Springer Berlin, New York.

[34] S. M. Sze, 1981, Physics of semiconductor devices, Wiley, New York, 2nd edition.