Asymptotic analysis of a semiconductor model based on fermi-dirac statistics

Mathematical Methods in the Applied Sciences

Volumn 19, Issue 5, 1996, Pages 401-424

  Jüngel, Ansgar ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CARRIER CONCENTRATION; CHARGE CARRIERS; CURRENT DENSITY; CURRENT VOLTAGE CHARACTERISTICS; ELECTRON TRANSPORT PROPERTIES; ERROR ANALYSIS; HYDRODYNAMICS; MATHEMATICAL MODELS; POLYNOMIALS; SEMICONDUCTOR DIODES; STATISTICAL METHODS;

BOLTZMANN STATISTICS; DRIFT DIFFUSION MODEL; FERMI DIRAC STATISTICS; NONLINEAR DIFFUSION; THRESHOLD VOLTAGE;

SEMICONDUCTOR DEVICE MODELS;

EID: 0030107756     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19960325)19:5<401::AID-MMA795>3.0.CO;2-L     Document Type: Article

References (23)

1. Baiocchi, C. and Capelo, A., Variational and Quasivariational Inequalities, Wiley, Chichester, 1984.
2. Blakemore, J., Semiconductor Statistics. Pergamon Press, Oxford, 1962.
3. Bonč-Bruevič, V. and Kalashnikov, S., Halbleiterphysik. VEB Verlag der Wissenschaften, Berlin, 1982.
4. Courant, R. and Friedrichs, K. O., Supersonic Flow and Shock Waves, Interscience, New York, 1967.
5. Gajewski, H., 'On the uniqueness of solutions to the drift-diffusion model of semiconductor devices', Math. Models Meth. Appl. Sci., 4, 121-133 (1994).
6. Gajewski, H. and Gröger, K., 'Semiconductor equations for variable mobilities based on Boltzmann statistics or Fermi-Dirac statistics', Math. Nachr., 140, 7-36 (1989).
7. Golse, F. and Poupaud, F., 'Limite fluide des équations de Boltzmann des semiconducteurs pour une statistique de Fermi-Dirac', Ph.D. Thesis, Université de Paris 6, Paris, France, 1988.
8. Jungel, A., 'A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modelling', Preprint Nr. 400, Fachbereich Mathematik, TU Berlin, Germany Math. Nachr. (to appear).
9. Jüngel, A., 'On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors', Math. Models Meth. Appl. Sci., 4, 677-703 (1994).
10. Jüngel, A., 'Numerical approximation of a drift-diffusion model for semiconductor with nonlinear diffusion', ZAMM 95, 783-799 (1995).
11. Jüngel, A., 'Qualitative behviour of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors', Math. Models Meth. Appl. Sci. 5, 497-518 (1995).
12. Jüngel, A. and Schmeiser, C., 'Voltage-current characteristics of a pn-diode from a drift-diffusion model with nonlinear diffusion'. Preprint Nr. 418, Fachbereich Mathematik, TU Berlin, Germany, 1994. Quart. Appl. Math. (to appear).
13. Markowich, P. A., Ringhofer, C. A. and Schmeiser, C., Semiconductor Equations, Springer, Berlin, 1990.
14. Mock, M., 'Transport equations in heavily doped silicon, and the current gain of a bipolar transistor', Solid-State Electr., 16, 1251-1259 (1973).
15. Nakagawa, A., 'One-dimensional device model of the npn bipolar transistor including heavy doping effects under Fermi statistics', Solid State Electr., 22, 943-949 (1979).
16. Van Overstraeten, R., Deman, H. and Mertens, R., 'Transport equations in heavy doped silicon', IEEE Trans. Electr. Devices, ED-20, 290-298 (1973).
17. Paul, R., Halbleiterphysik, Hüthig-Verlag, Heidelberg, 1975.
18. Polsky, B. and Rimshans, J., 'Two-dimensional numerical simulation of bipolar semiconductor devices taking into account heavy doping effects and Fermi statistics', Solid-State Electr., 26, 275-279 (1983).
19. Poupaud, F. and Schmeiser, C., 'Charge transport in semiconductors with degeneracy effects', Math. Meth. in the Appl. Sci., 14, 301-318 (1991).
20. Sah, C., Noyce, R. and Shockley, W., 'Carrier generation and recombination in p-n junctions and p-n junction characteristics', Proc. IRE, 45, 1228-1242 (1957).
21. Sze, S., Physics of Semiconductor Devices, Wiley, New York, 1981.
22. Troianiello, G. M., Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987.
23. Viallet, J. and Mottet, S., 'Transient simulation of heterostructure', in: NASECODE IV Conf., Dublin, (J. Miller, ed.), Boole Press, 1985.