Hydrodynamical modeling of charge carrier transport in semiconductors

Meccanica

Volumn 35, Issue 3, 2000, Pages 249-296

  Anile, Angelo Marcello ^a   Romano, Vittorio ^b  

^a UNIVERSITY OF CATANIA   (Italy)

^b UNIVERSITY OF BARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC WAVES; IMPACT IONIZATION; MATHEMATICAL MODELS; MICROELECTROMECHANICAL DEVICES; MONTE CARLO METHODS; OPTOELECTRONIC DEVICES; RELAXATION PROCESSES; SEMICONDUCTING SILICON; THERMODYNAMICS; TRANSPORT PROPERTIES;

AD HOC TREATMENT; CHARGE CARRIER TRANSPORT; ELECTROMAGNETO FLUIDS; ELECTRON MOMENTUM; HOT ELECTRON PROPAGATION; HYDRODYNAMICAL MODELING; STANDARD DRIFT DIFFUSION MODELS;

CHARGE CARRIERS;

EID: 0034468726     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010371810576     Document Type: Article

References (67)

1. Blotekjaer, K., 'Transport equations for electron in two-valley semiconductors', IEEE Trans. Electron Devices ED-17 (1970) 38-47.
2. Baccarani, G. and Wordeman, M. R., 'An investigation on steady-state velocity overshoot in silicon', Solid-State Elect. 29 (1982) 970-977.
3. Rudan, M. and Baccarani, G., 'On the structure and closure condition of the hydrodynamical model', Special Issue VLSI Design 3 (1995) 115-129.
4. Hänsch, W., The Drift-diffusion Equation and its Application in MOSFET Modeling, Springer-Verlag, Wien, 1991.
5. Thoma, R., Edmunds, A., Meinerzhagen, B., Peifer, H.J. and Engl, W., 'Hydrodynamic equations for semiconductors with nonparabolic band structure', IEEE Trans. Electron Devices 38 (1991) 1343-1353.
6. Stettler, M.A., Alam, M.A. and Lundstrom, M.S., 'A critical examination of the assumptions underlying macroscopic transport equations for silicon device', IEEE Trans. Electron Devices 40(4) (1993) 733-739.
7. + device', J. Phys. D: Appl. Phys. 30 (1997) 2343-2353.
8. Lee, S.-C. and Tang, T.-W., 'Transport coefficients for a silicon hydrodynamical model extracted from inhomogeneous Monte-Carlo simulation', Solid-State Elect. 35(4) (1992) 561-569.
9. Tang, T.-W., Ramaswamy, S. and Nam, J., 'An Improved Hydrodynamical Transport Model for Silicon', IEEE Electron Devices 40 (1993) 1469-1477 .
10. Woolard, D.L., Tian, H., Trew, R.J., Littlejohn, M.A. and Kim, W., 'Hydrodynamic electron-transport model: Nonparabolic corrections to the streaming terms', Phys Rev. B 44 (1991) 11119-11132 .
11. Ben Abdallah, N., Degond, P. and Genieys, S., 'An energy-transport model for semiconductors derived from the Boltzmann equation', J. Stat. Phys. 84 (1996) 205-231.
12. Ben Abdallah, N. and Degond, P., 'On a hierarchy of macroscopic models for semiconductors', J. Math. Phys. 37 (1996) 3306-3333.
13. Anile, A.M., Pennisi, S. and Trovato, M., 'Extended thermodynamics of charge transport in semiconductors', In: Donato, A. and Oliveri, F. (eds), Nonlinear Hyperbolic Problems: Theoretical, Applied and Computational Aspects, Notes in numerical fluid mechanics 43, Vieveg, Braunschweig, 1993, pp. 23-32.
14. Anile, A.M. and Pennisi, S., 'Thermodynamic derivation of the hydrodynamical model for charge transport in semiconductors', Phys. Rev. B 46 (1992) 13186-13193.
15. Anile, A.M. and Muscato, O., 'Improved hydrodynamical model for carrier transport in semiconductors', Phys. Rev. B 51 (1995) 16728-16740.
16. Anile, A.M., Romano, V. and G. Russo, 'Hyperbolic hydrodynamical model of carrier transport in semiconductors', VLSI Design 8/1-4 (1998) 521-526.
17. Anile, A.M., Romano, V. and Russo, G., 'Extended hydrodynamical model of carrier transport in semiconductors', SIAM J. Appl. Math. 11 (2000) 74-101.
18. Anile, A.M. and Romano, V., 'Nonparabolic band transport in semiconductors: closure of the moment equations', Cont. Mech. Thermodyn. 11 (1999) 307-325.
19. Romano, V., 'Nonparabolic band transport in semiconductors: closure of the production terms', Cont. Mech. Thermodyn. 12 (2000) 31-51.
20. 2 AS.
21. Müller, I. and Ruggeri, T., Rational Extended Thermodynamics, Springer-Verlag, Berlin, 1998.
22. Jou, D., Casas-Vazquez, J. and Lebon, G., Extended Irreversible Thermodynamics, Springer-Verlag, Berlin, 1993.
23. Ashcroft, N.C. and Mermin, N.D., Solid State Physics, Philadelphia, Holt-Sounders, 1976.
24. Jacoboni, C. and Reggiani, L., 'The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials', Rev. Mod. Phys. 55 (1983) 645-705.
25. Jacoboni, C. and Lugli, P., The Monte Carlo Method for Semiconductor Device Simulation, Springer-Verlag, Wien, New York, 1989.
26. Markowich, A., Ringhofer, C.A. and Schmeiser, C., Semiconductor Equations, Springer-Verlag, Wien, 1990.
27. Grinberg, A.A. and Luryi, S., 'Diffusion in a short base', Solid-State Elect. 35 (1992) 1299-1309.
28. Poupaud, F., 'On a system of nonlinear Boltzmann equations of semiconductor physics', SIAM J. Appl. Math. 50 (1990) 1593-1606.
29. Poupaud, F., 'Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory', Z. Angew. Math. Mech. 72 (1992) 359-372.
30. Majorana, A., 'Space homogeneous solutions of the Boltzmann equation describing electron-phonon interactions in semiconductors', Transp. Theory Stat. Phys. 20 (1991) 261-279.
31. Majorana, A., 'Conservation laws from the Boltzmann equation describing electron-phonon interactions in semiconductors', Transp. Theory Stat. Phys. 22 (1993) 849-859.
32. Majorana, A., 'Equilibrium solutions of the non-linear Boltzmann equation for an electron gas in a semiconductors', Il Nuovo Cimento 108B (1993) 871-877.
33. Levermore, C.D., 'Moment Closure Hierarchies for the Boltzmann-Poisson Equation', VLSI Design 8/1-4 (1995) 97-101 .
34. Romano, V., 'Maximum entropy principle for electron transport in semiconductors', Proc. Int. Conf. WASCOM 99, Vulcano (Eolie Isles) Italy, June 1999.
35. Cercignani, C., The Boltzmann Equation and its Applications, Applied Mathematical Sciences, Vol. 67, Springer-Verlag, Berlin, 1988.
36. Selberherr, S., Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Wien, New York, 1984.
37. Jerome, J.W., Analysis of Charge Transport, Springer, Berlin, 1996.
38. Wachutka, G., 'Unified framework for thermal electrical, magnetic and optical semiconductor devices modeling', COMPEL 10 (1991) 311-321.
39. de Groot, S.R. and Mazur, P., Non Equilibrium Thermodynamics, Dover Publications, New York, 1985.
40. Anile, A.M. and Pennisi, S., 'Extended thermodynamics of the Blotekjaer hydrodynamical model for semiconductors', Cont. Mech. Thermodyn. 4 (1992) 187-197.
41. Gardner, C.L., Jerome, J.W. and Rose, D.J., 'Numerical methods for hydrodynamic device model: subsonic flow', IEEE Trans. CAD 8 (1989) 501-507.
42. Gardner, C.L., 'Numerical simulation of a steady-state electron shock wave in a sub-micrometer semiconductor device', IEEE Transaction Electron Devices 38 (1991) 392-398.
43. + diode', IEEE Trans. Electron Devices ED-40 (1993) 455-457.
44. + device by a hydrodynamic model: subsonic and supersonic flow', COMPEL 14 (1995) 1-18.
45. Fatemi, E., Jerome, J. and Osher, S., 'Solution of hydrodynamic device model using high-order non-oscillatory shock capturing algorithms', IEEE Transaction Computer-Aided Design 10 (1991) 232-244.
46. 3 AS 10 (2000) 1033-1024.
47. Levermore, C.D., 'Moment closure hierarchies for kinetic theories', J. Stat. Phys 83 (1996) 331-407.
48. Dreyer, W., 'Maximization of the entropy in non-equilibrium', J. Phys. A: Math. Gen. 20 (1987) 6505-6517.
49. Berger, M. and Berger, M., Perspectives in Nonlinearity, W. A. Benjamin, New York, 1968.
50. Boillat, G. and Ruggeri, T., 'Hyperbolic principal subsystems: entropy, convexity and subcharacteristic conditions', Arch. Rational Mech. Anal. 137 (1997).
51. Jeffrey, A., Quasi-linear Hyperbolic Systems and Waves, Research Notes in Mathematics, Pitman, S. Francisco, 1976.
52. Fisher, A. and Marsden, D.P., 'The Einstein evolution equations as a first order quasi-linear symmetric hyperbolic system', Comm. Mathematical Physics 28 (1972) 1-38.
53. Anile, A.M. and Muscato, O., 'Extended thermodynamics tested beyond the linear regime: the case of electron transport in silicon semiconductors', Cont. Mech. Thermodyn. 8 (1996) 131-142.
54. Pennisi, S. and Trovato, M., 'Field equations for charge conducting fluids in electromagnetic fields', Cont. Mech. Thermodyn. 7 (1995) 489-520.
55. Anile, A.M. and Trovato, M., 'Nonlinear closures for hydrodynamical semiconductor transport models', Physics Letters A 230 (1997) 387-395.
56. Liu, I-S. and Müller, I., 'Extended thermodynamics of classical and degenerate ideal gases', Arch. Rational Mech. Anal. 83 (1983) 285-332.
57. Au, J.D., 'Nonlinear closure in molecolar extended thermodynamics with application to the shock wave structure', Supplemento ai Rendiconti del Circolo Matematico di Palermo vol. 45: In: Greco, A. and Rionero, S. (eds), Proc. Int. Conf. Wave and Stability, 1996, pp. 59-67.
58. LeVeque, R., Numerical Methods for Conservation Laws, Birkhäuser, Basel, 1990.
59. Toro, E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics, Berlin, Springer, 1997.
60. Harten, A. and Osher, S., 'Uniformly high-order accurate non-oscillatory schemes', SIAM J. Numer. Anal. 24(2) (1987) 279-309.
61. Nessyahu, H. and Tadmor, E., 'Non-oscillatory central differencing for hyperbolic conservation laws', J. Comput. Phys. 87(2) (1990) 408-463.
62. Liotta, F., Romano, V. and Russo, G., 'Central scheme for systems of balance laws', Int. Series of Numer. Math. 130 (1999) 651-660.
63. 3AS 10 (2000) 833-861.
64. Anile, A.M., Nikiforakis, N. and Pidatella, R.M., 'Assessment of a high resolution centered scheme for the solutions of hydrodynamical semiconductor equations', preprint, (to appear in SIAM J. Scient. Comp. (1999)).
65. Anile, A.M., Nikiforakis, N. and Pidatella, R.M., 'FLIC scheme for the numerical solution of semiconductor transport equations', preprint, In: EQUADIFF99, Wold Scientific, (1999).
66. Caflisch, R.E., Russo, G. and Jin, S., 'Uniformly accurate schemes for hyperbolic system with relaxation', SIAM J. Numer. Anal. 34(1) (1997) 246-281.
67. Tomizawa, K., Numerical Simulation of Sub-micron Semiconductor Devices, Artech House, Boston, 1993.