An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes

Journal of Computational Physics

Volumn 221, Issue 1, 2007, Pages 226-249

  Degond, Pierre ^a   Gallego, Samy ^a   Méhats, Florian ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

Current voltage characteristics; Density gradient; Density matrix; Entropic quantum drift diffusion; Quantum Liouville; Resonant tunneling diode; Schr dinger Poisson drift diffusion

Indexed keywords

DIFFUSION; ELECTRON TRANSPORT PROPERTIES; FINITE DIFFERENCE METHOD; POISSON EQUATION; QUANTUM CHEMISTRY; RESONANT TUNNELING; RESONANT TUNNELING DIODES;

CURRENT-VOLTAGE CHARACTERISTICS; DENSITY GRADIENTS; DENSITY MATRIX; DRIFT DIFFUSION; ENTROPIC QUANTUM DRIFT-DIFFUSION; LIOUVILLE; QUANTUM DRIFT DIFFUSION; QUANTUM LIOUVILLE; RESONANT-TUNNELING DIODES; SCHRÖDINGE-POISSON DRIFT-DIFFUSION;

CURRENT VOLTAGE CHARACTERISTICS;

EID: 33846177213     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.06.027     Document Type: Article

References (41)

1. Ben Abdallah N., Degond P., and Markowich P.A. On a one-dimensional Schrödinger-Poisson scattering model. Z. Angew. Math. Phys. 48 (1997) 135-155
2. Ben Abdallah N., and Unterreiter A. On the stationary quantum drift-diffusion model. Z. Angew. Math. Phys. 49 2 (1998) 251-275
3. Ben Abdallah N. A hybrid kinetic-quantum model for stationary electron transport in a resonant tunneling diode. J. Stat. Phys. 90 (1998) 627-662
4. Ben Abdallah N. On a multidimensional Schrödinger-Poisson scattering model for semiconductors. J. Math. Phys. 41 (2000) 4241-4261
5. Ancona M.G., and Iafrate G.J. Quantum correction of the equation of state of an electron gas in a semiconductor. Phys. Rev. B 39 (1989) 9536-9540
6. Ancona M.G., and Tiersten H.F. Macroscopic physics of the silicon inversion layer. Phys. Rev. B 39 (1987) 7959-7965
7. Arnold A., and Nier F. The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Math. Methods Appl. Sci. 14 9 (1991) 595-613
8. Arnold A. Mathematical concepts of open boundary conditions. Phys. Lett. 30 (2001) 561-584
9. Baro M., Ben Abdallah N., Degond P., and El Ayyadi A. A 1D coupled Schrödinger drift-diffusion model including collisions. J. Comput. Phys. 203 (2005) 129-153
10. Chang L.L., Esaki L., and Tsu R. Resonant tunneling in semiconductor double barriers. Appl. Phys. Lett. 24 (1974) 593-595
11. Chen R.-C., and Liu J.-L. A quantum corrected energy-transport model for nanoscale semiconductor devices. J. Comput. Phys. 204 (2005) 131-156
12. Degond P., and El Ayyadi A. A coupled Schrödinger drift-diffusion model for quantum semiconductor devices. J. Comput. Phys. 181 (2002) 222-259
13. Degond P., Méhats F., and Ringhofer C. Quantum energy-transport and drift-diffusion models. J. Stat. Phys. 118 3/4 (2005)
14. Degond P., Méhats F., and Ringhofer C. Quantum hydrodynamic models derived from the entropy principle. Contemp. Math. 371 (2005)
15. Degond P., and Ringhofer C. Binary quantum collision operators conserving mass momentum and energy. C.R. Acad. Sci. Paris, I 336 9 (2003) 785-790
16. Degond P., and Ringhofer C. Quantum moment hydrodynamics and the entropy principle. J. Stat. Phys. 112 314 (2003) 587-628
17. de Falco C., Gatti E., Lacaita A.L., and Sacco R. Quantum-corrected drift-diffusion models for transport in semiconductor devices. J. Comput. Phys. 204 2 (2005) 533-561
18. Gallego S., and Méhats F. Numerical approximation of a quantum drift-diffusion model. C.R. Acad. Sci. Paris, Ser. I 339 (2004) 519-524
19. Gallego S., and Méhats F. Entropic discretization of a quantum drift-diffusion model. SIAM J. Numer. Anal. 43 5 (2005) 1828-1849
20. Gardner C., and Ringhofer C. The smooth quantum potential for the hydrodynamic model. Phys. Rev. E 53 (1996) 157-167
21. Gardner C., and Ringhofer C. The Chapman-Enskog expansion and the quantum hydrodynamic model for semiconductor devices. VLSI Des. 10 (2000) 415-435
22. Gardner C. The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math. 54 2 (1994) 409-427
23. Gasser I., and Jnngel A. The quantum hydrodynamic model for semiconductors in thermal equilibrium. Z. Angew. Math. Phys. 48 1 (1997) 45-59
24. Gasser I., Markowich P.A., and Ringhofer C. Closure conditions for classical and quantum moment hierarchies in the small temperature limit. Transp. Theory Stat. Phys. 25 3-5 (1996) 409-423
25. Gasser I., and Markowich P.A. Quantum hydrodynamics, Wigner transforms and the classical limit. Asympt. Anal. 14 2 (1997) 97-116
26. Jnngel A., and El Ayyadi A. Semiconductor simulations using a coupled quantum drift-diffusion Schrödinger-Poisson model. SIAM J. Appl. Math. 66 2 (2005) 554-572
27. Jnngel A., and Pinnau R. A positivity preserving numerical scheme for a fourth order parabolic equation. SIAM J. Numer. Anal. 39 2 (2001) 385-406
28. Jnngel A. Quasi-hydrodynamic semiconductor equations. Progress in Nonlinear Differential Equations (2001), Birkhuser
29. Kluksdahl N.C., Kriman A.M., Ferry D.K., and Ringhofer C. Self-consistent study of the resonant-tunneling diode. Phys. Rev. B 39 (1989) 7720-7735
30. Lent C.S., and Kirkner D.J. The quantum transmitting boundary method. J. Appl. Phys. 67 (1990) 6353-6359
31. Levermore C.D. Moment closure hierarchies for kinetic theories. J. Stat. Phys 83 (1996) 1021-1065
32. Markowich P.A., Ringhofer C., and Schmeiser C. Semiconductor Equations (1990), Springer, Berlin
33. Micheletti S., Sacco R., and Simioni P. Numerical simulation of resonant tunnelling diodes with a quantum-drift-diffusion model. Scientific Computing in Electrical Engineering. Lecture Notes in Computer Science (2004), Springer, Berlin pp. 313-321
34. Mounaix P., VanbTsien O., and Lippens D. Effect of cathode spacer layer on the current voltage characteristics of resonant tunneling diodes. Appl. Phys. Lett. 2 5 (1990) 489-510
35. Nier F. A stationary Schrödinger-Poisson system arising from the modelling of electronic devices. Forum Math. 2 5 (1990) 489-510
36. Nier F. A variational formulation of Schrödinger-Poisson systems in dimension d ≤ 3. Comm. Partial Different. Equat. 18 7-8 (1993) 1125-1147
37. Pinaud O. Transient simulations of a resonant tunneling diode. J. Appl. Phys. 92 4 (2002) 1987-1994
38. Pirovano A., Lacaita A., and Spinelli A. Two-dimensional quantum effects in nanoscale MOSFETs. IEEE Trans. Electron Dev. 47 (2002) 25-31
39. Polizzi E., and Ben Abdallah N. Self-consistent three dimensional models for quantum ballistic transport in open systems. Phys. Rev. B 66 (2002)
40. Teufel S. Adiabatic Perturbation Theory in Quantum Dynamics (2003), Springer, Berlin
41. Unterreiter A., and Pinnau R. The stationary current-voltage characteristics of the quantum drift-diffusion model. SIAM J. Numer. Anal. 37 1 (1999) 211-245