A hybrid kinetic-quantum model for stationary electron transport

Journal of Statistical Physics

Volumn 90, Issue 3-4, 1998, Pages 627-662

  Ben Abdallah, Naoufel ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Boltzmann; Interface condition; Reflection transmission coefficients; Schr dinger; Semiclassical limit; Wigner transform

Indexed keywords

EID: 0032002061     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023216701688     Document Type: Article

References (42)

1. P. N. Argyres, Quantum Kinetic equations for electrons in high electric and phonon fields, Phys. Lett. A. 171:373-379 (1992).
2. A. M. Anile and O. Muscato, Extended thermodynamics tested beyond the linear regime: The case of electron transport in silicon semiconductors, Contin. Mech. Thermodyn. 8(3):131-142 (1996).
3. A. Arnold, Numerically Absorbing Boundary Conditions for Quantum Involution Equations, to appear 1996.
4. N. Ben Abdallah, On a multi-dimensional Schrödinger Poisson Scattering model for semiconductors, submitted.
5. N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, Journal of Mathematical Physics 37(7):3306-3333 (1996).
6. N. Ben Abdallah, P. Degond, and S. Génieys, An Energy-transport model derived from the Boltzmann equation of semiconductors, J. Stat. Phys. 84:1-2, 205-231 (1996).
7. N. Ben Abdallah, P. Degond and P. A. Markowich, On a one-dimensional Schrödinger Poisson Scattering model, ZAMP 48:135-155 (1997).
8. N. Ben Abdallah, P. Degond, and P. A. Markowich, The Quantum Child Langmuir Problem, Nonlinear Analysis TMA 31(5-6):629-648 (1998).
9. F. Brezzi and P. A. Markowich, A mathematical analysis of quantum transport in three dimensional crystals, Anna. di Matematica Pura Applicata 160:171-191 (1991).
10. R. Brunetti, C. Jacoboni and F. Rossi, Quantum Theory of Transient Transport in Semiconductors: A Monte Carlo Approach, Phys. Rev. B 39(15):10781-10790 (1989).
11. F. Chevoir, Effet tunnel résonant assisté par diffusion dans les diodes double-barrière, PHD thesis, (Univ. Orsay 1992).
12. F. Chevoir and B. Vinter, Scattering-assisted tunneling in double-barrier diodes: scattering rates and valley current, Phys. Rev B. 47(12):7260-7274 (1993).
13. P. Degond and P. A. Markowich, A quantum transport model for semiconductors: The Wigner Poisson model on a bounded Brillouin zone, M2AN 24:697-710 (1990).
14. P. Degond and C. Schmeiser, Kinetic boundary layers and fluid-kinetic coupling in semi-conductors, in preparation.
15. P. Degond and C. Schmeiser, Macroscopic models for semiconductor heterostructures, in preparation.
16. L. Di Menza, Transparent and Absorbing Boundary Conditions for the Schrödinger Equation in a Bounded Domain, Internal report, (Univ. Bordeaux 1, 1995).
17. W. R. Frensley, Boundary conditions for open quantum systems driven far from equilibrium, Reviews of Modern Physics 62(3):745-791 (1990).
18. W. R. Frensley, Wigner-function model of a resonant-tunneling semiconductor device, Phys. Rev. B. 36(3):1570-1580 (1987).
19. P. Gérard, Mesures semiclassiques et ondes de bloch, Seḿ. Ecole Polytechnique XVI: 1-19 (1990-1991).
20. P. Gérard, P. A. Markowich, N. J. Mauser, and F. Poupaud, Homogenization Limits and Wigner Transforms, submitted, 1996.
21. C. Greengard and P. A. Raviart, A boundary value problem for the stationary Vlasov Poisson equations: The plane diode, Comm. Pure Appl. Math. 43:473-507 (1990).
22. J. R. Hellums and W. R. Frensley, Non-Markovian open-system boundary conditions for the time-dependent Schrödinger equation, Phys. Rev. B. 49:2904-2906 (1994).
23. A. Klar, Asymptotic induced domain decomposition methods for kinetid and drift-diffusion semiconductor equation, preprint Univ. Kaiserslautern.
24. N. C. Kluksdahl, A. M. Kriman, D.K. Ferry, and C. Ringhofer, Self-consistent study of the resonant tunneling diode, Phys. Rev. B. 39(11):7720-7735 (1989).
25. C. Lent and D. Kirkner, The Quantum Transmitting Boundary Method, J. Appl. Phys. 67(10):6353-6359 (1990).
26. P. L. Lions and T. Paul, Sur les mesures de Wigner, Revista Mathematica Iberoamericana 9:553-618 (1993).
27. P. A. Markowich and N. J. Mauser, The classical limit of a selfconsistent quantum-Vlasov equation in 3-D, Math. Meth. Mod. 16(6):409-442 (1993).
28. P. A. Markowich, N. J. Mauser and F. Poupaud, A Wigner function approach to semi-classical limits: electrons in a periodic potential, J. Math. Phys. 35:1066-1094 (1994).
29. A. Messiah, Mécanique Quantique, Tome 1, 2, (Dunod, Paris, 1995).
30. P. Mounaix, O. Vanbésien and D. Lippens, Effect of cathode space layer on the current-voltage characteristics of resonant tunneling diodes, Appl. Phys. Lett. 57:8, 1517-1519 (1990).
31. F. Nier, A stationary Schrödinger Poisson system arising from the modeling of electronic devices, 2(5):489-510 (1990).
32. F. Nier, A variational formulation of Schrödinger-Poisson systems in dimension d ≤ 3, Comm. Part. Diff. Equations 18(7-8):1125-1147 (1993).
33. A. Nouri and F. Poupaud, Stationary solutions of boundary value problems for Maxwell Boltzmann system modeling degenerate semiconductors, SIAM J. Math. Anal. 26(5): 1143-1156 (1995).
34. O. Vanbésien and D. Lippens, Theoretical analysis of a branch line quantum directional coupler, Appl. Phys. Lett. 65(19):2439-2441 (1994).
35. F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system, Forum Mathematicum 4:499-527 (1992).
36. F. Poupaud, Diffusion approximation of the linear semiconductor equation: analysis of boundary layers, Asymp. Anal. 4:293-317 (1991).
37. K. Poupaud and C. Ringhofer, Quantum hydrodynamic models in a crystal, Appl. Math. Lett. 8(6):55-59 (1995).
38. C. Ringhofer, D. K. Ferry, and N. C. Kluksdahl, Absorbing boundary conditions for the simulation of quantum transport phenomena, Trans. Theo. Stat. Phys. 18:331-346 (1989).
39. C. Schmeiser and A. Zwirchmayr, Elastic and drift-diffusion limits of electron phonon interaction in semiconductors, M3AS to appear.
40. R. Stratton, Diffusion of hot and cold electrons in semiconductor barriers, Phys. Rev. 126:2002-2014 (1962).
41. D. Ventura, A. Gnudi, G. Baccarani, and F. Odeh, Multidimensional spherical harmonics expansion of Boltzmann equation for transport in semiconductors, Appl. Math. Lett. 5:85-90 (1992).
42. E. P. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40:749-759 (1932).