Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-poisson model

SIAM Journal on Applied Mathematics

Volumn 66, Issue 2, 2006, Pages 554-572

  El Ayyadi, Asma ^a   Jüngel, Ansgar ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Finite differences; Hysteresis; Quantum drift diffusion model; Quantum microscopic macroscopic coupling; Resonant tunneling diode; Schr dinger Poisson system

Indexed keywords

BALLISTICS; CARRIER CONCENTRATION; COMPUTER SIMULATION; CURRENT DENSITY; DIFFUSION; HYSTERESIS; QUANTUM THEORY; TUNNEL DIODES;

DRIFT-DIFFUSION MODEL; FINITE DIFFERENCES; QUANTUM MICROSCOPIC-MACROSCOPIC COUPLING; QUANTUM MOMENT METHOD; RESONANT TUNNELING DIODE; SCHRÖDINGER-POISSON SYSTEM; STATIONARY RESONANT TUNNELING SIMULATIONS;

SEMICONDUCTOR DEVICES;

EID: 33645770437     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040610805     Document Type: Article

References (28)

1. M. ANCONA AND G. IAFRATE, Quantum correction to the equation of state of an electron gas in a semiconductor, Phys. Rev. B, 39 (1989), pp. 9536-9540.
2. M. BARO, N. BEN ABDALLAH, P. DEGOND, AND A. EL AYYADI, A 1D coupled Schrödinger drift-diffusion model including collisions, J. Comput. Phys., 203 (2005), pp. 129-153.
3. M. BARO, H.-C. KAISER, H. NEIDHARDT, AND J. REHBERG, A quantum transmitting Schrödinger-Poisson system. Rev. Math. Phys., 16 (2004), pp. 281-330.
4. N. BEN ABDALLAH, A hybrid kinetic-quantum model for stationary electron transport in a resonant tunneling diode, J. Statist. Phys., 90 (1998), pp. 627-662.
5. N. BEN ABDALLAH, P. DEGOND, AND I. GAMBA, Coupling one-dimensional time-dependent classical and quantum transport models, J. Math. Phys., 43 (2002), pp. 1-24.
6. N. BEN ABDALLAH, F. MÉHATS, AND N. VAUCHELET, Analysis of a drift-diffusion-Schrödinger-Poisson model. C. R. Acad. Sci. Paris Ser. I, 335 (2002), pp. 1007-1012.
7. N. BEN ABDALLAH, O. PINAUD, C. GARDNER, AND C. RINGHOFER, A comparison of resonant tunneling based on Schrödinger's equation and quantum hydrodynamics, VLSI Design, 15 (2002), pp. 695-700.
8. B. BIEGEL, Simulation of Ultra-Small Electronic Devices: The Classical-Quantum Transition Regime, Technical Report 97-028, NASA, 1997.
9. Z. CHEN, B. COCKBURN, C. GARDNER, AND J. JEROME, Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode, J. Comput. Phys., 117 (1995), pp. 274-280.
10. P. DEGOND AND A. EL AYYADI, A coupled drift-diffusion model for quantum semiconductor device simulations, J. Comput. Phys., 181 (2002), pp. 222-259.
11. P. DEGOND, F. MÉHATS, AND C. RINGHOFER, Quantum energy-transport and drift-diffusion models, J. Statist. Phys., 118 (2005), pp. 625-665.
12. P. DEGOND, F. MÉHATS, AND C. RINGHOFER, Quantum hydrodynamic models derived from the entropy principle, Contemp. Math., 371 (2005), pp. 107-131.
13. P. DEGOND AND C. RINGHOFER, Quantum moment hydrodynamics and the entropy principle, J. Statist. Phys., 112 (2003), pp. 587-628.
14. C. DE FALCO, E. GATTI, A. LACAITA, AND R. SACCO, Quantum-corrected drift-diffusion model for transport in semiconductor devices, J. Comput. Phys., 204 (2005), pp. 533-561.
15. D. FERRY AND J.-R. ZHOU, Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling, Phys. Rev. B, 48 (1993) pp. 7944-7950.
16. W. FRENSLEY, Boundary conditions for open quantum systems driven far from equilibrium, Rev. Modern Phys., 62 (1990), pp. 745-791.
17. W. FRENSLEY AND N. EINSPRUCH, (eds.), Heterostructures and quantum devices, in VLSI Electronics: Microstructure Science, Academic Press, San Diego, 1994.
18. C. GARDNER, The quantum hydrodynamic model for semiconductor devices, SIAM J. Appl. Math., 54 (1994), pp. 409-427.
19. K. GULLAPALLI, D. MILLER, AND D. NEILIRK, Simulation of quantum transport in memory-switching double-barrier quantum-well diodes, Phys. Rev. B, 49 (1994), pp. 2622-2628.
20. J. HÖNTSCHEL, W. KLIX, AND R. STENZEL, Investigation of Quantum Transport Phenomena in Resonant Tunneling Structures by Simulations with a Novel Quantum Hydrodynamic Transport Model, IoP Conf. Ser. 174 (2002), pp. 255-258.
21. A. JÜNGEL, Quasi-Hydrodynamic Semiconductor Equations, Birkhäuser, Basel, 2001.
22. A. JÜNGEL AND R. PINNAU, A positivity-preserving numerical scheme for a nonlinear fourth-order parabolic equation, SIAM J. Numer. Anal., 39 (2001), pp. 385-406.
23. N. KLUKSDAHL, A. KRIMAN, D. FERRY, AND C. RINGHOFER, Self-consistent study of the resonant-tunneling diode, Phys. Rev. B, 39 (1989), pp. 7720-7735.
24. C. LENT AND D. KIRKNER, The quantum transmitting boundary method, J. Appl. Phys., 67 (1990), pp. 6353-6359.
25. M. LUNDSTROM, Fundamentals of Carrier Transport, 2nd ed., Cambridge University Press, Cambridge, UK, 2000.
26. O. PINAUD, Transient simulations of a resonant tuneling diode, J. Appl. Phys., 92 (2002), pp,. 1987-1994.
27. T. WAHO, Resonant tunneling diode and its application to multi-GHz analog-to-digital converters, Proceedings of Quantum Nanoelectronics for Meme-Media-Based Information Technologies, Sapporo, Japan, 2003, pp. 53-58.
28. A. WETTSTEIN, Quantum Effects in MOS Devices, Ph.D. thesis, ETH, Zürich, 2000.