Multiscale simulation of transport in an open quantum system: Resonances and WKB interpolation

Journal of Computational Physics

Volumn 213, Issue 1, 2006, Pages 288-310

  Abdallah, Naoufel Ben ^a   Pinaud, Olivier ^a  

^a CNRS   (France)

Author keywords

Numerical scheme; Resonant states; Resonant tunneling diode; Schr dinger equation; WKB approximation

Indexed keywords

INTERPOLATION; QUANTUM CHEMISTRY; QUANTUM OPTICS; RESONANT TUNNELING;

MULTI-SCALE SIMULATION; NUMERICAL SCHEME; ONE-DIMENSIONAL; OPEN QUANTUM SYSTEMS; POISSON MODEL; RESONANT STATE; RESONANT-TUNNELING DIODES; SCHRÖDINGE EQUATION; SYSTEM RESONANCES; WKB APPROXIMATIONS;

RESONANT TUNNELING DIODES;

EID: 31744433581     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.08.012     Document Type: Article

References (45)

1. Y. Ando T. Itoh Calculation of transmission tunneling current across arbitrary potential barriers J. Appl. Phys. 61 4 1986 1479-1502
2. T. Abboud J.-C. Nédélec B. Zhou Improvement of the integral equation method for high frequency problems Mathematical and Numerical Aspects of Wave Propagation 1995 SIAM Philadelphia pp. 178-187
3. X. Antoine C. Besse Construction, structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation J. Math. Pures Appl. (9) 80 7 2001 701-738
4. A. Arnold M. Ehrhardt I. Sofronov Discrete transparent boundary conditions for the Schrödinger equation Rev. Matematica Univ. Parma 4 2001 57-108
5. A. Arnold Mathematical concepts of open quantum boundary conditions Trans. Theory Stat. Phys. 30 2001 561-584
6. J. Aguilar J.M. Combes A class of analytic perturbations for one-body Schro7die;dinger Hamiltonians Commun. Math. Phys. 22 1971 269-279
7. W. Bao D. Jaksch P.-A. Markowich Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation J. Comput. Phys. 187 1 2003 318-342
8. W. Bao S. Jin P.-A. Markowich On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime J. Comput. Phys. 175 2 2002 487-524
9. M. Baro N. Ben Abdallah P. Degond A. El Ayyadi A 1D coupled Schrödinger drift-diffusion model including collisions J. Comput. Phys. 203 1 2005 129-153
10. V.A. Baskakov A.V. Popov Implementation of transparent boundaries for numerical solution of the Schrödinger equation Wave Motion 14 1991 123-128
11. N. Ben Abdallah A hybrid kinetic-quantum model for stationary electron transport J. Stat. Phys. 90 3-4 1998 627-662
12. N. Ben Abdallah On a multidimensional Schrödinger-Poisson scattering scattering model for semiconductors J. Math. Phys. 41 7 2000 4241-4261
13. N. Ben Abdallah P. Degond I. Gamba Coupling one-dimensional time-dependent classical and quantum transport models J. Math. Phys. 43 1 2002 1-24
14. N. Ben Abdallah P. Degond P.-A. Markowich On a one-dimensional Schrödinger-Poisson scattering model Z. Angew. Math. Phys. 48 1 1997 135-155
15. N. Ben Abdallah, C. Negulescu, M. Mouis, E. Polizzi, Simulation schemes for 2D nanoscale Mosfets, a WKB based method, J. Comput. Electron. (in press).
16. D. Bohm Quantum Theory 1989 Dover New York
17. M. Büttiker Four-terminal phase-coherent conductance Phys. Rev. Lett. 57 1986 1761-1769
18. S. Datta Electronic Transport in Mesoscopic Conductors 1995 Cambridge University Press Cambridge
19. S. Datta M.J. Mc Lennan Quantum transport in ultrasmall electronic devices Rep. Prog. Phys. 53 1990 1003-1114
20. P. Degond A. El Ayyadi A coupled Schrödinger drift-diffusion model for quantum semiconductor device simulations J. Comput. Phys. 181 1 2002 222-259
21. C. Fahrat A. Macedo M. Lesionne A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems Numer. Math. 85 2 2000 283-308
22. D.K. Ferry S.M. Goodnick Transport in Nanostructures 1997 Cambridge University Press Cambridge
23. B. Flannery W. Press S. Teukolsky W. Vetterling Numerical Recipes 1988 Academic Press New York
24. W.R. Frensley Boundary conditions for open quantum driven far from equilibrium Rev. Mod. Phys 62 1990 1570-1590
25. H.K. Gummel A self-consistent iterative scheme for one-dimensional steady state transistor calculations IEEE Trans. Electron. Devices ED-11 1964 455-465
26. G. Jona-Lasinio C. Presilla J. Sjöstrand On Schrödinger equations with concentrated nonlinearities Ann. Phys. 240 1995 1-21
27. R. Landauer Electrical resistance of disordered one-dimensional lattices Philos. Mag. 21 1970 863-876
28. C. Lent D. Kirkner The quantum transmitting boundary method J. Appl. Phys. 67 10 1990 6353-6359
29. S.E. Laux A. Kumar M. Fischetti Analysis of quantum ballistic electron transport in ultrasmall silicon devices including space-charge and geometric effects J. Appl. Phys. 95 10 2004 5545-5582
30. P. Lochak About the adiabatic stability of resonant states Ann. Inst. Henri Poincaré A 39 1983 119-143
31. F. Nier Schrödinger-Poisson systems in dimension d ≤ 3: The whole-space case Proc. Roy. Soc. Edinburgh A 123 6 1993 1179-1201
32. F. Nier A variational formulation of Schrödinger-Poisson systems in dimension d ≤ 3 Commun. Partial Diff. Equ. 18 7-8 1993 1125-1147
33. F. Nier The dynamics of some quantum open systems with short-range nonlinearities Nonlinearity 11 4 1998 1127-1172
34. F. Nier, M. Patel, Nonlinear asymptotics for quantum out of equilibrium 1D systems: Reduced models and algorithms, Conference "Multiscale methods in quantum mechanics, theory and experiments, Accademia dei Lincei Roma dec. 2002 (see http://name.math.univ-rennes1.fr/francis.nier/ recherche/liste.html).
35. M. Patel, Développement de modèles macroscopiques pour des systèques quantiques non linéaires hors équilibre, Ph.D. Thesis, Univ. Rennes, 2005, p. 1.
36. O. Pinaud Transient simulations of a resonant tunneling diode J. Appl. Phys. 92 4 2002 1987-1994
37. E. Polizzi N. Ben Abdallah Self-consistent three-dimensional models for quantum ballistic transport in open systems Phys. Rev. B 66 2002 245301
38. E. Polizzi N. Ben Abdallah Subband decomposition approach for the simulation of quantum electron transport in nanostructures J. Comput. Phys. 202 1 2005 150-180
39. E. Polizzi N. Ben Abdallah O. Vanbésien D. Lippens Space lateral transfer and negative differential conductance regimes in quantum waveguide junctions J. Appl. Phys. 87 2000 8700
40. C. Presilla J. Sjöstrand Transport properties in resonant tunneling heterostructures J. Math. Phys. 37 10 1996 4816-4844
41. B. Ricco M.Y. Azbel Physics of resonant tunneling, the one-dimensional barrier case Phys. Rev. B. 29 4 1984 1970-1976
42. A. Svizhenko M.P. Anantram T.R. Govindan B. Biegel R. Venugopal Two-dimensional quantum mechanical modeling of nanotransistors J. Appl. Phys. 91 2002 2343
43. R. Tsu L. Esaki Tunneling in a finite superlattice Appl. Phys. Lett. 22 1973 562-564
44. R. Venugopal Z. Ren S. Datta M.S. Lundstrom D. Jovanovic Simulating quantum transport in nanoscale transistors: Real versus mode-space approaches J. Appl. Phys. 92 2002 3730
45. B. Vinter C. Weisbuch Quantum Semiconductor Structures 1991 Academic Press New York