2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions and comparison to Monte Carlo methods

Journal of Computational Physics

Volumn 214, Issue 1, 2006, Pages 55-80

  Carrillo, José A ^a   Gamba, Irene M ^b   Majorana, Armando ^c   Shu, Chi Wang ^d  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c UNIVERSITY OF CATANIA   (Italy)

^d BROWN UNIVERSITY   (United States)

Author keywords

Boltzmann transport equation; Direct simulation Monte Carlo; MESFET; MOSFET; Semiconductor device simulation; Weighted essentially non oscillatory schemes

Indexed keywords

BOLTZMANN EQUATION; ELECTRIC FIELDS; MESFET DEVICES; MONTE CARLO METHODS; MOSFET DEVICES; NUMERICAL METHODS; POISSON EQUATION;

BOLTZMANN'S TRANSPORT EQUATIONS; DETERMINISTICS; DIRECT SIMULATION MONTE CARLO; ESSENTIALLY NON-OSCILLATORY; ESSENTIALLY NON-OSCILLATORY SCHEMES; MESFETS; MOS-FET; MOSFETS; SEMICONDUCTOR DEVICE SIMULATION; WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEME;

BOUNDARY CONDITIONS;

EID: 33644542461     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.09.005     Document Type: Article

References (26)

1. A.M. Anile G. Mascali V. Romano Recent developments in hydrodynamical modeling of semiconductors, mathematical problems in semiconductor physics Lect. Notes Math. 1823 2003 1-56
2. J.A. Carrillo I.M. Gamba A. Majorana C.-W. Shu A WENO-solver for the 1D non-stationary Boltzmann-Poisson system for semiconductor devices J. Comput. Electron. 1 2002 365-370
3. J.A. Carrillo I.M. Gamba A. Majorana C.-W. Shu A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices. Performance and comparisons with Monte Carlo methods J. Comput. Phys. 184 2003 498-525
4. J.A. Carrillo I.M. Gamba A. Majorana C.-W. Shu A direct solver for 2D non-stationary Boltzmann-Poisson systems for semiconductor devices: A MESFET simulation by WENO-Boltzmann schemes J. Comput. Electron. 2 2003 375-380
5. Z. Chen B. Cockburn Analysis of a finite element method for the drift-diffusion semiconductor device equations: The multidimensional case Numer. Math. 71 1995 1-28
6. P. Degond F. Delaurens F.J. Mustieles Semiconductor modelling via the Boltzmann equation Comput. Methods Appl. Sci. Eng. SIAM 1990 311-324
7. P. Degond Macroscopic limits of the Boltzmann equation: A review Modeling and Computational Methods for Kinetic Equations Modeling and Simulation in Science, Engineering and Technology 2004 Birkhauser Boston 3-57
8. E. Fatemi F. Odeh Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices J. Comput. Phys. 108 1993 209-217
9. M. Galler F. Schürrer A deterministic solution method for the coupled system of transport equations for the electrons and phonons in polar semiconductors J. Phys. A 37 2004 1479-1497
10. I.M. Gamba Behavior of the potential at the pn-Junction for a model in semiconductor theory Appl. Math. Lett. 3 1990 59-63
11. I.M. Gamba Asymptotic boundary conditions for an oxide region in a semiconductor device Asympt. Anal. 7 1993 37-48
12. I.M. Gamba Asymptotic behavior at the boundary of a semiconductor device in two space dimensions Ann. Mat. Pura App. (IV) CLXIII 1993 43-91
13. T. Gonzales D. Pardo Physical models of ohmic contact for Monte Carlo device simulation Solid-State Electron. 39 4 1996 555-562
14. P. Grisvard Elliptic Problems in Non-smooth Domains Monographs and Studies in Mathematics vol. 24 1985 Pitman London
15. C. Jacoboni P. Lugli The Monte Carlo Method for Semiconductor Device Simulation 1989 Springer New York
16. J.W. Jerome C.-W. Shu Energy models for one-carrier transport in semiconductor devices W. Coughran J. Cole P. Lloyd J. White IMA Volumes in Mathematics and Its Applications Vol. 59 1994 Springer New York 185-207
17. G. Jiang C.-W. Shu Efficient implementation of weighted ENO schemes J. Comput. Phys. 126 1996 202-228
18. A. Majorana C. Milazzo O. Muscato Charge transport in 1D silicon devices via Monte Carlo simulation and Boltzmann-Poisson solver COMPEL 23 2004 410-425
19. A. Majorana R.M. Pidatella A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices J. Comput. Phys. 174 2001 649-668
20. J.M. Mantas, J.A. Carrillo, A. Majorana, Parallelization of WENO-Boltzmann schemes for kinetic descriptions of 2D semiconductor devices, Mathematics for Industry Springer Series (2005), to appear.
21. P.A. Markowich C. Ringhofer C. Schmeiser Semiconductor Equations 1990 Springer New York
22. S. Selberherr Analysis and Simulations of Semiconductor Devices 1984 Springer Vienna
23. C.-W. Shu Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws Lect. Notes Math. 1697 1998 325-432
24. C.-W. Shu S. Osher Efficient implementation of essentially non-oscillatory shock capturing schemes J. Comput. Phys. 77 1988 439-471
25. K. Tomizawa Numerical Simulation of Submicron Semiconductor Devices 1993 Artech House Boston
26. W. Wagner Stochastic models and Monte Carlo algorithms for Boltzmann type equations Monte Carlo and Quasi-Monte Carlo Methods 2002 2004 Springer Berlin 129-153