A semi-Lagrangian deterministic solver for the semiconductor Boltzmann-Poisson system

Communications in Computational Physics

Volumn 2, Issue 5, 2007, Pages 1027-1054

  Carrillo, José A ^a   Majorana, Armando ^b   Vecil, Francesco ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF CATANIA   (Italy)

Author keywords

Kinetic equations for semiconductors; Semi Lagrangian schemes; Splitting schemes

Indexed keywords

EID: 38849155119     PISSN: 18152406     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. C. Auer, A. Majorana and E. Schürrer, Numerical schemes for solving the non-stationary Boltzmann-Poisson system for two-dimensional semiconductor devices, ESAIM: Proceedings, 15 (2005), 75-86.
2. M. J. Cáceres, J. A. Carrillo and A. Majorana, Deterministic simulation of the Boltzmann-Poisson system in GaAs-based semiconductors, SIAM J. Sci. Comput., 27 (2006), 1981-2009.
3. M. J. Cáceres, J. A. Carrillo, I. M. Gamba, A. Majorana and C.-W. Shu, Deterministic kinetic solvers for charged particle transport in semiconductor devices, in: C. Cercignani and E. Gabetta (Eds.), Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photons and Biological Systems, Series: Modelling and Simulation in Science, Engineering and Technology, Birkhäuser, 2007.
4. J. A. Carrillo, I. M. Gamba, A. Majorana and 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.
5. J. A. Carrillo, I. M. Gamba, A. Majorana and C.-W. Shu, 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods, J. Comput. Phys., 214 (2006), 55-80.
6. J. A. Carrillo and F. Vecil, Non oscillatory interpolation methods applied to Vlasov-based models, SIAM J. Sci. Comput, to appear.
7. C. Z. Cheng and G. Knorr, The integration of the Vlasov equation in configuration space, J. Comput. Phys., 22 (1976), 330-348.
8. F. Filbet and G. Russo, Accurate numerical methods for the Boltzmann equation, in: Modeling and Computational Methods for Kinetic Equations, Model. Simul. Sci. Eng. Technol., Birkhäuser Boston, Boston, 2004, pp. 117-145.
9. F. Filbet, E. Sonnendrcker and P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys., 172 (2001), 166-187.
10. M. Galler and E Schürrer, A deterministic solver for the transport of the AlGaN/GaN 2D electron gas including hot-phonon and degeneracy effects, J. Comput. Phys., 210 (2005), 519-534.
11. M. Galler, Multigroup equations for the description of the particle transport in semiconductors, Series on Advances in Mathematics for Applied Sciences 70, World Scientific Publishing, 2005.
12. M. Galler and A. Majorana, Deterministic and stochastic simulations of electron transport in semiconductors, Bulletin of the Institute of Mathematics, Academia Sinica, 6th MAFPD (Kyoto) Special Issue, 2007.
13. M. Galler and F. Schürrer, A direct multigroup-WENO solver for the 2D non-stationary Boltzmann-Poisson system for GaAs devices: GaAs-MESFET, J. Comput. Phys., 212 (2006), 778-797.
14. G. S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), 202-228.
15. A. Majorana, O. Muscato and C. Milazzo, Comparison of Monte Carlo and Boltzmann equation simulations for 1-D silicon devices, COMPEL, 23 (2004), 410-425.
16. A. Majorana and R. M. Pidatella, A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices, J. Comput. Phys., 174 (2001), 649-668.
17. P. A. Markowich, C. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, New-York, 1990.
18. C. Ringhofer, Space-time discretization of series expansion methods for the Boltzmann transport equation, SIAM J. Numer. Anal., 38 (2000), 442-465.
19. C. Ringhofer, A mixed spectral-difference method for the steady state Boltzmann-Poisson system, SIAM J. Numer. Anal., 41 (2003), 64-89.
20. L. Reggiani, Hot-electron transport in semiconductors, Topics in Applied Physics 58, Springer Verlag, Berlin, 1985.
21. K. Sebastian and C.-W. Shu, Multidomain WENO finite difference method with interpolation at subdomain interfaces, J. Sci. Comput., 19 (2003), 403-438.
22. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys., 77 (1988), 439-471.
23. G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), 506-517.
24. K. Tomizawa, Numerical Simulation of Submicron Semiconductor Devices, Artech House, Boston, 1983.