A discontinuous Galerkin solver for Boltzmann-Poisson systems in nano devices

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 37-40, 2009, Pages 3130-3150

  Cheng, Yingda ^a   Gamba, Irene M ^a   Majorana, Armando ^b   Shu, Chi Wang ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF CATANIA   (Italy)

^c BROWN UNIVERSITY   (United States)

Author keywords

Boltzmann Poisson systems; Deterministic numerical methods; Discontinuous Galerkin schemes; Semiconductor nano scale devices; Statistical hot electron transport

Indexed keywords

BOLTZMANN-POISSON SYSTEMS; DETERMINISTIC NUMERICAL METHODS; DISCONTINUOUS GALERKIN SCHEMES; SEMICONDUCTOR NANO-SCALE DEVICES; STATISTICAL HOT ELECTRON TRANSPORT;

ELECTRON TRANSITIONS; ELECTRON TRANSPORT PROPERTIES; HOT ELECTRONS; NANOSTRUCTURED MATERIALS; NUMBER THEORY; NUMERICAL METHODS; POISSON DISTRIBUTION; POISSON EQUATION; SEMICONDUCTOR DEVICE MANUFACTURE; SEMICONDUCTOR DEVICES;

GALERKIN METHODS;

EID: 67949089649     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.05.015     Document Type: Article

References (31)

1. Arnold D., Brezzi F., Cockburn B., and Marini L. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749-1779
2. Caceres M.J., Carrillo J.A., Gamba I.M., Majorana A., and Shu C.-W. Deterministic kinetic solvers for charged particle transport in semiconductor devices. In: Cercignani C., and Gabetta E. (Eds). Transport Phenomena and Kinetic Theory Applications to Gases Semiconductors Photons and Biological Systems (2006), Birkhäuser 151-171
3. Carrillo J.A., Gamba I.M., Majorana A., and Shu C.-W. A WENO-solver for 1D non-stationary Boltzmann-Poisson system for semiconductor devices. J. Comput. Electron. 1 (2002) 365-375
4. Carrillo J.A., Gamba I.M., Majorana A., and Shu C.-W. 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. Carrillo J.A., Gamba I.M., Majorana A., and Shu C.-W. 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
6. Carrillo J.A., Gamba I.M., Majorana A., and Shu C.-W. 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods. J. Comput. Phys. 214 (2006) 55-80
7. Chen Z., Cockburn B., Gardner C., and Jerome J. Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode. J. Comput. Phys. 274 (1995) 274-280
8. Chen Z., Cockburn B., Jerome J.W., and Shu C.-W. Mixed-RKDG finite element methods for the 2-d hydrodynamic model for semiconductor device simulation. VLSI Design 3 (1995) 145-158
9. Y. Cheng, I. Gamba, A. Majorana, C.-W. Shu, A discontinuous Galerkin solver for full-Band Boltzmann-Poisson models, in: The Proceeding of IWCE 13, 2009, pp. 211-214.
10. Cheng Y., Gamba I., Majorana A., and Shu C.-W. Discontinuous Galerkin solver for Boltzmann-Poisson transients. J. Comput. Electron. 7 (2008) 119-123
11. Cheng Y., Gamba I.M., Majorana A., and Shu C.-W. Discontinuous Galerkin solver for the semiconductor Boltzmann Equation. In: Grasser T., and Selberherr S. (Eds). SISPAD 07 (2007), Springer 257-260
12. Cockburn B., and Dong B. An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. J. Sci. Comput. 32 (2007) 233-262
13. Cockburn B., Hou S., and Shu C.-W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math. Comput. 54 (1990) 545-581
14. Cockburn B., Lin S.-Y., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84 (1989) 90-113
15. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52 (1989) 411-435
16. Cockburn B., and Shu C.-W. The Runge-Kutta local projection P1-discontinuous Galerkin finite element method for scalar conservation laws. Math. Model. Numer. Anal. 25 (1991) 337-361
17. Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141 (1998) 199-224
18. Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440-2463
19. Cockburn B., and Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173-261
20. Fatemi E., and Odeh F. Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices. J. Comput. Phys. 108 (1993) 209-217
21. Ferry D.K. Semiconductors (1991), Maxwell MacMillian, New-York
22. Galler M., and Majorana A. Deterministic and stochastic simulation of electron transport in semiconductors. Bull. Inst. Math., Acad. Sinica (New Series) 2 2 (2007) 349-365 6th MAFPD (Kyoto) special issue
23. Jacoboni C., and Lugli P. The Monte Carlo Method for Semiconductor Device Simulation (1989), Spring-Verlag, Wien-New York
24. Lundstrom M. Fundamentals of Carrier Transport (2000), Cambridge University Press, Cambridge
25. Liu Y.-X., and Shu C.-W. Local discontinuous Galerkin methods for moment models in device simulations: formulation and one dimensional results. J. Comput. Electron. 3 (2004) 263-267
26. Liu Y.-X., and Shu C.-W. Local discontinuous Galerkin methods for moment models in device simulations: performance assessment and two dimensional results. Appl. Numer. Math. 57 (2007) 629-645
27. Majorana A., and Pidatella R. A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices. J. Comput. Phys. 174 (2001) 649-668
28. Markowich P.A., Ringhofer C., and Schmeiser C. Semiconductor Equations (1990), Springer-Verlag, New York
29. Tomizawa K. Numerical Simulation of Sub Micron Semiconductor Devices (1993), Artech House, Boston
30. Zhou T., Li Y., and Shu C.-W. Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods. J. Sci. Comput. 16 (2001) 145-171
31. Ziman J.M. Electrons and Phonons. The Theory of Transport Phenomena in Solids (2000), Oxford University Press, Oxford