WENO

A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods. In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann-Poisson system for semiconductor devices. We follow the work in E. Fatemi and F. Odeh [J. Comput. Phys. 108, 209–217 (1993; Zbl 0792.65110)] and in A. Majorana and R. Pidatella [J. Comput. Phys. 174, 649–668 (2001; Zbl 0992.82047)] to formulate the Boltzmann-Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on today’s computers. The computational results have been compared with those by a Monte Carlo simulation and excellent agreements have been found. The advantage of the current solver over a Monte Carlo solver includes its faster speed, noise-free resolution, and easiness for arbitrary moment evaluations. This solver is thus a useful benchmark to check on the physical validity of various hydrodynamic and energy transport models. Some comparisons have been included in this paper.


References in zbMATH (referenced in 39 articles , 1 standard article )

Showing results 1 to 20 of 39.
Sorted by year (citations)

1 2 next

  1. He, Yuan; Gamba, Irene M.; Lee, Heung-Chan; Ren, Kui: On the modeling and simulation of reaction-transfer dynamics in semiconductor-electrolyte solar cells (2015)
  2. Li, Ruo; Lu, Tiao; Yao, Wenqi: Discrete kernel preserving model for 1D electron-optical phonon scattering (2015)
  3. Carrillo, José A.; Yan, Bokai: An asymptotic preserving scheme for the diffusive limit of kinetic systems for chemotaxis (2013)
  4. Jin, Shi; Wang, Li: Asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime (2013)
  5. Cheng, Yingda; Gamba, Irene M.; Proft, Jennifer: Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations (2012)
  6. Alekseenko, A.M.: Numerical properties of high order discrete velocity solutions to the BGK kinetic equation (2011)
  7. Cheng, Yingda; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang: A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations (2011)
  8. Cheng, Yingda; Gamba, Irene M.; Ren, Kui: Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model (2011)
  9. Ketcheson, David I.; Gottlieb, Sigal; Macdonald, Colin B.: Strong stability preserving two-step Runge-Kutta methods (2011)
  10. Yang, Jaw-Yen; Muljadi, Bagus Putra: Simulation of shock wave diffraction over $90^\circ $ sharp corner in gases of arbitrary statistics (2011)
  11. Ben Abdallah, N.; Cáceres, M.J.; Carrillo, J.A.; Vecil, F.: A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs (2009)
  12. Gottlieb, Sigal; Ketcheson, David I.; Shu, Chi-Wang: High order strong stability preserving time discretizations (2009)
  13. La Rosa, Salvatore; Mascali, Giovanni; Romano, Vittorio: Exact maximum entropy closure of the hydrodynamical model for si semiconductors: the 8-moment case (2009)
  14. Mantas, José M.; Cáceres, María J.: Efficient deterministic parallel simulation of 2D semiconductor devices based on WENO-Boltzmann schemes (2009)
  15. Shu, Chi-Wang: High order weighted essentially nonoscillatory schemes for convection dominated problems (2009)
  16. Gamba, I.M.; Tharkabhushanam, S.H.: Spectral solvers to non-conservative transport for non-linear interactive systems of Boltzmann type (2008)
  17. Auer, C.; Schürrer, F.; Russo, G.: Adaptive energy discretization of the semiconductor Boltzmann equation (2007)
  18. Cáceres, M.J.; Carrillo, J.A.; Gamba, I.M.; Majorana, A.; Shu, C.-W.: Deterministic kinetic solvers for charged particle transport in semiconductor devices (2007)
  19. Carrillo, J.A.; Vecil, F.: Nonoscillatory interpolation methods applied to Vlasov-based models (2007)
  20. Carrillo, José A.; Majorana, Armando; Vecil, Francesco: A semi-Lagrangian deterministic solver for the semiconductor Boltzmann-Poisson system (2007)

1 2 next