Volume 20, Issue 3
Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation

Zhicheng Hu, Ruo Li & Zhonghua Qiao

Commun. Comput. Phys., 20 (2016), pp. 551-582.

Published online: 2018-04

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  • Abstract

Extended hydrodynamic models for carrier transport are derived from the semiconductor Boltzmann equation with relaxation time approximation of the scattering term, by using the globally hyperbolic moment method and the moment-dependent relaxation time. Incorporating the microscopic relaxation time and the applied voltage bias, a formula is proposed to determine the relaxation time for each moment equation, which sets different relaxation rates for different moments such that higher moments damp faster. The resulting models would give more satisfactory results of macroscopic quantities of interest with a high-order convergence to those of the underlying Boltzmann equation as the involved moments increase, in comparison to the corresponding moment models using a single relaxation time. In order to simulate the steady states efficiently, a multigrid solver is developed for the derived moment models. Numerical simulations of an $n^+-n-n^+$ silicon diode are carried out to demonstrate the validation of the presented moment models, and the robustness and efficiency of the designed multigrid solver.

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@Article{CiCP-20-551, author = {}, title = {Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {3}, pages = {551--582}, abstract = {

Extended hydrodynamic models for carrier transport are derived from the semiconductor Boltzmann equation with relaxation time approximation of the scattering term, by using the globally hyperbolic moment method and the moment-dependent relaxation time. Incorporating the microscopic relaxation time and the applied voltage bias, a formula is proposed to determine the relaxation time for each moment equation, which sets different relaxation rates for different moments such that higher moments damp faster. The resulting models would give more satisfactory results of macroscopic quantities of interest with a high-order convergence to those of the underlying Boltzmann equation as the involved moments increase, in comparison to the corresponding moment models using a single relaxation time. In order to simulate the steady states efficiently, a multigrid solver is developed for the derived moment models. Numerical simulations of an $n^+-n-n^+$ silicon diode are carried out to demonstrate the validation of the presented moment models, and the robustness and efficiency of the designed multigrid solver.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.290615.020316a}, url = {http://global-sci.org/intro/article_detail/cicp/11164.html} }
TY - JOUR T1 - Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation JO - Communications in Computational Physics VL - 3 SP - 551 EP - 582 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.290615.020316a UR - https://global-sci.org/intro/article_detail/cicp/11164.html KW - AB -

Extended hydrodynamic models for carrier transport are derived from the semiconductor Boltzmann equation with relaxation time approximation of the scattering term, by using the globally hyperbolic moment method and the moment-dependent relaxation time. Incorporating the microscopic relaxation time and the applied voltage bias, a formula is proposed to determine the relaxation time for each moment equation, which sets different relaxation rates for different moments such that higher moments damp faster. The resulting models would give more satisfactory results of macroscopic quantities of interest with a high-order convergence to those of the underlying Boltzmann equation as the involved moments increase, in comparison to the corresponding moment models using a single relaxation time. In order to simulate the steady states efficiently, a multigrid solver is developed for the derived moment models. Numerical simulations of an $n^+-n-n^+$ silicon diode are carried out to demonstrate the validation of the presented moment models, and the robustness and efficiency of the designed multigrid solver.

Zhicheng Hu, Ruo Li & Zhonghua Qiao. (2020). Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation. Communications in Computational Physics. 20 (3). 551-582. doi:10.4208/cicp.290615.020316a
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