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Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation

Part of: Hyperbolic equations and systems Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application Applications to specific types of physical systems

Published online by Cambridge University Press:  31 August 2016

Zhicheng Hu ,
Ruo Li  and
Zhonghua Qiao
Zhicheng Hu*
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
Ruo Li*
Affiliation:
HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China
Zhonghua Qiao*
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
*
*Corresponding author. Email addresses:huzhicheng1986@gmail.com (Z. Hu), rli@math.pku.edu.cn (R. Li), zqiao@polyu.edu.hk (Z. Qiao)
*Corresponding author. Email addresses:huzhicheng1986@gmail.com (Z. Hu), rli@math.pku.edu.cn (R. Li), zqiao@polyu.edu.hk (Z. Qiao)
*Corresponding author. Email addresses:huzhicheng1986@gmail.com (Z. Hu), rli@math.pku.edu.cn (R. Li), zqiao@polyu.edu.hk (Z. Qiao)
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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.

Keywords

Boltzmann transport equationextended hydrodynamic modelmoment-dependent relaxation timemultigridsemiconductor device simulation

MSC classification

Secondary: 35L75: Nonlinear higher-order hyperbolic equations 35Q20: Boltzmann equations 65N55: Multigrid methods; domain decomposition 82D37: Semiconductors
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 3 , September 2016 , pp. 551 - 582
Copyright
Copyright © Global-Science Press 2016 

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