@Article{CiCP-20-551,
author = {Zhicheng Hu, Ruo Li and Zhonghua Qiao},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.290615.020316a},
url = {http://global-sci.org/intro/article_detail/cicp/11164.html}
}