Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation

Zhicheng Hu, Ruo Li, Zhonghua Qiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)551-582
Number of pages32
JournalCommunications in Computational Physics
Issue number3
Publication statusPublished - 1 Sept 2016


  • Boltzmann transport equation
  • extended hydrodynamic model
  • moment-dependent relaxation time
  • multigrid
  • semiconductor device simulation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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