Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation (Communications in Computational Physics, 2018)
Extended hydrodynamic models for carrier transport are derived from thesemiconductor Boltzmann equation with relaxation time approximation of the scatteringterm, by using the globally hyperbolic moment method and the moment-dependentrelaxation time. Incorporating the microscopic relaxation time and the applied voltagebias, a formula is proposed to determine the relaxation time for each moment equation,which sets different relaxation rates for different moments such that higher momentsdamp faster. The resulting models would give more satisfactory results of macroscopicquantities of interest with a high-order convergence to those of the underlying Boltzmannequation as the involved moments increase, in comparison to the correspondingmoment models using a single relaxation time. In order to simulate the steady statesefficiently, a multigrid solver is developed for the derived moment models. Numericalsimulations of an $n^+-n-n^+$ silicon diode are carried out to demonstrate the validationof the presented moment models, and the robustness and efficiency of the designedmultigrid solver.