Numerical solutions of a viscous‐hydrodynamic model for semiconductors: the supersonic case Available to Purchase

In this paper, we solve by a finite difference upwinded method an extended hydrodynamic model for semiconductors, with viscous terms in the momentum equation. In particular, we consider the simulation of a one‐dimensional n⁺‐n ‐n⁺ diode, whose solution exhibits at low temperatures strong discontinuities, and investigate the effect of the momentum viscosity on the shock waves. Numerical experiments, performed also on a two‐dimensional test case, demonstrate that the numerical scheme, working on non‐uniform grids, is suitable to describe solutions with strong variations in time and space. Well‐posedness for the boundary conditions is discussed, and a linear stability estimate is established for the one‐dimensional n⁺‐n ‐n⁺ diode benchmark problem.