Some results concerning the well‐posedness of the hydrodynamic model of semiconductor devices in two dimensions are given. We show the non‐ellipticity of the stationary model;…
Abstract
Some results concerning the well‐posedness of the hydrodynamic model of semiconductor devices in two dimensions are given. We show the non‐ellipticity of the stationary model; give representations which exhibit its elliptic and hyperbolic components, and obtain some appropriate boundary conditions from an examination of the time‐dependent problem.
Luca Ballestra and Fausto Saleri
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…
Abstract
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.