Semiconductor device simulation using a viscous-hydrodynamic model

In this article we deal with a hydrodynamic model of Navier–Stokes (NS) type for semiconductors including a physical viscosity in the momentum and energy equations. A stabilized finite difference scheme with upwinding based on the characteristic variables is used for the discretization of the NS equations, while a mixed finite element scheme is employed for the approximation of the Poisson equation. A consistency result for the method is established showing that the scheme is first-order accurate in both space and time. We also perform a stability analysis of the numerical method applied to a linearized incompletely parabolic system in two space dimensions with vanishing viscosity. A thorough numerical parametric study as a function of the heat conductivity and of the momentum viscosity is carried out in order to investigate their effect on the development of shocks in both one and two space dimensional devices.