A finite element method for the quantum hydrodynamic model for semiconductor devices

A finite element method for numerical simulation of the transient quantum hydrodynamic model for semiconductor devices is presented. This model treats electron flow in a semiconductor device in the same manner as the classical hydrodynamic model, but the energy density and stress tensor include additional quantum terms, which allow particles to tunnel through potential barriers and to build up in potential wells. The finite element method under consideration is based on use of a mixed method for the approximation of the electric field and a shock-capturing Runge-Kutta discontinuous Galerkin method for the quantum hydrodynamic conservation laws. Numerical simulations of a resonant tunneling diode are presented, which show charge buildup in the quantum well and negative differential resistance and a hysteresis in the current-voltage curve. A comparison between the present method and a finite difference method is given.