A THREE-DIMENSIONAL MIXED FINITE-ELEMENT APPROXIMATION OF THE SEMICONDUCTOR ENERGY-TRANSPORT EQUATIONS

The stationary energy-transport equations for semiconductors in three space dimensions are numerically discretized. The physical variables are the electron density, the energy density, and the electric potential. Physically motivated mixed Dirichlet-Neumann boundary conditions are employed. The numerical approximation is based on a hybridized mixed finite-element method with Raviart-Thomas- Nedelec elements, applied to the dual-entropy formulation of the energy-transport model. For the solution of the nonlinear discrete system, a Newton scheme with adaptive potential stepping and two decoupling Gummel-type strategies with reduced rank extrapolation are proposed. Multigate field-effect transistors in two dimensions and three dimensions are numerically simulated.