A mixed finite element discretization of the energy-transport model for semiconductors

Energy-transport models describe the flow of electrons through a semiconductor device, influenced by diffusive, electrical, and thermal effects. They consist of the continuity equations for the mass and energy, coupled with Poisson's equation for the electrostatic potential. The energy-transport model can be written in a drift-diffusion formulation which is used for the numerical approximation. The stationary equations are discretized with an exponential fitting mixed finite-element method in two space dimensions. Numerical simulations of a ballistic diode are performed and numerical convergence rates are computed. Furthermore, a two-dimensional MESFET device with parabolic band structure is simulated.