Numerical Discretization of Energy-Transport Models for Semiconductors with Nonparabolic Band Structure

The energy-transport models describe the flow of electrons through a semiconductor crystal, influenced by diffusive, electrical, and thermal effects. They consist of the continuity equations for the mass and the energy, coupled with Poisson's equation for the electric potential. These models can be derived from the semiconductor Boltzmann equation. This paper consists of two parts. The first part concerns the modeling of the energy-transport system. The diffusion coefficients and the energy relaxation term are computed in terms of the electron density and temperature, under the assumptions of nondegenerate statistics and nonparabolic band diagrams. The equations can be rewritten in a drift-diffusion formulation which is used for the numerical discretization. In the second part, the stationary energy-transport equations are discretized using the exponential fitting mixed finite element method in one space dimension. Numerical simulations of a ballistic diode are performed.