Numerical Discretization of
Energy-Transport Models for Semiconductors with non-parabolic band
structure
by Pierre Degond, Ansgar Jüngel and Paola Pietra
ABSTRACT
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 to 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 with the modelling
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 non-degenerate statistics and non-parabolic 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.
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