Institute for Mathematical Physics Numerical Discretization of Energy{transport Models for Semiconductors with Non{parabolic Band Structure Numerical Discretization of Energy-transport Models for Semiconductors with Non-parabolic Band Structure

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 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 ...

High-Field Approximations of the Energy-Transport Model for Semiconductors with Non-Parabolic Band Structure

A Novel Approach to Spherical Harmonics Expansion for Electron Transport in Semiconductors

Abstract. A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic band approximation are treated in detail. In these cases, the set of equations is equivalent to those obtained in the spherical-harmonics expansion....

Parallelization of WENO-Boltzmann schemes for kinetic descriptions of 2D semiconductor devices

The parallelization of a direct WENO (Weighted Essentially Non-Oscillatory) solver for the 2D-spatial Boltzmann-Poisson system describing electron transport in Si-based semiconductor devices has been addressed. A non-parabolic Kane energy-band and elastic acoustic and inelastic non-polar optical phonon operators have been used [CGMS03A] in the physical description of the electron transport in t...

Moment inequalities and high-energy tails for electron distribution function of the Boltzmann transport equation in semiconductors

In this paper we prove the existence of the high-energy tails for electron distribution function of the Boltzmann equation for semiconductors, in the stationary and homogeneous regime, in the analytic band approximation and scattering with acoustic and optical phonons and impurities. We also prove numerically that the tail is a global maxwellian in the parabolic band approximation, and in the q...