A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation

Abstract

We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC.

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

“…The dependence of the carrier energy on the wave vector in each valley can be analytically approximated by non-parabolic dispersion relations of the following form [1,9] …”

“…which, linearized with respect to the vector variables (small anisotropy assumption) [8,9,27], becomes…”

“…Following this procedure, mathematical models for the description of charge transport in unipolar and bipolar silicon devices have been constructed, see for example [10,30], while results relative to Si thermal properties can be found in [23,31]. The procedure has also been applied to compound semiconductors such as GaAs, GaN and SiC [8,9].…”

“…However, these various closure assumptions are, at best, only phenomenological and often a consistent physical and mathematical justification is lacking. Lately, a closure assumption based on the Maximum Entropy Principle of extended thermodynamics [6,7] has been successfully applied, both in the parabolic and non-parabolic band approximation, to various types of semiconductors [8][9][10][11][12][13]. The resulting models, which differ for the choice of the moments to assume as field variables, are, in fact, able to describe charge transport due both to electrons and holes and also heat transport due to phonons.…”

Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions

“…Compound semiconductors have found wide use in the microelectronic industry. The evolution equation for macroscopic variables is obtained by taking moments of the transport equation [9][10][11][12][13].…”