High field fluid dynamical models for the transport of charge carriers in semiconductors

An asymptotic solution for the SHE equations describing the charge transport in semiconductors

“…In order to close the moment equations relatively to the hot electrons they used a distribution function whose form is directly suggested by the L-M solution, whereas relatively to cold electrons a a standard maximum-entropy distribution function is utilized. A detailed study of the resulting high-energy hydrodynamical model is given in Anile, Liotta and Mascali (2000). Some works about the extension of this model to the case of Kane band, using the asymptotic solution found in this paper, are in progress.…”

“…Despite the very simple situation in which this solution was obtained, it has revealed to be very useful in order to develop new asymptotic hydrodynamical models describing the hot electron population in silicon devices (both in the homogeneous and non-homogeneous case). In particular see and Anile, Liotta and Mascali (2000), where this asymptotic solution was used in order to close the set of moment equations. The aim of this work is to show the possibility of finding a new asymptotic solution generalizing that derived in Liotta and Majorana (1999) to the case of a non-parabolic band structure (Kane model).…”

Two Dimensional MESFET Simulation of Transients and Steady State with Kinetic Based Hydrodynamical Models

“…are extra-variables which are to be determined as functions of the fundamental variables n, ff and W. This is achieved, as said, by assuming that the electron distribution function depends on n, and W in the following manner 3h2 )3/2 ne-3e/2w f 47rm*W 27h n _ _ -l/2e-3e/2Wuivi 327r W 2 (6) which follows directly from the L.-M. distribution function [3,4,9]. Substituting it in the kinetic expressions of the fluxes (4), we obtain KBTi j 2 W si 4 m----ciJ -Wui.…”

“…erf is the error function, while In [3] is shown that the system of balance laws (3) is strictly hyperbolic, and this permits us to use standard numerical methods developed for this kind of equations. In particular for the numerical integration of the system (3) we have used the two-dimensional extension of the Tadmor scheme [5] for the convective part completed with a splitting strategy to treat the scattering terms [6].…”

“…Since these assumptions are either ad hoc (like the Fourier law assumption) or at best phenomenological, in this paper we investigate a new hydrodynamical model recently proposed by Anile, Liotta and Corresponding author. Mascali (ALM model) [3], in which the closure of the equations is obtained in a systematic and rational way. In fact it is based on an asymptotic solution for high fields of the Boltzmann transport equation (BTE) for semiconductors recently found by Liotta and Majorana [4] and therefore it is not necessary to assume phenomenological closures or ad hoc expressions for the productions terms.…”