Similarity Reduction of Energy-Transport Models for Semiconductors

M Molati,C Soh

doi:10.3390/mca10020221

Abstract

The main purpose of this work is to perform symmetry classification of a system of partial differential equations for energy-transport in semiconductors. In the case where there are symmetries, they are used to reduce the number of independent variables which in turn enables one to construct invariant solutions. Invariant solutions of a given equation satisfy an equation with fewer independent variables. Thus, the search of invariant solutions can be viewed as a sort of dimensional reduction. From a computational standpoint, the reduced system is easier to analyse both numerically and analytically than the original system.

Highlights

The motion of charge carriers in semiconductors under the effect of an electric field and a carrier concentration gradient is an important phenomenon
This work employs the symmetry principle [2,5,7,8] to get the elements of the second group of the unknowns, that is, the forms of the energy production, the mobilities and the doping profile are obtained for which the model is maximally symmetric
Symmetries of a system of partial differential equations (PDEs) for the ET model will be calculated from the so-called determining equations

Summary

INTRODUTION

The motion of charge carriers (negatively charged particles, electrons and positively charged particles, holes) in semiconductors under the effect of an electric field and a carrier concentration gradient is an important phenomenon. The second group is formed by the energy production, the mobilities and the doping profile This work employs the symmetry principle [2,5,7,8] to get the elements of the second group of the unknowns, that is, the forms of the energy production, the mobilities and the doping profile are obtained for which the model is maximally symmetric. When the original system contains arbitrary parameters or functions, the consistency conditions of the determining equations provides a means to specify their forms. This is the essence of the group classification method [8]. We summarize our findings and hints on further work

ENERGY-TRANSPORT MODEL FOR SEMICONDUCTORS

THE SYMMETRY CLASSIFICATION OF THE ET MODEL FOR SEMICONDUCTORS

The two-dimensional ET model for semiconductors

SIMILARITY REDUCTIONS OF THE ET MODEL FOR SEMICONDUCTORS

CONCLUSION