Analysis of Energy-Transport Models for semiconductors

Abstract

In this thesis we study the energy transport models of the charge carriers in the semiconductors, in the unipolar and one-dimensional case. These are macroscopic models, that are useful to describe the thermal eff ects in the semiconductor devices. Usually the set of equations are given by the balance equations for density and energy of the charge carriers, coupled to the Poisson equation for the electric potential. Two energy transport models, with and without crystal heating, are presented with diff erent approaches. The fi rst energy transport model is the Chen model, in which the temperature lattice is assumed constant. We fi nd some particular solutions and we discuss them behavior depending on physical parameters, as example for the silicon. The second energy transport model includes as variable the lattice temperature. A symmetry analysis approach to this model is performed. We determine the group classi cation of the model equations, collecting them into equivalence classes and fi nd the functional forms of the constitutive functions appearing in the equations. In some cases the reduced system solutions are found.