A hydrodynamic model for silicon semiconductors including crystal heating

Abstract

We present a macroscopic model for describing the electrical and thermal behaviour of silicon devices. The model makes use of a set of macroscopic state variables for phonons and electrons that are moments of their respective distribution functions. The evolution equations for these variables are obtained starting from the Bloch–Boltzmann–Peierls kinetic equations for the phonon and the electron distributions, and are closed by means of the maximum entropy principle. All the main interactions between electrons and phonons, the scattering of electrons with impurities, as well as the scattering of phonons among themselves are considered. In particular, we propose a treatment of the optical phonon decay directly based on the expression of its transition rate (Klemens 1966Phys. Rev.148 845; Aksamija & Ravaioli 2010Appl. Phys. Lett.96, 091911). As an application of the model, we evaluate the silicon thermopower.