Kinetics of Phonon Interaction Taken into Account in Determining Thermal Conductivity of Silicon

Abstract

The thorough study of the heat carriers --- quasiparticles --- phonons interaction resulted in a pioneering method for calculating the thermal conductivity of nonmetallic solids. As the interactions of phonons are much more complicated than those of usual atoms and molecules, it is necessary to take into account the presence of two types of phonons with different properties; the decay of one phonon into two or the fusion of two phonons into one as a result of interaction; the presence of two types of interaction of phonons, one of which is elastic, the other is inelastic (moreover, the type of interaction results from solving the energy and quasi-momentum conservation equations). The existing methods for determining thermal conductivity, which typically involve solving the Boltzmann transport equation, use the iteration method, whose parameter is the average time between successive phonon interactions, and the calculation results provide little information on all types of interactions. In this research, we developed a method of direct Monte Carlo simulation of phonon diffusion with strict account for their interaction owing to the energy and quasi-momentum conservation laws. Calculations of the thermal conductivity coefficient for pure silicon in the temperature range of 100---300 K showed good agreement with the experiment and calculations of other authors, and also made it possible to consider the phonon kinetics in detail