Heat transfer modelling in the Si–Ge nanoparticle composites by numerical solution of the equation of phonon radiative transfer

Abstract

Phonon Boltzmann transport equation and consequently the Equation of Phonon Radiative Transfer govern the conductive heat transfer in semiconductors at the nanoscale. Here a semiconducting nanoparticle composite, consisting of cubic Si nanoparticles in a Ge substrate is considered. A detailed three-dimensional heat transfer analysis is done, the temperature distributions are generated, the Effective Thermal Conductivity (ETC) of the nanocomposite is obtained, and the effect of the Si nanoparticle size and the constituents' atomic percentage on the ETC is explored. As the most comprehensive study, the effect of the interface density on the ETC is investigated and the results are compared with those obtained using the Monte Carlo simulation. The results show that at a fixed atomic percentage, as the dimensions are decreased, the ETC reduces and the temperature jumps become larger. At a fixed Si nanoparticle size, as the Ge atomic percentage increases, the ETC also increases, and the ETC reduces as the interface density increases. Reducing the ETC is a way to improve the thermoelectric energy conversion.