Modeling the Thermal Conductivity and Phonon Transport in Nanoparticle Composites Using Monte Carlo Simulation

Abstract

This paper presents a Monte Carlo simulation scheme to study the phonon transport and the thermal conductivity of nanocomposites. Special attention has been paid to the implementation of periodic boundary condition in Monte Carlo simulation. The scheme is applied to study the thermal conductivity of silicon germanium (Si–Ge) nanocomposites, which are of great interest for high-efficiency thermoelectric material development. The Monte Carlo simulation was first validated by successfully reproducing the results of (two-dimensional) nanowire composites using the deterministic solution of the phonon Boltzmann transport equation reported earlier and the experimental thermal conductivity of bulk germanium, and then the validated simulation method was used to study (three-dimensional) nanoparticle composites, where Si nanoparticles are embedded in Ge host. The size effects of phonon transport in nanoparticle composites were studied, and the results show that the thermal conductivity of nanoparticle composites can be lower than that of the minimum alloy value, which is of great interest to thermoelectric energy conversion. It was also found that randomly distributed nanopaticles in nanocomposites rendered the thermal conductivity values close to that of periodic aligned patterns. We show that interfacial area per unit volume is a useful parameter to correlate the size effect of thermal conductivity in nanocomposites. The key for the thermal conductivity reduction is to have a high interface density where nanoparticle composites can have a much higher interface density than the simple 1D stacks, such as superlattices. Thus, nanocomposites further benefit the enhancement of thermoelectric performance in terms of thermal conductivity reduction. The thermal conductivity values calculated by this work qualitatively agrees with a recent experimental measurement of Si–Ge nanocomposites.