A model for predicting the thermal conductivity of SiO₂-Ge nanoparticle composites

We present a simple theoretical model that predicts the thermal conductivity of SiO₂ layers with embedded Ge quantum dots (QDs). Overall, the resulting nanoscale architecture comprising the structural relaxation in the SiO₂ matrix, deviation in mass density of the QDs compared to the surrounding matrix and local strains associated with the dots are all likely to enhance phonon scattering and thus reduce the thermal conductivity in these systems. We have found that the conductivity reduction can be predicted by the dot-induced local elastic perturbations in SiO₂. Our model is able to explain not only this large reduction but also the magnitude and temperature variation of the thermal conductivity with size and density of the dots. Within the error range, the theoretical calculations of the temperature-dependent thermal conductivity in different samples are in close agreement with the experimental measurements. Including the details of the strain fields in oxidized Si nanostructured layers is therefore essential for a better prediction of the heat pathways in on-chip thermoelectric devices and circuits.