Thermal transport in Si-Ge nano-grains using Ab-initio simulations.

Abstract

In this work, we intend to design nano-granular meta-materials in which phonon boundary scattering mechanisms induce strong reduction in the lattice thermal conductivity. Such systems are expected to show high thermoelectric figure of merit and contribute significantly to the efforts done so far to develop alternative energy technologies. We present a solution for spatial dependent Boltzmann equation within the single mode relaxation time approximation yielding an accurate expression for thermal conductivity of nano-sized materials or nano-grains. Upon using the conservation of heat flux theorem, we develop an expression for thermal conductivity of a monolayer of nano-grains. Then, we use the Diffuse Mismatch Model (DMM) to develop an expression for thermal conductivity of granular materials. The relaxation times are derived from Fermi's golden rule and the harmonic and anharmonic terms of the force constants involved in the model are derived from first principles techniques. We apply our model to calculate the thermal conductivity of a granular material made up of a mixture of nano-grains of silicon and germanium. The results demonstrate that such a material is characterized by a thermal conductivity as low as the thermal conductivity of SiGe alloy, which is a well-established thermoelectric material for application in environments of very high temperatures. We demonstrate that the mixture of silicon and germanium nano-grains can be more convenient than SiGe alloy in thermoelectric applications, as they do not present the alloys structure stability problems.