Thermal conductivity of silicon-germanium alloys from first-principles

Thermoelectric materials will become commercially viable for converting heat into electricity and for refrigeration once their figure of merit (ZT) is improved. One key approach to increase performance is to reduce thermal conductivity - e.g. in alloys it is lower than the binary endpoints due to increased scattering induced by strain and disorder. Understanding the thermal conductivity of complex materials is also important in other applications - from reducing hot-spot temperatures in electronic chips to better thermal-insulation materials. Here, we have calculated the thermal conductivity of silicon-germanium alloys using ab-initio density functional perturbation theory. The electronic strucure of the alloy is studied with the virtual crystal approximation and the single mode relaxation time approximation; perturbation theory up to the third order provides phonon lifetimes, and disorder effects are taken into account by ensemble averages over configurations with random mass disorder. The contribution of acoustic and optical phonons to the thermal conductivity is also presented, together with the phonon mean free paths. These calculations could be used to estimate the size of the nanostructures that could reduce the thermal conductivity below bulk values through increased scattering of phonons.