Thermal conductivity reduction by embedding nanoparticles

Abstract

Reduction of thermal conductivity is important to enhance the performance of thermoelectric materials. One possible way to achieve this goal consists in embedding nanoparticles in the material, since they act as extrinsic phonon-scattering centers. In this paper, we study the effects of this embedding by means of a new formula for thermal conductivity obtained on the base of a hierarchy of hydrodynamical models which describe the transport of acoustic phonons in semiconductors. These models use as state variables suitable moments of the phonon occupation number, evolution equations of which are found starting from the Boltzmann---Peierls transport equation, and are closed by means of the maximum entropy principle. All the main interactions of phonons among themselves, with isotopes, nanoparticles, and boundaries are taken into account. Numerical results relative to the case of germanium nanoparticles embedded in a Si$$_{0.7}$$0.7Ge$$_{0.3}$$0.3 alloy crystal show that the thermal conductivity can be significantly reduced even at room temperature.