A phonon-hydrodynamic approach to thermal conductivity of Si-Ge quantum dot superlattices

In this paper we attempt to provide an analysis of the effective thermal conductivity of Si/Ge quantum dot superlattices based on a phonon-hydrodynamic approach. We consider the inner Ge quantum dots as minute ellipsoidal obstacles which exert a thermal resistance against the phonon flow in the Si hosting matrix. This yields an additional reduction term to the effective medium reduction of the thermal conductivity. The contribution considered here depends on the size, the shape, the spatial distribution of the obstacles and plays an important role when the characteristic size of the Ge obstacles is much smaller than the phonon mean-free path in the Si matrix. The originality of the paper is that the physics of rarefied fluids is used to study the problem of heat transport.