Size and dimensionality dependent phonon conductivity in nanocomposites

We have studied size and dimensionality dependent phonon conductivity of PbTe-PbSe nanocomposites by considering three configurations: superlattice, embedded nanowire and embedded nanodot. Calculations have been performed in the framework of an effective medium theory. The required bulk thermal conductivities of PbTe and PbSe are evaluated by using Callaway's effective relaxation-time theory, and by accounting for relevant scattering mechanism including three-phonon Normal and Umklapp interactions involving acoustic as well as optical branches. The thermal interface resistance is computed using the diffuse mismatch theory. It is found that the size (thickness) and volume fraction of PbSe are the two main factors that control the effective thermal conductivity in these nanocomposites. In particular, for PbSe size d = 10 nm and volume fraction V-f = 0.1, our results predict significant reductions over the weighted average of room-temperature bulk results of 9%, 17% and 15% in the conductivity across the interfaces for the superlattice, embedded nanowire, and nanosphere structures, respectively. For a given Vf, an increase in d reduces the interface density Phi and the effective conductivity varies approximately as 1/root Phi. It is shown that nanocompositing in any of the three configurations can beat the alloy limit for lattice thermal conductivity.