Localization of vibrational modes leads to reduced thermal conductivity of amorphous heterostructures

Abstract

We investigate the vibrational heat transfer mechanisms in amorphous Stillinger-Weber silicon and germanium-based alloys and heterostructures via equilibrium and nonequilibrium molecular dynamics simulations along with lattice dynamics calculations. We find that similar to crystalline alloys, amorphous alloys demonstrate large size effects in thermal conductivity, while layering the constituent materials into superlattice structures leads to length-independent thermal conductivities. The thermal conductivity of an amorphous ${\mathrm{Si}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ alloy reduces by as much as $\ensuremath{\sim}53%$ compared to the thermal conductivity of amorphous silicon; compared to the larger reduction in crystalline phases due to alloying, we show that compositional disorder rather than structural disorder has a larger impact on the thermal conductivity reduction. Our thermal conductivity predictions for a-Si/a-Ge superlattices suggest that the alloy limit in amorphous SiGe-based structures can be surpassed with interface densities above $\ensuremath{\sim}0.35\phantom{\rule{4pt}{0ex}}{\mathrm{nm}}^{\ensuremath{-}1}$. We attribute the larger reduction in thermal conductivity of layered Si/Ge heterostructures to greater localization of modes at and around the cutoff frequency of the softer layer as demonstrated via lattice dynamics calculations and diffusivities of individual eigenmodes calculated according to the Allen-Feldman theory [P. B. Allen and J. L. Feldman, Phys. Rev. B 48, 12581 (1993)] for our amorphous SiGe-based alloys and superlattice structures.