Minimizing Heat Transport by Ballistic Confinement in Phononic Metalattices

We study the thermal conductivity of phononic metalattices, a class of newly synthesized nanostructures exhibiting long-range periodicity commensurate with the mean free paths of the phonons. In this work, we present a computational approach that is capable of computing the ballistic phonon mean free paths in periodic metamaterials by embedding an explicit model of phonon radiation into a continuum density of scatters, closing the gap between existing analytical models and numerical simulations. Our computational predictions supported by sensitive measurements indicate that the thermal conductivity minimum of metalattices can be as low as 0.15 W/m/K, which is among the smallest lattice conductivities reported for two- and three-dimensional silicon-based materials. This exceptional reduction in the heat conductivity establishes metalattices as a useful platform to achieve order-of-magnitude tunability in the thermal response of crystalline semiconductors.