Mode- and Space- Resolved Thermal Transport of Alloy Nanostructures

Nanostructured semiconducting alloys obtain ultra-low thermal conductivity as a result of the scattering of phonons with a wide range of mean-free-paths (MFPs). In these materials, long-MFP phonons are scattered at the nanoscale boundaries whereas short-MFP high-frequency phonons are impeded by disordered point defects introduced by alloying. While this trend has been validated by simplified analytical and numerical methods, an ab-initio space-resolved approach remains elusive. To fill this gap, we calculate the thermal conductivity reduction in porous alloys by solving the mode-resolved Boltzmann transport equation for phonons using the finite-volume approach. We analyze different alloys, length-scales, concentrations, and temperatures, obtaining a very large reduction in the thermal conductivity over the entire configuration space. For example, a ~97% reduction is found for Al$_{0.8}$In$_{0.2}$As with 25% porosity. Furthermore, we employ these simulations to validate our recently introduced "Ballistic Correction Model" (BCM), an approach that estimates the effective thermal conductivity using the characteristic MFP of the bulk alloy and the length-scale of the material. The BCM is then used to provide guiding principles in designing alloy-based nanostructures. Notably, it elucidates how porous alloys such as Si$_{x}$Ge$_{1-x}$ obtain larger thermal conductivity reduction compared to porous Si or Ge, while also explaining why we should not expect similar behavior in alloys such as Al$_{x}$In$_{1-x}$As. By taking into account the synergy from scattering at different scales, we provide a route for the design of materials with ultra-low thermal conductivity.