Mode- and space-resolved thermal transport of alloy nanostructures

•A mode- and space-resolved phonon transport model of alloy nanostructures is presented to find materials with ultra-low thermal conductivity•Opposite trends in the effectiveness of porosity on thermal conductivity reduction are explained•It is shown that alloy scattering in materials such as SiGe pushes medium MFP phonons to lower MFPs without hindering long MFP phonons.•It is shown that in contrast to SiGe in materials such as AlInAs the entire phonon spectrum scales to lower MFP•The opposite trends in the effect of porosity on thermal conductivity reduction in alloys is further explained using ballistic correction model. 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 Al0.8In0.2As 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 SixGe1−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 AlxIn1−xAs. 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.