The best nanoparticle size distribution for minimum thermal conductivity

Which sizes of nanoparticles embedded in a crystalline solid yield the lowest thermal conductivity? Nanoparticles have long been demonstrated to reduce the thermal conductivity of crystals by scattering phonons, but most previous works assumed the nanoparticles to have a single size. Here, we use optimization methods to show that the best nanoparticle size distribution to scatter the broad thermal phonon spectrum is not a similarly broad distribution but rather several discrete peaks at well-chosen nanoparticle radii. For SiGe, the best size distribution yields a thermal conductivity below that of amorphous silicon. Further, we demonstrate that a simplified distribution yields nearly the same low thermal conductivity and can be readily fabricated. Our work provides important insights into how to manipulate the full spectrum of phonons and will guide the design of more efficient thermoelectric materials.