Thermal transport in 2- And 3-dimensional periodic "holey" nanostructures

Understanding thermal transport in two- and three-dimensional periodic "holey" nanostructures is important for realizing applications of these structures in thermoelectrics, photonics and batteries. In terms of continuum heat diffusion physics, the effective medium theory provides the framework for obtaining the effective thermal conductivity of such structures. However, recently measured nanostructures possess thermal conductivities well below these continuum predictions. In some cases, their thermal conductivities are even lower than predictions that account for sub-continuum phonon transport. We analyze current understanding of thermal transport in such structures, discussing the various theories, the measurements and the insights gained from comparing the two.