  Nanostructured materials exhibit low thermal conductivity because of the
additional scattering due to phonon-boundary interactions. As these
interactions are highly sensitive to the mean free path (MFP) of a given phonon
mode, MFP distributions in nanostructures can be dramatically distorted
relative to bulk. Here we calculate the MFP distribution in periodic nanoporous
Si for different temperatures, using the recently developed MFP-dependent
Boltzmann Transport Equation. After analyzing the relative contribution of each
phonon branch to thermal transport in nanoporous Si, we find that at room
temperature optical phonons contribute 18 % to heat transport, compared to 5%
in bulk Si. Interestingly, we observe a steady thermal conductivity in the
nanoporous materials over a temperature range 200 K < T < 300 K, which we
attribute to the ballistic transport of acoustic phonons with long intrinsic
MFP. These results, which are also consistent with a recent experimental study,
shed light on the origin of the reduction of thermal conductivity in
nanostructured materials, and could contribute to multiscale heat transport
engineering, in which the bulk material and geometry are optimized
concurrently.
