Thermal conductivity model for nanoporous thin films

Nanoporous thin films have attracted great interest because of their extremely low thermal conductivity and potential applications in thin thermal insulators and thermoelectrics. Although there are some numerical and experimental studies about the thermal conductivity of nanoporous thin films, a simplified model is still needed to provide a straightforward prediction. In this paper, by including the phonon scattering lifetimes due to film thickness boundary scattering, nanopore scattering and the frequency-dependent intrinsic phonon-phonon scattering, a fitting-parameter-free model based on the kinetic theory of phonon transport is developed to predict both the in-plane and the cross-plane thermal conductivities of nanoporous thin films. With input parameters such as the lattice constants, thermal conductivity, and the group velocity of acoustic phonons of bulk silicon, our model shows a good agreement with available experimental and numerical results of nanoporous silicon thin films. It illustrates that the size effect of film thickness boundary scattering not only depends on the film thickness but also on the size of nanopores, and a larger nanopore leads to a stronger size effect of the film thickness. Our model also reveals that there are different optimal structures for getting the lowest in-plane and cross-plane thermal conductivities.