Effects of phonon pore scattering and pore randomness on effective conductivity of porous silicon

The observed low effective thermal conductivity of porous silicon makes for its convenient fabrication and integration as a thermal insulation layer in microelectronics. The observed average pore size is controlled by the etching process and ranges between 1 and 100 nm, which on the low end is much less than the bulk phonon mean-free path. This low effective conductivity, i.e., low effective phonon mean-free path, can be explained with the inclusion of the effects of the phonon pore scattering and the pore randomness. The available two-dimensional porous silicon pore-network simulations are used along with the Boltzmann transport equation to determine the effective conductivity. It is shown that the hindering effect of the phonon pore scattering (due to reflection from the solid-pore interface) is significant for small pore size. Also, due to the dendritic structure of the pores, the hindering effect of the pore-network randomness is significant. The predictions are compared with the existing experiments and a good agreement is found.