Transmission function and thermal conductivity of Si phononic crystals

We investigate phonon transport properties of Si phononic crystals by using an atomistic Green function method. By varying form factors such as thickness, orientation, and pore size of unit cells, mean-free path and associated thermal conductivity of phononic crystals are obtained. We present the empirical formula for thermal conductivity as a function of cell size and, by extrapolating results from it for realistic cell sizes, the thermal conductivity is compared with experimental ones. The formula is found to predict a nearly equal amount of the suppression in thermal conductivity to the experimental values, implying a feasible calculation method for predicting thermal properties of phononic crystals.