Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning

Phononic crystals (PnCs) are the acoustic wave equivalent of photonic crystals, where a periodic array of scattering inclusions located in a homogeneous host material causes certain frequencies to be completely reflected by the structure. In conjunction with creating a phononic band gap, anomalous dispersion accompanied by a large reduction in phonon group velocities can lead to a massive reduction in silicon thermal conductivity. We measured the cross plane thermal conductivity of a series of single crystalline silicon PnCs using time domain thermoreflectance. The measured values are over an order of magnitude lower than those obtained for bulk Si (from 148 W m^-1 K^-1 to as low as 6.8 W m^-1 K^-1). The measured thermal conductivity is much smaller than that predicted by only accounting for boundary scattering at the interfaces of the PnC lattice, indicating that coherent phononic effects are causing an additional reduction to the cross plane thermal conductivity.