Mechanism of Coherence Heat Conduction in Phononic Crystal

Heat in phononic crystals (PnCs) are carried by phonons, which can be divided to coherent (wave-like) and incoherent (particle-like) phonons. Many experiments have demonstrated reduction of thermal conductivity by PnCs at room temperature, however, comparison with theories suggest that it can be explained by surface and boundary scatterings, which not only backscatter phonons but also break their coherence. The logic here is that since average phonon wavelength at room temperature is only a few nanometers, the roughness at the surfaces and boundaries make the scattering diffusive (break the phase coherence of phonons), and thus only very long wavelength (low frequency) phonons with negligible contribute to total thermal conductivity remains coherent. Here, we will theoretically show that in a thin film PnCs, the low-frequency coherent phonons could significantly contribute to thermal conductivity when assuming Klemens model for intrinsic scattering due to low dimensional nature of those phonons. Yet, further analysis shows the contribution of the low frequency coherent phonons are still negligible due to Akhieser damping.