Mean free path dependent phonon contributions to interfacial thermal conductance

Interfacial thermal conductance as an accumulation function of the phonon mean free path is rigorously derived from the thermal conductivity accumulation function. Based on our theoretical model, the interfacial thermal conductance accumulation function between Si/Ge is calculated. The results show that the range of mean free paths (MFPs) for phonons contributing to the interfacial thermal conductance is far narrower than that for phonons contributing to the thermal conductivity. The interfacial thermal conductance is mainly contributed by phonons with shorter MFPs, and the size effects can be observed only for an interface constructed by nanostructures with film thicknesses smaller than the MFPs of those phonons mainly contributing to the interfacial thermal conductance. This is why most experimental measurements cannot detect size effects on interfacial thermal conductance. A molecular dynamics simulation is employed to verify our proposed model.