Critical angle for interfacial phonon scattering: Results from ab initio lattice dynamics calculations

Thermal boundary resistance is a critical quantity that controls heat transfer at the nanoscale, which is primarily related to interfacial phonon scattering. Here, we combine lattice dynamics calculations and inputs from first principles ab initio simulations to predict phonon transmission at the Si/Ge interface as a function of both the phonon frequency and the phonon wavevector. This technique allows us to determine the overall thermal transmission coefficient as a function of the phonon scattering direction and frequency. Our results show that the thermal energy transmission is highly anisotropic, while thermal energy reflection is almost isotropic. In addition, we found the existence of a global critical angle of transmission beyond which almost no thermal energy is transmitted. This critical angle around 50 degrees is found to be almost independent of the interaction range between Si and Ge, the interfacial bonding strength, and the temperature above 30 K. We interpret these results by carrying out a spectral and angular analysis of the phonon transmission coefficient and differential thermal boundary conductance.