Thermal boundary conductance across metal-nonmetal interfaces: effects of electron-phonon coupling both in metal and at interface

We theoretically investigate the thermal boundary conductance across metal-nonmetal interfaces in the presence of the electron-phonon coupling not only in metal but also at interface. The thermal energy can be transferred from metal to nonmetal via three channels: (1) the phonon-phonon coupling at interface; (2) the electron-phonon coupling at interface; and (3) the electron-phonon coupling within metal and then subsequently the phonon-phonon coupling at interface. We find that these three channels can be described by an equivalent series-parallel thermal resistor network, based on which we derive out the analytic expression of the thermal boundary conductance. We then exemplify different contributions from each channel to the thermal boundary conductance in three typical interfaces: Pb-diamond, Ti-diamond, and TiN-MgO. Our results reveal that the competition among above channels determines the thermal boundary conductance.