  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.
