  In this work, we use a combination of first-principles calculations under the
density functional theory framework and heat transport simulations using the
atomistic Green's function (AGF) method to quantitatively predict the
contribution of the different scattering mechanisms to the thermal interface
conductance of epitaxial CoSi$_2$-Si interfaces. An important development in
the present work is the direct computation of interfacial bonding from density
functional perturbation theory (DFPT) and hence the avoidance of commonly used
`mixing rules' to obtain the cross-interface force constants from bulk material
force constants. Another important algorithmic development is the integration
of the recursive Green's function (RGF) method with B\"{u}ttiker probe
scattering that enables computationally efficient simulations of inelastic
phonon scattering and its contribution to the thermal interface conductance.
First-principles calculations of electron-phonon coupling reveal that
cross-interface energy transfer between metal electrons and atomic vibrations
in the semiconductor is mediated by delocalized acoustic phonon modes that
extend on both sides of the interface, and phonon modes that are localized
inside the semiconductor region of the interface exhibit negligible coupling
with electrons in the metal. We also provide a direct comparison between
simulation predictions and experimental measurements of thermal interface
conductance of epitaxial CoSi$_2$-Si interfaces using the time-domain
thermoreflectance technique. Importantly, the experimental results, performed
across a wide temperature range, only agree well with predictions that include
all transport processes: elastic and inelastic phonon scattering,
electron-phonon coupling in the metal, and electron-phonon coupling across the
interface.
