We point out that the effective channel for the interfacial thermal conductance, the inverse of Kapitza resistance, of metal-insulator/semiconductor interfaces is governed by the electron-phonon interaction mediated by the surface states allowed in a thin region near the interface. Our detailed calculations demonstrate that the interfacial thermal conductance across Pb/Pt/Al/Au-diamond interfaces are only slightly different among these metals, and reproduce well the experimental results of the interfacial thermal conductance across metal-diamond interfaces observed by Stoner et al. [Phys. Rev. Lett. 68, 1563 (1992)] and most recently by Hohensee et al. [Nature Commun. 6, 6578 (2015)].
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