Thermal transport across transfer printed metal-dielectric interfaces: Influence of contact mechanics and nanoscale energy transport

Recent experiments suggest that the interfacial thermal conductance of transfer printed metal-dielectric interfaces is ~45 MW/m2K at 300K, approaching that of interfaces formed using physical vapor deposition. In this work, we investigate this anomalous result using a combination of theoretical deformation mechanics and nanoscale thermal transport. We establish that the plastic deformation and the capillary forces lead to significantly large fractional areal coverage of ~0.2 which enhances the thermal conductance. At the microscopic transport scale, existing models that account for the electron-phonon non-equilibrium at the interface employ a phonon thermal conductivity that is difficult to estimate. We remove this difficulty by obtaining the conductance directly from the Bloch-Boltzmann-Peierls formula, describing the matrix element using a deformation potential that can be estimated from the electrical resistivity data. We report calculations up to 500 K to show that electron-phonon coupling is not a major contributor to the thermal resistance across metal-dielectric interfaces. Our analysis of the thermal conductance based on the consideration of both deformation mechanics and nanoscale thermal transport yields a conductance that is on the same order of magnitude (~10 MW/m2K) as the experimental data and partially follows the temperature trend. There remains a quantitative discrepancy between data and theory that is not explained through deformation of the interface alone. We suggest that capillary bridges formed in the small asperities may account for this discrepancy. A preliminary analysis shows this to be plausible based on available data. Our work advances the understanding of the role of electron-phonon coupling in limiting thermal transport near metal-dielectric interfaces and shows that, in terms of heat flow characteristics, metallic interconnects formed using transfer printing are comparable to ones formed using vapor deposition