Metal/dielectric thermal interfacial transport considering cross-interface electron-phonon coupling: Theory, two-temperature molecular dynamics, and thermal circuit

The standard two-temperature equations for electron-phonon coupled thermal transport across metal/nonmetal interfaces are modified to include the possible coupling between metal electrons with substrate phonons. The previous two-temperature molecular dynamics (TT-MD) approach is then extended to solve these equations numerically at the atomic scale, and the method is demonstrated using Cu/Si interface as an example. A key parameter in TT-MD is the nonlocal coupling distance of metal electrons and nonmetal phonons, and here we use two different approximations. The first is based on Overhauser’s “joint-modes” concept, while we use an interfacial reconstruction region as the length scale of joint region rather than the phonon mean-free path as in Overhauser’s original model. In this region, the metal electrons can couple to the joint phonon modes. The second approximation is the “phonon wavelength” concept where electrons couple to phonons nonlocally within the range of one phonon wavelength. Compared with the original TT-MD, including the cross-interface electron-phonon coupling can slightly reduce the total thermal boundary resistance. Whether the electron-phonon coupling within the metal block is nonlocal or not does not make an obvious difference in the heat transfer process. Based on the temperature profiles from TT-MD, we construct a new mixed series-parallel thermal circuit. We show that such a thermal circuit is essential for understanding metal/nonmetal interfacial transport, while calculating a single resistance without solving temperature profiles as done in most previous studies is generally incomplete. As a comparison, the simple series circuit that neglects the cross-interface electron-phonon coupling could overestimate the interfacial resistance, while the simple parallel circuit in the original Overhauser’s model underestimates the total interfacial resistance.