Non-Equilibrium Heat Transport of Metal-Insulator Superlattice Considering Electron-Phonon Coupling near the Interface

In recent years, energy harvesting technology using thermoelectric conversion has attracted attention as a power source for IoT and wearable devices. To improve the thermoelectric conversion efficiency, a popular approach has been to reduce the thermal conductivity by utilizing the size effect of phonon transport in nanostructures such as polycrystalline, superlattice, and thin film. While more mechanism that reduces thermal conductivity in addition to phonon scattering is needed, an idea has been to utilize metallic/dielectric interface, where the heat carrier needs to change between electron and phonon (electron-phonon coupling, EPC) and the non-equilibrium in the vicinity of interface (non-equilibrium region) gives rise to additional thermal resistance. Although the phenomenon has been discussed for single interface, a system that can probe the length scale of the non-equilibrium region would help us gain further understanding in the characteristics of the non-equilibrium electron-phonon coupled transport and its impact to thermal conductivity. Here we study metal/dielectric superlattice structure, where the distance between the multiple interfaces can be systematically with respect to the non-equilibrium length scale.<br/>We measure the thermal conductivity of the metal/insulator superlattice using the time-domain thermoreflectance method (TDTR) and evaluate the effect of the imbalance between electron and phonon on the heat conduction. The metal/insulator superlattice samples with two types of structure (Type I and II) composed of three different kinds of metal layers (gold silicon alloy, tantalum, copper) and MgO (AuSi/MgO, Ta/MgO, Cu/MgO superlattice) are prepared considering their different EPC strengths. In Type I structures, both metal and insulator layers have the same thickness, and the unit layer thickness is varied. In Type II structure, the total thickness of metal and insulator unit layers is fixed to 20 nm, and the thickness of metal (and insulator) unit layer is varied. The thermal conductivity of Type I superlattices decreases as the unit layer thickness decreases. On the other hand, the thermal conductivity of Type II superlattices decreases as the metal layer thickness increases in AuSi/MgO and Cu/MgO superlattices but is independent of the thickness for Ta/MgO superlattice.<br/>To get further insights of the effect of EPC near the interface on the heat conduction in the above experimental systems, we performed analysis with the two-temperature model (TTM) and the thermal resistance circuit (TRC) based on thermal properties of Ta, Au, Cu and MgO derived from first-principles calculation (electron and phonon thermal conductivity and electron-phonon coupling factor). In TRC, total thermal resistance of the superlattice is calculated from thermal conductivity of metal, which considers electron and phonon channel in the metal layer as a parallel thermal resistance, and MgO layer and thermal boundary conductance (TBC) between metal and MgO. In TTM, thermal resistance caused by EPC is additionally considered as a thermal resistance to electron channel in the metal layer. Thermal boundary conductance (TBC) between the metal and MgO is obtained from a reference experiment, which minimizes the gap between experimental and estimated thermal conductivity from TTM.<br/>The estimated thermal conductivity obtained from both TRC and TTM fits well to the experimental results of Ta/MgO superlattices, where EPC is strong, while only TTM fits well to those of AuSi/MgO and Cu/MgO superlattices, where EPC is weak. This indicates that a significant role of the non-equilibrium region to thermal conductivity in the AuSi/MgO and Cu/MgO superlattices. The analysis also finds that the impact of the nonequilibrium region depends on the thickness of the metal unit layer, and thus successfully probes the length scale of the phenomenon.