Nondiffusive electron transport in metals: A two-temperature Boltzmann transport equation analysis of thermoreflectance experiments

We develop a theoretical framework based on the electron-phonon coupled Boltzmann transport equations (BTEs) for the interpretation of nondiffusive thermal conductivity measurements in metals made via frequency domain thermoreflectance (FDTR). The thermal conductivity of a bulk gold crystal was measured over a temperature range of 23--304 K as a function of FDTR's laser spot size. Our interpretation of these measurements by a two-temperature heat diffusion model finds that the thermal conductivity is suppressed when the laser spot size is comparable to electron mean free paths. Using a simplified spherical geometry that enables analytical solutions, we compare the two-temperature diffusion model with the coupled BTEs to identify a thermal conductivity suppression function. We also conclude that over the timescales of our experiment electron-phonon nonequilibrium is negligible, but that the length scale of heat deposition by hot electrons critically influences our interpretation.