Two-temperature time-fractional model for electron-phonon coupled interfacial thermal transport

Abstract

This research investigates electron-phonon coupled thermal transport in heterogeneous systems under femtosecond laser pulses. A two-temperature time-fractional (2T-TF) model based on the Caputo fractional derivative is presented, which is validated against experimental data and two-temperature Boltzmann transport equation (2T-BTE) results. The 2T-TF model is demonstrated to be more accurate than the diffusive two-temperature (2T) model based on Fourier's law, while its complexity can be much lower than 2T-BTE simulations. Moreover, various forms of thermal resistances can be readily implemented to the 2T-TF model. Using multi-layer metal-nonmetal thin films as model systems, we demonstrate that our 2T-TF model can reliably predict electron-phonon coupled thermal transport across metal-metal and metal-nonmetal interfaces as well as electron cooling in the top metallic layer after ultrafast laser irradiation. The 2T-TF model can serve as a convenient and reliable tool for simulating electron-phonon coupled thermal transport in heterogeneous systems that are vastly seen in laser manufacturing and micro-/nano-electronic devices.