Electron-phonon coupling and non-equilibrium thermal conduction in ultrafast heating systems

The electron-phonon coupling in ultrafast heating systems is studied within the framework of Boltzmann transport equation (BTE) with coupled electron and phonon transport. To directly solve the BTE, a discrete unified gas kinetic scheme is developed, in which the electron/phonon advection, scattering and electron-phonon interactions are coupled together within one time step by solving the BTE at the cell interface. Numerical results show that the present scheme can correctly predict the electron-phonon coupling constant, and is in excellent agreement with typical two-temperature model (TTM) and experimental results in existing literatures and our home-made time-domain thermoreflectance technique in ultrafast laser heating problem. In the transient thermal grating (TTG) geometry, the present scheme not only recovers the TTM in the diffusive regime, but also captures the ballistic and thermal wave effects when the characteristic length is comparable to or smaller than the mean free path where the TTM fails. More interestingly, an unexpected heat flow from phonon to electron is predicted in both the ballistic and diffusive regimes in the TTG geometry. It results from the competition of the thermal diffusivity and electron-phonon coupling in the diffusive regime, and in the ballistic regime it results from the competition of the phonon/electron advection and electron-phonon coupling.