Local Nonequilibrium Electron Transport in Metals after Femtosecond Laser Pulses: A Multi-Temperature Hyperbolic Model

ABSTRACT The trend toward miniaturization of electronic devices has increased the interest in nano scale heat transport, particularly, in laser-excited solids where electron–electron thermalization and electron-phonon coupling play a key role. Using a multi-temperature hyperbolic model, which takes into account the coupling between initially non-thermalized electrons and different phonon branches, we obtain a hierarchy of heat conduction equations for the electron temperature, which arises due to multi-length and time scales nature of coupling between different excitations. The hierarchy predicts that the ultrashort laser pulse induces a multi-front temperature wave propagating into the bulk of the material, which includes various heat transport regimes, ranging from the ballistic motion of the initially non-thermalized electrons propagating on the shortest time scale without interaction with the lattice as a temperature discontinuity, to the continuous wave-like temperature fronts arising on the intermediate time scale due to coupling between various excitations, and eventually to the classical Fourier transport on the longest time scale. The model is expected to be useful for modeling heat wave propagation phenomena in heterostructures and metamaterials.