Transient thermal and nonthermal electron and phonon relaxation after short-pulsed laser heating of metals

Abstract

Several dynamic thermal and nonthermal scattering processes affect ultrafast heat transfer in metals after short-pulsed laser heating. Even with decades of measurements of electron-phonon relaxation, the role of thermal vs. nonthermal electron and phonon scattering on overall electron energy transfer to the phonons remains unclear. In this work, we derive an analytical expression for the electron-phonon coupling factor in a metal that includes contributions from equilibrium and nonequilibrium distributions of electrons. While the contribution from the nonthermal electrons to electron-phonon coupling is non-negligible, the increase in the electron relaxation rates with increasing laser fluence measured by thermoreflectance techniques cannot be accounted for by only considering electron-phonon relaxations. We conclude that electron-electron scattering along with electron-phonon scattering have to be considered simultaneously to correctly predict the transient nature of electron relaxation during and after short-pulsed heating of metals at elevated electron temperatures. Furthermore, for high electron temperature perturbations achieved at high absorbed laser fluences, we show good agreement between our model, which accounts for d-band excitations, and previous experimental data. Our model can be extended to other free electron metals with the knowledge of the density of states of electrons in the metals and considering electronic excitations from non-Fermi surface states.