Ultrafast nonequilibrium dynamics of electrons in metals

Approximate analytic solutions for the athermal relaxation and diffusion of carriers in free-electron metals excited by ultrashort optical pulses are derived. The energy-loss time of the electrons is shown to be $\sim {\tau }_0^{1/3}{\tau }_S^{2/3},$ where ${\tau }_0$ and ${\tau }_S$ are characteristic electron-electron and electron-phonon scattering times. By evaluating the average excess energy per excitation we are able to establish an approximate criterion for the time of transition from an athermal electron distribution to a thermalized distribution. We thus demonstrate how one can calculate the evolution of the total energy and number densities of the nonequilibrium electrons at a given point in the metal, linking the athermal to the thermalized regime by interpolation. Quantitative agreement of the theory with some recent experiments on hot electrons in metals is good.