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Noble-metal nanoparticles for photocatalysis have become a major research object in recent years due to their plasmon-enhanced strong light-matter interaction. The dynamics of the hot electrons in the noble metal are crucial for the efficiency of the photocatalysis and for the selective control of reactions. In this work, we present a kinetic description of the non-equilibrium electron distribution created by photoexcitation, based on full energy-resolved Boltzmann collision integrals for the laser excitation as well as for the electron-electron thermalization. The laser-induced electronic non-equilibrium and the inherently included secondary electron generation govern the dynamics of non-thermal electrons. Applying our method to gold, we show a significant dependence of hot electron dynamics on kinetic energy. Specifically, the timescales of the relaxation as well as the qualitative behavior are depending on the evaluated energy window. During the thermalization processes there are cases of increasing electron density as well as of decreasing electron density. Studying the influence of excitation parameters, we find that the photon energy and the fluence of the exciting laser can be tuned to influence not only the initial excitation but also the subsequent characteristics of the time-resolved electronic spectral density dynamics. The electronic thermalization including secondary electron generation leads to time-dependent spectral densities which differ from their specific final equilibrium values for picoseconds after irradiation ended.

We investigate a temperature-based model, called extended two-temperature model (eTTM), that describes the electronic non-equilibrium and its effect on energy dissipation in metals after ultrashort laser excitation. We derive and discuss improvements in comparison to published versions of this model [E. Carpene, Phys. Rev. B 2006, 74, 024301; G. Tsibidis, Appl. Phys. A 2018, 124, 311]. The comparison of the results of the eTTM with results of the well-known two-temperature model (TTM) shows a delayed increase of the electronic temperature when being calculated with the eTTM. We find a good agreement in the non-equilibrium energy distribution after absorption of photons with results from a kinetic description using a Boltzmann collision term. The model provides a convenient tool for fast calculation of features of the non-equilibrium electrons. As an example we inspect the dynamics of high-energy electrons observable in photo-electron spectroscopy and demonstrate the advantage of the eTTM over the conventional two-temperature model., Comment: 14 pages, 8 figures (including 3 double figures)