Hot-electron dynamics at Cu(100), Cu(110), and Cu(111) surfaces:mComparison of experiment with Fermi-liquid theory

Lifetimes of hot electrons in the 1.3–3.2-eV energy range at low index surfaces of Cu((100),(110),(111)) are measured by two-photon time-resolved photoemission spectroscopy with <10 fs resolution. Energy dependence of the lifetimes deviates from the (E-${\mathrm{E}}_{\mathrm{F}}$ ${)}^{\mathrm{-}2}$ functional form predicted by the standard Fermi-liquid theory for free-electron metals, but a qualitative agreement with the theory is obtained by calculating the e-e scattering times from the band structure of Cu. However, the magnitude of the calculated lifetimes, assuming Thomas-Fermi screening length, is still about six times smaller than the measured. The failure of the free-electron model in predicting the energy dependence and magnitude of the scattering times is attributed in part to d-band electrons, which have a maximum density at -2 eV and can participate both in scattering and screening of hot electrons. The measured lifetimes also show a modest dependence on the crystal face, which is not reproduced by the band-structure calculations. The origins of this anisotropy may include coherence effects in the excitation, anisotropies in the e-e scattering cross sections, a contribution from e-p scattering to the hot-electron decay, or differences in surface electronic structure.