Ultrafast relaxation dynamics of highly excited hot electrons in silicon

Ultrafast relaxation dynamics of hot electrons with excess energies exceeding 1 eV in Si is studied using time-resolved photoemission spectroscopy and ab initio calculations. Experimentally, the photoemission peaks from hot electrons excited in bulk electronic states along the Γ−L and Γ−X directions with excess energy (Eex) 1.1–3.2 eV with respect to the conduction band minimum are identified, and the time constants that characterize the decay of transient populations are determined. The decay time, which is 30±3fs at Eex=3.0eV and increases to 115±5fs at Eex=1.1eV, has the same scaling with Eex irrespective of the location of hot electrons in the Brillouin zone. The calculations show that the momentum scattering time due to electron-phonon coupling is shorter than 10 fs for Eex larger than 1.5 eV, being too short to be measured. The combination of theoretical and experimental results reveals that hot electrons with high excess energy in Si are transformed into hot-electron ensembles quasiequilibrated only in momentum space by the ultrafast momentum scattering, and that the experimentally determined time constant of population decay corresponds to the energy relaxation taking place as a whole on a time scale ten times longer than that of the momentum relaxation. The detailed methodology of the analysis of experimental data which we provide in this work, as well as our conclusions which concern the relaxation dynamics of electrons with Eex exceeding 1 eV in Si, can be applied to interpret hot-carrier relaxation phenomena in a wide range of semiconducting materials.