Ultrafast dynamics of photoinjected electrons at the nonthermal regime in the intra- Γ -valley relaxation in InP studied by time- and angle-resolved photoemission spectroscopy

Abstract

We study ultrafast relaxation of photoinjected electrons confined within the \ensuremath{\Gamma} valley of InP, based on the transient electron distribution functions determined using time- and angle-resolved photoemission spectroscopy. To elucidate fundamental processes that lead to the quasithermalization of electron subsystem at the nonthermal regime of relaxation, the dynamics are investigated in two $p$-type samples with different doping levels, which exhibit different energy-relaxation rates of energetic electrons. In both samples, the photoinjected nonthermal-electron distributions are quasithermalized only at a finite time delay of several hundreds of femtoseconds. Although the magnitude of the time delay for quasithermalization depends on the initially prepared nascent electron distribution and on the energy-relaxation rates in different samples, the quasithermalization is established at the specific electron distribution of ensembles; electrons with a density of $\ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$ are condensed in the phase space characterized by the maximum energy of 0.27 eV and by the maximum wave vector of $0.09\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$. The essential features of quasithermalization observed in InP are the same as those recently reported for GaAs [Phys. Rev. B 104, 245201 (2021)], showing that the delayed quasithermalization is general for electrons photoinjected by ultrashort-laser excitation in the \ensuremath{\Gamma} valley of direct-gap semiconductors.