Fig. 2: Temporal information of ultrafast hot-electron emission from graphene.

a Fermi-Dirac distribution (f(E)) at different electron temperatures. b Electron occupation as a function of energy above the Dirac point at different temperatures. Electrons with energies above the work function (\(\phi\)) can escape from graphene for electron emission. c Temperature evolution after ~180 fs pulsed laser excitation. The electron temperature (T_e) increases within 100 fs time scale and quickly reaches equilibrium with phonons (T_ph). d Calculated ultrafast hot-electron emission pulse width in graphene. Based on the evolution of the hot-electron temperature, the time-resolved photoemission current can be calculated to have a full width at half maximum (FWHM) of ~85 fs. e Time-resolved autocorrelation of the photoemission current in graphene. Under pulsed laser excitation (~180 fs, 800 nm, 18 mW), two dynamic lifetimes (~60 fs and ~800 fs, faster one is defined as \({{\tau }}_{{e}}\)) can be derived from the decay part of the intensity behavior by exponential fitting. f Derived electron emission lifetimes for different excitation pulse widths. The test data with ~180 fs and ~40 fs excitations well matches the calculations. The error bars are from autocorrelation decay fitting standard error. Data in (e) together with derived data (180 fs laser pulse width in (f)) is obtained under 800 nm excitation within optical fiber. The 40 fs excitation data point in (f) is obtained under 800 nm excitation via free-space focusing.