  Characteristic properties of secondary electrons emitted from irradiated
two-dimensional materials arise from multi-length and time-scale relaxation
processes that connect the initial non-equilibrium excited electron
distribution with their eventual emission. To understand these processes, which
are critical for using secondary electrons as high-resolution thermalization
probes, we combine first-principles real-time electron dynamics with modern
experiments. Our data for cold and hot proton-irradiated graphene shows
signatures of kinetic and potential emission and generally good agreement for
electron yields between experiment and theory. The duration of the emission
pulse is about 1.5 femtoseconds, indicating high time resolution when used as a
probe. Our newly developed method to predict kinetic energy spectra shows good
agreement with electron and ion irradiation experiments and prior models. We
find that lattice temperature significantly increases secondary electron
emission, whereas electron temperature has a negligible effect.
