An apparatus for sub-nanosecond time-resolved ambient-pressure X-ray photoelectron spectroscopy studies with pulsed and constant wave X-ray light sources is presented. A differentially pumped hemispherical electron analyzer is equipped with a delay-line detector that simultaneously records the position and arrival time of every single electron at the exit aperture of the hemisphere with ∼ 0.1 mm spatial resolution and ?150 ps temporal accuracy. The kinetic energies of the photoelectrons are encoded in the hit positions along the dispersive axis of the two-dimensional detector. Pumpprobe time-delays are provided by the electron arrival times relative to the pump pulse timing. An average time-resolution of (780 ± 20) ps (FWHM) is demonstrated for a hemisphere pass energy Ep = 150 eV and an electron kinetic energy range KE = 503-508 eV. The time-resolution of the setup is limited by the electron time-of-flight (TOF) spread related to the electron trajectory distribution within the analyzer hemisphere and within the electrostatic lens system that images the interaction volume onto the hemisphere entrance slit. The TOF spread for electrons with KE = 430 eV varies between ∼ 9 ns at a pass energy of 50 eV and ∼1 ns at pass energies between 200 eV and 400 eV. The correlation between the retarding ratio and the TOF spread is evaluated by means of both analytical descriptions of the electron trajectories within the analyzer hemisphere and computer simulations of the entire trajectories including the electrostatic lens system. In agreement with previous studies, we find that the by far dominant contribution to the TOF spread is acquired within the hemisphere. However, both experiment and computer simulations show that the lens system indirectly affects the time resolution of the setup to a significant extent by inducing a strong dependence of the angular spread of electron trajectories entering the hemisphere on the retarding ratio. The scaling of the angular spread with the retarding ratio can be well approximated by applying Liouville's theorem of constant emittance to the electron trajectories inside the lens system. The performance of the setup is demonstrated by characterizing the laser fluence-dependent transient surface photovoltage response of a laser-excited Si(100) sample.
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