Space-charge effects in high-energy photoemission

Abstract

Pump-and-probe photoelectron spectroscopy (PES) with femtosecond pulsed sources opens new perspectives in the investigation of the ultrafast dynamics of physical and chemical processes at the surfaces and interfaces of solids. Nevertheless, for very intense photon pulses a large number of photoelectrons are simultaneously emitted and their mutual Coulomb repulsion is sufficiently strong to significantly modify their trajectory and kinetic energy. This phenomenon, referred as space-charge effect, determines a broadening and shift in energy for the typical PES structures and a dramatic loss of energy resolution. In this article we examine the effects of space charge in PES with a particular focus on time-resolved hard X-ray (∼10 keV) experiments. The trajectory of the electrons photoemitted from pure Cu in a hard X-ray PES experiment has been reproduced through N-body simulations and the broadening of the photoemission core-level peaks has been monitored as a function of various parameters (photons per pulse, linear dimension of the photon spot, photon energy). The energy broadening results directly proportional to the number N of electrons emitted per pulse (mainly represented by secondary electrons) and inversely proportional to the linear dimension a of the photon spot on the sample surface, in agreement with the literature data about ultraviolet and soft X-ray experiments. The evolution in time of the energy broadening during the flight of the photoelectrons is also studied. Despite its detrimental consequences on the energy spectra, we found that space charge has negligible effects on the momentum distribution of photoelectrons and a momentum broadening is not expected to affect angle-resolved experiments. Strategy to reduce the energy broadening and the feasibility of hard X-ray PES experiments at the new free-electron laser facilities are discussed

Multidimensional photoemission spectroscopy—the space-charge limit

“…Electrons with kinetic energies of 1000, 120 and 16 eV pass this distance in 3, 9 and 24 ns, respectively; a time scale much longer than that of figure 3. The simple model of a spherical electron cloud in the field of a point-symmetric capacitor [6] predicts the same magnitude of spacecharge shift and broadening as a true multi-particle simulation [7]. In the latter theoretical paper and experimental data using a HHG source [8] shift and broadening have approximately the same value.…”

“…Given the present state of knowledge it is not possible to directly compare these results with previous work using dispersive spectrometers [1][2][3][4][5][6][7][8][9]. In a cathode lens we have the special behaviour of trajectories of fast and slow electrons as sketched in figure 3, whereas in conventional spectroscopy the electrons travel for typically 60 mm in the field-free region in front of the sample.…”

“…A quantitative estimation of the space-charge limit for dispersive spectrometers in comparison with that of cathode-lens instruments would require comparative measurements at similar conditions; this was not intended in the present work. In particular, the positive sample bias for rapid redirecting of the secondaries as mentioned in [7] and our high-pass cutoff in the objective lens have both not been explored yet.…”

“…The high density of electrons released by intense, short photon pulses in a small area on the sample leads to significant Coulomb interaction, which alters the energy and angular distribution and sets the ultimate limit to the performance of photoemission experiments. Depending on the number of electrons in the cloud and their spatio-temporal distribution, this effect can deteriorate the photoelectron spectra dramatically [1][2][3][4][5][6][7][8][9][10][11].…”

“…In photoemission, the major contribution to space-charge induced energy shifts stems from the large number of secondary electrons. Intense clouds of slow electrons can also occur in pump-and-probe experiments when the pump laser gives rise to multiphoton photoemission [5][6][7][8][9][10]. The coexistence of a small number of fast photoelectrons with a large number of slow electrons (from the secondary cascade or generated by a pump laser) leads to a specific behaviour due to the different longitudinal and transversal momentum components of the two species.…”