Space-charge effect in electron time-of-flight analyzer for high-energy photoemission spectroscopy

Abstract

The space-charge effect, due to the instantaneous emission of many electrons after the absorption of a single photons pulse, causes distortion in the, photoelectron energy spectrum. Two calculation methods have been applied to simulate the expansion during a free flight of clouds of mono- and bi-energetic electrons generated by a high energy pulse of light and their results have been compared. The accuracy of a widely used tool, such as SIMION (R), in predicting, the energy distortion caused by the space-charge has been tested and the reliability of its results is verified. Finally we used SIMION (R) to take into account the space-charge effects in the simulation of simple photoemission experiments with a time-of-flight analyzer. (C) 2016 Elsevier B.V. All rights reserved

Photoemission from the gas phase using soft x-ray fs pulses: An investigation of the space-charge effects

“…Simulations of the deterministic effects are usually carried out following the trajectories as a function of time of a limited number of particles and apportioning the total charge of the electron cloud among the considered trajectories. The use of advanced softwares like SIMION R , based on the solution of the Laplace's equation, allowed to include the space-charge effects in the simulation of the motion of the photoelectrons inside a time-of-flight (TOF) spectrometer [4,50,51]. Long, Itchkawitz and Kabler proposed more than twenty years ago a model to predict the deterministic contribution to the energy broadening of the PES structures.…”

“…Hellmann et al [46] were the first to propose a N-body simulation scheme based on the Barnes-Hut algorithm [54], in which the trajectories of the N photoelectrons (representing the photoelectron cloud generated by a single pulse) are determined with an approximate calculation of the force acting on each particle and by performing a leapfrog integration of the equations of motion of each electron. This method requires the use of the Treecode software [55] with slight modifications [46,52] and has been applied to successfully reproduce the space-charge effects observed in numerous measurements [19,37,42,45,46,56] as well as for a feasibility study of future experiments [51,52]. Experiments and simulations were also carried out to study the contribution to the space charge from the photoelectrons generated by the optical or near ultraviolet pump radiation via multiphoton processes and its dependence on the delay time between the pump and probe pulses [37,44,45,56].…”

“…Nevertheless, the method of a full-spectrum N-body simulation of PES experiments has not been yet explored. Most of the calculations reported in literature for the photoemission from solid surfaces are focused on studying the space-charge effects on a single specific structure (a core level or the valence band), assuming for the secondary electrons a rude rectangular energy distribution [19,42,46] or a delta-function distribution [51,52] and neglecting the contribution of the higher-energy photoelectrons (other photoemission structures and inelastically scattered electrons). It must be said that a PES experiment from a solid sample is not the easiest test to attempt a full-spectrum simulation.…”

The influence of x-ray pulse length on space-charge effects in optical pump/x-ray probe photoemission

“…Several analytic [14] and numerical models, e.g. simulations of the electron cloud expansion with ASTRA [10], tree-code [15] or SIMION [16], have been used to quantify SC-effects for different initial electron distributions.…”