Quantification of hard X‐ray photoelectron spectroscopy: Calculating relative sensitivity factors for 1.5‐ to 10‐keV photons in any instrument geometry

Abstract

A method for the rapid determination of theoretical relative sensitivity factors (RSFs) for hard X‐ray photoelectron spectroscopy (HAXPES) instruments of any type and photon energy has been developed. We develop empirical functions to describe discrete theoretically calculated values for photoemission cross sections and asymmetry parameters across the photon energy range from 1.5 to 10 keV for all elements from lithium to californium. The formulae describing these parameters, in conjunction with similar practical estimates for inelastic mean free paths, allow the calculation of a full set of theoretical sensitivity factors for a given X‐ray photon energy, X‐ray polarisation and instrument geometry. We show that the anticipated errors on these RSFs are less than the typical errors generated by extracting X‐ray photoelectron spectroscopy (XPS) intensities from the spectra and thus enable adequate quantification for any XPS/HAXPES experiment up to 10 keV. A spreadsheet implementation of this method is provided in the supporting information, along with example RSFs for existing commercial instruments.

Characterization of buried interfaces using Ga Kα hard X-ray photoelectron spectroscopy (HAXPES)

“…50 HAXPES with Ga Kα X-rays increases the XPS sampling depth to 27.9 nm for Ta using Mn 2p, 10 and the equivalent sampling depth through MnAl is estimated to be similar (33 nm), 10 meaning that the MnAl layer is easily measured. The sampling depth does not exceed the total film thickness, hence the calculated relative sensitivity factors for each core level, 4,31 assuming a ‘thick’ sample (thickness > sampling depth), may be used to accurately measure the atomic concentrations of Mn and Al in the thin film. For this material system, HAXPES is therefore an ideal probe of the atomic makeup of the thin films beneath a capping layer.…”

Spiers Memorial Lecture: prospects for photoelectron spectroscopy

“…7). 107,108 Until recently, any form of lab-based HAXPES has utilised conventional low-intensity, unfocussed X-ray sources (typically of the twin-anode type using 5.41 keV Cr Ka or 2.9 keV Ag La sources), making many HAXPES experiments inviable in reality as unrealistic counting times are needed. The need for a brilliant photon source, however, led to rapid development of the technique at synchrotron facilities in the last 20 years (such as the GALAXIES beamline at SOLEIL, I09 at Diamond, 9.3.1 at ALS and no fewer than 12 beamlines at SPring-8), which in general became rapidly oversubscribed.…”

“…107,[128][129][130] Initial work to produce RSFs has been carried out for both Ag La 131 and Ga Ka, 126 and a method of calculating reasonably accurate theoretical RSFs applicable to all instrument geometries and photon energies in the range 1.5-10 keV has been proposed. 108 The geometry chosen for HAXPES experiments also needs special consideration, as it is necessary to consider both the effect of X-ray polarisation, and the applicability of the dipole approximation within HAXPES. The divergence from a dipole emission distribution becomes more signicant as the X-ray energy increases, 129 and is signicant in the tender X-ray range.…”

Testing and validating the improved estimation of the spectrometer‐transmission function with UNIFIT 2022

“…Likewise, the cross sections calculated by Yeh and Lindau can be used. 28 Recently, theoretical cross section for HAXPES were published which can be adopted [29][30][31] Furthermore, the accuracy of the quantification can be increased by using effective attenuation lengths. 32 Like for the settings used for the estimation of the transmission functions, the photoionization cross sections and mean free paths used for the quantification are always a compromise between effort or time and the accuracy, which is needed for a reliable statement.…”