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

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.