Intensity-energy response function of Al/Cr-Kα x-ray photoemission instruments: An inter-laboratory study

The question of the intensity-energy response of photoemission spectrometers has been approached through a round-robin involving 13 instruments working with low (Al/Mg-K$\alpha$) and high (Cr-K$\alpha$) energy photon sources. An algorithm based on the analysis of inelastic background previously proposed [S. Guilet et al., J. Electron Spectrosc. Relat. Phenom. 285 (2022) 147225)] was intensively tested against calibrated Al/Mg-K$\alpha$ instruments and calculated relative sensitivity factors (RSFs) over the 15 core level peaks of coinage metals (Ag, Au, Cu). In both cases, the linear correlation within $\pm 10$ %, over two orders of magnitude in intensity and for kinetic energies ranging from $\sim 400$ to $1400\mathrm{eV}$, showed the consistency of the approach. All the contributions to RSFs (e.g. non-dipolar terms in the photo-ionization cross section, elastic scattering effects, surface excitations, beam polarization by the monochromator) were critically reviewed and taken into account using the state-of-the-art modellings and databases. Strong variations were evidenced among instruments, regarding not only the response functions, but also the theoretical RSFs due to different measurement geometries. For the Cr-K$\alpha$ hard x-ray instruments, the same analysis was performed with a set of different materials (Al, Si, Ge, Fe, Co, Ni, Cu, Zn, Nb, Mo, Ag, W, Au). A $\pm 10$ % satisfactory agreement against theoretical RSFs over 69 core levels spanning a large kinetic energy range (300–4000 eV) could be achieved with a common response function. Despite limitations that are reviewed, this work opens interesting perspectives for a systematic calibration of photoemission instruments.