Galore: Broadening and weighting for simulation of photoelectron spectroscopy

Abstract

Licence Authors of papers retain copyright and release the work under a Creative Commons Attribution 4.0 International License (CC-BY). Galore simplifies and automates the process of simulating photoelectron spectra from ab initio calculations. This replaces the tedious process of extracting and interpolating cross-sectional weights from reference data and generates tabulated data or publication-ready plots as needed. The broadening tools may also be used to obtain realistic simulated spectra from a theoretical set of discrete lines (e.g. infrared or Raman spectroscopy). Photoelectron spectroscopy Photoelectron spectroscopy (PES) is a family of methods used to characterise the chemical nature and electronic structure of materials. PES is based on the photoelectric effect, which was discovered by Hertz. 1 It was explored extensively by Rutherford and colleagues 2 and within a few years researchers including de Broglie 3 and Robinson 4 were using the technique to measure electron binding energies through the relationship E k = hν − E B. Photons with energies hν ranging from 5 eV up to 12 keV eject electrons (referred to as "photoelectrons") from the occupied orbitals of a sample. The kinetic energy E k of each photoelectron therefore depends on its binding energy E B. The names of various PES methods refer to the photon energy range used: • ultraviolet photoelectron spectroscopy (UPS): 5-100 eV • X-ray photoelectron spectroscopy (XPS): 0.3-2 keV • hard X-ray photoelectron spectroscopy (HAXPES, HE-PES, HXPS, HX-PES): above 2 keV These methods generate spectra that are directly related to the electronic density of states (DOS), a distribution which is routinely calculated in ab initio materials chemistry. When comparing the computed DOS with a PES measurement, it is often possible to identify general peak agreement simply by reversing the energy scale (i.e. replacing negative or-bital energies with positive binding energies), applying a little broadening, and shifting the energy values to account for different references. This approach has been applied succesfully where peak positions are of interest. 5,6 Broadening is generally applied by convolution with a Gaussian and/or Lorentzian function: intrinsic lifetime broadening causes a Lorentzian energy distribution of the photoelectrons, while instrumental factors, including the width of the X-ray source and analyser resolution, give rise to a Gaussian line shape. Franck-Condon phonon broadening is caused by relaxation of atomic positions in response to creation of a photohole, as well as thermal population of vibrationally excited states before photoionisation, and gives around 0.8 eV Gaussian broadening in metal oxides. 7-9 Jackson et al., (2018). Galore: Broadening and weighting for simulation of photoelectron spectroscopy. Journal of Open Source Software, 3(26), 773. https://doi.org/10.21105/joss.00773 1