Rapid evaluation of the Voigt function and its use for interpreting X-ray photoelectron spectroscopic data

While the Voigt function is recognized as the best function to represent the photoelectron spectroscopic process, it is less frequently used because it cannot be represented as an analytical function and thus has to be evaluated numerically. This paper shows how the true Voigt function can be calculated rapidly with approximately the same speed as pseudo-Voigt functions by using approaches that have been used by the astronomical sciences community. The Voigt function is calculated using code previously published by Wells. The paper describes a method for calculating the function to generate photoelectron peaks for curve fitting X-ray photoelectron spectroscopic data. An appendix is provided with the listing of a Fortran 90 program which uses the subroutine HUMDEV published by Wells. Examples of using this approach for the fitting of experimental core X-ray photoelectron spectroscopic data are presented, and the fits compared with fits using a pseudo Voigt product function. The use of the true Voigt function in the calculation of spectra in the core and valence band region is also described and illustrated by comparing the calculated spectra with experimental spectra.