Paper AS-MoM4
Rapid Calculation Method of the Voigt Function for Use in the Analysis of Photoelectron Spectroscopic Data

Monday, October 22, 2018, 9:20 am, Room 204

The basic shape of a photoelectron peak is Lorentzian, which is modified by instrumental and other factors, such as phonon broadening, to give a Gaussian contribution resulting in a peak shape that is a convolution of a Gaussian and a Lorentzian peak shape. The use of the correct peak shape is important in the analysis of photoelectron spectroscopic data. X-ray photoelectron spectra (XPS) from the core region often contain overlapping peaks which can be analyzed by fitting the experimental spectrum to a spectrum generated by the sum of a series of functions, each of which represent the individual peaks together with a background function.¹ XPS from the valence band region can be interpreted by calculating a spectrum from an appropriate model for the solid under study such as a band structure calculation, an approach which requires the inclusion of the photoelectron peak shape in order to correctly model the experimental spectrum.²

The Voigt function is a convolution of a Gaussian and Lorentzian and is the best representation for photoelectron peaks. Unfortunately the Voigt function cannot be represented directly as an analytical function and has to be evaluated numerically. Analytical functions were developed to approximate the Voigt function, and a number of so-called pseudo-Voigt functions have been developed. Analytical functions and their partial differentials can be calculated rapidly. One of the early pseudo-Voigt functions was a product function published by the author in 1979.³

The presentation will focus on how the true Voigt function can be rapidly calculated at speeds that are comparable to the calculation of pseudo-Voigt functions, with CPU times of a fraction of a second for complex curve fitting calculations on computers using Intel Core i7 processors.⁴ The approach is based on the extensive work on the Voigt function by the atmospheric sciences community. Examples will be provided showing the application of the true Voigt function to the curve fitting of experimental core XPS data and the modelling of experimental valence band XPS data.

Reference

1.P.M.A. Sherwood, J. Vacuum Sci. Technol.1996, A14, 1424.

2. P.M.A. Sherwood, J. Vacuum Sci. Technol.1997, A15, 520.

3. R.O.Ansell,T.Dickinson,A.F.Povey,and P.M.A.Sherwood, J. Electroanal. Chem. 1979, 98, 79.

4. P.M.A. Sherwood, submitted for publication.