A detailed view of the Gaussian–Lorentzian sum and product functions and their comparison with the Voigt function

Abstract

The Gaussian–Lorentzian sum (GLS) and product (GLP) functions remain important in X‐ray photoelectron spectroscopy (XPS) peak fitting. Here, we present a detailed view of these functions, comparing them with each other and with the Voigt function (the “LA(m)” function). First, we show the GLS, GLP, and LA(m) functions as a function of their mixing parameters, m, which reveals differences between them. We then illustrate the use of these functions to fit a series of spectra acquired at different pass energies (resolutions). Next, we show the underlying Gaussian and Lorentzian components of a series of GLS and GLP functions as a function of m, which confirms that the GLS is a simple linear combination of Gaussian and Lorentzian functions. However, one of the two functions used to make the GLP can be very wide, that is, at its extremes, one of these functions has infinite width. We then discuss a plot of the areas of the GLS, GLP, and LA(m) functions as a function of m, which reveals the expected, linear increase in area of the GLS, but nonlinear changes in the areas of the other two functions. Finally, to better understand them, we fit these functions to each other. These results indicate that the GLS and GLP better match the LA(m) function at lower and higher values of the mixing parameter, respectively.