There are several good software for fitting XPS data. Before going into detail about fitting softwares, let me remind you a sound principle : the fitting results can be as good as the data is. There is no way you can get good fit with bad data (data is bad either because the acquisition conditions were not adequate or, worse, because the sample was bad). Contrary to what have you seen in recent Hollywood movies – where from a poor low resolution video, a smart tech person after 400 % zoom, does some fancy data enhancement procedure in order to see the face of the criminal- zooming and data treatement of poor data does nothing more than add to the noise.
Now, after this warning – and remember the Poisson distribution means that if you want data with a signal/noise ratios 10 times better … you need to acquire 100 times longer- the fitting software of the instruments is in general good. There are two problems in spectroscopy data fitting procedures : baseline and peak shape. Of the two, peak shape is tough to solve. In the old days we used Gaussian but nowadays pseudo-Voigt shapes are commonly used. Different shapes means more parameters to fit… With too many parameters, the result can be biased by the user.
Among the softwares used (besides classical peakfit programs like PeakFit, Igor, Origin…) for XPS the most common software used is CasaXPS. This is not a free program but it is powerful and can be used for other spectrocopic methods.
Another program used is Unifit and this one is free.
An XPS fit library for Igor is here
However, probably the best is the one that is provided with your instrument.