Tag Archives: curve fitting

Art of curve-fitting… or black magic of curve-fitting XPS spectra

Why talk about something so well known to the surface analysis community as curve fitting high resolution XPS spectra? Two reasons.

First is the skepticism I am running into every time I am showing curve fits of spectra to non-surface analysis communities of scientists. Their reaction is that curve fitting is meaningless as we can curve fit any particular spectrum with infinite number of combinations of peaks of different widths and shapes with the same goodness of fit. So every time I give presentation, which show curve fitting results to people who are not doing it for living, I am talking about physical reasons behind Gaussian-Lorentzian shape of peaks, fundamental limits contributing to FWHM and generals rules of accurate reproducible curve fitting.

And the second reason is that even though we all know the rules behind good practices of curve fitting scientific literature is filled with poorly fitted spectra and, therefore, incorrectly interpreted XPS data.

What’s wrong with set of spectra shown on the left. And why spectra on the right represent the “correct” way of curve fitting?


Let’s look at one example from the literature. Three N 1s spectra for three samples (unmodified and heated at two different temperatures) are analyzed.


The first sample is unpyrolyzed sample (unmodified)  which is used as a reference. Peak NI is of adequate width for N 1s spectral line. Why, suddenly, peak NII is twice as wide as peak NI?


Heat treatment of sample at 800C introduces changes which are obvious from the spectral shape. Peak NI is at the same position of Binding energy and has the same approximate width. Suddenly peak NII is twice more narrow then it is in unpyrolyzed sample. Peaks NIII and NIV is added to complete a curve fit. Curve fit of this spectrum by itself meets all necessary requiremenets of a good curve-fit in which main three peaks are of approximately the same FWHM. So why there is no peak NIII in unpyrolyzed sample? If one makes peak NII in unpyrolyzed sample of adequate width (being the same as in sample at 800 C), then a third peak NIII must be created to complete a curve fit in the unpyrolyzed sample as well.


At temperature 900 peak NI becomes twice as wide as it is in unpyrolyzed  sample. And peak NII becomes three times more narrow then in unpyrolyzed sample. And, my “intelligent” guess that authors make conclusion on significant decrease of species contributing to binding energy of peak NII from 800 to 900C.

This type of curve fit is exactly why there is so much reservations against use of curve fitting of spectra for quantitative evaluations of changes in chemistries.

And still itt is very easy to do an accurate reproducible curve fit if you remember a few things.

1. Fundamental processes contributing into width of the peak used for curve fitting N 1s, in this case, are the same for all peaks used, i.e. natural width of incident X-ray line,  thermal broadening, pass energy of the analyzer, lifetime of the electron hole, etc. From a reference sample with just one type of N, O or metal, for example, analyzed at your particular instrument it is easy to find what it the adequate width for particular line of the element. ALL peaks within this element should have +/- 0.2 eV the same FWHM. 

2. One of the basis of adequate interpretation of changes introduced by any type of modification is identification of peaks in unmodified sample. Once the spectra for reference sample are curve fitted, position in BE and FWHM have to be constrained to +/- 0.2 eV each. This curve fit can be then copied into a curve fit of spectra from all other samples in the series. If the set of peaks present in unmodified (reference) sample is not sufficient to complete a curve fit, new peaks of the same FWHM have to be added.

3. If you don’t have reference sample, any sample in a series can be used as “reference” for curve-fit. Then this curve fit can be propagated to all other samples for accurate within samples comparison of changes. CONSTRAINTS, CONSTRAINTS AND CONSTRAINTS! 

4. Cross-correlations of the elements is key! If you have identified, lets say, C-N=O in N 1s spectrum, there should be peak due to the same type of chemistry in both C 1s and O 1s spectra.

These little things will allow you to be as consistent as possible throughout your sample set and make sound conclusions on chemistry.

It is critical to publish and present high quality XPS data processing of spectra to ensure all the trust this powerful method deserves. Let’s do it!

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