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?

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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.

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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?

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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.

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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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11 thoughts on “Art of curve-fitting… or black magic of curve-fitting XPS spectra

  1. Sanat Kumar Mukherjee says:

    Your explanation is of great help for me as i have been struggling with the curve fitting of the XPS data my titanium oxide thin film samples deposited by using rf magnetron sputtering.

  2. Emily Smith says:

    Nicely explained in a form that my students will be able to follow – Thanks! Emily

  3. Emilia says:

    Excellent! I began using XPS at my PhD (in electrochemistry, not surface science group), studied A LOT, and I still do not understand WHY (OH WHY!) some scientists of several areas think that you learn how to fit a spectra in one day, and do all wrong, and when you explain them why that is not correct, they really seem not to care! … and this is for any experimental tool… XRD, XAS… I know someone that wanted to do EXAFS analysis, and so he went ONE AFTERNOON to learn with someone how to fit EXAFS data…. I´ve studied EXAFS less than XPS, and I have discussed my data fit by other person (the expert guy), and still I a not confident enough to do it by myself without help….. I am so happy I read this post, and find out I am not crazy, and there is other people that really knows what´s right…

  4. Berk says:

    Great help, thanks. For X-ray excited valence band spectroscopy, should I keep the FWHM conastant too?

  5. Tissa says:

    Great article! You have referred to the “Fundamental processes contributing into width of the peak”. Could you please explain those processes a bit further, or provide a reference?

    • kartyush says:

      Observed peak is a convolution of a Gaussian and Lorentzian function: Gaussian describes the measurement process (instrumental response, x-ray line-shape, Doppler and thermal broadening).Lorentzian models the lifetime broadening (Natural broadening) due to the uncertainty principle relating lifetime and energy of the ejected electrons.

  6. Dima says:

    Thank You for valuable information. Indeed, fitting XPS data can be a pure strugle. Especially, if XPS spectra is the only way to figure out the surface composition and one doesn’t simply know how many components should be introduced. Especially, if these components are the doublets..

  7. Isam says:

    Hi guys, Is there any one have experience in Avantage software
    please give a link or the best website to learn it
    Thanks.

  8. Hector says:

    Hey guys, where I can learn more about XPS fitting?. Any suggestions?. Forums, chat rooms, etc ?

    Thanks

  9. Hy, I have tried to fit XPS O1s and C1s regions from aromatic amino acid crystals on Si/SiO2-wafers. Best fitting results from the pure Lorentz-Fit, which is approximately the same like PearsonVII for my XP spectra. The Voigt and pseudo-Voigt fits looks very strange
    and the R²-value is below 0.99, while the pure Lorentz curve fit results in a R²-value of 0.998 (pearsonVII: R²= 0.994). Am I right to say that this is due to a very long hole lifetime,
    that leads to a broadening, which is worse described by taking acount of a negligable small broadening by the analyzer transmission or the k-alpha-line width of the source (here: Mg, non-monochromatized)? Is it wrong to use the Lorentz-fit instead of the pearsonVII for publication?

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