The chi2 analysis is a general method in statistics. A small chi2 means that your fit is good while a large chi2 then logically means it's bad. For more details, see

https://www.statisticshowto.com/probability-and-statistics/chi-square/

If you add more fitting curves, your chi2 will decrease since a better fit is always easier with more parameters. But always keep in mind that your peak widths should be meaningful and kept close to constant for deconvoluting the same peak group.

To oversimplify, the chi-squared value will give you an indication of the goodness-of-fit between a set of experimentally derived data points (e.g. your raw spectrum), and data point in a model (e.g. your XPS peak fit). In general, the lower of the chi-squared number, the "better" your fit. However one should not rely solely on the chi-squared value for determining a decent peak fit in XPS. Just because your chi-squared value is low, does not mean your fit is good or scientifically meaningful.

As an exercise, you can take any XPS peak, add lots of unconstrained components, fit the components to the data, and you would certainly get a "good" fit that fully minimises the chi-squared value. But such a peak model would be physically incorrect and functionally useless for drawing a scientific conclusion (e.g. chemical states). One potential use for the chi-squared value is to statistically compare two peak models for the same spectrum. That method is used in B. Singh et al., which I have linked below (in general, this paper is very useful, well worth reading!).

Article Good Practices for XPS (and other Types of) Peak Fitting. Us...

When peak fitting, the best approach is to always start from the base physical principles of XPS, constraining your components so that they make physical sense (e.g. fixing the FWHMs of like components based on core-hole broadening). Once you have a peak model that makes physical sense, then you can start loosening some of the constraints in order to improve the fit (i.e. to reduce the residual, chi-squared, improve Abbe's criterion, etc), BUT exercising caution so that your peak models do not stray into fantasy; do not let the statistical values tempt you into think you have a "good" fit.

Good luck.

Dear Dr. Vijayakumar Samiyappan ,

when performing nonlinear curve fitting, an iterative procedure is employed that minimizes the reduced chi-square value to obtain the optimal parameter values. The reduced chi-square is obtained by dividing the residual sum of squares (RSS) by the degrees of freedom (DOF). Although this is the quantity that is minimized in the iteration process, this quantity is typically not a good measure to determine the goodness of fit. For example, if the y data is multiplied by a scaling factor, the reduced chi-square will be scaled as well.

A better measure would be the r square value, which is also known as coefficient of detemination. The closer the fit is to the data points, the closer r-square will be to the value of 1. A larger value of r-square does not necessarily mean a better fit because the degress of freedom can also affect the value. Thus if more parameters are introduced, the r-square value will rise, but this does not imply a better fit. The adjusted r-square value accounts for the degrees of freedom and this could be a better measure of the goodness of fit.

For more details, please see the source:

-How do I know if my fit result is good? By OriginLab

Available at: http://d2mvzyuse3lwjc.cloudfront.net/doc/Quick-Help/measure-fitresult

Best regards, Pierluigi Traverso.

Dear Pierluigi Traverso Benjamen Reed Jürgen Weippert I was overwhelmed with your responses giving guidlines for mathematical and analytical understanding of the data fitting. For a begginer this means a lot.

Thank you very much for your time.

Just recall that a low chi2 means the peaks you put in repsresents the data envelope only - remember you muct be able to justify the chemistry of the peaks you have fitted

David J. Morgan Yes, Thank you very much.