### Quantitative Analysis

Semi-quantitative analysis is possible by measuring the peak areas of specific elemental core lines (I) and by applying appropriate atomic sensitivity factors (S), also known as relative sensitivity factors (RSF), using the general equation:

Cx = (Ix/Sx) / (∑Ii/Si

where Cx is the atomic fraction of element x in a sample[1]. The sensitivity factors can be calculated from theory or derived empirically from the analysis of standard samples. The use of standard samples is the preferred method (and is the method applied in the Kratos line of spectrometers). Peak areas are defined by applying an appropriate background correction across the binding energy range of the peaks of interest. In general, three types of backgrounds are used: 1) a simple straight line or linear background, 2) the Shirley background in which the background intensity at any given binding energy is proportional to the intensity of the total peak area above the background in the lower binding energy peak range[2] (i.e. the background goes up in proportion to the total number of secondary photoelectrons below its binding energy position) and 3) the Tougaard background (or Tougaard universal cross-section approach) which offers practical background computation (based on electron energy losses) with more control over the background shape then the Shirley procedure[3]. The simple linear background suffers from large peak area changes depending on the position of the chosen end points and is the least accurate. The Tougaard background is the most accurate but suffers from complications in practical use, particularly if there are peak overlaps at binding energies above the integrated peak. The Shirley background is reasonably accurate and its ease of use has resulted in its widespread adoption.

References:
[1] J.F. Moulder, W.F. Stickle, P.E. Sobol, K.D. Bomben, Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Corp, Eden Prairie, MN, 1992.
[2] M.P. Seah, Quantification of AES and XPS, in: D. Briggs, M.P.Seah (Eds.), Practical Surface Analysis by Auger and X-ray Photoelectron Spectroscopy, John Wiley & Sons, Chichester UK, 1983, p. 204.
[3] Neal Fairley, XPS lineshapes and Curve Fitting, in: D. Briggs, J.T. Grant (Eds.), Surface Analysis by Auger and X-ray Photoelectron Spectroscopy, IM Publications, Chichester UK, 2003, p. 398.