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:

C_x = (I_x/S_x) / (∑I_i/S_i) 

where C_x 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.

Background Selection

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[1] (i.e. the background goes up in proportion to the total number of photoelectrons below its binding energy position) and 3) the Tougaard background (or Tougaard universal cross-section approach) which is a methodology for integrating the intensity of the background at a given binding energy from the spectral intensities to higher kinetic energies[2]. 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 numerous peak overlaps. The Shirley background falls somewhere in between for accuracy, however its ease of use has resulted in its widespread adoption.

References:
[1] M.P. Seah Quantification of AES and XPS in Practical Surace Analysis by Auger and X-ray Photoelectron Spectroscopy ed. D Briggs & M.P.Seah , John Weley & Sons, Chichester UK, 1983 p. 204.
[2] Neal Fairly, XPS lineshapes and Curve Fitting in Surface Analysis by Auger and X-ray Photoelectron Spectroscopy ed. D Briggs & JT Grant, IM Publications, Chichester UK, 2003, p. 398.