24 Experimental setups and methods
pending on the particular definition of S three different approaches to XPS quantification
are described in the following paragraphs. It should be noticed that in
equation 2.4, the cross section A is the most important normalization factor as it
varies strongly for different elements and orbitals. T and exhibit in general a
lower variability, most of all if it is possible to compare XPS peaks with a similar
kinetic energy EA.
2.2.2 Sensitivity factors and quantification approaches
Before describing the three approaches, in equation 2.5 it is convenient to define
a normalized intensity ^IA = IA=SA, so that the problem of XPS quantification now
coincide with the determination of all the ^Ii for all the elements of a probed sample:
NA (%) =
Method 1. Scofield sensitivity factors
In this first approach the sensitivity factor includes the minimum amount of information,
namely it is equal to the simple cross section:
Si = i (h) . (2.7)
Theoretical values for these cross sections for the different elemental orbitals and
different excitation energies are easily accessible in literature, the most popular being
those calculated by Scofield in the single-potential Hartree-Slater atomic model
106. The normalized intensities will be:
The other terms of equation 2.8 need to be determined individually; the transmission
function T can usually be precisely measured on each particular XPS setup.
The mean free path , instead, has to be estimated through semi-empirical formulas.
In the last paragraph of this section (see Section 2.2.4) some examples of these
formulas are discussed.
Once a proper choice of the mean free path is made, this first approach provides
a quite simple quantification. The main limit consists in the accuracy of the
theoretical cross sections since large discrepancies with experimental data have
been reported in literature 107. These differences are probably mainly ascribed
to the experimental difficulties of choosing energy ranges and backgrounds effectively
corresponding to the calculated cross sections. The need of overcoming these
limits leads to the other two approaches discussed in the following paragraphs.