28 Experimental setups and methods
is often not the case.
A first possibility for the quantification of would be to directly choose experimentally
measured values from literature. This approach has two main problems.
The former is the scarce availability of large databases reporting the values for
different elements measured under the same conditions. The latter is related to
the low flexibility of this method: for instance, it does not allow to estimate the
mean free path of the electrons from a certain XPS peak traveling through different
materials. The difficulties of including such matrix effects strongly limits the applicability
to the quantification methods described previously: most of all because
the values reported in literature are typically measured on samples whose mass
densities can be very different.
Another option is to define semi-empirical formulas based on different databases
of experimental values, that can easily generalize the estimate to arbitrary energies
and matrices. The simplest of these, defines as: / E where is a numerical
value typically chosen between 0.5 and 1.0 110. Although it does not provide numerical
values of the mean free path, this expression might give sufficiently good
estimates of the relative values for different XPS signals. It should be noticed that
this formula makes sense in the case of a homogeneous sample; in this case the
mass density will be the same for all photoemitted electrons and can be quite well
considered as a pure function of the kinetic energy. More quantitative estimates are
provided by the so called Tanuma-Powell-Penn (TPP-2M) formula 111 or by the
one proposed by Cumpson and Seah 112. These expressions also take into considerations
some of the properties of the matrix and the mass density in particular.
The TPP-2M and the Cumpson-Seah formulas will assume particular importance in
Chapter 4, where the case of inhomogeneous samples will be considered. In the
rest of this thesis, for general quantification purposes, the relative concentrations
have been achieved by simply assuming / E0.6 (0.6 is the standard value used in
Thermo Avantage and Eclipse data systems).
2.2.5 Angle resolved XPS depth profiles
The quantification of the AR-XPS measurements was carried out by applying the
same principles described in the previous sections for each individual emission angle.
In brief, detailed XPS spectra of all relevant elements were acquired at 16
different emission angles between 20 to 80 from the surface normal; Shirley type
backgrounds were subtracted in order to quantify their intensities. These were normalized
according to one of the three methods described in 2.2.2. Once the relative
concentration of each element was determined as function of the emission angle,
the depth profiles were calculated using the simulation tool ARProcess (Thermo
Avantage software), which uses a maximum entropy method combined with a genetic
algorithm. Relative concentrations at emission angles higher than 65 were
omitted in order to reduce the influence of diffraction effects and elastic scattering.