TRENDS AND FUTURE PROSPECTS - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 459

7.2.4Reference-FreeQuantification
In general, appropriate standard reference materials are used for a quantifica-
tion of experimental results. Their matrix should be very similar to the sample
that has to be analyzed. However, for a number of samples, especially for new
materials, such reference materials are lacking. The theoretical dependence of
X-ray fluorescence intensity and concentration or area-related mass of an
element is well-known (e.g., Ref. [104]). Secondary and tertiary excitation
leading to notorious matrix-effects of absorption and enhancement can be
included. For excitation in total-reflection geometry, a standing wave of
incident and reflected beam has to be taken into account. This way, X-ray
spectra of TXRF, GI-XRF, and also of NEXAFS can be calculated. A
reference-free quantification is a demanding aim of a research group with
Beckhoff at the PTB in Berlin [62].
A theoretical calculation requires a response function of excitation and
detection. Two sets of different parameters have to be known: experimental
instrument parameters as well as fundamental atomic parameters. The first set
of experimental parameters involves (a) X-ray excitation of the sample with
radiant power and spectral distribution; (b) detection of X-ray fluorescence
with spectral resolution and efficiency; and (c) beam geometry with angles,
distances, and divergences. The second set of fundamental parameters includes
(a) photoelectric mass-absorption coefficients of pure elements for the exciting
photons; (b) total mass attenuation coefficient of the elements for the photons
to be detected, (c) transition probabilities of different spectral peaks or lines;
and (d) fluorescence yields and jump ratios at absorption edges.
All these values are listed in different tables, for example, in the X-ray data
booklet [105], or can be read from a database, www.cxro.lbl.gov [106]. How-
ever, many of them are based on experiments made in the 1970s. Their
uncertainty or reliability is not sufficient in many cases. For a better reliability,
they have to be determined experimentally as was done in a special case by the
PTB [62]. A synchrotron beam was used for excitation with intense and tunable
radiation. For detection with high efficiency and spectral resolution, a wave-
length dispersive spectrometer based on an SGM (spherical grating mono-
chromator) was built. Mass absorption coefficient, fluorescence yield, and
transition probability could be determined experimentally for the light ele-
ments B, C, and Al. The cross-sections for resonant Raman scattering below
the K edges of Si, V, and Ni were also measured.
A spectrum of a 200 mm silicon wafer was recorded at an excitation energy
of 1622 eV and a glancing angle of 0.9 ° (critical angle 1.10 ° ). A considerable
footprint effect was first corrected, and afterward the spectral background was
taken into account. Figure 7.13 shows fluorescence peaks of a few elements (0.1
to 2 ng/cm 2 ) above a continuous background, which results from different
components, such as Rayleigh and Compton scatter, resonant Raman scatter,
and continuous“bremsstrahlung”of emitted photoelectrons at synchrotron
excitation [32].