TRENDS AND FUTURE PROSPECTS - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 454

primary radiation. According to Equation 1.68, the critical angle for GE is
larger than that for GI inasmuch as the respective photon energy is
smaller.
• The information depth under the GE condition corresponds to the
emergence depth of the fluorescence beam and is somewhat smaller
than that under GI condition, which corresponds to the penetration depth
of the primary beam.
Back in 1983, Becker etal . performed GE experiments for surface
analysis [90]. Thereafter, the GE technique was used to characterize
submonolayers of adsorbates [91] and implantation profiles in wafers [92].
Angle-dependent profiles with an oscillation structure were observed for
thin layers on a substrate [85-87]. The results obtained for GE-XRF were
shown to agree quite well with those obtained by GI-XRF. For a
comparison, the reciprocity theorem of optics named for H.L.F. von
Helmholtz can be applied (see Ref. [93]). This theorem simplifies the
calculation of fluorescence intensities, which can be based on the recur-
sion formalism (Section 2.4). A straightforward calculation is also possible
but needs an asymptotic analysis of the Maxwell equations in a stratified
layer [94].
The new variants of GE- or GIE-XRF were mostly employed in
nondestructive surface or thin-layer analysis using a synchrotron beam
for excitation. They showed important advantages but also drawbacks. A
monochromatic excitation, such as is needed for GI-XRF, is not neces-
sary. This is the first distinct advantage of the GE configuration. Further-
more, the normal incidence of GE-XRF allows a spatially resolved
analysis by the focused microbeam of synchrotron radiation, offering a
lateral resolution of a few μ m. Concentration profiles along straight lines
or area maps can be recorded by scanning the sample. This possibility is
excluded for GI-XRF because grazing incidence is an inherent obstacle to
high spatial resolution. On the other side, the sensitivity of GE-XRF is
reduced due to a much smaller solid angle of the emitted radiation.
Detection limits are worse by two orders of magnitude.
A further advantage of GE-XRF is the possibility of simply replacing
the energy-dispersive detector by a wavelength-dispersive detector. The
choice of a crystal spectrometer enables a more reliable detection of light
elements because of far better resolution in the low-energy spectrum.
Such a combination is recommendable for GE-XRF but less suitable for
GI-XRF due to intensity limitations. On the other hand, absorption
effects become more severe under GE conditions and may diminish
the advantage. While self-absorption of the exciting incident beam is
strongly reduced because of a much shorter path length at normal
incidence, the path length of the emergent beam with photons of lower
energy is strongly increased and causes matrix effects that are detrimental
to the quantitative determination of elements.