Grazing-Incidence X-ray Fluorescence:
Achieving Monolayer Sensitivity

Detlef Smilgies

I. Grazing Incidence

The first step to achieve surface sensitivity is always to go to grazing incidence scattering geometry:

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II. Grazing Exit

By choosing grazing exit geometry the escape depth of x-rays from the bulk is reduced - this is essentially the time-reversed argument from part I.


III. 90° Scattering Geometry

By placing the detector in the direction of the polarization vector of the incident beam, dipole scattering is strongly reduced. This way both elastic diffuse scattering (Thompson scattering from defects) and inelastic diffuse scattering (Compton scattering) are minimized, again enhancing the signal-to-noise ratio. For an x-ray fluorescence event, the memory of the incident beam polarization is lost, and fluorescent radiation is unpolarized.
types of scattering


IV. Conclusion: Optimum Scattering Geometry

By orienting the sample horizontally and the fluorescent detector in the horizontal plane, all three conditions I - III can be fulfilled simultaneously. This scattering geometry can be achieved on a vertical four-circle diffractometer with an additional fixed arm to support the energy-dispersive detector. This way, the usual point detector can be used for taking the reflectivity curve while the fluorescence signal is recorded simultaneously. Another advantage of this geometry is, that this way the surface is well adapted to the incident beam profile with its narrow vertical width, whereas the full horizontal beam can be used.


V. Signatures of Surface and Bulk Scattering

If the fluorescing atoms are located on the surface, the fluorescent yield as a function of grazing angle should look like a Vineyard function with the characteristic enhancement at the critical angle.

If the fluorescing atoms are located in the bulk (bulk impurities) the fluorescence yield follows the penetration depth curve.  Because of total external reflection, the penetration depths changes rapidly while scanning through the critical angle and results in a distinct angle dependence. If we make the simplifying assumption that we have a constant density of scatterers r within a layer of thickness L, then we get a simple expression for the scattering intensity.

If there is a doping profile of impurities in the surface-near region or if we have a well-defined thin film, analysis is more involved, because interference effects within the wave fields have to be accounted for in a quantitative analysis [see: de Boer, PRB 44, 498 (1991)]. Again, angular scans through the critical angle are combined with fluorescence measurements. This technique to determine impurity or doping profiles has been termed Total Reflection X-ray Fluorescence (TRXRF) and is of importance for semiconductor industry.


VI. Detector Choices

For incident beam energies below the Ge K-edge (11.1 keV) a Ge detector is a good choice. Above this energy, a Si-Li detector is more suitable detector, avoiding the Ge escape peak. A Ge detector has the highest sensitivity due to its high stopping power. Both Ge and Si-Li detectors have a relatively large active area, and apertures can be adjusted to obtain good signal levels and good signal-to-noise.
Both Ge and Si-Li detectors have a rather limited maximum count rate of about 10,000 counts per second, before they reach saturation. For more intense scattering target, e.g. deposition of multiple monolayers, a PIN-diode based detector or a Si drift diode based detector may be a better choice. These detector have a small active area, but allow higher count rates (up to 300,000 counts per second for a Si drift diode).

All of the mentioned detectors feature an energy resolution of 150 to 250 eV. Using a multi-channel analyzer, fluorescence events over a large energy range can be recorded simultaneously. This energy range is limited by the incident beam energy (atoms need to be excited) and on the low-energy side by the transmission of windows and flight paths (the low-energy cutoff is typically at about 3 keV, unless special measures are taken).

For higher resolution requirements, a crystal analyzer would be needed. There are high-efficiency focussing analyzer designs with a resolution of a few 10 eV. A crystal analyzer can also collect a range of energies when combined with a linear detector.