Practical Electron Microscopy and Database

The critical sample thickness beyond which the absorption effect becomes significant decreases. If the analyzed film is “infinitely” thin, the effects of X-ray absorption and fluorescence are negligible, and the generated X-ray intensity and the X-ray intensity leaving the film are identical. This assumption is known as the thin film criterion (also called thin-film approximation). In thin foil specimens, the double-scattering processes of electrons are negligible as well. This thin film approximation simplifies the analysis of measured EDS data, as the ratio of X-ray peak intensities from the elements A and B, I_A/I_B, is simply proportional to the corresponding weight-fraction ratio and thus Cliff-Lorime sensitivity factors (k_AB) can be applied. Note k_AB is a constant for a given accelerating voltage and the efficiency of a specific EDS spectrometer at the relevant x-ray energies, and is independent of specimen thickness and composition.

Table 4642 lists examples of thicknesses at which the thin-film approximation is no longer valid due to X-ray absorption effects in specific materials.

However, X-rays cannot be deflected into an appropriate detector so that their collection is always inefficient (usually < 1%) and thus signal intensity can be a problem from a thin specimen.

If the incoming X-rays are very energetic, they may not be totally absorbed before they are detected by the EDS detector. The critical thickness is also wavelength dependent, being much smaller for soft X-rays than for hard X-rays. This is one of the contributing factors for the unreliability of oxygen stoichiometry determination.

In summary, in EDS measurements, the intensities of the X-ray peaks from various elements are determined by the factors below:
         i) The path and energy of the incident high-energy electrons penetrating through the specimen.
         ii) The ionization cross-sections of the elements.
         iii) The X-ray yields.
         iv) The collection probabilities of emitted X-rays (collected by the EDS detector).
All these factors above are constant for each particular characteristic X-ray if the thin film approximation is satisfied. Therefore, within this thin-specimen limit, the intensities of the peaks in EDS spectra increase with increase of specimen thickness, but the ratios of peak intensities remain unchanged if the elemental concentrations are constant. However, for thick specimens, the peak intensity ratios change due to a couple of reasons (e.g. X-ray absorption) and thus corrections are needed to obtain accurate quantifications.

[1] D. B. Williams: Practical Analytical Electron Microscopy in Materials Science (Philips Electron Optics Publishing Group, Mahwah, NJ 1984).