Critical Sample Thickness/Thin-Foil Criterion in EDS Measurement
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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, IA/IB, is simply proportional to the corresponding weight-fraction ratio and thus Cliff-Lorime sensitivity factors (kAB) can be applied. Note kAB 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Table 4642 lists examples of thicknesses at which the thin-film approximation is no longer valid due to X-ray absorption effects in specific materials.

Table 4642. Examples of limits to the thin-film approximation caused by X-ray absorption: Maximum thicknesses of thin specimens for which the absorption correction (or error) is less than ±10% and ±3%.

Material

10% error in kAB
3% error in kAB
Absorbed X-ray lines
Primary X-ray lines
Thickness (nm)
Al-7% Zn
336 94 Al Kα Al Kα (1.486 keV) and Zn Kα(8.63 keV)
CuAl2
40 12 Al Kα Al Kα (1.486 keV) and Cu Kα (8.04 keV)
NiAl
32 9 Al Kα Al Kα (1.486 keV) and Ni Kα (7.471 keV)
Ag2Al
33 10 Al Kα and Ag Lα Al Kα (1.486 keV) and Ag Lα (2.984 keV)
Ag3Al
31 9 Al Kα and Ag Lα Al Kα (1.486 keV) and Ag Lα (2.984 keV)
Fe3P
  22 PKα  
FeS
180 50 S Kα Fe Kα (6.398 keV) and S Kα (2.307 keV)
Al2O3
113 14 Al Kα and O Kα Al Kα (1.486 keV) and O Kα (0.525 keV)
MgO
  25 Mg Kα, O Kα  
SiO2
167 14 Si Kα and O Kα Si Kα (1.739 keV) and O Kα (0.525 keV)
Si3N4
413 6 Si Kα and N Kα Si Kα (1.739 keV) and N Kα (0.392 keV)
SiC
13 3 Si Kα and C Kα Si Kα (1.739 keV) and C Kα (0.277 keV)

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).

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