Accuracy of EDS Quantification
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In addition to the specimen itself, the X-ray generation process is also affected by the probe size, current, and convergence angle. Fortunately, elemental concentration quantification can be done with reasonable accuracy by comparing the peak intensities with k-factors in EDS spectra. Overall, the accuracy of EDS quantification is mainly limited by the counting statistics (random errors) for the collection of X-rays not only in the determination of the kAB factors but also in the acquisition of the intensities IA,B. Therefore, the total percentage error in concentration is determined by the percentage errors of kAB and counts. In other words, the total error will be higher than the error in kAB alone or the error in counts alone.
In principle, the counting statistics of X-ray spectra limits the accuracy of quantification. If the peaks are strong comparing with a weak background, the standard deviation, σ, can be given by,
For EDS and EELS techniques in EMs, if a series of measurements are repeatedly performed on a specimen, then the distribution of counts would often follow a Poisson distribution. If the number of the measurements is large, the distribution can be approximately given by a Gaussian distribution. In this case, the standard deviation of 3σ, when it has 99% confidence limit in the X-ray peak intensity, is usually used to estimate the error,
Therefore, in general, the greater N is, the lower the error in the EDS analysis is.
Table 2513a lists some examples of necessary measurement counts to satisfy the needed accuracies and confidence levels.
Table 2513a. Necessary measurement counts to satisfy the needed accuracies and confidence levels.
According to Equation 2513b, for a binary system with elements A and B, the error in IA/IB is given by,
On the other hand, the error in IA/IB can obviously be decreased if several EDS recordings are taken. For instance, the absolute error at the 95% confidence level in n recordings of IA/IB is given by,
It is necessary to highlight that except for the random errors from counting statistics discussed above, some factors, however, will contribute systematic errors. Those factors are mainly:
The accuracies of EDS quantitative analyses with and without standards are very different:
The methods of determination of k-factors are discussed on page4373 in detail.
Accurate, quantitative analysis based on EDS method can be done by the following procedure:
When there are no significant differences in their X-ray absorption coefficients for the elements in the specimen, or when the specimen is thin enough, X-ray absorption corrections may be neglected to obtain an accuracy of 10-20%. However, to obtain an accuracy in the range of 5-10%, an absorption correction should be applied with an estimate of the specimen thickness.
Table 2513b lists examples of dependence of accuracy of EDS quantification on atomic number (Z) of the elements in the Periodic Table. For instance, in extremely accurate EDS quantifications, elemental detection is possible down to a few % wt. for elements with atomic numbers Z << 11.
Because the EDS peaks are so broad, their Gaussian tails extend over a substantial energy range, interfering with the adjacent background. Therefore, the background measurements are difficult. For a material with multiple chemical elements, the spectrum becomes more complex, and thus the quantification and interpretation is less accurate.
For the TEM configuration with a top-entry type EDS detector, the detector is placed above the objective lens in a TEM system with a high viewing angle (e.g. 70 °) to a horizontal specimen. Since X-rays entering the detector take a large take-off angle (TOA) against the specimen, a high accuracy of quantitative analysis can be obtained. However, with such configuration, the solid angle of the detector against the specimen is small, resulting in low detection efficiency.
TEM specimens can be used to simplify EDS measurements, especially quantifications, as the thin specimens avoid significant X-ray absorption and secondary x-ray fluorescence events. Those two factors typically cause significant EDS inaccuracy with bulk specimens in an electron beam microprobe or a scanning electron microscope.
Furthermore, except for the quantification inaccuracies induced by the factors mentioned above, beam damage can also introduce error. For instance, in many cases, elements are partially removed from the EM specimens (especially when TEM thin films are used) during EDS measurements (see page3123).
In summary, in order to obtain accurate elemental quantification with the experimental k-factor approach for EDS measurement, the following conditions need to be satisfied: