Enhancing EDS Quantitative Accuracy with eZAF and the SCC Database

The “Quant” task is defined by the simple conversion of the elemental characteristic X-rays into weight fractions, revealing the concentrations of the elements. The element-related signal must be derivative of raw measured data, for example, from the spectrum.

Before obtaining the pure signal, a few processing and pre-evaluation steps are needed, such as correcting detector artifacts to determine the background (mostly the bremsstrahlung) and, if required, deconvolute unique element origin data if it was not possible to receive separate measured data caused by limits in the spectrometer resolution (peak deconvolution).

The EDAX spectra evaluation software has a state-of-the-art algorithm capable of handling all aspects of the spectra processing to arrive at the ideal determination of the pure-element signals extracted from spectra.

Results and Discussion

The signals used are typically:

• Net-counts of characteristic X-rays (meaning the bremsstrahlung background is already subtracted) for standardless evaluation
• K-ratios, which are net-count ratios of characteristic X-rays of an unknown specimen measurement divided by the measurements of the net-counts from one or several standard(s) with known element composition, for standards-based evaluation
• P/B-ratios, or net counts, of characteristic X-rays divided by measured bremsstrahlung of the same energy, for standardless evaluation

The measured elemental signals offer the raw data needed for the quantification algorithm. Initially, they rely on the excitation, or the primary electron energy, which can be determined through the high voltage (HV) of the electron microscope. This generation of X-rays relies on the element's concentration, which is the base analytical relation.

Net-counts = X-ray Generation (C, Z, E) * Absorption (Z, Zm, E) * Fluorescence (Z, Zm, E) * Efficiency (E)

In the above equation, Z stands for the atomic number of the element in consideration, E stands for the energy of the element line utilized for Quant, C stands for the concentration of the element, and Zm stands for all of the other elements within the composition that may have an effect dependent on their concentrations, noted as Cm.

It also depends on the other elements present in the sample and the whole composition via self-absorption of generated X-rays in the sample (Absorption) and the enhancement of the X-rays through additional fluorescence effects (Fluorescence).

The measured signals require correcting regarding the range of physical effects, fluorescence, and absorption. This process is called ‘matrix correction’ and relies on the composition of the matrix elements (Zm). The quantification algorithm, or Quant, requires iterative work due to the knowledge needed regarding the composition of all other elements, which remains unknown.

The effects with the greatest significance are absorption and generation.

Fluorescence is an enhanced effect from additional X-rays not generated by the primary electrons. This may be an important distinction between low-concentration elements and unique constellations of major elements found in the composition. However, it is often a minor effect, affecting the analytics only in special cases if element concentrations are minimal. It will not be considered in this discussion within the subject of general Quantitative accuracy improvement.

It is standard to believe that if an element in a specimen contains double the counts compared to another specimen, it can be assumed that the concentration of this element is doubled as well. It is close to accurate regarding the generation of X-rays for an HV. However, this is not often the case with Energy Dispersive Spectroscopy (EDS) in a Scanning Electron Microscope (SEM), a significantly non-linear analytical method.

The absorption of generated X-rays in a specimen influences the measured results. The uncertainty is even greater when the effect is high due to Mass Absorption Coefficients (MACs) jumping and determining the properties of absorption physics within a specimen.

The most significant uncertainty comes from X-ray energies near the electron shell energies (the jumps) of the elements in a specimen's composition.

Figure 1 shows an example of a simulated binary of an Al/Si compound, where the Si radiation has a high absorption effect of Al with non-linear behavior. This does not hold true for measurements with PeBaZAF, which use P/B-ratios with Si and remain largely linear.

Figure 1. Measured X-ray net-counts vs. P/B values with a calculated Al/Si binary sample (Al blue; Si red). The x-axis shows the element concentrations of Si or Al, and the y-axis depicts the P/B and net-counts arbitrary units. Image Credit: Gatan, Inc.

The P/B is akin to linearizing the Quant query. It is worth noting that the issue is, to some degree, delegated to determine the values of the P/B measurements, which are interpolations from the actual measured spectrum. The cause is that the pure bremsstrahlung measured counts of the same energy are not measurable precisely at the same energy where characteristic lines occur.

With modern Silicon Drift Detectors (SDDs) capable of measuring high count rates, statistical limitations on the P/B signal are no longer a concern.¹ Instead, the primary constraint comes from systematic errors in determining the divided bremsstrahlung background relative to P/B. However, the uncertainty in determining P/B values remains lower than the uncertainty introduced by absorption effects in net-count-based measurements.

Figure 2 illustrates the significant absorption effects of Si-K radiation in a specimen composition rich with Al. The effects are seen in the bremsstrahlung calculated absorption jumps and the heights of the peaks (net-counts) of both elements, which differ greatly, even though both contain the same concentration in the specimen.

Figure 2. A simulated spectrum example with 50% mass fraction of both elements (often named weight%) at 20 kV excitation, evaluated with the EDAX advanced spectra evaluation software tool. Image Credit: Gatan, Inc.

In Quant, everything deals with the specimen emitted X-rays rather than the measured net counts:

Net-counts (emitted) = Net-counts (measured) / Efficiency (E)

The first step involves calculating the true emitted X-rays utilizing essential knowledge of detector efficiency. However, this is not always a requirement. The efficiency is negated with a standards comparison measurement with Full Standards Quant (FSQ) when a standard was measured using the same geometry and detector for each unknown element.

The analytical results with standardless P/B-based quantification are also not influenced. However, with the PeBaZAF working only for energies >1 keV, P/B-based quantification makes it essential to consider the detector efficiency with Z < 11 elements, where the net counts are used.

As a result, the PeBaZAF standardless method can achieve approximately ±10% relative result accuracy (using the standard deviation of 5%) even without the requirement for further use of an empirically measured database.^1,2 The Quant question is partly linearized, and all Z ≥ 11 element determinations are uninfluenced by detector efficiency.

The detector efficiency is sensitive and complex, influencing all analytical results where an efficiency-independent method is not used (such as FSQ with measurement of standards with the same system; like PeBaZAF, all elements Z ≥11). Uncertainties with the detector and window-specific properties can arise, and each detector has residual uncertainties caused by manufacturing, aging, SEM geometry, and window contamination.

Efficiency knowledge is required, particularly for eZAF standardless and FSQ, when a standards data library must be created for use by other measurement systems without re-measurement of the standards.

Due to this, an Efficiency Correction Factor (ECF) can be determined and used empirically. It can offer efficiency corrections to consider the fundamental properties of used detectors.³

Figure 3. a) Efficiency curve of older EDAX detectors (the pink line is window transmission; the green line is complete detector efficiency) with diamonds representing the true used efficiency by Quant, which can differ from theory and Synchrotron measured values by using ECFs. The example shows Quant internally applied ECFs to address a divergence effect by Moxtek windows lamella ³. b) Originally calculated efficiency (curve) corrected by ECF values. Image Credit: Gatan, Inc.

Uncertainties exist in generating X-rays in Quant models and fundamental atomic data. The closer the primary electron energy is to the excited element shell energy, the greater the uncertainty. The Standards Customized Coefficients (SCC) for eZAF standardless are AMETEK Gatan’s empirical database, designed to optimize the model and parameters for any particular set of conditions.

Net-counts = X-ray Generation * SCC * Absorption * Fluorescence * Efficiency (E) * ECF

The detector-based effects on measured X-rays (possible to correct with ECF) require separation from the specimen’s internal generation of X-rays (SCC). The ECF Efficiency correction values should be separate from the model, eZAF, or PeBaZAF (Z < 11).

The SCC enables direct adjustment of the X-ray Generation physics. Applying SCC factors enables compensation for general deviations in X-ray yields for given elements over a large array of electron excitation energies.⁴ The eZAF can also be improved for applications where SCC values are measured empirically as compensation for standardless result deviations.

It is only a factor, however, so it is unable to address non-linearities caused by massive interdependencies between elements, as seen in Figure 1. Adhering to the “customized-standardless” method is useful for rare limited application uses and dedicated specimen composition ranges. It is possible to generate or measure a dedicated SCC dataset with known composition samples, enabling storage of this empirical dataset with a specified name. These created datasets can be recalled for standardless eZAF, where like samples are measured again.

Working with eZAF unnormalized results is mandatory for assessment and SCC determinations. Any normalization makes it difficult to find where the deviations originated.

Figure 4. Efficiency curve of more recent EDAX detectors (the pink line is window transmission; the green line is complete detector efficiency) with diamonds representing the true used efficiency by Quant. The theory and Synchrotron measured values are the same, and no divergence effect is visible with the new C2-type window grids. Image Credit: Gatan, Inc.

In the Al/Si example, the difficult element is not the Al; but rather the Si. It cannot be determined if the eZAF results are monitored continuously when normalized to 100%.

The incorrect determination of Al is also a result of the incorrect Si results caused by the effect of the normalization equation. The Si mistakes will be small and undetectable with real deviations. To get eZAF results that are not normalized, a “reference measurement” with a pure element specimen is required. This uses the unknown absolute relation of eZAF to calculate absolute results by adjusting the beam-current and/or detector solid angle.

In routine cases, eZAF should only be applied unnormalized to identify incorrect analysis results and avoid errors. It is recommended that the circumstances where the analysis goes out of reasonability be determined through concentration total.

In this example, a new reference measurement should be taken. If that measurement appears correct, the normalized results can be used for reporting and final analytical assessment. The reference value is the absolute adjustment of the measurement and, therefore, a key analytical parameter for eZAF. Stored with each spectrum, it is as critical as HV, count rate, and acquisition live time. The “reference measurement” is central to improving eZAF and gaining an absolute view.

A basic SCC factor for the element line series cannot address massive non-linear effects over big composition differences. The example below shows an SCC-based Quant adjustment demonstrating those limitations. The results are improved only for a specimen type and specific area of concentrations and compositions.

Figure 5a illustrates the unnormalized eZAF calculated element compositions for Al and Si over the Si content. For comparison, the broad light-red line indicates the original measurement effect (net-counts). Here, the eZAF correction algorithm functioned well. There are remaining deviations, particularly with lower Si concentrations, where the dominating Al largely absorbs X-rays.

The Si result deviations remain greater than 20% in relation to the Si compositions, up to 30% concentration. Figure 5b illustrates the same environment. However, the 10% Si spectrum determined Si's SCC value. The relative deviations for Si become < 10% in relation to all Quant results, up to a 30% Si concentration. The issue is that the deviations are relatively more significant than 30% for high Si concentrations.

The created empirical database (in this example, only one SCC value for Si-K) cannot be used in general but is applicable to Al/Si samples of low Si concentrations.

This special database can be named “Si in high concentration Al” and stored to be used for similar specimens and applications.

It is important to note that this is not recommended for general use to improve eZAF empirically; it would damage all other analytical results for Si if Si is in high concentrations and if no Al is in the specimen. With this scenario, the pure Si result would rise to above 130%. Where the result is normalized, it would be 100% if Al concentration is determined to be minimal.

However, in most other normalized cases, this does matter because the excitation relationships between atomic shells of different elements can become unbalanced. Therefore, avoid normalizing eZAF results indiscriminately. Normalization will distort results for pure element specimens and can only be accurately observed without it.

Figure 5. a) Calculated concentration results by eZAF for binary Al/Si example specimen (blue Al; red Si) over the Si nominal concentration, all in % units. The broad light-red line is the Si net-count raw data curve from Figure 1, arbitrary units, not yet ZAF corrected. b) The same sample but with low Si concentrations using SCC. Image Credit: Gatan, Inc.

Conclusion

The SCC database is dedicated to correcting and/or adjusting the excitation aspect of specimen physics with eZAF. It was required to assist with the standardless unnormalized calculation option.

Only a reference measurement with one pure element specimen is needed. Repeating is only required when the conditions have been altered (for example, the beam current changed and is not under precise measurement control).

• To correct/adjust the element’s X-ray lines excitation relative to each other (cross-sections of shell excitation and X-ray emission probabilities).
• To improve results, “customized standardless” can be utilized for dedicated applications (such as for a defined specimen and/or composition type) because it can change the calculation in a way that makes the accuracy of the same elements with entirely different concentrations or in completely different matrix composition worse with Quant.
• To get similar results over many used HV (primarily electron energies).

Software operators and analysts have access to the SCC database. Improved eZAF results with “customized standardless” are achievable with dedicated applications on your work. In addition, a factory all-purpose database will be available in the future.

It is the first step to achieving the focused goals for eZAF (Figure 6).

Figure 6. The goal of improving eZAF accuracy with empirical measurements and databases ^1,2. Image Credit: Gatan, Inc.

References

1. Eggert, F. (2020). Effect of the Silicon Drift Detector on EDAX Standardless Quant Methods. Microscopy Today, 28(2), pp.34–39. https://doi.org/10.1017/s1551929519001196.
2. EDAX-Insight (2019) “EDAX Standardless Quant Methods” 17/1 1-3
3. Eggert, F., et al. (2021). The Detector Efficiency Question with EDS. Microscopy and Microanalysis, (online) 27(S1), pp.1674–1676. https://doi.org/10.1017/S1431927621006152.
4. Rafaelsen, J., Eggert, F. and Kawabata, M. (2021). EDS Quantification Using Fe L Peaks and Low Beam Energy. Microscopy and Microanalysis, 27(S1), pp.1670–1672. https://doi.org/10.1017/s1431927621006140.

This information has been sourced, reviewed and adapted from materials provided by Gatan, Inc.

For more information on this source, please visit Gatan, Inc.