Tuesday, July 2, 2013

Light Element EDS

The ability to resolve very light elements is entirely depending upon the pulse shaping time constants used. The top images shows the lower energy portion of an EDS spectrum of magnetite (Fe2O3) taken at 30 kV using a 16 µs shaping time constant. The Fe Lα peak is clearly visible to the right of the O Kα peak. There is a small shoulder for the C Kα peak since the sample was coated with graphite to suppress charging. The peak just above the Si Kα line is actually the Si K absorption edge. Using data of this quality one could, with the use of standards, quantitate oxygen using O Kα. The Cr Lα peak is shown near the O Kα peak to illustrate a common overlap with O Kα. Chromium is also a common trace contaminant in mineralogical magnetite.

The detection efficiency of the light elements is less than the higher X-ray energy elements, and thus one might be tempted to decrease the shaping time constant, TC, to increase the throughput of the EDS detector allowing one to perform EDS with more beam current and higher acquisition rates.  The second image shows the same energy region with a time constant of 0.5 µs.  The energy range is attenuated around 2 keV and all information regarding light elements is lost. This is an artifact of pulse processing.

The point of this brief example is very simple: use the larger TC's for light element studies! A TC as small as 8 µs should allow for the resolution of C Kα, and for O Kα one can go as low as 1 µs.

Galena: An Illustration of EDS Spectral Overlaps

With an energy resolution of ~ 143 eV at the Mn Kα line (5.893 keV), the problem of spectral overlaps is a common problem with EDS applications. In the top image a spectrum of the mineral galena, PbS, is taken at 30 kV using a 0.5 µs pulse shaping time constant. The S Kα line is at 2.306 keV and the S Kβ is at 2.464 keV, with the Pb Mα and Mβ in the general vicinity-- at 2.342 keV and 2.442 keV respectively. Because of the high Z of Pb, there are other lines just above and below: the Pb Mz at 1.839 keV, the Mγ at 2.652 keV and the M2N4 at 3.124 keV. The difference between the S Kα, S Kβ, Pb Mα, Pb Mβ and Pb Mγ are all within the resolution of the EDS detector which is ~ 263 eV at this time constant.

Having an accurate estimate of the EDS detector resolution (the FWHM of the peaks) as a function of energy, together with the energies and relative intensities of the Kα/Kβ and Mα/Mβ doublets allows one to attempt to deconvolute the Pb and S contributions to this slightly asymmetric peak.  The result?  Pb:S is determined, without standards using ZAF matrix corrections, to be 73:27.

If one is to use EDS, the only possibility is to increase the resolution by increasing the pulse-shaping time constant as shown in a former application on this blog.  Increasing the TC from 0.5 µs  to 32 µs  drops the peak FWHM for Mn Kα from ~ 263 eV to ~ 142 eV. That data is shown in the second image. The increased resolution is immediately apparent. The Pb Mz is very clearly resolved as a separate peak on the left of the main peak, as is the Pb Mγ on the right. The S Kβ and Pb Mβ is apparent as a slight shoulder on the right of the main peak.  The S Kα and Pb Mα are still left unresolved.

Again, knowing the detector resolution as well as the energies and relative intensities of the Kα/Kβ and Mα/Mβ doublets one can attempt to deconvolute the Pb and S contributions in this higher resolution peak. The result: Pb:S is 61:39.  Better, but still far from being a convincing estimate of the 1:1 stoichiometry of galena. This is not a failure of not using standards or a limitation of the matrix corrections. The EDS spectrometer simply can not resolve the peak shape with sufficient resolution and statistical certainty to allow the deconvolution of S Kα and Pb Mα which are 36 eV apart.

How to do better?-- wavelength dispersive spectroscopy (WDS) where the X-rays are diffracted from crystals or multi-layers.

EDS Pulse Processing Time Constants

The fundamental principle of EDS is energy dispersion. By that it is meant that X-ray energies are measured by directly measuring their energy. In EDS detectors, X-rays generate an electrical cascade in a solid state detector where the resultant pulse height is proportional to the X-ray energy.

The pulse processing electronics of the EDS detector can be modified to change the performance of the detector. The most important parameter is the pulse shaping time constant, or as it is indicated in the software-- TC. The top graph shows the Mn Kα peak width as estimated by the FWHM as a function of the time constant, TC.  The smaller TC's result in wider peaks and thus lower spectral resolution.  As the TC is reduced the Mn Kα width reaches a floor of ~ 142 eV which represents the resolution of the EDS detector.  It should be noted that it is convention to measure the resolution of an EDS detector at the Mn Kα line: 5.893 keV.

An obvious question is why would anyone then want to increase the TC and thus reduce the resolution of the EDS detector given the potential problem of overlaps?

The second graph shows the maximum detected rate-- defined as the maximum rate at ~ 28% dead time-- on a Mn sample with a 30 kV beam. Note that empirically there is a power-law that relates TC to maximum rate through a negative exponent close to -1.  As such the maximum rate is nearly inversely  proportional (but not exactly) to TC.  At at 0.3 µs time constant the maximum rate is about 90 kc/s, while at the 32 µs time constant the maximum rate is 1.5 kc/s.

As such the smaller time constants are best for high throughput applications. These would include EDS mapping and the detection of trace elements in the absence of potential overlaps. The larger time constants are best suited to higher resolution applications, such as quantitation that requires deconvolution of overlapping peaks. The larger time constants are also useful for very light elements as will be demonstrated in a future application note.

When are Standards Necessary?

The EDS spectrum shown was taken at 30 kV on a piece of GaAs wafer with a 2 µs shaping time-constant. The Ga and As Lα peaks are visible just above 1 keV while the Ga and As Kα and Kβ peaks are from 9.2 to 11.7 keV. These two sets of peaks have overlaps that can be resolved by deconvolution, and the peak sets differ by roughly 10 keV.

This is a very good test example to illustrate when standards are absolutely necessary for EDS quantitation. Ga and As were quantitated using standard ZAF corrections which account for such effects as the excitation volume, back-scattered current, absorption and fluorescence in the sample matrix. Obviously Ga:As should be 1:1 for a GaAs wafer-- and in this example we will look at Ga:As when quantitating with different combinations of these lines.

Common practice would be to quant using the Ga Kα and Kβ lines as there is less overlap with the K-lines than the L-lines. Ga Kα:As Kα yields 49.7:50.3-- which is quite close to the 1:1 expected from a GaAs wafer. If one is concerned about an accurate estimation of the As Kα intensity given the need to deconvolute the Ga Kβ peak, one can also quant Ga Kα:As Kβ-- which yields 49.3:50.7.  Both approaches are very close to the expected 1:1 value.  The error in any component is < 1%.

For the sake of exploration, consider quantitating with the low energy Lα lines. Ga Lα:As Lα is 48.6:51.4. The quant is now more than 1%, but just marginally so.

Let's consider quantitating with one high energy Kα line and one low energy Lα line. Ga Lα:As Kα is 44.7:55.3 and Ga Kα:As Lα is 53.0:47.0. In the first case the lighter element, Ga, is underestimated by 5.3% and in the later case the heavier element is underestimated by 3.0%-- but in each case the lower-energy component is the component underestimated.  We are now unable to argue convincingly that the GaAs wafer is stoichiometric 1:1.

What we find is that we can adequately quantitate without standards if the X-ray lines are close in energy.  When the lines differ by close to 10 keV-- then there are problems. Why?  Without resorting to standards we are not accounting for detector-specific losses such as absorption in the EDS detector window and the material that is cryo-pumped on its surface, as well as absorption in the body of the silicon EDS detector itself.  Such absorption is more significant at lower energies and thus we tend to underestimate those  components without resorting to standards. Another important effect is the energy dependent quantum efficiency of the EDS detector itself.