Characterisation of sub-micrometre features with the FE-EPMA

The goal of this work is to compare two strategies for doing sub-micrometre analyses using the Fe-Ni binary system, as an example. The first approach involves reducing the overvoltage to 1 – 3 kV over the critical ionisation energy of the K X-ray lines. Using such a small overvoltage greatly restricts the size of the analytical volume. Upon entering the sample, the beam electrons quickly lose the additional energy required to excite the X-rays of interest. As a result, the K X-ray line for Fe and Ni will only be produced very near the surface. The second strategy is to use the L-lines for Fe and Ni, and drop the accelerating voltage to a level that will produce the smallest overall interaction volume of the beam electrons. Each strategy has its advantages and disadvantages that depend on the ultimate goal of the analysis and the elements involved. Both methods produce small analytical volumes. However, the L-lines from the transition elements are more problematic because of uncertainties with their mass absorption coefficients. Therefore, using the L-lines in low-kV analyses are more challenging to get good quantitative results. The advantage of using L-lines is that they travel a shorter distance within the sample, and therefore secondary fluorescence becomes less of an issue. The best results will come from a combination of these strategies. Using a multiple kV approach allows the user to select the optimum conditions for each element.


Introduction
The field emission electron column has dramatically changed electron imaging. The higher electron density and smaller electron energy spread allows for an electron beam spot size that is nearly an order of magnitude smaller than that produced by the traditional thermionic tungsten filament (figure 1). This smaller spot size results in images that have far improved spatial resolution particularly at high beam currents (figure 2). Earlier cold field emission electron guns were not suitable for the electron microprobe because of their poor beam stability (~ 10 %/hour) and their low beam currents (~ 1x10 -9 A).
With the thermal, field emission electron guns (TFE), both beam stability (< 0.1 %/hour) and high beam currents (~ 1x10 -6 A) can be achieved. This now makes the field emission gun ideal for the electron microprobe.
Some have previously argued that the field emission gun does not add to the analytical range of the electron microprobe because it's the scatter of electrons within the sample that controls the analytical area, not the beam diameter. The electron scatter is in turn controlled by the energy of the electron beam and the density/atomic number of the sample being analysed. However, with the thermal field  emission (TFE) electron gun, it is possible to work at much lower accelerating voltages and still maintain a very small spot size. This greatly reduces the analytical area. It should be pointed out that high-resolution imaging can also greatly improve the quality of microanalyses, even if one is not working at low-accelerating voltages. High spatial resolution imaging not only assists in determining what to analyze, but helps identify where not to analyse. Figure 3 is such an example. Shown are small crystallites in a volcanic glass. If the objective is to analyse the glass, it is critical to be able to identify areas where the crystallites exist in order to avoid them. Therefore, even if the analytical volume is much larger than the size of the crystallites, finding larger areas clear of them becomes paramount when attempting to analyse the glass.
Two general strategies have been suggested for analysing very small volumes [1]: (1) low voltage analyses, and (2) low overvoltage analyses. Both have advantages and disadvantages. This work will attempt to summarize the many issues that should be considered when attempting to decide which approach is best for a given analytical situation. These include: (1) the size of the analytical volumes, (2) minimum detection limits, (3) quality of the matrix corrections, (4) secondary fluorescence, and (5) effects of surface contamination, oxide layers, and carbon coatings.  Figure 3. Backscattered electron images of sub-micrometre dendritic crystallites in a volcanic glass collected on a JEOL JXA-8530F field emission electron microprobe. The crystallites are too small to analyse, but high-resolution imaging means that they can be avoided when preforming analyses of the glass.

Low voltage analyses (low-kV)
As one decreases the accelerating voltage, and therefore the energy of the beam electrons, the spread of the electrons within the sample is also reduced. The electrons have less energy and therefore can travel only a short distance before they have lost all their energy. As a result, one can greatly reduce the volume being analysed by dropping the accelerating voltage from the typical microprobe analytical range of 15 -25 kV to a low voltage range of 5 -10 kV (figure 4). Often, this will require switching to a lower energy X-ray line. However, there is a limit as to how low the accelerating voltage can be decreased and still improve the spatial resolution of the analyses. As the accelerating voltage is decreased, the interaction volume decreases, but the diameter of the electron beam increases (figure 5). Therefore, for each material, there is an optimum accelerating voltage, where the size of the area of electron scattering within the sample is equal to the diameter of the beam. A lower accelerating voltage will increase the analytical area because the beam diameter is bigger, and a higher accelerating voltage will increase the analytical areas because of the larger scatter volume. The optimum accelerating voltage depends on the material, but typically falls in the 5 to 8 kV range.   Figure 5. The analytical area is controlled by both the beam diameter and the scatter within the sample. For every material there is an optimum accelerating voltage that will produce the minimum analytical area. Commonly, this is in the 5 to 8 kV range. At a higher accelerating voltage, scattering within the sample generates a larger analytical area; at a lower accelerating voltage the expanding beam diameter makes for a larger analytical area. Beam diameters were measured on JEOL JXA-8530F field emission electron microprobe.
Size of X-ray generation volume calculated from the Castaing equation [2].

Low overvoltage analyses (low-U)
A second method that can be used to generate a small analytical volume is to minimize the overvoltage (U) (U = accelerating voltage / critical ionisation energy of X-ray) [1]. Typically an overvoltage of around 2 is recommended for routine analyses. This gives each beam electron enough energy to generate at least one characteristic X-ray, even if it has lost considerable energy due to other types of inelastic interactions within the sample. However, this high overvoltage results in considerable scattering of the beam electrons within the sample, making a large volume from which the X-rays will be generated. A low overvoltage analysis reduces the accelerating voltage to the minimum required to produce the characteristic X-ray of interest. An accelerating voltage of just 1 -3 kV over the critical ionisation energy is used. This dramatically reduces the number of X-rays generated, but also greatly reduces the volume from which the X-rays will be produced. The total electron interaction volume can still be very large, but the beam electrons quickly lose the required energy to create the characteristic X-rays of interest. As a result, all of the X-rays of interest are generated from a small volume near the surface (figure 6).

Figure 6.
Shown are Monte Carlo simulations of the size of the total electron interaction volume within Ni metal (blue) for a 10 kV accelerating voltage. Compared to that is the volume in which the electrons have enough energy (> 8.332 keV) to produce Ni-Kα X-rays (analytical volume in red). As the 10 keV beam electrons scatter within the sample, they quickly lose sufficient energy to produce the Ni-Kα X-rays, resulting in a small analytical volume. For the low-U analysis, 10 kV was selected for the accelerating voltage. This is only 1.7 kV higher than the critical ionisation energy required to produce the Ni Kα X-ray line (Table 1). A lower accelerating voltage would reduce the number of Ni Kα X-rays generated to a level less than acceptable. The alternative is to use the L-lines for Ni and Fe. The critical ionisation energy for these X-ray lines would, in theory, allow for an accelerating voltage as low as 1 kV to be used. However, considering the issues discussed in figure 5, and others to be discussed later, the low-kV analyses for this work will be limited to 7 kV. Table 1. Critical ionisation energy of Fe and Ni X-ray lines [3].
Both the low voltage method and the low overvoltage method for analysing sub-micron areas have advantages and disadvantages. The remainder of the paper will evaluate one binary system (Fe-Ni) in order to compare the differences between the two approaches. The purpose is not to determine which method is better overall. That will depend on the material being analysed and the objective of the analyses. For a given material, one method might work better for map analysis, while the other for quantitative analysis. One method might be better for the detection limits in trace element analyses, the other for accuracy in major element analyses. The objective is to highlight some of the issues that should be considered when attempting to achieve the smallest analytical volumes.

Analytical volumes
Monte Carlo modelling can be used to determine the size of the volume in which X-rays are generated by simply putting a threshold on the electrons, truncating the path once they have dropped below the critical ionisation energy of the X-ray in question. A comparison of the X-ray generation volumes for the low-U analysis method (using Fe-Kα, Ni-Kα, and 10 kV) and the low-kV analysis method (Fe-Lα, Ni-Lα, and 7 kV) is shown in figure 7.
For both Fe and Ni, the volume in which the L-lines can be generated at 7 kV in a metal containing 50 wt% Fe and 50 wt% Ni (figures 7a and b), is about 200 nm in diameter. For the K-lines at 10 kV, the Fe volume is also about 200 nm in diameter (figure 7c), whereas the Ni volume is closer to about 150 nm (figure 7d). The depths from which the X-rays can escape are generally smaller than the diameter of the X-ray generation volume. The ϕ(ρz)-plots in figure 8 show the depths at which the various X-rays are generated, and from which the X-rays can escape. For the K-lines, the generated and escaped profiles are nearly identical. For the L-lines, there is a significant difference. Due to the low energy of the L-lines, there is a large discrepancy between the number of X-rays generated in the sample and the number that ultimately escape from the surface (figures 8a and b). The sample absorbs many of the generated X-rays before they reach the surface. This discrepancy must be corrected for by the matrix correction routines. These large corrections are one of the reasons for the errors when using the lower energy L-lines in quantitative analyses. Because of the higher energy of the K-lines, most of the generated Kα X-rays for Fe and Ni will escape; therefore, the matrix corrections are much smaller.
The analytical depth for these X-ray lines in a metal that is 50:50 Fe:Ni can be defined using the 99 % escaped depths show in figure 8. This is the depth above which 99 % of the escaped X-rays came. For Fe-Lα and Ni-Lα this is between about 120 to 150 nm. For Fe-Kα this depth is about 156 nm, and for Ni-Kα it is about 100 nm. Therefore, there is not a huge difference in the analytical   156 nm, and for Ni-Kα it is about 100 nm. Therefore, there is not a huge difference in the analytical area between the low-kV and the low-U analytical method for this binary system. Both should allow for analyses of volumes that are in the range of about 200 nm in diameter, and about 150 nm in depth. This is similar to the empirical observations of McSwiggen et al. [4], where they report consistent quantitative analyses of Ag 3 Sn grains down to about 250 nm.

Secondary fluorescence
X-rays can be generated in a sample from more than just the beam electrons. In many samples, secondary fluorescence can also generate characteristic X-rays. X-rays produced by the primary electrons can fluoresce X-rays in another phase some distance from the primary electron interaction volume. These secondary X-rays are then mistakenly assumed to be coming from the phase being analysed [5,6]. Whether a secondary X-ray is fluoresced depends mostly on the energy of the primary X-ray relative to the critical ionisation energy of the secondary X-ray. The probability of fluorescence is at its greatest when the energies are the same. As the difference between the two energies increases, the probability of fluorescence decreases. If the primary X-ray has an energy greater than the critical ionisation energy of the secondary X-ray of more than about 3 keV, then there will be no significant fluorescence [3]. If the primary X-ray has less energy than the critical ionisation energy of the secondary X-ray, then it is not possible to create the secondary fluorescence.
To determine the degree to which secondary fluorescence may be a problem in the Fe-Ni system, the NIST programme DTSA II was used to model the effect [7]. It was assumed that an area of pure nickel was in contact with a pure iron metal phase. Spectra were generated for spots within a pure Ni phase at various distances from the interface with Fe. The weight percent of Fe was determined using both the Fe-Kα line and the Fe-Lα line. The results are shown in figure 9. When the Fe-Kα line is used, one can see that the effect of secondary Fe fluorescence is very significant (figure 9a). Even 10 to 20 µm from the interface, about 0.5 wt% Fe could be measured. This would be a major problem if trying to measure minor or trace concentrations of Fe in a nickel phase that was surrounded by an iron phase. However, figure 9b shows that if the Fe-Lα line is used, no Fe was detected beyond about 0.2 µm from the interface when a 7 kV accelerating voltage was used. Therefore, a sub-micrometre grain of nickel, surrounded by an iron phase, could still be analysed for trace amounts of Fe. The reason there is little fluorescence of the Fe-Lα line is that the energy of the Ni-Kα line is too high to fluoresce a Fe-Lα line, and the energy of the Ni-Lα is too low to allow it to travel very far within the sample.
The Fe-Ni system is particularly sensitive to secondary fluorescence when using the K-lines. Other systems would have to be evaluated individually to determine the importance of this process when analysing sub-micrometre grains.

Detection limits
Both methods for analysing small volumes, whether using a low kV or using a low overvoltage will result in a drop in X-ray counts relative to those produced using the typical microprobe analytical range of 15 -25 kV. As the accelerating voltage is reduced, each beam electron is capable of producing fewer X-rays. This in turn reduces the detection limits for the element in question. Figure 10 shows the calculated detection limits for Ni-Kα and Ni-Lα in Fe metal as a function of accelerating voltage. These detection limits were calculated using eq. 1, while keeping the counting time and beam current constant at 20 seconds and 100 nA, respectively. The absolute values shown in figure 10 are not significant. These will vary with the sensitivity of the spectrometer being used, the counting time, and the beam current. However, if one keeps these constant, the detection limit can degrade significantly as one attempts to minimize the analytical area by dropping the accelerating voltage. For the Ni-Kα line, the detection limits become asymptotic as the accelerating voltage approaches the critical ionisation energy (8.332 keV) (figure 10a). For the Ni-Lα line, the best detection limit is achieved at an accelerating voltage of around 10 to 15 kV (figure 10b). The  detection limit worsens when the accelerating voltage is either increased or decreased. Decreasing the accelerating voltage produces fewer X-rays, while increasing the voltage will produce more X-rays. However, the X-rays are produced deeper in the sample, thereby getting absorbed before they reach the surface. Therefore the maximum measured Ni-Lα X-rays occur at the intermediate accelerating voltage. (1) where I B = average counts of the background at the Ni peak position on Fe metal, and I P = net counts of the Ni peak on pure Ni. It is clear that there is a trade-off between trying to obtain the smallest analytical area and the best detection limits. Attempting to minimize the analytical area will result in a worse detection limit. Comparing a 10 kV Ni-Kα analysis with a 7 kV Ni-Lα analysis shows that the Ni-Lα analysis has the better detection limit for a comparable analytical area. However, for Fe the reverse is true. This is due to the low count rate for Fe-Lα on the TAP crystal. Again, every situation is different. Spectrometer performances vary, as do intensities from one element to another. Therefore, one cannot generalize to other element systems without preforming the measures on the specific electron microprobe that will be used.

Quality of quantitative analyses
One problem with low-kV analyses is that for many of the transition elements the K X-ray lines can no longer be used, if a 7 kV accelerating voltage is used, and the L-lines can be problematic in some cases. For example, Fe has an absorption edge between the Lα-and Lβ-lines. This absorption edge causes a shift in the combined peak position on a layered synthetic crystal (2d = 6 nm) with changes in Fe abundance. On the TAP crystal, Lα-and Lβ-peaks are separate, but their mass absorption coefficients are dramatically different and poorly known because of the position of this absorption edge [1]. For the low energy L-lines, this is a particular problem because of the massive absorption that they undergo within the sample. Figure 11 shows a plot of the measured Ni-Lα k-ratios at 5 different accelerating voltages for a set of standards along the Fe-Ni binary. At 20 kV, the measured k-ratio for a 50 wt% Ni standard is about 0.25. About half of the expected X-rays are being absorbed by the sample. At successively lower accelerating voltages, the depth the beam electrons can penetrate diminishes, and therefore, the volume the X-rays are generated in becomes smaller and closer to the surface. Since the path to the surface is shorter, fewer of the X-rays get absorbed. At a 2 kV accelerating voltage, the Ni-Lα k-ratio is equal to the weight fraction of the Ni in the binary sample, and no matrix corrections are required to obtain the correct values. In this case, simply using a sufficiently low accelerating voltage can overcome the uncertainty in the mass absorption coefficient.  For quantitative analyses of sub-micrometre grains, the low overvoltage method will work better in the Fe-Ni system because the K-lines perform better in the matrix corrections. However, analyses using the L-lines can be improved by using standards that are closer to the "unknown" in composition. Table 2 compares the results of three metals along the Fe-Ni binary. Consistently, the 10 kV Kα analyses are better than those of 7 kV Lα analyses using 100 % metals for standards. However, the Ni-Lα results are greatly improved when a 50 % Ni standard is used. If normal standards are not available, internal standards may greatly benefit low-kV analyses. In these situations, larger grains within the sample are analysed at a higher kV to determine their composition. These grains are then used as a standard for the low-kV analyses. These internal standards have the advantage of (1) potentially being more similar in composition, (2) having the same thickness of carbon coating, and (3) having the same surface oxidation or contamination as the unknown.

Surface coatings
Quantitative analyses at low kV can be very sensitive to surface coatings. Figure 13 shows the effect of various carbon coat thicknesses on the intensity of the Fe-Kα and Fe-Lα X-ray lines when compared to an uncoated Fe standard. Plotted are both the calculated curves using the equation of Reed (1997), assuming a density of 1.8 g cm -3 for carbon, and measured values (red dots) from an iron standard with an approximately 15 nm carbon film. These results show close agreement between the measured and calculated results. One can interpolate the amount of error that will result when different thicknesses of carbon are used on the standard versus the unknown. Figure 13. Effect of carbon coating on X-ray intensity. Plotted are the calculated curves showing the decrease in X-ray Fe counts resulting from carbon films that are 10 nm, 20 nm and 30 nm thick, with a density of 1.8 g cm -3 and using the formula from Reed [8]. The red dots are measured values from an iron metal standard which was expected to have about 15 nm of carbon on its surface.
At high accelerating voltages, when using the Fe Kα-line, the difference in counts between a coated and uncoated sample is in the 0.5 wt% range. However, at 10 kV, a standard with a 10 nm coating and an unknown with a 30 nm coating will result in a difference of up to 6 wt% in Fe Kα-counts. For the Fe Lα-line (figure 13b), the impact of the carbon coating is much greater. At 7 kV there will be approximately a 15 wt% difference in X-ray counts between iron samples coated with 10 nm of carbon versus 30 nm.
Similar impacts can be expected as a result of oxide layers on sulphide minerals, sputtered metal coatings, or residue from polishing. To minimize these effects, make sure the surface of both the standard and the unknown are recently polished and clean, and that any deposited coatings are applied simultaneously to the standards and unknowns to ensure consistency.

Conclusions
Using either the L-lines and a low accelerating voltage, or the K-lines and a very low overvoltage will produce very small analytical volumes in the Fe-Ni binary. However, both methods have their advantages and disadvantages. If the objective is to produce the best quality, quantitative analyses of the major elements, then the low overvoltage method is preferable, because of the better-understood behaviour of the K X-rays lines. However, for quantitative analyses involving minor or trace elements, then one should consider using the L-line, because they are less likely to be produced by secondary fluorescence, and a better spatial resolution can be obtained. For many systems, though, using multiple accelerating voltages to perform a single analysis might be the best approach. It would allow the user to optimize their analytical conditions for each element. This strategy allows the user to measure the k-ratio of each element at the accelerating voltage that is best for that particular X-ray line. The k-ratios are then converted to weight percent using an off-line matrix correction programme that allows for multiple accelerating voltages. In a mineral system involving SiO 2 , Al 2 O 3 , CaO, MgO and FeO, for example, the FeO could be analysed at 10 kV, using the Kα X-ray line for better quantitative accuracy, and the other elements could be analysed at 6 or 7 kV. For a typical silicate, the analytical volume for all of the elements would be around 0.5 µm under these conditions, and good quantitative results could also be obtained.
Regardless of the methods used, care should be taken when carbon coating the samples to ensure that identical thickness are applied to both the standards and the unknowns, and the surfaces should be cleaned of any oxide layers or polishing residue.