Simulation of the spatial resolution of X-ray measurements in SEM

For a more detailed analysis of the spatial resolution of X-ray measurements, including the effect of x-ray absorption, the Monte Carlo Simulation Program CASINO [61] can be used. This program simulates the interaction of electrons with matter and helps to analyze the generated signals including characteristic X-rays in different ways. Pinard et al. for instance employed the program to calculate the depth resolution for C during a microprobe measurement [62]. They defined the depth resolution as the depth down to which 90 % of the C X-ray signal is emitted. In the study at hand, the interaction of an electron beam with the analysed material has been simulated using CASINO (Version 2.42). The simulated beam diameter was set to 5 nm. The accelerating voltage has been varied between 5 and 15 kV. The specimen was tilted to 0°. The composition used for the simulation is presented in Table 3 on page 55.

Figure 2-16, the energy of the electrons in the steel is plotted in dependence on position. The accelerating voltage was set to 15 kV. The different coloured lines indicate the kinetic energy of the electrons at the given positions. Knowing the ionization energy of a specific line allows one to roughly estimate the lateral resolution of the X-ray signal. It is also possible to plot the intensity of the generated X-rays either in dependence of the depth of the material or in dependence of the radial distance to the electron beam.

Figure 2-16: Energy of the electrons in % of the starting energy in depdendence of the position.

The simulation was performed with CASINO (Version 2.42) at 15 kV.

Figure 2-17: Depth resolution of the K-alpha line of Mn in the DP-steel calculated at 15 kV with CASINO (Version 2.42).

Figure 2-17-a) illustrates the calculated intensity profiles for Mn in the DP-steel. The black line shows the intensity of K-alpha X-rays in dependence of the depth. The red line shows how much of the signal is actually leaving the material. One can clearly see that nearly no absorption takes place in the case of the Mn-K-alpha line. In Figure 2-17-b) the integrated intensity fraction of the total intensity is plotted in dependence of the depth. The black cross indicates the depth from which 90 % of the signal is emitted.

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Figure 2-18 Depth resolution of the K-alpha line of Mn in DP-steel calculated at 15 kV with CASINO (Version 2.42).

For the C K-α line, absorption plays a much bigger role. As shown in Figure 2-18-a) most of the Characteristic C X-rays are absorbed in the specimen and do not leave it. The difference in generated X-rays and measured X-rays is even more visible in Figure 2-18-b. The depth where one finds 90% of the generated X-rays is 466 nm. However, once absorption has been taken into account the depth reduces to 148 nm. Comparing the simulations of the K-alpha line of Mn and C shows that the C signal is generated in a greater depth compared to Mn. Yet, once absorption has been taken into account; the depth resolution of C is more than twice as good as the Mn resolution. In order to reveal the influence of the accelerating voltage, several simulations with varying accelerating voltage have been performed. In Figure 2-19, the depth resolution for Mn and C is plotted for different accelerating voltages. The plotted depth values are again the depths from which 90 % of the emitted signal including absorption is coming from. It appears evident that for the Mn K-alpha line the depth resolution depends much more on the accelerating voltage compared to the C-alpha line. This is due to the stronger dependence of the depth resolution on the effect of absorption of soft X-rays. Almost every K-alpha X-ray of C is absorbed if it is created deeper than 150 nm.

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Figure 2-19: Comparison of the depth resolution for the K-alpha line of Mn and C in the DP-steel for different accelerating voltages calculated with CASINO (Version 2.42).

Figure 2-20: Result of the simulated linescan for C with CASINO (Version 2.42). The used accelerating voltage is 10 kV and the measured C line is the K-alpha line. The grey area shows the length in which the C signal rises from 10 % to 90 %. The spot size of the beam is 5 nm.

In order to measure the lateral resolution, a procedure similar to the one described by Pinard et al. was used [62]. A linescan over a boundary, separating two areas which differ in the content of Mn and C, was simulated using Casino 2.42. The step size was 25 nm. The boundary itself is orientated perpendicular to the surface and has no thickness itself. The scan is started 1000 nm away from the boundary and stops 1000 nm after it. On the left side

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of the boundary the material had a C content of 0.0138 Wt. % and a Mn content of 1.82 Wt. % . On the right side of the boundary the material had a C concentration of 0.138 Wt. % and a Mn content of 6 Wt. %. The Fe content is on both sides of the boundary balanced and the other substitutional elements have the same concentration levels as shown in Table 3 on page 55. The X-ray intensity was normalized in a way that 0 % is the element concentration in the lower concentrated region and 100 % is the concentration in the higher concentration region. The lateral resolution was determined by measuring the length on which the intensity of the characteristic X-ray line of Mn or C dropped from 90 % to 10 %. A typical result of such a simulation can be seen in Figure 2-20. Here the linescan was simulated with an accelerating voltage of 10 kV. The lateral resolution for C lies here at 230 nm, which is much higher than the depth resolution of C at 10 kV, which lies at 130 nm. For a comparison of the lateral resolution calculated with Monte Carlo simulations and the resolution derived by Equation (2.15), Figure 2-21 was derived. In order to calculate the lateral resolution with Equation (2.15), the density of Fe (7,874 ^𝑔

𝑐𝑚³) was used. For C as well as for Mn the Monte Carlo simulations deliver a smaller lateral resolution than the equation. It appears evident that for higher accelerating voltages the difference between the values calculated with the equation and the ones calculated with Monte Carlo simulations increases. Equation (2.15) can only be used to obtain a safe upper limit for the lateral resolution. For a detailed analysis,