Monte Carlo Simulator
Table 1: EDS detector parameters modifiable by user in libMCXray.
Input properties for simulated EDS detector Crystal type (Al or Si) Crystal elemental density
Crystal dimensions (radius and thickness) Dead layer thickness Diffusion length Detector efficiency Take-off angle of detector Position of detector in space Number of energy channels
sample surface at steps specified by the user input resolution. Once the sample material is constructed, it is placed so that the beam and the sample are along the same axis. Teir vertical distance is specified by the desired working distance. Detectors may then be added to the simulator. Te BSE
detector may be defined as a disc or circular annulus below the electron gun. Te input in this case is the inner and outer radius of the annulus or the radius of the disc. BSEs are defined as those which have exited the sample and intersected the detector. Te EDS detector is defined by the properties speci- fied in Table 1 and are similar to the stand-alone version of MC X-ray. Multiple detectors can be added to the simulator, each with their own properties. Last, bright-field and dark- field detectors can be added below the sample. Each is defined by their distance from the exit surface of the sample and their inner and outer solid angles. Again, intensities of either signal are constructed from the number of electrons intersecting the respective detectors upon exit from the sample. Te program output is separated into two parts: electron and X-ray data. From the rasterizing, the BSE image and any
Table 2: Compositions of the simulated system assigned to the MultiROI of Figure 1.
Phase number 1 2 3
Element Ni
Fe Cr
Color in Figure 1 Transparent Red Blue
possible transmitted signal images are output as 2D arrays of floating-point real numbers. Te EDS maps are output as 3D arrays where the first two dimensions are the point coordinates and the third dimension is the energy spectrum. Finally, if point analyses are chosen, the X-ray depth distribution curves, ϕ(ρz), of specified transitions may be output.
Results and Discussion BSE image simulation. A MultiROI of a three-phase alloy
compiled from a focused ion beam image dataset was used to simulate backscattered images. A 3D perspective of the Mul- tiROI is depicted in Figure 1. Elemental compositions were assigned to the phases prior to performing the Monte Carlo simulation. A Ni-Fe-Cr system was investigated where each element was associated to a pure single phase. Te phases to which each element is associated are presented in Table 2. Te incident probe position was rasterized across the top surface of the sample shown in Figure 1. Te sample plane at the incident direction is displayed in Figure 2. Simulations were performed at 15 keV using 5,000 elec-
trons. Because the simulations of each probe position are inde- pendent, the method is easily parallelized, allowing for an acceleration of 80 to 100 times the computing time of the origi- nal program. Te simulated BSE image corresponding to a sub- section of the incident plane of Figure 2 is presented in Figure 3. Te image consists of 512 × 512 pixels situated about the
center of the plane. Tis area is indicated in Figure 2 by a dashed rectangle. Here, the three pure element phases are clearly dis- tinguished with the fine structures from the underlying geom- etry clearly visible. Te differences in signal level clearly reflect
Figure 1: 3D representation of sample geometry used in simulation experi- ment. Phase 1 is the matrix, phase 2 is in red, and phase 3 is in blue. The matrix phase is transparent.
2020 September •
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Figure 2: View of simulated material from beam incident direction. The area across which the beam was rasterized is indicated by a dashed rectangle.
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