258 Michal Dagan et al.
position of an atom protruding from the surface of the sample. It is created by thousands of imaging gas atoms ionized at this position and projected by the field onto the phosphor screen. The crystallographic nature of the sample is clearly reflected in the image. A well-defined pole structure is apparent with a symmetry characteristic to the BCC tungsten lattice, which can be indexed appropriately. The imaging and evaporation sequence of the atoms is
fundamental to the reconstruction procedure. The terrace patterns are created as a result of the higher electric field generated above the more exposed surface sites at kink positions around the poles. Outer terrace atoms protrude to a greater extent than inner plane atoms, therefore higher gas ion current will be generated at these locations, giving brighter imaging and desired surface contrast. As the eva- poration of constituent atoms progresses, the outer terrace is removed first due to the higher electric field, exposing the inner plane atoms for imaging. The layer-by-layer field eva- poration process is demonstrated in Figure 1b, and in the Supplementary Videos 1 and 2.
Supplementary Videos 1 and 2
Supplementary Videos 1 and 2 can be found online. Please visit
journals.cambridge.org/jid_MAM.
3D RECONSTRUCTION ALGORITHM
The reconstruction algorithm consists of the following key steps: first, atomic positions are identified automatically across all images. Next, a tracking algorithm is implemented in order to identify the same atom as it appears in several images across the data set. Finally, the relative crystallographic plane of each atomis determined, completing the coordinates needed to create the final 3D reconstruction. These analysis stages are discussed in details in the following sections.
Gaussian Filter (GF) and Automated Detection of Atomic Coordinates In the first stage of the process, a GF is applied to each digital image to remove high frequency noise. The filter used is 2 + y - h
given by GF=exp - x - w 2
ðÞ ðÞ ,where w, h correspond 2
2 2σ2 As the imaging through the depth of the specimen
continues, the repeating pattern provides a distinct metric as required for the automatic detection of the number of planes evaporated within a stack of FIM images. Figure 1c presents the integrated intensity measured from the center pixels of the [2,2,2] pole across the first 500 consecutive FIM images. Due to the imaging sequence outlined in Figure 1b, each crystallographic layer will first exhibit low intensity in the middle of the pole, followed by the sequential imaging of atoms at the center of the pole, corresponding to the sudden increase in intensity in Figure 1c. Once the final atoms are evaporated, and a lower layer is exposed to the surface, the intensity at the center of the pole drops again. This drop in intensity is usually sharp, as the final three atoms of a plane tend to field evaporate almost simultaneously, or at least within a time delay that the experiment cannot resolve. Hence, each cycle of intensity intervals as shown in
Figure 1c represents the imaging and complete evaporation of a crystallographic layer. From this plot it can be concluded that in the first 500FIM images, six [2,2,2] planes are imaged, and five of them have been fully evaporated. From the intensity drop points on the plot, the final FIM image in the sequence that corresponds to a particular plane can be determined, that is, one image before point labeled 4 in the example in Figures 1b and 1c. As the images are taken at a constant rate, the width of each intensity interval corre- sponds to the evaporation time of each plane. This will evolve through the experiment due to changing field condi- tions as the shape of the specimen evolves.
to the width and height dimensions (in pixels) of the image, respectively, and σ determines the width of GF, which here is set to 40. The atomically resolved poles of interest are then selected and cropped out to reduce the size of the data and increase calculation speed. In this study, the steps compris- ing the 3D FIM reconstruction are demonstrated on the [2,2,2] pole, as it evolves on the atomic scale across 7771FIM images. However, the process can be applied to all poles that exhibit atomic resolution and where the evaporation of atoms can be highly controlled. Next, within each FIM image the intensity values of all
pixels are scanned and the coordinates of the local intensity maxima are identified, as marked by the black dots in Figures 2a and 2b (a demonstration of this step on a larger portion of the data can be seen in Supplementary Video 1). These maximum intensity pixels represent coordinates of all atoms appearing along the stack of images. Note that a threshold value is defined for the intensity peaks to be identified as atoms to avoid false identification due to remaining noise. (In this particular study the threshold was set at ~1.5 times the average intensity of background pixels.) As can be seen in Figure 2a, because of this threshold, not all atoms on this image have been positively identified. The unidentified atoms are marked manually in Figure 2a with white circles for clarity. Local field effects must be taken into consideration here, as these are responsible for atoms being imaged with different intensities. A higher field will result in an atom imaging more brightly, and will also increase the probability of evaporation for that atom. Thus, atoms are usually imaged with the highest intensity directly before evaporation. The evaporation process continues from the image in Figure 2a to the point in time represented by Figure 2b. The brightly imaged atoms in Figure 2a have evaporated, as indicated by the red circles in Figures 2a and 2b. Subsequent to the evaporation of these atoms, the intensity of the unidentified atoms increases above the identification threshold. Therefore, although not all atoms will be positively identified across all images inwhich they appear, all atomswill be identified eventually before their evaporation.
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