Automated Atom-By-Atom 3D FIM Reconstruction 261


of intensity points in respect to the number of images describing the evaporation of the respective planes. This can be interpreted as two separate evaporation events occurring in the sequence and the overall imaging of three distinct atoms. Thus, the blue group will be further separated into three atoms. In comparison blinking, observable in the close- ups of Figure 3b, is found to be relatively short to the determinedmetric and therefore the groups of atoms will not be further divided. Figure 6b shows the whole point cloud at the end of the


separation procedure. The original intensity points are now colored by their group number, where each group represents a single atom, imaged across several images. Finally, once all atoms have been tracked across all images, the total displacement in the recorded coordinates of


each atom is calculated (displacement between the last and first recorded positions of the atom) as well as the duration of each atom on the surface (the number of images it appears in). These can then used to identify and resolve “suspicious” atoms that seem to have very large displacements or very long durations in comparison with the lengths of their cor- respondent intensity interval in Figure 1c.


Separation to Crystallographic Planes


The final step in the reconstruction procedure is placing the atoms in their correct crystallographic planes or in other words, correctly determining their in-depth, z, coordinate. Again, this is not a straight forward task due to the frequent divergence from the simplified “layer-by-layer” evaporation sequence. According to this simplified picture, a kink atom from an upper layer will evaporate before an atom in the layer below, and before an atom in the center on the same plane. In this case, all that is needed to determine which atoms belong on the same plane is given by the plot in Figure 1c. Each intensity interval on the figure represents the evaporation of one layer, and the atoms can be classified to the different layers according to the number of image in which they were last identified. However, the true nature of the evaporation sequence is


that of a stochastic process. Although center atoms will rarely evaporate before a kink atom on the same layer in the absence of a close-by defect (Stiller & Andrén, 1982), it is more common for kink atoms from lower planes to evapo- rate before the removal of the entire atomic layer above them. Examples of this behavior can be seen in Figure 4. In Figure 4a, atoms markedwith the number “2” are kink atoms from a lower plane than the three central atoms marked with the number “1”. It is apparent in Figure 4b that one of the kink atoms, marked with a white arrow, has evaporated before the atoms from the plane above. In fact, out of all the atoms that were analyzed for this study, ~27% were found to be such “cross-layer” evaporation events. In light of these frequent deviations from an over-simplified “layer-by- layer” evaporation model, a different approach must be taken to determine the crystallographic plane to assign to each atom.


Figure 4. a: Two planes are imaged here. The final three atoms from the higher plane are marked with the number “1,” and outer terrace sites from the lower plane are marked with “2.” b: An atom from a lower layer (marked with a white arrow) is evapo- rated before the three central ones of the upper layer. The two layers can be resolved by detecting decrease in intensity across the black arrow in (a).


In the example in Figure 4, the outer terrace of the lower plane can be spatially distinguished from the final three center atoms of the higher plane, by the “dark” region in the image, separating the two. By examining the intensity profile across the black line in Figure 4a, fromthe evaporating atom on the outer terrace to the center of the pole, this dark region is evident. Kink atoms evaporated before central atoms of higher plane were found to demonstrate highly repetitive profile shapes in several atomic configurations. These have been incorporated into the reconstruction algorithm, and along with derivative behaviors are used to identify such atoms. Figure 5 summarizes intensity profiles of repeating evaporation events. The profiles are always taken across a straight line from the atom in question to the center of the pole. They are calculated according to intensities of pixels along this line, on the image where the highest intensity was recorded for that particular atom (this usually corresponded to the image directly before its evaporation). In Figures 5a, a characteristic profile is shown for an “out of sequence” event. This intensity profile clearly demonstrates the decrease in intensity corresponding to the transition across the image from a kink atom belonging to a lower plane to the central atoms contained within the plane above it. For comparison, Figure 5b shows the same profile for a terrace atomthat obeys the simple layer-by-layer evaporation pattern, with its final imaging within the correct intensity interval of the plane on which it resides. Unlike the profile in Figure 5a, the decrease in intensity toward the center of the pole is not followed by a subsequent increase, as all the atoms from the plane above have already been evaporated, and thus do not appear in this image. However, the cases presented in Figures 5c and 5d, demonstrate an additional complexity to the problem. Atoms in these examples exhibit very similar intensity profiles. However, although the atomthe case of Figure 5c is a central atom evaporating “in sequence” with its plane, the atom in Figure 5d is a kink atomfroma lower layer, evaporating “out of sequence” and ahead of central atoms of the plane above it.


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