Automated Atom-By-Atom 3D FIM Reconstruction 263


Figure 6. The three steps of reconstruction demonstrated across the entire analyzed data set. a: Intensity peaks are identified on all images. b: Intensity peaks are grouped according to atoms. c: Final reconstruction: each atom is posi- tioned in its crystallographic layer in its initial position, coordinates converted to real space. d: The fifth plane is shown. Initial positions (blue) of the atoms on this plane and final positions (in red) are shown together for compar- ison in the lower window. e: As the final reconstruction is rotated and tilted, additional crystallographic planes are evident. On the right is a close-up view on some of the reconstructed [2,2,2] planes.


belong to, from the surface and into the depth of the sample, in a direction normal to the plane. Thus, in the conversion from plane numbers to actual z coordinates, each layer will be separated from the next by the theoretical plane constant of the [2,2,2] planes in tungsten. The x–y coordinates can be transformed from “image dimensions” to real tungsten lat- tice dimensions by calibrating interatomic distances to the corresponding theoretical values on a tungsten [2,2,2] plane. This procedure is done by finding the average nearest neighbor (NN) distance, measured in terms of number of pixels across the FIM image, between all NNs atoms in the data set. This distance can then be used to calibrate number of pixels to SI units of length, using the expected theoretical NNs distance in these planes in tungsten. Although the procedure provides an estimation to the average corre- sponding distances, deviations from the resultant calibration are expected due to changes in local magnification condi- tions, as well as changes to the imaged positions of the atoms before evaporation (as discussed further in later sections). These will of course result in a slightly different “pixel to real space” calibration at each point in time. Figure 6 summarizes all the key stages of this recon- struction approach as applied to all of the analyzed images.


Figure 6c presents the final reconstruction, once all atoms have been identified, tracked, and placed in their crystal- lographic planes. In the final reconstruction all atoms are placed in the initial positions recorded for them, that is, their coordinates on the image on which they were first identified. The difference between initial and final coordinates can be seen in the “close-up” view of plane number five, in


Figure 6d, where initial positions are marked in blue and final positions in red. Note, that as the final reconstruction is rotated and tilted, additional crystallographic planes other than [2,2,2] are clearly resolvable as demonstrated in Figure 6e.


RECONSTRUCTION OF MICROSTRUCTURAL FEATURES


The reconstruction algorithm described above was designed with the goal of developing a highly accurate approach to the reconstruction of atomically resolved poles, where each atom can be precisely mapped onto the crystal lattice. It is in these volumes where reliable study of vacancies and atomic-sized defects can be performed. Implementation of this algorithm


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