edfas.org 9 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 4 Because STEM data are 2D projections of a 3D structure, it can be difficult to unambiguously detect or fully quantify features that vary through the thickness of the sample. Thus, 3D ptychographic reconstructions create many opportunities, such as improved accuracy in the dimensional metrology of rough interfaces or characterizing point defect complexes and extended defects, such as dislocations. These methods could also be used to isolate real sample features from artifacts induced during the sample preparation process. The true lattice strain of a thinned sample could be measured without complication from surface relaxations which inevitably occur to name but one example. The scope of applications realized will depend on the magnitude of the depth resolution. Compared to the lateral resolution, the depth resolution of multislice ptychographic reconstructions are at least an order of magnitude worse (e.g., depth resolution values of approximately 4 to 23 nm have been reported[19,23,41,42]) and are currently insufficient to resolve the 3D structure with atomic resolution. One potential pathway to improve the depth resolution of ptychographic reconstructions is to incorporate tomographic methods, where the 3D structure of a sample is reconstructed from a series of 2D images acquired at different orientations. Results from multislice ptychography advantageously showed that the phase change at different atomic positions was linear as a function of thickness[19] and therefore satisfy the projection requirement where the recorded dataset should exhibit a linear relationship to an integral of a physical property along the projection direction.[43] By comparison, even HAADF-STEM signals can exhibit non-linear behavior,[44] which suggests that ptychography will be a valuable addition to the 3D structure determination toolbox. Implementation could be done by serially recording and reconstructing ptychography data at multiple tilt angles and then combining with a tomography rou- tine.[45,46] This approach has been demonstrated to resolve individual atoms and point defects on datasets generated by numerical simulations[45] and was used to solve the structures of ZnTe filled CNTs[46] and a DNA origami scaffold.[47] This serial approach is not the only possible workflow and there are proposed algorithms that integrate both in a single reconstruction routine to generate the 3D reconstructed volume.[48] Furthermore, these examples were using 2D ptychographic reconstructions as input for the tomographic reconstruction. An alternative approach is to combine tilt-series acquisition with optical sectioning and multislice ptychography. Combining optical sectioning with a tilt-series has improved the resolution of the tomographic reconstruction for conventional STEM imaging.[49] Therefore, this approach when combined with ptychography could potentially lead to tomographic reconstructions with 3D atomic resolution. One such report on a Co3O4 nanoparticle has recently been made. [50] RECONSTRUCTION FIDELITY While the results discussed demonstrate the power of ptychography, some caution is warranted as there is no guarantee that a reconstructed image faithfully represents the structure or properties of the sample. This is exemplified in Fig. 4 where a 2D reconstruction algorithm is applied to an increasingly thick sample and fails because the algorithm did not appropriately model the physical parameters of the probe and sample. Other reports in the literature identify additional artifacts or limitations and attempt to address them.[6,19,51,52] In a systematic treatment, Cao et al. examined different experimental limitations that are present in the illumination, sampling, and detection processes and discussed algorithms to account for these imperfections.[53] Using these improved algorithms, a previously published experimental dataset,[54] whose reconstruction exhibited artifacts, was reprocessed and exhibited improved fidelity. Other approaches to facili- tate high fidelity reconstructions include statistical Fig. 4 Reconstruction of PrScO3 [001] at different depths comparing a multislice (top row) and 2D or single-slice algorithm (bottom row). The 2D reconstruction algorithm fails to faithfully reconstruct the structure at larger thicknesses. The scale bar is equal to 0.2 nm. Reproduced with permission from Chen et al.[19]
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