edfas.org 7 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 4 Since the report by Nellist et al., advances in detector technology, algorithms, and computing power have led to further gains in resolution. A reconstructed image of MoS2 reported spatial frequencies in the diffractogram of 25.6 nm-1 or approximately 0.039 nm. This value was a considerable improvement over the value of 10.2 nm-1 or approximately 0.098 nm observed in the diffractogram of a conventional annular dark field STEM image formed using the same imaging conditions.[21] This study also demonstrated the effect of the maximum scattering angle on the reconstruction by processing the same dataset whose maximum scattering angle was artificially truncated at different multiples of α. As the cutoff angle increased, the maximum frequency in the diffractogram increased and the atoms in the reconstructed image became sharper. This behavior mimics previously derived relationships for the resolution of ankylography and x-ray ptychography reconstructions; the resolution along the lateral (x and y) directions of the reconstruction is described by the relationship dx,y = λ / sin(θ max), where λ is the wavelength, and θmax is the maximum scattering angle in the diffraction pattern.[36] This equation suggests the spatial resolution of ptychography is limited by the maximum diffraction angle at which intensities can be measured with sufficient statistics. However, a study by Chen et al.[19] demonstrated that the motion of the atoms (due to thermal and zero-point effects) also constrains the spatial resolution. This phenomenon was identified by analyzing a reconstruction of PrScO3 (Fig. 2, Panel II) to quantify the different contributions that broadened the projected width of individual atomic columns. And while atomic motion poses a limit to the attainable resolution, sensitivity to the effects of atomic motion coupled with the spatial resolution of ptychography creates new measurement opportunities, such as extracting Debye-Waller factors of individual atomic columns. Such a level of sensitivity would be particularly useful around interfaces or defects, as existing techniques to measure Debye-Waller factors sample large regions thereby making it difficult to detect highly localized variations. OPTICAL SECTIONING AND THREEDIMENSIONAL STRUCTURE DETERMINATION Many electron ptychography studies to date involve nano or 2D materials, and this is not by chance but rather by design. The approximation introduced earlier to describe the exit wave as a product of the probe and the sample functions becomes untenable in thicker samples because it uses two dimensional functions to approximate three-dimensional objects. Conceptually, the breakdown Table 1 A compilation of references detailing resolution as a function of technique and accelerating voltage Description Accelerating voltage, kV Resolution, nm d/λ Reference High voltage TEM on an uncorrected instrument 1250 0.098 133.2 Ichinose, 1999[33] Intermediate voltage STEM on an uncorrected instrument 200 0.136 54.2 James, 1999[32] Intermediate voltage STEM with early generation geometric aberration correction 100 0.136 40.6 Delby, 2001[56] Early demonstration of electron ptychography 100 0.136 36.7 Nellist, 1995[34] Intermediate voltage STEM with geometric aberration correction 300 0.0405 20.6 Morishita, 2018[35] Low voltage STEM with geometric aberration correction 30 0.107 15.3 Sawada, 2015[57] Low voltage TEM with geometric and chromatic aberration correction 40 0.09 15.0 Linck, 2016[58] Ptychography, intermediate voltage, defocused probe, multislice algorithm 300 0.023 11.7 Chen, 2021[19] Ptychography, low voltage, focused probe, ePIE algorithm 80 0.039 9.3 Jiang, 2018[21]
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