edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 4 6 results should be compared to simulations to ensure accurate interpretation. By comparison, the phase signal resulting from ptychography tends to be linear and amenable to quantification. Furthermore, when comparing ptychography with conventional imaging techniques ptychography has been reported to be more dose effi- cient.[13,19-22] This dose efficiency facilitates the study of materials that are particularly sensitive to radiation damage, such as zeolites,[23] halide perovskites,[24] polymers,[25] and biological specimens.[26] The change in phase of the electron is sensitive to a host of phenomena beyond determining the atomic arrangement of a material. For example, charge redistribution due to changes in bonding, which might be a result of a defect, can be detected.[27] Magnetic potentials will also induce a phase shift and can be distinguished from the electrostatic potential of the sample.[28] Taking advantage of this, Chen et al. mapped the distribution of skyrmions in an FeGe sample.[29] Notably, the reported spatial resolution of the FeGe ptychography reconstruction was better than an induction map derived using center of mass (COM) data analysis (which was covered in Part II).[29] This ability of ptychography to surpass the resolution limits imposed by the optics of the microscope is a significant benefit and covered in the next section. SUPER RESOLUTION The spatial resolution of STEM is many times larger than the fundamental limit posed by the electron wavelength due to lens aberrations and diffraction from the probe forming aperture. Increasing the convergence semi-angle (α) mitigates diffraction effects[30] and increases the infor- mation limit.[31] However, α cannot be increased bound- lessly due to the geometric and chromatic aberrations of the microscope lens, which become resolution limiting as α is increased. As a result, the spatial resolution of microscopes without aberration correction is about 0.1 to 0.3 nm, depending on focal length of the objective lens and the electron wavelength set by the accelerating voltage.[30,32-34] Aberration corrected microscopes, which are equipped with advanced optical elements that reduce the lens aberrations, can achieve resolutions of 0.06 nm or better.[35] Aberration correctors are a hardware solution to improving spatial resolution, which comes at great cost and increased microscope complexity. Whereas ptychography offers a software-based approach, which has even been demonstrated to achieve “super resolution,” where the resolution of the reconstructed images surpasses the physical limit of the microscope. Super resolution is possible because the diffraction patterns in a ptychographic dataset are not corrupted by lens aberrations or other sources of incoherence and instability, which limit conventional image formation. The first demonstration of super resolution was by Nellist et al. where the reconstructed image possessed a spatial resolution of 0.136 nm using data collected on a microscope whose incoherent image resolution at best would be approximately 0.27 nm.[34] Due to the dependence of resolution on several factors, including wavelength, it can be difficult to make comparisons, and these quoted values start to lack context. Table 1 compares traditional imaging and ptychography through a set of performance metrics normalizing the reported resolution (d) as a function of wavelength (λ). In short, d/λ decreased with aberration correction and now even further with ptychography. Fig. 2 Panel I: A reconstructed modulus and phase image of GaN [210] compared to traditional ADF and annular bright field (ABF) images. The Ga and N atomic columns are clearly observed in the phase image. Reproduced under the terms of a Creative Commons CC BY license.[16] Panel II: Reconstruction of PrScO3 [001] (a) showing information transfer to 43.9 nm-1 in the FFT, (b) well beyond the information limit set by the microscope optics. The scale bar is equal to 0.2 nm. Reproduced with permission from Chen et al.[19] (a) (b)
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