edfas.org 7 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 1 composites,[26] where data dimensionality reduction techniques, including principal or independent component analysis, can aid in identifying variations in the PDF.[26,27] Because the PDF is a two-body distribution function it is sensitive to SRO; but it does not elucidate MRO well,[28,29] where MRO are correlations on length scales of approximately 1.0 to 2.5 nm. Whereas fluctuation electron microscopy (FEM) is dependent on higher order (two, three, and four body) pair-pair combinations and thereby gains sensitivity to MRO.[29] Intensity fluctuations in diffraction patterns due to coherent interference, sometimes called speckle, can result from regions of local order. From a series of diffraction patterns the variance about the mean can be computed and it is this operation that creates the dependence on higher order pair-pair combinations. In a more intuitive sense, the variance identifies the scattering angles, hence length scales, exhibiting the greatest fluctuation (Fig. 2, Panel I). Furthermore, the size of the electron probe can then be varied through control of the convergence angle as an additional variable to interrogate MRO because the sensitivity of FEM to any ordering will depend on the relative length scales of the probe size and ordered domain.[29] FEM has been used to characterize amorphous semiconductors,[30,31] dielectrics,[32,33] and metallic glasses.[34] It has also been used to elucidate structure-property relationships (Fig. 2, Panel II).[33,35,36] In amorphous silicon, FEM has been used to test the validity of different theoretical models of the structure (e.g., continuous random network versus paracrystalline) and it was concluded that paracrystalline models match the data best.[37,38] Other analysis routines have been used to identify specific rotational symmetries, e.g., twofold up to tenfold, within diffraction patterns.[33,39,40] This would include symmetry elements (e.g., five-fold) that are prohibited in translational symmetry, but which are highly relevant for glasses which contain quasicrystals. When combined with spatially resolved measurements, one can map the spatial extent of different symmetry elements (Fig. 2, Panel III). In a Zr36Cu64 metallic glass Liu et al. [39] used this approach to identify icosahedral clusters as the dominant feature and from spatial distribution maps made inferences into the nature of MRO. While Huang et al.[41] was able to identify the coexistence of SRO with icosahedral, bicapped square antiprisms, and tricapped trigonal prism geometries in Pd77.5Cu6Si16.5. INTERNAL FIELDS Beyond crystallography and structure, STEM can also directly detect other physical properties of a material. For instance, it is possible to map and measure electromagnetic fields distributed within materials, due to the interaction between electromagnetic fields and the electron beam. The origin of the signal can be understood in a classical physics context as the Lorentz force acting upon the electron beam, or through quantum mechanics and the Aharonov-Bohm effect, which describes how an electromagnetic potential introduces a phase shift to the electron wave.[42] Using STEM to detect magnetic fields can be traced back to the 1970s. Shortly after Rose[43] proposed that new modes of phase contrast could be achieved using two detectors in parallel, Dekkers and de Lang[44] described an implementation of differential phase contrast (DPC) in the scanning transmission electron microscope relying on a split detector where the DPC signal is the difference of the signal from the two individual segments. In 1978, Chapman and coworkers[45] then demonstrated that DPCSTEM could map magnetic domains in permalloy and iron. These studies using segmented detectors do not qualify as 4D-STEM, because they do not use a pixelated detector that enables fine angular sampling of the diffraction plane. Yet through coarse angular sampling of reciprocal space, segmented detectors are gaining sensitivity to the distribution of electrons in the diffraction plane as a function of probe and can therefore be considered as an approximate of recording the full diffraction pattern.[46] Even though this article focuses on 4D-STEM measurements, some of the articles cited will be those using segmented detectors. These articles are included because many salient points for the theory and measurement artifacts of mapping electromagnetic fields are relevant regardless of detector type. A sampling of electromagnetic field mapping applications using 4D-STEM includes: mapping magnetic domains in various materials including permalloy,[47,48] Fe 60Al40, [49,50] FeRh,[51] NiFe,[52] plus identifying skyrmions in FeGe thin films[53,54] and the local magnetization in Fe 2As, [55] an antiferromagnet. Electric fields have been measured in Si[56,57] and GaAs[58] p-n junctions, along with polarization-induced internal electric fields in AlN/GaN nanowire heterostructures.[59] This set of applications extends even further if one considers studies using segmented detectors.[60] While the discussion here only covers long-range fields, there is an active body of research which studies the measurement of atomic electric fields as well.[61,62] If we consider the action of the Lorentz force on the electron beam in a sample, the angular deflection (β) due to the projected in-plane magnetic field is described as β = eB0lt/h, where B0 is the local magnetic field, e is the electron charge, λ is the wavelength of the electron beam,
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