edfas.org 17 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 3 of the EWPC peaks can be determined far less ambiguously and therefore the precision of the strain measurement is improved. This method has been used to map the strain state in core-shell nanoparticles and to visualize domain distributions in ferroelectric materials.[39] While NBED has been used for many years for spatially resolved strain measurements, the development of high-speed direct detection cameras and 4D-STEM has increased the capabilities and ease of data collection for this technique. This has two major advantages. First, the high speed of acquisition allows for strain analysis over much larger fields of view with no loss in spatial resolution. Second, the high sensitivity of these detectors allows data of similar quality to be collected using a far lower electron dose. The advantage of an increased field of view for strain mapping has been demonstrated by Ozdol et al. in analyzing a GaAs/GaAsP multilayer specimen (Fig. 3 panel ii).[40] While maintaining a spatial resolution of 1 nm, they were able to map the in-plane strain fields over a 1 µm field of view with a precision of 1 x 10-3. The high speed of 4D-STEM-based strain analysis can also be leveraged to carry out in situ experiments where the strain distribution in a specimen can be monitored as a function of external stimuli such as mechanical deformation or thermal cycling. Pekin et al.[41] used this approach to study strain development in stainless steel using a holder capable of pulling the specimen in tension during STEM analysis. With this setup, they were able to simultaneously collect real-space images and reciprocalspace diffraction patterns to monitor dislocation creation and lattice expansion directly. Further, the introduction of pump-probe experimental configurations can extend this technique into the realm of sub-ns dynamic processes. For example, the time and spatially dependent strain state of single crystalline silicon patterned with tungsten discs was measured as acoustic waves propagated from the tungsten upon absorbing energy from laser pulses.[42] Finally, since STEM is inherently a projection-based technique, all the applications mentioned thus far in this section involve two-dimensional mapping of various aspects of the strain field perpendicular to the incident beam (i.e., in the plane of a thin specimen) and the value measured at each point is an average over the thickness of the sample. Typically, four components of the deformation tensor can be derived: these are the strain in the x- and y-directions as well as the in-plane shear and rotational components. Retrieving additional components of the tensor requires either tilting the specimen to make measurements at different orientations or analysis of higher order Laue zone (HOLZ) information. The high-speed and sensitivity of 4D-STEM may enable the use of electron tomographic techniques to measure the full, three-dimensional strain tensor at high spatial resolution at each threedimensional position within the specimen.[43] In electron tomography, multiple images are collected as the sample is tilted with respect to the electron beam. This image series is then used to calculate a three-dimensional image of the material. By collecting a full 4D-STEM NBED dataset at each specimen orientation, the projected strain maps can potentially be used as input for a three-dimensional reconstruction algorithm to recover the information lost in projection. This reconstruction process is non-trivial and development is on-going. DEFECTS Defects have significant implications for device performance and having the tools to reliably detect, categorize, and characterize them is crucial. Because the structure and characteristics of defects are incredibly diverse, spanning a range of length scales from macroscopic bulk defects to zero-dimensional point defects, a variety of characterization techniques are needed. Two such cases include images acquired under two-beam conditions to identify the Burgers vector of dislocations and HAADFSTEM images to reveal the position of individual, high atomic number dopant atoms in a low atomic number matrix.[44] As we previously discussed, 4D-STEM can reproduce traditional methods of defect characterization through virtual imaging, but more importantly, it can also be used to enhance existing methods or even enable new techniques. Case in point, Shao et al. have shown that a cepstral analysis of 4D-STEM data can be used to separate electron diffuse scattering from Bragg diffraction. This is performed by calculating the difference between the cepstral transforms of each individual diffraction pattern and the region averaged diffraction pattern.[45] The result is a spatial map of the diffuse scattering produced at each point in the sample that results from thermal or static atomic displacements of the periodic crystal lattice.[20] This technique, while recently developed, has already been used to identify the distorted region around a dislocation core in a SiGe thin film,[45] chemical short range order in a medium-entropy CrCoNi alloy,[46] and phase domains in MnO2 undergoing an intercalation reaction. [47] Some methods for defect characterization are adaptations of existing electron microscopy techniques that benefit from the spatially resolved sampling of 4D-STEM. Structure factor refinement is one such approach. A structure factor describes the scattering of an electron (continued on page 20)
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