edfas.org 15 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 3 diffraction reflections even in structures with large unit cells or multiphase materials. Image generation is not limited to integrating a subset of pixels within the 4D dataset. Matched illumination detector interferometry STEM (MIDI-STEM) uses a patterned phase plate with concentric rings to form the electron probe in lieu of the traditional circular probe-forming aperture. This concentric ring pattern is transferred to the transmitted and diffracted beams in the resulting diffraction patterns. The MIDI-STEM image signal is then computed by taking the difference between the sum of all odd ring intensities and the sum of all even ring intensities. The result is an imaging mode that produces nominally linear phase-contrast, thereby enhancing the image contrast of weakly scattering materials, which is particularly useful if they are prone to electron beam-induced dam- age.[22] Similar approaches of recording a 4D dataset while utilizing a phase plate to modify contrast has been repor- ted.[23,24] The combined parameter space of 4D datasets and structuring the incident probe characteristics creates a large parameter space to enable information rich measurement schemes that would not be accessible otherwise. STRAIN The strain state of a material or the interface between two materials can have a large effect on the resulting properties. For example, the charge carrier mobility in silicon-based MOSFET devices is often finely tuned by carefully controlling the amount of lattice strain in the material which in turn alters the electronic band structure.[25] Defects can also arise when the strain state of a material becomes large, as the crystal will relax through the formation of stacking faults or dislocations. Therefore, it is critical for process control, failure analysis, and materials development to be able to quantitatively measure strain at high spatial resolutions, and fortunately many TEM-based methods exist for doing so. For crystalline materials, the lattice periodicity can be directly visualized using highresolution TEM (HRTEM) and relative deviations in lattice parameter can be extracted via comparison of Fourier transforms calculated from various subregions in an image. This image-based approach is simple, but quantification can be problematic. Diffraction methods are much preferred for high-precision measurements and there are two primary approaches that are commonly employed: CBED and NBED. The CBED method relies on analyzing the features due to higher-order Laue zone diffraction in images of a highly-convergent electron probe.[26,27] Strain measurement via CBED has the advantage of high precision (values as high as 2 x 10-4 have been reported[28]) and can provide an absolute measure of the lattice parameter present in a material. However, to achieve this precision the specimen must be made very thin so that multiple scattering can effectively be ignored or, alternatively, an energy filter must be employed. Further, the analysis of the diffraction features can be complex and difficult to automate, which makes performing the measurement in a spatially resolved manner problematic. NBED, by contrast, is based on measuring the displacement of the diffraction spot and is well-suited to spatially resolved strain measurements with a slight tradeoff in precision. The resulting 4D dataset is then processed to determine the diffraction disc spacings and inversely the lattice spacing, at each probe position. NBED is conceptually simple and in theory should easily provide a straightforward, high-precision method for measuring strain at subnanometer-length scales. However, there are various challenges with data processing that must be carefully addressed to achieve the best result. The primary difficulty is in the measurement of the diffraction disc locations. In contrast to conventional electron diffraction where the diffraction maxima are strongly peaked and easily located, the use of a convergent probe in NBED distributes the diffracted intensity over a disc in reciprocal space whose diameter is defined by the angular extent of the incident probe. The best-case scenario is for very thin specimens where the contrast variation within the transmitted and diffracted discs will be minimal due to the lack of dynamical effects. In these cases, determination of the diffraction disc centers can be done via simple circle detection algorithms or by cross correlation of a template image of the transmitted central disc through vacuum. As the specimen thickness increases, these approaches to disc position detection become problematic as the intensity in each disc becomes less uniform and varies non-systematically. To overcome these problems, a number of different algorithms, including machine learning, have been employed to improve precision of disc position identification.[29-34] Several other approaches have been pursued to make NBED-based strain measurements more robust, including the use of patterned probe forming apertures.[35,36] Aperture shapes such as crosses or bullseyes are overlaid on the transmitted and diffracted discs in the NBED patterns, thus making centroid determination less ambiguous and sensitive to contrast variation in the discs. Significant improvements in precision of the measurement have been reported. However, it has also been shown by Mahr et al.[37] that the patterned apertures produce distorted probes with extended tails which can sample parts of the
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