Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction

Mahr, Christoph; Müller‐Caspary, Knut; Grieb, Tim; Schowalter, Marco; Mehrtens, Thorsten; Krause, Florian; Zillmann, Dennis; Rosenauer, A.

doi:10.1016/j.ultramic.2015.06.011

Cited by 48 publications

(55 citation statements)

References 34 publications

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“…Radial gradient maximization is another method used [21,8,22], in which concentric circles or ellipses are placed around an estimated disk center and their rotational averages are calculated. Since most disks have sharp edges, when the difference between the rotational average of concentric shapes are a maximum, the concentric shapes are properly placed around the center of the disk.…”

Section: Methods For Determining Diffraction Disk Positionsmentioning

confidence: 99%

“…However, this method performs best when there are whole disks without missing portions or strong contrast changes along the disks' edges, which is not always experimentally possible. Finally, this is an iterative method, and while it is faster than edge detection [22], it still requires several computational steps per disk.…”

Section: Methods For Determining Diffraction Disk Positionsmentioning

confidence: 99%

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Optimizing disk registration algorithms for nanobeam electron diffraction strain mapping

et al. 2017

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Scanning nanobeam electron diffraction strain mapping is a technique by which the positions of diffracted disks sampled at the nanoscale over a crystalline sample can be used to reconstruct a strain map over a large area. However, it is important that the disk positions are measured accurately, as their positions relative to a reference are directly used to calculate strain. In this study, we compare several correlation methods using both simulated and experimental data in order to directly probe susceptibility to measurement error due to non-uniform diffracted disk illumination structure. We found that prefiltering the diffraction patterns with a Sobel filter before performing cross correlation or performing a square-root magnitude weighted phase correlation returned the best results when inner disk structure was present. We have tested these methods both on simulated datasets, and experimental data from unstrained silicon as well as a twin grain boundary in 304 stainless steel.

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Section: Methods For Determining Diffraction Disk Positionsmentioning

confidence: 99%

Section: Methods For Determining Diffraction Disk Positionsmentioning

confidence: 99%

Optimizing disk registration algorithms for nanobeam electron diffraction strain mapping

et al. 2017

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“…This precision is not sufficient for several potential applications of 4D-STEM strain mapping, such as temperature mapping by thermal expansion measurement or mapping certain structural transformations via the lattice parameters, where strains may be on the order of 10 −4 . We note that direct comparison between precision limits reported in the literature is difficult because the precision limit depends on the sample properties, microscope image distortions, and the electron dose [20,26,27].…”

Section: Introductionmentioning

confidence: 95%

“…However, this procedure requires specialized hardware in order to precess the beam in combination with scanning, and longer acquisition times. Mahr et al [26] showed simulations of the precision of 4D-STEM strain measurements for different experimental conditions, and suggested the use of patterned probes, but found no substantial improvement over standard circular apertures when imprinting a single cross on the probe. "Hollow-cone" or Bessel structured probes, produced using an annular condenser aperture, are akin to precession diffraction, but with all tilts illuminated simultaneously (and thus added coherently).…”

Section: Introductionmentioning

confidence: 99%

Patterned probes for high precision 4D-STEM bragg measurements

et al. 2020

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Nanoscale strain mapping by four-dimensional scanning transmission electron microscopy (4D-STEM) relies on determining the precise locations of Bragg-scattered electrons in a sequence of diffraction patterns, a task which is complicated by dynamical scattering, inelastic scattering, and shot noise. These features hinder accurate automated computational detection and position measurement of the diffracted disks, limiting the precision of measurements of local deformation. Here, we investigate the use of patterned probes to improve the precision of strain mapping. We imprint a "bullseye" pattern onto the probe, by using a binary mask in the probe-forming aperture, to improve the robustness of the peak finding algorithm to intensity modulations inside the diffracted disks. We show that this imprinting leads to substantially improved strain-mapping precision at the expense of a slight decrease in spatial resolution. In experiments on an unstrained silicon reference sample, we observe an improvement in strain measurement precision from 2.7% of the reciprocal lattice vectors with standard probes to 0.3% using bullseye probes for a thin sample, and an improvement from 4.7% to 0.8% for a thick sample. We also use multislice simulations to explore how sample thickness and electron dose limit the attainable accuracy and precision for 4D-STEM strain measurements.

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“…Strain can be measured through convergent beam electron diffraction (CBED), high resolution conventional and scanning TEM imaging (HRTEM and HRSTEM) including Moiré fringe analysis (Moiré fringes appear when using a HRSTEM setup to scan at a lower magnification, due to the low-frequency sampling of the crystal lattice) as well as nano beam electron diffraction (NBED) which can also be performed in conjunction with precession electron diffraction (N-PED) [6][7][8][9][10] . Of these techniques, the best accuracy and precision are offered by nano beam precession electron diffraction with a spatial resolution better than 1nm, a strain sensitivity of σ = 2×10 −4 and an accuracy of ∆ = 1×10 −3 , though it requires additional specialised hardware 11,12 . Conventional nano beam electron diffraction is also a highly precise (σ = 6×10 −4 ) and accurate (∆ = 2×10 −3 ) technique, though it is not on par with N-PED and suffers the same limits in term of resolution.…”

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confidence: 99%

Electron Bessel beam diffraction for precise and accurate nanoscale strain mapping

Guzzinati

Ghielens

Mahr

et al. 2019

Applied Physics Letters

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Strain has a strong effect on the properties of materials and the performance of electronic devices. Their ever shrinking size translates into a constant demand for accurate and precise measurement methods with very high spatial resolution. In this regard, transmission electron microscopes are key instruments thanks to their ability to map strain with sub-nanometer resolution. Here we present a novel method to measure strain at the nanometer scale based on the diffraction of electron Bessel beams. We demonstrate that our method offers a strain sensitivity better than 2.5· 10 −4 and an accuracy of 1.5·10 −3 , competing with, or outperforming, the best existing methods with a simple and easy to use experimental setup. a) Electronic mail: giulio.guzzinati@uantwerpen.be 1 arXiv:1902.06979v3 [cond-mat.mtrl-sci]

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Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction

Cited by 48 publications

References 34 publications

Optimizing disk registration algorithms for nanobeam electron diffraction strain mapping

Optimizing disk registration algorithms for nanobeam electron diffraction strain mapping

Patterned probes for high precision 4D-STEM bragg measurements

Electron Bessel beam diffraction for precise and accurate nanoscale strain mapping

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