Quantitative analysis of the accuracy and sensitivity of strain measurements from nanobeam electron diffraction

Abstract

It is difficult to determine the accuracy of NBD measurements for several reasons including, the uncertainty in the actual value of the strain in the reference patterns, uncertainty in the strain of known reference samples due to sample preparation, and uncertainty in the algorithms used measure the reflection positions. In order to quantify the accuracy and sensitivity of NBD analysis several reflection fitting algorithms have been tested using simulated diffraction patterns and experimental data from structures of known composition.

py4DSTEM: A Software Package for Four-Dimensional Scanning Transmission Electron Microscopy Data Analysis

“…Second, the negative kernel intensity penalizes the cross-correlation values where a Bragg disk and a template are slightly misaligned, enhancing the detectability of correlation maxima where disk/template alignment is perfect. The method of subtraction of a Gaussian reported here is found to be a useful heuristic and has a similar effect to other edge filtering methods such as Laplacian of Gaussian filtering or pre-filtering with a Sobel filter; other similar approaches are described elsewhere (Williamson et al, 2015;Grieb et al, 2017Grieb et al, , 2018Pekin et al, 2017;Mahr et al, 2019;Padgett et al, 2019). Adding structure to the electron probes using an amplitude mask in the condenser aperture has also been shown to significantly enhance the precision of Bragg disk detection (Zeltmann et al, 2020).…”

Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond

“…This was also the focus of the work by Pekin et al (2017), who analyzed using different correlation methods where a vacuum reference probe was compared with experimental and synthetic diffraction patterns. Other authors have analyzed the accuracy of NBED strain measurements including Williamson et al (2015), Grieb et al (2017), and Grieb et al (2018), or the influence of artifacts such as elliptic distortion by Mahr et al (2019).…”

Quantification and mapping of elastic strains in ferroelectric [BaZrO3]xᴧ/[BaTiO3](1-x)ᴧ superlattices

“…The strain measurements performed using NBED technique is based on the analysis of acquired diffraction patterns collected from strained and unstrained (reference) areas of the sample. The accuracy and the sensitivity of the strain measurement using this technique were explored extensively by Williamson and co-workers [39].These authors applied a diffraction reflection fitting algorithm to both simulated and experimental diffraction patterns collected from known composition of strained SiGe. These authors processed the recorded diffraction patterns with and without autocorrelation method.…”

“…) SLs having periods of Λ = 6.6 nm and Λ = 11 nm respectively, grown by pulsed laser deposition (PLD) on SrTiO 3 (STO) substrate to investigate the periodicity effect on the epitaxial strain and interfaces for a fixed total thickness of the SL and for BZ ratio of about x = 0.6. The dedicated software used in this study is similar to the one used by Beche and co-workers [41] and including the processing capabilities developed by Wialliamson and co-workers [39].…”