Patterned probes for high precision 4D-STEM bragg measurements

Abstract

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.

Fast Pixelated Detectors in Scanning Transmission Electron Microscopy. Part II: Post-Acquisition Data Processing, Visualization, and Structural Characterization

“…Using test data obtained in the SPED mode of acquisition (Vincent & Midgley, 1994) of a custom system (MacLaren et al, 2020), we demonstrate that a lattice parameter fractional precision of 6 ×10 −4 is possible using a probe with a spatial resolution of 1.1 nm. This precision value is approximately 2–3× larger than the best ones reported in the literature using standard probes in a SPED mode (Rouvière et al, 2013) and patterned probes in standard STEM mode (Guzzinati et al, 2019; Zeltmann et al, 2020).…”

“…At the small level of material distortion found here, the fractional precision of the lattice parameters is the same as that of the associated strain parameters. Very recent reports of strain measurements using patterned probes in the literature (Guzzinati et al, 2019; Zeltmann et al, 2020) approach the best values reported from standard Airy probes in SPED acquisitions (Rouvière et al, 2013), but with potential benefits of improved dose efficiency. The fractional precision of 6 × 10 −4 obtained here with a DED is approximately 3× higher than the value from the latter (of ≤ 2 × 10 −4 ) with a similar spatial resolution, but using exposures 100× smaller and a detector with 64× fewer pixels (256 × 256 DED versus a 2k × 2k CCD).…”

“…Analysis of such 2D lattice images can be performed with a range of packages, including Atomap, optimized for atomic resolution STEM imaging (Nord et al, 2017); CrysTBox for HRTEM, SAED, and convergent beam electron diffraction (CBED) imaging (Klinger, 2017); library-based approaches to crystal phase and orientation identification (Rauch et al, 2010); and ones recently developed specifically for 4D-STEM (Savitzky et al, 2019;Zeltmann et al, 2020). With the rise in the use of fast pixelated detectors in TEM and STEM and the consequent ability to record large data volumes in short times, the need arises for the ability to analyze large numbers of diffraction patterns accurately and automatically.…”

“…A number of techniques for strain measurements have been developed (Béché et al, 2013), including dark-field electron holography (DFEH; Hÿtch et al, 2008; Cooper et al, 2009; Béché et al, 2011), NBED (Béché et al, 2009), SPED (also referred to as nanobeam precession electron diffraction (NPED); Rouvière et al, 2013; Midgley & Eggeman, 2015), scanning moiré fringe (SMF) analysis (Su & Zhu, 2010; Naden et al, 2018), HRTEM geometrical phase analysis (GPA; Hÿtch et al, 1998), and atomic column spacing displacement characterization (Nord et al, 2017). Of these, the best fractional strain precision reported is with SPED at 2 × 10 −4 (Rouvière et al, 2013); however, very recent work with patterned probes (Guzzinati et al, 2019; Zeltmann et al, 2020) have achieved precisions approaching the same value.…”

Recording 4D-STEM Datasets at a Range of Beam Tilts Simultaneously with Multi-Beam Electron Diffraction

“…In this talk we introduce an alternative method of simultaneously recording diffraction patterns with multiple beam tilts: multi-beam electron diffraction (MBED). We produce these beams with a modified condenser system in a ThermoFisher Titan instrument similarly to [5], with a schematic and some experimental results shown in Figure 1. In this experiment, eight simultaneous diffraction patterns were recorded from a single crystal of gold, covering an angular range of +/-3 degrees.…”