# Patterned Probes for High Precision 4D-STEM Bragg Measurements

## TL;DR

This paper introduces patterned 'bullseye' probes in 4D-STEM to significantly enhance nanoscale strain measurement precision, overcoming challenges posed by scattering effects and noise, with minimal impact on spatial resolution.

## Contribution

The study demonstrates that imprinting a bullseye pattern on the probe improves strain mapping precision in 4D-STEM, providing a novel approach to enhance measurement accuracy.

## Key findings

- Strain measurement precision improved from 2.7% to 0.3% in thin samples.
- Strain measurement precision improved from 4.7% to 0.8% in thick samples.
- Patterned probes increase robustness of peak detection in diffraction patterns.

## 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.