Multi-angle precession electron diffraction (MAPED): a versatile approach to 4D-STEM precession

TL;DR

MAPED tackles the challenge that dynamical diffraction and misalignment degrade strain and orientation mapping in 4D-STEM. It introduces a sequential, few-tilt data acquisition and post-processing workflow that emulates the averaging effect of hardware precession. On SiGe multilayers and polycrystalline Al, MAPED delivers more accurate strain maps (e.g., $\epsilon_{xx}\approx 1.2\%$ tensile) and clearer ACOM orientation results, with improvements observed across several microscopes and detectors. Dynamical diffraction simulations show that a small tilt set reduces thickness-dependent intensity oscillations and brings disk intensities closer to the kinematic limit, supporting broader applicability. The open-source MAPED pipeline thus lowers barriers to precession-enhanced analysis and enables more robust 4D-STEM characterization in non-integrated setups.

Abstract

Precession of a converged beam during acquisition of a 4D-STEM dataset improves strain, orientation, and phase mapping accuracy by averaging over continuous angles of illumination. Precession experiments usually rely on integrated systems, where automatic alignments lead to fast, high-quality results. The dependence of these experiments on specific hardware and software is evident even when switching to non-integrated detectors on a precession tool, as experimental set-up becomes challenging and time-consuming. Here, we introduce multi-angle precession electron diffraction (MAPED): a method to perform electron diffraction by collecting sequential 4D-STEM scans at different incident beam tilts. The multiple diffraction datasets are averaged together post-acquisition, resulting in a single dataset that minimizes the impact of the curvature and orientation of the Ewald sphere relative to the crystal under study. Our results demonstrate that even four additional tilts improved measurement of material properties, namely strain and orientation, as compared to single-tilt 4D-STEM experiments. We show the versatility and flexibility of our MAPED approach with data collected on a number of microscopes with different hardware configurations and a variety of detectors.

Figures (18)

• Figure 1: MAPED experimental method and processing. (a) Diffraction patterns measured from five unique beam tilts. (b) Descan of the diffraction patterns as a function of probe position is corrected first. (c) After, real space field-of-view shifts are corrected across the five 4D-STEM experiments.
• Figure 2: (a) Single and (b) mean diffraction pattern from conventional experiment and corresponding (c--d) MAPED experiment. Strain maps from the (e) conventional and (f) MAPED experiment. Black arrows indicate location of alloy regions, where we expect large $\epsilon_{xx}$. Compared to MAPED, the conventional experiments show more error in the strain maps.
• Figure 3: (a) dark-field image of polycrystalline aluminum film. (b--e) Conventional diffraction patterns from 4 spots in (a). (f--i) Corresponding MAPED diffraction patterns show enhanced peaks at high scattering angles and reduction of Kikuchi diffraction lines. ACOM maps and dilation ($\epsilon_{xx}$ + $\epsilon_{yy}$) from (j--k) conventional and (l--m) MAPED data with (n) legend
• Figure 4: Dynamical diffraction simulations to explore impact of few tilt precession on intensity quantification. (a) Si [011] diffraction pattern. The ($\overline{2}00$) and ($\overline{11}1$) intensity values are shown in (b) and (c) as a function of thickness and number of tilts. Intensity values normalized to show percent difference from the intensity value with the highest number of tilts.
• Figure 5: Example of beam tilting in an uncorrected microscope. Here, the rotation center is use to tilt the beam by 1$^\circ$ (17.5 mrad) shown by the magenta circle on a silicon [110] sample. Diffraction from the sample is used as a calibration for reciprocal sampling, which is used to determine the rotation center value for a desired beam tilt. The unscattered beam is circled in blue.