Deep Learning Enabled Strain Mapping of Single-Atom Defects in Two-Dimensional Transition Metal Dichalcogenides with Sub-Picometer Precision

Two-dimensional (2D) materials offer an ideal platform to study the strain fields induced by individual atomic defects, yet challenges associated with radiation damage have so far limited electron microscopy methods to probe these atomic-scale strain fields. Here, we demonstrate an approach to probe single-atom defects with sub-picometer precision in a monolayer 2D transition metal dichalcogenide, WSe_2-2<i>x</i>Te_2<i>x</i>. We utilize deep learning to mine large data sets of aberration-corrected scanning transmission electron microscopy images to locate and classify point defects. By combining hundreds of images of nominally identical defects, we generate high signal-to-noise class averages which allow us to measure 2D atomic spacings with up to 0.2 pm precision. Our methods reveal that Se vacancies introduce complex, oscillating strain fields in the WSe_2-2<i>x</i>Te_2<i>x</i> lattice that correspond to alternating rings of lattice expansion and contraction. These results indicate the potential impact of computer vision for the development of high-precision electron microscopy methods for beam-sensitive materials.