Picometer-Scale Characterization of Structure, Fields and Defects in 2D Materials Using 4D-STEM

Electron microscopy is a widespread and often essential tool for structural and chemical analysis at the atomic level. Image resolution is dominated by the energy (or wavelength) of the electron beam and the quality of the lens. Two-dimensional materials are imaged with low beam energies to avoid damaging the samples, limiting spatial resolution to ~1 Å. By combining the full 4D-phase space information collected by a new generation of direct electron detectors, which have the dynamic range to record the complete distribution of transmitted electrons at every beam position (4D-STEM), and a ptychographic phase retrieval algorithm to process the data, we have been able to increase the spatial resolution well beyond the traditional lens limitations reaching a 0.39 Å resolution for MoS₂, at the same dose and imaging conditions where conventional imaging modes reach only 0.98 Å [1]. The ultimate limit to spatial resolution in an electron microscope is set by the thermal vibrations of the atoms themselves, which are on the order of 10-20 pm [2]. Using multislice electron ptychography, we are now able to see the details of thermal vibrations of individual atom columns.<br/>The improved resolution, dose efficiency and robustness to environmental noise enabled by ptychography make it easy to identify defects such as sulfur monovacancies, as well as subtle structural arrangements and tilts on the chalcogenide sublattice that are undetectable by conventional imaging modes. For twisted bilayers, we are able to resolve the shear distortions and interactions between the layers. Ptychography is also sensitive to the phase shift from magnetic fields, making it possible to map magnetic order in both 2D and stacked materials.<br/>[1] Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller. “Electron Ptychography of 2D Materials to Deep Sub-Ångström Resolution” <i>Nature</i> 559, (2018): 343–349.<br/>[2] Z. Chen, Y. Jiang, Y.-T. Shao, M. E. Holtz, M. Odstrčil, M. Guizar-Sicairos, I. Hanke, S. Ganschow, D. G. Schlom, and D. A. Muller. “Electron Ptychography Achieves Atomic-Resolution Limits Set by Lattice Vibrations” <i>Science</i> <b>372</b>, (2021), 826–831.<br/>[3] Research supported by US National Science Foundation (grants DMR-1539918, DMR-1429155, DMR-1719875) & US AFOSR MURI program