Three-Dimensional Imaging of 2D Materials with Tilted Multislice Electron Ptychography

Because of its exceptionally high spatial resolution perpendicular (10s of pm) and parallel (2-3 nm) to the electron beam direction, multislice electron ptychography offers a new potential route for 3D atomic resolution characterization [1, 2]. Compared to existing atomic-scale imaging methods in scanning transmission electron microscopy (STEM), multislice ptychography obtains improved depth information at each tilt. For example, in optical depth sectioning using annular dark field (ADF)-STEM, the depth resolution is limited by diffraction and residual aberrations to several nanometers [3]. Electron tomography overcomes this limitation by acquiring and combining data from multiple tilts to solve 3D structures [4], but requires careful image alignment and reconstruction, and its depth resolution is closely tied to the tilt range acquired. In contrast, multislice electron ptychography reconstructs the sample in 3D from a single 4D-STEM dataset. The sample is modeled as a stack of slices through which a probe propagates; the probe and the sample are solved for in an iterative process. However, this is still not enough to easily separate atoms that are overlapping in projection. Here, we use multislice electron ptychography to extract 3D atomic coordinates in twisted bilayer 2D materials. By collecting 4D-STEM data from a tilted sample, we minimize overlap between atoms in projection, allowing us to locate most of the atoms within the field of view. Through simulations, we show that this approach can produce atomic coordinates with sub-angstrom accuracy and precision in all three dimensions, though with persistent systematic errors in the z-coordinates. Our results show the potential of multislice electron ptychography for studying 3D atomic structure, whether from a single view angle or as part of a tomographic tilt series. Figure 1a shows an experimental multislice ptychographic reconstruction of twisted bilayer WSe2 viewed nearly face-on. Each WSe2 layer is composed of three planes of atoms, with a plane of W atoms in between two planes of Se atoms. Here, pairs of atoms from the two Se planes are overlapping in projection. Therefore, we also collect 4D-STEM data of twisted bilayer WSe2 tilted by 5-15 degrees, thereby separating the Se atom pairs and allowing most atoms in the field of view to be distinguished individually (Fig. 1b). This approach takes advantage of the extremely high lateral resolution of ptychography to obtain layer-by-layer information in a tilted, thin specimen. Next, we obtain 3D coordinates to the atoms by searching for peak locations in an interpolated version of the object phase. While this approach produced atomic coordinates with precision slightly better than the real-space sampling of the reconstruction, there remain systematic errors with the atoms’ z coordinates, which shift the W planes relative to their Se nearest neighbors. To understand the accuracy of those coordinates, we turn to simulation, generating 4D-STEM data sets of twisted bilayer WSe2 using the multislice method, and recovering atomic coordinates from the ptychography results (Fig. 2a). Superimposing the ground truth atomic model with the model recovered from ptychography, we find that ptychography can recover x, y coordinates with a root-mean-square deviation (RMSD) of 14 pm and z-coordinates with 65 pm (Fig. 2b-d) [5]. Experimental multislice ptychographic reconstructions of twisted bilayer WSe2. (a) A composite image of all depth slices formed by taking the maximum phase value along the z direction. The stage is not tilted. Some W (blue) and Se (yellow) atoms from the first (solid) and second (dashed) layers are labeled. Pairs of Se atoms overlap in projection. (b) A composite image from a different sample with the stage tilted by 10 degrees, separating the Se atom pairs. Accuracy of atomic positions in simulated ptychography. (a) Atomic model of a simulated twisted bilayer WSe2 sample tilted by 10 degrees, with W atoms in gray and Se atoms in yellow. Atomic positions were estimated by finding peaks in an interpolated version of the reconstructed object phase. (b-d) Deviations between the atomic coordinates used in the 4D-STEM simulation and those found from multislice ptychography. (b) shows the distribution of the position deviations, while (c) shows only the magnitude of the in-plane deviation, and (d) the component of the deviation along the beam direction (z).