Atomic Electron Tomography for Multi-Dimensional Data

By employing the quasi-linear nature of annular dark-field scanning transmission electron microscopy (ADF-STEM) image contrast, 3D tomograms can be reconstructed through the Fourier slice theorem or equivalent linear formulations. With atomic-scale resolution ADF-STEM images achieved using aberration correctors, atomic electron tomography (AET) has been demonstrated, offering quantitative three-dimensional structural information of nanomaterials by determining the 3D atomic coordinates with sub-Angstrom precision [1-15]. Utilizing these 3D atomic coordinates enables direct calculation of 3D polarization vector fields from the relative displacement of cation atoms, providing multi-dimensional vector field maps. This multi-dimensional data reveals polar topological textures (fractional Skyrmions, Bloch points, etc.) for general ferroelectric nanostructures even without epitaxial strain, consistent with theoretical predictions [15]. Additionally, we recently proposed the use of tilt series based on the 4D-STEM scheme (referring to 2D diffraction images of a converged electron beam at each point in a 2D STEM raster [16-18]) for AET reconstructions. This approach allows for the reconstruction of atomic resolution tomograms without relying on linearity assumptions, using a multislice-based 3D reconstruction approach. Our simulations confirmed that the multislice-based approach effectively reduces undesirable artifacts arising from nonlinear contrast, increases sensitivity for light elements, and reduces electron dose requirements [16, 19].