Convergent and divergent beam electron holography and reconstruction of adsorbates on free-standing two-dimensional crystals

Abstract

Van der Waals heterostructures have been lately intensively studied because they offer a large variety of properties that can be controlled by selecting 2D materials and their sequence in the stack. The exact arrangement of the layers as well as the exact arrangement of the atoms within the layers, both are important for the properties of the resulting device. Recently it has been demonstrated that convergent beam electron diffraction (CBED) allows quantitative three-dimensional mapping of atomic positions in three-dimensional materials from a single CBED pattern. In this study we investigate CBED in more detail by simulating and performing various CBED regimes, with convergent and divergent wavefronts, on a somewhat simplified system: a 2D monolayer crystal. In CBED, each CBED spot is in fact an in-line hologram of the sample, where in-line holography is known to exhibit high intensity contrast in detection of weak phase objects that are not detectable in conventional in-focus imaging mode. Adsorbates exhibit strong intensity contrast in zero and higher order CBED spots, whereas lattice deformation such as strain or rippling cause noticeable intensity contrast only in the first and higher order CBED spots. The individual CBED spots can be reconstructed as typical in-line holograms, and the resolution of 2.13 A can be in principle achieved in the reconstructions. We provide simulated and experimental examples of CBED of a 2D monolayer crystal. The simulations show that individual CBED spots can be treated as in-line holograms and sample distributions such as adsorbates, can be reconstructed. Individual atoms can be reconstructed from a single CBED pattern provided the later exhibits high-order CBED spots. Examples of reconstructions obtained from experimental CBED patterns, at a resolution of 2.7 A, are shown.

References in corpus (8)

• On the roughness of single- and bi-layer graphene membranes
• Practical algorithms for simulation and reconstruction of digital in-line holograms
• Graphene as a transparent conductive support for studying biological molecules by transmission electron microscopy
• When holography meets coherent diffraction imaging
• Simultaneous reconstruction of phase and amplitude contrast from a single holographic record
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• Convergent beam electron holography for analysis of van der Waals heterostructures
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Cited by in corpus (8)

• Moire structures in twisted bilayer graphene studied by transmission electron microscopy
• Convergent beam electron diffraction of multilayer van der Waals structures
• Holographic reconstruction of the interlayer distance of bilayer two-dimensional crystal samples from their convergent beam electron diffraction patterns
• Stacking control in graphene-based materials: a promising way for fascinating physical properties
• Imaging defects in two-dimensional crystals by convergent beam electron diffraction
• Dynamics of single Au nanoparticles on graphene simultaneously in real- and diffraction space by time-series convergent beam electron diffraction
• Holographic convergent electron beam diffraction (CBED) imaging of two-dimensional crystals
• How to image single isolated atoms by using coherent low-energy electrons