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Bragg interferometry (BI) is an imaging technique based on four-dimensional scanning transmission electron microscopy (4D-STEM) wherein the intensities of select overlapping Bragg disks are fit or more qualitatively analyzed in the context of simple trigonometric equations to determine local stacking order. In 4D-STEM based approaches, the collection of full diffraction patterns at each real-space position of the scanning probe allows the use of precise virtual apertures much smaller and more variable in shape than those used in conventional dark field imaging such that even buried interfaces marginally twisted from other layers can be targeted. With a coarse-grained form of dark field ptychography, BI uses simple physically derived fitting functions to extract the average structure within the illumination region and is, therefore, viable over large fields of view. BI has shown a particular advantage for selectively investigating the interlayer stacking and associated moiré reconstruction of bilayer interfaces within complex multi-layered structures. This has enabled investigation of reconstruction and substrate effects in bilayers through encapsulating hexagonal boron nitride and of select bilayer interfaces within trilayer stacks. However, the technique can be improved to provide a greater spatial resolution and probe a wider range of twisted structures, for which current limitations on acquisition parameters can lead to large illumination regions and the computationally involved post-processing can fail. Here, we analyze these limitations and the computational processing in greater depth, presenting a few methods for improvement over previous works, discussing potential areas for further expansion, and illustrating the current capabilities of this approach for extracting moiré-scale strain. 

In conventional ferroelectric materials, polarization is an intrinsic property limited by bulk crystallographic structure and symmetry. Recently, it has been demonstrated that polar order can also be accessed using inherently non-polar van der Waals materials through layer-by-layer assembly into heterostructures, wherein interfacial interactions can generate spontaneous, switchable polarization. Here, we show that deliberate interlayer rotations in multilayer vdW heterostructures modulate both the spatial ordering and switching dy- namics of polar domains. The engendered tunability is unparalleled in conventional bulk ferroelectrics or polar bilayers. By means of operando transmission electron microscopy we show how alterations of the relative rotations of three WSe2 layers produce structural poly- types with distinct arrangements of polar domains with either a global or localized switching response. Furthermore, the presence of uniaxial strain generates structural anisotropy that yields a range of switching behaviors, coercivities, and even tunable biased responses. We also provide evidence of mechanical coupling between the two interfaces of the trilayer, a key consideration for the control of switching dynamics in polar multilayer structures more broadly.