High precision orientation mapping from 4D-STEM precession electron diffraction data through quantitative analysis of diffracted intensities

The association of scanning transmission electron microscopy (STEM) and detection of a diffraction pattern at each probe position (so-called 4D-STEM) represents one of the most promising approaches to analyze structural properties of materials with nanometric resolution and low irradiation levels. This is widely used for texture analysis of materials using automated crystal orientation mapping (ACOM). Herein, we perform orientation mapping in InP nanowires exploiting precession electron diffraction (PED) patterns acquired by an axial CMOS camera. Crystal orientation is determined at each probe position by the quantitative analysis of diffracted intensities minimizing a residue comparing experiments and simulations in analogy to x-ray structural refinement. Our simulations are based on the two-beam dynamical diffraction approximation and yield a high angular precision (∼0.03°), much lower than the traditional ACOM based on pattern matching algorithms (∼1°). We anticipate that simultaneous exploration of both spot positions and high precision crystal misorientation will allow the exploration of the whole potentiality provided by PED-based 4D-STEM for the characterization of deformation fields in nanomaterials.

Framework of compressive sensing and data compression for 4D-STEM

Four-dimensional Scanning Transmission Electron Microscopy (4D-STEM) is a powerful technique for high-resolution and high-precision materials characterization at multiple length scales, including the characterization of beam-sensitive materials. However, the field of view of 4D-STEM is relatively small, which in absence of live processing is limited by the data size required for storage. Furthermore, the rectilinear scan approach currently employed in 4D-STEM places a resolution- and signal-dependent dose limit for the study of beam sensitive materials. Improving 4D-STEM data and dose efficiency, by keeping the data size manageable while limiting the amount of electron dose, is thus critical for broader applications. Here we introduce a general method for reconstructing 4D-STEM data with subsampling in both real and reciprocal spaces at high fidelity. The approach is first tested on the subsampled datasets created from a full 4D-STEM dataset, and then demonstrated experimentally using random scan in real-space. The same reconstruction algorithm can also be used for compression of 4D-STEM datasets, leading to a large reduction (100 times or more) in data size, while retaining the fine features of 4D-STEM imaging, for crystalline samples.

Aberration Correction for Large-Angle Illumination Scanning Transmission Electron Microscopy by Using Iterative Electron Ptychography Algorithms

Modern aberration correctors in the scanning transmission electron microscope (STEM) have dramatically improved the attainable spatial resolution and enabled atomical structure and spectroscopic analysis even at low acceleration voltages (≤80 kV). For a large-angle illumination, achieving successful aberration correction to high angles is challenging with an aberration corrector, which limits further improvements in applications such as super-resolution, three-dimensional atomic depth resolution, or atomic surface morphology analyses. Electron ptychography based on four-dimensional STEM can provide a postprocessing strategy to overcome the current technological limitations. In this work, we have demonstrated that aberration correction for large-angle illumination is feasible by pushing the capabilities of regularized ptychographic iterative engine algorithms to reconstruct 4D data sets acquired using a relatively low-efficiency complementary metal oxide semiconductor camera. We report super resolution (0.71 Å) with large-angle illumination (50-60 mrad) and under 60 kV accelerating voltage.

Direct Quantifying Charge Transfer by 4D-STEM: A Study on Perfect and Defective Hexagonal Boron Nitride

Four-dimensional scanning transmission electron microscopy (4D-STEM) offers an attractive approach to simultaneously obtain precise structural determinations and capture details of local electric fields and charge densities. However, accurately extracting quantitative data at the atomic scale poses challenges, primarily due to probe propagation and size-related effects, which may even lead to misinterpretations of qualitative effects. In this study, we present a comprehensive analysis of electric fields and charge densities in both pristine and defective h-BN flakes. Through a combination of experiments and first-principle simulations, we demonstrate that while precise charge quantification at individual atomic sites is hindered by probe effects, 4D-STEM can directly measure charge transfer phenomena at the monolayer edge with sensitivity down to a few tenths of an electron and a spatial resolution on the order of a few angstroms.

Valence-Ordered Thin-Film Nickelate with Tri-component Nickel Coordination Prepared by Topochemical Reduction

The metal-hydride-based "topochemical reduction" process has produced several thermodynamically unstable phases across various transition metal oxide series with unusual crystal structures and nontrivial ground states. Here, by such an oxygen (de-)intercalation method we synthesis a samarium nickelate with ordered nickel valences associated with tri-component coordination configurations. This structure, with a formula of Sm9Ni9O22 as revealed by four-dimensional scanning transmission electron microscopy (4D-STEM), emerges from the intricate planes of {303}pc ordered apical oxygen vacancies. X-ray spectroscopy measurements and ab initio calculations show the coexistence of square planar, pyramidal, and octahedral Ni sites with mono-, bi-, and tri-valences. It leads to an intense orbital polarization, charge-ordering, and a ground state with a strong electron localization marked by the disappearance of ligand-hole configuration at low temperature. This nickelate compound provides another example of previously inaccessible materials enabled by topotactic transformations and presents an interesting platform where mixed Ni valence can give rise to exotic phenomena.

Ultrasmooth Epitaxial Pt Thin Films Grown by Pulsed Laser Deposition

Platinum (Pt) thin films are useful in applications requiring high-conductivity electrodes with excellent thermal and chemical stability. Ultrasmooth and epitaxial Pt thin films with single-crystalline domains have the added benefit of providing ideal templates for the subsequent growth of heteroepitaxial structures. Here, we grow epitaxial Pt (111) electrodes (ca. 30 nm thick) on sapphire (α-Al2O3 (0001)) substrates with pulsed laser deposition. This versatile technique allows control of the growth process and fabrication of films with carefully tailored parameters. X-ray scattering, atomic-force microscopy, and electron microscopy provide structural characterization of the films. Various gaseous atmospheres and temperatures were explored to achieve epitaxial growth of films with low roughness. A two-step (500 °C/300 °C) growth process was developed, yielding films with improved epitaxy without compromising roughness. The resulting films possess ultrasmooth interfaces (<3 Å) and high electrical conductivity (6.9 × 106 S/m). Finally, Pt films were used as current collectors and templates to grow lithium manganese oxide (LiMn2O4 (111)) epitaxial thin films, a cathode material used in Li-ion batteries. Using a solid-state ionogel electrolyte, the films were highly stable when electrochemically cycled in the 3.5-4.3 V vs Li/Li+ range.

Importance of TEM sample thickness for measuring strain fields

Transmission electron microscopy (TEM) has emerged as a valuable tool for assessing and mapping strain fields within materials. By directly analyzing local atomic spacing variations, TEM enables the precise measurement of local strain with high spatial resolution. However, it is standard practice to use thin specimens in TEM analysis to ensure electron transparency and minimize issues such as projection artifacts and contributions from multiple scattering. This raises an important question regarding the extent of structural modification, such as strain relaxation, induced in thin samples due to the increased surface-to-volume ratio and the thinning process. In this study, we conducted a systematic investigation to quantify the influence of TEM sample thickness on the residual strain field using deformed Fe-based and Zr-based metallic glasses as model systems. The samples were gradually thinned from 300 nm to 70 nm, and the same area was examined using 4D-STEM with identical imaging settings. Our results demonstrate that thinning the sample affects the atomic configuration at both the short-range (SR) and medium-range (MR) scales. Consequently, when the sample is thinned too much, it no longer preserves the native deformation structure. These findings highlight the critical importance of maintaining sufficient TEM sample thickness for obtaining meaningful and accurate strain measurements.

Scanning precession electron diffraction data analysis approaches for phase mapping of precipitates in aluminium alloys

Mapping the spatial distribution of crystal phases with nm-scale spatial resolution is an important characterisation task in studies of multi-phase materials. One popular approach is to use scanning precession electron diffraction which enables semi-automatic phase mapping at the nanoscale by collecting a single precession electron diffraction pattern at every probe position over regions spanning up to a few micrometers. For a successful phase mapping each diffraction pattern must be correctly identified. In this work four different approaches for phase mapping of embedded precipitates in an Al-Cu-Li alloy are compared on a sample containing three distinct crystal phases. These approaches are based on: non-negative matrix factorisation, vector matching, template matching and artificial neural networks. To evaluate the success of each approach a ground truth phase map was manually created from virtual images based on characteristic phase morphologies and compared with the deduced phase maps. The percentage accuracy of all methods when compared to the ground truth was satisfactory, with all approaches obtaining scores above 98%. The optimal method depends on the specific task at hand. Non-negative matrix factorisation is suitable with limited prior data knowledge but performs best with few unique diffraction patterns and requires substantial post-processing. It has the advantage of reducing the dimensionality of the dataset and handles weak diffracted intensities well given that they occur repeatedly. The current vector matching implementation is fast, simple, based only on the Bragg spot geometry and requires few parameters. It does however demand that each Bragg spot is accurately detected in each pattern and the current implementation is limited to zone axis patterns. Template matching handles a large range of orientations, including off-axis patterns. However, achieving successful and reliable results often require thorough data pre-processing and do require adequate diffraction simulations. For artificial neural networks a substantial setup effort is demanded but once trained it excels for routine tasks, offering fast predictions. The implemented codes and the data used are available open-source. These resources and the detailed assessment of the methods will allow others to make informed decisions when selecting a data analysis approach for 4D-STEM phase mapping tasks on other material systems.

Observation of Sub-10 nm Transition Metal Dichalcogenide Nanocrystals in Rapidly Heated van der Waals Heterostructures

Two-dimensional materials, such as transition metal dichalcogenides (TMDCs), have the potential to revolutionize the field of electronics and photonics due to their unique physical and structural properties. This research presents a novel method for synthesizing crystalline TMDCs crystals with <10 nm size using ultrafast migration of vacancies at elevated temperatures. Through in situ and ex situ processing and using atomic-level characterization techniques, we analyzed the shape, size, crystallinity, composition, and strain distribution of these nanocrystals. These nanocrystals exhibit electronic structure signatures that differ from the 2D bulk: i.e., uniform mono- and multilayers. Further, our in situ, vacuum-based synthesis technique allows observation and comparison of defect and phase evolution in these crystals formed under van der Waals heterostructure confinement versus unconfined conditions. Overall, this research demonstrates a solid-state route to synthesizing uniform nanocrystals of TMDCs and lays the foundation for materials science in confined 2D spaces under extreme conditions.

Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy

In a scanning transmission electron microscope (STEM), producing a high-resolution image generally requires an electron beam focused to the smallest point possible. However, the magnetic lenses used to focus the beam are unavoidably imperfect, introducing aberrations that limit resolution. Modern STEMs overcome this by using hardware aberration correctors comprised of many multipole elements, but these devices are complex, expensive, and can be difficult to tune. We demonstrate a design for an electrostatic phase plate that can act as an aberration corrector. The corrector is comprised of annular segments, each of which is an independent two-terminal device that can apply a constant or ramped phase shift to a portion of the electron beam. We show the improvement in image resolution using an electrostatic corrector. Engineering criteria impose that much of the beam within the probe-forming aperture be blocked by support bars, leading to large probe tails for the corrected probe that sample the specimen beyond the central lobe. We also show how this device can be used to create other STEM beam profiles such as vortex beams and probes with a high degree of phase diversity, which improve information transfer in ptychographic reconstructions.

Wafer-Scale Fabrication of 2D Nanostructures via Thermomechanical Nanomolding

With shrinking dimensions in integrated circuits, sensors, and functional devices, there is a pressing need to develop nanofabrication techniques with simultaneous control of morphology, microstructure, and material composition over wafer length scales. Current techniques are largely unable to meet all these conditions, suffering from poor control of morphology and defect structure or requiring extensive optimization or post-processing to achieve desired nanostructures. Recently, thermomechanical nanomolding (TMNM) has been shown to yield single-crystalline, high aspect ratio nanowires of metals, alloys, and intermetallics over wafer-scale distances. Here, TMNM is extended for wafer-scale fabrication of 2D nanostructures. Using In, Al, and Cu, nanomold nanoribbons with widths < 50 nm, depths ≈0.5-1 µm and lengths ≈7 mm into Si trenches at conditions compatible is successfully with back end of line processing . Through SEM cross-section imaging and 4D-STEM grain orientation maps, it is shown that the grain size of the bulk feedstock is transferred to the nanomolded structures up to and including single crystal Cu. Based on the retained microstructures of molded 2D Cu, the deformation mechanism during molding for 2D TMNM is discussed.

Quantitative electric field mapping between electrically biased needles by scanning transmission electron microscopy and electron holography

Stray electric fields in free space generated by two biased gold needles have been quantified in comprehensive finite-element (FE) simulations, accompanied by first moment (FM) scanning TEM (STEM) and electron holography (EH) experiments. The projected electrostatic potential and electric field have been derived numerically under geometrical variations of the needle setup. In contrast to the FE simulation, application of an analytical model based on line charges yields a qualitative understanding. By experimentally probing the electric field employing FM STEM and EH under alike conditions, a discrepancy of about 60% became apparent initially. However, the EH setup suggests the reconstructed phase to be significantly affected by the perturbed reference wave effect, opposite to STEM where the field-free reference was recorded subsequently with unbiased needles in which possibly remaining electrostatic influences are regarded as being minor. In that respect, the observed discrepancy between FM imaging and EH is resolved after including the long-range potential landscape from FE simulations into the phase of the reference wave in EH.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Advanced techniques in automated high-resolution scanning transmission electron microscopy

Scanning transmission electron microscopy is a common tool used to study the atomic structure of materials. It is an inherently multimodal tool allowing for the simultaneous acquisition of multiple information channels. Despite its versatility, however, experimental workflows currently rely heavily on experienced human operators and can only acquire data from small regions of a sample at a time. Here, we demonstrate a flexible pipeline-based system for high-throughput acquisition of atomic-resolution structural data using an all-piezo sample stage applied to large-scale imaging of nanoparticles and multimodal data acquisition. The system is available as part of the user program of the Molecular Foundry at Lawrence Berkeley National Laboratory.

Development of temporal series 4D-STEM and application to relaxation time measurement

Diffraction patterns contain useful information about the materials. Recent developments in four-dimensional scanning transmission electron microscopy and the acquisition of the spatial distribution of diffraction patterns have produced significant results. The acquisition of a temporal series of diffractions is achieved for a stationary beam. However, the acquisition of spatiotemporal distribution of diffraction patterns has only been established under limited conditions. In this study, we developed a simple method that enables the recording of the spatiotemporal distribution of diffraction patterns and applied it to the relaxation time measurement that is robust to sample drift.

Robust Local Thickness Estimation of Sub-Micrometer Specimen by 4D-STEM

A quantitative four-dimensional scanning transmission electron microscopy (4D-STEM) imaging technique (q4STEM) for local thickness estimation across amorphous specimen such as obtained by focused ion beam (FIB)-milling of lamellae for (cryo-)TEM analysis is presented. This study is based on measuring spatially resolved diffraction patterns to obtain the angular distribution of electron scattering, or the ratio of integrated virtual dark and bright field STEM signals, and their quantitative evaluation using Monte Carlo simulations. The method is independent of signal intensity calibrations and only requires knowledge of the detector geometry, which is invariant for a given instrument. This study demonstrates that the method yields robust thickness estimates for sub-micrometer amorphous specimen using both direct detection and light conversion 2D-STEM detectors in a coincident FIB-SEM and a conventional SEM. Due to its facile implementation and minimal dose reauirements, it is anticipated that this method will find applications for in situ thickness monitoring during lamella fabrication of beam-sensitive materials.

Mapping Nanoscale Electrostatic Field Fluctuations around Graphene Dislocation Cores Using Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM)

Defects in crystalline lattices cause modulation of the atomic density, and this leads to variations in the associated electrostatics at the nanoscale. Mapping these spatially varying charge fluctuations using transmission electron microscopy has typically been challenging due to complicated contrast transfer inherent to conventional phase contrast imaging. To overcome this, we used four-dimensional scanning transmission electron microscopy (4D-STEM) to measure electrostatic fields near point dislocations in a monolayer. The asymmetry of the atomic density in a (1,0) edge dislocation core in graphene yields a local enhancement of the electric field in part of the dislocation core. Through experiment and simulation, the increased electric field magnitude is shown to arise from "long-range" interactions from beyond the nearest atomic neighbor. These results provide insights into the use of 4D-STEM to quantify electrostatics in thin materials and map out the lateral potential variations that are important for molecular and atomic bonding through Coulombic interactions.

Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy

One approach to three-dimensional structure determination using the wealth of scattering data in four-dimensional (4D) scanning transmission electron microscopy (STEM) is the parallax method proposed by Ophus et al. (2019. Advanced phase reconstruction methods enabled by 4D scanning transmission electron microscopy, Microsc Microanal25, 10-11), which determines the scattering matrix and uses it to synthesize a virtual depth-sectioning reconstruction of the sample structure. Drawing on an equivalence with a hypothetical confocal imaging mode, we derive contrast transfer and point spread functions for this parallax method applied to weakly scattering objects, showing them identical to earlier depth-sectioning STEM modes when only bright field signal is used, but that improved depth resolution is possible if dark field signal can be used. Through a simulation-based study of doped Si, we show that this depth resolution is preserved for thicker samples, explore the impact of shot noise on the parallax reconstructions, discuss challenges to making use of dark field signal, and identify cases where the interpretation of the parallax reconstruction breaks down.

Electron Ptychographic Phase Imaging of Beam-sensitive All-inorganic Halide Perovskites Using Four-dimensional Scanning Transmission Electron Microscopy

Halide perovskites (HPs) are promising candidates for optoelectronic devices, such as solar cells or light-emitting diodes. Despite recent progress in performance optimization and low-cost manufacturing, their commercialization remains hindered due to structural instabilities. While essential to the development of the technology, the relation between the microscopic properties of HPs and the relevant degradation mechanisms is still not well understood. The sensitivity of HPs toward electron-beam irradiation poses significant challenges for transmission electron microscopy (TEM) investigations of structure and degradation mechanisms at the atomic scale. However, technological advances and the development of direct electron cameras (DECs) have opened up a completely new field of electron microscopy: four-dimensional scanning TEM (4D-STEM). From a 4D-STEM dataset, it is possible to extract not only the intensity signal for any STEM detector geometry but also the phase information of the specimen. This work aims to show the potential of 4D-STEM, in particular, electron exit-wave phase reconstructions via focused probe ptychography as a low-dose and dose-efficient technique to image the atomic structure of beam-sensitive HPs. The damage mechanism under conventional irradiation is described and atomically resolved almost aberration-free phase images of three all-inorganic HPs, CsPbBr3, CsPbIBr2, and CsPbI3, are presented with a resolution down to the aperture-constrained diffraction limit.

Defect Contrast with 4D-STEM: Understanding Crystalline Order with Virtual Detectors and Beam Modification

Material properties strongly depend on the nature and concentration of defects. Characterizing these features may require nano- to atomic-scale resolution to establish structure-property relationships. 4D-STEM, a technique where diffraction patterns are acquired at a grid of points on the sample, provides a versatile method for highlighting defects. Computational analysis of the diffraction patterns with virtual detectors produces images that can map material properties. Here, using multislice simulations, we explore different virtual detectors that can be applied to the diffraction patterns that go beyond the binary response functions that are possible using ordinary STEM detectors. Using graphene and lead titanate as model systems, we investigate the application of virtual detectors to study local order and in particular defects. We find that using a small convergence angle with a rotationally varying detector most efficiently highlights defect signals. With experimental graphene data, we demonstrate the effectiveness of these detectors in characterizing atomic features, including vacancies, as suggested in simulations. Phase and amplitude modification of the electron beam provides another process handle to change image contrast in a 4D-STEM experiment. We demonstrate how tailored electron beams can enhance signals from short-range order and how a vortex beam can be used to characterize local symmetry.

Atomic Resolution Cryogenic 4D-STEM Imaging via Robust Distortion Correction

Cryogenic four-dimensional scanning transmission electron microscopy (4D-STEM) imaging is a useful technique for studying quantum materials and their interfaces by simultaneously probing charge, lattice, spin, and chemistry on the atomic scale with the sample held at temperatures ranging from room to cryogenic. However, its applications are currently limited by the instabilities of cryo-stages and electronics. To overcome this challenge, we develop an algorithm to effectively correct the complex distortions present in atomic resolution cryogenic 4D-STEM data sets. This method uses nonrigid registration to identify localized distortions in a 4D-STEM and relate them to an undistorted experimental STEM image, followed by a series of affine transformations for distortion corrections. This method allows a minimum loss of information in both reciprocal and real spaces, enabling the reconstruction of sample information from 4D-STEM data sets. This method is computationally cheap, fast, and applicable for on-the-fly data analysis in future in situ cryogenic 4D-STEM experiments.

Synchronization of scanning probe and pixelated sensor for image-guided diffraction microscopy

A 4-dimensional modality of a scanning transmission electron microscope (4D-STEM) acquires diffraction images formed by a coherent and focused electron beam scanning the specimen. Newly developed ultrafast detectors offer a possibility to acquire high throughput diffraction patterns at each pixel of the scan, enabling rapid tilt series acquisition for 4D-STEM tomography. Here we present a solution to the problem of synchronizing the electron probe scan with the diffraction image acquisition, and demonstrate on a fast hybrid-pixel detector camera (ARINA, DECTRIS). Image-guided tracking and autofocus corrections are handled by the freely-available microscope-control software SerialEM, in conjunction with a high angle annular dark field (HAADF) image acquired simultaneously. The open source SavvyScan system offers a versatile set of scanning patterns, operated by commercially available multi-channel acquisition and signal generator computer cards (Spectrum Instrumentation GmbH). Images are recorded only within a sub-region of the total field, so as to avoid spurious data collection during flyback and/or acceleration periods in the scan. Hence, the trigger of the fast camera follows selected pulses from the scan generator clock gated according to the chosen scan pattern. Software and protocol are provided for gating the trigger pulses via a microcontroller (ST Microelectronics ARM Cortex). We demonstrate the system on a standard replica grating and by diffraction imaging of a ferritin specimen.

Angstrom-scale imaging of magnetization in antiferromagnetic Fe2As via 4D-STEM

We demonstrate a combination of computational tools and experimental 4D-STEM methods to image the local magnetic moment in antiferromagnetic Fe₂As with 6 angstrom spatial resolution. Our techniques utilize magnetic diffraction peaks, common in antiferromagnetic materials, to create imaging modes that directly visualize the magnetic lattice. Using this approach, we show that center-of-mass analysis can determine the local magnetization component in the plane perpendicular to the path of the electron beam. Moreover, we develop Magnstem, a quantum mechanical electron scattering simulation code, to model electron scattering of an angstrom-scale probe from magnetic materials. Using these tools, we identify optimal experimental conditions for separating weak magnetic signals from the much stronger interactions of an angstrom-scale probe with electrostatic potentials. Our techniques should be useful for characterizing the local magnetic order in systems such in thin films, interfaces, and domain boundaries of antiferromagnetic materials, which are difficult to probe with existing methods.

Thickness-Dependent Interface Polarity in Infinite-Layer Nickelate Superlattices

The interface polarity plays a vital role in the physical properties of oxide heterointerfaces because it can cause specific modifications of the electronic and atomic structure. Reconstruction due to the strong polarity of the NdNiO₂/SrTiO₃ interface in recently discovered superconducting nickelate films may play an important role, as no superconductivity has been observed in the bulk. By employing four-dimensional scanning transmission electron microscopy and electron energy-loss spectroscopy, we studied effects of oxygen distribution, polyhedral distortion, elemental intermixing, and dimensionality in NdNiO₂/SrTiO₃ superlattices grown on SrTiO₃ (001) substrates. Oxygen distribution maps show a gradual variation of the oxygen content in the nickelate layer. Remarkably, we demonstrate thickness-dependent interface reconstruction due to a polar discontinuity. An average cation displacement of ∼0.025 nm at interfaces in 8NdNiO₂/4SrTiO₃ superlattices is twice larger than that in 4NdNiO₂/2SrTiO₃ superlattices. Our results provide insights into the understanding of reconstructions at NdNiO₂/SrTiO₃ polar interfaces.

Uncovering polar vortex structures by inversion of multiple scattering with a stacked Bloch wave model

Nanobeam electron diffraction can probe local structural properties of complex crystalline materials including phase, orientation, tilt, strain, and polarization. Ideally, each diffraction pattern from a projected area of a few unit cells would produce a clear Bragg diffraction pattern, where the reciprocal lattice vectors can be measured from the spacing of the diffracted spots, and the spot intensities are equal to the square of the structure factor amplitudes. However, many samples are too thick for this simple interpretation of their diffraction patterns, as multiple scattering of the electron beam can produce a highly nonlinear relationship between the spot intensities and the underlying structure. Here, we develop a stacked Bloch wave method to model the diffracted intensities from thick samples with structure that varies along the electron beam. Our method reduces the large parameter space of electron scattering to just a few structural variables per probe position, making it fast enough to apply to very large fields of view. We apply our method to SrTiO₃/PbTiO₃/SrTiO₃ multilayer samples, and successfully disentangle specimen tilt from the mean polarization of the PbTiO₃ layers. We elucidate the structure of complex vortex topologies in the PbTiO₃ layers, demonstrating the promise of our method to extract material properties from thick samples.

Direct Observation of Quadrupolar Strain Fields forming a Shear Band in Metallic Glasses

For decades, scanning/transmission electron microscopy (S/TEM) techniques have been employed to analyze shear bands in metallic glasses and understand their formation in order to improve the mechanical properties of metallic glasses. However, due to a lack of direct information in reciprocal space, conventional S/TEM cannot characterize the local strain and atomic structure of amorphous materials, which are key to describe the deformation of glasses. For this work, 4-dimensional-STEM (4D-STEM) is applied to map and directly correlate the local strain and the atomic structure at the nanometer scale in deformed metallic glasses. Residual strain fields are observed with quadrupolar symmetry concentrated at dilated Eshelby inclusions. The strain fields percolate in a vortex-like manner building up the shear band. This provides a new understanding of the formation of shear bands in metallic glass.

Improving Magnetic STEM-Differential Phase Contrast Imaging using Precession

Differential phase contrast in scanning transmission electron microscopy (STEM-DPC) is a technique used to image electromagnetic fields in materials. STEM-DPC is based on tracking the minute changes in the position of the bright-field disk, so any effects which cause inhomogeneities in the intensity or geometry of the disk can lead to the contrast from the electromagnetic fields to be obscured. Structural changes, like grain boundaries, thickness variations, or local crystallographic orientation, are a major cause of these inhomogeneities. In this paper, we present how precession of the STEM probe with the objective lens turned off, providing a near field-free environment for magnetic imaging, can average out nonsystematic inhomogeneities in the electron beam. The methodology was tested on a polycrystalline Fe60Al40 thin film with embedded ferromagnetic structures. The effect of precession was assessed on magnetic induction maps created by three different processing algorithms. Results demonstrate that precessed STEM-DPC with the objective lens turned off shows an improvement in the form of smoothing of the variations found in the DPC signal arising from the underlying polycrystalline background.

Systematic Errors of Electric Field Measurements in Ferroelectrics by Unit Cell Averaged Momentum Transfers in STEM

When using the unit cell average of first moment data from four-dimensional scanning transmission electron microscopy (4D-STEM) to characterize ferroelectric materials, a variety of sources of systematic errors needs to be taken into account. In particular, these are the magnitude of the acceleration voltage, STEM probe semi-convergence angle, sample thickness, and sample tilt out of zone axis. Simulations show that a systematic error of calculated electric fields using the unit cell averaged momentum transfer originates from violation of point symmetry within the unit cells. Thus, values can easily exceed those of potential polarization-induced electric fields in ferroelectrics. Importantly, this systematic error produces deflection gradients between different domains seemingly representing measured fields. However, it could be shown that for PbZr0.2Ti0.8O3, many adjacent domains exhibit a relative crystallographic mistilt and in-plane rotation. The experimental results show that the method gives qualitative domain contrast. Comparison of the calculated electric field with the systematic error showed that the domain contrast of the unit cell averaged electric fields is mainly caused by dynamical scattering effects and the electric field plays only a minor role, if present at all.

Optimized detector configurations for the reconstruction of phase-contrast images in scanning transmission electron microscopy

Using the differential phase contrast mechanism and anti-symmetric detector geometries it is possible to image distributions of electric and magnetic fields in a scanning transmission electron microscope. Different detector geometries can be used for imaging and, due to their efficiency, mainly ring quadrant detectors and pixelated detectors have been used in recent high resolution differential phase contrast experiments. In 4D-Scanning Transmission Electron Microscopy one uses a pixelated (2D) detector to obtain the complete scattering distribution for every (2D) image point. The accuracy of pixelated detectors increases with an increasing number of pixels, which in turn also leads to a larger amount of data that needs to be evaluated. To reduce the required numerical effort, we are looking for alternative detector geometries by further segmenting ring quadrant detectors. To compare the different geometries, their signal-to-noise ratios are calculated for an ideal STEM and several weak phase objects. Images can be obtained by combining the data of different detector pixels using a scheme similar to a reconstruction from a focal series. The procedure can be interpreted as the simplest example of ptychography including only the first-order diffraction disks. Our results show that a 50-segment annular bright-field detector can reach a signal-to-noise ratio close to that of a 128 × 128 pixelated detector, while having a significantly lower number of segments that need to be evaluated.

Fluctuation cepstral scanning transmission electron microscopy of mixed-phase amorphous materials

Four-dimensional scanning transmission electron microscopy (4D-STEM) is a versatile analytical tool for characterizing materials structural properties. However, extending such analysis to disordered materials is challenging, especially in technologically important samples with mixed ordered and disordered phases. Here, we present a new 4D-STEM method, called fluctuation cepstral STEM (FC-STEM), based on the fluctuation analysis of cepstral transform of diffraction patterns. The peaks in the associated transformation relate to inter-atomic distances in a thin sample. By varying the real-space range over which fluctuations are calculated, distinct ordered and disordered phases can be mapped in a diffractive image reconstruction. We demonstrate the principles of FC-STEM by characterizing a silicon anode, harvested from a cycled lithium-ion battery. A mixture of amorphous and nanocrystalline silicon, graphitic carbon, and electrolyte by-products is identified and mapped. Comparisons with conventional electron imaging and energy-dispersive X-ray spectroscopy show that FC-STEM is highly effective for the structure determination of mixed-phase amorphous materials.

Developing a Chemical and Structural Understanding of the Surface Oxide in a Niobium Superconducting Qubit

Superconducting thin films of niobium have been extensively employed in transmon qubit architectures. Although these architectures have demonstrated improvements in recent years, further improvements in performance through materials engineering will aid in large-scale deployment. Here, we use information retrieved from secondary ion mass spectrometry and electron microscopy to conduct a detailed assessment of the surface oxide that forms in ambient conditions for transmon test qubit devices patterned from a niobium film. We observe that this oxide exhibits a varying stoichiometry with NbO and NbO₂ found closer to the niobium film/oxide interface and Nb₂O₅ found closer to the surface. In terms of structural analysis, we find that the Nb₂O₅ region is semicrystalline in nature and exhibits randomly oriented grains on the order of 1-3 nm corresponding to monoclinic N-Nb₂O₅ that are dispersed throughout an amorphous matrix. Using fluctuation electron microscopy, we are able to map the relative crystallinity in the Nb₂O₅ region with nanometer spatial resolution. Through this correlative method, we observe that the highly disordered regions are more likely to contain oxygen vacancies and exhibit weaker bonds between the niobium and oxygen atoms. Based on these findings, we expect that oxygen vacancies likely serve as a decoherence mechanism in quantum systems.

Analysis of Interpretable Data Representations for 4D-STEM Using Unsupervised Learning

Understanding the structure of materials is crucial for engineering devices and materials with enhanced performance. Four-dimensional scanning transmission electron microscopy (4D-STEM) is capable of mapping nanometer-scale local crystallographic structure over micron-scale field of views. However, 4D-STEM datasets can contain tens of thousands of images from a wide variety of material structures, making it difficult to automate detection and classification of structures. Traditional automated analysis pipelines for 4D-STEM focus on supervised approaches, which require prior knowledge of the material structure and cannot describe anomalous or deviant structures. In this article, a pipeline for engineering 4D-STEM feature representations for unsupervised clustering using non-negative matrix factorization (NMF) is introduced. Each feature is evaluated using NMF and results are presented for both simulated and experimental data. It is shown that some data representations more reliably identify overlapping grains. Additionally, real space refinement is applied to identify spatially distinct sample regions, allowing for size and shape analysis to be performed. This work lays the foundation for improved analysis of nanoscale structural features in materials that deviate from expected crystallographic arrangement using 4D-STEM.

Conditions near a crack tip: Advanced experiments for dislocation analysis and local strain measurement

The local stress state and microstructure near the crack-tip singularity control the fracture process. In ductile materials multiple toughening mechanisms are at play that dynamically influence stress and microstructure at the crack tip. In metals, crack-tip shielding is typically associated with the emission of dislocations. Therefore, to understand crack propagation on the most fundamental level, in situ techniques are required that are capable to combine imaging and stress mapping at high resolution. Recent experimental advances in x-ray diffraction, scanning electron microscopy, and transmission electron microscopy enable quantifying deformation stress fields from the bulk level down to the individual dislocation. Furthermore, through modern detector technology the temporal resolution has sufficiently improved to enable stress mapping during in situ experiments.

Automated Experiment in 4D-STEM: Exploring Emergent Physics and Structural Behaviors

Automated experiments in 4D scanning transmission electron microscopy (STEM) are implemented for rapid discovery of local structures, symmetry-breaking distortions, and internal electric and magnetic fields in complex materials. Deep kernel learning enables active learning of the relationship between local structure and 4D-STEM-based descriptors. With this, efficient and "intelligent" probing of dissimilar structural elements to discover desired physical functionality is made possible. This approach allows effective navigation of the sample in an automated fashion guided by either a predetermined physical phenomenon, such as strongest electric field magnitude, or in an exploratory fashion. We verify the approach first on preacquired 4D-STEM data and further implement it experimentally on an operational STEM. The experimental discovery workflow is demonstrated using graphene and subsequently extended toward a lesser-known layered 2D van der Waals material, MnPS₃. This approach establishes a pathway for physics-driven automated 4D-STEM experiments that enable probing the physics of strongly correlated systems and quantum materials and devices, as well as exploration of beam-sensitive materials.

Mapping 1D Confined Electromagnetic Edge States in 2D Monolayer Semiconducting MoS2 Using 4D-STEM

Four-dimensional (4D) scanning transmission electron microscopy is used to study the electric fields at the edges of 2D semiconducting monolayer MoS₂. Sub-nanometer 1D features in the 2D electric field maps are observed at the outermost region along zigzag edges and also along nanowire MoS-terminated MoS₂ edges. Atomic-scale oscillations are detected in the magnitude of the 1D electromagnetic edge state, with spatial variations that depend on the specific periodic edge reconstructions. Electric field reconstructions, along with integrated differential phase contrast reconstructions, reveal the presence of low Z number atoms terminating many of the uniform edges, which are difficult to detect by annular dark field scanning transmission electron microscopy due to its limited dynamic range. Density functional theory calculations support the formation of periodic 1D edge states and also show that enhancement of the electric field magnitude can occur for some edge terminations. The experimentally observed electric fields at the edges are attributed to the absence of an opposing electric field from a nearest neighbor atom when the electron beam propagates through the 2D monolayer and interacts. These results show the potential of 4D-STEM to map the atomic scale structure and fluctuations of electric fields around edge atoms with different bonding states than bulk atoms in 2D materials, beyond conventional imaging.

Visualizing Grain Statistics in MOCVD WSe2 through Four-Dimensional Scanning Transmission Electron Microscopy

Using four-dimensional scanning transmission electron microscopy, we demonstrate a method to visualize grains and grain boundaries in WSe₂ grown by metal organic chemical vapor deposition (MOCVD) directly onto silicon dioxide. Despite the chemical purity and uniform thickness and texture of the MOCVD-grown WSe₂, we observe a high density of small grains that corresponds with the overall selenium deficiency we measure through ion beam analysis. Moreover, reconstruction of grain information permits the creation of orientation maps that demonstrate the nucleation mechanism for new layers-triangular domains with the same orientation as the layer underneath induces a tensile strain increasing the lattice parameter at these sites.

Accurate and Robust Calibration of the Uniform Affine Transformation Between Scan-Camera Coordinates for Atom-Resolved In-Focus 4D-STEM Datasets

Accurate geometrical calibration between the scan coordinates and the camera coordinates is critical in four-dimensional scanning transmission electron microscopy (4D-STEM) for both quantitative imaging and ptychographic reconstructions. For atomic-resolved, in-focus 4D-STEM datasets, we propose a hybrid method incorporating two sub-routines, namely a J-matrix method and a Fourier method, which can calibrate the uniform affine transformation between the scan-camera coordinates using raw data, without a priori knowledge of the crystal structure of the specimen. The hybrid method is found robust against scan distortions and residual probe aberrations. It is also effective even when defects are present in the specimen, or the specimen becomes relatively thick. We will demonstrate that a successful geometrical calibration with the hybrid method will lead to a more reliable recovery of both the specimen and the electron probe in a ptychographic reconstruction. We will also show that, although the elimination of local scan position errors still requires an iterative approach, the rate of convergence can be improved, and the residual errors can be further reduced if the hybrid method can be firstly applied for initial calibration. The code is made available as a simple-to-use tool to correct affine transformations of the scan-camera coordinates in 4D-STEM experiments.

Halide perovskite dynamics at work: Large cations at 2D-on-3D interfaces are mobile

SignificanceSurface engineering of halide perovskites (HaPs), semiconductors with amazing optoelectronic properties, is critical to improve the performance and ambient stability of HaP-based solar cells and light emitting diodes (LEDs). Ultrathin layers of two-dimensional (2D) analogs of the three-dimensional (3D) HaPs are particularly attractive for this because of their chemical similarities but higher ambient stability. But do such 2D/3D interfaces actually last, given that ions in HaPs move readily-i.e., what happens at those interfaces on the atomic scale? A special electron microscopy, which as a bonus also reveals the true conditions for nondestructive analysis, shows that the large ions that are a necessary part of the 2D films can move into the 3D HaP, a fascinating illustration of panta rei in HaPs.

Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution

We report a study of scattering dynamics in crystals employing momentum-resolved scanning transmission electron microscopy under varying illumination conditions. As we perform successive changes of the probe focus, multiple real-space signals are obtained in dependence of the shape of the incident electron wave. With support from extensive simulations, each signal is shown to be characterised by an optimum focus for which the contrast is maximum and which differs among different signals. For instance, a systematic focus mismatch is found between images formed by high-angle scattering, being sensitive to thickness and chemical composition, and the first moment in diffraction space, being sensitive to electric fields. It follows that a single recording at one specific probe focus is usually insufficient to characterise materials comprehensively. Most importantly, we demonstrate in experiment and simulation that the second moment μ20+μ02=〈p2〉 of the diffracted intensity exhibits a contrast maximum when the electron probe is focused at the top and bottom faces of the specimen, making the presented concept attractive for measuring local topography. Given the versatility of 〈p2〉, we furthermore present a detailed study of its large-angle convergence both analytically using the Mott scattering approach, and by dynamical simulations using the multislice algorithm including thermal diffuse scattering. Both approaches are in very good agreement and yield logarithmic divergence with increasing scattering angle.

Robust Atomic-Resolution Imaging of Lithium in Battery Materials by Center-of-Mass Scanning Transmission Electron Microscopy

The performance of energy storage materials is often governed by their structure at the atomic scale. Conventional electron microscopy can provide detailed information about materials at these length scales, but direct imaging of light elements such as lithium presents a challenge. While several recent techniques allow lithium columns to be distinguished, these typically either involve complex contrast mechanisms that make image interpretation difficult or require significant expertise to perform. Here, we demonstrate how center-of-mass scanning transmission electron microscopy (CoM-STEM) provides an enhanced ability for simultaneous imaging of lithium and heavier element columns in lithium ion conductors. Through a combination of experiments and multislice electron scattering calculations, we show that CoM-STEM is straightforward to perform and produces directly interpretable contrast for thin samples, while being more robust to variations in experimental parameters than previously demonstrated techniques. As a result, CoM-STEM is positioned to become a reliable and facile method for directly probing all elements within energy storage materials at the atomic scale.

STEM Tools for Semiconductor Characterization: Beyond High-Resolution Imaging

The smart engineering of novel semiconductor devices relies on the development of optimized functional materials suitable for the design of improved systems with advanced capabilities aside from better efficiencies. Thereby, the characterization of these materials at the highest level attainable is crucial for leading a proper understanding of their working principle. Due to the striking effect of atomic features on the behavior of semiconductor quantum- and nanostructures, scanning transmission electron microscopy (STEM) tools have been broadly employed for their characterization. Indeed, STEM provides a manifold characterization tool achieving insights on, not only the atomic structure and chemical composition of the analyzed materials, but also probing internal electric fields, plasmonic oscillations, light emission, band gap determination, electric field measurements, and many other properties. The emergence of new detectors and novel instrumental designs allowing the simultaneous collection of several signals render the perfect playground for the development of highly customized experiments specifically designed for the required analyses. This paper presents some of the most useful STEM techniques and several strategies and methodologies applied to address the specific analysis on semiconductors. STEM imaging, spectroscopies, 4D-STEM (in particular DPC), and in situ STEM are summarized, showing their potential use for the characterization of semiconductor nanostructured materials through recent reported studies.

High Resolution Powder Electron Diffraction in Scanning Electron Microscopy

A modern scanning electron microscope equipped with a pixelated detector of transmitted electrons can record a four-dimensional (4D) dataset containing a two-dimensional (2D) array of 2D nanobeam electron diffraction patterns; this is known as a four-dimensional scanning transmission electron microscopy (4D-STEM). In this work, we introduce a new version of our method called 4D-STEM/PNBD (powder nanobeam diffraction), which yields high-resolution powder diffractograms, whose quality is fully comparable to standard TEM/SAED (selected-area electron diffraction) patterns. Our method converts a complex 4D-STEM dataset measured on a nanocrystalline material to a single 2D powder electron diffractogram, which is easy to process with standard software. The original version of 4D-STEM/PNBD method, which suffered from low resolution, was improved in three important areas: (i) an optimized data collection protocol enables the experimental determination of the point spread function (PSF) of the primary electron beam, (ii) an improved data processing combines an entropy-based filtering of the whole dataset with a PSF-deconvolution of the individual 2D diffractograms and (iii) completely re-written software automates all calculations and requires just a minimal user input. The new method was applied to Au, TbF₃ and TiO₂ nanocrystals and the resolution of the 4D-STEM/PNBD diffractograms was even slightly better than that of TEM/SAED.

Probing Multiscale Disorder in Pyrochlore and Related Complex Oxides in the Transmission Electron Microscope: A Review

Transmission electron microscopy (TEM), and its counterpart, scanning TEM (STEM), are powerful materials characterization tools capable of probing crystal structure, composition, charge distribution, electronic structure, and bonding down to the atomic scale. Recent (S)TEM instrumentation developments such as electron beam aberration-correction as well as faster and more efficient signal detection systems have given rise to new and more powerful experimental methods, some of which (e.g., 4D-STEM, spectrum-imaging, in situ/operando (S)TEM)) facilitate the capture of high-dimensional datasets that contain spatially-resolved structural, spectroscopic, time- and/or stimulus-dependent information across the sub-angstrom to several micrometer length scale. Thus, through the variety of analysis methods available in the modern (S)TEM and its continual development towards high-dimensional data capture, it is well-suited to the challenge of characterizing isometric mixed-metal oxides such as pyrochlores, fluorites, and other complex oxides that reside on a continuum of chemical and spatial ordering. In this review, we present a suite of imaging and diffraction (S)TEM techniques that are uniquely suited to probe the many types, length-scales, and degrees of disorder in complex oxides, with a focus on disorder common to pyrochlores, fluorites and the expansive library of intermediate structures they may adopt. The application of these techniques to various complex oxides will be reviewed to demonstrate their capabilities and limitations in resolving the continuum of structural and chemical ordering in these systems.

Determination of Grain-Boundary Structure and Electrostatic Characteristics in a SrTiO3 Bicrystal by Four-Dimensional Electron Microscopy

The grain boundary (GB) plays a critical role in a material's properties and device performance. Therefore, the characterization of a GB's atomic structure and electrostatic characteristics is a matter of great importance for materials science. Here, we report on the atomic structure and electrostatic analysis of a GB in a SrTiO₃ bicrystal by four-dimensional scanning transmission electron microscopy (4D-STEM). We demonstrate that the Σ5 GB is Ti-rich and poor in Sr. We investigate possible effects on the variation in the atomic electrostatic field, including oxygen vacancies, Ti-valence change, and accumulation of cations. A negative charge resulting from a space-charge zone in SrTiO₃ compensates a positive charge accumulated at the GB, which is in agreement with the double-Schottky-barrier model. It demonstrates the feasibility of characterizing the electrostatic properties at the nanometer scale by 4D-STEM, which provides comprehensive insights to understanding the GB structure and its concomitant effects on the electrostatic properties.

Extracting weak magnetic contrast from complex background contrast in plan-view FeGe thin films

The desire to design and build skyrmion-based devices has led to the need to characterize magnetic textures in thin films of functional materials. This can usually be achieved through the Lorentz transmission electron microscopy (LTEM) and the Lorentz scanning transmission electron microscopy (LSTEM) in thin film cross-section and single crystal specimens. However, direct imaging of the magnetic texture in plan-view samples of thin (< 50 nm) films has proved to be challenging due to the complex "background" contrast associated with the microstructure and defects, as well as contributions from bending of the specimens. Using a mechanically polished 35 nm plan-view FeGe thin film, we have explored three methods to extract magnetic contrast from the complex background contrast observed; (1) background subtraction in defocused LTEM images, (2) frequency filtered CoM-DPC reconstructed from LSTEM datasets and 3) registration of 4D-STEM datasets acquired at different tilt angles. Using these methods, we have successfully implemented real space imaging of both the helical phase and skyrmion phase. The ability to understand nanoscale magnetic behavior from plan-view thin films is a fundamental step towards development of highly integrated spin electronics.

py4DSTEM: A Software Package for Four-Dimensional Scanning Transmission Electron Microscopy Data Analysis

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

Fast Grain Mapping with Sub-Nanometer Resolution Using 4D-STEM with Grain Classification by Principal Component Analysis and Non-Negative Matrix Factorization

High-throughput grain mapping with sub-nanometer spatial resolution is demonstrated using scanning nanobeam electron diffraction (also known as 4D scanning transmission electron microscopy, or 4D-STEM) combined with high-speed direct-electron detection. An electron probe size down to 0.5 nm in diameter is used and the sample investigated is a gold–palladium nanoparticle catalyst. Computational analysis of the 4D-STEM data sets is performed using a disk registration algorithm to identify the diffraction peaks followed by feature learning to map the individual grains. Two unsupervised feature learning techniques are compared: principal component analysis (PCA) and non-negative matrix factorization (NNMF). The characteristics of the PCA versus NNMF output are compared and the potential of the 4D-STEM approach for statistical analysis of grain orientations at high spatial resolution is discussed.

Interferometric 4D-STEM for Lattice Distortion and Interlayer Spacing Measurements of Bilayer and Trilayer 2D Materials

Van der Waals materials composed of stacks of individual atomic layers have attracted considerable attention due to their exotic electronic properties that can be altered by, e.g., manipulating the twist angle of bilayer materials or the stacking sequence of trilayer materials. To fully understand and control the unique properties of these few-layer materials, a technique that can provide information about their local in-plane structural deformations, twist direction, and out-of-plane structure is needed. In principle, interference in overlap regions of Bragg disks originating from separate layers of a material encodes 3D information about the relative positions of atoms in the corresponding layers. Here, an interferometric 4D scanning transmission electron microscopy technique is described that utilizes this phenomenon to extract precise structural information from few-layer materials with nm-scale resolution. It is demonstrated how this technique enables measurement of local pm-scale in-plane lattice distortions as well as twist direction and average interlayer spacings in bilayer and trilayer graphene, and therefore provides a means to better understand the interplay between electronic properties and precise structural arrangements of few-layer 2D materials.

ab initio description of bonding for transmission electron microscopy

The simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret their contrast and extract specimen features. This is especially true for high-resolution phase-contrast imaging of materials, but electron scattering simulations based on atomistic models are widely used in materials science and structural biology. Since electron scattering is dominated by the nuclear cores, the scattering potential is typically described by the widely applied independent atom model. This approximation is fast and fairly accurate, especially for scanning TEM (STEM) annular dark-field contrast, but it completely neglects valence bonding and its effect on the transmitting electrons. However, an emerging trend in electron microscopy is to use new instrumentation and methods to extract the maximum amount of information from each electron. This is evident in the increasing popularity of techniques such as 4D-STEM combined with ptychography in materials science, and cryogenic microcrystal electron diffraction in structural biology, where subtle differences in the scattering potential may be both measurable and contain additional insights. Thus, there is increasing interest in electron scattering simulations based on electrostatic potentials obtained from first principles, mainly via density functional theory, which was previously mainly required for holography. In this Review, we discuss the motivation and basis for these developments, survey the pioneering work that has been published thus far, and give our outlook for the future. We argue that a physically better justified ab initio description of the scattering potential is both useful and viable for an increasing number of systems, and we expect such simulations to steadily gain in popularity and importance.

Cepstral scanning transmission electron microscopy imaging of severe lattice distortions

The development of four-dimensional (4D) scanning transmission electron microscopy (STEM) using fast detectors has opened-up new avenues for addressing some of longstanding challenges in electron imaging. One of these challenges is how to image severely distorted crystal lattices, such as at a dislocation core. Here we develop a new 4D-STEM technique, called Cepstral STEM, for imaging disordered crystals using electron diffuse scattering. In contrast to analysis based on Bragg diffraction, which measures the average and periodic scattering potential, electron diffuse scattering can detect fluctuations caused by crystal disorder. Local fluctuations of diffuse scattering are captured by scanning electron nanodiffraction (SEND) using a coherent probe. The harmonic signals in electron diffuse scattering are detected through Cepstral analysis and used for imaging. By integrating Cepstral analysis with 4D-STEM, we demonstrate that information about the distortive part of electron scattering potential can be separated and imaged at nm spatial resolution. We apply the technique to the analysis of a dislocation core in SiGe and lattice distortions in a high entropy alloy.