Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts

Precise positional alignment of atom-resolved HAADF images of heteroepitaxial interface with low signal-to-noise ratio

Heteroepitaxial interfaces are important because they determine the performance of devices such that career mobility is sensitive to the distribution of roughness, strain and composition at the interface. High-angle annular dark field imaging in scanning transmission electron microscopy has been utilized to capture them at an atomic scale. For precise identification of atomic column positions, a technique has been proposed to average multiple image frames taken at a high scanning rate by their positional alignment for increasing signal-to-noise ratio. However, the positional alignment between frames is sometimes incorrectly estimated because of the almost perfect periodic structure at the interfaces. Here, we developed an approach for precise positional alignment, where the images are first aligned by two consecutive images and then are aligned more precisely against the integrated image of the first alignment. We demonstrated our method by applying it to the heterointerface of Si0.8Ge0.2 (Si: silicon, Ge: germanium) epitaxial thin films on a Si substrate.

DFT-Assisted Investigation of the Electric Field and Charge Density Distribution of Pristine and Defective 2D WSe2 by Differential Phase Contrast Imaging

Most properties of solid materials are defined by their internal electric field and charge density distributions which so far are difficult to measure with high spatial resolution. Especially for 2D materials, the atomic electric fields influence the optoelectronic properties. In this study, the atomic-scale electric field and charge density distribution of WSe2 bi- and trilayers are revealed using an emerging microscopy technique, differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). For pristine material, a higher positive charge density located at the selenium atomic columns compared to the tungsten atomic columns is obtained and tentatively explained by a coherent scattering effect. Furthermore, the change in the electric field distribution induced by a missing selenium atomic column is investigated. A characteristic electric field distribution in the vicinity of the defect with locally reduced magnitudes compared to the pristine lattice is observed. This effect is accompanied by a considerable inward relaxation of the surrounding lattice, which according to first principles DFT calculation is fully compatible with a missing column of Se atoms. This shows that DPC imaging, as an electric field sensitive technique, provides additional and remarkable information to the otherwise only structural analysis obtained with conventional STEM imaging.

Artifactual atomic displacements on surfaces using annular dark-field images with image simulation

We investigated artifactual atomic displacements on a Pt (111) surface using annular dark-field (ADF) scanning transmission electron microscopy images under ideal conditions with multi-slice image simulation. Pt atomic columns on the surface exhibited artifact displacement. The bright spots shifted slightly toward the interior of the crystal, indicating that ADF imaging underestimates atomic distance measurements on the crystal surface. Multiple peak fitting is an effective method for determining the positions of bright spots and obtaining more accurate atomic positions while reducing the impact of surface-related artifacts. This is important for the measurement of interatomic distances on crystal surfaces, particularly for catalyst particles.

Full automation of point defect detection in transition metal dichalcogenides through a dual mode deep learning algorithm

Point defects often appear in two-dimensional (2D) materials and are mostly correlated with physical phenomena. The direct visualisation of point defects, followed by statistical inspection, is the most promising way to harness structure-modulated 2D materials. Here, we introduce a deep learning-based platform to identify the point defects in 2H-MoTe2: synergy of unit cell detection and defect classification. These processes demonstrate that segmenting the detected hexagonal cell into two unit cells elaborately cropped the unit cells: further separating a unit cell input into the Te2/Mo column part remarkably increased the defect classification accuracies. The concentrations of identified point defects were 7.16 × 1020 cm2 of Te monovacancies, 4.38 × 1019 cm2 of Te divacancies and 1.46 × 1019 cm2 of Mo monovacancies generated during an exfoliation process for TEM sample-preparation. These revealed defects correspond to the n-type character mainly originating from Te monovacancies, statistically. Our deep learning-oriented platform combined with atomic structural imaging provides the most intuitive and precise way to analyse point defects and, consequently, insight into the defect-property correlation based on deep learning in 2D materials.

Defeating depolarizing fields with artificial flux closure in ultrathin ferroelectrics

Material surfaces encompass structural and chemical discontinuities that often lead to the loss of the property of interest in so-called dead layers. It is particularly problematic in nanoscale oxide electronics, where the integration of strongly correlated materials into devices is obstructed by the thickness threshold required for the emergence of their functionality. Here we report the stabilization of ultrathin out-of-plane ferroelectricity in oxide heterostructures through the design of an artificial flux-closure architecture. Inserting an in-plane-polarized ferroelectric epitaxial buffer provides the continuity of polarization at the interface; despite its insulating nature, we observe the emergence of polarization in our out-of-plane-polarized model of ferroelectric BaTiO3 from the very first unit cell. In BiFeO3, the flux-closure approach stabilizes a 251° domain wall. Its unusual chirality is probably associated with the ferroelectric analogue to the Dzyaloshinskii-Moriya interaction. We, thus, see that in an adaptively engineered geometry, the depolarizing-field-screening properties of an insulator can even surpass those of a metal and be a source of functionality. This could be a useful insight on the road towards the next generation of oxide electronics.

A decade of atom-counting in STEM: From the first results toward reliable 3D atomic models from a single projection

Quantitative structure determination is needed in order to study and understand nanomaterials at the atomic scale. Materials characterisation resulting in precise structural information is a crucial point to understand the structure-property relation of materials. Counting the number of atoms and retrieving the 3D atomic structure of nanoparticles plays an important role here. In this paper, an overview will be given of the atom-counting methodology and its applications over the past decade. The procedure to count the number of atoms will be discussed in detail and it will be shown how the performance of the method can be further improved. Furthermore, advances toward mixed element nanostructures, 3D atomic modelling based on the atom-counting results, and quantifying the nanoparticle dynamics will be highlighted.

Probing Electron Beam Induced Transformations on a Single-Defect Level via Automated Scanning Transmission Electron Microscopy

A robust approach for real-time analysis of the scanning transmission electron microscopy (STEM) data streams, based on ensemble learning and iterative training (ELIT) of deep convolutional neural networks, is implemented on an operational microscope, enabling the exploration of the dynamics of specific atomic configurations under electron beam irradiation via an automated experiment in STEM. Combined with beam control, this approach allows studying beam effects on selected atomic groups and chemical bonds in a fully automated mode. Here, we demonstrate atomically precise engineering of single vacancy lines in transition metal dichalcogenides and the creation and identification of topological defects in graphene. The ELIT-based approach facilitates direct on-the-fly analysis of the STEM data and engenders real-time feedback schemes for probing electron beam chemistry, atomic manipulation, and atom by atom assembly.

Critical ionic transport across an oxygen-vacancy ordering transition

Phase transition points can be used to critically reduce the ionic migration activation energy, which is important for realizing high-performance electrolytes at low temperatures. Here, we demonstrate a route toward low-temperature thermionic conduction in solids, by exploiting the critically lowered activation energy associated with oxygen transport in Ca-substituted bismuth ferrite (Bi_1-xCa_xFeO_3-δ) films. Our demonstration relies on the finding that a compositional phase transition occurs by varying Ca doping ratio across x_Ca ≃ 0.45 between two structural phases with oxygen-vacancy channel ordering along <100> or <110> crystal axis, respectively. Regardless of the atomic-scale irregularity in defect distribution at the doping ratio, the activation energy is largely suppressed to 0.43 eV, compared with ~0.9 eV measured in otherwise rigid phases. From first-principles calculations, we propose that the effective short-range attraction between two positively charged oxygen vacancies sharing lattice deformation not only forms the defect orders but also suppresses the activation energy through concerted hopping.

Phase transition points can be used to reduce the ionic migration activation energy. Here, the authors find a lowered activation energy associated with oxygen transport at a compositional phase transition point in Ca-doped bismuth ferrite films.

Atomic-Resolution STEM Image Denoising by Total Variation Regularization

Atomic-resolution electron microscopy imaging of solid state material is a powerful method for structural analysis. Scanning transmission electron microscopy (STEM) is one of the actively used techniques to directly observe atoms in materials. However, some materials are easily damaged by the electron beam irradiation, and only noisy images are available when we decrease the electron dose to avoid beam damages. Therefore, a denoising process is necessary for precise structural analysis in low-dose STEM. In this study, we propose total variation (TV) denoising algorithm to remove quantum noise in a STEM image. We defined an entropy of STEM image that corresponds to the image contrast to determine a hyperparameter and we found that there is a hyperparameter that maximize the entropy. We acquired atomic resolution STEM image of CaF2 viewed along the [001] direction, and executed TV denoising. The atomic columns of Ca and F are clearly visualized by the TV denoising, and atomic position of Ca and F are determined with the error of ± 1 pm and ± 4 pm, respectively.

Multilevel polarization switching in ferroelectric thin films

Ferroic order is characterized by hystereses with two remanent states and therefore inherently binary. The increasing interest in materials showing non-discrete responses, however, calls for a paradigm shift towards continuously tunable remanent ferroic states. Device integration for oxide nanoelectronics furthermore requires this tunability at the nanoscale. Here we demonstrate that we can arbitrarily set the remanent ferroelectric polarization at nanometric dimensions. We accomplish this in ultrathin epitaxial PbZr_0.52Ti_0.48O₃ films featuring a dense pattern of decoupled nanometric 180° domains with a broad coercive-field distribution. This multilevel switching is achieved by driving the system towards the instability at the morphotropic phase boundary. The phase competition near this boundary in combination with epitaxial strain increases the responsiveness to external stimuli and unlocks new degrees of freedom to nano-control the polarization. We highlight the technological benefits of non-binary switching by demonstrating a quasi-continuous tunability of the non-linear optical response and of tunnel electroresistance.

Setting any polarization value in ferroelectric thin films is a key step for their implementation in neuromorphic devices. Here, the authors demonstrate continuous modulation of the remanent polarization at the nanoscale in PbZr_0.52Ti_0.48O₃ films.

Ingrained: An Automated Framework for Fusing Atomic-Scale Image Simulations into Experiments

To fully leverage the power of image simulation to corroborate and explain patterns and structures in atomic resolution microscopy, an initial correspondence between the simulation and experimental image must be established at the outset of further high accuracy simulations or calculations. Furthermore, if simulation is to be used in context of highly automated processes or high-throughput optimization, the process of finding this correspondence itself must be automated. In this work, "ingrained," an open-source automation framework which solves for this correspondence and fuses atomic resolution image simulations into the experimental images to which they correspond, is introduced. Herein, the overall "ingrained" workflow, focusing on its application to interface structure approximations, and the development of an experimentally rationalized forward model for scanning tunneling microscopy simulation are described.

Exploring Blob Detection to Determine Atomic Column Positions and Intensities in Time-Resolved TEM Images with Ultra-Low Signal-to-Noise

Spatially resolved in situ transmission electron microscopy (TEM), equipped with direct electron detection systems, is a suitable technique to record information about the atom-scale dynamics with millisecond temporal resolution from materials. However, characterizing dynamics or fluxional behavior requires processing short time exposure images which usually have severely degraded signal-to-noise ratios. The poor signal-to-noise associated with high temporal resolution makes it challenging to determine the position and intensity of atomic columns in materials undergoing structural dynamics. To address this challenge, we propose a noise-robust, processing approach based on blob detection, which has been previously established for identifying objects in images in the community of computer vision. In particular, a blob detection algorithm has been tailored to deal with noisy TEM image series from nanoparticle systems. In the presence of high noise content, our blob detection approach is demonstrated to outperform the results of other algorithms, enabling the determination of atomic column position and its intensity with a higher degree of precision.

Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data

As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 μm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.

Towards automating structural discovery in scanning transmission electron microscopy *

Scanning transmission electron microscopy is now the primary tool for exploring functional materials on the atomic level. Often, features of interest are highly localized in specific regions in the material, such as ferroelectric domain walls, extended defects, or second phase inclusions. Selecting regions to image for structural and chemical discovery via atomically resolved imaging has traditionally proceeded via human operators making semi-informed judgements on sampling locations and parameters. Recent efforts at automation for structural and physical discovery have pointed towards the use of ‘active learning’ methods that utilize Bayesian optimization with surrogate models to quickly find relevant regions of interest. Yet despite the potential importance of this direction, there is a general lack of certainty in selecting relevant control algorithms and how to balance a priori knowledge of the material system with knowledge derived during experimentation. Here we address this gap by developing the automated experiment workflows with several combinations to both illustrate the effects of these choices and demonstrate the tradeoffs associated with each in terms of accuracy, robustness, and susceptibility to hyperparameters for structural discovery. We discuss possible methods to build descriptors using the raw image data and deep learning based semantic segmentation, as well as the implementation of variational autoencoder based representation. Furthermore, each workflow is applied to a range of feature sizes including NiO pillars within a La:SrMnO3 matrix, ferroelectric domains in BiFeO3, and topological defects in graphene. The code developed in this manuscript is open sourced and will be released at github.com/nccreang/AE_Workflows.

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.

Atomic-Resolution Cryogenic Scanning Transmission Electron Microscopy for Quantum Materials

ConspectusThe rich physics permeating the phase diagrams of quantum materials have commanded the attention of the solid-state chemistry, materials science, and condensed-matter physics communities, sparking immense research into quantum phase transitions including superconducting, ferroic, and charge-order transitions. Many of these transitions occur at low temperatures and involve electronic, magnetic, or lattice order, which emerges on the atomic to mesoscopic scales. The complex interplay of these states and the heterogeneity that arises due to competition and intertwining of phases, however, is not fully understood and requires probes that capture ordering over multiple length scales down to the local atomic symmetries. Advances in scanning transmission electron microscopy (STEM) have enabled atomic-resolution imaging as well as mapping of functional picometer-scale atomic displacements inside materials. In this Account, we discuss our group's work to expand the reach of atomic-resolution STEM to cryogenic temperatures (cryo-STEM) to study quantum materials with focus on charge-ordered systems.Charge-ordered phases, in which electrons as well as the atomic lattice form periodic patterns that lift the translational symmetries of the crystal, are not only intertwined with superconductivity but also underlie other exotic electronic phenomena such as colossal magnetoresistance and metal-insulator transitions. The periodic lattice distortions (PLDs) modulate the positions of the crystal's nuclei, which can be readily probed by electron microscopy. In a set of examples, we demonstrate cryo-STEM as a powerful technique for probing local order, nanometer-scale heterogeneities, and topological defects in charge-ordered manganites and in transition metal dichalcogenide charge density wave (CDW) systems.With the nearly commensurate-to-commensurate CDW transition upon cooling in 1T-TaS₂, we show that nanoscale lattice textures in CDW phases can be revealed through direct imaging. These early atomic-resolution results, however, also highlighted the need for improvements in cryo-STEM imaging, which led to a push to advance data collection and analysis for direct spatial mapping and quantification of PLDs. By introducing an image registration algorithm developed specifically to accommodate fast, low signal-to-noise image acquisitions of crystalline lattices, we address previous limitations due to sample drift in cryo-STEM experiments. This has enabled subangstrom cryo-STEM imaging with sufficient signal-to-noise to reveal the low temperature structure of 1T'-TaTe₂. Furthermore, it allows mapping and quantification of PLD atomic displacements in the charge-ordered manganites Bi_0.35Sr_0.18Ca_0.47MnO₃ and Nd_0.5Sr_0.5MnO₃ with picometer precision at ∼95 K to resolve not only distinct ordered phases (i.e., site- and bond-centered charge order) but also their nanoscale coexistence within the same sample.Atomic-resolution cryo-STEM opens new opportunities for understanding the microscopic underpinnings of quantum phases. In this Account, we focus on spatial mapping of lattice degrees of freedom in phases that are present at temperatures down to liquid nitrogen. Further advances in instrumentation are needed to expand the temperature range and to also enable atomic-resolution measurements that rely on weaker signals such as electron energy loss spectroscopy (EELS) for probing of electronic structure or 4D-STEM approaches to map electric and magnetic fields.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

Subpercent Local Strains Due to the Shapes of Gold Nanorods Revealed by Data-Driven Analysis

Analysis of subpercent local strain is important for a deeper understanding of nanomaterials, whose properties often depend on the strain. Conventional strain analysis has been performed by measuring interatomic distances from scanning transmission electron microscopy (STEM) images. However, measuring subpercent strain remains a challenge because the peak positions in STEM images do not precisely correspond to the real atomic positions due to disturbing influences, such as random noise and image distortion. Here, we utilized an advanced data-driven analysis method, Gaussian process regression, to predict the true strain distribution by reconstructing the true atomic positions. As a result, a precision of 0.2% was achieved in strain measurement at the atomic scale. The method was applied to gold nanoparticles of different shapes to reveal the shape dependence of the strain distribution. A spherical gold nanoparticle showed a symmetric strain distribution with a contraction of ∼1% near the surface owing to surface relaxation. By contrast, a gold nanorod, which is a cylinder terminated by hemispherical caps on both sides, showed nonuniform strain distributions with lattice expansions of ∼0.5% along the longitudinal axis around the caps except for the contraction at the surface. Our results indicate that the strain distribution depends on the shape of the nanomaterials. The proposed data-driven analysis is a convenient and powerful tool to measure the strain distribution with high precision at the atomic scale.

Identification and correction of temporal and spatial distortions in scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) has become the technique of choice for quantitative characterization of atomic structure of materials, where the minute displacements of atomic columns from high-symmetry positions can be used to map strain, polarization, octahedra tilts, and other physical and chemical order parameter fields. The latter can be used as inputs into mesoscopic and atomistic models, providing insight into the correlative relationships and generative physics of materials on the atomic level. However, these quantitative applications of STEM necessitate understanding the microscope induced image distortions and developing the pathways to compensate them both as part of a rapid calibration procedure for in situ imaging, and the post-experimental data analysis stage. Here, we explore the spatiotemporal structure of the microscopic distortions in STEM using multivariate analysis of the atomic trajectories in the image stacks. Based on the behavior of principal component analysis (PCA), we develop the Gaussian process (GP)-based regression method for quantification of the distortion function. The limitations of such an approach and possible strategies for implementation as a part of in-line data acquisition in STEM are discussed. The analysis workflow is summarized in a Jupyter notebook that can be used to retrace the analysis and analyze the reader's data.

Combining quantitative ADF STEM with SiNx membrane-based MEMS devices: A simulation study with Pt nanoparticles

Computer simulations are used to assess the influence of a 20-nm-thick SiN_x membrane on the quantification of atomic-resolution annular dark-field (ADF) scanning transmission electron microscopy images of Pt nanoparticles. The discussions include the effect of different nanoparticle/membrane arrangements, accelerating voltage, nanoparticle thickness and the presence of adjacent atomic columns on the accuracy with which the number of Pt atoms in each atom column can be counted. The results, which are based on the use of ADF scattering cross-sections, show that an accuracy of better than a single atom is attainable at 200 and 300 kV. At 80kV, the scattering in a typical SiN_x membrane is sufficiently strong that the best possible atom counting accuracy is reduced to +/- 2 atoms. The implications of the work for quantitative studies of Pt nanoparticles imaged through SiN_x membranes are discussed.

Layer and spontaneous polarizations in perovskite oxides and their interplay in multiferroic bismuth ferrite

We review the concept of surface charge, first, in the context of the polarization in ferroelectric materials and, second, in the context of layers of charged ions in ionic insulators. While the former is traditionally discussed in the ferroelectrics community and the latter in the surface science community, we remind the reader that the two descriptions are conveniently unified within the modern theory of polarization. In both cases, the surface charge leads to electrostatic instability-the so-called "polar catastrophe"-if it is not compensated, and we review the range of phenomena that arise as a result of different compensation mechanisms. We illustrate these concepts using the example of the prototypical multiferroic bismuth ferrite, BiFeO₃, which is unusual in that its spontaneous ferroelectric polarization and the polarization arising from its layer charges can be of the same magnitude. As a result, for certain combinations of polarization orientation and surface termination, its surface charge is self-compensating. We use density functional calculations of BiFeO₃ slabs and superlattices, analysis of high-resolution transmission electron micrographs, and examples from the literature to explore the consequences of this peculiarity.

Optimizing Experimental Conditions for Accurate Quantitative Energy-Dispersive X-ray Analysis of Interfaces at the Atomic Scale

The invention of silicon drift detectors has resulted in an unprecedented improvement in detection efficiency for energy-dispersive X-ray (EDX) spectroscopy in the scanning transmission electron microscope. The result is numerous beautiful atomic-scale maps, which provide insights into the internal structure of a variety of materials. However, the task still remains to understand exactly where the X-ray signal comes from and how accurately it can be quantified. Unfortunately, when crystals are aligned with a low-order zone axis parallel to the incident beam direction, as is necessary for atomic-resolution imaging, the electron beam channels. When the beam becomes localized in this way, the relationship between the concentration of a particular element and its spectroscopic X-ray signal is generally nonlinear. Here, we discuss the combined effect of both spatial integration and sample tilt for ameliorating the effects of channeling and improving the accuracy of EDX quantification. Both simulations and experimental results will be presented for a perovskite-based oxide interface. We examine how the scattering and spreading of the electron beam can lead to erroneous interpretation of interface compositions, and what approaches can be made to improve our understanding of the underlying atomic structure.

Exploring order parameters and dynamic processes in disordered systems via variational autoencoders

We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on atomic positions are available. This approach is predicated on the synergy of two concepts, the parsimony of physical descriptors and general rotational invariance of noncrystalline solids, and is implemented using a rotationally invariant extension of the variational autoencoder applied to semantically segmented atom-resolved data seeking the most effective reduced representation for the system that still contains the maximum amount of original information. This approach allowed us to explore the dynamic evolution of electron beam-induced processes in a silicon-doped graphene system, but it can be also applied for a much broader range of atomic scale and mesoscopic phenomena to introduce the bottom-up order parameters and explore their dynamics with time and in response to external stimuli.

TEMImageNet training library and AtomSegNet deep-learning models for high-precision atom segmentation, localization, denoising, and deblurring of atomic-resolution images

Atom segmentation and localization, noise reduction and deblurring of atomic-resolution scanning transmission electron microscopy (STEM) images with high precision and robustness is a challenging task. Although several conventional algorithms, such has thresholding, edge detection and clustering, can achieve reasonable performance in some predefined sceneries, they tend to fail when interferences from the background are strong and unpredictable. Particularly, for atomic-resolution STEM images, so far there is no well-established algorithm that is robust enough to segment or detect all atomic columns when there is large thickness variation in a recorded image. Herein, we report the development of a training library and a deep learning method that can perform robust and precise atom segmentation, localization, denoising, and super-resolution processing of experimental images. Despite using simulated images as training datasets, the deep-learning model can self-adapt to experimental STEM images and shows outstanding performance in atom detection and localization in challenging contrast conditions and the precision consistently outperforms the state-of-the-art two-dimensional Gaussian fit method. Taking a step further, we have deployed our deep-learning models to a desktop app with a graphical user interface and the app is free and open-source. We have also built a TEM ImageNet project website for easy browsing and downloading of the training data.

Optimizing Nonrigid Registration for Scanning Transmission Electron Microscopy Image Series

Achieving sub-picometer precision measurements of atomic column positions in high-resolution scanning transmission electron microscope images using nonrigid registration (NRR) and averaging of image series requires careful optimization of experimental conditions and the parameters of the registration algorithm. On experimental data from SrTiO3 [100], sub-pm precision requires alignment of the sample to the zone axis to within 1 mrad tilt and sample drift of less than 1 nm/min. At fixed total electron dose for the series, precision in the fast scan direction improves with shorter pixel dwell time to the limit of our microscope hardware, but the best precision along the slow scan direction occurs at 6 μs/px dwell time. Within the NRR algorithm, the “smoothness factor” that penalizes large estimated shifts is the most important parameter for sub-pm precision, but in general, the precision of NRR images is robust over a wide range of parameters.

Evaluation of the Nanodomain Structure in In-Zn-O Transparent Conductors

The optimization of novel transparent conductive oxides (TCOs) implies a better understanding of the role that the dopant plays on the optoelectronic properties of these materials. In this work, we perform a systematic study of the homologous series Zn_kIn₂O_k+3 (IZO) by characterizing the specific location of indium in the structure that leads to a nanodomain framework to release structural strain. Through a systematic study of different terms of the series, we have been able to observe the influence of the k value in the nano-structural features of this homologous series. The stabilization and visualization of the structural modulation as a function of k is discussed, even in the lowest term of the series (k = 3). The strain fields and atomic displacements in the wurtzite structure as a consequence of the introduction of In³⁺ are evaluated.

Atomic-Level Manipulations in Oxides and Alloys for Electrocatalysis of Oxygen Evolution and Reduction

As chemical reactions and charge-transfer simultaneously occur on the catalyst surface during electrocatalysis, numerous studies have been carried out to attain an in-depth understanding on the correlation among the surface structure and composition, the electrical transport, and the overall catalytic activity. Compared with other catalysis reactions, a relatively larger activation barrier for oxygen evolution/reduction reactions (OER/ORR), where multiple electron transfers are involved, is noted. Many works over the past decade thus have been focused on the atomic-scale control of the surface structure and the precise identification of surface composition change in catalyst materials to achieve better conversion efficiency. In particular, recent advances in various analytical tools have enabled noteworthy findings of unexpected catalytic features at atomic resolution, providing significant insights toward reducing the activation barriers and subsequently improving the catalytic performance. In addition to summarizing important surface issues, including lattice defects, related to the OER and ORR in this Review, we present the current status and discuss future perspectives of oxide- and alloy-based catalysts in terms of atomic-scale observation and manipulation.

Shedding Light on the Role of Misfit Strain in Controlling Core-Shell Nanocrystals

Heteroepitaxial modification of nanomaterials has become a powerful means to create novel functionalities for various applications. One of the most elementary factors in heteroepitaxial nanostructures is the misfit strain arising from mismatched lattices of the constituent parts. Misfit strain not only dictates epitaxy kinetics for diversifying nanocrystal morphologies but also provides rational control over materials properties. In recent years, advances in chemical synthesis along with the rapid development of electron microscopy and X-ray diffraction techniques have enabled a substantial understanding of strain-related processes, which offers theoretical foundation and experimental guidance for researchers to refine heteroepitaxial nanostructures and their properties. Herein, recent investigations on heterogeneous core-shell nanocrystals containing misfit strains are summarized, with a focus on the mechanistic understanding of strain and strain-induced effects such as tuning the epitaxial habit, modulating the optical emission, and enhancing the catalytic activity and magnetic coercivity.

Direct Visualization of Trimerized States in 1T^{'}-TaTe_{2}

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulated structures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy (STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT) modulated phases in 1T^{'}-TaTe_{2}. At HT, we directly show in-plane metal distortions which form trimerized clusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additional trimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrast modulations in plan-view STEM data. Coupled with density functional theory calculations and image simulations, this approach opens the door for atomic-scale visualizations of low temperature phase transitions and complex displacements in a variety of layered systems.

Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition

Tensor singular value decomposition (SVD) is a method to find a low-dimensional representation of data with meaningful structure in three or more dimensions. Tensor SVD has been applied to denoise atomic-resolution 4D scanning transmission electron microscopy (4D STEM) data. On data simulated from a SrTiO₃ [100] perfect crystal and a Si [110] edge dislocation, tensor SVD achieved an average peak signal-to-noise ratio (PSNR) of ~40 dB, which matches or exceeds the performance of other denoising methods, with processing times at least 100 times shorter. On experimental data from SrTiO₃ [100] and LiZnSb [112¯0]/GaSb [110] samples, tensor SVD denoises multiple GB 4D STEM data sets in ten minutes on a typical personal computer. Denoising with tensor SVD improves both convergent beam electron diffraction patterns and virtual-aperture annular dark field images.

Polar Nanodomains in a Ferroelectric Superconductor

The mechanisms by which itinerant carriers compete with polar crystal distortions are a key unresolved issue for polar superconductors, which offer new routes to unconventional Cooper pairing. Strained, doped SrTiO₃ films undergo successive ferroelectric and superconducting transitions, making them ideal candidates to elucidate the nature of this competition. Here, we reveal these interactions using scanning transmission electron microscopy studies of the evolution of polar nanodomains as a function of doping. These nanodomains are a precursor to the ferroelectric phase and a measure of long-range Coulomb interactions. With increasing doping, the magnitude of the polar displacements, the nanodomain size, and the Curie temperature are systematically suppressed. In addition, we show that disorder caused by the dopant atoms themselves presents a second contribution to the destabilization of the ferroelectric state. The results provide evidence for two distinct mechanisms that suppress the polar transition with doping in a ferroelectric superconductor.

Order-Disorder Ferroelectric Transition of Strained SrTiO_{3}

SrTiO_{3} is an incipient ferroelectric that is believed to exhibit a prototype displacive, soft mode ferroelectric transition when subjected to mechanical stress or alloying. We use high-angle annular dark-field imaging in scanning transmission electron microscopy to reveal local polar regions in the room-temperature, paraelectric phase of strained SrTiO_{3} films, which undergo a ferroelectric transition at low temperatures. These films contain nanometer-sized domains in which the Ti columns are displaced. In contrast, these nanodomains are absent in unstrained films, which do not become ferroelectric. The results show that the ferroelectric transition of strained SrTiO_{3} is an order-disorder transition. We discuss the impact of the results on the nature of the ferroelectric transition of SrTiO_{3}.

Nanoparticle Recognition on Scanning Probe Microscopy Images Using Computer Vision and Deep Learning

Identifying, counting and measuring particles is an important component of many research studies. Images with particles are usually processed by hand using a software ruler. Automated processing, based on conventional image processing methods (edge detection, segmentation, etc.) are not universal, can only be used on good-quality images and need to set a number of parameters empirically. In this paper, we present results from the application of deep learning to automated recognition of metal nanoparticles deposited on highly oriented pyrolytic graphite on images obtained by scanning tunneling microscopy (STM). We used the Cascade Mask-RCNN neural network. Training was performed on a dataset containing 23 STM images with 5157 nanoparticles. Three images containing 695 nanoparticles were used for verification. As a result, the trained neural network recognized nanoparticles in the verification set with 0.93 precision and 0.78 recall. Predicted contour refining with 2D Gaussian function was a proposed option. The accuracies for mean particle size calculated from predicted contours compared with ground truth were in the range of 0.87-0.99. The results were compared with outcomes from other generally available software, based on conventional image processing methods. The advantages of deep learning methods for automatic particle recognition were clearly demonstrated. We developed a free open-access web service "ParticlesNN" based on the trained neural network, which can be used by any researcher in the world.

Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose

Both high resolution and high precision are required to quantitatively determine the atomic structure of complex nanostructured materials. However, for conventional imaging methods in scanning transmission electron microscopy (STEM), atomic resolution with picometer precision cannot usually be achieved for weakly-scattering samples or radiation-sensitive materials, such as 2D materials. Here, we demonstrate low-dose, sub-angstrom resolution imaging with picometer precision using mixed-state electron ptychography. We show that correctly accounting for the partial coherence of the electron beam is a prerequisite for high-quality structural reconstructions due to the intrinsic partial coherence of the electron beam. The mixed-state reconstruction gains importance especially when simultaneously pursuing high resolution, high precision and large field-of-view imaging. Compared with conventional atomic-resolution STEM imaging techniques, the mixed-state ptychographic approach simultaneously provides a four-times-faster acquisition, with double the information limit at the same dose, or up to a fifty-fold reduction in dose at the same resolution.

With conventional scanning transmission electron microscopy, some sensitive materials are difficult to image with atomic resolution. The authors present a method of mixed-state electron ptychography that enables picometer precision with fast acquisition and low dosage.

Deep Learning Enabled Strain Mapping of Single-Atom Defects in Two-Dimensional Transition Metal Dichalcogenides with Sub-Picometer Precision

Two-dimensional (2D) materials offer an ideal platform to study the strain fields induced by individual atomic defects, yet challenges associated with radiation damage have so far limited electron microscopy methods to probe these atomic-scale strain fields. Here, we demonstrate an approach to probe single-atom defects with sub-picometer precision in a monolayer 2D transition metal dichalcogenide, WSe_2-2xTe_2x. We utilize deep learning to mine large data sets of aberration-corrected scanning transmission electron microscopy images to locate and classify point defects. By combining hundreds of images of nominally identical defects, we generate high signal-to-noise class averages which allow us to measure 2D atomic spacings with up to 0.2 pm precision. Our methods reveal that Se vacancies introduce complex, oscillating strain fields in the WSe_2-2xTe_2x lattice that correspond to alternating rings of lattice expansion and contraction. These results indicate the potential impact of computer vision for the development of high-precision electron microscopy methods for beam-sensitive materials.

The exit-wave power-cepstrum transform for scanning nanobeam electron diffraction: robust strain mapping at subnanometer resolution and subpicometer precision

Scanning nanobeam electron diffraction (NBED) with fast pixelated detectors is a valuable technique for rapid, spatially resolved mapping of lattice structure over a wide range of length scales. However, intensity variations caused by dynamical diffraction and sample mistilts can hinder the measurement of diffracted disk centers as necessary for quantification. Robust data processing techniques are needed to provide accurate and precise measurements for complex samples and non-ideal conditions. Here we present an approach to address these challenges using a transform, called the exit wave power cepstrum (EWPC), inspired by cepstral analysis in audio signal processing. The EWPC transforms NBED patterns into real-space patterns with sharp peaks corresponding to inter-atomic spacings. We describe a simple analytical model for interpretation of these patterns that cleanly decouples lattice information from the intensity variations in NBED patterns caused by tilt and thickness. By tracking the inter-atomic spacing peaks in EWPC patterns, strain mapping is demonstrated for two practical applications: mapping of ferroelectric domains in epitaxially strained PbTiO₃ films and mapping of strain profiles in arbitrarily oriented core-shell Pt-Co nanoparticle fuel-cell catalysts. The EWPC transform enables lattice structure measurement at sub-pm precision and sub-nm resolution that is robust to small sample mistilts and random orientations.

Imaging and quantification of charged domain walls in BiFeO3

Charged domain walls in ferroelectrics hold great promise for the design of novel electronic devices due to their enhanced local conductivity. In fact, charged domain walls show unique properties including the possibility of being created, moved and erased by an applied voltage. Here, we demonstrate that the charged domain walls are constituted by a core region where most of the screening charge is localized and such charge accumulation is responsible for their enhanced conductivity. In particular, the link between the local structural distortions and charge screening phenomena in 109° tail-to-tail domain walls of BiFeO3 is elucidated by a series of multiscale analysis performed by means of scanning probe techniques, including conductive atomic force microscopy (cAFM) and atomic resolution differential phase contrast scanning transmission electron microscopy (DPC-STEM). The results prove that an accumulation of oxygen vacancies occurs at the tail-to-tail domain walls as the leading charge screening process. This work constitutes a new insight in understanding the behavior of such complex systems and lays down the fundaments for their implementation into novel nanoelectronic devices.

Probing local order in multiferroics by transmission electron microscopy

The ongoing trend toward miniaturization has led to an increased interest in the magnetoelectric effect, which could yield entirely new device concepts, such as electric field-controlled magnetic data storage. As a result, much work is being devoted to developing new robust room temperature (RT) multiferroic materials that combine ferromagnetism and ferroelectricity. However, the development of new multiferroic devices has proved unexpectedly challenging. Thus, a better understanding of the properties of multiferroic thin films and the relation with their microstructure is required to help drive multiferroic devices toward technological application. This review covers in a concise manner advanced analytical imaging methods based on (scanning) transmission electron microscopy which can potentially be used to characterize complex multiferroic materials. It consists of a first broad introduction to the topic followed by a section describing the so-called phase-contrast methods, which can be used to map the polar and magnetic order in magnetoelectric multiferroics at different spatial length scales down to atomic resolution. Section 3 is devoted to electron nanodiffraction methods. These methods allow measuring local strains, identifying crystal defects and determining crystal structures, and thus offer important possibilities for the detailed structural characterization of multiferroics in the ultrathin regime or inserted in multilayers or superlattice architectures. Thereafter, in Section 4, methods are discussed which allow for analyzing local strain, whereas in Section 5 methods are addressed which allow for measuring local polarization effects on a length scale of individual unit cells. Here, it is shown that the ferroelectric polarization can be indirectly determined from the atomic displacements measured in atomic resolution images. Finally, a brief outlook is given on newly established methods to probe the behavior of ferroelectric and magnetic domains and nanostructures during in situ heating/electrical biasing experiments. These in situ methods are just about at the launch of becoming increasingly popular, particularly in the field of magnetoelectric multiferroics, and shall contribute significantly to understanding the relationship between the domain dynamics of multiferroics and the specific microstructure of the films providing important guidance to design new devices and to predict and mitigate failures.

Approaches to Exploring Spatio-Temporal Surface Dynamics in Nanoparticles with In Situ Transmission Electron Microscopy

Many nanoparticles in fields such as heterogeneous catalysis undergo surface structural fluctuations during chemical reactions, which may control functionality. These dynamic structural changes may be ideally investigated with time-resolved in situ electron microscopy. We have explored approaches for extracting quantitative information from large time-resolved image data sets with a low signal to noise recorded with a direct electron detector on an aberration-corrected transmission electron microscope. We focus on quantitatively characterizing beam-induced dynamic structural rearrangements taking place on the surface of CeO2 (ceria). A 2D Gaussian fitting procedure is employed to determine the position and occupancy of each atomic column in the nanoparticle with a temporal resolution of 2.5 ms and a spatial precision of 0.25 Å. Local rapid lattice expansions/contractions and atomic migration were revealed to occur on the (100) surface, whereas (111) surfaces were relatively stable throughout the experiment. The application of this methodology to other materials will provide new insights into the behavior of nanoparticle surface reconstructions that were previously inaccessible using other methods, which will have important consequences for the understanding of dynamic structure-property relationships.

Atomic resolution convergent beam electron diffraction analysis using convolutional neural networks

Two types of convolutional neural network (CNN) models, a discrete classification network and a continuous regression network, were trained to determine local sample thickness from convergent beam diffraction (CBED) patterns of SrTiO₃ collected in a scanning transmission electron microscope (STEM) at atomic column resolution. Acquisition of atomic resolution CBED patterns for this purpose requires careful balancing of CBED feature size in pixels, acquisition speed, and detector dynamic range. The training datasets were derived from multislice simulations, which must be convolved with incoherent source broadening. Sample thicknesses were also determined using quantitative high-angle annular dark-field (HAADF) STEM images acquired simultaneously. The regression CNN performed well on sample thinner than 35 nm, with 70% of the CNN results within 1 nm of HAADF thickness, and 1.0 nm overall root mean square error between the two measurements. The classification CNN was trained for a thicknesses up to 100 nm and yielded 66% of CNN results within one classification increment of 2 nm of HAADF thickness. Our approach depends on methods from computer vision including transfer learning and image augmentation.

Building and exploring libraries of atomic defects in graphene: Scanning transmission electron and scanning tunneling microscopy study

The presence and configurations of defects are primary components determining materials functionality. Their population and distribution are often nonergodic and dependent on synthesis history, and therefore rarely amenable to direct theoretical prediction. Here, dynamic electron beam-induced transformations in Si deposited on a graphene monolayer are used to create libraries of possible Si and carbon vacancy defects. Deep learning networks are developed for automated image analysis and recognition of the defects, creating a library of (meta) stable defect configurations. Density functional theory is used to estimate atomically resolved scanning tunneling microscopy (STM) signatures of the classified defects from the created library, allowing identification of several defect types across imaging platforms. This approach allows automatic creation of defect libraries in solids, exploring the metastable configurations always present in real materials, and correlative studies with other atomically resolved techniques, providing comprehensive insight into defect functionalities.

Understanding semiconductor nanostructures via advanced electron microscopy and spectroscopy

Transmission electron microscopy (TEM) offers an ample range of complementary techniques which are able to provide essential information about the physical, chemical and structural properties of materials at the atomic scale, and hence makes a vast impact on our understanding of materials science, especially in the field of semiconductor one-dimensional (1D) nanostructures. Recent advancements in TEM instrumentation, in particular aberration correction and monochromation, have enabled pioneering experiments in complex nanostructure material systems. This review aims to address these understandings through the applications of the methodology for semiconductor nanostructures. It points out various electron microscopy techniques, in particular scanning TEM (STEM) imaging and spectroscopy techniques, with their already-employed or potential applications on 1D nanostructured semiconductors. We keep the main focus of the paper on the electronic and optoelectronic properties of such semiconductors, and avoid expanding it further. In the first part of the review, we give a brief introduction to each of the STEM-based techniques, without detailed elaboration, and mention the recent technological and conceptual developments which lead to novel characterization methodologies. For further reading, we refer the audience to a handful of papers in the literature. In the second part, we highlight the recent examples of application of the STEM methodology on the 1D nanostructure semiconductor materials, especially III-V, II-V, and group IV bare and heterostructure systems. The aim is to address the research questions on various physical properties and introduce solutions by choosing the appropriate technique that can answer the questions. Potential applications will also be discussed, the ones that have already been used for bulk and 2D materials, and have shown great potential and promise for 1D nanostructure semiconductors.