Abstract: Single atom detection is of key importance to solving a wide range of scientific and technological problems. The strong interaction of electrons with matter makes transmission electron microscopy one of the most promising techniques. In particular, aberration correction using scanning transmission electron microscopy has made a significant step forward toward detecting single atoms. However, to overcome radiation damage, related to the use of high-energy electrons, the incoming electron dose should be kept low enough. This results in images exhibiting a low signal-to-noise ratio and extremely weak contrast, especially for light-element nanomaterials. To overcome this problem, a combination of physics-based model fitting and the use of a model-order selection method is proposed, enabling one to detect single atoms with high reliability.

Abstract: We report the mapping of polarization-induced internal electric fields in AlN/GaN nanowire heterostructures at unit cell resolution as a key for the correlation of optical and structural phenomena in semiconductor optoelectronics. Momentum-resolved aberration-corrected scanning transmission electron microscopy is employed as a new imaging mode that simultaneously provides four-dimensional data in real and reciprocal space. We demonstrate how internal mesoscale and atomic electric fields can be separated in an experiment, which is verified by comprehensive dynamical simulations of multiple electron scattering. A mean difference of 5.3 +- 1.5 MV/cm is found for the polarization-induced electric fields in AlN and GaN, being in accordance with dedicated simulations and photoluminescence measurements in previous publications.

Abstract: In oxide heterostructures, different materials are integrated into a single artificial crystal, resulting in a breaking of inversion symmetry across the heterointerfaces. A notable example is the interface between polar and nonpolar materials, where valence discontinuities lead to otherwise inaccessible charge and spin states. This approach paved the way for the discovery of numerous unconventional properties absent in the bulk constituents. However, control of the geometric structure of the electronic wave functions in correlated oxides remains an open challenge. Here, we create heterostructures consisting of ultrathin SrRuO3, an itinerant ferromagnet hosting momentum-space sources of Berry curvature, and
LaAlO3, a polar wide-band-gap insulator. Transmission electron microscopy reveals an atomically sharp LaO/RuO2/SrO interface configuration, leading to excess charge being pinned near the LaAlO3/SrRuO3 interface. We demonstrate through magneto-optical characterization, theoretical calculations and transport measurements that the real-space charge reconstruction drives a reorganization of the topological charges in the band structure, thereby modifying the momentum-space Berry curvature in SrRuO3. Our results illustrate how the topological and magnetic features of oxides can be manipulated by engineering charge discontinuities at oxide interfaces.

Abstract: Reducible supports can affect the performance of metal catalysts by the formation of suboxide overlayers upon reduction, a process referred to as the strong metal-support interaction (SMSI). A combination of operando electron microscopy and vibrational spectroscopy revealed that thin TiOx overlayers formed on nickel/titanium dioxide catalysts during 400 degrees C reduction were completely removed under carbon dioxide hydrogenation conditions. Conversely, after 600 degrees C reduction, exposure to carbon dioxide hydrogenation reaction conditions led to only partial reexposure of nickel, forming interfacial sites in contact with TiOx and favoring carbon-carbon coupling by providing a carbon species reservoir. Our findings challenge the conventional understanding of SMSIs and call for more-detailed operando investigations of nanocatalysts at the single-particle level to revisit static models of structure-activity relationships.

Abstract: Functional interfaces are at the core of research in the emerging field of domain boundary engineering where polar, conducting, chiral, and other interfaces and twin boundaries have been discovered. Ferroelectricity was found in twin walls of paraelectric CaTiO3. We show that the effect of functional interfaces can be optimized if the number of twin boundaries is increased in densely twinned materials. Such materials can be produced by shear in the ferroelastic phase rather than by rapid quench from the paraelastic phase.

Abstract: In the present paper, the optimal detector design is investigated for both detecting and locating light atoms from high resolution scanning transmission electron microscopy (HR STEM) images. The principles of detection theory are used to quantify the probability of error for the detection of light atoms from HR STEM images. To determine the optimal experiment design for locating light atoms, use is made of the so-called Cramer-Rao Lower Bound (CRLB). It is investigated if a single optimal design can be found for both the detection and location problem of light atoms. Furthermore, the incoming electron dose is optimised for both research goals and it is shown that picometre range precision is feasible for the estimation of the atom positions when using an appropriate incoming electron dose under the optimal detector settings to detect light atoms.

Abstract: In quantitative scanning transmission electron microscopy (STEM), scattering cross-sections have been shown to be very sensitive to the number of atoms in a column and its composition. They correspond to the integrated intensity over the atomic column and they outperform other measures. As compared to atomic column peak intensities, which saturate at a given thickness, scattering cross-sections increase monotonically. A study of the electron wave propagation is presented to explain the sensitivity of the scattering cross-sections. Based on the multislice algorithm, we analyse the wave propagation inside the crystal and its link to the scattered signal for the different probe positions contained in the scattering cross-section for detector collection in the low-, middle- and high-angle regimes. The influence to the signal from scattering of neighbouring columns is also discussed.

Abstract: In this work, a recently developed quantitative approach based on the principles of detection theory is used in order to determine the possibilities and limitations of High Resolution Scanning Transmission Electron Microscopy (HR STEM) and HR TEM for atom-counting. So far, HR STEM has been shown to be an appropriate imaging mode to count the number of atoms in a projected atomic column. Recently, it has been demonstrated that HR TEM, when using negative spherical aberration imaging, is suitable for atom-counting as well. The capabilities of both imaging techniques are investigated and compared using the probability of error as a criterion. It is shown that for the same incoming electron dose, HR STEM outperforms HR TEM under common practice standards, i.e. when the decision is based on the probability function of the peak intensities in HR TEM and of the scattering cross-sections in HR STEM. If the atom-counting decision is based on the joint probability function of the image pixel values, the dependence of all image pixel intensities as a function of thickness should be known accurately. Under this assumption, the probability of error may decrease significantly for atom-counting in HR TEM and may, in theory, become lower as compared to HR STEM under the predicted optimal experimental settings. However, the commonly used standard for atom-counting in HR STEM leads to a high performance and has been shown to work in practice.

Abstract: In this paper, we investigate how precise atoms of a small nanocluster can ultimately be located in three dimensions (3D) from a tilt series of images acquired using annular dark field (ADF) scanning transmission electron microscopy (STEM). Therefore, we derive an expression for the statistical precision with which the 3D atomic position coordinates can be estimated in a quantitative analysis. Evaluating this statistical precision as a function of the microscope settings also allows us to derive the optimal experimental design. In this manner, the optimal angular tilt range, required electron dose, optimal detector angles, and number of projection images can be determined.

Abstract: A hybrid statistics-simulations based method for atom-counting from annular dark field scanning transmission electron microscopy (ADF STEM) images of monotype crystalline nanostructures is presented. Different atom-counting methods already exist for model-like systems. However, the increasing relevance of radiation damage in the study of nanostructures demands a method that allows atom-counting from low dose images with a low signal-to-noise ratio. Therefore, the hybrid method directly includes prior knowledge from image simulations into the existing statistics-based method for atom-counting, and accounts in this manner for possible discrepancies between actual and simulated experimental conditions. It is shown by means of simulations and experiments that this hybrid method outperforms the statistics-based method, especially for low electron doses and small nanoparticles. The analysis of a simulated low dose image of a small nanoparticle suggests that this method allows for far more reliable quantitative analysis of beam-sensitive materials.

Abstract: The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.

Abstract: Recently, the maximum a posteriori (MAP) probability rule has been proposed as an objective and quantitative method to detect atom columns and even single atoms from high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images. The method combines statistical parameter estimation and model-order selection using a Bayesian framework and has been shown to be especially useful for the analysis of the structure of beam-sensitive nanomaterials. In order to avoid beam damage, images of such materials are usually acquired using a limited incoming electron dose resulting in a low contrast-to-noise ratio (CNR) which makes visual inspection unreliable. This creates a need for an objective and quantitative approach. The present paper describes the methodology of the MAP probability rule, gives its step-by-step derivation and discusses its algorithmic implementation for atom column detection. In addition, simulation results are presented showing that the performance of the MAP probability rule to detect the correct number of atomic columns from HAADF STEM images is superior to that of other model-order selection criteria, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Moreover, the MAP probability rule is used as a tool to evaluate the relation between STEM image quality measures and atom detectability resulting in the introduction of the so-called integrated CNR (ICNR) as a new image quality measure that better correlates with atom detectability than conventional measures such as signal-to-noise ratio (SNR) and CNR.

Abstract: In electron microscopy, the maximum a posteriori (MAP) probability rule has been introduced as a tool to determine the most probable atomic structure from high-resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM) images exhibiting low contrast-to-noise ratio (CNR). Besides ADF imaging, STEM can also be applied in the annular bright-field (ABF) regime. The ABF STEM mode allows to directly visualize light-element atomic columns in the presence of heavy columns. Typically, light-element nanomaterials are sensitive to the electron beam, limiting the incoming electron dose in order to avoid beam damage and leading to images exhibiting low CNR. Therefore, it is of interest to apply the MAP probability rule not only to ADF STEM images, but to ABF STEM images as well. In this work, the methodology of the MAP rule, which combines statistical parameter estimation theory and model-order selection, is extended to be applied to simultaneously acquired ABF and ADF STEM images. For this, an extension of the commonly used parametric models in STEM is proposed. Hereby, the effect of specimen tilt has been taken into account, since small tilts from the crystal zone axis affect, especially, ABF STEM intensities. Using simulations as well as experimental data, it is shown that the proposed methodology can be successfully used to detect light elements in the presence of heavy elements.

Abstract: A small sample tilt away from a main zone axis orientation results in an elongation of the atomic columns in ADF STEM images. An often posed research question is therefore whether the ADF STEM image intensities of tilted nanomaterials should be quantified using a parametric imaging model consisting of elliptical rather than the currently used symmetrical peaks. To this purpose, simulated ADF STEM images corresponding to different amounts of sample tilt are studied using a parametric imaging model that consists of superimposed 2D elliptical Gaussian peaks on the one hand and symmetrical Gaussian peaks on the other hand. We investigate the quantification of structural parameters such as atomic column positions and scattering cross sections using both parametric imaging models. In this manner, we quantitatively study what can be gained from this elliptical model for quantitative ADF STEM, despite the increased parameter space and computational effort. Although a qualitative improvement can be achieved, no significant quantitative improvement in the estimated structure parameters is achieved by the elliptical model as compared to the symmetrical model. The decrease in scattering cross sections with increasing sample tilt is even identical for both types of parametric imaging models. This impedes direct comparison with zone axis image simulations. Nonetheless, we demonstrate how reliable atom-counting can still be achieved in the presence of small sample tilt.

Abstract: This paper investigates the possible benefits for counting atoms of different chemical nature when analysing multiple 2D scanning transmission electron microscopy (STEM) images resulting from independent annular dark field (ADF) detector regimes. To reach this goal, the principles of statistical detection theory are used to quantify the probability of error when determining the number of atoms in atomic columns consisting of multiple types of elements. In order to apply this theory, atom-counting is formulated as a statistical hypothesis test, where each hypothesis corresponds to a specific number of atoms of each atom type in an atomic column. The probability of error, which is limited by the unavoidable presence of electron counting noise, can then be computed from scattering-cross sections extracted from multiple ADF STEM images. Minimisation of the probability of error as a function of the inner and outer angles of a specified number of independent ADF collection regimes results in optimal experimental designs. Based on simulations of spherical Au@Ag and Au@Pt core–shell nanoparticles, we investigate how the combination of two non-overlapping detector regimes helps to improve the probability of error when unscrambling two types of atoms. In particular, the combination of a narrow low angle ADF detector with a detector formed by the remaining annular collection regime is found to be optimal. The benefit is more significant if the atomic number Z difference becomes larger. In
addition, we show the benefit of subdividing the detector regime into three collection areas for heterogeneous nanostructures based on a structure consisting of three types of elements, e.g., a mixture of Au, Ag and Al atoms. Finally, these results are compared with the probability of error resulting when one would ultimately use a pixelated 4D STEM detector and how this could help to further reduce the incident electron dose.