Abstract: Semiconductor heterostructures are used for the fabrication of optoelectronic devices. Performance of such devices is governed by their chemical morphology. The composition distribution of quantum wells and dots is influenced by kinetic growth processes which are not understood completely at present. To obtain more information about these effects, methods for composition determination with a spatial resolution at a near atomic scale are necessary. In this paper we focus on the present state of the composition evaluation by the lattice fringe analysis (CELFA) technique and explain the basic ideas, optimum imaging conditions, precision and accuracy.

Abstract: In epitaxial thin film systems, the crystal structure and its symmetry deviate from the bulk counterpart due to various mechanisms such as epitaxial strain and interfacial structural coupling, which induce an accompanying change in their properties. In perovskite materials, the crystal symmetry can be described by rotations of 6-fold coordinated transition metal oxygen octahedra, which are found to be altered at interfaces. Here, we unravel how the local oxygen octahedral coupling (OOC) at perovskite heterostructural interfaces initiates a different symmetry in epitaxial films and provide design rules to induce various symmetries in thin films by careful selecting appropriate combinations of substrate/buffer/film. Very interestingly we discovered that these combinations lead to symmetry changes throughout the full thickness of the film. Our results provide a deep insight into understanding the origin of induced crystal symmetry in a perovskite heterostructure and an intelligent route to achieve unique functional properties.

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 chapter, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high-resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. We show that this method can be applied to nanocrystals of arbitrary shape, size, and atom type. The validity of the atom-counting results is confirmed by means of detailed image simulations and it is shown that the high sensitivity of our method enables us to count atoms with single atom sensitivity.

Abstract: This chapter provides an overview of statistical and quantitative methodologies that have pushed (scanning) transmission electron microscopy ((S)TEM) toward accurate and precise measurements of unknown structure parameters for understanding the relation between the structure of a material and its properties. Hereby, statistical parameter estimation theory has extensively been used which enabled not only measuring atomic column positions, but also quantifying the number of atoms, and detecting atomic columns as accurately and precisely as possible from experimental images. As a general conclusion, it can be stated that advanced statistical techniques are ideal tools to perform quantitative electron microscopy at the atomic scale. In the future, statistical methods will continue to be developed and novel quantification procedures will open up new possibilities for studying material structures at the atomic scale.

Abstract: In this chapter, the principles of statistical parameter estimation theory for a quantitative analysis of atomic-resolution electron microscopy images are introduced. Within this framework, electron microscopy images are described by a parametric statistical model. Here, parametric models are introduced for different types of electron microscopy images: reconstructed exit waves, annular dark-field (ADF) scanning transmission electron microscopy (STEM) images, and simultaneously acquired ADF and annular bright-field (ABF) STEM images. Furthermore, the Cramér-Rao lower bound (CRLB) is introduced, i.e. a theoretical lower bound on the variance of any unbiased estimator. This CRLB is used to quantify the precision of the structure parameters of interest, such as the atomic column positions and the integrated atomic column intensities.

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: Determining the three-dimensional (3D) atomic structure of nanoparticles (NPs) is critical to understand their structure-dependent properties. It is hereby important to perform such analyses under conditions relevant for the envisioned application. Here, we investigate the 3D structure of supported Au NPs at high temperature, which is of importance to understand their behavior during catalytic reactions. To overcome limitations related to conventional high-resolution electron tomography at high temperature, 3D characterization of NPs with atomic resolution has been performed by applying atom-counting using atomic resolution annular darkfield scanning transmission electron microscopy (ADF STEM) images followed by structural relaxation. However, at high temperatures, thermal displacements, which affect the ADF STEM intensities, should be taken into account. Moreover, it is very likely that the structure of a NP investigated at elevated temperature deviates from a ground state configuration, which is difficult to determine using purely computational energy minimization approaches. In this paper, we therefore propose an optimized approach using an iterative local minima search algorithm followed by molecular dynamics (MD) structural relaxation of candidate structures associated with each local minimum. In this manner, it becomes possible to investigate the 3D atomic structure of supported NPs, which may deviate from their ground state configuration.

Abstract: A real-time image reconstruction method for scanning transmission electron microscopy (STEM) is proposed. With an algorithm requiring only the center of mass of the diffraction pattern at one probe position at a time, it is able to update the resulting image each time a new probe position is visited without storing any intermediate diffraction patterns. The results show clear features at high spatial frequency, such as atomic column positions. It is also demonstrated that some common post-processing methods, such as band-pass filtering, can be directly integrated in the real-time processing flow. Compared with other reconstruction methods, the proposed method produces high-quality reconstructions with good noise robustness at extremely low memory and computational requirements. An efficient, interactive open source implementation of the concept is further presented, which is compatible with frame-based, as well as event-based camera/file types. This method provides the attractive feature of immediate feedback that microscope operators have become used to, for example, conventional high-angle annular dark field STEM imaging, allowing for rapid decision-making and fine-tuning to obtain the best possible images for beam-sensitive samples at the lowest possible dose.

Abstract: Structural analysis of metal clusters confined in nanoporous materials is typically performed by X-ray-driven techniques. Although X-ray analysis has proved its strength in the characterization of metal clusters, it provides averaged structural information. Therefore, we here present an alternative workflow for bringing the characterization of confined metal clusters towards the local scale. This workflow is based on the combination of aberration-corrected transmission electron microscopy (TEM), TEM image simulations, and powder X-ray diffraction (XRD) with advanced statistical techniques. In this manner, we were able to characterize the clustering of Pb atoms in Linde Type A (LTA) zeolites with Pb loadings as low as 5 wt%. Moreover, individual Pb clusters could be directly detected. The proposed methodology thus enables a local-scale characterization of confined metal clusters in zeolites. This is important for further elucidation of the connection between the structure and the physicochemical properties of such systems.

Abstract: A new methodology is presented to count the number of atoms in multimetallic nanocrystals by combining energy dispersive X-ray spectroscopy (EDX) and high angle annular dark field scanning transmission electron microscopy (HAADF STEM). For this purpose, the existence of a linear relationship between the incoherent HAADF STEM and EDX images is exploited. Next to the number of atoms for each element in the atomic columns, the method also allows quantification of the error in the obtained number of atoms, which is of importance given the noisy nature of the acquired EDX signals. Using experimental images of an Au@Ag core–shell nanorod, it is demonstrated that 3D structural information can be extracted at the atomic scale. Furthermore, simulated data of an Au@Pt core–shell nanorod show the prospect to characterize heterogeneous nanostructures with adjacent atomic numbers.