Abstract: An efficient model-based estimation algorithm is introduced to quantify the atomic column positions and intensities from atomic-resolution (scanning) transmission electron microscopy ((S)TEM) images. This algorithm uses the least squares estimator on image segments containing individual columns fully accounting for overlap between neighboring columns, enabling the analysis of a large field of view. To provide end-users with this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license. In this chapter, this efficient algorithm is applied to three different nanostructures for which the analysis of a large field of view is required.

Abstract: The maximum a posteriori (MAP) probability rule for atom column detection can also be used as a tool to evaluate the relation between scanning transmission electron microscopy (STEM) image quality and atom detectability. In this chapter, a new image-quality measure is proposed that correlates well with atom detectability, namely the integrated contrast-to-noise ratio (ICNR). Furthermore, the working principle of the MAP probability rule is described in detail showing a close relation to the principles of model-selection methods.

Abstract: In this chapter, the principles of detection theory are used to quantify the probability of error for atom counting from high-resolution scanning transmission electron microscopy (HRSTEM) images. Binary and multiple hypothesis testing have been investigated in order to determine the limits to the precision with which the number of atoms in a projected atomic column can be estimated. The probability of error has been calculated when using STEM images, scattering cross-sections or peak intensities as a criterion to count atoms. Based on this analysis, we conclude that scattering cross-sections perform almost equally well as images and perform better than peak intensities. Furthermore, the optimal STEM detector design can be derived for atom counting using the expression of the probability of error. We show that for very thin objects the low-angle annular dark-field (LAADF) regime is optimal and that for thicker objects the optimal inner detector angle increases.

Abstract: We present a study of the relation between the surface chemistry and nanocrystal shape of PbSe nanocrystals with a variable Pb-to-Se stoichiometry and density of oleate ligands. The oleate ligand density and binding configuration are monitored by nuclear magnetic resonance and Fourier transform infrared absorbance spectroscopy, allowing us to quantify the number of surface-attached ligands per NC and the nature of the surface−Pb−oleate configuration. The three-dimensional shape of the PbSe nanocrystals is obtained from high-angle annular dark field scanning transmission electron microscopy combined with an atom counting method. We show that the enhanced oleate capping results in a stabilization and extension of the {111} facets, and a crystal shape transformation from a truncated nanocube to a truncated octahedron.

Abstract: The synthesis of materials with well-controlled composition and structure improves our understanding of their intrinsic electrical transport properties. Recent developments in atomically controlled growth have been shown to be crucial in enabling the study of new physical phenomena in epitaxial oxide heterostructures. Nevertheless, these phenomena can be influenced by the presence of defects that act as extrinsic sources of both doping and impurity scattering. Control over the nature and density of such defects is therefore necessary to fully understand the intrinsic materials properties and exploit them in future device technologies. Here, it is shown that incorporation of a strontium copper oxide nano-layer strongly reduces the impurity scattering at conducting interfaces in oxide LaAlO3SrTiO3(001) heterostructures, opening the door to high carrier mobility materials. It is proposed that this remote cuprate layer facilitates enhanced suppression of oxygen defects by reducing the kinetic barrier for oxygen exchange in the hetero-interfacial film system. This design concept of controlled defect engineering can be of significant importance in applications in which enhanced oxygen surface exchange plays a crucial role.

Abstract: Over the last two decades, three-dimensional (3D) imaging by transmission electron microscopy or “electron tomography” has evolved into a powerful tool to investigate a variety of nanomaterials in different fields, such as life sciences, chemistry, solid-state physics, and materials science. Most of these results were obtained with nanometer-scale resolution, but different approaches have recently pushed the resolution to the atomic level. Such information is a prerequisite to understand the specific relationship between the atomic structure and the physicochemical properties of (nano) materials. We provide an overview of the latest progress in the field of atomic-resolution electron tomography. Different imaging and reconstruction approaches are presented, and state-of-the-art results are discussed. This article demonstrates the power and importance of electron tomography with atomic-scale resolution.

Abstract: The charge density is among the most fundamental solid state properties determining bonding, electrical characteristics, and adsorption or catalysis at surfaces. While atomic-scale charge densities have as yet been retrieved by solid state theory, we demonstrate both charge density and electric field mapping across a mono-/bilayer boundary in 2D MoS2 by momentum-resolved scanning transmission electron microscopy. Based on consistency of the four-dimensional experimental data, statistical parameter estimation and dynamical electron scattering simulations using strain-relaxed supercells, we are able to identify an AA-type bilayer stacking and charge depletion at the Mo-terminated layer edge.

Abstract: Many microscopic investigations of materials may benefit from the recording of multiple successive images. This can include techniques common to several types of microscopy such as frame averaging to improve signal-to-noise ratios (SNR) or time series to study dynamic processes or more specific applications. In the scanning transmission electron microscope, this might include focal series for optical sectioning or aberration measurement, beam damage studies or camera-length series to study the effects of strain; whilst in the scanning tunnelling microscope, this might include bias-voltage series to probe local electronic structure. Whatever the application, such investigations must begin with the careful alignment of these data stacks, an operation that is not always trivial. In addition, the presence of low-frequency scanning distortions can introduce intra-image shifts to the data. Here, we describe an improved automated method of performing non-rigid registration customised for the challenges unique to scanned microscope data specifically addressing the issues of low-SNR data, images containing a large proportion of crystalline material and/or local features of interest such as dislocations or edges. Careful attention has been paid to artefact testing of the non-rigid registration method used, and the importance of this registration for the quantitative interpretation of feature intensities and positions is evaluated.

Abstract: Annular dark-field (ADF) scanning transmission electron microscopy (STEM) has become widely used in quantitative studies based on the opportunity to directly compare experimental and simulated images. This comparison merely requires the experimental data to be normalised and expressed in units of fractional beam-current. However, inhomogeneities in the response of electron detectors can complicate this normalisation. The quantification procedure becomes both experiment and instrument specific, requiring new simulations for the particular response of each instrument's detector, and for every camera-length used. This not only impedes the comparison between different instruments and research groups, but can also be computationally very time consuming. Furthermore, not all image simulation methods allow for the inclusion of an inhomogeneous detector response. In this work, we propose an alternative method for normalising experimental data in order to compare these with simulations that consider a homogeneous detector response. To achieve this, we determine the electron flux distribution reaching the detector by means of a camera-length series or a so-called atomic column cross-section averaged convergent beam electron diffraction (XSACBED) pattern. The result is then used to determine the relative weighting of the detector response. Here we show that the results obtained by this new electron flux weighted (EFW) method are comparable to the currently used method, while considerably simplifying the needed simulation libraries. The proposed method also allows one to obtain a metric that describes the quality of the detector response in comparison with the ideal detector response.

Abstract: Modern TEM enables the investigation of nanostructures at the atomic scale. However, TEM images are only two-dimensional (2D) projections of a three-dimensional (3D) object. Electron tomography can overcome this limitation. The technique is increasingly focused towards quantitative measurements and reaching atomic resolution in 3D has been the ultimate goal for many years. Therefore, one needs to optimize the acquisition of the data, the 3D reconstruction techniques as well as the quantification methods. Here, we will review a broad range of methodologies and examples. Finally, we will provide an outlook and will describe future challenges in the field of electron tomography.