Abstract: To understand the structure–property relationship of nanostructures, reliably quantifying parameters, such as the number of atoms along the projection direction, is important. Advanced statistical methodologies have made it possible to count the number of atoms for monotype crystalline nanoparticles from a single ADF STEM image. Recent developments enable one to simultaneously acquire multiple ADF STEM images. Here, we present an extended statistics-based method for atom counting from a combination of multiple statistically independent ADF STEM images reconstructed from non-overlapping annular detector collection regions which improves the accuracy and allows one to retrieve precise atom-counts, especially for images acquired with low electron doses and multiple element structures.

Abstract: In this paper convexity constraints are derived for a background model of electron energy loss spectra (EELS) that is linear in the fitting parameters. The model outperforms a power-law both on experimental and simulated backgrounds, especially for wide energy ranges, and thus improves elemental quantification results. Owing to the model’s linearity, the constraints can be imposed through fitting by quadratic programming. This has important advantages over conventional nonlinear power-law fitting such as high speed and a guaranteed unique solution without need for initial parameters. As such, the need for user input is significantly reduced, which is essential for unsupervised treatment of large datasets. This is demonstrated on a demanding spectrum image of a semiconductor device sample with a high number of elements over a wide energy range.

Abstract: Quantification of annular dark field (ADF) scanning transmission electron microscopy (STEM) images in terms
of composition or thickness often relies on probe-position integrated scattering cross sections (PPISCS). In
order to compare experimental PPISCS with theoretically predicted ones, expensive simulations are needed for
a given specimen, zone axis orientation, and a variety of microscope settings. The computation time of such
simulations can be in the order of hours using a single GPU card. ADF STEM simulations can be efficiently
parallelized using multiple GPUs, as the calculation of each pixel is independent of other pixels. However, most
research groups do not have the necessary hardware, and, in the best-case scenario, the simulation time will
only be reduced proportionally to the number of GPUs used. In this manuscript, we use a learning approach and
present a densely connected neural network that is able to perform real-time ADF STEM PPISCS predictions as
a function of atomic column thickness for most common face-centered cubic (fcc) crystals (i.e., Al, Cu, Pd, Ag,
Pt, Au and Pb) along [100] and [111] zone axis orientations, root-mean-square displacements, and microscope
parameters. The proposed architecture is parameter efficient and yields accurate predictions for the PPISCS
values for a wide range of input parameters that are commonly used for aberration-corrected transmission
electron microscopes.

Abstract: Advanced materials often consist of multiple elements which are arranged in a complicated structure. Quantitative scanning transmission electron microscopy is useful to determine the composition and thickness of nanostructures at the atomic scale. However, significant difficulties remain to quantify mixed columns by comparing the resulting atomic resolution images and spectroscopy data with multislice simulations where dynamic scattering needs to be taken into account. The combination of the computationally intensive nature of these simulations and the enormous amount of possible mixed column configurations for a given composition indeed severely hamper the quantification process. To overcome these challenges, we here report the development of an incoherent non-linear method for the fast prediction of ADF-EDX scattering cross-sections of mixed columns under channelling conditions. We first explain the origin of the ADF and EDX incoherence from scattering physics suggesting a linear dependence between those two signals in the case of a high-angle ADF detector. Taking EDX as a perfect incoherent reference mode, we quantitatively examine the ADF longitudinal incoherence under different microscope conditions using multislice simulations. Based on incoherent imaging, the atomic lensing model previously developed for ADF is now expanded to EDX, which yields ADF-EDX scattering cross-section predictions in good agreement with multislice simulations for mixed columns in a core–shell nanoparticle and a high entropy alloy. The fast and accurate prediction of ADF-EDX scattering cross-sections opens up new opportunities to explore the wide range of ordering possibilities of heterogeneous materials with multiple elements.

Abstract: Four dimensional scanning transmission electron microscopy (4D STEM) records the scattering of electrons in a material in great detail. The benefits offered by 4D STEM are substantial, with the wealth of data it provides facilitating for instance high precision, high electron dose efficiency phase imaging via centre of mass or ptychography based analysis. However the requirement for a 2D image of the scattering to be recorded at each probe position has long placed a severe bottleneck on the speed at which 4D STEM can be performed. Recent advances in camera technology have greatly reduced this bottleneck, with the detection efficiency of direct electron detectors being especially well suited to the technique. However even the fastest frame driven pixelated detectors still significantly limit the scan speed which can be used in 4D STEM, making the resulting data susceptible to drift and hampering its use for low dose beam sensitive applications. Here we report the development of the use of an event driven Timepix3 direct electron camera that allows us to overcome this bottleneck and achieve 4D STEM dwell times down to 100 ns; orders of magnitude faster than what has been possible with frame based readout. We characterize the detector for different acceleration voltages and show that the method is especially well suited for low dose imaging and promises rich datasets without compromising dwell time when compared to conventional STEM imaging.

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.

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: In computed tomography, the reconstruction is typically obtained on a voxel grid. In this work, however, we propose a mesh-based reconstruction method. For tomographic problems, 3D meshes have mostly been studied to simulate data acquisition, but not for reconstruction, for which a 3D mesh means the inverse process of estimating shapes from projections. In this paper, we propose a differentiable forward model for 3D meshes that bridge the gap between the forward model for 3D surfaces and optimization. We view the forward projection as a rendering process, and make it differentiable by extending recent work in differentiable rendering. We use the proposed forward model to reconstruct 3D shapes directly from projections. Experimental results for single-object problems show that the proposed method outperforms traditional voxel-based methods on noisy simulated data. We also apply the proposed method on electron tomography images of nanoparticles to demonstrate the applicability of the method on real data.

Abstract: Colloidal nanoparticles (NPs) including nanowires and nanosheets made by chemical methods involve many organic ligands. When the structure of NPs is investigated via transmission electron microscopy (TEM), the organic ligands act as a source for e-beam induced deposition and this causes substantial build-up of carbon layers in the investigated areas, which is typically referred to as “contamination” in the eld of electron mi- croscopy. This contamination is often more severe for scanning TEM, a technique that is based on a focused electron beam and hence higher electron dose rate. In this paper, we report a simple and effective method to clean drop-cast TEM grids that contain NPs with ligands. Using a combination of activated carbon and ethanol, this method effectively reduces the amount of ligands on TEM grids, and therefore greatly improves the quality of electron microscopy images and subsequent analytical measurements. This ef cient and facile method can be helpful during electron microscopy investigation of different kinds of nanomaterials that suffer from ligand- induced contamination.

Abstract: Lattice strain measurement of nanoscale semiconductor devices is crucial for the semiconductor industry as strain substantially improves the electrical performance of transistors. High resolution scanning transmission electron microscopy (HR-STEM) imaging is an excellent tool that provides spatial resolution at the atomic scale and strain information by applying Geometric Phase Analysis or image fitting procedures. However, HR-STEM images regularly suffer from scanning distortions and sample drift during image acquisition. In this paper, we propose a new scanning strategy that drastically reduces artefacts due to drift and scanning distortion, along with extending the field of view. It consists of the acquisition of a series of independent small subimages containing an atomic resolution image of the local lattice. All subimages are then analysed individually for strain by fitting a nonlinear model to the lattice images. The method allows flexible tuning of spatial resolution and the field of view within the limits of the dynamic range of the scan engine while maintaining atomic resolution sampling within the subimages. The obtained experimental strain maps are quantitatively benchmarked against the Bessel diffraction technique. We demonstrate that the proposed scanning strategy approaches the performance of the diffraction technique while having the advantage that it does not require specialized diffraction cameras.

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: Transmission electron microscopy (TEM) is carried out in vacuum to minimize the interaction of the imaging electrons with gas molecules while passing through the microscope column. Nevertheless, in typical devices, the pressure remains at 10(-7) mbar or above, providing a large number of gas molecules for the electron beam to crack, which can lead to structural changes in the sample. Here, we describe experiments carried out in a modified scanning TEM (STEM) instrument, based on the Nion UltraSTEM 100. In this instrument, the base pressure at the sample is around 2 x 10(-10 )mbar, and can be varied up to 10(-6) mbar through introduction of gases directly into the objective area while maintaining atomic resolution imaging conditions. We show that air leaked into the microscope column during the experiment is efficient in cleaning graphene samples from contamination, but ineffective in damaging the pristine lattice. Our experiments also show that exposure to O(2 )and H2O lead to a similar result, oxygen providing an etching effect nearly twice as efficient as water, presumably due to the two 0 atoms per molecule. H(2 )and N-2 environments have no influence on etching. These results show that the residual gas environment in typical TEM instruments can have a large influence on the observations, and show that chemical etching of carbon-based structures can be effectively carried out with oxygen.

Abstract: This study addresses the comparison of scanning transmission electron microscopy (STEM) measurements of momentum transfers using the first moment approach and the established method that uses segmented annular detectors. Using an ultrafast pixelated detector to acquire four-dimensional, momentum-resolved STEM signals, both the first moment calculation and the calculation of the differential phase contrast (DPC) signals are done for the same experimental data. In particular, we investigate the ability to correct the segment-based signal to yield a suitable approximation of the first moment for cases beyond the weak phase object approximation. It is found that the measurement of momentum transfers using segmented detectors can approach the first moment measurement as close as 0.13 h/nm in terms of a root mean square (rms) difference in 10 nm thick SrTiO3 for a detector with 16 segments. This amounts to 35% of the rms of the momentum transfers. In addition, we present a statistical analysis of the precision of first moment STEM as a function of dose. For typical experimental settings with recent hardware such as a Medipix3 Merlin camera attached to a probe-corrected STEM, we find that the precision of the measurement of momentum transfers stagnates above certain doses. This means that other instabilities such as specimen drift or scan noise have to be taken into account seriously for measurements that target, e.g., the detection of bonding effects in the charge density.

Abstract: Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These typically use the independent atom approximation that neglects bonding effects, which may, however, be measurable and of physical interest. Since all electrons and the nuclear cores contribute to the scattering potential, simulations that go beyond this approximation have relied on computationally highly demanding all-electron calculations. Here, we describe a new method to generate ab initio electrostatic potentials when describing the core electrons by projector functions. Combined with an interface to quantitative image simulations, this implementation enables an easy and fast means to model electron scattering. We compare simulated transmission electron microscopy images and diffraction patterns to experimental data, showing an accuracy equivalent to earlier all-electron calculations at a much lower computational cost.