Effects of instrument imperfections on quantitative scanning transmission electron microscopy

Characterization of structure and mixing in nanoparticle hetero-aggregates using convolutional neural networks: 3D-reconstruction versus 2D-projection

Structural and chemical characterization of nanomaterials provides important information for understanding their functional properties. Nanomaterials with characteristic structure sizes in the nanometer range can be characterized by scanning transmission electron microscopy (STEM). In conventional STEM, two-dimensional (2D) projection images of the samples are acquired, information about the third dimension is lost. This drawback can be overcome by STEM tomography, where the three-dimensional (3D) structure is reconstructed from a series of projection images acquired using various projection directions. However, 3D measurements are expensive with respect to acquisition and evaluation time. Furthermore, the method is hardly applicable to beam-sensitive materials, i.e. samples that degrade under the electron beam. For this reason, it is desirable to know whether sufficient information on structural and chemical information can be extracted from 2D-projection measurements. In the present work, a comparison between 3D-reconstruction and 2D-projection characterization of structure and mixing in nanoparticle hetero-aggregates is provided. To this end, convolutional neural networks are trained in 2D and 3D to extract particle positions and material types from the simulated or experimental measurement. Results are used to evaluate structure, particle size distributions, hetero-aggregate compositions and mixing of particles quantitatively and to find an answer to the question, whether an expensive 3D characterization is required for this material system for future characterizations.

Ultra-fast Digital DPC Yielding High Spatio-temporal Resolution for Low-Dose Phase Characterization

In the scanning transmission electron microscope, both phase imaging of beam-sensitive materials and characterization of a material's functional properties using in situ experiments are becoming more widely available. As the practicable scan speed of 4D-STEM detectors improves, so too does the temporal resolution achievable for both differential phase contrast (DPC) and ptychography. However, the read-out burden of pixelated detectors, and the size of the gigabyte to terabyte sized data sets, remain a challenge for both temporal resolution and their practical adoption. In this work, we combine ultra-fast scan coils and detector signal digitization to show that a high-fidelity DPC phase reconstruction can be achieved from an annular segmented detector. Unlike conventional analog data phase reconstructions from digitized DPC-segment images yield reliable data, even at the fastest scan speeds. Finally, dose fractionation by fast scanning and multi-framing allows for postprocess binning of frame streams to balance signal-to-noise ratio and temporal resolution for low-dose phase imaging for in situ experiments.

Sampling Real-Time Atomic Dynamics in Metal Nanoparticles by Combining Experiments, Simulations, and Machine Learning

Even at low temperatures, metal nanoparticles (NPs) possess atomic dynamics that are key for their properties but challenging to elucidate. Recent experimental advances allow obtaining atomic-resolution snapshots of the NPs in realistic regimes, but data acquisition limitations hinder the experimental reconstruction of the atomic dynamics present within them. Molecular simulations have the advantage that these allow directly tracking the motion of atoms over time. However, these typically start from ideal/perfect NP structures and, suffering from sampling limits, provide results that are often dependent on the initial/putative structure and remain purely indicative. Here, by combining state-of-the-art experimental and computational approaches, how it is possible to tackle the limitations of both approaches and resolve the atomistic dynamics present in metal NPs in realistic conditions is demonstrated. Annular dark-field scanning transmission electron microscopy enables the acquisition of ten high-resolution images of an Au NP at intervals of 0.6 s. These are used to reconstruct atomistic 3D models of the real NP used to run ten independent molecular dynamics simulations. Machine learning analyses of the simulation trajectories allow resolving the real-time atomic dynamics present within the NP. This provides a robust combined experimental/computational approach to characterize the structural dynamics of metal NPs in realistic conditions.

Electron counting detectors in scanning transmission electron microscopy via hardware signal processing

Transmission electron microscopy is a pivotal instrument in materials and biological sciences due to its ability to provide local structural and spectroscopic information on a wide range of materials. However, the electron detectors used in scanning transmission electron microscopy are often unable to provide quantified information, that is the number of electrons impacting the detector, without exhaustive calibration and processing. This results in arbitrary signal values with slow response times that cannot be used for quantification or comparison to simulations. Here we demonstrate and optimise a hardware signal processing approach to augment electron detectors to perform single electron counting.

Dose efficient annular bright field contrast with the ISTEM method: A proof of principle demonstration

The ISTEM mode for TEM has been demonstrated to have several advantages in regard to resolution and precision. While previous works primarily focussed on the advantages due to the reduced spatial coherence, the actual image contrast, i.e. how bright or dark certain atom columns are imaged, has mostly been of secondary concern. The present work sets out to achieve the contrast of annular bright field STEM in ISTEM, producing the high contrast of light elements, for which this method is popular. It is shown from theoretical considerations that using an annular condenser aperture this aim can be realised. The optimal size of this aperture is found by simulative studies. It is then manufactured from platinum foil and installed in an image-aberration corrected microscope. ABF-like ISTEM images of strontium titanate in [100] projection are acquired. The pure oxygen columns are clearly resolved with significant contrast. The image pattern is indeed identical to what is achieved by ABF STEM. A close look at the image formation also shows that the dose needed for a given signal-to-noise ratio is at least a quarter smaller for ABF-like ISTEM compared to ABF STEM, assuming detectors of similar detective quantum efficiency.

Atomic-scale detection of individual lead clusters confined in Linde Type A zeolites

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.

Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution

We report a study of scattering dynamics in crystals employing momentum-resolved scanning transmission electron microscopy under varying illumination conditions. As we perform successive changes of the probe focus, multiple real-space signals are obtained in dependence of the shape of the incident electron wave. With support from extensive simulations, each signal is shown to be characterised by an optimum focus for which the contrast is maximum and which differs among different signals. For instance, a systematic focus mismatch is found between images formed by high-angle scattering, being sensitive to thickness and chemical composition, and the first moment in diffraction space, being sensitive to electric fields. It follows that a single recording at one specific probe focus is usually insufficient to characterise materials comprehensively. Most importantly, we demonstrate in experiment and simulation that the second moment μ20+μ02=〈p2〉 of the diffracted intensity exhibits a contrast maximum when the electron probe is focused at the top and bottom faces of the specimen, making the presented concept attractive for measuring local topography. Given the versatility of 〈p2〉, we furthermore present a detailed study of its large-angle convergence both analytically using the Mott scattering approach, and by dynamical simulations using the multislice algorithm including thermal diffuse scattering. Both approaches are in very good agreement and yield logarithmic divergence with increasing scattering angle.

Quantification of STEM Images in High Resolution SEM for Segmented and Pixelated Detectors

The segmented semiconductor detectors for transmitted electrons in ultrahigh resolution scanning electron microscopes allow observing samples in various imaging modes. Typically, two standard modes of objective lens, with and without a magnetic field, differ by their resolution. If the beam deceleration mode is selected, then an electrostatic field around the sample is added. The trajectories of transmitted electrons are influenced by the fields below the sample. The goal of this paper is a quantification of measured images and theoretical study of the capability of the detector to collect signal electrons by its individual segments. Comparison of measured and ray-traced simulated data were difficult in the past. This motivated us to present a new method that enables better comparison of the two datasets at the cost of additional measurements, so-called calibration curves. Furthermore, we also analyze the measurements acquired using 2D pixel array detector (PAD) that provide a more detailed angular profile. We demonstrate that the radial profiles of STEM and/or 2D-PAD data are sensitive to material composition. Moreover, scattering processes are affected by thickness of the sample as well. Hence, comparing the two experimental and simulation data can help to estimate composition or the thickness of the sample.

3D Atomic Structure of Supported Metallic Nanoparticles Estimated from 2D ADF STEM Images: A Combination of Atom-Counting and a Local Minima Search Algorithm

Determining the 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, the 3D structure of supported Au NPs at high temperature, which is of importance to understand their behavior during catalytic reactions, is investigated. 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 dark-field 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 an 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, an optimized approach is therefore proposed using an iterative local minima search algorithm followed by molecular dynamics 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.

Optimization of imaging conditions for composition determination by annular dark field STEM

Quantitative scanning transmission electron microscopy (STEM) allows composition determination for nanomaterials at an atomic scale. To improve the accuracy of the results obtained, optimized imaging parameters should be chosen for annular dark field imaging. In a simulation study, we investigate the influence of imaging parameters on the accuracy of the composition determination with the example of ternary III-V semiconductors. It is shown that inner and outer detector angles and semi-convergence angle can be optimized, also in dependence on specimen thickness. Both, a minimum sampling of the image and a minimum electron dose are required. These findings are applied experimentally by using a fast pixelated detector to allow free choice of detector angles.

Modelling ADF STEM images using elliptical Gaussian peaks and its effects on the quantification of structure parameters in the presence of sample tilt

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.

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.

Development of a Practicable Digital Pulse Read-Out for Dark-Field STEM

When characterizing beam-sensitive materials in the scanning transmission electron microscope (STEM), low-dose techniques are essential for the reliable observation of samples in their true state. A simple route to minimize both the total electron-dose and the dose-rate is to reduce the electron beam-current and/or raster the probe at higher speeds. At the limit of these settings, and with current detectors, the resulting images suffer from unacceptable artifacts, including signal-streaking, detector-afterglow, and poor signal-to-noise ratios (SNRs). In this article, we present an alternative approach to capture dark-field STEM images by pulse-counting individual electrons as they are scattered to the annular dark-field (ADF) detector. Digital images formed in this way are immune from analog artifacts of streaking or afterglow and allow clean, high-SNR images to be obtained even at low beam-currents. We present results from both a ThermoFisher FEI Titan G2 operated at 300 kV and a Nion UltraSTEM200 operated at 200 kV, and compare the images to conventional analog recordings. ADF data are compared with analog counterparts for each instrument, a digital detector-response scan is performed on the Titan, and the overall rastering efficiency is evaluated for various scanning parameters.

Three-dimensional atomic structure of supported Au nanoparticles at high temperature

Au nanoparticles (NPs) deposited on CeO2 are extensively used as thermal catalysts since the morphology of the NPs is expected to be stable at elevated temperatures. Although it is well known that the activity of Au NPs depends on their size and surface structure, their three-dimensional (3D) structure at the atomic scale has not been completely characterized as a function of temperature. In this paper, we overcome the limitations of conventional electron tomography by combining atom counting applied to aberration-corrected scanning transmission electron microscopy images and molecular dynamics relaxation. In this manner, we are able to perform an atomic resolution 3D investigation of supported Au NPs. Our results enable us to characterize the 3D equilibrium structure of single NPs as a function of temperature. Moreover, the dynamic 3D structural evolution of the NPs at high temperatures, including surface layer jumping and crystalline transformations, has been studied.

Angle-resolved STEM using an iris aperture: Scattering contributions and sources of error for the quantitative analysis in Si

The angle-resolved electron scattering is investigated in scanning-transmission electron microscopy (STEM) using a motorised iris aperture placed above a conventional annular detector. The electron intensity scattered into various angle ranges is compared with simulations that were carried out in the frozen-lattice approximation. As figure of merit for the agreement of experiment and simulation we evaluate the specimen thickness which is compared with the thickness obtained from position-averaged convergent beam electron diffraction (PACBED). We find deviations whose strengths depend on the angular range of the detected electrons. As possible sources of error we investigate, for example, the influences of amorphous surface layers, inelastic scattering (plasmon excitation), phonon-correlation within the frozen-lattice approach, and distortions in the diffraction plane of the microscope. The evaluation is performed for four experimental thicknesses and two angle-resolved STEM series under different camera lengths. The results clearly show that especially for scattering angles below 50 mrad, it is mandatory that the simulations take scattering effects into account which are usually neglected for simulating high-angle scattering. Most influences predominantly affect the low-angle range, but also high scattering angles can be affected (e.g. by amorphous surface covering).

Hidden Markov model for atom-counting from sequential ADF STEM images: Methodology, possibilities and limitations

We present a quantitative method which allows us to reliably measure dynamic changes in the atomic structure of monatomic crystalline nanomaterials from a time series of atomic resolution annular dark field scanning transmission electron microscopy images. The approach is based on the so-called hidden Markov model and estimates the number of atoms in each atomic column of the nanomaterial in each frame of the time series. We discuss the origin of the improved performance for time series atom-counting as compared to the current state-of-the-art atom-counting procedures, and show that the so-called transition probabilities that describe the probability for an atomic column to lose or gain one or more atoms from frame to frame are particularly important. Using these transition probabilities, we show that the method can also be used to estimate the probability and cross section related to structural changes. Furthermore, we explore the possibilities for applying the method to time series recorded under variable environmental conditions. The method is shown to be promising for a reliable quantitative analysis of dynamic processes such as surface diffusion, adatom dynamics, beam effects, or in situ experiments.

Influence of plasmon excitations on atomic-resolution quantitative 4D scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) allows to gain quantitative information on the atomic-scale structure and composition of materials, satisfying one of todays major needs in the development of novel nanoscale devices. The aim of this study is to quantify the impact of inelastic, i.e. plasmon excitations (PE), on the angular dependence of STEM intensities and answer the question whether these excitations are responsible for a drastic mismatch between experiments and contemporary image simulations observed at scattering angles below \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 40 mrad. For the two materials silicon and platinum, the angular dependencies of elastic and inelastic scattering are investigated. We utilize energy filtering in two complementary microscopes, which are representative for the systems used for quantitative STEM, to form position-averaged diffraction patterns as well as atomically resolved 4D STEM data sets for different energy ranges. The resulting five-dimensional data are used to elucidate the distinct features in real and momentum space for different energy losses. We find different angular distributions for the elastic and inelastic scattering, resulting in an increased low-angle intensity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 10–40 mrad). The ratio of inelastic/elastic scattering increases with rising sample thickness, while the general shape of the angular dependency is maintained. Moreover, the ratio increases with the distance to an atomic column in the low-angle regime. Since PE are usually neglected in image simulations, consequently the experimental intensity is underestimated at these angles, which especially affects bright field or low-angle annular dark field imaging. The high-angle regime, however, is unaffected. In addition, we find negligible impact of inelastic scattering on first-moment imaging in momentum-resolved STEM, which is important for STEM techniques to measure internal electric fields in functional nanostructures. To resolve the discrepancies between experiment and simulation, we present an adopted simulation scheme including PE. This study highlights the necessity to take into account PE to achieve quantitative agreement between simulation and experiment. Besides solving the fundamental question of missing physics in established simulations, this finally allows for the quantitative evaluation of low-angle scattering, which contains valuable information about the material investigated.

Imaging Beam-Sensitive Materials by Electron Microscopy

Electron microscopy allows the extraction of multidimensional spatiotemporally correlated structural information of diverse materials down to atomic resolution, which is essential for figuring out their structure-property relationships. Unfortunately, the high-energy electrons that carry this important information can cause damage by modulating the structures of the materials. This has become a significant problem concerning the recent boost in materials science applications of a wide range of beam-sensitive materials, including metal-organic frameworks, covalent-organic frameworks, organic-inorganic hybrid materials, 2D materials, and zeolites. To this end, developing electron microscopy techniques that minimize the electron beam damage for the extraction of intrinsic structural information turns out to be a compelling but challenging need. This article provides a comprehensive review on the revolutionary strategies toward the electron microscopic imaging of beam-sensitive materials and associated materials science discoveries, based on the principles of electron-matter interaction and mechanisms of electron beam damage. Finally, perspectives and future trends in this field are put forward.

Composition determination for quaternary III-V semiconductors by aberration-corrected STEM

Quantitative scanning transmission electron microscopy (STEM) is a powerful tool for the characterization of nano-materials. Absolute composition determination for ternary III-V semiconductors by direct comparison of experiment and simulation is well established. Here, we show a method to determine the composition of quaternary III-V semiconductors with two elements on each sub lattice from the intensities of one STEM image. As an example, this is applied to (GaIn)(AsBi). The feasibility of the method is shown in a simulation study that also explores the influence of detector angles and specimen thickness. Additionally, the method is applied to an experimental STEM image of a (GaIn)(AsBi) quantum well grown by metal organic vapour phase epitaxy. The obtained concentrations are in good agreement with X-ray diffraction and photoluminescence results.

Simultaneous determination of local thickness and composition for ternary III-V semiconductors by aberration-corrected STEM

Scanning transmission electron microscopy (STEM) is a suitable method for the quantitative characterization of nanomaterials. For an absolute composition determination on an atomic scale, the thickness of the specimen has to be known locally with high accuracy. Here, we propose a method to determine both thickness and composition of ternary III-V semiconductors locally from one STEM image as shown for the example material systems Ga(AsBi) and (GaIn)As. In a simulation study, the feasibility of the method is proven and the influence of specimen thickness and detector angles used is investigated. An application to an experimental STEM image of a Ga(AsBi) quantum well grown by metal organic vapour phase epitaxy yields an excellent agreement with composition results from high resolution X-ray diffraction.

Atomic-scale 3D reconstruction of antiphase boundaries in GaP on (001) silicon by STEM

In order to overcome the limitations of silicon-based electronics, the integration of optically active III-V compounds is a promising approach. Nonetheless, their integration is far from trivial and control as well as understanding of corresponding growth kinetics, and in particular the occurrence and termination of antiphase defects, is of great relevance. In this work, we focus on the three-dimensional reconstruction of such boundaries in gallium phosphide from single scanning transmission electron microscopy images. In the high angle annular dark-field imaging mode, the appearance of these antiphase boundaries is strongly determined by the chemical composition of each atomic column and reflects the ratio of transmitted anti- to mainphase. Therefore it is possible to translate measured intensities to the depth location of these boundaries by utilizing simulation data. The necessary spatial resolution for these column-by-column mappings is achieved via electron optical aberration correction within the microscope. Hence, the complete 3D orientation of these defects can be measured at atomic resolution and correlated to growth parameters. Finally, we present a method to reconstruct large areas from well sampled images and retrieve information about complex embedded nanoscale structures at the atomic scale.

Using molecular dynamics for multislice TEM simulation of thermal diffuse scattering in AlGaN

For simulation of transmission electron microscopic images and diffraction patterns, the accurate inclusion of thermal diffuse scattering by phonons is important. In the frozen phonon multislice algorithm, this is possible, if thermal displacements according to the realistic, quantum mechanical distribution can be generated. For pure crystals, quantum mechanical calculations based on DFT yield those displacements. But for alloys one is usually restricted to the Einstein approximation, where correlations between atoms are neglected. In this article, molecular dynamics simulations are discussed and used as an alternative method for displacement calculation. Employing an empirical Stillinger-Weber type potential, classical motion is used as an approximation for the quantum mechanical dynamics. Thereby, correlations and possible static atomic displacements are inherently included. An appropriate potential is devised for AlGaN by fitting to force constant matrices determined from DFT and elastic constants of AlN and GaN. A comparison shows that the empiric potential reproduces phonon dispersions and displacement expectations from DFT references. The validity for alloys is successfully demonstrated by comparison to DFT calculations in special quasirandom structures. Subsequently, molecular dynamics were used in multislice simulations of both conventional and scanning TEM images. The resulting images are in very good agreement with DFT based calculations, while a slight yet significant deviation from Einstein approximation results can be seen, which can be attributed to the neglect of correlations in the latter. The presented potential hence proves to be a useful tool for accurate TEM simulations of AlGaN alloys.

An optical configuration for fastidious STEM detector calibration and the effect of the objective-lens pre-field

In the scanning transmission electron microscope, an accurate knowledge of detector collection angles is paramount in order to quantify signals on an absolute scale. Here we present an optical configuration designed for the accurate measurement of collection angles for both image-detectors and energy-loss spectrometers. By deflecting a parallel electron beam, carefully calibrated using a diffraction pattern from a known material, we can directly observe the projection-distortion in the post-specimen lenses of probe-corrected instruments, the 3-fold caustic when an image-corrector is fitted, and any misalignment of imaging detectors or spectrometer apertures. We also discuss for the first time, the effect that higher-order aberrations in the objective-lens pre-field has on such an angle-based detector mapping procedure.

High-throughput, semi-automated quantitative STEM mass measurement of supported metal nanoparticles using a conventional TEM/STEM

The adaptation of quantitative STEM techniques to enable atom-counting in supported metal nanoparticles with a modern, conventional (non-aberration-corrected) TEM/STEM (a JEOL JEM2100F) without the need for any modifications or special hardware is presented. No image simulation is required, either. This technique enables the practical analysis of the size, mass, and basic shape information of statistically robust populations of hundreds to thousands of nanoparticles. The methods for performing the necessary calibrations of the microscope and images are detailed. A user-friendly semi-automated analysis program was also written to facilitate high throughput. The program optimizes the analysis parameters, applying the procedure consistently across the entire dataset, enhancing the meaningfulness of the statistics as well as the reproducibility and transferability of the results. A series of atomically precise Au nanoparticles were used to validate the technique, which was determined to be accurate within a (nearly uniform) scaling factor of around two for the given instrument, and could be brought into better agreement with a calibration standard. The magnitude of the disparity was found to significantly and unexpectedly rely on the chosen magnification and spot size, the underlying reasons for which are unclear and likely instrument-dependent. The possible sources of error from the calibration and acquisition were examined and their impact on the accuracy and precision of quantification were estimated. The scattering cross-sections measured using this technique are relatively insensitive to moderate errors in the various detector calibrations but particularly sensitive to pixel size error.

Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy

This study sheds light on the prerequisites, possibilities, limitations and interpretation of high-resolution differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). We draw particular attention to the well-established DPC technique based on segmented annular detectors and its relation to recent developments based on pixelated detectors. These employ the expectation value of the momentum transfer as a reliable measure of the angular deflection of the STEM beam induced by an electric field in the specimen. The influence of scattering and propagation of electrons within the specimen is initially discussed separately and then treated in terms of a two-state channeling theory. A detailed simulation study of GaN is presented as a function of specimen thickness and bonding. It is found that bonding effects are rather detectable implicitly, e.g., by characteristics of the momentum flux in areas between the atoms than by directly mapping electric fields and charge densities. For strontium titanate, experimental charge densities are compared with simulations and discussed with respect to experimental artifacts such as scan noise. Finally, we consider practical issues such as figures of merit for spatial and momentum resolution, minimum electron dose, and the mapping of larger-scale, built-in electric fields by virtue of data averaged over a crystal unit cell. We find that the latter is possible for crystals with an inversion center. Concerning the optimal detector design, this study indicates that a sampling of 5mrad per pixel is sufficient in typical applications, corresponding to approximately 10×10 available pixels.

Accuracy and precision of thickness determination from position-averaged convergent beam electron diffraction patterns using a single-parameter metric

Position-averaged convergent beam electron diffraction patterns are formed by averaging the transmission diffraction pattern while scanning an atomically-fine electron probe across a sample. Visual comparison between experimental and simulated patterns is increasingly being used for sample thickness determination. We explore automating the comparison via a simple sum square difference metric. The thickness determination is shown to be accurate (i.e. the best-guess deduced thickness generally concurs with the true thickness), though factors such as noise, mistilt and inelastic scattering reduce the precision (i.e. increase the uncertainty range). Notably, the precision tends to be higher for smaller probe-forming aperture angles.

Correlative micro-diffraction and differential phase contrast study of mean inner potential and subtle beam-specimen interaction

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22 V and 14.15 ± 0.22 V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

Hybrid statistics-simulations based method for atom-counting from ADF STEM images

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.

Materials characterisation by angle-resolved scanning transmission electron microscopy

Solid-state properties such as strain or chemical composition often leave characteristic fingerprints in the angular dependence of electron scattering. Scanning transmission electron microscopy (STEM) is dedicated to probe scattered intensity with atomic resolution, but it drastically lacks angular resolution. Here we report both a setup to exploit the explicit angular dependence of scattered intensity and applications of angle-resolved STEM to semiconductor nanostructures. Our method is applied to measure nitrogen content and specimen thickness in a GaN_xAs_1-x layer independently at atomic resolution by evaluating two dedicated angular intervals. We demonstrate contrast formation due to strain and composition in a Si- based metal-oxide semiconductor field effect transistor (MOSFET) with Ge_xSi_1-x stressors as a function of the angles used for imaging. To shed light on the validity of current theoretical approaches this data is compared with theory, namely the Rutherford approach and contemporary multislice simulations. Inconsistency is found for the Rutherford model in the whole angular range of 16-255 mrad. Contrary, the multislice simulations are applicable for angles larger than 35 mrad whereas a significant mismatch is observed at lower angles. This limitation of established simulations is discussed particularly on the basis of inelastic scattering.

Nanoscopic Insights into InGaN/GaN Core-Shell Nanorods: Structure, Composition, and Luminescence

Nitride-based three-dimensional core-shell nanorods (NRs) are promising candidates for the achievement of highly efficient optoelectronic devices. For a detailed understanding of the complex core-shell layer structure of InGaN/GaN NRs, a systematic determination and correlation of the structural, compositional, and optical properties on a nanometer-scale is essential. In particular, the combination of low-temperature cathodoluminescence (CL) spectroscopy directly performed in a scanning transmission electron microscope (STEM), and quantitative high-angle annular dark field imaging enables a comprehensive study of the nanoscopic attributes of the individual shell layers. The investigated InGaN/GaN core-shell NRs, which were grown by metal-organic vapor-phase epitaxy using selective-area growth exhibit an exceptionally low density of extended defects. Using highly spatially resolved CL mapping of single NRs performed in cross-section, we give a direct insight into the optical properties of the individual core-shell layers. Most interesting, we observe a red shift of the InGaN single quantum well from 410 to 471 nm along the nonpolar side wall. Quantitative STEM analysis of the active region reveals an increasing thickness of the single quantum well (SQW) from 6 to 13 nm, accompanied by a slight increase of the indium concentration along the nonpolar side wall from 11% to 13%. Both effects, the increased quantum-well thickness and the higher indium incorporation, are responsible for the observed energetic shift of the InGaN SQW luminescence. Furthermore, compositional mappings of the InGaN quantum well reveal the formation of locally indium rich regions with several nanometers in size, leading to potential fluctuations in the InGaN SQW energy landscape. This is directly evidenced by nanometer-scale resolved CL mappings that show strong localization effects of the excitonic SQW emission.