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Element specific atom counting for heterogeneous nanostructures: Combining multiple ADF STEM images for simultaneous thickness and composition determination

In this paper, a methodology is presented to count the number of atoms in heterogeneous nanoparticles based on the combination of multiple annular dark field scanning transmission electron microscopy (ADF STEM) images. The different non-overlapping annular detector collection regions are selected based on the principles of optimal statistical experiment design for the atom-counting problem. To count the number of atoms, the total intensities of scattered electrons for each atomic column, the so-called scattering cross-sections, are simultaneously compared with simulated library values for the different detector regions by minimising the squared differences. The performance of the method is evaluated for simulated Ni@Pt and Au@Ag core-shell nanoparticles. Our approach turns out to be a dose efficient alternative for the investigation of beam-sensitive heterogeneous materials as compared to the combination of ADF STEM and energy dispersive X-ray spectroscopy.

Negative mixing enthalpy solid solutions deliver high strength and ductility

Body-centred cubic refractory multi-principal element alloys (MPEAs), with several refractory metal elements as constituents and featuring a yield strength greater than one gigapascal, are promising materials to meet the demands of aggressive structural applications1-6. Their low-to-no tensile ductility at room temperature, however, limits their processability and scaled-up application7-10. Here we present a HfNbTiVAl10 alloy that shows remarkable tensile ductility (roughly 20%) and ultrahigh yield strength (roughly 1,390 megapascals). Notably, these are among the best synergies compared with other related alloys. Such superb synergies derive from the addition of aluminium to the HfNbTiV alloy, resulting in a negative mixing enthalpy solid solution, which promotes strength and favours the formation of hierarchical chemical fluctuations (HCFs). The HCFs span many length scales, ranging from submicrometre to atomic scale, and create a high density of diffusive boundaries that act as effective barriers for dislocation motion. Consequently, versatile dislocation configurations are sequentially stimulated, enabling the alloy to accommodate plastic deformation while fostering substantial interactions that give rise to two unusual strain-hardening rate upturns. Thus, plastic instability is significantly delayed, which expands the plastic regime as ultralarge tensile ductility. This study provides valuable insights into achieving a synergistic combination of ultrahigh strength and large tensile ductility in MPEAs.

Atom counting based on Voronoi averaged STEM intensities using a crosstalk correction scheme

If quantitative scanning transmission electron microscopy is used for very precise thickness measurements with atomic resolution, it is commonly referred to as »atom counting«. Due to scattering and the finite probe extent the signal recorded in one atomic column is dependent not only on its own height but also on the height of its neighbours. Especially for thicker specimens this crosstalk effect can have significant impact on the measured intensity. If it is not appropriately accounted for in the evaluation, it can result in a deterioration of accuracy that impedes the possibility of actual atom counting. However, as the number of possible neighbour configurations can be excessively large, a comprehensive consideration of all in the evaluation reference is neigh impossible. This work proposes a method that allows for the a-posteriori reduction of crosstalk during the evaluation by algebraic means. Based on a parametric model, which is described in detail in the article, the crosstalk is expressed by an invertible matrix. Applying the inverted matrix to the measurement yields crosstalk corrected intensity values with very little computational effort. These can subsequently be evaluated by direct comparison to simple reference data. The working principle of the method is presented on the example of crystalline gold. The crosstalk parametrisation is found by fitting a model to sets of specifically created multislice simulations. The parameters are given for both aberration corrected and uncorrected STEM. Subsequently the abilities and potential of the technique are assessed in simulative studies on multiple model systems including gold nanoparticles. Overall a significant and robust improvement of the attainable precision can be demonstrated making the proposed method a promising tool for reference-based atom counting.

Real-time simulations of ADF STEM probe position-integrated scattering cross-sections for single element fcc crystals in zone axis orientation using a densely connected neural network

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.

A decade of atom-counting in STEM: From the first results toward reliable 3D atomic models from a single projection

Quantitative structure determination is needed in order to study and understand nanomaterials at the atomic scale. Materials characterisation resulting in precise structural information is a crucial point to understand the structure-property relation of materials. Counting the number of atoms and retrieving the 3D atomic structure of nanoparticles plays an important role here. In this paper, an overview will be given of the atom-counting methodology and its applications over the past decade. The procedure to count the number of atoms will be discussed in detail and it will be shown how the performance of the method can be further improved. Furthermore, advances toward mixed element nanostructures, 3D atomic modelling based on the atom-counting results, and quantifying the nanoparticle dynamics will be highlighted.

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.

Element Specific Atom Counting at the Atomic Scale by Combining High Angle Annular Dark Field Scanning Transmission Electron Microscopy and Energy Dispersive X-ray Spectroscopy

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.

Ingrained: An Automated Framework for Fusing Atomic-Scale Image Simulations into Experiments

To fully leverage the power of image simulation to corroborate and explain patterns and structures in atomic resolution microscopy, an initial correspondence between the simulation and experimental image must be established at the outset of further high accuracy simulations or calculations. Furthermore, if simulation is to be used in context of highly automated processes or high-throughput optimization, the process of finding this correspondence itself must be automated. In this work, "ingrained," an open-source automation framework which solves for this correspondence and fuses atomic resolution image simulations into the experimental images to which they correspond, is introduced. Herein, the overall "ingrained" workflow, focusing on its application to interface structure approximations, and the development of an experimentally rationalized forward model for scanning tunneling microscopy simulation are described.

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.

Substitutional synthesis of sub-nanometer InGaN/GaN quantum wells with high indium content

InGaN/GaN quantum wells (QWs) with sub-nanometer thickness can be employed in short-period superlattices for bandgap engineering of efficient optoelectronic devices, as well as for exploiting topological insulator behavior in III-nitride semiconductors. However, it had been argued that the highest indium content in such ultra-thin QWs is kinetically limited to a maximum of 33%, narrowing down the potential range of applications. Here, it is demonstrated that quasi two-dimensional (quasi-2D) QWs with thickness of one atomic monolayer can be deposited with indium contents far exceeding this limit, under certain growth conditions. Multi-QW heterostructures were grown by plasma-assisted molecular beam epitaxy, and their composition and strain were determined with monolayer-scale spatial resolution using quantitative scanning transmission electron microscopy in combination with atomistic calculations. Key findings such as the self-limited QW thickness and the non-monotonic dependence of the QW composition on the growth temperature under metal-rich growth conditions suggest the existence of a substitutional synthesis mechanism, involving the exchange between indium and gallium atoms at surface sites. The highest indium content in this work approached 50%, in agreement with photoluminescence measurements, surpassing by far the previously regarded compositional limit. The proposed synthesis mechanism can guide growth efforts towards binary InN/GaN quasi-2D QWs.

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.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

Combining quantitative ADF STEM with SiNx membrane-based MEMS devices: A simulation study with Pt nanoparticles

Computer simulations are used to assess the influence of a 20-nm-thick SiN_x membrane on the quantification of atomic-resolution annular dark-field (ADF) scanning transmission electron microscopy images of Pt nanoparticles. The discussions include the effect of different nanoparticle/membrane arrangements, accelerating voltage, nanoparticle thickness and the presence of adjacent atomic columns on the accuracy with which the number of Pt atoms in each atom column can be counted. The results, which are based on the use of ADF scattering cross-sections, show that an accuracy of better than a single atom is attainable at 200 and 300 kV. At 80kV, the scattering in a typical SiN_x membrane is sufficiently strong that the best possible atom counting accuracy is reduced to +/- 2 atoms. The implications of the work for quantitative studies of Pt nanoparticles imaged through SiN_x membranes are discussed.

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).

Experimental quantification of atomically-resolved HAADF-STEM images using EDX

Atomically-resolved mappings of the indium composition in InGaN/GaN multi-quantum well structures have been obtained by quantifying the contrast in HAADF-STEM. The quantification procedure presented here does not rely on computation-intensive simulations, but rather uses EDX measurements to calibrate the HAADF-STEM contrast. The histogram of indium compositions obtained from the mapping provides unique insights into the growth of InGaN: the transition from GaN to InGaN and vice versa occurs in discreet increments of composition; each increment corresponds to one monolayer of the interface, indicating that nucleation takes longer than the lateral growth of the step. Strain-state analysis is also performed by applying Peak-Pair Analysis to the positions of the atomic columns identified the quantification of the contrast. The strain mappings yield an estimate of the composition in good agreement with the one obtained from quantified HAADF-STEM, albeit with a lower precision. Possible improvements to increase the precision of the strain mappings are discussed, opening potential pathways for the quantification of arbitrary quaternary alloys at atomic scales.

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.

Investigation on Sb distribution for InSb/InAs sub-monolayer heterostructure using TEM techniques

InSb/InAs sub-monolayer (SML) nanostructures such as SML quantum dots offer sharper emission spectra, a better modal gain and a larger modulation bandwidth compared to its Stranski-Krastanov counterpart. In this work, the Sb distribution of SML InSb layers grown by migration enhanced epitaxy has been analyzed by transmission electron microscopy (TEM) techniques. The analysis of the material by diffraction contrast in 002 dark field conditions and by atomic column resolved high angle annular dark field-scanning TEM reveal the presence of a low Sb content InSbAs continuous layer with scarce Sb-rich InSbAs agglomerates. The intensity profiles obtained by both techniques point to Sb segregation during growth. This segregation has been quantified using the Muraki segregation model obtaining a high segregation coefficient R of 0.81 towards the growth direction. The formation of a continuous InSbAs wetting layer as a result of a SML deposition of Sb on the InAs surface is discussed.

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.

Composition determination of semiconductor alloys towards atomic accuracy by HAADF-STEM

This paper presents a comprehensive investigation of an extended method to determine composition of materials by scanning transmission electron microscopy (STEM) high angle annular darkfield (HAADF) images and using complementary multislice simulations. The main point is to understand the theoretical capabilities of the algorithm and address the intrinsic limitations of using STEM HAADF intensities for composition determination. A special focus is the potential of the method regarding single-atom accuracy. All-important experimental parameters are included into the multislice simulations to ensure the best possible fit between simulation and experiment. To demonstrate the capabilities of the extended method, results for three different technical important semiconductor samples are presented. Overall the method shows a high lateral resolution combined with a high accuracy towards single-atom accuracy.

Control of Knock-On Damage for 3D Atomic Scale Quantification of Nanostructures: Making Every Electron Count in Scanning Transmission Electron Microscopy

Understanding nanostructures down to the atomic level is the key to optimizing the design of advanced materials with revolutionary novel properties. This requires characterization methods capable of quantifying the three-dimensional (3D) atomic structure with the highest possible precision. A successful approach to reach this goal is to count the number of atoms in each atomic column from 2D annular dark field scanning transmission electron microscopy images. To count atoms with single atom sensitivity, a minimum electron dose has been shown to be necessary, while on the other hand beam damage, induced by the high energy electrons, puts a limit on the tolerable dose. An important challenge is therefore to develop experimental strategies to optimize the electron dose by balancing atom-counting fidelity vs the risk of knock-on damage. To achieve this goal, a statistical framework combined with physics-based modeling of the dose-dependent processes is here proposed and experimentally verified. This model enables an investigator to theoretically predict, in advance of an experimental measurement, the optimal electron dose resulting in an unambiguous quantification of nanostructures in their native state with the highest attainable precision.

Influence of the crosstalk on the intensity of HAADF-STEM images of quaternary semiconductor materials

The influence of the neighbouring atomic-columns in determining the composition at atomic column scale of quaternary semiconductor compounds, using simulated HAADF-STEM images is evaluated. The InAlAsSb alloy, a promising material in the photovoltaic field, is considered. We find that the so called 'crosstalk' effect plays an important role for the aimed compositional determination. The intensity transfer is larger from neighbouring atomic columns with higher average Z, and towards atomic columns with smaller Z. Our results show that in order to obtain precise information on the column composition, the HAADF-STEM intensities of both columns need to be taken into account simultaneously.

Quantitative evaluation of the interface lattice quality of a strain superlattice by strain analysis

The lattice quality of strain superlattice structures in Quantum Cascade Lasers (QCLs) directly influences the photoelectric properties and service life of the lasers. However, the evaluation method for lattice quality on the nanoscale is not very well developed at present, especially for interface lattice quality assessment. In this investigation, all atoms positioned in the multiple interface layers can be simultaneously and accurately determined through Subset Geometric Phase Analysis (S-GPA) combined with a Peak Finding (PF) method and an Optimal Approximation Algorithm (OAA) with a sensitivity of about 0.04 Å. Based on the determined interface location, the strain distribution in all layers of the superlattice structure was simultaneously measured using the improved S-GPA by means of the optimal selection of multiple reference areas. A quantitative evaluation of the strain/stress compensation effect was then carried out based on the theoretical model of elastic mechanics. The proposed method was successfully applied to evaluating the lattice quality of an In0.6Ga0.4As/In0.44Al0.56As superlattice structure grown by Molecular Beam Epitaxy (MBE). The obtained results show that the interface lattices are almost perfect with a uniform thickness of layers, without any defects and stress concentration. Each In0.44Al0.56As layer and adjacent In0.6Ga0.4As layers provided effective strain/stress compensation for each other, reducing the possibility of forming dislocations. In one period, the active region has been properly strain-balanced to give a nearly net zero strain. The proposed method can not only be applied in evaluating the growth quality of the superlattice structure with a large field of view, but also provide quantitative experimental data for further improving the superlattice design.

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.

Absolute Scale Quantitative Off-Axis Electron Holography at Atomic Resolution

An absolute scale match between experiment and simulation in atomic-resolution off-axis electron holography is demonstrated, with unknown experimental parameters determined directly from the recorded electron wave function using an automated numerical algorithm. We show that the local thickness and tilt of a pristine thin WSe_{2} flake can be measured uniquely, whereas some electron optical aberrations cannot be determined unambiguously for a periodic object. The ability to determine local specimen and imaging parameters directly from electron wave functions is of great importance for quantitative studies of electrostatic potentials in nanoscale materials, in particular when performing in situ experiments and considering that aberrations change over time.

Thickness dependence of scattering cross-sections in quantitative scanning transmission electron microscopy

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.

Composition determination of multinary III/V semiconductors via STEM HAADF multislice simulations

Knowledge of the microscopic elemental composition of multinary III/V semiconductor materials is crucial to the development of functionalized opto-electronic devices. Well-proven composition analysis methods, such as high resolution X-ray diffraction (HRXRD), fail to determine the elemental composition when more than three atomic species are involved. In this work we propose a procedure for the composition analysis of multinary III/V semiconductors at atomic resolution using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image simulations. Our method exploits the dependence of HAADF-STEM image intensities on the atomic number and static atomic displacements (SAD) at different detector inner angles. Here, we describe the proposed method in detail using Ga(NAsP) as an example multinary material.

Bias-Controlled Optical Transitions in GaN/AlN Nanowire Heterostructures

We report on the control and modification of optical transitions in 40× GaN/AlN heterostructure superlattices embedded in GaN nanowires by an externally applied bias. The complex band profile of these multi-nanodisc heterostructures gives rise to a manifold of optical transitions, whose emission characteristic is strongly influenced by polarization-induced internal electric fields. We demonstrate that the superposition of an external axial electric field along a single contacted nanowire leads to specific modifications of each photoluminescence emission, which allows to investigate and identify their origin and to control their characteristic properties in terms of transition energy, intensity and decay time. Using this approach, direct transitions within one nanodisc, indirect transitions between adjacent nanodiscs, transitions at the top/bottom edge of the heterostructure, and the GaN near-band-edge emission can be distinguished. While the transition energy of the direct transition can be shifted by external bias over a range of 450 meV and changed in intensity by a factor of 15, the indirect transition exhibits an inverse bias dependence and is only observable and spectrally separated when external bias is applied. In addition, by tuning the band profile close to flat band conditions, the direction and magnitude of the internal electric field can be estimated, which is of high interest for the polar group III-nitrides. The direct control of emission properties over a wide range bears possible application in tunable optoelectronic devices. For more fundamental studies, single-nanowire heterostructures provide a well-defined and isolated system to investigate and control interaction processes in coupled quantum structures.

Frozen lattice and absorptive model for high angle annular dark field scanning transmission electron microscopy: A comparison study in terms of integrated intensity and atomic column position measurement

In this paper, both the frozen lattice (FL) and the absorptive potential (AP) approximation models are compared in terms of the integrated intensity and the precision with which atomic columns can be located from an image acquired using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM). The comparison is made for atoms of Cu, Ag, and Au. The integrated intensity is computed for both an isolated atomic column and an atomic column inside an FCC structure. The precision has been computed using the so-called Cramér-Rao Lower Bound (CRLB), which provides a theoretical lower bound on the variance with which parameters can be estimated. It is shown that the AP model results into accurate measurements for the integrated intensity only for small detector ranges under relatively low angles and for small thicknesses. In terms of the attainable precision, both methods show similar results indicating picometer range precision under realistic experimental conditions.

Entropy-limited topological protection of skyrmions

Magnetic skyrmions are topologically protected whirls that decay through singular magnetic configurations known as Bloch points. We used Lorentz transmission electron microscopy to infer the energetics associated with the topological decay of magnetic skyrmions far from equilibrium in the chiral magnet Fe_1-x Co _x Si. We observed that the lifetime τ of the skyrmions depends exponentially on temperature, [Formula: see text]. The prefactor τ₀ of this Arrhenius law changes by more than 30 orders of magnitude for small changes of the magnetic field, reflecting a substantial reduction of the lifetime of skyrmions by entropic effects and, thus, an extreme case of enthalpy-entropy compensation. Such compensation effects, being well known across many different scientific disciplines, affect topological transitions and, thus, topological protection on an unprecedented level.

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.

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.

Atomic Resolution Interfacial Structure of Lead-free Ferroelectric K0.5Na0.5NbO3 Thin films Deposited on SrTiO3

Oxide interface engineering has attracted considerable attention since the discovery of its exotic properties induced by lattice strain, dislocation and composition change at the interface. In this paper, the atomic resolution structure and composition of the interface between the lead-free piezoelectric (K_0.5Na_0.5)NbO₃ (KNN) thin films and single-crystalline SrTiO₃ substrate were investigated by means of scanning transmission electron microscopy (STEM) combining with electron energy loss spectroscopy (EELS). A sharp epitaxial interface was observed to be a monolayer composed of Nb and Ti cations with a ratio of 3/1. The First-Principles Calculations indicated the interface monolayer showed different electronic structure and played the vital role in the asymmetric charge distribution of KNN thin films near the interface. We also observed the gradual relaxation process for the relatively large lattice strains near the KNN/STO interface, which remarks a good structure modulation behavior of KNN thin films via strain engineering.

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.