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

High-speed 4-dimensional scanning transmission electron microscopy using compressive sensing techniques

Here we show that compressive sensing allows 4-dimensional (4-D) STEM data to be obtained and accurately reconstructed with both high-speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4-D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal-to-noise ratio in the recovered phase using 0.3% of the total data. Lay abstract: Four-dimensional scanning transmission electron microscopy (4-D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2-dimensional signal is acquired at each 2-D probe location, equating to a 4-D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4-D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100-1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4-D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10-100 times. The acquired data is then processed to fill-in or inpaint the missing data, taking advantage of the inherently low-complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4-D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4-D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100-300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

DFT-Assisted Investigation of the Electric Field and Charge Density Distribution of Pristine and Defective 2D WSe2 by Differential Phase Contrast Imaging

Most properties of solid materials are defined by their internal electric field and charge density distributions which so far are difficult to measure with high spatial resolution. Especially for 2D materials, the atomic electric fields influence the optoelectronic properties. In this study, the atomic-scale electric field and charge density distribution of WSe2 bi- and trilayers are revealed using an emerging microscopy technique, differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). For pristine material, a higher positive charge density located at the selenium atomic columns compared to the tungsten atomic columns is obtained and tentatively explained by a coherent scattering effect. Furthermore, the change in the electric field distribution induced by a missing selenium atomic column is investigated. A characteristic electric field distribution in the vicinity of the defect with locally reduced magnitudes compared to the pristine lattice is observed. This effect is accompanied by a considerable inward relaxation of the surrounding lattice, which according to first principles DFT calculation is fully compatible with a missing column of Se atoms. This shows that DPC imaging, as an electric field sensitive technique, provides additional and remarkable information to the otherwise only structural analysis obtained with conventional STEM imaging.

Direct Quantifying Charge Transfer by 4D-STEM: A Study on Perfect and Defective Hexagonal Boron Nitride

Four-dimensional scanning transmission electron microscopy (4D-STEM) offers an attractive approach to simultaneously obtain precise structural determinations and capture details of local electric fields and charge densities. However, accurately extracting quantitative data at the atomic scale poses challenges, primarily due to probe propagation and size-related effects, which may even lead to misinterpretations of qualitative effects. In this study, we present a comprehensive analysis of electric fields and charge densities in both pristine and defective h-BN flakes. Through a combination of experiments and first-principle simulations, we demonstrate that while precise charge quantification at individual atomic sites is hindered by probe effects, 4D-STEM can directly measure charge transfer phenomena at the monolayer edge with sensitivity down to a few tenths of an electron and a spatial resolution on the order of a few angstroms.

Differential phase contrast (DPC) mapping electric fields: Optimising experimental conditions

DPC in Scanning Transmission Electron Microscopy (STEM) is a valuable method for mapping the electric fields in semiconductor materials. However, optimising the experimental conditions can be challenging. In this paper, we test and compare critical experimental parameters, including the convergence angle, camera length, acceleration voltage, sample configuration, and orientation using a four-quadrant segmented detector and a Si specimen containing layers of different As concentrations. The DPC measurements show a roughly linear correlation with the estimated electric fields, until the field gets close to the detection limitation, which is ∼0.5 mV/nm with a sample thickness of ∼145 nm. These results can help inform which technique to use for different user cases: When the electric field at a planar junction is above ∼0.5 mV/nm, DPC with a segmented detector is practical for electric field mapping. With a planar junction, the DPC signal-to-noise ratio can be increased by increasing the specimen thickness. However, for semiconductor devices with electric fields smaller than ∼0.5 mV/nm, or for devices containing curved junctions, DPC is unreliable and techniques with higher sensitivity will need to be explored, such as 4D STEM using a pixelated detector.

GaN atomic electric fields from a segmented STEM detector: Experiment and simulation

Atomic electric fields in a thin GaN sample are measured with the centre-of-mass approach in 4D-scanning transmission electron microscopy (4D-STEM) using a 12-segmented STEM detector in a Spectra 300 microscope. The electric fields, charge density and potential are compared to simulations and an experimental measurement using a pixelated 4D-STEM detector. The segmented detector benefits from a high recording speed, which enables measurements at low radiation doses. However, there is measurement uncertainty due to the limited number of segments analysed in this study.

Imaging built-in electric fields and light matter by Fourier-precession TEM

We report the precise measurement of electric fields in nanostructures, and high-contrast imaging of soft matter at ultralow electron doses by transmission electron microscopy (TEM). In particular, a versatile method based on the theorem of reciprocity is introduced to enable differential phase contrast imaging and ptychography in conventional, plane-wave illumination TEM. This is realised by a series of TEM images acquired under different tilts, thereby introducing the sampling rate in reciprocal space as a tuneable parameter, in contrast to momentum-resolved scanning techniques. First, the electric field of a p-n junction in GaAs is imaged. Second, low-dose, in-focus ptychographic and DPC characterisation of Kagome pores in weakly scattering covalent organic frameworks is demonstrated by using a precessing electron beam in combination with a direct electron detector. The approach offers utmost flexibility to record relevant spatial frequencies selectively, while acquisition times and dose requirements are significantly reduced compared to the 4D-STEM counterpart.

Reliable phase quantification in focused probe electron ptychography of thin materials

Electron ptychography provides highly sensitive, dose efficient phase images which can be corrected for aberrations after the data has been acquired. This is crucial when very precise quantification is required, such as with sensitivity to charge transfer due to bonding. Drift can now be essentially eliminated as a major impediment to focused probe ptychography, which benefits from the availability of easily interpretable simultaneous Z-contrast imaging. However challenges have remained when quantifying the ptychographic phases of atomic sites. The phase response of a single atom has a negative halo which can cause atoms to reduce in phase when brought closer together. When unaccounted for, as in integrating methods of quantification, this effect can completely obscure the effects of charge transfer. Here we provide a new method of quantification that overcomes this challenge, at least for 2D materials, and is robust to experimental parameters such as noise, sample tilt.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Impact of beam size and diffraction effects in the measurement of long-range electric fields in crystalline samples via 4DSTEM

Measuring long-range electric fields by 4-dimensional scanning transmission electron microscopy (4DSTEM) is on the verge to becoming an established method, though quantifying and understanding all underlying processes remains a challenge. To gain further insight into these processes, experimental studies employing the center-of-mass (COM) method of the model system of a GaAs p-n junction are carried out in which three ranges of the semi-convergence angle α are identified, with an intermediate one where measuring the built-in potential Vbi is not feasible. STEM multislice simulations including both atomic and nm-scale fields prove that this intermediate range begins once diffraction disks start overlapping with the undiffracted beam. The range ends when the diffraction disks' intensities become so low that they do not affect the measurement significantly anymore and when high-intensity diffractions overlap the center disk completely. From simulations without influence of atoms it is concluded that measuring Vbi has advantages over measuring the electric-field strength, as the potential difference does neither show a significant dependence on the beam size, nor on the specimen thickness.

Quantitative electric field mapping between electrically biased needles by scanning transmission electron microscopy and electron holography

Stray electric fields in free space generated by two biased gold needles have been quantified in comprehensive finite-element (FE) simulations, accompanied by first moment (FM) scanning TEM (STEM) and electron holography (EH) experiments. The projected electrostatic potential and electric field have been derived numerically under geometrical variations of the needle setup. In contrast to the FE simulation, application of an analytical model based on line charges yields a qualitative understanding. By experimentally probing the electric field employing FM STEM and EH under alike conditions, a discrepancy of about 60% became apparent initially. However, the EH setup suggests the reconstructed phase to be significantly affected by the perturbed reference wave effect, opposite to STEM where the field-free reference was recorded subsequently with unbiased needles in which possibly remaining electrostatic influences are regarded as being minor. In that respect, the observed discrepancy between FM imaging and EH is resolved after including the long-range potential landscape from FE simulations into the phase of the reference wave in EH.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Mapping Nanoscale Electrostatic Field Fluctuations around Graphene Dislocation Cores Using Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM)

Defects in crystalline lattices cause modulation of the atomic density, and this leads to variations in the associated electrostatics at the nanoscale. Mapping these spatially varying charge fluctuations using transmission electron microscopy has typically been challenging due to complicated contrast transfer inherent to conventional phase contrast imaging. To overcome this, we used four-dimensional scanning transmission electron microscopy (4D-STEM) to measure electrostatic fields near point dislocations in a monolayer. The asymmetry of the atomic density in a (1,0) edge dislocation core in graphene yields a local enhancement of the electric field in part of the dislocation core. Through experiment and simulation, the increased electric field magnitude is shown to arise from "long-range" interactions from beyond the nearest atomic neighbor. These results provide insights into the use of 4D-STEM to quantify electrostatics in thin materials and map out the lateral potential variations that are important for molecular and atomic bonding through Coulombic interactions.

Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy

One approach to three-dimensional structure determination using the wealth of scattering data in four-dimensional (4D) scanning transmission electron microscopy (STEM) is the parallax method proposed by Ophus et al. (2019. Advanced phase reconstruction methods enabled by 4D scanning transmission electron microscopy, Microsc Microanal25, 10-11), which determines the scattering matrix and uses it to synthesize a virtual depth-sectioning reconstruction of the sample structure. Drawing on an equivalence with a hypothetical confocal imaging mode, we derive contrast transfer and point spread functions for this parallax method applied to weakly scattering objects, showing them identical to earlier depth-sectioning STEM modes when only bright field signal is used, but that improved depth resolution is possible if dark field signal can be used. Through a simulation-based study of doped Si, we show that this depth resolution is preserved for thicker samples, explore the impact of shot noise on the parallax reconstructions, discuss challenges to making use of dark field signal, and identify cases where the interpretation of the parallax reconstruction breaks down.

In Situ and Emerging Transmission Electron Microscopy for Catalysis Research

Catalysts are the primary facilitator in many dynamic processes. Therefore, a thorough understanding of these processes has vast implications for a myriad of energy systems. The scanning/transmission electron microscope (S/TEM) is a powerful tool not only for atomic-scale characterization but also in situ catalytic experimentation. Techniques such as liquid and gas phase electron microscopy allow the observation of catalysts in an environment conducive to catalytic reactions. Correlated algorithms can greatly improve microscopy data processing and expand multidimensional data handling. Furthermore, new techniques including 4D-STEM, atomic electron tomography, cryogenic electron microscopy, and monochromated electron energy loss spectroscopy (EELS) push the boundaries of our comprehension of catalyst behavior. In this review, we discuss the existing and emergent techniques for observing catalysts using S/TEM. Challenges and opportunities highlighted aim to inspire and accelerate the use of electron microscopy to further investigate the complex interplay of catalytic systems.

Atomic motifs govern the decoration of grain boundaries by interstitial solutes

Grain boundaries, the two-dimensional defects between differently oriented crystals, tend to preferentially attract solutes for segregation. Solute segregation has a significant effect on the mechanical and transport properties of materials. At the atomic level, however, the interplay of structure and composition of grain boundaries remains elusive, especially with respect to light interstitial solutes like B and C. Here, we use Fe alloyed with B and C to exploit the strong interdependence of interface structure and chemistry via charge-density imaging and atom probe tomography methods. Direct imaging and quantifying of light interstitial solutes at grain boundaries provide insight into decoration tendencies governed by atomic motifs. We find that even a change in the inclination of the grain boundary plane with identical misorientation impacts grain boundary composition and atomic arrangement. Thus, it is the smallest structural hierarchical level, the atomic motifs, that controls the most important chemical properties of the grain boundaries. This insight not only closes a missing link between the structure and chemical composition of such defects but also enables the targeted design and passivation of the chemical state of grain boundaries to free them from their role as entry gates for corrosion, hydrogen embrittlement, or mechanical failure.

Determining the Projected Crystal Structure from Four-dimensional Scanning Transmission Electron Microscopy via the Scattering Matrix

We present a gradient-descent-based approach to determining the projected electrostatic potential from four-dimensional scanning transmission electron microscopy measurements of a periodic, crystalline material even when dynamical scattering occurs. The method solves for the scattering matrix as an intermediate step, but overcomes the so-called truncation problem that limited previous scattering-matrix-based projected structure determination methods. Gradient descent is made efficient by using analytic expressions for the gradients. Through simulated case studies, we show that iteratively improving the scattering matrix determination can significantly improve the accuracy of the projected structure determination.

Optimizing experimental parameters of integrated differential phase contrast (iDPC) for atomic resolution imaging

Integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM) technique has been well developed for studying atomic structures at sub-Å resolution with the capability of simultaneously imaging heavy and light atoms even at an extremely low electron dose. As a direct phase contrast imaging technique, atomic resolution iDPC-STEM is sensitive to the imaging conditions. Although great achievements have been made both in aspect of theory and experiments, the influence of experimental parameters on the contrast of atomic resolution iDPC-STEM images has not been systematically investigated. Here, we perform the iDPC-STEM simulations on the prototypical example of SrTiO₃ with respect to the routine experimental factors, including the defocus, specimen thickness, accelerating voltage, convergence angle, collection angle, sample tilt and electron dose. Through the evaluation of image contrast and atom column intensity, the parameters are discussed to improve the image contrast and the visibility of light elements. Moreover, the dose-dependent simulations demonstrate the advantage of low dose iDPC-STEM imaging over other conventional STEM modes. Our results provide a practical guideline to experimentally obtain accessible atomic resolution iDPC-STEM images.

Accuracy of Local Polarization Measurements by Scanning Transmission Electron Microscopy

Accurately determining local polarization at atomic resolution can unveil the mechanisms by which static and dynamical behaviors of the polarization occur, including domain wall motion, defect interaction, and switching mechanisms, advancing us toward the better control of polarized states in materials. In this work, we explore the potential of atomic-resolution scanning transmission electron microscopy to measure the projected local polarization at the unit cell length scale. ZnO and PbMg1/3Nb2/3O3 are selected as case studies, to identify microscope parameters that can significantly affect the accuracy of the measured projected polarization vector. Different STEM imaging modalities are used to determine the location of the atomic columns, which, when combined with the Born effective charges, allows for the calculation of local polarization. Our results indicate that differentiated differential phase contrast (dDPC) imaging enhances the accuracy of measuring local polarization relative to other imaging modalities, such as annular bright-field or integrated-DPC imaging. For instance, under certain experimental conditions, the projected spontaneous polarization for ZnO can be calculated with 1.4% error from the theoretical value. Furthermore, we quantify the influence of sample thickness, probe defocus, and crystal mis-tilt on the relative errors of the calculated polarization.

Measuring and directing charge transfer in heterogenous catalysts

Precise control of charge transfer between catalyst nanoparticles and supports presents a unique opportunity to enhance the stability, activity, and selectivity of heterogeneous catalysts. While charge transfer is tunable using the atomic structure and chemistry of the catalyst-support interface, direct experimental evidence is missing for three-dimensional catalyst nanoparticles, primarily due to the lack of a high-resolution method that can probe and correlate both the charge distribution and atomic structure of catalyst/support interfaces in these structures. We demonstrate a robust scanning transmission electron microscopy (STEM) method that simultaneously visualizes the atomic-scale structure and sub-nanometer-scale charge distribution in heterogeneous catalysts using a model Au-catalyst/SrTiO₃-support system. Using this method, we further reveal the atomic-scale mechanisms responsible for the highly active perimeter sites and demonstrate that the charge transfer behavior can be readily controlled using post-synthesis treatments. This methodology provides a blueprint for better understanding the role of charge transfer in catalyst stability and performance and facilitates the future development of highly active advanced catalysts.

Direct observation of elemental fluctuation and oxygen octahedral distortion-dependent charge distribution in high entropy oxides

The enhanced compositional flexibility to incorporate multiple-principal cations in high entropy oxides (HEOs) offers the opportunity to expand boundaries for accessible compositions and unconventional properties in oxides. Attractive functionalities have been reported in some bulk HEOs, which are attributed to the long-range compositional homogeneity, lattice distortion, and local chemical bonding characteristics in materials. However, the intricate details of local composition fluctuation, metal-oxygen bond distortion and covalency are difficult to visualize experimentally, especially on the atomic scale. Here, we study the atomic structure-chemical bonding-property correlations in a series of perovskite-HEOs utilizing the recently developed four-dimensional scanning transmission electron microscopy techniques which enables to determine the structure, chemical bonding, electric field, and charge density on the atomic scale. The existence of compositional fluctuations along with significant composition-dependent distortion of metal-oxygen bonds is observed. Consequently, distinct variations of metal-oxygen bonding covalency are shown by the real-space charge-density distribution maps with sub-ångström resolution. The observed atomic features not only provide a realistic picture of the local physico-chemistry of chemically complex HEOs but can also be directly correlated to their distinctive magneto-electronic properties.

Fundamental understanding of local atomic features of high entropy oxides (HEOs) is limited due to their compositional complexity. Here the authors show composition fluctuation induced local oxygen octahedral distortion, chemical bond covalency and correlated properties in a series of HEOs.

Mapping 1D Confined Electromagnetic Edge States in 2D Monolayer Semiconducting MoS2 Using 4D-STEM

Four-dimensional (4D) scanning transmission electron microscopy is used to study the electric fields at the edges of 2D semiconducting monolayer MoS₂. Sub-nanometer 1D features in the 2D electric field maps are observed at the outermost region along zigzag edges and also along nanowire MoS-terminated MoS₂ edges. Atomic-scale oscillations are detected in the magnitude of the 1D electromagnetic edge state, with spatial variations that depend on the specific periodic edge reconstructions. Electric field reconstructions, along with integrated differential phase contrast reconstructions, reveal the presence of low Z number atoms terminating many of the uniform edges, which are difficult to detect by annular dark field scanning transmission electron microscopy due to its limited dynamic range. Density functional theory calculations support the formation of periodic 1D edge states and also show that enhancement of the electric field magnitude can occur for some edge terminations. The experimentally observed electric fields at the edges are attributed to the absence of an opposing electric field from a nearest neighbor atom when the electron beam propagates through the 2D monolayer and interacts. These results show the potential of 4D-STEM to map the atomic scale structure and fluctuations of electric fields around edge atoms with different bonding states than bulk atoms in 2D materials, beyond conventional imaging.

Atomically sharp domain walls in an antiferromagnet

The interest in understanding scaling limits of magnetic textures such as domain walls spans the entire field of magnetism from its physical fundamentals to applications in information technologies. Here, we explore antiferromagnetic CuMnAs in which imaging by x-ray photoemission reveals the presence of magnetic textures down to nanoscale, reaching the detection limit of this established microscopy in antiferromagnets. We achieve atomic resolution by using differential phase-contrast imaging within aberration-corrected scanning transmission electron microscopy. We identify abrupt domain walls in the antiferromagnetic film corresponding to the Néel order reversal between two neighboring atomic planes. Our work stimulates research of magnetic textures at the ultimate atomic scale and sheds light on electrical and ultrafast optical antiferromagnetic devices with magnetic field-insensitive neuromorphic functionalities.

Integrated Differential Phase Contrast (IDPC)-STEM Utilizing a Multi-Sector Detector for Imaging Thick Samples

The integrated differential phase contrast (IDPC) method is useful for generating the potential map of a thin sample. We evaluate theoretically the potential of IDPC imaging for thick samples by varying the focus at different sample thicknesses. Our calculations show that high defocus values result in enhanced anisotropy of the contrast transfer function (CTF) and uninterpretable images, if a quadrant detector is applied. We further show that applying a multi-sector detector can result in an almost isotropic CTF. By sector number-dependent calculations for both Cc/C3-corrected and C3-corrected scanning transmission electron microscopy (STEM), we show that the increase of detector sectors not only removes the anisotropy of the CTF, but also improves image contrast and resolution. For a proof-of-principle IDPC-STEM (uncorrected) experiment, we realize the functionality of a 12-sector detector from a physical quadrant detector and demonstrate the improvement in contrast and resolution on the example of InGaN/GaN quantum well structure.

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.

Factors limiting quantitative phase retrieval in atomic-resolution differential phase contrast scanning transmission electron microscopy using a segmented detector

Quantitative differential phase contrast imaging of materials in atomic-resolution scanning transmission electron microscopy using segmented detectors is limited by various factors, including coherent and incoherent aberrations, detector positioning and uniformity, and scan-distortion. By comparing experimental case studies of monolayer and few-layer graphene with image simulations, we explore which parameters require the most precise characterisation for reliable and quantitative interpretation of the reconstructed phases. Coherent and incoherent lens aberrations are found to have the most significant impact. For images over a large field of view, the impact of noise and non-periodic boundary conditions are appreciable, but in this case study have less of an impact than artefacts introduced by beam deflections coupling to beam scanning (imperfect tilt-shift purity).

Robust Atomic-Resolution Imaging of Lithium in Battery Materials by Center-of-Mass Scanning Transmission Electron Microscopy

The performance of energy storage materials is often governed by their structure at the atomic scale. Conventional electron microscopy can provide detailed information about materials at these length scales, but direct imaging of light elements such as lithium presents a challenge. While several recent techniques allow lithium columns to be distinguished, these typically either involve complex contrast mechanisms that make image interpretation difficult or require significant expertise to perform. Here, we demonstrate how center-of-mass scanning transmission electron microscopy (CoM-STEM) provides an enhanced ability for simultaneous imaging of lithium and heavier element columns in lithium ion conductors. Through a combination of experiments and multislice electron scattering calculations, we show that CoM-STEM is straightforward to perform and produces directly interpretable contrast for thin samples, while being more robust to variations in experimental parameters than previously demonstrated techniques. As a result, CoM-STEM is positioned to become a reliable and facile method for directly probing all elements within energy storage materials at the atomic scale.

STEM Tools for Semiconductor Characterization: Beyond High-Resolution Imaging

The smart engineering of novel semiconductor devices relies on the development of optimized functional materials suitable for the design of improved systems with advanced capabilities aside from better efficiencies. Thereby, the characterization of these materials at the highest level attainable is crucial for leading a proper understanding of their working principle. Due to the striking effect of atomic features on the behavior of semiconductor quantum- and nanostructures, scanning transmission electron microscopy (STEM) tools have been broadly employed for their characterization. Indeed, STEM provides a manifold characterization tool achieving insights on, not only the atomic structure and chemical composition of the analyzed materials, but also probing internal electric fields, plasmonic oscillations, light emission, band gap determination, electric field measurements, and many other properties. The emergence of new detectors and novel instrumental designs allowing the simultaneous collection of several signals render the perfect playground for the development of highly customized experiments specifically designed for the required analyses. This paper presents some of the most useful STEM techniques and several strategies and methodologies applied to address the specific analysis on semiconductors. STEM imaging, spectroscopies, 4D-STEM (in particular DPC), and in situ STEM are summarized, showing their potential use for the characterization of semiconductor nanostructured materials through recent reported studies.

Engineering of atomic-scale flexoelectricity at grain boundaries

Flexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the electrical polarization response to mechanical strain gradients that is not restricted by the symmetry of materials. However, large elastic deformation is usually difficult to achieve in most solids, and the strain gradient at minuscule is challenging to control. Here, we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~1.2 nm-1) within 3-4-unit cells, and thus obtain atomic-scale flexoelectric polarization of up to ~38 μC cm-2 at a 24° LaAlO3 grain boundary. Accompanied by the generation of the nanoscale flexoelectricity, the electronic structures of grain boundaries also become different. Hence, the flexoelectric effect at grain boundaries is essential to understand the electrical activities of oxide ceramics. We further demonstrate that for different materials, altering the misorientation angles of grain boundaries enables tunable strain gradients at the atomic scale. The engineering of grain boundaries thus provides a general and feasible pathway to achieve tunable flexoelectricity.

Determination of Grain-Boundary Structure and Electrostatic Characteristics in a SrTiO3 Bicrystal by Four-Dimensional Electron Microscopy

The grain boundary (GB) plays a critical role in a material's properties and device performance. Therefore, the characterization of a GB's atomic structure and electrostatic characteristics is a matter of great importance for materials science. Here, we report on the atomic structure and electrostatic analysis of a GB in a SrTiO₃ bicrystal by four-dimensional scanning transmission electron microscopy (4D-STEM). We demonstrate that the Σ5 GB is Ti-rich and poor in Sr. We investigate possible effects on the variation in the atomic electrostatic field, including oxygen vacancies, Ti-valence change, and accumulation of cations. A negative charge resulting from a space-charge zone in SrTiO₃ compensates a positive charge accumulated at the GB, which is in agreement with the double-Schottky-barrier model. It demonstrates the feasibility of characterizing the electrostatic properties at the nanometer scale by 4D-STEM, which provides comprehensive insights to understanding the GB structure and its concomitant effects on the electrostatic properties.

Extracting weak magnetic contrast from complex background contrast in plan-view FeGe thin films

The desire to design and build skyrmion-based devices has led to the need to characterize magnetic textures in thin films of functional materials. This can usually be achieved through the Lorentz transmission electron microscopy (LTEM) and the Lorentz scanning transmission electron microscopy (LSTEM) in thin film cross-section and single crystal specimens. However, direct imaging of the magnetic texture in plan-view samples of thin (< 50 nm) films has proved to be challenging due to the complex "background" contrast associated with the microstructure and defects, as well as contributions from bending of the specimens. Using a mechanically polished 35 nm plan-view FeGe thin film, we have explored three methods to extract magnetic contrast from the complex background contrast observed; (1) background subtraction in defocused LTEM images, (2) frequency filtered CoM-DPC reconstructed from LSTEM datasets and 3) registration of 4D-STEM datasets acquired at different tilt angles. Using these methods, we have successfully implemented real space imaging of both the helical phase and skyrmion phase. The ability to understand nanoscale magnetic behavior from plan-view thin films is a fundamental step towards development of highly integrated spin electronics.

Spatial Mapping of Electrostatic Fields in 2D Heterostructures

In situ electron microscopy is an effective tool for understanding the mechanisms driving novel phenomena in 2D structures. However, due to practical challenges, it is difficult to address these technologically relevant 2D heterostructures with electron microscopy. Here, we use the differential phase contrast (DPC) imaging technique to build a methodology for probing local electrostatic fields during electrical operation with nanoscale spatial resolution in such materials. We find that, by combining a traditional DPC setup with a high-pass filter, we can largely eliminate electric fluctuations emanating from short-range atomic potentials. Using a method based on this filtering algorithm, a priori electric field expectations can be directly compared with experimentally derived values to readily identify inhomogeneities and potentially problematic regions. We use this platform to analyze the electric field and charge density distribution across layers of hBN and MoS₂.

Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

4D-STEM at interfaces to GaN: Centre-of-mass approach & NBED-disc detection

4D-scanning transmission electron microscopy (4D-STEM) can be used to measure electric fields such as atomic fields or polarization-induced electric fields in crystal heterostructures. The paper focuses on effects occurring in 4D-STEM at interfaces, where two model systems are used: an AlN/GaN nanowire superlattice as well as a GaN/vacuum interface. Two different methods are applied: First, we employ the centre-of mass (COM) technique which uses the average momentum transfer evaluated from the intensity distribution in the diffraction pattern. Second, we measure the shift of the undiffracted disc (disc-detection method) in nano-beam electron diffraction (NBED). Both methods are applied to experimental and simulated 4D-STEM data sets. We find for both techniques distinct variations in the momentum transfer at interfaces between materials: In both model systems, peaks occur at the interfaces and we investigate possible sources and routes of interpretation. In case of the AlN/GaN superlattice, the COM and disc-detection methods are used to measure internal polarization-induced electric fields and we observed a reduction of the measured fields with increasing specimen thickness.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document.  This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document.  This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

Manganese Migration in Li1-xMn2O4 Cathode Materials

LiMn₂O₄ has been considered one of the most promising cathode materials for Li-ion batteries due to its thermal stability, abundance, environmental affinity, and the possibility to exchange Li-ions in three-dimensions. However, it still suffers from major problems, such as capacity fading and voltage decay, which has been associated to phase transformations and dissolution of transition metals. In this report, we use scanning transmission electron microscopy, coupled with differential phase contrast (DPC), to better understand the mechanisms behind the structural transformations occurring in LiMn₂O₄. We use the fact that DPC has the ability to observe simultaneously light and heavy elements, as well as measure projected electric fields and charge distribution at the atomic level. This approach allows us to monitor the migration of very low amounts of Mn to the Li atomic positions, at the surface and subsurface regions, which otherwise is very challenging to observe using other techniques such as HAADF and ABF. These observations not only provide a fundamental understanding of the structure of LiMn₂O₄ but also reveal DPC as a novel technique to determine local structural changes in materials consisting of heavy and light elements, as well as identify the location of light elements, monitor low concentrations of substitutional species and identify phase transformations.

Direct visualization of anionic electrons in an electride reveals inhomogeneities

Electrides are an unusual family of materials that feature loosely bonded electrons that occupy special interstitial sites and serve as anions. They are attracting increasing attention because of their wide range of exotic physical and chemical properties. Despite the critical role of the anionic electrons in inducing these properties, their presence has not been directly observed experimentally. Here, we visualize the columnar anionic electron density within the prototype electride Y₅Si₃ with sub-angstrom spatial resolution using differential phase-contrast imaging in a scanning transmission electron microscope. The data further reveal an unexpected charge variation at different anionic sites. Density functional theory simulations show that the presence of trace H impurities is the cause of this inhomogeneity. The visualization and quantification of charge inhomogeneities in crystals will serve as valuable input in future theoretical predictions and experimental analysis of exotic properties in electrides and materials beyond.

ab initio description of bonding for transmission electron microscopy

The simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret their contrast and extract specimen features. This is especially true for high-resolution phase-contrast imaging of materials, but electron scattering simulations based on atomistic models are widely used in materials science and structural biology. Since electron scattering is dominated by the nuclear cores, the scattering potential is typically described by the widely applied independent atom model. This approximation is fast and fairly accurate, especially for scanning TEM (STEM) annular dark-field contrast, but it completely neglects valence bonding and its effect on the transmitting electrons. However, an emerging trend in electron microscopy is to use new instrumentation and methods to extract the maximum amount of information from each electron. This is evident in the increasing popularity of techniques such as 4D-STEM combined with ptychography in materials science, and cryogenic microcrystal electron diffraction in structural biology, where subtle differences in the scattering potential may be both measurable and contain additional insights. Thus, there is increasing interest in electron scattering simulations based on electrostatic potentials obtained from first principles, mainly via density functional theory, which was previously mainly required for holography. In this Review, we discuss the motivation and basis for these developments, survey the pioneering work that has been published thus far, and give our outlook for the future. We argue that a physically better justified ab initio description of the scattering potential is both useful and viable for an increasing number of systems, and we expect such simulations to steadily gain in popularity and importance.

Toward quantitative electromagnetic field imaging by differential-phase-contrast scanning transmission electron microscopy

Differential-phase-contrast scanning transmission electron microscopy (DPC STEM) is a technique to directly visualize local electromagnetic field distribution inside materials and devices at very high spatial resolution. Owing to the recent progress in the development of high-speed segmented and pixelated detectors, DPC STEM now constitutes one of the major imaging modes in modern aberration-corrected STEM. While qualitative imaging of electromagnetic fields by DPC STEM is readily possible, quantitative imaging by DPC STEM is still under development because of the several fundamental issues inherent in the technique. In this report, we review the current status and future prospects of DPC STEM for quantitative electromagnetic field imaging from atomic scale to mesoscopic scale.

A symmetry-derived mechanism for atomic resolution imaging

We introduce an image-contrast mechanism for scanning transmission electron microscopy (STEM) that derives from the local symmetry within the specimen. For a given position of the electron probe on the specimen, the image intensity is determined by the degree of similarity between the exit electron-intensity distribution and a chosen symmetry operation applied to that distribution. The contrast mechanism detects both light and heavy atomic columns and is robust with respect to specimen thickness, electron-probe energy, and defocus. Atomic columns appear as sharp peaks that can be significantly narrower than for STEM images using conventional disk and annular detectors. This fundamentally different contrast mechanism complements conventional imaging modes and can be acquired simultaneously with them, expanding the power of STEM for materials characterization.

Influence of lens aberrations, specimen thickness and tilt on differential phase contrast STEM images

Differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM) allows for measuring electric and magnetic fields in solids on scales ranging from picometres to micrometres. The DPC technique mainly uses the direct beam, which is deflected by the electric and magnetic fields of the specimen and measured with a beam position sensitive detector. The beam deflection and thus the DPC signal is strongly influenced by specimen thickness, specimen tilt and lens aberrations. Understanding these influences is critical for a solid interpretation and quantification of contrasts in DPC images. To this end, the present study employs DPC-STEM image simulations of SrTiO₃ [001] at atomic resolution to analyse the influence of lens aberrations, specimen tilt and thickness and also to give a guideline for the detection of parameters affecting the contrast by performing an analysis of associated scattergrams. Simulations are obtained using the multislice algorithm implemented in the Dr. Probe software with conditions corresponding to a JEOL ARM200F microscope equipped with an octa-segmented annular detector, but results should be similar for other microscopes. Simulations show that due to a non-rigid shift of the detected intensity distribution correct values of projected potentials of specimens thicker than one unit-cell cannot be determined. Regarding the impact of residual lens aberrations, it is found that the shape of the lens aberration phase function determines the symmetry and features in the DPC image. Specimen tilt leads to an elongation of features perpendicular to the tilt axis. The results are confirmed by comparing simulated with experimental DPC images of Si [110] yielding good agreement. Overall, a high sensitivity of DPC-STEM imaging to lens aberrations, specimen tilt and diffraction effects is evidenced.

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.

Mapping valence electron distributions with multipole density formalism using 4D-STEM

Recent advancement in aberration correction and detector technology opened a door to various applications using 4D-STEM, which yields a diffraction pattern for each scanning position within a crystal unit-cell in scanning transmission electron microscopy (STEM) and generates incredible amounts of data in momentum space. Currently 4D-STEM analysis relies on the center-of-mass of the diffraction patterns in electric field and charge density mapping. It only derives the total projected charge density and is limited to phase objects, e.g. extremely thin samples. Here, we propose a new analytical method to accurately map aspherical valence electron distributions with atom-centered multipolar functions formalism using the whole 4D-STEM dataset. We demonstrate that, with the full dynamical calculations for various sample thicknesses, the method is sensitive not only to the miniscule charge transfer, but also to the atomic site symmetry and aspherical electron orbitals. The process of the refinement is much more robust and reliable than quantitative convergent beam electron diffraction.

Electrochemical and Structural Analysis in All-Solid-State Lithium Batteries by Analytical Electron Microscopy: Progress and Perspectives

Advanced scanning transmission electron microscopy (STEM) and its associated instruments have made significant contributions to the characterization of all-solid-state (ASS) Li batteries, as these tools provide localized information on the structure, morphology, chemistry, and electronic state of electrodes, electrolytes, and their interfaces at the nano- and atomic scale. Furthermore, the rapid development of in situ techniques has enabled a deep understanding of interfacial dynamic behavior and heterogeneous characteristics during the cycling process. However, due to the beam-sensitive nature of light elements in the interphases, e.g., Li and O, thorough and reliable studies of the interfacial structure and chemistry at an ultrahigh spatial resolution without beam damage is still a formidable challenge. Herein, the following points are discussed: (1) the recent contributions of advanced STEM to the study of ASS Li batteries; (2) current challenges associated with using this method; and (3) potential opportunities for combining cryo-electron microscopy and the STEM phase contrast imaging techniques.

Direct measurement of electrostatic potentials at the atomic scale: A conceptual comparison between electron holography and scanning transmission electron microscopy

Off-axis electron holography and first moment STEM are sensitive to electromagnetic potentials or fields, respectively. In this work, we investigate in what sense the results obtained from both techniques are equivalent and work out the major differences. The analysis is focused on electrostatic (Coulomb) potentials at atomic spatial resolution. It is shown that the probe-forming/objective aperture strongly affects the reconstructed electrostatic potentials and that, as a result of the different illumination setups, dynamical diffraction effects show a specific response with increasing specimen thickness. It is shown that thermal diffuse scattering is negligible for a wide range of specimen thicknesses, when evaluating the first moment of diffraction patterns.

Nano-architectural complexity of zinc oxide nanowall hollow microspheres and their structural properties

Zinc oxide (ZnO) hollow spheres with defined morphology and micro-/nanostructure are prepared by a hydrothermal synthesis approach. The materials possess fine-leaved structures at their particle surface (nanowall hollow micro spheres). Morphology control is achieved by citric acid used as an additive in variable relative quantities during the synthesis. The structure formation is studied by various time-dependent ex situ methods, such as scanning electron microscopy, x-ray diffraction, and Raman spectroscopy. The fine-leaved surface structure is characterized by high-resolution transmission electron microscopy techniques (HRTEM, STEM), using a high-angle annular dark field detector, as well as by differential phase contrast analysis. In-depth structural characterization of the nanowalls by drop-by-drop ex situ FE-SEM analysis provides insight into possible structure formation mechanisms. Further investigation addresses the thermal stability of the particle morphology and the enhancement of the surface-to-volume ratio by heat treatment (examined by N₂ physisorption).

Thickness and defocus dependence of inter-atomic electric fields measured by scanning diffraction

Scanning diffraction uses the diffraction pattern from the sub-angstrom electron probe in scanning transmission electron microscopy (STEM) to record the probe's interaction with the sample structure. The diffraction intensity distribution carries information about the Coulomb interaction between the probe and the sample, from which the local electric field can be calculated. Although measurement of the electric field from scanning diffraction data is relatively simple under ideal conditions, theoretical and simulation studies indicate that interpretation of momentum transfer measurements is still complicated by the effects of sample thickness, dynamic scattering, and the depth of focus from the electron probe. Especially for thick samples of more than a few nanometers, simulations predicted that the measured momentum transfer in scanning diffraction is not directly correlated with the electric field. However, in our experiments, we have found that the technique is more robust than previously predicted when using specific imaging conditions. Here we systematically studied the effect of sample thickness and probe defocus on the momentum transfer of the electron probe in STEM, showing that the strong electric field close to atoms can be measured quantitatively for samples up to 5 nm and that the weak electric field in inter-atomic regions can be measured for samples up to 15 nm while maintaining qualitative accuracy in the full electric field image.