Spatially resolved diffractometry with atomic-column resolution

Recent progresses in transmission electron microscopy studies of two-dimensional ferroelectrics

The rich potential of two-dimensional materials endows them with superior properties suitable for a wide range of applications, thereby attracting substantial interest across various fields. The ongoing trend towards device miniaturization aligns with the development of materials at progressively smaller scales, aiming to achieve higher integration density in electronics. In the realm of nano-scaling ferroelectric phenomena, numerous new two-dimensional ferroelectric materials have been predicted theoretically and subsequently validated through experimental confirmation. However, the capabilities of conventional tools, such as electrical measurements, are limited in providing a comprehensive investigation into the intrinsic origins of ferroelectricity and its interactions with structural factors. These factors include stacking, doping, functionalization, and defects. Consequently, the progress of potential applications, such as high-density memory devices, energy conversion systems, sensing technologies, catalysis, and more, is impeded. In this paper, we present a review of recent research that employs advanced transmission electron microscopy (TEM) techniques for the direct visualization and analysis of ferroelectric domains, domain walls, and other crucial features at the atomic level within two-dimensional materials. We discuss the essential interplay between structural characteristics and ferroelectric properties on the nanoscale, which facilitates understanding of the complex relationships governing their behavior. By doing so, we aim to pave the way for future innovative applications in this field.

Unsupervised machine learning combined with 4D scanning transmission electron microscopy for bimodal nanostructural analysis

Unsupervised machine learning techniques have been combined with scanning transmission electron microscopy (STEM) to enable comprehensive crystal structure analysis with nanometer spatial resolution. In this study, we investigated large-scale data obtained by four-dimensional (4D) STEM using dimensionality reduction techniques such as non-negative matrix factorization (NMF) and hierarchical clustering with various optimization methods. We developed software scripts incorporating knowledge of electron diffraction and STEM imaging for data preprocessing, NMF, and hierarchical clustering. Hierarchical clustering was performed using cross-correlation instead of conventional Euclidean distances, resulting in rotation-corrected diffractions and shift-corrected maps of major components. An experimental analysis was conducted on a high-pressure-annealed metallic glass, Zr-Cu-Al, revealing an amorphous matrix and crystalline precipitates with an average diameter of approximately 7 nm, which were challenging to detect using conventional STEM techniques. Combining 4D-STEM and optimized unsupervised machine learning enables comprehensive bimodal (i.e., spatial and reciprocal) analyses of material nanostructures.

Fast Grain Mapping with Sub-Nanometer Resolution Using 4D-STEM with Grain Classification by Principal Component Analysis and Non-Negative Matrix Factorization

High-throughput grain mapping with sub-nanometer spatial resolution is demonstrated using scanning nanobeam electron diffraction (also known as 4D scanning transmission electron microscopy, or 4D-STEM) combined with high-speed direct-electron detection. An electron probe size down to 0.5 nm in diameter is used and the sample investigated is a gold–palladium nanoparticle catalyst. Computational analysis of the 4D-STEM data sets is performed using a disk registration algorithm to identify the diffraction peaks followed by feature learning to map the individual grains. Two unsupervised feature learning techniques are compared: principal component analysis (PCA) and non-negative matrix factorization (NNMF). The characteristics of the PCA versus NNMF output are compared and the potential of the 4D-STEM approach for statistical analysis of grain orientations at high spatial resolution is discussed.

Non-negative matrix factorization for mining big data obtained using four-dimensional scanning transmission electron microscopy

Scientific instruments for material characterization have recently been improved to yield big data. For instance, scanning transmission electron microscopy (STEM) allows us to acquire many diffraction patterns from a scanning area, which is referred to as four-dimensional (4D) STEM. Here we study a combination of 4D-STEM and a statistical technique called non-negative matrix factorization (NMF) to deduce sparse diffraction patterns from a 4D-STEM data consisting of 10,000 diffraction patterns. Titanium oxide nanosheets are analyzed using this combined technique, and we discriminate the two diffraction patterns from pristine TiO₂ and reduced Ti₂O₃ areas, where the latter is due to topotactic reduction induced by electron irradiation. The combination of NMF and 4D-STEM is expected to become a standard characterization technique for a wide range materials.

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.

Methods for orientation and phase identification of nano-sized embedded secondary phase particles by 4D scanning precession electron diffraction

The diffraction patterns acquired with transmission electron microscopes gather reflections from all crystallites that overlap in the foil thickness. The superimposition renders automated orientation or phase mapping difficult, in particular when secondary phase particles are embedded in a dominant diffracting matrix. Several numerical approaches specifically developed to overcome this issue for 4D scanning precession electron diffraction data sets are described. They consist either in emphasizing the signature of the particles or in subtracting the matrix information out of the collected set of patterns. The different strategies are applied successively to a steel sample containing precipitates that are in Burgers orientation relationship with the matrix and to an aluminium alloy with randomly oriented Mn-rich particles.

Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond

Scanning transmission electron microscopy (STEM) is widely used for imaging, diffraction, and spectroscopy of materials down to atomic resolution. Recent advances in detector technology and computational methods have enabled many experiments that record a full image of the STEM probe for many probe positions, either in diffraction space or real space. In this paper, we review the use of these four-dimensional STEM experiments for virtual diffraction imaging, phase, orientation and strain mapping, measurements of medium-range order, thickness and tilt of samples, and phase contrast imaging methods, including differential phase contrast, ptychography, and others.

Theory and practice of electron diffraction from single atoms and extended objects using an EMPAD

What does the diffraction pattern from a single atom look like? How does it differ from the scattering from long-range potential? With the development of new high-dynamic range pixel array detectors to measure the complete momentum distribution, these questions have immediate relevance for designing and understanding momentum-resolved imaging modes. We explore the asymptotic limits of long-range and short-range potentials. We use a simple quantum mechanical model to explain the general and asymptotic limits for the probability distribution in both real and reciprocal space. Features in the scattering potential much larger than the probe size cause the bright field (BF) disk to deflect uniformly, while features much smaller than the probe size, instead of a deflection, cause a redistribution of intensity within the BF disk. Because long-range and short-range features are encoded differently in the diffraction pattern, it is possible to separate their contributions in differential phase-contrast (DPC) or center-of-mass (CoM) imaging. The shape profiles for atomic resolution CoM imaging are dominated by the shape of the probe gradient and not the highly singular atomic potentials or their local fields. Instead, only the peak height shows an atomic number sensitivity, whose precise dependence is determined by the convergence angle. At lower convergence angles, the contrast oscillates with increasing atomic number, similar to BF imaging. The range of collection angles impacts DPC and CoM imaging differently, with CoM being more sensitive to the upper cutoff limit, while DPC is more sensitive to the lower cutoff.

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.

High Dynamic Range Pixel Array Detector for Scanning Transmission Electron Microscopy

We describe a hybrid pixel array detector (electron microscope pixel array detector, or EMPAD) adapted for use in electron microscope applications, especially as a universal detector for scanning transmission electron microscopy. The 128×128 pixel detector consists of a 500 µm thick silicon diode array bump-bonded pixel-by-pixel to an application-specific integrated circuit. The in-pixel circuitry provides a 1,000,000:1 dynamic range within a single frame, allowing the direct electron beam to be imaged while still maintaining single electron sensitivity. A 1.1 kHz framing rate enables rapid data collection and minimizes sample drift distortions while scanning. By capturing the entire unsaturated diffraction pattern in scanning mode, one can simultaneously capture bright field, dark field, and phase contrast information, as well as being able to analyze the full scattering distribution, allowing true center of mass imaging. The scattering is recorded on an absolute scale, so that information such as local sample thickness can be directly determined. This paper describes the detector architecture, data acquisition system, and preliminary results from experiments with 80-200 keV electron beams.

Quantitative STEM normalisation: The importance of the electron flux

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

Quantitative evaluation of annular bright-field phase images in STEM

A phase reconstruction method based on multiple scanning transmission electron microscope (STEM) images was evaluated quantitatively using image simulations. The simulation results indicated that the phase shift caused by a single atom was proportional to the 0.6th power of the atomic number Z. For a thin SrTiO3 [001] crystal, the reconstructed phase at each atomic column increased according to the specimen thickness. The STEM phase images can quantify the oxygen vacancy concentration if the thickness is less than several nanometers.