Quantitative measurement of mean inner potential and specimen thickness from high-resolution off-axis electron holograms of ultra-thin layered WSe2

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.

Mean inner potential of elemental crystals from density-functional theory calculations: Efficient computation and trends

The mean inner potential (V0) of crystals plays an important role in electron microscopy. In a few cases, it has been measured experimentally, using mostly electron holography; however, it is not uncommon to find reports that disagree by a few volts regarding the mean inner potential of the same material. Different levels of theory have also been used to estimate its value, often by building the crystal as a superposition of isolated atoms or ions-an independent-atom approximation that does not take bonding into account. In a few cases, density-functional theory (DFT) calculations were done to capture such bonding, frequently using computer-intensive all-electron approaches. In this article, we describe in detail a faster implementation based on postprocessing files produced by a DFT code that relies on the projector-augmented wave method. We deployed this approach to compute values of V0 for 44 elemental solids, and we provide the first quantum-mechanical calculation of the mean inner potential beyond the independent-atom approximation for many of them. We also report instances in which different surface terminations for the same material led to differences in V0 of more than 3 V, highlighting the dependence of the mean inner potential on the boundary conditions of the sample. Finally, by comparing our values of V0 with other material properties, we show that it correlates mostly linearly with the mass density, that it can be used to compute a good approximation to the orbital diamagnetic contribution to the magnetic susceptibility, and that it provides a simple route to compute atomic scattering amplitudes for forward scattering of electrons.

Reconstruction of Angstrom resolution exit-waves by the application of drift-corrected phase-shifting off-axis electron holography

Phase-shifting electron holography is an excellent method to reveal electron wave phase information with very high phase sensitivity over a large range of spatial frequencies. It circumvents the limiting trade-off between fringe spacing and visibility of standard off-axis holography. Previous implementations have been limited by the independent drift of biprism and sample. We demonstrate here an advanced drift correction scheme for the hologram series that exploits the presence of an interface of the TEM specimen to the vacuum area in the hologram. It allows to obtain reliable phase information up to 2π/452 at the 1 Å information limit of the Titan 80-300 kV environmental transmission electron microscope used, by applying a moderate voltage of 250 V to a single biprism for a fringe spacing of 1 Å. The obtained phase and amplitude information is validated at a thin Pt sample by use of multislice image simulation with the frozen lattice approximation and shows excellent agreement. The presented method is applicable in any TEM equipped with at least one electron biprism and thus enables achieving high resolution off-axis holography in various instruments including those for in-situ applications. A software implementation for the acquisition, calibration and reconstruction is provided.

The Mean Inner Potential of Hematite α-Fe2O3 Across the Morin Transition

We measure the mean inner potential (MIP) of hematite, α-Fe2O3, using electron holography and transmission electron microscopy. Since the MIP is sensitive to valence electrons, we propose its use as a chemical bonding parameter for solids. Hematite can test the sensitivity of the MIP as a bonding parameter because of the Morin magnetic phase transition. Across this transition temperature, no change in the corundum crystal structure can be distinguished, while a change in hybridized Fe-3d and O-2p states was reported, affecting ionic bonding. For a given crystallographic phase, the change in the MIP with temperature is expected to be minor due to thermal expansion. Indeed, we measure the temperature dependence in corundum α-Al2O3(112¯0) between 95 and 295 K showing a constant MIP value of ∼16.8 V within the measurement accuracy of 0.45 V. Thus, our objectives are as follows: measure the MIP of hematite as a function of temperature and examine the sensitivity of the MIP as a bonding parameter for crystals. Measured MIPs of α-Fe2O3(112¯0) above the Morin transition are equal, 17.85 ± 0.50 V, 17.93 ± 0.50 V, at 295 K, 230 K, respectively. Below the Morin transition, at 95 K, a significant reduction of ∼1.3 V is measured to 16.56 ± 0.46 V. We show that this reduction follows charge redistribution resulting in increased ionic bonding.

Imaging Simulation of Charged Nanowires in TEM with Large Defocus Distance

In transmission electron microscope (TEM), both the amplitude and phase of electron beam change when electrons traverse a specimen. The amplitude is easily obtained by the square root of the intensity of a TEM image, while the phase affects defocused images. In order to obtain the phase map and verify the theoretical model of the interaction between electron beam and specimen, a lot of simulations have been performed by researchers. In this work, we have simulated defocus images of a SiC nanowire in TEM with the method of electron optics. Mean inner potential and charge distribution on the nanowire have been considered in the simulation. Besides, due to electron scattering coherence loss of the electron beam has been introduced. A dynamic process with Bayesian optimization was used in the simulation. With the infocus image as input and by adjusting fitting parameters the defocus image is determined with a reasonable charge distribution. The calculated defocus images are in a good agreement with the experimental ones. Here, we present a complete solution and verification method for solving nanoscale charge distribution in TEM.

Interference and interferometry in electron holography

This paper reviews the basics of electron holography as an introduction of the holography part of this special issue in Microscopy. We discuss the general principle of holography and interferometry regarding measurements and analyses of phase distributions, first using the optical holography. Next, we discuss physical phenomena peculiar to electron waves that cannot be realized by light waves and principles of electromagnetic field detection and observation methods. Furthermore, we discuss the interference optical systems of the electron waves and their features, and methods of reconstruction of the phase information from electron holograms, which are essential for realization of practical electron holography. We note that following this review application of electron holography will be discussed in detail in the papers of this special issue.

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.

Probing local order in multiferroics by transmission electron microscopy

The ongoing trend toward miniaturization has led to an increased interest in the magnetoelectric effect, which could yield entirely new device concepts, such as electric field-controlled magnetic data storage. As a result, much work is being devoted to developing new robust room temperature (RT) multiferroic materials that combine ferromagnetism and ferroelectricity. However, the development of new multiferroic devices has proved unexpectedly challenging. Thus, a better understanding of the properties of multiferroic thin films and the relation with their microstructure is required to help drive multiferroic devices toward technological application. This review covers in a concise manner advanced analytical imaging methods based on (scanning) transmission electron microscopy which can potentially be used to characterize complex multiferroic materials. It consists of a first broad introduction to the topic followed by a section describing the so-called phase-contrast methods, which can be used to map the polar and magnetic order in magnetoelectric multiferroics at different spatial length scales down to atomic resolution. Section 3 is devoted to electron nanodiffraction methods. These methods allow measuring local strains, identifying crystal defects and determining crystal structures, and thus offer important possibilities for the detailed structural characterization of multiferroics in the ultrathin regime or inserted in multilayers or superlattice architectures. Thereafter, in Section 4, methods are discussed which allow for analyzing local strain, whereas in Section 5 methods are addressed which allow for measuring local polarization effects on a length scale of individual unit cells. Here, it is shown that the ferroelectric polarization can be indirectly determined from the atomic displacements measured in atomic resolution images. Finally, a brief outlook is given on newly established methods to probe the behavior of ferroelectric and magnetic domains and nanostructures during in situ heating/electrical biasing experiments. These in situ methods are just about at the launch of becoming increasingly popular, particularly in the field of magnetoelectric multiferroics, and shall contribute significantly to understanding the relationship between the domain dynamics of multiferroics and the specific microstructure of the films providing important guidance to design new devices and to predict and mitigate failures.

Quantitative Mapping of the Charge Density in a Monolayer of MoS2 at Atomic Resolution by Off-Axis Electron Holography

The electric potential, electric field, and charge density of a monolayer of MoS₂ have been quantitatively measured at atomic-scale resolution. This has been performed by off-axis electron holography using a double aberration-corrected transmission electron microscope operated at 80 kV and a low electron beam current density. Using this low dose rate and acceleration voltage, the specimen damage is limited during imaging. In order to improve the sensitivity of the measurement, a series of holograms have been acquired. Instabilities of the microscope such as the drifts of the specimen, biprism, and optical aberrations during the acquisition have been corrected by data processing. Phase images of the MoS₂ monolayer have been acquired with a sensitivity of 2π/698 rad associated with a spatial resolution of 2.4 Å. The improvement in the signal-to-noise ratio allows the charge density to be directly calculated from the phase images using Poisson's equation. Density functional theory simulations of the potential and charge density of this MoS₂ monolayer were performed for comparison to the experiment. The experimental measurements and simulations are consistent with each other, and notably, the charge density in a sulfur monovacancy (V_S) site is shown.

The rapid electrochemical activation of MoTe2 for the hydrogen evolution reaction

The electrochemical generation of hydrogen is a key enabling technology for the production of sustainable fuels. Transition metal chalcogenides show considerable promise as catalysts for this reaction, but to date there are very few reports of tellurides in this context, and none of these transition metal telluride catalysts are especially active. Here, we show that the catalytic performance of metallic 1T′-MoTe₂ is improved dramatically when the electrode is held at cathodic bias. As a result, the overpotential required to maintain a current density of 10 mA cm⁻² decreases from 320 mV to just 178 mV. We show that this rapid and reversible activation process has its origins in adsorption of H onto Te sites on the surface of 1T′-MoTe₂. This activation process highlights the importance of subtle changes in the electronic structure of an electrode material and how these can influence the subsequent electrocatalytic activity that is displayed.

The performance of electrocatalysts for the renewable production of hydrogen is currently limited due to the difficulty of materials design. We show that tailoring the electronic structure under applied reductive bias is key to optimal electrocatalytic performance of a 2D chalcogenide material.

Emerging Electron Microscopy Techniques for Probing Functional Interfaces in Energy Materials

Interfaces play a fundamental role in many areas of chemistry. However, their localized nature requires characterization techniques with high spatial resolution in order to fully understand their structure and properties. State-of-the-art atomic resolution or in situ scanning transmission electron microscopy and electron energy-loss spectroscopy are indispensable tools for characterizing the local structure and chemistry of materials with single-atom resolution, but they are not able to measure many properties that dictate function, such as vibrational modes or charge transfer, and are limited to room-temperature samples containing no liquids. Here, we outline emerging electron microscopy techniques that are allowing these limitations to be overcome and highlight several recent studies that were enabled by these techniques. We then provide a vision for how these techniques can be paired with each other and with in situ methods to deliver new insights into the static and dynamic behavior of functional interfaces.

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.

Fine electron biprism on a Si-on-insulator chip for off-axis electron holography

Off-axis electron holography allows both the amplitude and the phase shift of an electron wavefield propagating through a specimen in a transmission electron microscope to be recovered. The technique requires the use of an electron biprism to deflect an object wave and a reference wave to form an interference pattern. Here, we introduce an approach based on semiconductor processing technology to fabricate fine electron biprisms with rectangular cross-sections. By performing electrostatic calculations and preliminary experiments, we demonstrate that such biprisms promise improved performance for electron holography experiments.

Quantitative Agreement between Electron-Optical Phase Images of WSe_{2} and Simulations Based on Electrostatic Potentials that Include Bonding Effects

The quantitative analysis of electron-optical phase images recorded using off-axis electron holography often relies on the use of computer simulations of electron propagation through a sample. However, simulations that make use of the independent atom approximation are known to overestimate experimental phase shifts by approximately 10%, as they neglect bonding effects. Here, we compare experimental and simulated phase images for few-layer WSe_{2}. We show that a combination of pseudopotentials and all-electron density functional theory calculations can be used to obtain accurate mean electron phases, as well as improved atomic-resolution spatial distribution of the electron phase. The comparison demonstrates a perfect contrast match between experimental and simulated atomic-resolution phase images for a sample of precisely known thickness. The low computational cost of this approach makes it suitable for the analysis of large electronic systems, including defects, substitutional atoms, and material interfaces.