Interference and interferometry in electron holography

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.

Self-Heterodyne Diffractive Imaging of Ultrafast Electron Dynamics Monitored by Single-Electron Pulses

The direct imaging of time-evolving molecular charge densities on atomistic scale and at femtosecond resolution has long been an elusive task. In this theoretical study, we propose a self-heterodyne electron diffraction technique based on single electron pulses. The electron is split into two beams, one passes through the sample and its interference with the second beam produces a heterodyne diffraction signal that images the charge density. Application to probing the ultrafast electronic dynamics in Mg-phthalocyanine demonstrates its potential for imaging chemical dynamics.

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.

Direct identification of the charge state in a single platinum nanoparticle on titanium oxide

A goal in the characterization of supported metal catalysts is to achieve particle-by-particle analysis of the charge state strongly correlated with the catalytic activity. Here, we demonstrate the direct identification of the charge state of individual platinum nanoparticles (NPs) supported on titanium dioxide using ultrahigh sensitivity and precision electron holography. Sophisticated phase-shift analysis for the part of the NPs protruding into the vacuum visualized slight potential changes around individual platinum NPs. The analysis revealed the number (only one to six electrons) and sense (positive or negative) of the charge per platinum NP. The underlying mechanism of platinum charging is explained by the work function differences between platinum and titanium dioxide (depending on the orientation relationship and lattice distortion) and by first-principles calculations in terms of the charge transfer processes.

Electron holography for observing magnetic bubbles and stripe-shaped domains in magnetic fields

An electron holography optical system was developed for relatively high magnetic fields up to 500 mT. The objective lens worked as a magnetic field generator for the specimen and the first intermediate lens worked for imaging as one of the pair lens composed of the objective lens. Specimen images were first formed on the object plane of the second intermediate lens. Electron biprism for conventional holography was installed under the second intermediate lens. Reconstruction of phase distributions was performed by the Fourier transform method and the vector maps were used to clarify small phase modulations. By using the developed system, magnetic characteristics of hexaferrite magnets (BaFe_12-x-δSc_xMg_δO₁₉), such as magnetic bubbles and stripe-shaped magnetic domains, were observed at smaller than 200 mT. Their magnetization structures and their interactions are demonstrated with the experimental results.

Analysis of Spatial Point Patterns in Electron Counting Images

In this study, the spatial counting statistics of free electron beams, which were released via field emission from cold metal and propagated through a vacuum region, were investigated to examine the normal functioning of the counting equipment for electron correlation spectroscopy. The beam electrons were recorded separately according to the locations of individual events as they reached the direct detection transmission CMOS sensor. We examined the spatial point patterns arising from the locations of the individual events of each primary electron being detected in the case of electrons in a state in which the wave function is constant on the sensor. The quadrat method, which compares the observed frequencies of the number of electron-counts in subsets of the study region with the predicted frequencies from a Poisson distribution, indicates a clustering-type departure from complete spatial randomness. To explore some of the basic principles governing the location of coherent electrons being counted, Ripley's K-function and the corresponding L-function of a stationary spatial point process were used to test the complete spatial randomness from the data. The maximum peak in the average of the L-functions was sensitive only to the mean counts per frame. Thus, clustering of spatial point patterns may result from abnormalities in the direct detection camera. When the interaction of the beam electrons with the sensor is included in the simulation, there is a reasonable match between the average of the L-functions and the experimental curves with the theoretically simulated curves.

Electron holography by planar electron backscattered diffraction patterns

Since Dennis Gabor introduced holography in 1948, it has been of interest to apply it to atomic scales. Electrons with high kinetic energies may indeed be used for electron holography. We describe the holographic process with electron backscatter diffraction (EBSD) as a non-invasive surface structure analysis. We show that typical parameters of current experiments already provide the requirements to collect sufficient data for a successful holographic reconstruction. As a first example, we describe how holography may be applied to planar EBSD patterns. Furthermore, we discuss the influence of experimental parameters to improve the quality of the reconstruction.

Lorentz Scanning Electron/Ion Microscopy

We have developed an observation and measurement method for spatial electromagnetic fields by using scanning electron/ion microscopes, combined with electron holography reconstruction technique. A cross-grating was installed below the specimen, and the specimens were observed under the infocus condition, and the grating was simultaneously observed under the defocus condition. Electromagnetic fields around the specimen were estimated from grating-image distortions. This method is effective for low and middle magnification and resolution ranges; furthermore, this method can in principle be realizable in any electron/ion beam instruments because it is based on the Lorentz force model for charged particle beams.

Recent advances in small-angle electron diffraction and Lorentz microscopy

We describe small-angle electron diffraction (SmAED) and Lorentz microscopy using a conventional transmission electron microscope. In SmAED, electron diffraction patterns with a wide-angular range on the order of 1 × 10-2 rad to 1 × 10-7 rad can be obtained. It is demonstrated that magnetic information of nanoscale magnetic microstructures can be obtained by Fresnel imaging, Foucault imaging and SmAED. In particular, we report magnetic microstructures associated with magnetic stripes and magnetic skyrmions revealed by Lorentz microscopy with SmAED. SmAED can be applied to the analysis of microstructures in functional materials such as dielectric, ferromagnetic and multiferroic materials.