State of the art in atomic resolution off-axis electron holography

Enhancing performance of electron holography with mathematical and machine learning-based denoising techniques

Electron holography is a useful tool for analyzing functional properties, such as electromagnetic fields and strains of materials and devices. The performance of electron holography is limited by the 'shot noise' inherent in electron micrographs (holograms), which are composed of a finite number of electrons. A promising approach for addressing this issue is to use mathematical and machine learning-based image-processing techniques for hologram denoising. With the advancement of information science, denoising methods have become capable of extracting signals that are completely buried in noise, and they are being applied to electron microscopy, including electron holography. However, these advanced denoising methods are complex and have many parameters to be tuned; therefore, it is necessary to understand their principles in depth and use them carefully. Herein, we present an overview of the principles and usage of sparse coding, the wavelet hidden Markov model and tensor decomposition, which have been applied to electron holography. We also present evaluation results for the denoising performance of these methods obtained through their application to simulated and experimentally recorded holograms. Our analysis, review and comparison of the methods clarify the impact of denoising on electron holography research.

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.

Improved Efficiency in Automated Acquisition of Ultra-high Resolution Electron Holograms Using Automated Target Detection

An automated hologram acquisition system for big-data analysis and for improving the statistical precision of phase analysis has been upgraded with automated particle detection technology. The coordinates of objects in low-magnification images are automatically detected using zero-mean normalized cross-correlation with preselected reference images. In contrast with the conventional scanning acquisitions from the whole area of a microgrid and/or a thin specimen, the new method allows efficient data collections only from the desired fields of view including the particles. The acquisition time of the cubic/triangular nanoparticles that were observed was shortened by about 1/58 that of the conventional scanning acquisition method because of the efficient data collections. The developed technology can improve statistical precision in electron holography with shorter acquisition time and is applicable to the analysis of electromagnetic fields for various kinds of nanoparticles.

Holography: application to high-resolution imaging

Electron holography was invented for correcting aberrations of the lenses of electron microscopes. It was used to observe the atomic arrangements in crystals after decades of research. Then it was combined with a hardware aberration corrector to enable high-resolution and high-precision analysis. Its applications were further extended to magnetic observations with sub-nanometer resolution. High-resolution electron holography has become a powerful technique for observing electromagnetic distributions in functional materials.

Magnetic flux density measurements from narrow grain boundaries produced in sintered permanent magnets

This review examines methods of magnetic flux density measurements from the narrow grain boundary (GB) regions, the thickness of which is of the order of nanometers, produced in Nd-Fe-B-based sintered magnets. Despite of the complex crystallographic microstructure and the significant stray magnetic field of the sintered magnet, recent progress in electron holography allowed for the determination of the intrinsic magnetic flux density due to the GB which is embedded in the polycrystalline thin-foil. The methods appear to be useful as well for intensive studies about interface magnetism in a variety of systems.

Measuring Dynamic Structural Changes of Nanoparticles at the Atomic Scale Using Scanning Transmission Electron Microscopy

We propose a new method to measure atomic scale dynamics of nanoparticles from experimental high-resolution annular dark field scanning transmission electron microscopy images. By using the so-called hidden Markov model, which explicitly models the possibility of structural changes, the number of atoms in each atomic column can be quantified over time. This newly proposed method outperforms the current atom-counting procedure and enables the determination of the probabilities and cross sections for surface diffusion. This method is therefore of great importance for revealing and quantifying the atomic structure when it evolves over time via adatom dynamics, surface diffusion, beam effects, or during in situ experiments.

Automated acquisition of vast numbers of electron holograms with atomic-scale phase information

An automated acquisition system for collecting a large number of electron holograms, to improve the statistical precision of phase analysis, was developed. A technique for shifting the electron beam in combination with stage movement allows data to be acquired over a wide area of a TEM-specimen grid. Undesired drift in the hologram position, which may occur during the hologram acquisition, can be corrected in real time by automated detection of the interference-fringe region in an image. To demonstrate the usefulness of the developed automated hologram acquisition system, gold nanoparticles dispersed on a carbon foil were observed with a 1.2-MV atomic resolution holography electron microscope. The system could obtain 1024 holograms, which provided phase maps for more than 500 nanoparticles with a lateral resolution of 0.14 nm, in just 1 h. The observation results revealed an anomalous increase in mean inner potential for a particle size smaller than 4 nm. The developed automated hologram acquisition system can be applied to improve the precision of phase measurement by averaging many phase images, as demonstrated by single particle analysis for biological entities. Moreover, the system makes it possible to study electrostatic potential of catalysts and other functional nanoparticles at atomic resolution.

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.

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.

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.

Advanced Electron Holography Applied to Electromagnetic Field Study in Materials Science

Advances and applications of electron holography to the study of electromagnetic fields in various functional materials are presented. In particular, the development of split-illumination electron holography, which introduces a biprism in the illumination system of a holography electron microscope, enables highly accurate observations of electromagnetic fields and the expansion of the observable area. First, the charge distributions on insulating materials were studied by using split-illumination electron holography and including a mask in the illumination system. Second, the three-dimensional spin configurations of skyrmion lattices in a helimagnet were visualized by using a high-voltage holography electron microscope. Third, the pinning of the magnetic flux lines in a high-temperature superconductor YBa₂ Cu₃ O_7-y was analyzed by combining electron holography and scanning ion microscopy. Finally, the dynamic accumulation and collective motions of electrons around insulating biomaterial surfaces were observed by utilizing the amplitude reconstruction processes of electron holography.

Electric field imaging of single atoms

In scanning transmission electron microscopy (STEM), single atoms can be imaged by detecting electrons scattered through high angles using post-specimen, annular-type detectors. Recently, it has been shown that the atomic-scale electric field of both the positive atomic nuclei and the surrounding negative electrons within crystalline materials can be probed by atomic-resolution differential phase contrast STEM. Here we demonstrate the real-space imaging of the (projected) atomic electric field distribution inside single Au atoms, using sub-Å spatial resolution STEM combined with a high-speed segmented detector. We directly visualize that the electric field distribution (blurred by the sub-Å size electron probe) drastically changes within the single Au atom in a shape that relates to the spatial variation of total charge density within the atom. Atomic-resolution electric field mapping with single-atom sensitivity enables us to examine their detailed internal and boundary structures.

The ability of scanning transmission electron microscopy (STEM) to image single atoms is becoming increasingly sophisticated. Here, the authors use differential phase contrast STEM to map the atomic electric fields within single Au atoms and SrTiO₃ crystals, a step toward visualizing such intra- and interatomic electronic structure as chemical bonds.

Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples

We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si₃N₄ wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.

Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of light and heavy elements in complex nanostructures

The aberration-corrected scanning transmission electron microscope (STEM) has emerged as a key tool for atomic resolution characterization of materials, allowing the use of imaging modes such as Z-contrast and spectroscopic mapping. The STEM has not been regarded as optimal for the phase-contrast imaging necessary for efficient imaging of light materials. Here, recent developments in fast electron detectors and data processing capability is shown to enable electron ptychography, to extend the capability of the STEM by allowing quantitative phase images to be formed simultaneously with incoherent signals. We demonstrate this capability as a practical tool for imaging complex structures containing light and heavy elements, and use it to solve the structure of a beam-sensitive carbon nanostructure. The contrast of the phase image contrast is maximized through the post-acquisition correction of lens aberrations. The compensation of defocus aberrations is also used for the measurement of three-dimensional sample information through post-acquisition optical sectioning.

The use of ptychography with electrons has been limited. Here, Yang et al. demonstrate that the combination of Z-contrast and phase imaging reveals the structure of complex nanomaterials. This practical tool can be used to solve the structure of a beam-sensitive carbon nanostructure at atomic-resolution.

Mapping the electrostatic potential of Au nanoparticles using hybrid electron holography

Electron holography is a powerful technique for characterizing electrostatic potentials, charge distributions, electric and magnetic fields, strain distributions and semiconductor dopant distributions with sub-nm spatial resolution. Mapping internal electrostatic and magnetic fields within nanoparticles and other low-dimensional materials by TEM requires both high spatial resolution and high phase sensitivity. Carrying out such an analysis fully quantitatively is even more challenging, since artefacts such as dynamical electron scattering may strongly affect the measurement. In-line electron holography, one of the variants of electron holography, features high phase sensitivity at high spatial frequencies, but suffers from inefficient phase recovery at low spatial frequencies. Off-axis electron holography, in contrast, can recover low spatial frequency phase information much more reliably, but is less effective in retrieving phase information at high spatial frequencies when compared to in-line holography. We investigate gold nanoparticles using hybrid electron holography at both atomic-resolution and intermediate magnification. Hybrid electron holography is a novel technique that synergistically combines off-axis and in-line electron holography, allowing the measurement of the complex wave function describing the scattered electrons with excellent signal-to-noise properties at both high and low spatial frequencies. The effect of dynamical electron scattering is minimized by beam tilt averaging.

Determination of the 3D shape of a nanoscale crystal with atomic resolution from a single image

Although the overall atomic structure of a nanoscale crystal is in principle accessible by modern transmission electron microscopy, the precise determination of its surface structure is an intricate problem. Here, we show that aberration-corrected transmission electron microscopy, combined with dedicated numerical evaluation procedures, allows the three-dimensional shape of a thin MgO crystal to be determined from only one single high-resolution image. The sensitivity of the reconstruction procedure is not only sufficient to reveal the surface morphology of the crystal with atomic resolution, but also to detect the presence of adsorbed impurity atoms. The single-image approach that we introduce offers important advantages for three-dimensional studies of radiation-sensitive crystals.

Electron holography for fields in solids: problems and progress

Electron holography initially was invented by Dennis Gabor for solving the problems raised by the aberrations of electron lenses in Transmission Electron Microscopy. Nowadays, after hardware correction of aberrations allows true atomic resolution of the structure, for comprehensive understanding of solids, determination of electric and magnetic nanofields is the most challenging task. Since fields are phase objects in the TEM, electron holography is the unrivaled method of choice. After more than 40 years of experimental realization and steady improvement, holography is increasingly contributing to these highly sophisticated and essential questions in materials science, as well to the understanding of electron waves and their interaction with matter.