An Efficient Electron Ptychography Method for Retrieving the Object Spectrum from Only a Few Iterations.

We present an efficient approach for electron ptychography based on a mathematical relationship that differs from that underlying the established algorithms of the ptychography iterative engine or the noniterative algorithms like the Wigner-distribution-deconvolution or the single-side-band method. Three variables are handled in this method-the transfer function of the objective lens, the object spectrum, and the diffraction wave whose phase is unknown. In the case of an aberration-corrected electron microscope, one is able to obtain a well-estimated transfer function of the lens. After reducing the number of three variables down to two, we construct an iterative loop between the object spectrum and the diffraction wave, which retrieves the object spectrum within a small number of iterations. We tested this object spectrum retrieval method on both a calculated and an experimental 4D-STEM datasets. By applying this method, we explore the influence of sampling, dose, and the size of illumination aperture on the reconstructed phase images.

Effect of self and extrinsic encapsulation on electron resilience of porous 2D polymer nanosheets.

Despite the exceptional resolution in aberration-corrected high-resolution transmission electron microscope (AC-HRTEM) images of inorganic two-dimensional (2D) materials, achieving high-resolution imaging of organic 2D materials remains a daunting challenge due to their low electron resilience. Optimizing the critical dose (the electron exposure, the material can accept before it is noticeably damaged) is vital to mitigate this challenge. An understanding of electron resilience in porous crystalline 2D polymers including the effect of sample thickness has not been derived thus far. It is assumed, that additional layers of the sample form a cage around inner layers, which are preventing fragments from escaping into the vacuum and enabling recombination. In the literature this so called caging effect has been reported for perylene and pythalocyanine. In this work we determine the critical dose of a porous, triazine-based 2D polymer as function of the sample thickness. The results show that the caging effect should not be generalized to more sophisticated polymer systems. We argue that pore channels in the framework structure serve as escape routes for free fragments preventing the caging effect and thus showing surprisingly a thickness-independent critical dose. Moreover, we demonstrate that graphene encapsulation prevents fragment escape and results in an increase in the critical electron dose and unit-cell image resolution.

Exploiting the full potential of the advanced two-hexapole corrector for STEM exemplified at 60kV.

Ultimate resolution in scanning transmission electron microscopy (STEM) with state-of-the-art aberration correctors requires careful tuning of the experimental parameters. The optimum aperture semi-angle depends on the chosen high tension, the chromatic aberration and the energy width of the source as well as on potentially limiting intrinsic residual aberrations. In this paper we derive simple expressions and criteria for choosing the aperture semi-angle and for counterbalancing the intrinsic sixth-order three-lobe aberration of two-hexapole aberration correctors by means of the fourth-order three-lobe aberration. It is noteworthy that for such an optimally adjusted electron probe the so-called flat area of the Ronchigram is explicitly not maximized. The above considerations are validated by experiments with a CEOS ASCOR in a C-FEG-equipped JEOL NEOARM operated at 60 kV. Sub-Angstrom resolution is demonstrated for a Si[112] single crystal as well as for a single-layered MoS2 crystalline film. Lattice reflections of 73 pm for silicon and 93 pm for molybdenum disulfide are visible in the Fourier transform of the images, respectively. Moreover, single sulfur vacancies can be clearly identified in the MoS2.

Aberration corrected STEM by means of diffraction gratings.

In the past 15 years, the advent of aberration correction technology in electron microscopy has enabled materials analysis on the atomic scale. This is made possible by precise arrangements of multipole electrodes and magnetic solenoids to compensate the aberrations inherent to any focusing element of an electron microscope. Here, we describe an alternative method to correct for the spherical aberration of the objective lens in scanning transmission electron microscopy (STEM) using a passive, nanofabricated diffractive optical element. This holographic device is installed in the probe forming aperture of a conventional electron microscope and can be designed to remove arbitrarily complex aberrations from the electron's wave front. In this work, we show a proof-of-principle experiment that demonstrates successful correction of the spherical aberration in STEM by means of such a grating corrector (GCOR). Our GCOR enables us to record aberration-corrected high-resolution high-angle annular dark field (HAADF-) STEM images, although yet without advancement in probe current and resolution. Improvements in this technology could provide an economical solution for aberration-corrected high-resolution STEM in certain use scenarios.

Origins and demonstrations of electrons with orbital angular momentum.

The surprising message of Allen et al. (Allen et al. 1992 Phys. Rev. A 45, 8185 (doi:10.1103/PhysRevA.45.8185)) was that photons could possess orbital angular momentum in free space, which subsequently launched advancements in optical manipulation, microscopy, quantum optics, communications, many more fields. It has recently been shown that this result also applies to quantum mechanical wave functions describing massive particles (matter waves). This article discusses how electron wave functions can be imprinted with quantized phase vortices in analogous ways to twisted light, demonstrating that charged particles with non-zero rest mass can possess orbital angular momentum in free space. With Allen et al. as a bridge, connections are made between this recent work in electron vortex wave functions and much earlier works, extending a 175 year old tradition in matter wave vortices.This article is part of the themed issue 'Optical orbital angular momentum'.

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 ß-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.

Chromatic Aberration Correction for Atomic Resolution TEM Imaging from 20 to 80 kV.

Atomic resolution in transmission electron microscopy of thin and light-atom materials requires a rigorous reduction of the beam energy to reduce knockon damage. However, at the same time, the chromatic aberration deteriorates the resolution of the TEM image dramatically. Within the framework of the SALVE project, we introduce a newly developed C_{c}/C_{s} corrector that is capable of correcting both the chromatic and the spherical aberration in the range of accelerating voltages from 20 to 80 kV. The corrector allows correcting axial aberrations up to fifth order as well as the dominating off-axial aberrations. Over the entire voltage range, optimum phase-contrast imaging conditions for weak signals from light atoms can be adjusted for an optical aperture of at least 55 mrad. The information transfer within this aperture is no longer limited by chromatic aberrations. We demonstrate the performance of the microscope using the examples of 30 kV phase-contrast TEM images of graphene and molybdenum disulfide, showing unprecedented contrast and resolution that matches image calculations.

A flexible multi-stimuli in situ (S)TEM: concept, optical performance, and outlook.

The progress in (scanning) transmission electron microscopy development had led to an unprecedented knowledge of the microscopic structure of functional materials at the atomic level. Additionally, although not widely used yet, electron holography is capable to map the electric and magnetic potential distributions at the sub-nanometer scale. Nevertheless, in situ studies inside a (scanning) transmission electron microscope ((S)TEM) are extremely challenging because of the much restricted size and accessibility of the sample space. Here, we introduce a concept for a dedicated in situ (S)TEM with a large sample chamber for flexible multi-stimuli experimental setups and report about the electron optical performance of the instrument. We demonstrate a maximum resolving power of about 1 nm in conventional imaging mode and substantially better than 5 nm in scanning mode while providing an effectively usable "pole piece gap" of 70 mm.

Atomic resolution imaging of grain boundary defects in monolayer chemical vapor deposition-grown hexagonal boron nitride.

Grain boundaries are observed and characterized in chemical vapor deposition-grown sheets of hexagonal boron nitride (h-BN) via ultra-high-resolution transmission electron microscopy at elevated temperature. Five- and seven-fold defects are readily observed along the grain boundary. Dynamics of strained regions and grain boundary defects are resolved. The defect structures and the resulting out-of-plane warping are consistent with recent theoretical model predictions for grain boundaries in h-BN.

Optimum aberration coefficients for recording high-resolution off-axis holograms in a Cs-corrected TEM.

Amongst the impressive improvements in high-resolution electron microscopy, the Cs-corrector also has significantly enhanced the capabilities of off-axis electron holography. Recently, it has been shown that the signal above noise in the reconstructable phase can be significantly improved by combining holography and hardware aberration correction. Additionally, with a spherical aberration close to zero, the traditional optimum focus for recording high-resolution holograms ("Lichte's defocus") has become less stringent and both, defocus and spherical aberration, can be selected freely within a certain range. This new degree of freedom can be used to improve the signal resolution in the holographically reconstructed object wave locally, e.g. at the atomic positions. A brute force simulation study for an aberration corrected 200 kV TEM is performed to determine optimum values for defocus and spherical aberration for best possible signal to noise in the reconstructed atomic phase signals. Compared to the optimum aberrations for conventional phase contrast imaging (NCSI), which produce "bright atoms" in the image intensity, the resulting optimum values of defocus and spherical aberration for off-axis holography enable "black atom contrast" in the hologram. However, they can significantly enhance the local signal resolution at the atomic positions. At the same time, the benefits of hardware aberration correction for high-resolution off-axis holography are preserved. It turns out that the optimum is depending on the object and its thickness and therefore not universal.

Imaging modes for potential mapping in semiconductor devices by electron holography with improved lateral resolution.

Electron holography is the highest resolving tool for dopant profiling at nanometre-scale resolution. In order to measure the object areas of interest in a hologram, both a wide field of view and a sufficient lateral resolution are required. The usual path of rays for recording holograms with an electron biprism using the standard objective lens does not meet these requirements, because the field of view amounts to some 10 nm only, however, at a resolution of 0.1 nm better than needed here. Therefore, instead of the standard objective lens, the Lorentz lens is widely used for holography of semiconductors, since it provides a field of view up to 1000 nm at a sufficient lateral resolution of about 10nm. Since the size of semiconductor structures is steadily shrinking, there is now a need for better lateral resolution at an appropriate field of view. Therefore, additional paths of rays for recording holograms are studied with special emphasis on the parameters field of view and lateral resolution. The findings allow an optimized scheme with a field of view of 200 nm and a lateral resolution of 3.3 nm filling the gap between the existing set-ups. In addition, the Lorentz lens is no longer required for investigation of non-magnetic materials, since the new paths of rays are realized with the standard objective lens and diffraction lens. An example proves the applicability of this arrangement for future semiconductor technology.

Aberration correction and electron holography.

Electron holography has been shown to allow a posteriori aberration correction. Therefore, an aberration corrector in the transmission electron microscope does not seem to be needed with electron holography to achieve atomic lateral resolution. However, to reach a signal resolution sufficient for detecting single light atoms and very small interatomic fields, the aberration corrector has turned out to be very helpful. The basic reason is the optimized use of the limited number of "coherent" electrons that are provided by the electron source, as described by the brightness. Finally, quantitative interpretation of atomic structures benefits from the holographic facilities of fine-tuning of the aberration coefficients a posteriori and from evaluating both amplitude and phase.

Off-axis electron holography in an aberration-corrected transmission electron microscope.

Electron holography allows the reconstruction of the complete electron wave, and hence offers the possibility of correcting aberrations. In fact, this was shown by means of the uncorrected CM30 Special Tübingen transmission electron microscope (TEM), revealing, after numerical aberration correction, a resolution of approximately 0.1 nm, both in amplitude and phase. However, it turned out that the results suffer from a comparably poor signal-to-noise ratio. The reason is that the limited coherent electron current, given by gun brightness, has to illuminate a width of at least four times the point-spread function given by the aberrations. As, using the hardware corrector, the point-spread function shrinks considerably, the current density increases and the signal-to-noise ratio improves correspondingly. Furthermore, the phase shift at the atomic dimensions found in the image plane also increases because the collection efficiency of the optics increases with resolution. In total, the signals of atomically fine structures are better defined for quantitative evaluation. In fact, the results achieved by electron holography in a Tecnai F20 Cs-corr TEM confirm this.

Electron holography with a Cs-corrected transmission electron microscope.

Cs correctors have revolutionized transmission electron microscopy (TEM) in that they substantially improve point resolution and information limit. The object information is found sharply localized within 0.1 nm, and the intensity image can therefore be interpreted reliably on an atomic scale. However, for a conventional intensity image, the object exit wave can still not be detected completely in that the phase, and hence indispensable object information is missing. Therefore, for example, atomic electric-field distributions or magnetic domain structures cannot be accessed. Off-axis electron holography offers unique possibilities to recover completely the aberration-corrected object wave with uncorrected microscopes and hence we would not need a Cs-corrected microscope for improved lateral resolution. However, the performance of holography is affected by aberrations of the recording TEM in that the signal/noise properties ("phase detection limit") of the reconstructed wave are degraded. Therefore, we have realized off-axis electron holography with a Cs-corrected TEM. The phase detection limit improves by a factor of four. A further advantage is the possibility of fine-tuning the residual aberrations by a posteriori correction. Therefore, a combination of both methods, that is, Cs correction and off-axis electron holography, opens new perspectives for complete TEM analysis on an atomic scale.