Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy.

One approach to three-dimensional structure determination using the wealth of scattering data in four-dimensional (4D) scanning transmission electron microscopy (STEM) is the parallax method proposed by Ophus et al. (2019. Advanced phase reconstruction methods enabled by 4D scanning transmission electron microscopy, Microsc Microanal25, 10-11), which determines the scattering matrix and uses it to synthesize a virtual depth-sectioning reconstruction of the sample structure. Drawing on an equivalence with a hypothetical confocal imaging mode, we derive contrast transfer and point spread functions for this parallax method applied to weakly scattering objects, showing them identical to earlier depth-sectioning STEM modes when only bright field signal is used, but that improved depth resolution is possible if dark field signal can be used. Through a simulation-based study of doped Si, we show that this depth resolution is preserved for thicker samples, explore the impact of shot noise on the parallax reconstructions, discuss challenges to making use of dark field signal, and identify cases where the interpretation of the parallax reconstruction breaks down.

Factors limiting quantitative phase retrieval in atomic-resolution differential phase contrast scanning transmission electron microscopy using a segmented detector.

Quantitative differential phase contrast imaging of materials in atomic-resolution scanning transmission electron microscopy using segmented detectors is limited by various factors, including coherent and incoherent aberrations, detector positioning and uniformity, and scan-distortion. By comparing experimental case studies of monolayer and few-layer graphene with image simulations, we explore which parameters require the most precise characterisation for reliable and quantitative interpretation of the reconstructed phases. Coherent and incoherent lens aberrations are found to have the most significant impact. For images over a large field of view, the impact of noise and non-periodic boundary conditions are appreciable, but in this case study have less of an impact than artefacts introduced by beam deflections coupling to beam scanning (imperfect tilt-shift purity).

Suppressing dynamical diffraction artefacts in differential phase contrast scanning transmission electron microscopy of long-range electromagnetic fields via precession.

It is well known that dynamical diffraction varies with changes in sample thickness and local crystal orientation (due to sample bending). In differential phase contrast scanning transmission electron microscopy (DPC-STEM), this can produce contrast comparable to that arising from the long-range electromagnetic fields probed by this technique. Through simulation we explore the scale of these dynamical diffraction artefacts and introduce a metric for the magnitude of their contribution to the contrast. We show that precession over an angular range of a few milliradian can suppress this contribution to the contrast by one-to-two orders of magnitude. Our exploration centres around a case study of GaAs near the [011] zone-axis orientation using a probe-forming aperture semiangle on the order of 0.1 mrad at 300 keV, but the trends found and methodology used are expected to apply more generally.

High contrast at low dose using a single, defocussed transmission electron micrograph.

For many soft-matter specimens, transmission electron microscopists face the double-bind of low contrast images, due to weakly-scattering specimens, alongside severe limits on the electron dose that can be used before the specimen is damaged by the electron beam. The combination of these effects causes the resultant micrographs to have very low signal-to-noise. It is well known that varying the defocus aberration can enhance image contrast in electron microscopy. For single-material objects where the variation of absorption and phase contrast are functions of one another, since both are governed by the variation in thickness profile, we show that the thickness profile can be reconstructed at very low dose. The algorithm, first established in X-ray imaging, requires some a priori information but only a single defocussed image of the region of interest, making it more dose efficient than either a conventional transport-of-intensity phase reconstruction (which would require two images and tends to amplify noise), or an absorption-contrast analysis of a single in-focus image recorded at the same electron dose (which does not benefit from the significant signal-to-noise enhancement of the present algorithm). These findings are presented through both simulations and experimental data.

Atomic resolution electron microscopy in a magnetic field free environment.

Atomic-resolution electron microscopes utilize high-power magnetic lenses to produce magnified images of the atomic details of matter. Doing so involves placing samples inside the magnetic objective lens, where magnetic fields of up to a few tesla are always exerted. This can largely alter, or even destroy, the magnetic and physical structures of interest. Here, we describe a newly developed magnetic objective lens system that realizes a magnetic field free environment at the sample position. Combined with a higher-order aberration corrector, we achieve direct, atom-resolved imaging with sub-Å spatial resolution with a residual magnetic field of less than 0.2 mT at the sample position. This capability enables direct atom-resolved imaging of magnetic materials such as silicon steels. Removing the need to subject samples to high magnetic field environments enables a new stage in atomic resolution electron microscopy that realizes direct, atomic-level observation of samples without unwanted high magnetic field effects.

Large angle illumination enabling accurate structure reconstruction from thick samples in scanning transmission electron microscopy.

Most reconstructions of the electrostatic potential of a specimen at atomic resolution assume a thin and weakly scattering sample, restricting accurate quantification to specimens only tens of Ångströms thick. We demonstrate that using large-angle-illumination scanning transmission electron microscopy (STEM)-a probe forming aperture with convergence angle larger than about 50 mrad-allows us to better meet the weak phase object approximation and thereby accurately reconstruct the electrostatic potential in samples thicker than the order of 100 Å.

Structure Retrieval at Atomic Resolution in the Presence of Multiple Scattering of the Electron Probe.

The projected electrostatic potential of a thick crystal is reconstructed at atomic resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast-readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin (≲50 Å) samples. Instruments already coming on line can overcome the remaining resolution-limiting effects in this method due to finite probe-forming aperture size, spatial incoherence, and residual lens aberrations.

A quantum mechanical exploration of phonon energy-loss spectroscopy using electrons in the aloof beam geometry.

Phonon energy-loss spectroscopy using electrons has both high resolution and low resolution components, associated with short- and long-range interactions, respectively. In this paper, we discuss how these two contributions arise from a fundamental quantum mechanical perspective. Starting from a correlated model for the atomic motion we show how short range 'impact' scattering and long range 'dipole' scattering arises. The latter dominates in aloof beam imaging, an imaging geometry in which radiation damage can be avoided.

A menu of electron probes for optimising information from scanning transmission electron microscopy.

We assess a selection of electron probes in terms of the spatial resolution with which information can be derived about the structure of a specimen, as opposed to the nominal image resolution. Using Ge [001] as a study case, we investigate the scattering dynamics of these probes and determine their relative merits in terms of two qualitative criteria: interaction volume and interpretability. This analysis provides a 'menu of probes' from which an optimum probe for tackling a given materials science question can be selected. Hollow cone, vortex and spherical wave fronts are considered, from unit cell to Ångstrom size, and for different defocus and specimen orientations.

Measuring nanometre-scale electric fields in scanning transmission electron microscopy using segmented detectors.

Electric field mapping using segmented detectors in the scanning transmission electron microscope has recently been achieved at the nanometre scale. However, converting these results to quantitative field measurements involves assumptions whose validity is unclear for thick specimens. We consider three approaches to quantitative reconstruction of the projected electric potential using segmented detectors: a segmented detector approximation to differential phase contrast and two variants on ptychographical reconstruction. Limitations to these approaches are also studied, particularly errors arising from detector segment size, inelastic scattering, and non-periodic boundary conditions. A simple calibration experiment is described which corrects the differential phase contrast reconstruction to give reliable quantitative results despite the finite detector segment size and the effects of plasmon scattering in thick specimens. A plasmon scattering correction to the segmented detector ptychography approaches is also given. Avoiding the imposition of periodic boundary conditions on the reconstructed projected electric potential leads to more realistic reconstructions.

Accuracy and precision of thickness determination from position-averaged convergent beam electron diffraction patterns using a single-parameter metric.

Position-averaged convergent beam electron diffraction patterns are formed by averaging the transmission diffraction pattern while scanning an atomically-fine electron probe across a sample. Visual comparison between experimental and simulated patterns is increasingly being used for sample thickness determination. We explore automating the comparison via a simple sum square difference metric. The thickness determination is shown to be accurate (i.e. the best-guess deduced thickness generally concurs with the true thickness), though factors such as noise, mistilt and inelastic scattering reduce the precision (i.e. increase the uncertainty range). Notably, the precision tends to be higher for smaller probe-forming aperture angles.

The atomic structure of polar and non-polar InGaN quantum wells and the green gap problem.

We have used high resolution transmission electron microscopy (HRTEM), aberration-corrected quantitative scanning transmission electron microscopy (Q-STEM), atom probe tomography (APT) and X-ray diffraction (XRD) to study the atomic structure of (0001) polar and (11-20) non-polar InGaN quantum wells (QWs). This paper provides an overview of the results. Polar (0001) InGaN in QWs is a random alloy, with In replacing Ga randomly. The InGaN QWs have atomic height interface steps, resulting in QW width fluctuations. The electrons are localised at the top QW interface by the built-in electric field and the well-width fluctuations, with a localisation energy of typically 20meV. The holes are localised near the bottom QW interface, by indium fluctuations in the random alloy, with a localisation energy of typically 60meV. On the other hand, the non-polar (11-20) InGaN QWs contain nanometre-scale indium-rich clusters which we suggest localise the carriers and produce longer wavelength (lower energy) emission than from random alloy non-polar InGaN QWs of the same average composition. The reason for the indium-rich clusters in non-polar (11-20) InGaN QWs is not yet clear, but may be connected to the lower QW growth temperature for the (11-20) InGaN QWs compared to the (0001) polar InGaN QWs.

Composition measurement in substitutionally disordered materials by atomic resolution energy dispersive X-ray spectroscopy in scanning transmission electron microscopy.

The increasing use of energy dispersive X-ray spectroscopy in atomic resolution scanning transmission electron microscopy invites the question of whether its success in precision composition determination at lower magnifications can be replicated in the atomic resolution regime. In this paper, we explore, through simulation, the prospects for composition measurement via the model system of AlxGa1-xAs, discussing the approximations used in the modelling, the variability in the signal due to changes in configuration at constant composition, and the ability to distinguish between different compositions. Results are presented in such a way that the number of X-ray counts, and thus the expected variation due to counting statistics, can be gauged for a range of operating conditions.

Influence of experimental conditions on atom column visibility in energy dispersive X-ray spectroscopy.

Here we report the influence of key experimental parameters on atomically resolved energy dispersive X-ray spectroscopy (EDX). In particular, we examine the role of the probe forming convergence semi-angle, sample thickness, lattice spacing, and dwell/collection time. We show that an optimum specimen-dependent probe forming convergence angle exists to maximize the signal-to-noise ratio of the atomically resolved signal in EDX mapping. Furthermore, we highlight that it can be important to select an appropriate dwell time to efficiently process the X-ray signal. These practical considerations provide insight for experimental parameters in atomic resolution energy dispersive X-ray analysis.

Practical aspects of diffractive imaging using an atomic-scale coherent electron probe.

Four-dimensional scanning transmission electron microscopy (4D-STEM) is a technique where a full two-dimensional convergent beam electron diffraction (CBED) pattern is acquired at every STEM pixel scanned. Capturing the full diffraction pattern provides a rich dataset that potentially contains more information about the specimen than is contained in conventional imaging modes using conventional integrating detectors. Using 4D datasets in STEM from two specimens, monolayer MoS2 and bulk SrTiO3, we demonstrate multiple STEM imaging modes on a quantitative absolute intensity scale, including phase reconstruction of the transmission function via differential phase contrast imaging. Practical issues about sampling (i.e. number of detector pixels), signal-to-noise enhancement and data reduction of large 4D-STEM datasets are emphasized.

Low magnification differential phase contrast imaging of electric fields in crystals with fine electron probes.

To correlate atomistic structure with longer range electric field distribution within materials, it is necessary to use atomically fine electron probes and specimens in on-axis orientation. However, electric field mapping via low magnification differential phase contrast imaging under these conditions raises challenges: electron scattering tends to reduce the beam deflection due to the electric field strength from what simple models predict, and other effects, most notably crystal mistilt, can lead to asymmetric intensity redistribution in the diffraction pattern which is difficult to distinguish from that produced by long range electric fields. Using electron scattering simulations, we explore the effects of such factors on the reliable interpretation and measurement of electric field distributions. In addition to these limitations of principle, some limitations of practice when seeking to perform such measurements using segmented detector systems are also discussed.

Quantitative atomic resolution elemental mapping via absolute-scale energy dispersive X-ray spectroscopy.

Quantitative agreement on an absolute scale is demonstrated between experiment and simulation for two-dimensional, atomic-resolution elemental mapping via energy dispersive X-ray spectroscopy. This requires all experimental parameters to be carefully characterized. The agreement is good, but some discrepancies remain. The most likely contributing factors are identified and discussed. Previous predictions that increasing the probe forming aperture helps to suppress the channelling enhancement in the average signal are confirmed experimentally. It is emphasized that simple column-by-column analysis requires a choice of sample thickness that compromises between being thick enough to yield a good signal-to-noise ratio while being thin enough that the overwhelming majority of the EDX signal derives from the column on which the probe is placed, despite strong electron scattering effects.

Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons.

Differential phase contrast images in scanning transmission electron microscopy can be directly and quantitatively related to the gradient of the projected specimen potential provided that (a) the specimen can be treated as a phase object and (b) full 2D diffraction patterns as a function of probe position can be obtained. Both are challenging to achieve in atomic resolution imaging. The former is fundamentally limited by probe spreading and dynamical electron scattering, and we explore its validity domain in the context of atomic resolution differential phase contrast imaging. The latter, for which proof-of-principle experimental data sets exist, is not yet routine. We explore the extent to which more established segmented detector geometries can instead be used to reconstruct a quantitatively good approximation to the projected specimen potential.

Energy dispersive X-ray analysis on an absolute scale in scanning transmission electron microscopy.

We demonstrate absolute scale agreement between the number of X-ray counts in energy dispersive X-ray spectroscopy using an atomic-scale coherent electron probe and first-principles simulations. Scan-averaged spectra were collected across a range of thicknesses with precisely determined and controlled microscope parameters. Ionization cross-sections were calculated using the quantum excitation of phonons model, incorporating dynamical (multiple) electron scattering, which is seen to be important even for very thin specimens.

Modelling the inelastic scattering of fast electrons.

Imaging at atomic resolution based on the inelastic scattering of electrons has become firmly established in the last three decades. Harald Rose pioneered much of the early theoretical work on this topic, in particular emphasising the role of phase and the importance of a mixed dynamic form factor. In this paper we review how the modelling of inelastic scattering has subsequently developed and how numerical implementation has been achieved. A software package µSTEM is introduced, capable of simulating various imaging modes based on inelastic scattering in both scanning and conventional transmission electron microscopy.