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.

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.

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).

Atomic-scale imaging of individual dopant atoms in a buried interface.

Determining the atomic structure of internal interfaces in materials and devices is critical to understanding their functional properties. Interfacial doping is one promising technique for controlling interfacial properties at the atomic scale, but it is still a major challenge to directly characterize individual dopant atoms within buried crystalline interfaces. Here, we demonstrate atomic-scale plan-view observation of a buried crystalline interface (an yttrium-doped alumina high-angle grain boundary) using aberration-corrected Z-contrast scanning transmission electron microscopy. The focused electron beam transmitted through the off-axis crystals clearly highlights the individual yttrium atoms located on the monoatomic layer interface plane. Not only is their unique two-dimensional ordered positioning directly revealed with atomic precision, but local disordering at the single-atom level, which has never been detected by the conventional approaches, is also uncovered. The ability to directly probe individual atoms within buried interface structures adds new dimensions to the atomic-scale characterization of internal interfaces and other defect structures in many advanced materials and devices.

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.

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.

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.

Volcano structure in atomic resolution core-loss images.

A feature commonly present in simulations of atomic resolution electron energy loss spectroscopy images in the scanning transmission electron microscope is the volcano or donut structure. In the past this has been understood in terms of a geometrical perspective using a dipole approximation. It is shown that the dipole approximation for core-loss spectroscopy begins to break down as the probe forming aperture semi-angle increases, necessitating the inclusion of higher order terms for a quantitative understanding of volcano formation. Using such simulations we further investigate the mechanisms behind the formation of such structures in the single atom case and extend this to the case of crystals. The cubic SrTiO3 crystal is used as a test case to show the effects of nonlocality, probe channelling and absorption in producing the volcano structure in crystal images.

Three-dimensional imaging in double aberration-corrected scanning confocal electron microscopy, part I: elastic scattering.

A transmission electron microscope fitted with both pre-specimen and post-specimen spherical aberration correctors enables the possibility of aberration-corrected scanning confocal electron microscopy. Imaging modes available in this configuration can make use of either elastically or inelastically scattered electrons. In this paper we consider image contrast for elastically scattered electrons. It is shown that there is no linear phase contrast in the confocal condition, leading to very low contrast for a single atom. Multislice simulations of a thicker crystalline sample show that sample vertical location and thickness can be accurately determined. However, buried impurity layers do not give strong, nor readily interpretable contrast. The accompanying paper examines the detection of inelastically scattered electrons in the confocal geometry.

Three-dimensional imaging in double aberration-corrected scanning confocal electron microscopy, part II: inelastic scattering.

The implementation of spherical aberration-corrected pre- and post-specimen lenses in the same instrument has facilitated the creation of sub-Angstrom electron probes and has made aberration-corrected scanning confocal electron microscopy (SCEM) possible. Further to the discussion of elastic SCEM imaging in our previous paper, we show that by performing a 3D raster scan through a crystalline sample using inelastic SCEM imaging it will be possible to determine the location of isolated impurity atoms embedded within a bulk matrix. In particular, the use of electron energy loss spectroscopy based on inner-shell ionization to uniquely identify these atoms is explored. Comparisons with scanning transmission electron microscopy (STEM) are made showing that SCEM will improve both the lateral and depth resolution relative to STEM. In particular, the expected poor resolution of STEM depth sectioning for extended objects is overcome in the SCEM geometry.

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.

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.

Imaging using inelastically scattered electrons in CTEM and STEM geometry.

It is shown that energy filtered transmission electron microscopy images are closely related to energy spectroscopic scanning transmission electron microscopy images. For the case of a single atom, we explore this similarity using both the coupled channels and density matrix approaches. We extend the result to the crystal case and find that the similarity persists, the limiting effects due to energy differences in the scattered electrons being small for typical specimen thicknesses in high-resolution transmission electron microscopy.

Depth sectioning in scanning transmission electron microscopy based on core-loss spectroscopy.

Recent and ongoing improvements in aberration correction have opened up the possibility of depth sectioning samples using the scanning transmission electron microscope in a fashion similar to the confocal scanning optical microscope. We explore questions of principle relating to image interpretability in the depth sectioning of samples using electron energy loss spectroscopy. We show that provided electron microscope probes are sufficiently fine and detector collection semi-angles are sufficiently large we can expect to locate dopant atoms inside a crystal. Furthermore, unlike high angle annular dark field imaging, electron energy loss spectroscopy can resolve dopants of smaller atomic mass than the supporting crystalline matrix.

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.

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.

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.

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.

Modelling high-resolution electron microscopy based on core-loss spectroscopy.

There are a number of factors affecting the formation of images based on core-loss spectroscopy in high-resolution electron microscopy. We demonstrate unambiguously the need to use a full nonlocal description of the effective core-loss interaction for experimental results obtained from high angular resolution electron channelling electron spectroscopy. The implications of this model are investigated for atomic resolution scanning transmission electron microscopy. Simulations are used to demonstrate that core-loss spectroscopy images formed using fine probes proposed for future microscopes can result in images that do not correspond visually with the structure that has led to their formation. In this context, we also examine the effect of varying detector geometries. The importance of the contribution to core-loss spectroscopy images by dechannelled or diffusely scattered electrons is reiterated here.