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.

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.

Addressing preservation of elastic contrast in energy-filtered transmission electron microscopy.

Energy-filtered transmission electron microscopy (EFTEM) images with resolutions of the order of an Ångström can be obtained using modern microscopes corrected for chromatic aberration. However, the delocalized nature of the transition potentials for atomic ionization often confounds direct interpretation of EFTEM images, leading to what is known as "preservation of elastic contrast". In this paper we demonstrate how more interpretable images might be obtained by scanning with a focused coherent probe and incoherently averaging the energy-filtered images over probe position. We dub this new imaging technique energy-filtered imaging scanning transmission electron microscopy (EFISTEM). We develop a theoretical framework for EFISTEM and show that it is in fact equivalent to precession EFTEM, where the plane wave illumination is precessed through a range of tilts spanning the same range of angles as the probe forming aperture in EFISTEM. It is demonstrated that EFISTEM delivers similar results to scanning transmission electron microscopy with an electron energy-loss spectrometer but has the advantage that it is immune to coherent aberrations and spatial incoherence of the probe and is also more resilient to scan distortions.

Surface determination through atomically resolved secondary-electron imaging.

Unique determination of the atomic structure of technologically relevant surfaces is often limited by both a need for homogeneous crystals and ambiguity of registration between the surface and bulk. Atomically resolved secondary-electron imaging is extremely sensitive to this registration and is compatible with faceted nanomaterials, but has not been previously utilized for surface structure determination. Here we report a detailed experimental atomic-resolution secondary-electron microscopy analysis of the c(6 × 2) reconstruction on strontium titanate (001) coupled with careful simulation of secondary-electron images, density functional theory calculations and surface monolayer-sensitive aberration-corrected plan-view high-resolution transmission electron microscopy. Our work reveals several unexpected findings, including an amended registry of the surface on the bulk and strontium atoms with unusual seven-fold coordination within a typically high surface coverage of square pyramidal TiO5 units. Dielectric screening is found to play a critical role in attenuating secondary-electron generation processes from valence orbitals.

Optimal ADF STEM imaging parameters for tilt-robust image quantification.

An approach towards experiment design and optimisation is proposed for achieving improved accuracy of ADF STEM quantification. In particular, improved robustness to small sample mis-tilts can be achieved by optimising detector collection and probe convergence angles. A decrease in cross section is seen for tilted samples due to the reduction in channelling, resulting in a quantification error, if this is not taken into account. At a smaller detector collection angle the increased contribution from elastic scattering, which initially increases with tilt, can be used to offset the decrease in the TDS signal.

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.

Direct observation of depth-dependent atomic displacements associated with dislocations in gallium nitride.

We demonstrate that the aberration-corrected scanning transmission electron microscope has a sufficiently small depth of field to observe depth-dependent atomic displacements in a crystal. The depth-dependent displacements associated with the Eshelby twist of dislocations in GaN normal to the foil with a screw component of the Burgers vector are directly imaged. We show that these displacements are observed as a rotation of the lattice between images taken in a focal series. From the sense of the rotation, the sign of the screw component can be determined.

Probe integrated scattering cross sections in the analysis of atomic resolution HAADF STEM images.

The physical basis for using a probe-position integrated cross section (PICS) for a single column of atoms as an effective way to compare simulation and experiment in high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) is described, and the use of PICS in order to make quantitative use of image intensities is evaluated. It is based upon the calibration of the detector and the measurement of scattered intensities. Due to the predominantly incoherent nature of HAADF STEM, it is found to be robust to parameters that affect probe size and shape such as defocus and source coherence. The main imaging parameter dependencies are on detector angle and accelerating voltage, which are well known. The robustness to variation in other parameters allows for a quantitative comparison of experimental data and simulation without the need to fit parameters. By demonstrating the application of the PICS to the chemical identification of single atoms in a heterogeneous catalyst and in thin, layered-materials, we explore some of the experimental considerations when using this approach.

The interaction of a nanoscale coherent helium-ion probe with a crystal.

Thickness fringing was recently observed in helium ion microscopy (HIM) when imaging magnesium oxide cubes using a 40 keV convergent probe in scanning transmission mode. Thickness fringing is also observed in electron microscopy and is due to quantum mechanical, coherent, multiple elastic scattering attenuated by inelastic phonon excitation (thermal scattering). A quantum mechanical model for elastic scattering and phonon excitation correctly models the thickness fringes formed by the helium ions. However, unlike the electron case, the signal in the diffraction plane is due mainly to the channeling of ions which have first undergone inelastic thermal scattering in the first few atomic layers so that the origin of the thickness fringes is not due to coherent interference effects. This quantum mechanical model affords insight into the interaction of a nanoscale, focused coherent ion probe with the specimen and allows us to elucidate precisely what is needed to achieve atomic resolution HIM.

Nanohalos: a manifestation of electron channelling in gold nanoparticles.

We discuss interesting haloing effects observed in experimental images of gold nanoparticles obtained using aberration-corrected scanning transmission electron microscopy (STEM) employing the low-angle annular dark-field (LAADF) imaging mode. The LAADF images contained bright rings of intensity (halos) with a diameter equal to or smaller than the diameter of the nanoparticle, the diameter varying as a function of the defocus of the STEM probe. Numerical simulations reveal that the halos are only present if the nanoparticles are imaged down a zone axis. Since the halos were observed in nearly all experimental images, this suggests that the nanoparticles become oriented along crystal zone axes during imaging.

Thermal diffuse scattering in transmission electron microscopy.

In conventional transmission electron microscopy, thermal scattering significantly affects the image contrast. It has been suggested that not accounting for this correctly is the main cause of the Stobbs factor, the ubiquitous, large contrast mismatch found between theory and experiment. In the case where a hard aperture is applied, we show that previous conclusions drawn from work using bright field scanning transmission electron microscopy and invoking the principle of reciprocity are reliable in the presence of thermal scattering. In the aperture-free case it has been suggested that even the most sophisticated mathematical models for thermal diffuse scattering lack in their numerical implementation, specifically that there may be issues in sampling, including that of the contrast transfer function of the objective lens. We show that these concerns can be satisfactorily overcome with modest computing resources; thermal scattering can be modelled accurately enough for the purpose of making quantitative comparison between simulation and experiment. Spatial incoherence of the source is also investigated. Neglect or inadequate handling of thermal scattering in simulation can have an appreciable effect on the predicted contrast and can be a significant contribution to the Stobbs factor problem.

Direct exit-wave reconstruction from a single defocused image.

We propose a direct, non-iterative method for the exact recovery of the complex wave in the exit-surface plane of a coherently illuminated object from a single defocused image. The method is applicable for a wide range of illumination conditions. The defocus range is subject to certain conditions, which if satisfied allow the complex exit-surface wave to be directly recovered by solving a set of linear equations. These linear equations, whose coefficients depend on the incident illumination, are obtained by analyzing the autocorrelation function of an auxiliary wave which is related to the exit-surface wave in a simple way. This autocorrelation is constructed by taking the inverse Fourier transform of the defocused image. We present an experimental proof of concept by recovering the exit-surface wave of a microfiber illuminated by a plane wave formed using a HeNe laser.

Scanning transmission electron microscopy imaging dynamics at low accelerating voltages.

Motivated by the desire to minimize specimen damage in beam sensitive specimens, there has been a recent push toward using relatively low accelerating voltages (<100 kV) in scanning transmission electron microscopy. To complement experimental efforts on this front, this paper seeks to explore the variations with accelerating voltage of the imaging dynamics, both of the channelling of the fast electron and of the inelastic interactions. High-angle annular-dark field, electron energy loss spectroscopic imaging and annular bright field imaging are all considered.

Contrast reversal in atomic-resolution chemical mapping.

We report an unexpected result obtained using chemical mapping on the new, aberration corrected Nion UltraSTEM at Daresbury. Using different energy windows above the L2,3 edge in 011 silicon to map the position of the atomic columns we find a contrast reversal which produces an apparent and misleading translation of the silicon columns. Using simulations of the imaging process, we explain the intricate physical mechanisms leading to this effect.

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.

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.

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.

Two-dimensional mapping of chemical information at atomic resolution.

The simultaneous measurement of structural and chemical information at the atomic scale provides fundamental insights into the connection between form and function in materials science and nanotechnology. We demonstrate structural and chemical mapping in Bi(0.5) Sr(0.5) MnO3 using an aberration-corrected scanning transmission electron microscope. Two-dimensional mapping is made possible by an adapted method for fast acquisition of electron energy-loss spectra. The experimental data are supported by simulations, which help to explain the less intuitive features.