The atomic lensing model: New opportunities for atom-by-atom metrology of heterogeneous nanomaterials.

The atomic lensing model has been proposed as a promising method facilitating atom-counting in heterogeneous nanocrystals [1]. Here, image simulations will validate the model, which describes dynamical diffraction as a superposition of individual atoms focussing the incident electrons. It will be demonstrated that the model is reliable in the annular dark field regime for crystals having columns containing dozens of atoms. By using the principles of statistical detection theory, it will be shown that this model gives new opportunities for detecting compositional differences.

Single Atom Detection from Low Contrast-to-Noise Ratio Electron Microscopy Images.

Single atom detection is of key importance to solving a wide range of scientific and technological problems. The strong interaction of electrons with matter makes transmission electron microscopy one of the most promising techniques. In particular, aberration correction using scanning transmission electron microscopy has made a significant step forward toward detecting single atoms. However, to overcome radiation damage, related to the use of high-energy electrons, the incoming electron dose should be kept low enough. This results in images exhibiting a low signal-to-noise ratio and extremely weak contrast, especially for light-element nanomaterials. To overcome this problem, a combination of physics-based model fitting and the use of a model-order selection method is proposed, enabling one to detect single atoms with high reliability.

Thickness dependence of scattering cross-sections in quantitative scanning transmission electron microscopy.

In quantitative scanning transmission electron microscopy (STEM), scattering cross-sections have been shown to be very sensitive to the number of atoms in a column and its composition. They correspond to the integrated intensity over the atomic column and they outperform other measures. As compared to atomic column peak intensities, which saturate at a given thickness, scattering cross-sections increase monotonically. A study of the electron wave propagation is presented to explain the sensitivity of the scattering cross-sections. Based on the multislice algorithm, we analyse the wave propagation inside the crystal and its link to the scattered signal for the different probe positions contained in the scattering cross-section for detector collection in the low-, middle- and high-angle regimes. The influence to the signal from scattering of neighbouring columns is also discussed.

An optical configuration for fastidious STEM detector calibration and the effect of the objective-lens pre-field.

In the scanning transmission electron microscope, an accurate knowledge of detector collection angles is paramount in order to quantify signals on an absolute scale. Here we present an optical configuration designed for the accurate measurement of collection angles for both image-detectors and energy-loss spectrometers. By deflecting a parallel electron beam, carefully calibrated using a diffraction pattern from a known material, we can directly observe the projection-distortion in the post-specimen lenses of probe-corrected instruments, the 3-fold caustic when an image-corrector is fitted, and any misalignment of imaging detectors or spectrometer apertures. We also discuss for the first time, the effect that higher-order aberrations in the objective-lens pre-field has on such an angle-based detector mapping procedure.

Observation of metal nanoparticles at atomic resolution in Pt-based cancer chemotherapeutics.

The chemotherapeutics cisplatin and oxaliplatin are important tools in the fight against cancer. Both compounds are platinum complexes. Aberration-corrected scanning transmission electron microscopy using the annular dark-field imaging mode now routinely provides single-atom sensitivity with atomic number contrast. Here, this imaging mode is used to directly image the platinum within the two drugs in their dried form on an amorphous carbon support film. The oxaliplatin is found to have wetted the supporting amorphous carbon, forming disordered clusters suggesting that the platinum has remained within the complex. Conversely, the cisplatin sample reveals 1.8-nm-diameter metallic platinum clusters. The size and shape of the clusters do not appear to be dependent on drying rate nor formed by beam damage, which may suggest that they were present in the original drug solution.

Three-dimensional atomic models from a single projection using Z-contrast imaging: verification by electron tomography and opportunities.

In order to fully exploit structure-property relations of nanomaterials, three-dimensional (3D) characterization at the atomic scale is often required. In recent years, the resolution of electron tomography has reached the atomic scale. However, such tomography typically requires several projection images demanding substantial electron dose. A newly developed alternative circumvents this by counting the number of atoms across a single projection. These atom counts can be used to create an initial atomic model with which an energy minimization can be applied to obtain a relaxed 3D reconstruction of the nanoparticle. Here, we compare, at the atomic scale, this single projection reconstruction approach with tomography and find an excellent agreement. This new approach allows for the characterization of beam-sensitive materials or where the acquisition of a tilt series is impossible. As an example, the utility is illustrated by the 3D atomic scale characterization of a nanodumbbell on an in situ heating holder of limited tilt range.

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.

Quantitative STEM normalisation: The importance of the electron flux.

Annular dark-field (ADF) scanning transmission electron microscopy (STEM) has become widely used in quantitative studies based on the opportunity to directly compare experimental and simulated images. This comparison merely requires the experimental data to be normalised and expressed in units of 'fractional beam-current'. However, inhomogeneities in the response of electron detectors can complicate this normalisation. The quantification procedure becomes both experiment and instrument specific, requiring new simulations for the particular response of each instrument's detector, and for every camera-length used. This not only impedes the comparison between different instruments and research groups, but can also be computationally very time consuming. Furthermore, not all image simulation methods allow for the inclusion of an inhomogeneous detector response. In this work, we propose an alternative method for normalising experimental data in order to compare these with simulations that consider a homogeneous detector response. To achieve this, we determine the electron flux distribution reaching the detector by means of a camera-length series or a so-called atomic column cross-section averaged convergent beam electron diffraction (XSACBED) pattern. The result is then used to determine the relative weighting of the detector response. Here we show that the results obtained by this new electron flux weighted (EFW) method are comparable to the currently used method, while considerably simplifying the needed simulation libraries. The proposed method also allows one to obtain a metric that describes the quality of the detector response in comparison with the 'ideal' detector response.

Imaging screw dislocations at atomic resolution by aberration-corrected electron optical sectioning.

Screw dislocations play an important role in materials' mechanical, electrical and optical properties. However, imaging the atomic displacements in screw dislocations remains challenging. Although advanced electron microscopy techniques have allowed atomic-scale characterization of edge dislocations from the conventional end-on view, for screw dislocations, the atoms are predominantly displaced parallel to the dislocation line, and therefore the screw displacements are parallel to the electron beam and become invisible when viewed end-on. Here we show that screw displacements can be imaged directly with the dislocation lying in a plane transverse to the electron beam by optical sectioning using annular dark field imaging in a scanning transmission electron microscope. Applying this technique to a mixed [a+c] dislocation in GaN allows direct imaging of a screw dissociation with a 1.65-nm dissociation distance, thereby demonstrating a new method for characterizing dislocation core structures.

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.

Dose limited reliability of quantitative annular dark field scanning transmission electron microscopy for nano-particle atom-counting.

Quantitative annular dark field scanning transmission electron microscopy (ADF STEM) has become a powerful technique to characterise nano-particles on an atomic scale. Because of their limited size and beam sensitivity, the atomic structure of such particles may become extremely challenging to determine. Therefore keeping the incoming electron dose to a minimum is important. However, this may reduce the reliability of quantitative ADF STEM which will here be demonstrated for nano-particle atom-counting. Based on experimental ADF STEM images of a real industrial catalyst, we discuss the limits for counting the number of atoms in a projected atomic column with single atom sensitivity. We diagnose these limits by combining a thorough statistical method and detailed image simulations.

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.

Three-dimensional optical transfer functions in the aberration-corrected scanning transmission electron microscope.

In the scanning transmission electron microscope, hardware aberration correctors can now correct for the positive spherical aberration of round electron lenses. These correctors make use of nonround optics such as hexapoles or octupoles, leading to the limiting aberrations often being of a nonround type. Here we explore the effect of a number of potential limiting aberrations on the imaging performance of the scanning transmission electron microscope through their resulting optical transfer functions. In particular, the response of the optical transfer function to changes in defocus are examined, given that this is the final aberration to be tuned just before image acquisition. The resulting three-dimensional optical transfer functions also allow an assessment of the performance of a system for focal-series experiments or optical sectioning applications.

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.

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.

Aberration measurement using the Ronchigram contrast transfer function.

The bright field contrast transfer function is one of the most useful concepts in conventional transmission electron microscopy. However, the electron Ronchigram contrast transfer function, as derived by Cowley, is inherently more complicated since it is not isoplanatic. Here, we derive a local contrast transfer function for small patches in a Ronchigram and demonstrate its utility for the direct measurement of aberrations from single Ronchigrams of an amorphous film. We describe the measurement of aberrations from both simulated and experimental images and elucidate the effects due to higher-order aberrations, separating those arising from the pre- and post-sample optics, and partial coherence.

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.

Imaging modes for scanning confocal electron microscopy in a double aberration-corrected transmission electron microscope.

Aberration correction leads to reduced focal depth of field in the electron microscope. This reduced depth of field can be exploited to probe specific depths within a sample, a process known as optical sectioning. An electron microscope fitted with aberration correctors for both the pre- and postspecimen optics can be used in a confocal mode that provides improved depth resolution and selectivity over optical sectioning in the scanning transmission electron microscope (STEM). In this article we survey the coherent and incoherent imaging modes that are likely to be used in scanning confocal electron microscopy (SCEM) and provide simple expressions to describe the images that result. Calculations compare the depth response of SCEM to optical sectioning in the STEM. The depth resolution in a crystalline matrix is also explored by performing a Bloch wave calculation for the SCEM geometry in which the pre- and postspecimen optics are defocused away from their confocal conditions.