Practical methods for the measurement of spatial coherence—A comparative study

A symmetry-derived mechanism for atomic resolution imaging

We introduce an image-contrast mechanism for scanning transmission electron microscopy (STEM) that derives from the local symmetry within the specimen. For a given position of the electron probe on the specimen, the image intensity is determined by the degree of similarity between the exit electron-intensity distribution and a chosen symmetry operation applied to that distribution. The contrast mechanism detects both light and heavy atomic columns and is robust with respect to specimen thickness, electron-probe energy, and defocus. Atomic columns appear as sharp peaks that can be significantly narrower than for STEM images using conventional disk and annular detectors. This fundamentally different contrast mechanism complements conventional imaging modes and can be acquired simultaneously with them, expanding the power of STEM for materials characterization.

Deep Quality Assessment of a Solar Reflector Based on Synthetic Data: Detecting Surficial Defects from Manufacturing and Use Phase

Vision technologies are used in both industrial and smart city applications in order to provide advanced value products due to embedded self-monitoring and assessment services. In addition, for the full utilization of the obtained data, deep learning is now suggested for use. To this end, the current work presents the implementation of image recognition techniques alongside the original the quality assessment of a Parabolic Trough Collector (PTC) reflector surface to locate and identify surface irregularities by classifying images as either acceptable or non-acceptable. The method consists of a three-step solution that promotes an affordable implementation in a relatively small time period. More specifically, a 3D Computer Aided Design (CAD) of the PTC was used for the pre-training of neural networks, while an aluminum reflector surface was used to verify algorithm performance. The results are promising, as this method proved applicable in cases where the actual part was manufactured in small batches or under the concept of customized manufacturing. Consequently, the algorithm is capable of being trained with a limited number of data.

Simultaneous determination of local thickness and composition for ternary III-V semiconductors by aberration-corrected STEM

Scanning transmission electron microscopy (STEM) is a suitable method for the quantitative characterization of nanomaterials. For an absolute composition determination on an atomic scale, the thickness of the specimen has to be known locally with high accuracy. Here, we propose a method to determine both thickness and composition of ternary III-V semiconductors locally from one STEM image as shown for the example material systems Ga(AsBi) and (GaIn)As. In a simulation study, the feasibility of the method is proven and the influence of specimen thickness and detector angles used is investigated. An application to an experimental STEM image of a Ga(AsBi) quantum well grown by metal organic vapour phase epitaxy yields an excellent agreement with composition results from high resolution X-ray diffraction.

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.

Image feature delocalization in defocused probe electron ptychography

Electron ptychography can in principle convert a conventional scanning electron microscope (SEM) into a good quality transmission electron microscope (TEM). An improvement in resolution of about a factor of 5 over the lens-defined resolution of an SEM was first demonstrated by Humphry et al. (2012). However, the results from that work showed some delocalization in the atomic fringes of the gold particles used as a test specimen for the technique. Here we explore factors that result in the delocalization effect when a defocused probe is used for the ptychographic data collection: source incoherence, the effects of detector faults, data truncation and a poorly calibrated illumination step size (or camera length). Various mitigation strategies are tested, including modal decomposition of the incoherence in the beam. We reprocess the data from the original SEM experiment to show that these refinements significantly improve the reconstruction.

Precise method for measuring spatial coherence in TEM beams using Airy diffraction patterns

We have developed a method to precisely measure spatial coherence in electron beams. The method does not require an electron biprism and can be implemented in existing analytical transmission electron microscopes equipped with a post-column energy filter. By fitting the Airy diffraction pattern of the selector aperture, various parameters such as geometric aberrations of the lens system and the point-spread function of the diffraction blurring are precisely determined. From the measurements of various beam diameters, components that are attributed to the partial spatial coherence are successfully separated from the point-spread functions. A linear relationship between the spatial coherence length and beam diameter is revealed, thus indicating that a wide range of coherence lengths can be determined by our proposed method as long as the coherence length remains >80% of the aperture diameter. A remarkable feature of this method is its ability to simultaneously determine diffraction blurring and lens aberrations. Possible applications of this method are also discussed.

Influence of cathode geometry on electron dynamics in an ultrafast electron microscope

Efforts to understand matter at ever-increasing spatial and temporal resolutions have led to the development of instruments such as the ultrafast transmission electron microscope (UEM) that can capture transient processes with combined nanometer and picosecond resolutions. However, analysis by UEM is often associated with extended acquisition times, mainly due to the limitations of the electron gun. Improvements are hampered by tradeoffs in realizing combinations of the conflicting objectives for source size, emittance, and energy and temporal dispersion. Fundamentally, the performance of the gun is a function of the cathode material, the gun and cathode geometry, and the local fields. Especially shank emission from a truncated tip cathode results in severe broadening effects and therefore such electrons must be filtered by applying a Wehnelt bias. Here we study the influence of the cathode geometry and the Wehnelt bias on the performance of a photoelectron gun in a thermionic configuration. We combine experimental analysis with finite element simulations tracing the paths of individual photoelectrons in the relevant 3D geometry. Specifically, we compare the performance of guard ring cathodes with no shank emission to conventional truncated tip geometries. We find that a guard ring cathode allows operation at minimum Wehnelt bias and improve the temporal resolution under realistic operation conditions in an UEM. At low bias, the Wehnelt exhibits stronger focus for guard ring than truncated tip cathodes. The increase in temporal spread with bias is mainly a result from a decrease in the accelerating field near the cathode surface. Furthermore, simulations reveal that the temporal dispersion is also influenced by the intrinsic angular distribution in the photoemission process and the initial energy spread. However, a smaller emission spot on the cathode is not a dominant driver for enhancing time resolution. Space charge induced temporal broadening shows a close to linear relation with the number of electrons up to at least 10 000 electrons per pulse. The Wehnelt bias will affect the energy distribution by changing the Rayleigh length, and thus the interaction time, at the crossover.

Ultra-high resolution electron microscopy

The last two decades have seen dramatic advances in the resolution of the electron microscope brought about by the successful correction of lens aberrations that previously limited resolution for most of its history. We briefly review these advances, the achievement of sub-Ångstrom resolution and the ability to identify individual atoms, their bonding configurations and even their dynamics and diffusion pathways. We then present a review of the basic physics of electron scattering, lens aberrations and their correction, and an approximate imaging theory for thin crystals which provides physical insight into the various different imaging modes. Then we proceed to describe a more exact imaging theory starting from Yoshioka's formulation and covering full image simulation methods using Bloch waves, the multislice formulation and the frozen phonon/quantum excitation of phonons models. Delocalization of inelastic scattering has become an important limiting factor at atomic resolution. We therefore discuss this issue extensively, showing how the full-width-half-maximum is the appropriate measure for predicting image contrast, but the diameter containing 50% of the excitation is an important measure of the range of the interaction. These two measures can differ by a factor of 5, are not a simple function of binding energy, and full image simulations are required to match to experiment. The Z-dependence of annular dark field images is also discussed extensively, both for single atoms and for crystals, and we show that temporal incoherence must be included accurately if atomic species are to be identified through matching experimental intensities to simulations. Finally we mention a few promising directions for future investigation.

Influence of spatial and temporal coherences on atomic resolution high angle annular dark field imaging

Aberration-corrected (scanning) transmission electron microscopy ((S)TEM) has become a widely used technique when information on the chemical composition is sought on an atomic scale. To extract the desired information, complementary simulations of the scattering process are inevitable. Often the partial spatial and temporal coherences are neglected in the simulations, although they can have a huge influence on the high resolution images. With the example of binary gallium phosphide (GaP) we elucidate the influence of the source size and shape as well as the chromatic aberration on the high angle annular dark field (HAADF) intensity. We achieve a very good quantitative agreement between the frozen phonon simulation and experiment for different sample thicknesses when a Lorentzian source distribution is assumed and the effect of the chromatic aberration is considered. Additionally the influence of amorphous layers introduced by the preparation of the TEM samples is discussed. Taking into account these parameters, the intensity in the whole unit cell of GaP, i.e. at the positions of the different atomic columns and in the region between them, is described correctly. With the knowledge of the decisive parameters, the determination of the chemical composition of more complex, multinary materials becomes feasible.

Quantum Confined Stark Effect in a GaAs/AlGaAs Nanowire Quantum Well Tube Device: Probing Exciton Localization

In this Letter, we explore the nature of exciton localization in single GaAs/AlGaAs nanowire quantum well tube (QWT) devices using photocurrent (PC) spectroscopy combined with simultaneous photoluminescence (PL) and photoluminescence excitation (PLE) measurements. Excitons confined to GaAs quantum well tubes of 8 and 4 nm widths embedded into an AlGaAs barrier are seen to ionize at high bias levels. Spectroscopic signatures of the ground and excited states confined to the QWT seen in PL, PLE, and PC data are consistent with simple numerical calculations. The demonstration of good electrical contact with the QWTs enables the study of Stark effect shifts in the sharp emission lines of excitons localized to quantum dot-like states within the QWT. Atomic resolution cross-sectional TEM measurements and an analysis of the quantum confined Stark effect of these dots provide insights into the nature of the exciton localization in these nanostructures.

Quantitative annular dark-field imaging of single-layer graphene-II: atomic-resolution image contrast

We have investigated how accurately atomic-resolution annular dark-field (ADF) images match between experiments and simulations to conduct more reliable crystal structure analyses. Quantitative ADF imaging, in which the ADF intensity at each pixel represents the fraction of the incident probe current, allows us to perform direct comparisons with simulations without the use of fitting parameters. Although the conventional comparison suffers from experimental uncertainties such as an amorphous surface layer and specimen thickness, in this study we eliminated such uncertainties by using a single-layer graphene as a specimen. Furthermore, to reduce image distortion and shot noises in experimental images, multiple acquisitions with drift correction were performed, and the atomic ADF contrast was quantitatively acquired. To reproduce the experimental ADF contrast, we used three distribution functions as the effective source distribution in simulations. The optimum distribution function and its full-width at half-maximum were evaluated by measuring the residuals between the experimental and simulated images. It was found that the experimental images could be explained well by a linear combination of a Gaussian function and a Lorentzian function with a longer tail than the Gaussian function.

Interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens

The interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens is examined. It is found that in general there are odd symmetries in experimental electron nanodiffraction patterns. Using simulation, it is demonstrated that this effect can be attributed to dynamical scattering, rather than other divergences from the ideal experimental conditions such as probe-forming lens aberrations and camera noise. The departure of opposing diffracted intensities from Friedel's law in the phase grating formalism is calculated using a general structure factor for disordered materials. On the basis of this, a simple correction procedure is suggested to recover the kinematical angular symmetries, and thus readily interpretable information that reflects the symmetries of the original projected object. This correction is numerically tested using both the phase object and multislice calculations, and is demonstrated to fully recover all the kinematical diffracted symmetries from a simulated atomic model of a metallic glass.

Local observation of the site occupancy of Mn in a MnFePSi compound

MnFePSi compounds are promising materials for magnetic refrigeration as they exhibit a giant magnetocaloric effect. From first principles calculations and experiments on bulk materials, it has been proposed that this is due to the Mn and Fe atoms preferentially occupying two different sites within the atomic lattice. A recently developed technique was used to deconvolve the obscuring effects of both multiple elastic scattering and thermal diffuse scattering of the probe in an atomic resolution electron energy-loss spectroscopy investigation of a MnFePSi compound. This reveals, unambiguously, that the Mn atoms preferentially occupy the 3g site in a hexagonal crystal structure, confirming the theoretical predictions. After deconvolution, the data exhibit a difference in the Fe L_{2,3} ratio between the 3f and 3g sites consistent with differences in magnetic moments calculated from first principles, which are also not observed in the raw data.

Stability of crystal facets in gold nanorods

Metal nanocrystals can be grown in a variety of shapes through the modification of surface facet energies via surfactants. However, the surface facets are only a few atoms wide, making it extremely challenging to measure their geometries and energies. Here, we locate and count atoms in Au nanorods at successive time intervals using quantitative scanning transmission electron microscopy. This enables us to determine the atomic-level geometry and the relative stability of the facets and to expound their relationship to the overall three-dimensional nanocrystal shape and size. We reveal coexisting high- and low-index facets with comparable stability and dimensions and find the geometry of the nanorods is remarkably stable, despite significant atom movements. This information provides unique insights into the mechanisms that govern growth kinetics and nanocrystal morphology.

Determination of localized visibility in off-axis electron holography

Off-axis electron holography is a wavefront-split interference method for the transmission electron microscope that allows the phase shift and amplitude of the electron wavefront to be separated and quantitatively measured. An additional, third component of the holographic signal is the coherence of the electron wavefront. Historically, wavefront coherence has been evaluated by measurement of the holographic fringe visibility (or contrast) based on the minimum and maximum intensity values. We present a method based on statistical moments is presented that allows allow the visibility to be measured in a deterministic and reproducible fashion suitable for quantitative analysis. We also present an algorithm, based on the Fourier-ratio method, which allows the visibility to be resolved in two-dimensions, which we term the local visibility. The local visibility may be used to evaluate the loss of coherence due to electron scattering within a specimen, or as an aid in image analysis and segmentation. The relationship between amplitude and visibility may be used to evaluate the composition and mass thickness of a specimen by means of a 2-D histogram. Results for a selection of elements (C, Al, Si, Ti, Cr, Cu, Ge, and Au) are provided. All presented visibility metrics are biased at low-dose conditions by the presence of shot-noise, for which we provide methods for empirical normalization to achieve linear response.

Measurement of spatial coherence of electron beams by using a small selected-area aperture

A new method for measuring the spatial coherence of an electron beam in a transmission electron microscope is proposed. In this method, an Airy pattern produced by a circular selected-area (SA) aperture with an effective diameter of several nanometers is analyzed to obtain the degree of coherence as a function of separation in the specimen plane. Using typical TEM illumination conditions, demonstrative measurements were carried out to determine the spatial coherence length, angular size of the electron source and shape of the coherence function. Based on the results, it was shown that the ratio of the spatial coherence length to the beam radius is about 5% for a condenser aperture with a diameter of 100 μm. This means that perfectly coherent illumination exists within the small SA aperture for beam diameters larger than 560 nm. As an example application of these results, the advantage of SA diffraction over nano-beam diffraction in electron diffractive imaging is discussed. The proposed method is unaffected by temporal coherence or geometric aberrations of the lenses. The possibility of carrying out future measurements using SA apertures with conventional sizes is also discussed.

Atom-scale ptychographic electron diffractive imaging of boron nitride cones

Ptychographic coherent diffractive imaging (CDI) has been extensively applied using both x rays and electrons. The extension to atomic resolution has been elusive. This Letter demonstrates ptychographic electron diffractive imaging at atomic resolution, permitting identification of structure in a boron nitride helical cone at a resolution of order 1 Å, beyond that of comparative Z-contrast images. A scanning transmission electron microscope is used to create a diverging illumination in a defocused Fresnel CDI geometry, providing a robust strategy leading to a unique solution.