Thermal vibrations in convergent-beam electron diffraction

Modelling dynamical 3D electron diffraction intensities. I. A scattering cluster algorithm

Three-dimensional electron diffraction (3D-ED) is a powerful technique for crystallographic characterization of nanometre-sized crystals that are too small for X-ray diffraction. For accurate crystal structure refinement, however, it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D-ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Proposed here is an alternative method, the `scattering cluster algorithm' (SCA), that replaces the eigen-decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by intensity transfer (i.e. `scattering') from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to the multislice approach. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA are demonstrated on tri-isopropyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells.

Modelling dynamical 3D electron diffraction intensities. II. The role of inelastic scattering

The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave-Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.

Modeling Temperature-Dependent Electron Thermal Diffuse Scattering via Machine-Learned Interatomic Potentials and Path-Integral Molecular Dynamics

Electron thermal diffuse scattering is shown to be sensitive to subtle changes in atomic vibrations and shows promise in assessing lattice dynamics at nanometer resolution. Here, we demonstrate that machine-learned interatomic potentials (MLIPs) and path-integral molecular dynamics can accurately capture the potential energy landscape and lattice dynamics needed to describe electron thermal diffuse scattering. Using SrTiO_{3} as a test bed at cryogenic and room temperatures, we compare electron thermal diffuse scattering simulations using different approximations to incorporate thermal motion. Only when the simulations are based on quantum mechanically accurate MLIPs in combination with path-integral molecular dynamics that include nuclear quantum effects is there excellent agreement with experiments.

Quantifying Molecular Disorder in Tri-Isopropyl Silane (TIPS) Pentacene Using Variable Coherence Transmission Electron Microscopy

Structural disorder in molecular crystals is a fundamental limitation for achieving high charge carrier mobilities. Quantifying and uncovering the mechanistic origins of disorder are, however, extremely challenging. Here we use variable coherence transmission electron microscopy to analyze disorder in tri-isopropyl silane pentacene films, utilizing diffuse scattering that is present both as linear streaks and as a slowly varying, isotropic background. The former is due to thermal vibration of the pentacene molecules along their long axis, while the latter is due to static defects kinetically frozen during film deposition. The thermal vibrational amplitude is ∼0.4 Å, while the static displacement parameter in our simplified analysis is much larger (1.0 Å), because it represents the cumulative scattering of all defect configurations that are frozen in the film. Thin film fabrication therefore has an important effect on crystallinity; our technique can be readily used to compare samples prepared under different conditions.

A "Phase Scrambling" Algorithm for Parallel Multislice Simulation of Multiple Phonon and Plasmon Scattering Configurations

Multislice simulations of 4D scanning transmission electron microscopy (4D STEM) data are computationally demanding due to the large number of STEM probe positions that must be calculated. For accurate analysis, inelastic scattering from phonons and plasmons must also be included. However, current frozen phonon and Monte Carlo plasmon techniques require a separate calculation for each different phonon/plasmon configuration, and are therefore not suitable for scaling up to 4D STEM. Here a phase scrambling algorithm (PSA) is proposed, which treats all phonon/plasmon configurations simultaneously. A random phase is introduced to maintain incoherence between the different inelastic scattering events; this is the phase scrambling part of the algorithm. While for most applications, a few tens of frozen phonon iterations are sufficient for convergence, in the case of plasmon scattering as many as tens of thousands of iterations may be required. A PSA is statistically more representative of inelastic scattering, and achieves significant savings in computation time for plasmons. The increase in speed is a pre-requisite for 4D STEM inelastic scattering simulations.

Towards Electron Energy Loss Compton Spectra Free From Dynamical Diffraction Artifacts

The Compton signal in electron energy loss spectroscopy (EELS) is used to determine the projected electron momentum density of states for the solid. A frequent limitation however is the strong dynamical scattering of the incident electron beam within a crystalline specimen, i.e. Bragg diffracted beams can be additional sources of Compton scattering that distort the measured profile from its true shape. The Compton profile is simulated via a multislice method that models dynamical scattering both before and after the Compton energy loss event. Simulations indicate the importance of both the specimen illumination condition and EELS detection geometry. Based on this, a strategy to minimize diffraction artifacts is proposed and verified experimentally. Furthermore, an inversion algorithm to extract the projected momentum density of states from a Compton measurement performed under strong diffraction conditions is demonstrated. The findings enable a new route to more accurate electron Compton data from crystalline specimens.

Scattering angle dependence of temperature susceptivity of electron scattering in scanning transmission electron microscopy

The sensitivity of electron scattering to sample temperature (T) as a function of the scattering angle in scanning transmission electron microscopy (STEM) is investigated. Thermal vibration of atoms in crystal lattice results in attenuated Bragg reflections and a diffuse background in electron diffraction patterns, which have direct implications on STEM images. The scattering intensities at higher angle are known to be dominated by thermal diffuse scattering (TDS) and the column intensity is expected to have a negative correlation with increasing T because of the disrupted channeling, but the T susceptivity of the scattering intensity at smaller angles is less known. Our experiment shows that the T dependency of annular averaged diffraction intensity inverts its sign two times outside the direct beam, and the T sensitivity varies significantly as a function of scattering angle. The intensity shows a positive correlation with increasing T at the low to intermediate angular ranges before it returns to the negative correlation at the higher angle range. A reasonable agreement is found between the experimental data and multislice simulation data. Absorptive model is used to provide theoretical insights into the observed trends. Similar inversions of T dependency of column intensities are also observed in experimental and simulated atomic-resolution STEM images. The findings provide an important implication to the precise quantification of local T at high spatial resolution by optimizing the collection angles in STEM.

Optimization of imaging conditions for composition determination by annular dark field STEM

Quantitative scanning transmission electron microscopy (STEM) allows composition determination for nanomaterials at an atomic scale. To improve the accuracy of the results obtained, optimized imaging parameters should be chosen for annular dark field imaging. In a simulation study, we investigate the influence of imaging parameters on the accuracy of the composition determination with the example of ternary III-V semiconductors. It is shown that inner and outer detector angles and semi-convergence angle can be optimized, also in dependence on specimen thickness. Both, a minimum sampling of the image and a minimum electron dose are required. These findings are applied experimentally by using a fast pixelated detector to allow free choice of detector angles.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

A local structure analysis method based on convergent-beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low-order structure factors with sin θ/λ ≤ 0.28 Å^-1 of potassium tantalate (KTaO₃). Comparison between structure factors determined from CBED patterns taken at the zone-axis (ZA) and Bragg-excited conditions is made in order to discuss their precision and sensitivities. Bragg-excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg-excited CBED patterns has been found only for structure factors of the outer zeroth-order Laue-zone reflections with larger reciprocal-lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg-excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors.

Angle-resolved STEM using an iris aperture: Scattering contributions and sources of error for the quantitative analysis in Si

The angle-resolved electron scattering is investigated in scanning-transmission electron microscopy (STEM) using a motorised iris aperture placed above a conventional annular detector. The electron intensity scattered into various angle ranges is compared with simulations that were carried out in the frozen-lattice approximation. As figure of merit for the agreement of experiment and simulation we evaluate the specimen thickness which is compared with the thickness obtained from position-averaged convergent beam electron diffraction (PACBED). We find deviations whose strengths depend on the angular range of the detected electrons. As possible sources of error we investigate, for example, the influences of amorphous surface layers, inelastic scattering (plasmon excitation), phonon-correlation within the frozen-lattice approach, and distortions in the diffraction plane of the microscope. The evaluation is performed for four experimental thicknesses and two angle-resolved STEM series under different camera lengths. The results clearly show that especially for scattering angles below 50 mrad, it is mandatory that the simulations take scattering effects into account which are usually neglected for simulating high-angle scattering. Most influences predominantly affect the low-angle range, but also high scattering angles can be affected (e.g. by amorphous surface covering).

Inelastic Scattering in Electron Backscatter Diffraction and Electron Channeling Contrast Imaging

Electron backscatter diffraction (EBSD) and electron channeling contrast imaging (ECCI) are used to extract crystallographic information from bulk samples, such as their crystal structure and orientation as well as the presence of any dislocation and grain boundary defects. These techniques rely on the backscattered electron signal, which has a large distribution in electron energy. Here, the influence of plasmon excitations on EBSD patterns and ECCI dislocation images is uncovered by multislice simulations including inelastic scattering. It is shown that the Kikuchi band contrast in an EBSD pattern for silicon is maximum at small energy loss (i.e., few plasmon scattering events following backscattering), consistent with previous energy-filtered EBSD measurements. On the other hand, plasmon excitation has very little effect on the ECCI image of a dislocation. These results are explained by examining the role of the characteristic plasmon scattering angle on the intrinsic contrast mechanisms in EBSD and ECCI.

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.

Layer Dependence of Dielectric Response and Water-Enhanced Ambient Degradation of Highly Anisotropic Black As

Black arsenic (BAs) is a van der Waals layered material with a puckered honeycomb structure and has received increased interest due to its anisotropic properties and promising performance in devices. Here, crystalline structure, thickness-dependent dielectric responses, and ambient stability of BAs nanosheets are investigated using scanning transmission electron microscopy (STEM) imaging and spectroscopy. Atomic-resolution high-angle annular dark-field (HAADF)-STEM images directly visualize the three-dimensional structure and evaluate the degree of anisotropy. STEM-electron energy loss spectroscopy is used to measure the dielectric response of BAs as a function of the number of layers. Finally, BAs degradation under different ambient environments is studied, highlighting high sensitivity to moisture in the air.

Theory underpinning multislice simulations with plasmon energy losses

The theoretical conditions for small-angle inelastic scattering where the incident electron can effectively be treated as a particle moving in a uniform potential is examined. The motivation for this work is the recent development of a multislice method that combines plasmon energy losses with elastic scattering using Monte Carlo methods. Since plasmon excitation is delocalized, it was assumed that the Bloch wave nature of the incident electron in the crystal does not affect the scattering cross-section. It is shown here that for a delocalized excitation the mixed dynamic form factor term of the scattering cross-section is zero and the scattered intensities follow a Poisson distribution. These features are characteristic of particle-like scattering and validate the use of Monte Carlo methods to model plasmon losses in multislice simulations.

Efficient and Versatile Model for Vibrational STEM-EELS

We introduce a novel method for the simulation of the impact scattering in vibrational scanning transmission electron microscopy electron energy loss spectroscopy simulations. The phonon-loss process is modeled by a combination of molecular dynamics and elastic multislice calculations within a modified frozen phonon approximation. The key idea is thereby to use a so-called δ thermostat in the classical molecular dynamics simulation to generate frequency dependent configurations of the vibrating specimen's atomic structure. The method includes correlated motion of atoms and provides vibrational spectrum images at a cost comparable to standard frozen phonon calculations. We demonstrate good agreement of our method with simulations and experiments for a 15 nm flake of hexagonal boron nitride.

Quantifying oxygen distortions in lithium-rich transition-metal-oxide cathodes using ABF STEM

Lithium-rich cathodes can store excess charge beyond the transition metal redox capacity by participation of oxygen in reversible anionic redox reactions. Although these processes are crucial for achieving high energy densities, their structural origins are not yet fully understood. Here, we explore the use of annular bright-field (ABF) imaging in scanning transmission electron microscopy (STEM) to measure oxygen distortions in charged Li_1.2Ni_0.2Mn_0.6O₂. We show that ABF STEM data can provide positional accuracies below 20 pm but this is restricted to cases where no specimen mistilt is present, and only for a range of thicknesses above 3.5 nm. The reliability of these measurements is compromised even when the experimental and post-processing designs are optimised for accuracy and precision, indicating that extreme care must be taken when attempting to quantify distortions in these materials.

Unconventional Defects in a Quasi-One-Dimensional KMn6Bi5

Quasi-one-dimensional (Q1D) structures comprising a compact array of indefinitely long 1D nanowires (NWs) are scarce, especially in a bulk device-scale showing metallic and semiconducting behaviors along different axes. Unlike plentiful observations of nature of defects in three-/two-dimensional materials, there is a notable paucity of such reports in Q1D. Herein we present unconventional motific defects and their properties in a bulk Q1D KMn₆Bi₅ crystal, in which an individual NW motif acts as one body. We discovered motific inter- and intra-NW defects, such that a linear set of 1D motifs are displaced. Stress generates two domains with altered inter-NW spacings and a Bi-Mn solid solution grain, leading to a local bulk plasmon shift due to NW array reconfiguration as well as atomic rearrangement. The observation of such exotic defects and associated phenomena in this Q1D may provide guidance on overall defect mechanism in other Q1D systems and their collective anisotropic properties.

Wave-packet numerical investigation of thermal diffuse scattering: A time-dependent quantum approach to electron diffraction simulations

The effects of thermal diffuse scattering on diffraction of highly-accelerated electrons by crystal lattices are investigated with a method that combines the frozen phonon approximation with an exact numerical solution of the time-dependent Schrödinger equation. The phonon configuration for each single-electron diffraction process is determined by means of Einstein's model. It is shown that this procedure provides the possibility of describing and explaining, in a natural way, after averaging over a number of electron realizations, how the typical diffraction features that characterize a fully coherent pattern are gradually suppressed by thermally-induced incoherence. This is achieved by a controlled increase of the lattice atomic vibrations and is in contrast to the use of attenuating Debye-Waller factors and complex potential absorbers. A lattice with reduced dimensionality is first considered as a working model, where the method renders results compatible with those reported in the literature. Subsequently, a full three-dimensional system is simulated and results are compared to experimental imaging displaying the method's reliability.

Inelastic scattering and solvent scattering reduce dynamical diffraction in biological crystals

Multi-slice simulations of electron diffraction by three-dimensional protein crystals have indicated that structure solution would be severely impeded by dynamical diffraction, especially when crystals are more than a few unit cells thick. In practice, however, dynamical diffraction turned out to be less of a problem than anticipated on the basis of these simulations. Here it is shown that two scattering phenomena, which are usually omitted from multi-slice simulations, reduce the dynamical effect: solvent scattering reduces the phase differences within the exit beam and inelastic scattering followed by elastic scattering results in diffusion of dynamical scattering out of Bragg peaks. Thus, these independent phenomena provide potential reasons for the apparent discrepancy between theory and practice in protein electron crystallography.

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.

Subatomic Channeling and Helicon-Type Beams in SrTiO_{3}

Inspired by recent experimental subatomic measurements using analytical aberration-corrected scanning transmission electron microscopes, we study electron probe propagation in crystalline SrTiO_{3} at the subatomic length scale. Here, we report the existence of subatomic channeling and the formation of a helicon-type beam at this scale. The results of beam propagation simulations, which are performed at various crystal temperatures, STEM probe convergence angles (10-50 mrad), and beam energies (80-300 keV), showed that reducing the ambient temperature can enhance the subatomic channeling and STEM probe parameters can be used to control the features of helicon-type beams.

Phonon Spectroscopy at Atomic Resolution

Advances in source monochromation in transmission electron microscopy have opened up new possibilities for investigations of condensed matter using the phonon-loss sector of the energy-loss spectrum. Here, we explore the spatial variations of the spectrum as an atomic-sized probe is scanned across a thin flake of hexagonal boron nitride. We demonstrate that phonon spectral mapping of atomic structure is possible. These results are consistent with a model for the quantum excitation of phonons and confirm that Z-contrast imaging is based on inelastic scattering associated with phonon excitation.

Hollow Electron Ptychographic Diffractive Imaging

We report a method for quantitative phase recovery and simultaneous electron energy loss spectroscopy analysis using ptychographic reconstruction of a data set of "hollow" diffraction patterns. This has the potential for recovering both structural and chemical information at atomic resolution with a new generation of detectors.

Atomic-scale 3D reconstruction of antiphase boundaries in GaP on (001) silicon by STEM

In order to overcome the limitations of silicon-based electronics, the integration of optically active III-V compounds is a promising approach. Nonetheless, their integration is far from trivial and control as well as understanding of corresponding growth kinetics, and in particular the occurrence and termination of antiphase defects, is of great relevance. In this work, we focus on the three-dimensional reconstruction of such boundaries in gallium phosphide from single scanning transmission electron microscopy images. In the high angle annular dark-field imaging mode, the appearance of these antiphase boundaries is strongly determined by the chemical composition of each atomic column and reflects the ratio of transmitted anti- to mainphase. Therefore it is possible to translate measured intensities to the depth location of these boundaries by utilizing simulation data. The necessary spatial resolution for these column-by-column mappings is achieved via electron optical aberration correction within the microscope. Hence, the complete 3D orientation of these defects can be measured at atomic resolution and correlated to growth parameters. Finally, we present a method to reconstruct large areas from well sampled images and retrieve information about complex embedded nanoscale structures at the atomic scale.

Thickness and Stacking Sequence Determination of Exfoliated Dichalcogenides (1T-TaS2, 2H-MoS2) Using Scanning Transmission Electron Microscopy

Layered transition metal dichalcogenides (TMDs) have attracted interest due to their promise for future electronic and optoelectronic technologies. As one approaches the two-dimensional (2D) limit, thickness and local topology can greatly influence the macroscopic properties of a material. To understand the unique behavior of TMDs it is therefore important to identify the number of atomic layers and their stacking in a sample. The goal of this work is to extract the thickness and stacking sequence of TMDs directly by matching experimentally recorded high-angle annular dark-field scanning transmission electron microscope images and convergent-beam electron diffraction (CBED) patterns to quantum mechanical, multislice scattering simulations. Advantageously, CBED approaches do not require a resolved lattice in real space and are capable of neglecting the thickness contribution of amorphous surface layers. Here we demonstrate the crystal thickness can be determined from CBED in exfoliated 1T-TaS2 and 2H-MoS2 to within a single layer for ultrathin ≲9 layers and ±1 atomic layer (or better) in thicker specimens while also revealing information about stacking order-even when the crystal structure is unresolved in real space.

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.

Accuracy of surface strain measurements from transmission electron microscopy images of nanoparticles

Strain analysis from high-resolution transmission electron microscopy (HRTEM) images offers a convenient tool for measuring strain in materials at the atomic scale. In this paper we present a theoretical study of the precision and accuracy of surface strain measurements directly from aberration-corrected HRTEM images. We examine the influence of defocus, crystal tilt and noise, and find that absolute errors of at least 1–2% strain should be expected. The model structures include surface relaxations determined using molecular dynamics, and we show that this is important for correctly evaluating the errors introduced by image aberrations.

Frozen lattice and absorptive model for high angle annular dark field scanning transmission electron microscopy: A comparison study in terms of integrated intensity and atomic column position measurement

In this paper, both the frozen lattice (FL) and the absorptive potential (AP) approximation models are compared in terms of the integrated intensity and the precision with which atomic columns can be located from an image acquired using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM). The comparison is made for atoms of Cu, Ag, and Au. The integrated intensity is computed for both an isolated atomic column and an atomic column inside an FCC structure. The precision has been computed using the so-called Cramér-Rao Lower Bound (CRLB), which provides a theoretical lower bound on the variance with which parameters can be estimated. It is shown that the AP model results into accurate measurements for the integrated intensity only for small detector ranges under relatively low angles and for small thicknesses. In terms of the attainable precision, both methods show similar results indicating picometer range precision under realistic experimental conditions.

Simplifying Electron Beam Channeling in Scanning Transmission Electron Microscopy (STEM)

Sub-angstrom scanning transmission electron microscopy (STEM) allows quantitative column-by-column analysis of crystalline specimens via annular dark-field images. The intensity of electrons scattered from a particular location in an atomic column depends on the intensity of the electron probe at that location. Electron beam channeling causes oscillations in the STEM probe intensity during specimen propagation, which leads to differences in the beam intensity incident at different depths. Understanding the parameters that control this complex behavior is critical for interpreting experimental STEM results. In this work, theoretical analysis of the STEM probe intensity reveals that intensity oscillations during specimen propagation are regulated by changes in the beam's angular distribution. Three distinct regimes of channeling behavior are observed: the high-atomic-number (Z) regime, in which atomic scattering leads to significant angular redistribution of the beam; the low-Z regime, in which the probe's initial angular distribution controls intensity oscillations; and the intermediate-Z regime, in which the behavior is mixed. These contrasting regimes are shown to exist for a wide range of probe parameters. These results provide a new understanding of the occurrence and consequences of channeling phenomena and conditions under which their influence is strengthened or weakened by characteristics of the electron probe and sample.

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.

Influence of surface relaxation of strained layers on atomic resolution ADF imaging

Surface relaxation of thin transmission electron microscopy (TEM) specimens of strained layers results in a severe bending of lattice planes. This bending significantly displaces atoms from their ideal channeling positions which has a strong impact on the measured annular dark field (ADF) intensity. With the example of GaAs quantum wells (QW) embedded in a GaP barrier, we model the resulting displacements by elastic theory using the finite element (FE) formalism. Relaxed and unrelaxed super cells served as input for state of the art frozen phonon simulation of atomic resolution ADF images. We systematically investigate the dependencies on the sample´s geometric parameters, i.e. QW width and TEM sample thickness, by evaluating the simulated intensities at the atomic column´s positions as well as at the background positions in between. Depending on the geometry the ADF intensity can be affected in a range several nm from the actual interface. Moreover, we investigate the influence of the surface relaxation on the angular distribution of the scattered intensity. At high scattering angles we observe an intensity reduction at the interface as well as in the GaP barrier due to de-channeling. The amount of intensity reduction at an atomic column is directly proportional to its mean square displacement. On the contrary we find a clearly increased intensity at low angles caused by additional diffuse scattering. We discuss the implications for quantitative evaluations as well as strategies to compensate for the reduced intensities.

On the role of the second-order derivative term in the calculation of convergent beam diffraction patterns

The simulation of (scanning) transmission electron microscopy images and diffraction patterns is most often performed using the forward-scattering approximation where the second-order derivative term in z is assumed to be small with respect to the first-order derivative term in the modified Schrödinger equation. This assumption is very good at high incident electron energies, but breaks down at low energies. In order to study the differences between first- and second-order methods, convergent beam electron diffraction patterns were simulated for silicon at the [111] zone-axis orientation at 20 keV and compared using electron intensity difference maps and integrated intensity profiles. The geometrical differences in the calculated diffraction patterns could be explained by an Ewald surface analysis. Furthermore, it was found that solutions based on the second-order derivative equation contained small amplitude oscillations that need to be resolved in order to ensure numerical integration stability. This required the use of very small integration steps resulting in significantly increased computation time compared to the first-order differential equation solution. Lastly, the efficiency of the numerical integration technique is discussed.

Effects of small-angle mistilts on dopant visibility in ADF-STEM imaging of nanocrystals

Quantitative ADF-STEM imaging paired with image simulations has proven to be a powerful technique for determining the three dimensional location of substitutionally doped atoms in thin films. Expansion of this technique to lightly-doped nanocrystals requires an understanding of the influence of specimen mistilt on dopant visibility due to the difficulty of accurate orientation determination in such systems as well as crystal movement under the beam. In this study, the effects of specimen mistilt on ADF-STEM imaging are evaluated using germanium-doped silicon nanocrystals as model systems. It is shown that dopant visibility is a strong function of specimen mistilt, and the accuracy of specimen orientation is an important factor in the analysis of three-dimensional dopant location, but the sensitivity to mistilt can be weakened by increasing the STEM probe convergence angle and optimizing ADF detector inner angle.

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.

Materials characterisation by angle-resolved scanning transmission electron microscopy

Solid-state properties such as strain or chemical composition often leave characteristic fingerprints in the angular dependence of electron scattering. Scanning transmission electron microscopy (STEM) is dedicated to probe scattered intensity with atomic resolution, but it drastically lacks angular resolution. Here we report both a setup to exploit the explicit angular dependence of scattered intensity and applications of angle-resolved STEM to semiconductor nanostructures. Our method is applied to measure nitrogen content and specimen thickness in a GaN_xAs_1-x layer independently at atomic resolution by evaluating two dedicated angular intervals. We demonstrate contrast formation due to strain and composition in a Si- based metal-oxide semiconductor field effect transistor (MOSFET) with Ge_xSi_1-x stressors as a function of the angles used for imaging. To shed light on the validity of current theoretical approaches this data is compared with theory, namely the Rutherford approach and contemporary multislice simulations. Inconsistency is found for the Rutherford model in the whole angular range of 16-255 mrad. Contrary, the multislice simulations are applicable for angles larger than 35 mrad whereas a significant mismatch is observed at lower angles. This limitation of established simulations is discussed particularly on the basis of inelastic scattering.

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.

Reducing dynamic disorder in small-molecule organic semiconductors by suppressing large-amplitude thermal motions

Thermal vibrations and the dynamic disorder they create can detrimentally affect the transport properties of van der Waals bonded molecular semiconductors. The low-energy nature of these vibrations makes it difficult to access them experimentally, which is why we still lack clear molecular design rules to control and reduce dynamic disorder. In this study we discuss the promising organic semiconductors rubrene, 2,7-dioctyl[1]benzothieno[3,2-b][1]benzothio-phene and 2,9-di-decyl-dinaphtho-[2,3-b:20,30-f]-thieno-[3,2-b]-thiophene in terms of an exceptionally low degree of dynamic disorder. In particular, we analyse diffuse scattering in transmission electron microscopy, to show that small molecules that have their side chains attached along the long axis of their conjugated core are better encapsulated in their crystal structure, which helps reduce large-amplitude thermal motions. Our work provides a general strategy for the design of new classes of very high mobility organic semiconductors with a low degree of dynamic disorder.

Thermal vibration is harmful to charge transport in molecular semiconductors, which hinders the use of these materials in flexible electronics. Here, Illig et al. show that the vibration is suppressed when molecular side chains are attached to the long axis of conjugated cores.

Computation in electron microscopy

Some uses of the computer and computation in high-resolution transmission electron microscopy are reviewed. The theory of image calculation using Bloch wave and multislice methods with and without aberration correction is reviewed and some applications are discussed. The inverse problem of reconstructing the specimen structure from an experimentally measured electron microscope image is discussed. Some future directions of software development are given.