Intrinsic instability of aberration-corrected electron microscopes

Cost and Capability Compromises in STEM Instrumentation for Low-Voltage Imaging

Low-voltage transmission electron microscopy (≤80 kV) has many applications in imaging beam-sensitive samples, such as metallic nanoparticles, which may become damaged at higher voltages. To improve resolution, spherical aberration can be corrected for in a scanning transmission electron microscope (STEM); however, chromatic aberration may then dominate, limiting the ultimate resolution of the microscope. Using image simulations, we examine how a chromatic aberration corrector, different objective lenses, and different beam energy spreads each affect the image quality of a gold nanoparticle imaged at low voltages in a spherical aberration-corrected STEM. A quantitative analysis of the simulated examples can inform the choice of instrumentation for low-voltage imaging. We here demonstrate a methodology whereby the optimum energy spread to operate a specific STEM can be deduced. This methodology can then be adapted to the specific sample and instrument of the reader, enabling them to make an informed economical choice as to what would be most beneficial for their STEM in the cost-conscious landscape of scientific infrastructure.

Quantitative analysis of spectroscopic low energy electron microscopy data: High-dynamic range imaging, drift correction and cluster analysis

For many complex materials systems, low-energy electron microscopy (LEEM) offers detailed insights into morphology and crystallography by naturally combining real-space and reciprocal-space information. Its unique strength, however, is that all measurements can easily be performed energy-dependently. Consequently, one should treat LEEM measurements as multi-dimensional, spectroscopic datasets rather than as images to fully harvest this potential. Here we describe a measurement and data analysis approach to obtain such quantitative spectroscopic LEEM datasets with high lateral resolution. The employed detector correction and adjustment techniques enable measurement of true reflectivity values over four orders of magnitudes of intensity. Moreover, we show a drift correction algorithm, tailored for LEEM datasets with inverting contrast, that yields sub-pixel accuracy without special computational demands. Finally, we apply dimension reduction techniques to summarize the key spectroscopic features of datasets with hundreds of images into two single images that can easily be presented and interpreted intuitively. We use cluster analysis to automatically identify different materials within the field of view and to calculate average spectra per material. We demonstrate these methods by analyzing bright-field and dark-field datasets of few-layer graphene grown on silicon carbide and provide a high-performance Python implementation.

Determination of atomic-scale chemical composition at semiconductor heteroepitaxial interfaces by high-resolution transmission electron microscopy

The determination of atomic structures and further quantitative information such as chemical compositions at atomic scale for semiconductor defects or heteroepitaxial interfaces can provide direct evidence to understand their formation, modification, and/or effects on the properties of semiconductor films. The commonly used method, high-resolution transmission electron microscopy (HRTEM), suffers from difficulty in acquiring images that correctly show the crystal structure at atomic resolution, because of the limitation in microscope resolution or deviation from the Scherzer-defocus conditions. In this study, an image processing method, image deconvolution, was used to achieve atomic-resolution (∼1.0 Å) structure images of small lattice-mismatch (∼1.0%) AlN/6H-SiC (0001) and large lattice-mismatch (∼8.5%) AlSb/GaAs (001) heteroepitaxial interfaces using simulated HRTEM images of a conventional 300-kV field-emission-gun transmission electron microscope under non-Scherzer-defocus conditions. Then, atomic-scale chemical compositions at the interface were determined for the atomic intermixing and Lomer dislocation with an atomic step by analyzing the deconvoluted image contrast. Furthermore, the effect of dynamical scattering on contrast analysis was also evaluated for differently weighted atomic columns in the compositions.

A quantitative method for measuring small residual beam tilts in high-resolution transmission electron microscopy

In a transmission electron microscope, electron illumination beam tilt, or the degree of deviation of electron beam from its optical axis, is an important parameter that has a significant impact on image contrast and image interpretation. Although a large beam tilt can easily be noticed and corrected by the standard alignment procedure, a small residual beam tilt is difficult to measure and, therefore, difficult to account for quantitatively. Here we report a quantitative method for measuring small residual beam tilts, including its theoretical schemes, numerical simulation testing and experimental verification. Being independent of specimen thickness and taking specimen drifts into account in measurement, the proposed method is supplementary to the existing "rotation center" and "coma-free" alignment procedures. It is shown that this method can achieve a rather good accuracy of 94% in measuring small residual beam tilts of about 0.1° or less.

The Relationship Between Atomic Structure and Strain Distribution of Misfit Dislocation Cores at Cubic Heteroepitaxial Interfaces

The atomic reconstruction of a misfit dislocation (MD) core causes change in the strain distribution around the core. Several MD cores at the AlSb/GaAs (001) cubic zincblende interface, including a symmetrical glide set Lomer dislocation (LD), a left-displaced glide set LD, a glide set LD with an atomic step, a symmetrical shuffle set LD, and a 60° dislocation pair, were studied using simulated projected potential and aberration-corrected transmission electron microscope images. Image deconvolution was also used to restore structure images from nonoptimum-defocus images. The corresponding biaxial strain maps, ε xx (in-plane) and ε yy (out-of-plane), were obtained by geometric phase analysis using the GaAs substrate as the reference lattice. The results show that atomic structure characteristics of MD cores can be revealed by the strain maps. The strain maps should be measured from optimum-defocus images or restored structure images. Furthermore, the ε xx strain map has been found more accurate than the ε yy strain map for MD cores, and the specimen thickness should be below the critical thickness due to the influence of dynamical scattering.

Comparing Fourier optics and contrast transfer function modeling of image formation in low energy electron microscopy

A theoretical understanding of image formation in cathode lens microscopy can facilitate image interpretation. We compare Fourier Optics (FO) and Contrast Transfer Function (CTF) approaches that were recently adapted from other realms of microscopy to model image formation in low energy electron microscopy (LEEM). Although these two approaches incorporate imaging errors from several sources similarly, they differ in the way that the image intensity is calculated. The simplification that is used in the CTF calculation advantageously leads to its computational efficiency. However, we find that lens aberrations, and spatial and temporal coherence may affect the validity of the CTF approach to model LEEM image formation under certain conditions. In particular, these effects depend strongly on the nature of the object being imaged and also become more pronounced with increasing defocus. While the use of the CTF approach appears to be justified for objects that are routinely imaged with LEEM, comparison of theory to experimental observations of a focal image series for rippled, suspended graphene reveals one example where FO works, but CTF does not. This work alerts us to potential pitfalls and guides the effective use of FO and CTF approaches. It also lays the foundation for quantitative image evaluation using these methods.

Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples

We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si₃N₄ wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.

Impact of dynamical scattering on quantitative contrast for aberration-corrected transmission electron microscope images

Aberration-corrected transmission electron microscope images taken under optimum-defocus conditions or processed offline can correctly reflect the projected crystal structure with atomic resolution. However, dynamical scattering, which will seriously influence image contrast, is still unavoidable. Here, the multislice image simulation approach was used to quantify the impact of dynamical scattering on the contrast of aberration-corrected images for a 3C-SiC specimen with changes in atomic occupancy and thickness. Optimum-defocus images with different spherical aberration (CS) coefficients, and structure images restored by deconvolution processing, were studied. The results show that atomic-column positions and the atomic occupancy for SiC 'dumbbells' can be determined by analysis of image contrast profiles only below a certain thickness limit. This limit is larger for optimum-defocus and restored structure images with negative CS coefficient than those with positive CS coefficient. The image contrast of C (or Si) atomic columns with specific atomic occupancy changes differently with increasing crystal thickness. Furthermore, contrast peaks for C atomic columns overlapping with neighboring peaks of Si atomic columns with varied Si atomic occupancy, which is enhanced with increasing crystal thickness, can be neglected in restored structure images, but the effect is substantial in optimum-defocus images.

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.

eV-TEM: Transmission electron microscopy in a low energy cathode lens instrument

We are developing a transmission electron microscope that operates at extremely low electron energies, 0-40 eV. We call this technique eV-TEM. Its feasibility is based on the fact that at very low electron energies the number of energy loss pathways decreases. Hence, the electron inelastic mean free path increases dramatically. eV-TEM will enable us to study elastic and inelastic interactions of electrons with thin samples. With the recent development of aberration correction in cathode lens instruments, a spatial resolution of a few nm appears within range, even for these very low electron energies. Such resolution will be highly relevant to study biological samples such as proteins and cell membranes. The low electron energies minimize adverse effects due to radiation damage.

The correction of electron lens aberrations

The progress of electron lens aberration correction from about 1990 onwards is chronicled. Reasonably complete lists of publications on this and related topics are appended. A present for Max Haider and Ondrej Krivanek in the year of their 65th birthdays. By a happy coincidence, this review was completed in the year that both Max Haider and Ondrej Krivanek reached the age of 65. It is a pleasure to dedicate it to the two leading actors in the saga of aberration corrector design and construction. They would both wish to associate their colleagues with such a tribute but it is the names of Haider and Krivanek (not forgetting Joachim Zach) that will remain in the annals of electron optics, next to that of Harald Rose. I am proud to know that both regard me as a friend as well as a colleague.

Catadioptric aberration correction in cathode lens microscopy

In this paper I briefly review the use of electrostatic electron mirrors to correct the aberrations of the cathode lens objective lens in low energy electron microscope (LEEM) and photo electron emission microscope (PEEM) instruments. These catadioptric systems, combining electrostatic lens elements with a reflecting mirror, offer a compact solution, allowing simultaneous and independent correction of both spherical and chromatic aberrations. A comparison with catadioptric systems in light optics informs our understanding of the working principles behind aberration correction with electron mirrors, and may point the way to further improvements in the latter. With additional developments in detector technology, 1 nm spatial resolution in LEEM appears to be within reach.

Atomic resolution imaging of graphene by transmission electron microscopy

The atomic structure of a material influences its electronic, chemical, magnetic and mechanical properties. Characterising carbon nanomaterials, such as fullerenes, nanotubes and graphene, at the atomic level is challenging due to their chemical reactivity and low atomic mass. Transmission electron microscopy and scanning probe microscopy are two of the leading methods for imaging graphene at the atomic level. Here, we report on recent advances in atomic resolution imaging of graphene using aberration-corrected high resolution transmission electron microscopy and how it has revealed many of the structural deviations from the pristine monolayer form. Structures in graphene such as vacancy defects, edges, grain boundaries, linear chains, impurity dopants, layer number, layer stacking and bond rotations are explored.