Materials characterisation by angle-resolved scanning transmission electron microscopy

Element specific atom counting for heterogeneous nanostructures: Combining multiple ADF STEM images for simultaneous thickness and composition determination

In this paper, a methodology is presented to count the number of atoms in heterogeneous nanoparticles based on the combination of multiple annular dark field scanning transmission electron microscopy (ADF STEM) images. The different non-overlapping annular detector collection regions are selected based on the principles of optimal statistical experiment design for the atom-counting problem. To count the number of atoms, the total intensities of scattered electrons for each atomic column, the so-called scattering cross-sections, are simultaneously compared with simulated library values for the different detector regions by minimising the squared differences. The performance of the method is evaluated for simulated Ni@Pt and Au@Ag core-shell nanoparticles. Our approach turns out to be a dose efficient alternative for the investigation of beam-sensitive heterogeneous materials as compared to the combination of ADF STEM and energy dispersive X-ray spectroscopy.

Atom counting from a combination of two ADF STEM images

To understand the structure-property relationship of nanostructures, reliably quantifying parameters, such as the number of atoms along the projection direction, is important. Advanced statistical methodologies have made it possible to count the number of atoms for monotype crystalline nanoparticles from a single ADF STEM image. Recent developments enable one to simultaneously acquire multiple ADF STEM images. Here, we present an extended statistics-based method for atom counting from a combination of multiple statistically independent ADF STEM images reconstructed from non-overlapping annular detector collection regions which improves the accuracy and allows one to retrieve precise atom-counts, especially for images acquired with low electron doses and multiple element structures.

A decade of atom-counting in STEM: From the first results toward reliable 3D atomic models from a single projection

Quantitative structure determination is needed in order to study and understand nanomaterials at the atomic scale. Materials characterisation resulting in precise structural information is a crucial point to understand the structure-property relation of materials. Counting the number of atoms and retrieving the 3D atomic structure of nanoparticles plays an important role here. In this paper, an overview will be given of the atom-counting methodology and its applications over the past decade. The procedure to count the number of atoms will be discussed in detail and it will be shown how the performance of the method can be further improved. Furthermore, advances toward mixed element nanostructures, 3D atomic modelling based on the atom-counting results, and quantifying the nanoparticle dynamics will be highlighted.

Element Specific Atom Counting at the Atomic Scale by Combining High Angle Annular Dark Field Scanning Transmission Electron Microscopy and Energy Dispersive X-ray Spectroscopy

A new methodology is presented to count the number of atoms in multimetallic nanocrystals by combining energy dispersive X-ray spectroscopy (EDX) and high angle annular dark field scanning transmission electron microscopy (HAADF STEM). For this purpose, the existence of a linear relationship between the incoherent HAADF STEM and EDX images is exploited. Next to the number of atoms for each element in the atomic columns, the method also allows quantification of the error in the obtained number of atoms, which is of importance given the noisy nature of the acquired EDX signals. Using experimental images of an Au@Ag core-shell nanorod, it is demonstrated that 3D structural information can be extracted at the atomic scale. Furthermore, simulated data of an Au@Pt core-shell nanorod show the prospect to characterize heterogeneous nanostructures with adjacent atomic numbers.

Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution

We report a study of scattering dynamics in crystals employing momentum-resolved scanning transmission electron microscopy under varying illumination conditions. As we perform successive changes of the probe focus, multiple real-space signals are obtained in dependence of the shape of the incident electron wave. With support from extensive simulations, each signal is shown to be characterised by an optimum focus for which the contrast is maximum and which differs among different signals. For instance, a systematic focus mismatch is found between images formed by high-angle scattering, being sensitive to thickness and chemical composition, and the first moment in diffraction space, being sensitive to electric fields. It follows that a single recording at one specific probe focus is usually insufficient to characterise materials comprehensively. Most importantly, we demonstrate in experiment and simulation that the second moment μ20+μ02=〈p2〉 of the diffracted intensity exhibits a contrast maximum when the electron probe is focused at the top and bottom faces of the specimen, making the presented concept attractive for measuring local topography. Given the versatility of 〈p2〉, we furthermore present a detailed study of its large-angle convergence both analytically using the Mott scattering approach, and by dynamical simulations using the multislice algorithm including thermal diffuse scattering. Both approaches are in very good agreement and yield logarithmic divergence with increasing scattering angle.

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.

Detecting minute amounts of nitrogen in GaNAs thin films using STEM and CBED

Nitrogen (N) is a common element added to GaAs for band gap engineering and strain compensation. However, detection of small amounts of N is difficult for electron microscopy as well as for other chemical analysis techniques. In this work, N in GaAs is examined by using different transmission electron microscopy (TEM) techniques. While both dark-field TEM imaging using the composition sensitive (002) reflections and selected area diffraction reveal a significant difference between the doped thin-film and the GaAs substrate, spectroscopy techniques such as electron energy loss and energy dispersive X-ray spectroscopy are not able to detect N. To quantify the N content, quantitative convergent beam electron diffraction (QCBED) is used, which gives a direct evidence of N substitution and As vacancies. The measurements are enabled by the electron energy-filtered scanning CBED technique. These results demonstrate a sensitive method for composition analysis based on quantitative electron diffraction.

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).

Influence of plasmon excitations on atomic-resolution quantitative 4D scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) allows to gain quantitative information on the atomic-scale structure and composition of materials, satisfying one of todays major needs in the development of novel nanoscale devices. The aim of this study is to quantify the impact of inelastic, i.e. plasmon excitations (PE), on the angular dependence of STEM intensities and answer the question whether these excitations are responsible for a drastic mismatch between experiments and contemporary image simulations observed at scattering angles below \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 40 mrad. For the two materials silicon and platinum, the angular dependencies of elastic and inelastic scattering are investigated. We utilize energy filtering in two complementary microscopes, which are representative for the systems used for quantitative STEM, to form position-averaged diffraction patterns as well as atomically resolved 4D STEM data sets for different energy ranges. The resulting five-dimensional data are used to elucidate the distinct features in real and momentum space for different energy losses. We find different angular distributions for the elastic and inelastic scattering, resulting in an increased low-angle intensity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 10–40 mrad). The ratio of inelastic/elastic scattering increases with rising sample thickness, while the general shape of the angular dependency is maintained. Moreover, the ratio increases with the distance to an atomic column in the low-angle regime. Since PE are usually neglected in image simulations, consequently the experimental intensity is underestimated at these angles, which especially affects bright field or low-angle annular dark field imaging. The high-angle regime, however, is unaffected. In addition, we find negligible impact of inelastic scattering on first-moment imaging in momentum-resolved STEM, which is important for STEM techniques to measure internal electric fields in functional nanostructures. To resolve the discrepancies between experiment and simulation, we present an adopted simulation scheme including PE. This study highlights the necessity to take into account PE to achieve quantitative agreement between simulation and experiment. Besides solving the fundamental question of missing physics in established simulations, this finally allows for the quantitative evaluation of low-angle scattering, which contains valuable information about the material investigated.

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.

Using molecular dynamics for multislice TEM simulation of thermal diffuse scattering in AlGaN

For simulation of transmission electron microscopic images and diffraction patterns, the accurate inclusion of thermal diffuse scattering by phonons is important. In the frozen phonon multislice algorithm, this is possible, if thermal displacements according to the realistic, quantum mechanical distribution can be generated. For pure crystals, quantum mechanical calculations based on DFT yield those displacements. But for alloys one is usually restricted to the Einstein approximation, where correlations between atoms are neglected. In this article, molecular dynamics simulations are discussed and used as an alternative method for displacement calculation. Employing an empirical Stillinger-Weber type potential, classical motion is used as an approximation for the quantum mechanical dynamics. Thereby, correlations and possible static atomic displacements are inherently included. An appropriate potential is devised for AlGaN by fitting to force constant matrices determined from DFT and elastic constants of AlN and GaN. A comparison shows that the empiric potential reproduces phonon dispersions and displacement expectations from DFT references. The validity for alloys is successfully demonstrated by comparison to DFT calculations in special quasirandom structures. Subsequently, molecular dynamics were used in multislice simulations of both conventional and scanning TEM images. The resulting images are in very good agreement with DFT based calculations, while a slight yet significant deviation from Einstein approximation results can be seen, which can be attributed to the neglect of correlations in the latter. The presented potential hence proves to be a useful tool for accurate TEM simulations of AlGaN alloys.

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.

Composition determination of multinary III/V semiconductors via STEM HAADF multislice simulations

Knowledge of the microscopic elemental composition of multinary III/V semiconductor materials is crucial to the development of functionalized opto-electronic devices. Well-proven composition analysis methods, such as high resolution X-ray diffraction (HRXRD), fail to determine the elemental composition when more than three atomic species are involved. In this work we propose a procedure for the composition analysis of multinary III/V semiconductors at atomic resolution using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image simulations. Our method exploits the dependence of HAADF-STEM image intensities on the atomic number and static atomic displacements (SAD) at different detector inner angles. Here, we describe the proposed method in detail using Ga(NAsP) as an example multinary material.

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.