Quantitative atomic resolution mapping using high-angle annular dark field scanning transmission electron microscopy

A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.     

Column ratio mapping: a processing technique for atomic resolution high-angle annular dark-field (HAADF) images

An image processing technique is presented for atomic resolution high-angle annular dark-field (HAADF) images that have been acquired using scanning transmission electron microscopy (STEM). This technique is termed column ratio mapping and involves the automated process of measuring atomic column intensity ratios in high-resolution HAADF images. This technique was developed to provide a fuller analysis of HAADF images than the usual method of drawing single intensity line profiles across a few areas of interest. For instance, column ratio mapping reveals the compositional distribution across the whole HAADF image and allows a statistical analysis and an estimation of errors. This has proven to be a very valuable technique as it can provide a more detailed assessment of the sharpness of interfacial structures from HAADF images. The technique of column ratio mapping is described in terms of a [110]-oriented zinc-blende structured AlAs/GaAs superlattice using the 1 angstroms-scale resolution capability of the aberration-corrected SuperSTEM 1 instrument.     

Essential experimental parameters for quantitative structure analysis using spherical aberration-corrected HAADF-STEM

The accuracy of quantitative analysis for Z-contrast images with a spherical aberration (C_s) corrected high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) using SrTiO₃(0 0 1) was systematically investigated. Atomic column and background intensities were measured accurately from the experimental HAADF-STEM images obtained under exact experimental condition. We examined atomic intensity ratio dependence on experimental conditions such as defocus, convergent semi-angles, specimen thicknesses and digitalized STEM image acquisition system: brightness and contrast. In order to carry out quantitative analysis of C_s-corrected HAADF-STEM, it is essential to determine defocus, to measure specimen thickness and to fix setting of brightness, contrast and probe current. To confirm the validity and accuracy of the experimental results, we compared experimental and HAADF-STEM calculations based on the Bloch wave method.     

High-angle annular dark-field STEM imaging of immunogold labels

High-angle annular dark-field (HAADF) STEM imaging is a sensitive and efficient technique for detecting immunogold labels. Larger (5–15 nm) gold labels can be distinguished clearly from the heavy metal stain on tissue sections, but for smaller (<5 nm) labels the distinction is less clear. It is not possible to differentiate between ultra-small (<1–3 nm) labels and stain, but the HAADF image shows sufficient contrast so specimens can remain unstained. On a TEM/STEM equipped with a LaB₆ filament the smallest labels that are detectable are 1–2 nm. Efficient detection of ultra-small labels requires a field emission microscope.     

A practical approach for STEM image simulation based on the FFT multislice method

It has been demonstrated that a high-angle annular dark-field (HAADF) STEM technique gives an image resolving atomic columns. Due to the diffusion of this technique and an improvement of its resolution, a practical procedure for image simulation becomes important for a quantitative interpretation of the HAADF image. In this report a new practical scheme for a STEM image simulation is developed based on the FFT multislice algorithm. Here, a HAADF intensity due to thermal diffuse scattering (TDS) is calculated from the absorptive potential corresponding to high-angle TDS and the wave function equivalent to the propagating probe within the sample. Contrary to the commonly used Bloch wave method, a coherent bright-field intensity and a coherent HAADF intensity are also obtained straightforwardly. The HAADF image contrast calculated for GaAs is not simply proportional to Z2 as expected from the Rutherford scattering at high-angle, and the As/Ga contrast ratio depends on the specimen thickness. This suggests that the generation of the HAADF signal is appreciably affected by the coherent dynamical scattering. The developed procedure here will have a definitive advantage over the Bloch wave approach for simulating the HAADF images expected from a defect and interface or amorphous materials, and also the HAADF image obtained by using a Cs-corrected microscope. This is because the former requires a huge super cell, while the latter needs a large objective aperture including a large number of incident beam directions.     

An expanded approach to noise reduction from high-resolution STEM images based on the maximum entropy method

An expanded use of the maximum entropy method (MEM) is suggested to reduce noise from an experimental high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) image. The MEM is combined with an estimate of the standard deviation of noise from an experimental HAADF STEM image and low-pass filtering using the information limit for an incoherent STEM image. Consequently, the present method has just one parameter of a Lagrange multiplier. It is demonstrated that the present method can reduce noise efficiently in high-resolution HAADF STEM images.     

High-Angle annular dark-field imaging on a tem/stem system

The technique of high-angle annular dark-field (HAADF) imaging, which is highly sensitive to atomic-number contrast, can be performed on TEM/STEM systems using the standard annular dark-field detector. For optimum HAADF imaging, the TEM/STEM must have a high maximum diffraction angle, small minimum camera length, and a descanning facility. The sensitivity of the technique is demonstrated to be about 10⁵ to 10⁶ times higher than energy-dispersive X-ray spectroscopy. Examples are shown from semiconductor, catalysis, ceramics, and particle analysis applications.     

StripeSTEM, a technique for the isochronous acquisition of high angle annular dark-field images and monolayer resolved electron energy loss spectra

A technique capable of producing monolayer resolved electron energy loss (EEL) spectroscopy data along one direction in crystal structures is introduced. Unambiguous assignment of EEL spectra to atomic planes is possible via the execution of high angle annular dark-field (HAADF) imaging and EEL spectrum acquisition in parallel. The recording of instrumental instabilities in the HAADF image during the measurement enables a proper quantification by virtue of post-acquisition correction. Compared to the conventional line profile technique a dose reduction by several orders of magnitude can be achieved. The technique is applied to bulk SrTiO₃ and ZnO:In₂O₃in order to explore its capabilities and limits. Monolayer resolution was achieved for the Ti–L₂₃ and In–M₄₅ core-losses. Multislice calculations were carried out for the purpose of assessing the residual delocalisation of the inelastic signal. Fundamental limits to the resolution are imposed by dynamical dispersion of the electron wave in the crystal combined with the extension of the inelastic potential. In the present case, owing to the requirement of a high beam current, the geometrical probe size cannot be neglected when compared to the width of an inelastic scattering potential.     

Deconvolution processing of HAADF STEM images

A deconvolution processing of high-resolution high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images, combined with maximum entropy method, is applied to two experimental [0 11]-Si images; one having unresolved dumbbells and the other having resolved dumbbells and artificial bright spots. The deconvoluted images for these images show bright spots corresponding to the projected atomic columns and no artificial bright spots. Thus, the deconvolution processing provides almost a real projected atomic structure by eliminating effects of the probe function from HAADF STEM images.     

Imaging of high-angle annular dark-field scanning transmission electron microscopy and observations of GaN-based violet laser diodes

The first part of this paper is devoted to physics, to explain high‐angle annular dark‐field scanning transmission electron microscopy (HAADF‐STEM) imaging and to interpret why HAADF‐STEM imaging is incoherent, instructing a strict definition of interference and coherence of electron waves. Next, we present our recent investigations of InGaN/GaN multiple quantum wells and AlGaN/GaN strained‐layer superlattice claddings in GaN‐based violet laser diodes, which have been performed by HAADF‐STEM and high‐resolution field‐emission gun scanning electron microscopy.     

Supported metal sulphide nanoclusters studied by HAADF-STEM

The morphology of MoS₂ and WS₂ nanoclusters supported on high‐surface area graphitic carbon was investigated using high angular annular dark field scanning transmission electron microscopy (HAADF‐STEM). Most of the MoS₂ (WS₂) nanoclusters contain only a single S‐Mo‐S (S‐W‐S) layer and the most commonly encountered morphology is truncated triangular. This is in contrast to the hexagonal morphology of macroscopic MoS₂ (WS₂) crystals. When in addition to molybdenum (tungsten), nickel is also present, the regular nanoclusters are truncated to a larger extent, indicating that Ni has influenced the morphology by the formation of so‐called Ni‐Mo‐S (Ni‐W‐S) structures. For these structures, the additional truncations are observed to lead to dodecahedral‐like shapes.     

The structure and continuous stoichiometry change of 1DTbBrx@SWCNTs

HRTEM and HAADF STEM of 1DTbBr_x@SWCNT meta‐nanotubes reveal three structural modifications of 1D nanocrystals within single wall carbon nanotube channels attributed to a different stoichiometry of the guest crystal. For SWCNTs with diameters D_m > 1.4 nm a most complete tetragonal unit cell is observed. When crystallization occurs inside SWCNT with D_m < 1.4 nm 1D TbBr_x crystal deforms a nanotube to elliptical shape in cross section. In this case the 1D crystal unit cell becomes monoclinic, with possible loss of a part of bromine atoms. Two modifications of a monoclinic unit cell appear. One of them is characterized by single or pair vacancies in the structure of the 1D crystal. Another structure is explained by peripheral and central bromine atoms loss. An appearance of such modifications can be stimulated by electron irradiation. The loss of bromine atoms is in agreement with chemical analysis data. Electronic properties of obtained meta‐nanotubes are investigated using optical absorption and Raman spectroscopy. It is shown that intercalation of terbium bromide into SWCNTs leads to acceptor doping of SWCNTs. According to local EDX analysis and elemental mapping this doping can arise from significant stoichiometry change in 1D nanocrystal indicating an average Tb:Br atomic ratio of 1:2.8 ± 0.1.     

Morphology visualization of irregular shape bacteria by electron holography and tomography

In the current work, irregular morphology of Staphylococcus aureus bacteria has been visualized by phase retrieval employing off‐axis electron holography (EH) and 3D reconstruction electron tomography using high‐angle annular dark field scanning transmission electron microscopy (HAADF‐STEM). Bacteria interacting with gold nanoparticles (AuNP) acquired a shrunken or irregular shape due to air dehydration processing. STEM imaging shows the attachment of AuNP on the surface of cells and suggests an irregular 3D morphology of the specimen. The phase reconstruction demonstrates that off‐axis electron holography can reveal with a single hologram the morphology of the specimen and the distribution of the functionalized AuNPs. In addition, EH reduces significantly the acquisition time and the cumulative radiation damage (in three orders of magnitude) over biological samples in comparison with multiple tilted electron expositions intrinsic to electron tomography, as well as the processing time and the reconstruction artifacts that may arise during tomogram reconstruction.     

Bloch-wave-based STEM image simulation with layer-by-layer representation

In a dynamical STEM image simulation by the Bloch-wave method, Allen et al. formulated a framework for calculating the cross-section for any incoherent scattering process from the inelastic scattering coefficients: thermal diffuse scattering (TDS) for high-angle annular dark-field (HAADF) and back-scattered electron (BSE) STEM, and ionization for electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDX) STEM. Furthermore, their method employed a skilful approach for deriving the excitation amplitude and block diagonalization in the eigenvalue equation. In the present work, we extend their scheme to a layer-by-layer representation for application to inhomogeneous crystals that include precipitates, defects and atomic displacement. Calculations for a multi-layer sample of Si–Sb–Si were performed by multiplying Allen et al.'s block-diagonalized matrices. Electron intensities within the sample and EDX STEM images, as an example of the inelastic scattering, were calculated at various conditions. From the calculations, 3-dimensional STEM analysis was considered.     

IMAGE-WARP: a real-space restoration method for high-resolution STEM images using quantitative HRTEM analysis

We have developed a new method for processing distorted high-resolution scanning transmission electron microscopy (STEM) images. The method is based on finding the displaced vertices in the experimental STEM image and warping to geometrically correct reference grid of the object. As a reference grid for warping a structural model obtained using a high-resolution transmission electron microscopy (HRTEM) analysis of the area of interest is utilised. Combined with quantitative HRTEM analysis the IMAGE-WARP method provides a real-space restoration of high-resolution high-angle annular dark-field (HAADF) STEM images without affecting the original Z-contrast information. The method can be applied to extract valuable compositional atomic-column data from any HAADF-STEM image of any kind of bulk crystals with local occupancy or chemistry fluctuations, stacking faults, special grain boundaries or interfaces, for which we have an available structural model. After the warping, distortion-corrected images can be further enhanced using conventional image-filtering techniques, and finally quantified with HAADF-STEM image simulations. The applicability of the IMAGE-WARP method was illustrated using experimental HAADF-STEM images of a strontium titanate crystal disrupted with a Ruddlesden-Popper-type antiphase boundary.     

Symmetries in BF and HAADF STEM image calculations

Reductions in bright-field (BF) scanning transmission electron microscopy (STEM) and high-angle annular dark-field (HAADF) STEM image calculations with the aid of Bloch wave symmetry are discussed under assumptions that an absorption potential is written by a local potential and a zero-order Laue zone lies parallel to the crystal surface. Translational symmetry allows us to take only partial incident beams in the first Brillouin zone instead of enormous number of partial incident beams in a large convergent disk. Two dimensional point group confines partial incident beams to an irreducible area in addition to factoring a dispersion matrix into noninteracting submatrices on a high symmetry line using the projection operator. The drastic reductions in computing time and memory enable us to readily calculate various BF STEM and HAADF STEM images. The validity and accuracy are demonstrated in comparisons with high resolution experimental BF STEM and HAADF STEM images.     

Compositional analysis of mixed–cation-anion III–V semiconductor interfaces using phase retrieval high-resolution transmission electron microscopy

Employing exit‐plane wave function (EPWF) reconstruction in high‐resolution transmission electron microscopy (HRTEM), we have developed an approach to atomic scale compositional analysis of III‐V semiconductor interfaces, especially suitable for analyzing quaternary heterostructures with intermixing in both cation and anion sub‐lattices. Specifically, we use the focal‐series reconstruction technique, which retrieves the complex‐valued EPWF from a thru‐focus series of HRTEM images. A study of interfaces in Al_0.4Ga_0.6As–GaAs and In_0.25Ga_0.75Sb–InAs heterostructures using focal‐series reconstruction shows that change in chemical composition along individual atomic columns across an interface is discernible in the phase image of the reconstructed EPWF. To extract the interface composition profiles along the cation and anion sub‐lattices, quantitative analysis of the phase image is performed using factorial analysis of correspondence. This enabled independent quantification of changes in the In–Ga and As–Sb contents across ultra‐thin interfacial regions (approximately 0.6 nm wide) with true atomic resolution, in the In_0.25Ga_0.75Sb–InAs heterostructure. The validity of the method is demonstrated by analyzing simulated HRTEM images of an InAs–GaSb–InAs model structure with abrupt and graded interfaces. Our approach is general, permitting atomic‐level compositional analysis of heterostructures with two species per sub‐lattice, hitherto unfeasible with existing HRTEM methods.     

Comparison of intensity distributions in tomograms from BF TEM,ADF STEM,HAADF STEM,and calculated tilt series

The three-dimensional (3D) morphology of a nanometer-sized object can be obtained using electron tomography. Variations in composition or density of the object cause variations in the reconstructed intensity. When imaging homogeneous objects, variations in reconstructed intensity are caused by the imaging technique, imaging conditions, and reconstruction. In this paper, we describe data acquisition, image processing, and 3D reconstruction to obtain and compare tomograms of magnetite crystals from bright field (BF) transmission electron microscopy (TEM), annular dark-field (ADF) scanning transmission electron microscopy (STEM), and high-angle annular dark field (HAADF) STEM tilt series. We use histograms, which plot the number of volume elements (voxels) at a given intensity vs. the intensity, to measure and quantitatively compare intensity distributions among different tomograms. In combination with numerical simulations, we determine the influence of maximum tilt angle, tilt increment, contrast changes with tilt (diffraction contrast), and the signal-to-noise ratio (SNR) as well as the choice of the reconstruction approach (weighted backprojection (WB) and sequential iterative reconstruction technique (SIRT)) on the histogram. We conclude that because ADF and HAADF STEM techniques are less affected by diffraction, and because they have a higher SNR than BF TEM, they are better suited for tomography of nanometer-sized crystals.