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.     

The tuning of a Zernike phase plate with defocus and variable spherical aberration and its use in HRTEM imaging

With the advent of the double-hexapole aberration corrector in transmission electron microscopy the spherical aberration of the imaging system has become a tunable imaging parameter like the objective lens defocus. Now Zernike phase plates, altering the phase of the diffracted electron wave, can be approximated more perfectly than with the lens defocus alone, and the amount of phase change can be adjusted within wide limits. The tuning of the phase change allows an optimum contrast transfer in high-resolution imaging even for thick crystalline objects, thus surpassing the limits of the well-known Scherzer lamda/4 phase plate to the imaging of thin objects. The optimum values for the spherical aberration and the lens defocus are derived, and the limits and imperfections of the approximation explored. A mathematical link to the channelling approximation of high-energy electron diffraction shows how the image contrast of atomic columns can be improved systematically within wide thickness limits. Depending on the specimen thickness different combinations of spherical aberration and defocus are favourable: positive spherical aberration with an underfocus, zero spherical aberration with zero defocus, as well as negative spherical aberration with an overfocus.     

Structural imaging of β-Si3N4 by spherical aberration-corrected high-resolution transmission electron microscopy

Modern transmission electron microscopes (TEM) allow utilizing the spherical aberration coefficient as an additional free parameter for optimizing resolution and contrast. By tuning the spherical aberration coefficient of the objective lens, isolated nitrogen atom columns as well as the Si–N dumbbells within the six-membered ring were imaged in β-Si₃N₄ along [0 0 0 1] and [0 0 0 1¯] projections with a dumbbell spacing of 0.94 Å in white atom contrast. This has been obtained with negative or positive spherical aberration coefficient. We clarify contrast details in β-Si₃N₄ by means of extended image calculations. A simple procedure has been shown for pure phase imaging, which is restricted to linear imaging conditions.     

Quantitative atom column position analysis at the incommensurate interfaces of a (PbS)(1.14)NbS(2) misfit layered compound with aberration-corrected HRTEM

Aberration-corrected HRTEM is applied to explore the potential of NCSI contrast imaging to quantitatively analyse the complex atomic structure of misfit layered compounds and their incommensurate interfaces. Using the (PbS)_1.14NbS₂ misfit layered compound as a model system it is shown that atom column position analyses at the incommensurate interfaces can be performed with precisions reaching a statistical accuracy of ±6 pm. The procedure adopted for these studies compares experimental images taken from compound regions free of defects and interface modulations with a structure model derived from XRD experiments and with multi-slice image simulations for the corresponding NCSI contrast conditions used. The high precision achievable in such experiments is confirmed by a detailed quantitative analysis of the atom column positions at the incommensurate interfaces, proving a tetragonal distortion of the monochalcogenide sublattice.     

In-focus electron microscopy of frozen-hydrated biological samples with a Boersch phase plate

We report the implementation of an electrostatic Einzel lens (Boersch) phase plate in a prototype transmission electron microscope dedicated to aberration-corrected cryo-EM. The combination of phase plate, C_s corrector and Diffraction Magnification Unit (DMU) as a new electron-optical element ensures minimal information loss due to obstruction by the phase plate and enables in-focus phase contrast imaging of large macromolecular assemblies. As no defocussing is necessary and the spherical aberration is corrected, maximal, non-oscillating phase contrast transfer can be achieved up to the information limit of the instrument. A microchip produced by a scalable micro-fabrication process has 10 phase plates, which are positioned in a conjugate, magnified diffraction plane generated by the DMU. Phase plates remained fully functional for weeks or months. The large distance between phase plate and the cryo sample permits the use of an effective anti-contaminator, resulting in ice contamination rates of <0.6 nm/h at the specimen. Maximal in-focus phase contrast was obtained by applying voltages between 80 and 700 mV to the phase plate electrode. The phase plate allows for in-focus imaging of biological objects with a signal-to-noise of 5-10 at a resolution of 2-3 nm, as demonstrated for frozen-hydrated virus particles and purple membrane at liquid-nitrogen temperature.     

High-resolution imaging with an aberration-corrected transmission electron microscope

Recently an electromagnetic hexapole system for the correction of the spherical aberration of the objective lens of a 200 kV transmission electron microscope has been constructed by Haider and coworkers. By appropriately exciting the hexapole elements it is possible to adjust specific values of the spherical aberration coefficient ranging from the value of the original uncorrected instrument over zero even to negative values. In the first part of the paper the consequences of the tunable spherical aberration are investigated. New imaging modes are available: By adjustment of an optimum value for the spherical-aberration coefficient, the point resolution of phase-contrast imaging can be extended to the information limit. Phase-contrast imaging can be improved by a reduced level of contrast delocalisation. For zero aberration contrast delocalisation does not occur. In this case high-resolution investigations are carried out under amplitude-contrast conditions, where the local image intensity of crystalline objects is controlled by electron diffraction channelling. The defocus and spherical aberration values related to the new imaging modes are given. In the second part novel applications of the instrument to semiconductor heterostructures and ceramic grain boundaries are examined.     

Measurement of spherical aberration,beam tilt and image rotation in tem with a focussed probe

When a crystalline specimen in a transmission microscope is illuminated by a small focussed probe parallel to a zone axis, electrons diffracted at large angles by planes in higher order Laue zones (HOLZ) are imaged as a circle surrounding the direct beam. The diameter of this HOLZ image circle is directly related to the spherical aberration coefficient C_s of the objective lens. For the Philips EM430 at voltages between 50 and 300 kV, the 〈111〉 zone axis in silicon was used to measure an averaged C_s of 2.12 ± 0.04 mm. A displacement of the HOLZ image circle relative to the central probe image is attributed to a small tilt of the beam axis induced by lens interactions when switching between image and diffraction modes. This tilt could affect the quality of lattice images, where we require that both the beam and zone axes should be parallel with the optic axis. Even in an aberration-free lens, multiple diffracted images are observed when the probe is focussed and imaged in a plane below the specimen. This effect is proposed as a convenient method for measuring the direction and sign of g in two-beam defect analysis.     

Imaging of radiation-sensitive samples in transmission electron microscopes equipped with Zernike phase plates

We have optimized a bright-field transmission electron microscope for imaging of high-resolution radiation-sensitive materials by calculating the imaging dose n(0) needed to obtain a signal-to-noise ratio (SNR)=5. Installing a Zernike phase plate (ZP) decreases the dose needed to detect single atoms by as much as a factor of two at 300 kV. For imaging larger objects, such as Gaussian objects with full-width at half-maximum larger than 0.15 nm, ZP appears more efficient in reducing the imaging dose than correcting for spherical aberration. The imaging dose n(0) does not decrease with extending of chromatic resolution limit by reducing chromatic aberration, using high accelerating potential (U(0)=300 kV), because the image contrast increases slower than the reciprocal of detection radius. However, reducing chromatic aberration would allow accelerating potential to be reduced leading to imaging doses below 10 e(-)/A(2) for a single iodine atom when a CS-corrector and a ZP are used together. Our simulations indicate that, in addition to microscope hardware, optimization is heavily dependent on the nature of the specimen under investigation.     

Phase and amplitude contrast in electron microscopy of stained biological objects.

For biological objects negatively stained with heavy atom material, electron microscope images show best contrast for image detail on the scale of 10--20 A when a small objective aperture is used. In images taken under the optimum phase contrast imaging conditions of Scherzer, the required image detail is lost in unwanted noise. Both of these conditions may be described in terms of phase contrast imaging for a thin phase object. Calculations of image intensities and noise are reported for a model object consisting of heavy and light atoms randomly distributed to simulate a negatively stained protein molecule. The results are consistent with experimental observations.     

Effect of the phase shift due to dynamical scattering on the contrast of crystal structure images

The contrast of through-focus images of a niobium tungsten bronze, 2Nb₂O₅·7WO₃, taken by a 1 MV high resolution electron microscope, is discussed in terms of the transfer function, in which, in addition to the conventional phase aberration, the phase shift due to the dynamical scattering is taken into account. It is found that the phase shift may be advantagous in the formation of structure images, as long as the crystal very thin, i.e., a few nanometers in thickness. It is also made clear why the best defocus for optimum structure images differs from the Scherzer defocus, depending on the crystal thickness. An almost exact contrast reversal occurs at overfocus only in the images of extremely thin crystals, because the positive range of the transfer function is made narrower due to the above phase shift. The discussion is supported by the computer simulation of the image contrast.     

Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy

We report a local crystal structure analysis with a high precision of several picometers on the basis of scanning transmission electron microscopy (STEM). Advanced annular dark-field (ADF) imaging has been demonstrated using software-based experimental and data-processing techniques, such as the improvement of signal-to-noise ratio, the reduction of image distortion, the quantification of experimental parameters (e.g., thickness and defocus) and the resolution enhancement by maximum-entropy deconvolution. The accuracy in the atom position measurement depends on the validity of the incoherent imaging approximation, in which an ADF image is described as the convolution between the incident probe profile and scattering objects. Although the qualitative interpretation of ADF image contrast is possible for a wide range of specimen thicknesses, the direct observation of a crystal structure with deep-sub-angstrom accuracy requires a thin specimen (e.g., 10 nm), as well as observation of the structure image by conventional high-resolution transmission electron microscopy.     

Displacement field measurement of metal sub-lattice in inversion domains of indium-doped zinc oxide

The displacement field of the metal sub-lattice in homologous compounds In₂O₃(ZnO)_m is investigated by means of aberration-corrected high-resolution transmission electron microscopy. The elastic state in these compounds is characterised by plane strain where little column bending occurs due to surface relaxation. The compound contains inversion domain boundaries (IDBs) on basal and pyramidal planes of ZnO where the displacements are concentrated. The structure is imaged in <1 1¯ 0 0> of ZnO with negative spherical aberration and using bright atom contrast condition. Local atomic shifts are measured with precision of ca. 5 picometres in real space with a peak finding algorithm. The strain tensor and lattice rotations are calculated from displacements displaying dilatation, shear and rotation at pyramidal IDBs which reveal a mirror plane through the centre of each inversion domain.     

Theoretical aspects of image formation in the aberration-corrected electron microscope

The theoretical aspects of image formation in the transmission electron microscope (TEM) are outlined and revisited in detail by taking into account the elastic and inelastic scattering. In particular, the connection between the exit wave and the scattering amplitude is formulated for non-isoplanatic conditions. Different imaging modes are investigated by utilizing the scattering amplitude and employing the generalized optical theorem. A novel obstruction-free anamorphotic phase shifter is proposed which enables one to shift the phase of the scattered wave by an arbitrary amount over a large range of spatial frequencies. In the optimum case, the phase of the scattered wave and the introduced phase shift add up to −π/2 giving negative contrast. We obtain these optimum imaging conditions by employing an aberration-corrected electron microscope operating at voltages below the knock-on threshold for atom displacement and by shifting optimally the phase of the scattered electron wave. The optimum phase shift is achieved by adjusting appropriately the constant phase shift of the phase plate and the phase shift resulting from the defocus and the spherical aberration of the corrected objective lens. The realization of this imaging mode is the aim of the SALVE project (Sub-Å Low-Voltage Electron microscope).     

Direct imaging of local atomic ordering in a Pd-Ni-P bulk metallic glass using Cs-corrected transmission electron microscopy

In amorphous alloys, crystalline atomic clusters as small as 1-2 nm are frequently observed as local lattice fringe images by high-resolution electron microscopy (HREM). These clusters can be understood as local structures of amorphous alloys corresponding to "medium-range-order (MRO)". The MRO structure can be observed only under suitable defocusing conditions of the objective lens in HREM. A clear imaging of the MRO structure is difficult in conventional TEMs, mainly due to the delocalization of the image, caused mainly by the spherical aberration of the objective lens and eventually by the chosen defocus. In the present study, we have examined MRO in a Pd-based bulk metallic glass (Pd(40)Ni(40)P(20)) using a high-resolution TEM (acceleration voltage 200 kV) fitted with a spherical aberration constant corrector (Cs corrector) for aberration correction. We found that when Cs was close to zero and defocus values were near the Gaussian focus, MRO regions with an FCC-Pd structure could be clearly observed with a low image disturbance. Under these conditions, the phase-contrast transfer function was understood to act as an ideal filter function, which distinctly selects specific lattice periods of the FCC-Pd clusters. The obtained atomic images of the glass structure including the FCC-Pd clusters are in good agreement with those expected from image simulation according to our amorphous structure model. In this study, we have demonstrated that the Cs-corrected HREM is a powerful tool to directly image locally ordered structures in metallic glasses.     

Transmission electron microscopy at 20 kV for imaging and spectroscopy

The electron optical performance of a transmission electron microscope (TEM) is characterized for direct spatial imaging and spectroscopy using electrons with energies as low as 20 keV. The highly stable instrument is equipped with an electrostatic monochromator and a C_S-corrector. At 20 kV it shows high image contrast even for single-layer graphene with a lattice transfer of 213 pm (tilted illumination). For 4 nm thick Si, the 200 reflections (271.5 pm) were directly transferred (axial illumination). We show at 20 kV that radiation-sensitive fullerenes (C₆₀) within a carbon nanotube container withstand an about two orders of magnitude higher electron dose than at 80 kV. In spectroscopy mode, the monochromated low-energy electron beam enables the acquisition of EELS spectra up to very high energy losses with exceptionally low background noise. Using Si and Ge, we show that 20 kV TEM allows the determination of dielectric properties and narrow band gaps, which were not accessible by TEM so far. These very first results demonstrate that low kV TEM is an exciting new tool for determination of structural and electronic properties of different types of nano-materials.     

Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has different effects on the transfer of the linear and non-linear terms, such that the non-linear imaging contributions are damped less than the linear imaging contributions at high spatial frequencies. This will be important when coherent aberrations such as spherical aberration and defocus are reduced.     

Aspects regarding measurement of thickness of intergranular glassy films

Materials such as Si₃N₄, SiC and SrTiO₃ can have grain boundaries characterized by the presence of a thin intergranular amorphous film of nearly constant thickness, in some cases (e.g. Si₃N₄) almost independent of the orientation of the bounding grains, but dependent on the composition of the ceramic. Microscopy techniques such as high‐resolution lattice fringe imaging, Fresnel fringe imaging and diffuse dark field imaging have been applied to the study of intergranular glassy films. The theme of the current investigation is the use of Fresnel fringes and Fourier filtering for the measurement of the thickness of intergranular glassy films. Fresnel fringes hidden in high‐resolution micrographs can be used to objectively demarcate the glass–crystal interface and to measure the thickness of intergranular glassy films. Image line profiles obtained from Fourier filtering the high‐resolution micrographs can yield better estimates of the thickness. Using image simulation, various kinds of deviation from an ideal square‐well potential profile and their effects on the Fresnel image contrast are considered. A method is also put forth to objectively retrieve Fresnel fringe spacing data by Fourier filtering Fresnel contrast images. Difficulties arising from the use of the standard Fresnel fringe extrapolation technique are outlined and an alternative method for the measurement of the thickness of intergranular glassy films, based on zero‐defocus (in‐focus) Fresnel contrast images is suggested. The experimental work is from two ceramic systems: Lu‐Mg‐doped Si₃N₄ and SrTiO₃ (stoichiometric and nonstoichiometric). Further, a comparison is made between the standard high‐resolution lattice fringe technique, the standard Fresnel fringe extrapolation technique and the methods of analyses introduced in the current work, to illustrate their utility and merits. Taking experimental difficulties into account, this work is intended to be a practical tool kit for the study of intergranular glassy films.     

A new aberration-corrected,energy-filtered LEEM/PEEM instrument. I. Principles and design

We describe a new design for an aberration-corrected low energy electron microscope (LEEM) and photo electron emission microscope (PEEM), equipped with an in-line electron energy filter. The chromatic and spherical aberrations of the objective lens are corrected with an electrostatic electron mirror that provides independent control over the chromatic and spherical aberration coefficients C_c and C₃, as well as the mirror focal length, to match and correct the aberrations of the objective lens. For LEEM (PEEM) the theoretical resolution is calculated to be ∼1.5 nm (∼4 nm). Unlike previous designs, this instrument makes use of two magnetic prism arrays to guide the electron beam from the sample to the electron mirror, removing chromatic dispersion in front of the mirror by symmetry. The aberration correction optics was retrofitted to an uncorrected instrument with a base resolution of 4.1 nm in LEEM. Initial results in LEEM show an improvement in resolution to ∼2 nm.     

Extraction of structural and chemical information from high angle annular dark‐field image by an improved peaks finding method

With the development of spherical aberration (Cs) corrected scanning transmission electron microscopy (STEM), high angle annular dark filed (HAADF) imaging technique has been widely applied in the microstructure characterization of various advanced materials with atomic resolution. However, current qualitative interpretation of the HAADF image is not enough to extract all the useful information. Here a modified peaks finding method was proposed to quantify the HAADF‐STEM image to extract structural and chemical information. Firstly, an automatic segmentation technique including numerical filters and watershed algorithm was used to define the sub‐areas for each atomic column. Then a 2D Gaussian fitting was carried out to determine the atomic column positions precisely, which provides the geometric information at the unit‐cell scale. Furthermore, a self‐adaptive integration based on the column position and the covariance of statistical Gaussian distribution were performed. The integrated intensities show very high sensitivity on the mean atomic number with improved signal‐to‐noise (S/N) ratio. Consequently, the polarization map and strain distributions were rebuilt from a HAADF‐STEM image of the rhombohedral and tetragonal BiFeO₃ interface and a MnO₂ monolayer in LaAlO₃/SrMnO₃/SrTiO₃ heterostructure was discerned from its neighbor TiO₂ layers. Microsc. Res. Tech. 79:820–826, 2016. © 2016 Wiley Periodicals, Inc.     

Optimum HRTEM image contrast at 20 kV and 80 kV--exemplified by graphene

The dependence of high-resolution transmission electron microscopy (HRTEM) image contrast of graphene on the adjustable parameters of an aberration-corrected microscope operated at 80 and 20 kV has been calculated and, for 80 kV, compared with measurements. We used density functional theory to determine the projected atom potential and obtained the image intensity by averaging over the energy distribution of the imaging electrons, as derived from the electron energy loss spectroscopy measurements. Optimum image contrast has been determined as a function of energy spread of the imaging electrons and chromatic aberration coefficient, showing that significant improvement of contrast can be achieved at 80 kV with the help of a monochromator, however at 20 kV only with chromatic aberration correction and bright atom contrast conditions.