Sub-Angstrom high-resolution transmission electron microscopy at 300 keV

Determination of the point resolution of high-resolution transmission electron microscope using the through-focus technique

From the viewpoint of evaluating the instrumental performance of high-resolution electron microscopy (HREM), the Scherzer condition was investigated using information theory. As a result, the optimum defocus amount Δf can be expressed based on [Formula: see text] , and the formula [Formula: see text] is obtained. Furthermore, a procedure for measuring point resolution using the through-focus technique is developed, and a new method for determining the spherical aberration coefficient using the variance of Δf is introduced in the procedure.

The Relevance of Building an Appropriate Environment around an Atomic Resolution Transmission Electron Microscope as Prerequisite for Reliable Quantitative Experiments: It Should Be Obvious, but It Is a Subtle Never-Ending Story!

The realization of electron microscopy facilities all over the world has experienced a paramount increase in the last decades. This means huge investments of public and private money due to the high costs of equipment, but also for maintenance and running costs. The proper design of a transmission electron microscopy facility is mandatory to fully use the advanced performances of modern equipment, capable of atomic resolution imaging and spectroscopies, and it is a prerequisite to conceive new methodologies for future advances of the knowledge. Nonetheless, even today, in too many cases around the world, the realization of the environment hosting the equipment is not appropriate and negatively influences the scientific quality of the results during the life of the infrastructure, practically vanishing the investment made. In this study, the key issues related to the realization of an advanced electron microscopy infrastructure are analyzed based on personal experience of more than thirty years, and on the literature.

The influence of chromatic aberration on the dose-limited spatial resolution of transmission electron microscopy

The effect of chromatic aberration (CC) on the spatial resolution in transmission electron microscopy (TEM) was studied in thick specimens in which the sample becomes the limiting factor in the resolution. The sample influences the energy spread of the electron beam, allows only a limited electron dose, and modulates electron scattering events. The experimental set-up consisted of a thin silicon nitride membrane and a silicon wedge containing gold nanoparticles. The resolution was measured as a function of electron dose and sample thickness for different sample configurations and for different microscopy modalities including regular TEM, energy filtered TEM (EFTEM) and CC-corrected TEM. Comparison with an analytical model aided the understanding of the experimental data applied over varied conditions. The general trend for all microscopy modalities was a transition from a noise-limited resolution at low electron dose to a CC-limited resolution at high-dose in the absence of beam blurring. EFTEM required an accurate energy slit offset and an optimal energy spread to energy-slit width ratio to surpass regular TEM. The key advantage of CC correction appeared to be the best possible resolution for larger sample thickness at low electron dose outperforming EFTEM by about fifty percent. Several hypothetical sample configurations relevant to liquid phase electron microscopy were evaluated as well to demonstrate the capabilities of the analytical model and to determine the most optimal microscopy modality for this type of experiment. The analytical model included an automated optimization of the EFTEM settings and may aid in optimizing the sample-limited resolution for experimental analysis and planning.

Low-energy electron irradiation induced synthesis of molecular nanosheets: influence of the electron beam energy

Aromatic self-assembled monolayers (SAMs) can be cross-linked into molecular nanosheets - carbon nanomembranes (CNMs) -via low-energy electron irradiation. Due to their favorable mechanical stability and tunable functional properties, they possess a high potential for various applications including nanosensors and separation membranes for osmosis or energy conversion devices. Despite this potential, the mechanistic details of the electron irradiation induced cross-linking process still need to be understood in more detail. Here, we studied the cross-linking of 4'-nitro-1,1'-biphenyl-4-thiol SAM on gold. The SAM samples were irradiated with different electron energies ranging from 2.5 to 100 eV in ultra-high vacuum and subsequently analysed by complementary techniques. We present results obtained via spectroscopy and microscopy characterization by high-resolution X-ray photoelectron spectroscopy (XPS), low-energy electron diffraction with micrometre sized electron beams (μLEED) and low-energy electron microscopy (LEEM). To demonstrate the formation of CNMs, the formed two-dimensional molecular materials were transferred onto grids and oxidized wafer and analyzed by optical, scanning electron microscopy (SEM) and atomic force microscopy (AFM). We found a strong energy dependence for the cross section for the cross-linking process, the rate of which decreases exponentially towards lower electron energies by about four orders of magnitude. We conduct a comparative analysis of the cross sections for the C-H bond scission via electron impact ionization and dissociative electron attachment and find that these different ionization mechanisms are responsible for the variation of the cross-linking cross section with electron energy.

Modulating electron density of vacancy site by single Au atom for effective CO2 photoreduction

The surface electron density significantly affects the photocatalytic efficiency, especially the photocatalytic CO₂ reduction reaction, which involves multi-electron participation in the conversion process. Herein, we propose a conceptually different mechanism for surface electron density modulation based on the model of Au anchored CdS. We firstly manipulate the direction of electron transfer by regulating the vacancy types of CdS. When electrons accumulate on vacancies instead of single Au atoms, the adsorption types of CO₂ change from physical adsorption to chemical adsorption. More importantly, the surface electron density is manipulated by controlling the size of Au nanostructures. When Au nanoclusters downsize to single Au atoms, the strong hybridization of Au 5d and S 2p orbits accelerates the photo-electrons transfer onto the surface, resulting in more electrons available for CO₂ reduction. As a result, the product generation rate of Au_SA/Cd_1−xS manifests a remarkable at least 113-fold enhancement compared with pristine Cd_1−xS.

The electron density of reactive sites significantly affects catalytic performances. Here, authors demonstrate the electron density of different reactive sites can be modulated by regulating the type of vacancy and the size of Au, leading to effective CO₂ photoreduction.

An ImageJ tool for simplified post-treatment of TEM phase contrast images (SPCI)

Tools for taking advantage of phase-contrast in transmission electron microscopy are of great interest for both biological and material sciences studies as shown by the recent use of phase plates and the development of holography. Nevertheless, these tools most often require highly qualified experts and access to advanced equipment that can only be considered after preliminary investigations. Here we propose to address this issue by the development of an ImageJ plugin that allow the retrieval of a phase image by simple numerical treatment applied to two defocused images. This treatment based on Tikhonov regularization requires the adjustment of a single parameter. Moreover, it is possible to use this approach on one-image. Although in that case the retrieved image gives only qualitative information, it is able to enhance the image contrast appropriately. This can be of interest for specimens producing low contrast images under the electron microscopes, such as some frozen hydrated biological samples or those sensible to electron radiation unsuitable for holographic studies.

Analytical ABF-STEM imaging of Li ions in rechargeable batteries

Rechargeable batteries are being intensively investigated in an attempt to solve the energy issues while meeting the environmental demands. Even though Li-ion batteries (LIB) with high energy and light weight have been commercialized within the last 20 years, these devices currently require higher energy density, output power and sustainability characteristics. The atomic behavior of Li ion that determines LIB's performance is hardly characterized by transmission electron microscopy (TEM) owing to its weak electron-scattering power. In this sense, annular bright-field (ABF) scanning TEM (STEM), in which the contrast has a low scaling rate with the atomic number, has been proven to be a robust technique for simultaneous imaging of light and heavy elements. The s-state model, in which electron channeling along the atomic column allows the intensity to be focusing in the forward direction, has successfully explained the theory of ABF contrast. Furthermore, the detector angle range, the defocus-thickness dependence and the accelerating voltage (among other parameters) were discussed for optimized imaging conditions. ABF-STEM has shown powerful capabilities in resolving the atomic structure and the chemistry of electrodes (e.g. Li-ion occupation and diffusion, phase transformation and interface reaction), thereby providing critical insights into the physical properties, the battery performance and the design guidance of LIB. The future directions of ABF imaging for the characterization of LIB materials were also reviewed.

Atomic-scale structure evolution in a quasi-equilibrated electrochemical process of electrode materials for rechargeable batteries

Lithium-ion batteries have proven to be extremely attractive candidates for applications in portable electronics, electric vehicles, and smart grid in terms of energy density, power density, and service life. Further performance optimization to satisfy ever-increasing demands on energy storage of such applications is highly desired. In most of cases, the kinetics and stability of electrode materials are strongly correlated to the transport and storage behaviors of lithium ions in the lattice of the host. Therefore, information about structural evolution of electrode materials at an atomic scale is always helpful to explain the electrochemical performances of batteries at a macroscale. The annular-bright-field (ABF) imaging in aberration-corrected scanning transmission electron microscopy (STEM) allows simultaneous imaging of light and heavy elements, providing an unprecedented opportunity to probe the nearly equilibrated local structure of electrode materials after electrochemical cycling at atomic resolution. Recent progress toward unraveling the atomic-scale structure of selected electrode materials with different charge and/or discharge state to extend the current understanding of electrochemical reaction mechanism with the ABF and high angle annular dark field STEM imaging is presented here. Future research on the relationship between atomic-level structure evolution and microscopic reaction mechanisms of electrode materials for rechargeable batteries is envisaged.

Maintaining the genuine structure of 2D materials and catalytic nanoparticles at atomic resolution

The recent development of atomic resolution, low dose-rate electron microscopy allows investigating 2D materials as well as catalytic nano particles without compromising their structural integrity. For graphene and a variety of nanoparticle compositions, it is shown that a critical dose rate exists of <100 e(-)/Å(2) s at 80 keV of electron acceleration that allows maintaining the genuine object structures including their surfaces and edges even if particles are only 3 nm large or smaller. Moreover, it is demonstrated that electron beam-induced phonon excitation from outside the field of view contributes to a contrast degradation in recorded images. These degradation effects can be eliminated by delivering electrons onto the imaged area, only, by using a Nilsonian illumination scheme in combination with a suitable aperture at the electron gun/monochromator assembly.

Atomic resolution phase contrast imaging and in-line holography using variable voltage and dose rate

The TEAM 0.5 electron microscope is employed to demonstrate atomic resolution phase contrast imaging and focal series reconstruction with acceleration voltages between 20 and 300 kV and a variable dose rate. A monochromator with an energy spread of ≤0.1 eV is used for dose variation by a factor of 1,000 and to provide a beam-limiting aperture. The sub-Ångstrøm performance of the instrument remains uncompromised. Using samples obtained from silicon wafers by chemical etching, the [200] atom dumbbell distance of 1.36 Å can be resolved in single images and reconstructed exit wave functions at 300, 80, and 50 kV. At 20 kV, atomic resolution <2 Å is readily available but limited by residual lens aberrations at large scattering angles. Exit wave functions reconstructed from images recorded under low dose rate conditions show sharper atom peaks as compared to high dose rate. The observed dose rate dependence of the signal is explained by a reduction of beam-induced atom displacements. If a combined sample and instrument instability is considered, the experimental image contrast can be matched quantitatively to simulations. The described development allows for atomic resolution transmission electron microscopy of interfaces between soft and hard materials over a wide range of voltages and electron doses.

APPLICATION OF EXIT-PLANE WAVE FUNCTION IMAGES IN HIGH-RESOLUTION TRANSMISSION ELECTRON MICROSCOPY FOR QUANTITATIVE ANALYSIS OF III–V SEMICONDUCTOR INTERFACES

An image simulation study is performed to investigate the applicability of exit-plane wave function (EPWF) images for an atomic-level compositional mapping of interfaces in the GaAs – AlAs system. A simple procedure for quantifying the composition across an interface, which is based on the method of factorial analysis of correspondence is proposed. A test of this procedure on a simulated EPWF-phase image of Al 0.4 Ga 0.6 As/GaAs/Al 0.4 Ga 0.6 As structure, with an atomically abrupt interface on one side and a graded interface on the other, yields profiles which mimic the model-profiles.

Direct imaging of hydrogen-atom columns in a crystal by annular bright-field electron microscopy

Enhancing the imaging power of microscopy to identify all chemical types of atom, from low- to high-atomic-number elements,would significantly contribute for a direct determination of material structures. Electron microscopes have successfully provided images of heavy-atom positions, particularly by the annular dark-field method, but detection of light atoms was difficult owing to their weak scattering power. Recent developments of aberration-correction electron optics have significantly advanced the microscope performance, enabling identification of individual light atoms such as oxygen, nitrogen, carbon, boron and lithium. However, the lightest hydrogen atom has not yet been observed directly, except in the specific condition of hydrogen adatoms on a graphene membrane. Here we show the first direct imaging of the hydrogen atom in a crystalline solid YH(2), based on a classic 'hollow-cone' illumination theory combined with state-of-the-art scanning transmission electronmicroscopy. The optimized hollow-cone condition derived from the aberration-corrected microscope parameters confirms that the information transfer can be extended to 22.5 nm(-1), which corresponds to a spatial resolution of about 44.4 pm. These experimental conditions can be readily realized with the annular bright-field imaging in scanning transmission electron microscopy according to reciprocity, revealing successfully the hydrogen-atom columns as dark dots, as anticipated from phase contrast of a weak-phase object.

Quantitative HRTEM investigation of an obtuse angle dislocation reaction in gold with a CScorrected field emission microscope

We investigate quantitatively the non periodic arrangement of atom columns surrounding an obtuse angle dislocation reaction in gold utilizing a CM200 FEG instrument equipped with a spherical aberration corrector. The in-plane component of the Burgers vector of the observed stair-rod dislocation is ⅙ [110]. Column positions are determined from single lattice images and compared with those from a reconstructed electron exit wave. We find that absolute position measurements of 1–3 pm require knowledge of the defocus to better than 1 nm which can be achieved by a reconstruction of the exit-plane wave. In contrast, a defocus value of 8.9 nm already leads to apparent displacements as large as 35 pm if single lattice images are considered. Such discrepancies are either caused by residual lens aberrations or by the superposition of delocalization effects at interfaces caused by defocusing of the objective lens. Commonly, however, only relative displacements are of interest. In this case the CS corrector improves the interpretability of single defocused lattice images with a remarkable signal to noise ratio which is advantageous for in-situ experiments. As an example for analyzing in-situ experiments we determine displacements recorded in a time resolved experiment of radiation induced atom motion on surfaces.

Microstructure and a nucleation mechanism for nanoprecipitates in PbTe-AgSbTe2

Many recent advances in thermoelectric (TE) materials are attributed to their nanoscale constituents. Determination of the nanocomposite structures has represented a major experimental and computational challenge and eluded previous attempts. Here we present the first atomically resolved structures of high performance TE material PbTe-AgSbTe2 by transmission electron microscopy imaging and density functional theory calculations. The results establish an accurate structural characterization for PbTe-AgSbTe2 and identify the interplay of electric dipolar interactions and strain fields as the driving mechanism for nanoprecipitate nucleation and aggregation.

Multiply twinned morphologies of FePt and CoPt nanoparticles

Based on large-scale density functional theory calculations we provide a systematic overview of the size dependence of the energetic order and magnetic properties of various morphologies of FePt and CoPt clusters with diameters of up to 2.5 nm. For FePt, ordered multiply twinned icosahedra and decahedra are more favorable than the L1_(0) phase throughout the investigated size range. For CoPt, segregated morphologies predominate with considerably increased energy differences to the L1_(0) structure. The compositional trends are traced back to differences between the morphologies in the partial electronic density of states associated with the 3d element.

Contrast transfer and resolution limits for sub-angstrom high-resolution transmission electron microscopy

The optimum imaging of an object structure at the sub-angstrom length scale requires precise adjustment of the lens aberrations of a high-resolution instrument up to the fifth order. A least-squares optimization of defocus aberration C1, third-order spherical aberration C3, and fifth-order spherical aberration C5 yields two sets of aberration coefficients for strong phase contrast up to the information limit: one for variable C1 and C3, at fixed C5, another for variable C1, C3, and C5. An additional correction to the defocus aberration, dependent on object thickness, is described, which becomes important for the use of image simulation programs in predicting optimum high-resolution contrast from thin objects at the sub-angstrom scale. For instruments with a sub-angstrom information limit the ultimate structure resolution, the power to resolve adjacent atom columns in a crystalline object, depends on both the instrumental pointspread and an object pointspread due to finite width of the atomic column potentials. A simulation study on a simple double-column model yields a range for structure resolutions, dependent on the atomic scattering power, from 0.070 nm down to 0.059 nm, for a hypothetical 300-kV instrument with an information limit of 0.050 nm.

Development of aberration-corrected electron microscopy

The successful correction of spherical aberration is an exciting and revolutionary development for the whole field of electron microscopy. Image interpretability can be extended out to sub-Angstrom levels, thereby creating many novel opportunities for materials characterization. Correction of lens aberrations involves either direct (online) hardware attachments in fixed-beam or scanning TEM or indirect (off-line) software processing using either off-axis electron holography or focal-series reconstruction. This review traces some of the important steps along the path to realizing aberration correction, including early attempts with hardware correctors, the development of online microscope control, and methods for accurate measurement of aberrations. Recent developments and some initial applications of aberration-corrected electron microscopy using these different approaches are surveyed. Finally, future prospects and problems are briefly discussed.

Progress and perspectives for atomic-resolution electron microscopy

The transmission electron microscope (TEM) has evolved into a highly sophisticated instrument that is ideally suited to the characterization of advanced materials. Atomic-level information is routinely accessible using both fixed-beam and scanning TEMs. This report briefly considers developments in the field of atomic-resolution electron microscopy. Recent activities include renewed attention to on-line microscope control ('autotuning'), and assessment and correction of aberrations. Aberration-corrected electron microscopy has developed rapidly in several forms although more work needs to be done to identify standard imaging conditions and to explore novel operating modes. Preparation of samples and image interpretation have also become more demanding. Ongoing problems include discrepancies between measured and simulated image contrast, concerns about radiation damage, and inversion of electron scattering.

Bright-field TEM imaging of single molecules: Dream or near future?

We examine the suitability of spherical aberration (C(S))-corrected (CS) and uncorrected (UC) transmission electron microscopes (TEM) for conventional bright-field imaging of radiation-sensitive materials. We have chosen an individual molecule suspended in vacuum as a hypothetical example of a well-defined radiation-sensitive sample. We find that for this particular sample, CS instruments provide about 30% improvement over an UC instrument in terms of signal/noise ratio per unit electron dose at 300kV. The lowest imaging doses can be achieved in CS instruments equipped with high-brightness electron source operated at low incident electron energies. Our calculations suggest that it may be possible to image individual, iodine- or bromine-substituted organic molecules in bright-field mode, at doses lower than the accepted values for radiation damage of aromatic molecules.

First experimental test of a new monochromated and aberration-corrected 200kV field-emission scanning transmission electron microscope

The first 200 kV scanning transmission electron microscope (STEM) with an imaging energy filter, a monochromator and a corrector for the spherical aberration (Cs-corrector) of the illumination system has been built and tested. The STEM/TEM concept with Koehler illumination allows to switch easily between STEM mode for analytical and TEM mode for high-resolution or in situ studies. The Cs-corrector allows the use of large illumination angles for retaining a sufficiently high beam current despite the intensity loss in the monochromator. With the monochromator on and a 3 microm slit in the dispersion plane that gives 0.26 eV full-width at half-maximum (FWHM) energy resolution we have obtained so far an electron beam smaller than 0.20 nm in diameter (FWHM as measured by scanning the spot quickly over the CCD) which contains 7 pA current and, according to simulations, should be around 0.12 nm in true size. A high-angle annular dark field (ADF) image with isotropic resolution better than 0.28 nm has been recorded with the monochromator in the above configuration and the Cs-corrector on. The beam current is still somewhat low for electron energy-loss spectroscopy (EELS) but is expected to increase substantially by optimising the condenser set-up and using a somewhat larger condenser aperture.

Progress in aberration-corrected high-resolution transmission electron microscopy using hardware aberration correction

The design and construction of a double-hexapole aberration corrector has made it possible to build the prototype of a spherical-aberration corrected transmission electron microscope dedicated to high-resolution imaging on the atomic scale. The corrected instrument, a Philips CM200 FEG ST, has an information limit of better than 0.13 nm, and the spherical aberration can be varied within wide limits, even to negative values. The aberration measurement and the corrector control provide instrument alignments stable enough for materials science investigations. Analysis of the contrast transfer with the possibility of tunable spherical aberration has revealed new imaging modes: high-resolution amplitude contrast, extension of the point resolution to the information limit, and enhanced image intensity modulation for negative phase contrast. In particular, through the combination of small negative spherical aberration and small overfocus, the latter mode provides the high-resolution imaging of weakly scattering atom columns, such as oxygen, in the vicinity of strongly scattering atom columns. This article reviews further lens aberration theory, the principle of aberration correction through multipole lenses, aspects for practical work, and materials science applications.

Image deconvolution in spherical aberration-corrected high-resolution transmission electron microscopy

The method of image deconvolution developed previously for FEG high-resolution transmission electron microscope (HRTEM) without a spherical aberration (C(s)) corrector was for the first time applied to FEG HRTEM with a C(s)-corrector. The principle and the procedure of image deconvolution are briefly described. Four qualified [1 1 0] images of Si were selected from a through-focus series to perform image deconvolution. The projected potential is successfully derived from all the images, and the obtained "dumbbell" structure maps of Si [1 1 0] are in good agreement with the calculated potential map. The criterion of selecting qualified images for performing image deconvolution is indicated. The possibility of applying image deconvolution to defect study and to ab initio crystal structure determination is discussed.

On the importance of fifth-order spherical aberration for a fully corrected electron microscope

Next generation aberration correctors will not only eliminate the third-order spherical aberration, but also improve the information limit by correction of chromatic aberration. As a result of these improvements, higher order aberrations, which have largely been neglected in image analysis, will become important. In this paper, we concern ourselves with situations where sub-A resolution can be achieved, and where the third-order spherical aberration is corrected and the fifth-order spherical aberration is measurable. We derive formulae to explore the maximum value of the fifth-order spherical aberration for directly interpretable imaging and discuss the optimum imaging conditions and their applicable range.

A transmission electron microscopy study of mineralization in age-induced transparent dentin

It is known that fractures are more likely to occur in altered teeth, particularly following restoration or endodontic repair; consequently, it is important to understand the structure of altered forms of dentin, the most abundant tissue in the human tooth, in order to better define the increased propensity for such fractures. Transparent (or sclerotic) dentin, wherein the dentinal tubules become occluded with mineral as a natural progressive consequence of aging, is one such altered form. In the present study, high-resolution transmission electron microscopy is used to investigate the effect of aging on the mineral phase of dentin. Such studies revealed that the intertubular mineral crystallites were smaller in transparent dentin, and that the intratubular mineral (larger crystals deposited within the tubules) was chemically similar to the surrounding intertubular mineral. Exit-wave reconstructed lattice-plane images suggested that the intratubular mineral had nanometer-size grains. These observations support a "dissolution and reprecipitation" mechanism for the formation of transparent dentin.

Calculations of HREM image intensity using Monte Carlo integration

We have developed a numerical approach for the accurate and efficient calculation of HREM image intensity formed using a partially coherent source. The approach is based on Monte Carlo integration, and is suitable for use in general image restoration methods using a series of images. The accuracy of this approach is compared with calculations based on the transmission cross coefficient (TCC) for strong scattering objects, as a function of the number of sampling points, defocus, atomic number and specimen thickness. Its efficiency is compared with that of exact TCC calculations based on equally-spaced sampling of the beam divergence and focal spread distributions. The results indicate that the Monte Carlo approach is particularly advantageous for nonlinear image restoration algorithms.

Distortion and segregation in a dislocation core region at atomic resolution

The structure of an isolated, Ga terminated, 30 degree partial dislocation in GaAs:Be is determined by high resolution transmission electron microscopes and focal series reconstruction. The positions of atomic columns in the core region are measured to an accuracy of better than 10 pm. A quantitative comparison of the structure predicted by an ab initio electronic structure total energy calculation to the experiment indicates that theory and experiment agree to within 20 pm. Further analysis shows the deviations between theory and experiment appear to be systematic. Electron energy loss spectroscopy establishes that defects segregate to the core region, thus accounting for the systematic deviations.

HRTEM imaging of atoms at sub-Ångström resolution

John Cowley and his group at Arizona State University pioneered the use of transmission electron microscopy for high-resolution imaging. Images were achieved three decades ago showing the crystal unit cell content at better than 4 A resolution. This achievement enabled researchers to pinpoint the positions of heavy atom columns within the unit cell. Lighter atoms appear as resolution is improved to sub-Angström levels. Currently, advanced microscopes can image the columns of the light atoms (carbon, oxygen, nitrogen) that are present in many complex structures, and even the lithium atoms present in some battery materials. Sub-Angström imaging, initially achieved by focal-series reconstruction of the specimen exit surface wave, will become commonplace for next-generation electron microscopes with C(S)-corrected lenses and monochromated electron beams. Resolution can be quantified in terms of peak separation and inter-peak minimum, but the limits imposed on the attainable resolution by the properties of the microscope specimen need to be considered. At extreme resolution the 'size' of atoms can mean that they will not be resolved even when spaced farther apart than the resolution of the microscope.

Effective phase correction function for high-resolution exit wave reconstruction by a three-dimensional Fourier filtering method

The phase correction function used in the three-dimensional Fourier filtering method (3D-FFM) for compensating lens aberrations was investigated to reconstruct a high-resolution exit wave of a sample. An appropriate function, which hardly suffered from imperfect illumination conditions, was determined by comparing two types of phase correction functions with numerical calculations and experiments using through-focus images of an amorphous thin film and a [110]-oriented Si single crystal taken under tilted illumination or partially coherent illumination. Theoretical calculations indicated that a function in terms of w (an axial Fourier component), available uniquely in the 3D Fourier space, compensated for the phase shift due to the spherical aberration more precisely than did a conventional function in terms of g (the two-dimensional (2D) planar Fourier components). Experimentally, exit waves reconstructed using the w-function showed sample structures at approximately 20% higher resolution than those reconstructed using the g-function. Image contrast simulations proved that the w-function had a significant advantage over the g-function: the former canceled out the effect of illumination divergence, resulting in a high-resolution exit wave. These results demonstrated that exit waves, which are uniquely realized in the 3D-FFM, should be reconstructed using the w-type phase correction function.

Direct Sub-Angstrom Imaging of a Crystal Lattice

Despite the use of electrons with wavelengths of just a few picometers, spatial resolution in a transmission electron microscope (TEM) has been limited by spherical aberration to typically around 0.15 nanometer. Individual atomic columns in a crystalline lattice can therefore only be imaged for a few low-order orientations, limiting the range of defects that can be imaged at atomic resolution. The recent development of spherical aberration correctors for transmission electron microscopy allows this limit to be overcome. We present direct images from an aberration-corrected scanning TEM that resolve a lattice in which the atomic columns are separated by less than 0.1 nanometer.

Image formation in the high-resolution transmission electron microscope

A recent article in these pages compares STEM images with an image obtained with the One-Ångstrom Microscope (OÅM) at Lawrence Berkeley National Laboratory (LBNL). Although the experimental work is of excellent quality, Diebold et al. (2003) offer an incorrect explanation of the image formation process in the high-resolution transmission electron microscope. It is important that this misinterpretation be corrected before it comes to be accepted as factual by other scientists who are not expert in the field of high-resolution transmission electron microscopy.

"Indirect" high-resolution transmission electron microscopy: aberration measurement and wavefunction reconstruction

Improvements in instrumentation and image processing techniques mean that methods involving reconstruction of focal or beam-tilt series of images are now realizing the promise they have long offered. This indirect approach recovers both the phase and the modulus of the specimen exit plane wave function and can extend the interpretable resolution. However, such reconstructions require the a posteriori determination of the objective lens aberrations, including the actual beam tilt, defocus, and twofold and threefold astigmatism. In this review, we outline the theory behind exit plane wavefunction reconstruction and describe methods for the accurate and automated determination of the required coefficients of the wave aberration function. Finally, recent applications of indirect reconstruction in the structural analysis of complex oxides are presented.

Exit wave reconstruction at atomic resolution

An iterative method for exit wave function reconstruction based on wave function propagation in free space is presented. The method, which has the potential for application to many forms of microscopy, has been tailored to work with a through focal series of images measured in a high-resolution transmission electron microscope. Practical difficulties for exit wave reconstruction which are pertinent in this experimental environment are the slight incoherence of the electron beam, sample drift and its effect upon the defocus step size that can be utilised, and the number of image measurements that need to be made. To gauge the effectiveness of the method it is applied to experimental data that has been analysed previously using a maximum likelihood formalism (the MAL method).

High-resolution transmission electron microscopy using negative spherical aberration

A novel imaging mode for high-resolution transmission electron microscopy is described. It is based on the adjustment of a negative value of the spherical aberration C S of the objective lens of a transmission electron microscope equipped with a multipole aberration corrector system. Negative spherical aberration applied together with an overfocus yields high-resolution images with bright-atom contrast. Compared to all kinds of images taken in conventional transmission electron microscopes, where the then unavoidable positive spherical aberration is combined with an underfocus, the contrast is dramatically increased. This effect can only be understood on the basis of a full nonlinear imaging theory. Calculations show that the nonlinear contrast contributions diminish the image contrast relative to the linear image for a positive-C S setting whereas they reinforce the image contrast relative to the linear image for a negative-C S setting. The application of the new mode to the imaging of oxygen in SrTiO3 and YBa2Cu3O7 demonstrates the benefit to materials science investigations. It allows us to image directly, without further image processing, strongly scattering heavy-atom columns together with weakly scattering light-atom columns.

Off-axis STEM or TEM holography combined with four-dimensional diffraction imaging

Ultrahigh-resolution imaging may be achieved using modifications of the off-axis holography scheme in a scanning transmission electron microscopy (STEM) instrument equipped with one or more electrostatic biprisms in the illuminating system. The resolution is governed by the diameter of a reference beam, reduced by channeling through a line of atoms in an atomic-focuser crystal. Alternatively, the off-axis holography may be combined with the Rodenburg method in which a four-dimensional data set is obtained by recording a nanodiffraction pattern from each point of the specimen as the incident beams are scanned. An ultrahigh-resolution image is derived by computer processing to give a particular two-dimensional section of this data set. The large amount of data recording and data processing involved with this method may be avoided if the two-dimensional section is derived by recording the hologram while the four beams produced by two perpendicular biprisms are scanned in opposing directions across the specimen by varying the voltages on the biprisms. An equivalent scheme for conventional TEM is also possible. In each case, the complex transmission function of the specimen may be derived and resolutions of about 0.05 nm may be expected.

Sub-angstrom atomic-resolution imaging from heavy atoms to light atoms

John Cowley and his group at Arizona State University pioneered the use of transmission electron microscopy (TEM) for high-resolution imaging. Three decades ago they achieved images showing the crystal unit cell content at better than 4 angstroms resolution. Over the years, this achievement has inspired improvements in resolution that have enabled researchers to pinpoint the positions of heavy atom columns within the cell. More recently, this ability has been extended to light atoms as resolution has improved. Sub-angstrom resolution has enabled researchers to image the columns of light atoms (carbon, oxygen, and nitrogen) that are present in many complex structures. By using sub-angstrom focal-series reconstruction of the specimen exit surface wave to image columns of cobalt, oxygen, and lithium atoms in a transition metal oxide structure commonly used as positive electrodes in lithium rechargeable batteries, we show that the range of detectable light atoms extends to lithium. HRTEM at sub-angstrom resolution will provide the essential role of experimental verification for the emergent nanotech revolution. Our results foreshadow those to be expected from next-generation TEMs with CS-corrected lenses and monochromated electron beams.