Determination of the 3D shape of a nanoscale crystal with atomic resolution from a single image.

Although the overall atomic structure of a nanoscale crystal is in principle accessible by modern transmission electron microscopy, the precise determination of its surface structure is an intricate problem. Here, we show that aberration-corrected transmission electron microscopy, combined with dedicated numerical evaluation procedures, allows the three-dimensional shape of a thin MgO crystal to be determined from only one single high-resolution image. The sensitivity of the reconstruction procedure is not only sufficient to reveal the surface morphology of the crystal with atomic resolution, but also to detect the presence of adsorbed impurity atoms. The single-image approach that we introduce offers important advantages for three-dimensional studies of radiation-sensitive crystals.

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(0.4)Ga(0.6)As-GaAs and In(0.25)Ga(0.75)Sb-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(0.25)Ga(0.75)Sb-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.

Atomic-precision determination of the reconstruction of a 90 degree tilt boundary in YBa2Cu3O7-delta by aberration corrected HRTEM.

Aberration corrected high-resolution transmission electron microscopy is used to determine the reconstruction of atomic bonds of a 90 degree [100] grain boundary in YBa(2)Cu(3)O(7-delta). A precise measurement of atom positions within the grain boundary and the assessment of the oxygen stoichiometry require at the same time a high control of residual lens aberrations of the electron microscope and a good signal-to-noise ratio. This goal is achieved by the combination of spherical-aberration correction in the microscope with the numerical exit-plane wave function reconstruction from focal series. Atomic column positions for individual cations and anions are determined by the regression analysis of peak maxima in the phase image of the retrieved exit-plane wave function. The measurement accuracy is quantitatively assessed, including the statistical error related to residual noise. Changes in bondlengths between copper atoms and the apical oxygen are measured, indicating the distortion of the square pyramidal oxygen coordination of plane copper sites and the square coordination of chain copper sites in the grain boundary.

Imaging columns of the light elements carbon, nitrogen and oxygen with sub Angstrom resolution.

It is reported that lattice imaging with a 300 kV field emission microscope in combination with numerical reconstruction procedures can be used to reach an interpretable resolution of about 80 pm for the first time. A retrieval of the electron exit wave from focal series allows for the resolution of single atomic columns of the light elements carbon, nitrogen, and oxygen at a projected nearest neighbor spacing down to 85 pm. Lens aberrations are corrected on-line during the experiment and by hardware such that resulting image distortions are below 80 pm. Consequently, the imaging can be aberration-free to this extent. The resolution enhancement results from increased electrical and mechanical stability of the instrument coupled with a low spherical aberration coefficient of 0.595 + 0.005 mm.

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.

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

Sub-Angstrom transmission electron microscopy has been achieved at the National Center for Electron Microscopy (NCEM) by a one-Angstrom microscope (OAM) project using software and enhanced hardware developed within a Brite-Euram project (Ultramicroscopy 64 (1996) 1). The NCEM OAM provides materials scientists with transmission electron microscopy at a resolution better than 1 A by using extensive image reconstruction to exploit the significantly higher information limit of an FEG-TEM over its Scherzer resolution limit. Reconstruction methods chosen used off-axis holograms and focal series of underfocused images. Measured values of coherence parameters predict an information limit of 0.78 A. Images from a [1 1 0] diamond test specimen show that sub-Angstrom resolution of 0.89 A has been achieved with the OAM using focal series reconstruction.

On the optical stability of high-resolution transmission electron microscopes.

In the recent two decades the technique of high-resolution transmission electron microscopy experienced an unprecedented progress through the introduction of hardware aberration correctors and by the improvement of the achievable resolution to the sub-Ångström level. The important aspect that aberration correction at a given resolution requires also a well defined amount of optical stability has received little attention so far. Therefore we investigate the qualification of a variety of high-resolution electron microscopes to maintain an aberration corrected optical state in terms of an optical lifetime. We develop a comprehensive statistical framework for the estimation of the optical lifetime and find remarkably low values between tens of seconds and a couple of minutes. Probability curves are introduced, which inform the operator about the chance to work still in the fully aberration corrected state.

REPRINT OF: Aberration measurement in HRTEM: Implementation and diagnostic use of numerical procedures for the highly precise recognition of diffractogram patterns.

The precise characterisation of the instrumental imaging properties in the form of aberration parameters constitutes an almost universal necessity in quantitative HRTEM, and is underlying most hardware and software techniques established in this field. We focus in this paper on the numerical analysis of individual diffractograms as a first preparatory step for further publications on HRTEM aberration measurement. The extraction of the defocus and the 2-fold astigmatism from a diffractogram is a classical pattern recognition problem, which we believe to have solved in a near-optimum way concerning precision, speed, and robustness. The newly gained measurement precision allows us to resolve fluctuations of the defocus and the 2-fold astigmatism and to assess thereby the optical stability of electron microscopes. Quantitative stability criteria are elaborated, which may serve as helpful guidelines for daily work as well as for microscope acceptance tests.

Aberration measurement in HRTEM: implementation and diagnostic use of numerical procedures for the highly precise recognition of diffractogram patterns.

The precise characterisation of the instrumental imaging properties in the form of aberration parameters constitutes an almost universal necessity in quantitative HRTEM, and is underlying most hardware and software techniques established in this field. We focus in this paper on the numerical analysis of individual diffractograms as a first preparatory step for further publications on HRTEM aberration measurement. The extraction of the defocus and the 2-fold astigmatism from a diffractogram is a classical pattern recognition problem, which we believe to have solved in a near-optimum way concerning precision, speed, and robustness. The newly gained measurement precision allows us to resolve fluctuations of the defocus and the 2-fold astigmatism and to assess thereby the optical stability of electron microscopes. Quantitative stability criteria are elaborated, which may serve as helpful guidelines for daily work as well as for microscope acceptance tests.

High-resolution transmission electron microscopy on an absolute contrast scale.

A fully quantitative approach to high-resolution transmission electron microscopy requires a satisfactory match between image simulations and experiments. While almost perfect agreement between simulations and experiments is routinely achieved on a relative contrast level, a huge mutual discrepancy in the absolute image contrast by a factor of 3 has been frequently reported. It is shown that a major reason for this well-known contrast discrepancy, which is often called Stobbs-factor problem, lies in the neglect of the detector modulation-transfer function in image simulations.

Quantification of the information limit of transmission electron microscopes.

The resolving power of high-resolution transmission electron microscopes is characterized by the information limit, which reflects the size of the smallest object detail observable with a particular instrument. We introduce a highly accurate measurement method for the information limit, which is suitable for modern aberration-corrected electron microscopes. An experimental comparison with the traditionally applied Young's fringe method yields severe discrepancies and confirms theoretical considerations according to which the Young's fringe method does not reveal the information limit.

Atomic-scale analysis of the oxygen configuration at a SrTiO3 dislocation core.

The atomic structure of a SrTiO3 dislocation is revealed directly by phase-retrieval electron microscopy. In particular, atomic columns of light oxygen are observed simultaneously with the columns of considerably heavier Sr and Ti. A distinct structural modification of the oxygen octahedra at the dislocation core as well as a significant nonstoichiometry, including a deficiency of oxygen, are observed. Deviations from the bulk chemical concentration are quantified column by column by means of structure modeling and quantum-mechanical simulations of the electron scattering process.

Spherical aberration correction in tandem with exit-plane wave function reconstruction: interlocking tools for the atomic scale imaging of lattice defects in GaAs.

With the availability of resolution boosting and delocalization minimizing techniques, for example, spherical aberration correction and exit-plane wave function reconstruction, high-resolution transmission electron microscopy is drawing to a breakthrough with respect to the atomic-scale imaging of common semiconductor materials. In the present study, we apply a combination of these two state-of-the-art techniques to investigate lattice defects in GaAs-based heterostructures at atomic resolution. Focusing on the direct imaging of stacking faults as well as the core structure of edge and partial dislocations, the practical capabilities of both techniques are illustrated. For the first time, we apply the technique of bright-atom contrast imaging at negative spherical aberration together with an appropriate overfocus setting for the investigation of lattice defects in a semiconductor material. For these purposes, the elastic displacements associated with lattice defects in GaAs viewed along the 110 zone axis are measured from experimental images using reciprocal space strain map algorithms. Moreover, we demonstrate the benefits of the retrieval of the exit-plane wave function not only for the elimination of residual imaging artefacts but also for the proper on-line alignment of specimens during operation of the electron microscope--a basic prerequisite to obtain a fair agreement between simulated images and experimental micrographs.