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

Carbon-film-based Zernike phase plates with smooth thickness gradient for phase-contrast transmission electron microscopy with reduced fringing artifacts

Phase plates (PPs) in transmission electron microscopy (TEM) improve the contrast of weakly scattering objects under in-focus imaging conditions. A well-established PP type is the Zernike (Z)PP, which consists of a thin amorphous carbon (aC) film with a micro-scaled hole in the center. The mean inner potential of the aC film is exploited to shift the phase of the scattered electrons while the unscattered electrons in the zero-order beam propagate through the hole and remain unaffected. However, the abrupt thickness increase at the hole edge induces an abrupt change of the phase-shift distribution and leads to fringing, i.e., intensity oscillations around imaged objects, in TEM images. In this work, we have used focused-ion-beam milling to fabricate ZPPs with abrupt and graded thickness profiles around the center hole. Depending on the thickness gradient and inner hole radius, graded-ZPP-TEM images of an aC/vacuum interface and bundles of carbon nanotubes (CNTs) show strongly reduced fringing. Image simulations were performed with ZPP-phase-shift distributions derived from measured thickness profiles of graded ZPPs, which show good agreement with the experimental images. Fringing artifacts, i.e. intensity oscillations around imaged objects, are strongly reduced for Zernike phase plates with a graded thickness profile around the center hole. Focused-ion-beam milling is used to fabricate graded Zernike phase plates with specific inner hole radius and thickness gradients. The phase-shift distribution is obtained from measured thickness profiles around the center hole. Image simulations based on experimentally measured thickness/phase-shift distributions show good agreement with experimental Zernike phase-plate TEM images. This article is protected by copyright. All rights reserved.

Dynamics of the charging-induced imaging instability in transmission electron microscopy

Revolutionary microscopy technologies for aberration correction in spatial and energy aspects have exhibited continuous progress, pushing forward the information limit of materials research down to a scale of sub-angstrom and milli-electron voltage. Nevertheless, imaging quality could still suffer due to sample instability, e.g. the charging effect, which always comes along with electron microscopy characterizations. Herein, using a defocus estimation algorithm and an in situ image feature tracking method, we quantitatively studied the image drifting dynamics induced by the charging on transmission electron microscopy (TEM) carrier grids with tunable electrical conductivity. Experimental evidence clarifies the debate about the charge types, proving that the irradiation of the electron beam induces a positive charge on the grid sample of poor electrical conductivity. Such charge accumulation accounts for subsequent imaging instability, including the increase of defocus and the drift of lateral images. Particularly, the competition between charging and discharging was found to dynamically modulate the propagation of electron beam, resulting in a periodically reciprocating movement on TEM images. These findings enrich understanding on the dynamic principle of charging effects as well as the details of image drifting behaviors. It also suggests specific attention on the importance of conductivity control on a TEM specimen, beyond all the efforts for instrumental improvements.

Investigation of hole-free phase plate performance in transmission electron microscopy under different operation conditions by experiments and simulations

Hole-free phase plates (HFPPs), also known as Volta phase plates, were already demonstrated to be well suited for in-focus transmission electron microscopy imaging of organic objects. However, the underlying physical processes have not been fully understood yet. To further elucidate the imaging properties of HFPPs, phase shift measurements were carried out under different experimental conditions. Both positive and negative phase shifts occur depending on the diameter of the zero-order electron beam and the HFPP film temperature. The analysis of Thon ring patterns of an amorphous carbon test sample reveals that the phase-shifting patch can be significantly larger than the size of the zero-order beam on the HFPP film. An HFPP was used for in-focus phase contrast imaging of carbon nanotube (CNT) bundles under positive and negative phase-shifting conditions. The comparison of experimental and simulated images of CNT bundles gives detailed information on the phase shift profile, which depends on the spatial frequency in the vicinity of the zero-order beam. The shape of the phase shift profile also explains halo-like image artifacts that surround the imaged objects.

Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples

We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si₃N₄ wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.

Observation of lens aberrations for high resolution electron microscopy II: simple expressions for optimal estimates

This paper lists simple closed-form expressions estimating aberration coefficients (defocus, astigmatism, three-fold astigmatism, coma / misalignment, spherical aberration) on the basis of image shift or diffractogram shape measurements as a function of injected beam tilt. Simple estimators are given for a large number of injected tilt configurations, optimal in the sense of least-squares fitting of all the measurements, and so better than most reported previously. Standard errors are given for most, allowing different approaches to be compared. Special attention is given to the measurement of the spherical aberration, for which several simple procedures are given, and the effect of foreknowledge of this on other aberration estimates is noted. Details and optimal expressions are also given for a new and simple method of analysis, requiring measurements of the diffractogram mirror axis direction only, which are simpler to make than the focus and astigmatism measurements otherwise required.

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.

Atomic-scale measurement of structure and chemistry of a single-unit-cell layer of LaAlO3 embedded in SrTiO3

A single layer of LaAlO3 with a nominal thickness of one unit cell, which is sandwiched between a SrTiO3 substrate and a SrTiO3 capping layer, is quantitatively investigated by high-resolution transmission electron microscopy. By the use of an aberration-corrected electron microscope and by employing sophisticated numerical image simulation procedures, significant progress is made in two aspects. First, the structural as well as the chemical features of the interface are determined simultaneously on an atomic scale from the same specimen area. Second, the evaluation of the structural and chemical data is carried out in a fully quantitative way on the basis of the absolute image contrast, which has not been achieved so far in materials science investigations using high-resolution electron microscopy. Considering the strong influence of even subtle structural details on the electronic properties of interfaces in oxide materials, a fully quantitative interface analysis, which makes positional data available with picometer precision together with the related chemical information, can contribute to a better understanding of the functionality of such interfaces.

Intrinsic instability of aberration-corrected electron microscopes

Aberration-corrected microscopes with subatomic resolution will impact broad areas of science and technology. However, the experimentally observed lifetime of the corrected state is just a few minutes. Here we show that the corrected state is intrinsically unstable; the higher its quality, the more unstable it is. Analyzing the contrast transfer function near optimum correction, we define an "instability budget" which allows a rational trade-off between resolution and stability. Unless control systems are developed to overcome these challenges, intrinsic instability poses a fundamental limit to the resolution practically achievable in the electron microscope.