Structure Determination by Quantitative High-Resolution Transmission Electron Microscopy

Abstract

High-resolution transmission electron microscopy (HRTEM) comprises techniques of image formation by bright-field phase contrast with the aim of resolving the lattice fringes of a crystal lattice. There is no specific resolution threshold value separating “HR”-TEM from conventional TEM. Instead, the distinction is based on the fact that several diffracted beams are necessary to form the image of crystal planes. HRTEM is most important and powerful for studies of crystal defect structures in real space. For this, the aperture of the objective lens must be large enough to allow the diffracted beams corresponding to the projected crystal planes to pass and the passband of the contrast-transfer function (aberrations and incoherence envelopes) must extend sufficiently far. Many non-equivalent diffracted electron waves then build up an interference pattern in the image plane according to Abbe’s optical microscope theory. Conventional TEM, on the other hand, uses scattering around a single diffracted beam only. An HRTEM image pattern normally mirrors well the atomic geometry and symmetry of the material examined, but not necessarily the atom positions. Visual interpretation is therefore routinely assisted by computer simulations of the experimental image formation process. The image is correctly interpreted in terms of the atomic structure once the simulated and experimental image match sufficiently. For many years, experimental and simulated HRTEM images were compared visually, but recently interest has shifted towards digital and automated interpretation of the micrographs. This trend towards computer-controlled atomic-resolution structure retrieval (as opposed to just verifying or falsifying a few structure models) has three main motivations:

• 1. Present trends in materials science. The need for accurate knowledge of the structure of crystal defects at atomic resolution has increased rapidly along with the engineering and designing of materials down to the nanometre scale. For example, the semiconductor device industry and fundamental research on quantum confinement rely on the knowledge and control of defect structure, such as interfaces, dislocations and composition fluctuations at the nanometre level. Nanostructured and nanocrystalline metals, alloys, and ceramics, and especially compound materials, thin films, and multilayered coatings likewise depend on atomic scale characterisation and control. Furthermore, the history of the development of “novel materisls” such as carbon nanotubes, high-temperature superconductors, magnetic nanostructures, or metallic quantum wires, was closely linked to their observation in the high-resolution electron microscope.

• 2 Progress in instrumentation. Several important milestones have been passed in the last ten years. Nwe ultra-resolution lens designs combining low spherical aberration with acceptable tilting ranges have been introduced for 200kV–300kV instruments. Field-emission guns now combine very high brightness with high spatial and temporal coherence. The development of very stable and comfortable high-voltage/high-resolution instruments has resulted in a point-resolution of about 1Å thanks to the reduction in wavelength at 1250kV. Finally, the most recent milestone was the demonstration of sub-1.4Å Scherzer-resolution by correcting the spherical aberration at 200kV. See Chap. 6 for more details. All these modern microscope techologies share the common advantage of pushing the information resolution limit (the ultimate detectable spatial frequency, independent of associated aberrations) to regions near or even below 1Å. The information resolution has become a major figure of merit now that image processing allows image evaluation techniques that are less dependent on a Rayleigh-type point resolution limit to be employed. The development of slow-scan CCD cameras and, more recently, the image palte system was another milestone; these complement the conventional photographic film, which can, however, still be reliably used for quantitative work combined with digitisation in a high-quality scanner. The revolutionary increase of CPU power over the last decade can be appreciated from the following numbers: Thecomputing time to convert one small defect structure model into one HRTEM-image on a stata-of-the-art laboratory workstation decreased from 2–3 hours in 1990 (e.g. DEC μ VAX II) to 10–20 seconds in 1999 (e.g. DEC Alpha AXP).

• 3 Progress in modelling of materials. The development of large-scale atomic modelling of defect structures now allows thousands of atomas to be included in a calculation cell, covering whole misfit dislocation networks at heterophase boundaries, for example. Methods of quantum chemistry and solid-state physics thus generate another challenge but also provide an important boost for HRTEM quantification : getting theory and experiment to agree on the Å -scale with accuracy of atom location on the pm-scale.