A quantum mechanical exploration of phonon energy-loss spectroscopy using electrons in the aloof beam geometry.

Phonon energy-loss spectroscopy using electrons has both high resolution and low resolution components, associated with short- and long-range interactions, respectively. In this paper, we discuss how these two contributions arise from a fundamental quantum mechanical perspective. Starting from a correlated model for the atomic motion we show how short range 'impact' scattering and long range 'dipole' scattering arises. The latter dominates in aloof beam imaging, an imaging geometry in which radiation damage can be avoided.

Atomic resolution elemental mapping using energy-filtered imaging scanning transmission electron microscopy with chromatic aberration correction.

This paper addresses a novel approach to atomic resolution elemental mapping, demonstrating a method that produces elemental maps with a similar resolution to the established method of electron energy-loss spectroscopy in scanning transmission electron microscopy. Dubbed energy-filtered imaging scanning transmission electron microscopy (EFISTEM) this mode of imaging is, by the quantum mechanical principle of reciprocity, equivalent to tilting the probe in energy-filtered transmission electron microscopy (EFTEM) through a cone and incoherently averaging the results. In this paper we present a proof-of-principle EFISTEM experimental study on strontium titanate. The present approach, made possible by chromatic aberration correction, has the advantage that it provides elemental maps which are immune to spatial incoherence in the electron source, coherent aberrations in the probe-forming lens and probe jitter. The veracity of the experiment is supported by quantum mechanical image simulations, which provide an insight into the image-forming process. Elemental maps obtained in EFTEM suffer from the effect known as preservation of elastic contrast, which, for example, can lead to a given atomic species appearing to be in atomic columns where it is not to be found. EFISTEM very substantially reduces the preservation of elastic contrast and yields images which show stability of contrast with changing thickness. The experimental application is demonstrated in a proof-of-principle study on strontium titanate.

Addressing preservation of elastic contrast in energy-filtered transmission electron microscopy.

Energy-filtered transmission electron microscopy (EFTEM) images with resolutions of the order of an Ångström can be obtained using modern microscopes corrected for chromatic aberration. However, the delocalized nature of the transition potentials for atomic ionization often confounds direct interpretation of EFTEM images, leading to what is known as "preservation of elastic contrast". In this paper we demonstrate how more interpretable images might be obtained by scanning with a focused coherent probe and incoherently averaging the energy-filtered images over probe position. We dub this new imaging technique energy-filtered imaging scanning transmission electron microscopy (EFISTEM). We develop a theoretical framework for EFISTEM and show that it is in fact equivalent to precession EFTEM, where the plane wave illumination is precessed through a range of tilts spanning the same range of angles as the probe forming aperture in EFISTEM. It is demonstrated that EFISTEM delivers similar results to scanning transmission electron microscopy with an electron energy-loss spectrometer but has the advantage that it is immune to coherent aberrations and spatial incoherence of the probe and is also more resilient to scan distortions.

Elemental mapping in achromatic atomic-resolution energy-filtered transmission electron microscopy.

We present atomic-resolution energy-filtered transmission electron microscopy (EFTEM) images obtained with the chromatic-aberration-corrected FEI Titan PICO at the Ernst-Ruska Centre, Jülich, Germany. We find qualitative agreement between experiment and simulation for the background-subtracted EFTEM images of the Ti-L2,3 and O-K edges for a specimen of SrTiO3 oriented down the [110] zone axis. The simulations utilize the transition potential formulation for inelastic scattering, which permits a detailed investigation of contributions to the EFTEM image. We find that energy-filtered images of the Ti-L2,3 and O-K edges are lattice images and that the background-subtracted core-loss maps may not be directly interpretable as elemental maps. Simulations show that this is a result of preservation of elastic contrast, whereby the qualitative details of the image are determined primarily by elastic, coherent scattering. We show that this effect places a constraint on the range of specimen thicknesses which could theoretically yield directly useful elemental maps. In general, interpretation of EFTEM images is ideally accompanied by detailed simulations.

The interaction of a nanoscale coherent helium-ion probe with a crystal.

Thickness fringing was recently observed in helium ion microscopy (HIM) when imaging magnesium oxide cubes using a 40 keV convergent probe in scanning transmission mode. Thickness fringing is also observed in electron microscopy and is due to quantum mechanical, coherent, multiple elastic scattering attenuated by inelastic phonon excitation (thermal scattering). A quantum mechanical model for elastic scattering and phonon excitation correctly models the thickness fringes formed by the helium ions. However, unlike the electron case, the signal in the diffraction plane is due mainly to the channeling of ions which have first undergone inelastic thermal scattering in the first few atomic layers so that the origin of the thickness fringes is not due to coherent interference effects. This quantum mechanical model affords insight into the interaction of a nanoscale, focused coherent ion probe with the specimen and allows us to elucidate precisely what is needed to achieve atomic resolution HIM.

Thermal diffuse scattering in transmission electron microscopy.

In conventional transmission electron microscopy, thermal scattering significantly affects the image contrast. It has been suggested that not accounting for this correctly is the main cause of the Stobbs factor, the ubiquitous, large contrast mismatch found between theory and experiment. In the case where a hard aperture is applied, we show that previous conclusions drawn from work using bright field scanning transmission electron microscopy and invoking the principle of reciprocity are reliable in the presence of thermal scattering. In the aperture-free case it has been suggested that even the most sophisticated mathematical models for thermal diffuse scattering lack in their numerical implementation, specifically that there may be issues in sampling, including that of the contrast transfer function of the objective lens. We show that these concerns can be satisfactorily overcome with modest computing resources; thermal scattering can be modelled accurately enough for the purpose of making quantitative comparison between simulation and experiment. Spatial incoherence of the source is also investigated. Neglect or inadequate handling of thermal scattering in simulation can have an appreciable effect on the predicted contrast and can be a significant contribution to the Stobbs factor problem.