Coherence and incoherence of inelastically scattered electron waves

Whether the elastically and inelastically scattered electron waves are mutually coherent is a key question for the quantitative evaluation of the contrast of a high resolution transmission electron microscope image and for confirming the energy filtering ability of electron holography. Using a simplified object model composed of only two scattering centers the elastically and inelastically scattered electron waves and their detection are discussed. The only used proof for the main results of this paper is the orthogonality of the object states. The reasoning can be extended straightforward to a general case, e.g. a complicated object as well as complicated interaction Hamiltonians as long as they remain time independent. The results of this paper are: (1) The elastically and inelastically scattered waves which have different energy losses are mutually incoherent. The reason for that is simply that the corresponding excited object states are mutually orthogonal; (2) the inelastically scattered waves which have the same energy loss and are scattered by the same object state are coherent, whereas they are incoherent if they are scattered by different object states though they have the same energy; (3) the coherence degree of the scattered electron waves is proportional to the modulus of the scalar product of the corresponding object states.     

Inelastic scattering and holography

The controversy about whether or not an inelastically scattered electron wave can still interfere with a reference wave is solved by treating the whole problem rigorously and describing electron, source and object in one Hamiltonian. It turns out that, in principle, interference can occur between an inelastically scattered wave and a reference wave from the incident beam spectrum provided the energy difference is smaller than about 10(-15) eV. However, it is argued that the density of states in source object and electron wave is much too small to make this effect observable.     

Three-dimensional imaging in double aberration-corrected scanning confocal electron microscopy, part I: elastic scattering

A transmission electron microscope fitted with both pre-specimen and post-specimen spherical aberration correctors enables the possibility of aberration-corrected scanning confocal electron microscopy. Imaging modes available in this configuration can make use of either elastically or inelastically scattered electrons. In this paper we consider image contrast for elastically scattered electrons. It is shown that there is no linear phase contrast in the confocal condition, leading to very low contrast for a single atom. Multislice simulations of a thicker crystalline sample show that sample vertical location and thickness can be accurately determined. However, buried impurity layers do not give strong, nor readily interpretable contrast. The accompanying paper examines the detection of inelastically scattered electrons in the confocal geometry.     

Contrast in the electron spectroscopic imaging mode of a TEM

The ratio of inelastic-to-elastic total cross-sections has been measured in an energy-filtering electron microscope for different elements. Formulae for the transmission of elastically and inelastically scattered electrons in part I were used to calculate the optimum conditions for a Z-ratio contrast in the electron spectroscopic imaging mode. Structure-sensitive contrast can be observed for all non-carbon atoms in biological sections when filtering with an energy loss at ΔE ～ 250 eV below the carbon K edge. Model experiments with evaporated layers of different elements on a carbon film allow measurement of the contrast increase. Filtering with the carbon plasmon loss shows a lower phase contrast than with zero-loss filtering. This can be explained by calculating contrast transfer functions for inelastically scattered electrons.     

Experiments on inelastic electron holography

Using the combination of an electron biprism and an energy filter, the coherence distribution in an inelastically scattered wave-field is measured. It is found that the degree of coherence decreases rapidly with increasing distance between two superimposed points in the object, and with increasing energy-loss. In a Si sample, coherence of plasmon scattering increases in vacuum with the distance from the edge of the sample.     

Computation of contrasts in atomic resolution electron spectroscopic images of planar defects in crystalline specimens

The image obtained in a conventional transmission electron microscope contains contributions from elastically and from inelastically scattered electrons. The electron spectroscopic imaging mode of an energy-filtering transmission electron microscope allows us to separate these two different contributions by inserting an energy-selecting slit in the energy-dispersive plane of an imaging energy filter. Selecting a specific energy loss corresponding to the ionization of the inner shell of a particular element one can obtain information on the distribution of the element within the specimen. The contrast is then caused by inelastically scattered electrons. For crystalline specimens, however, the contrast will be influenced additionally by the elastic contrast. This elastic contrast arises from electron diffraction and increases with increasing crystal thickness. Therefore the intensity distribution in the image cannot directly be interpreted as an elemental map. For a reliable interpretation of contrast formation in elemental maps it is therefore necessary to compute theoretical energy-loss images for various crystal thicknesses and compare these images with the experimental images. As an example we discuss the influence of electron diffraction effects on energy-loss images of two crystals with planar defects. Linescans are computed for various thicknesses of these crystals. Our calculations are performed using first-order perturbation theory to describe the transitions between the Bloch-wave states of the incident electron. The computed linescans for various crystal thicknesses show clearly that the influence of the elastic contrast on an image increases when we investigate thicker specimens. Furthermore, the comparison between elastic and energy-loss images demonstrates the partial preservation of the elastic contrast as a function of thickness. We find that for specimens thicker than about one third of the extinction length (here approximately 80-100 A) it is impossible to interpret an energy-loss image directly as elemental map.     

Energy-filtered electron-diffracted beam holography

A method of energy-filtered electron holography is described where any two electron-diffracted beams can be interfered using an electron biprism. A Gatan image filter is used to select the energy loss of the electrons produced in the holograms. Gallium arsenide is used as the TEM specimen. This method of microscopy confirms that fringes extending beyond a limiting aperture were due to inelastically scattered electrons and specifically electrons scattered from the bulk plasmon. The degree of coherence of the zero-loss and energy-loss electrons were high and measured to be approximately 0.3, which was maintained even for the high energy-loss electrons up to 100 eV. Future systematic studies using this method should help understand the Stobbs factor and contribute to the development of quantitative high-resolution electron microscopy.     

Quantitative high resolution transmission electron microscopy: the need for energy filtering and the advantages of energy-loss imaging

Evidence is presented that inelastically scattered electrons contribute significant detail at the atomic level to high resolution images, particularly in high voltage instruments. The implications for quantitative image interpretation are shown to be serious and a case is made for incorporating facilities for energy-filtered imaging in future high resolution electron microscopes.     

Identification of precipitable Ca2+ by electron spectroscopic imaging and electron energy loss spectroscopy in the organ of Corti of the guinea pig

Ca2+ cations were precipitated with potassium antimonate in the cochlea of the guinea pig, and the formed precipitates were localized by electron microscopy using either elastically or inelastically scattered electrons. The elemental composition of the precipitates was determined by electron spectroscopic imaging (ESI) and electron energy loss spectroscopy (EELS). It was found that calcium, antimony and oxygen were the dominating elements in the precipitates formed in different cell types in the inner ear.     

Elastic scattering in EELS-fundamental corrections to quantification

Amazingly, elastic scattering has been so far totally ignored in quantitative analytical electron energy-loss spectroscopy. Yet the majority of the electrons typically recorded suffer elastic scattering including a large fraction which, though elastically scattered to beyonf the collecting angle, are inelastically scattered back. A simple procedure, based on a semi-empirical multiple elastic scattering distribution, is described which cam be adopted to take account of multiple elastic-inelastic scattering. With this treatment a fundamental understanding is obtained of many features of EELS which have previously appeared anomalous.     

Annular electron energy-loss spectroscopy in the scanning transmission electron microscope

We study atomic-resolution annular electron energy-loss spectroscopy (AEELS) in scanning transmission electron microscopy (STEM) imaging with experiments and numerical simulations. In this technique the central part of the bright field disk is blocked by a beam stop, forming an annular entry aperture to the spectrometer. The EELS signal thus arises only from electrons scattered inelastically to angles defined by the aperture. It will be shown that this method is more robust than conventional EELS imaging to variations in specimen thickness and can also provide higher spatial resolution. This raises the possibility of lattice resolution imaging of lighter elements or ionization edges previously considered unsuitable for EELS imaging.     

Zero-loss electron microscopy with the Zeiss EM902

The recently introduced Zeiss EM902 is the first commercially available electron microscope to incorporate a magnetic spectrometer capable of forming directly energy-filtered images and diffraction patterns. We have briefly assessed the potential usefulness of this microscope for structural studies of thin biological specimens, through removal of inelastically scattered electrons. The improvements we find in image contrast, without significant loss of resolution, suggest energy-filtering may prove particularly worthwhile with unstained specimens.     

Exploring different inelastic projection mechanisms for electron tomography

Several different projection mechanisms that all make use of inelastically scattered electrons are used for electron tomography. The advantages and the disadvantages of these methods are compared to HAADF-STEM tomography, which is considered as the standard electron tomography technique in materials science. The different inelastic setups used are energy filtered transmission electron microscopy (EFTEM), thickness mapping based on the log-ratio method and bulk plasmon mapping. We present a comparison that can be used to select the best inelastic signal for tomography, depending on different parameters such as the beam stability and nature of the sample. The appropriate signal will obviously also depend on the exact information which is requested.     

Energy filtering transmission electron microscopy using the new JEM-2010FEF

The new JEM-2010FEF electron microscope provides useful techniques based on energy filtering as an omega-type energy filter is integrated into a thermal field-emission 200 kV transmission electron microscope. For example, the zero-loss imaging improves the contrast of high resolution lattice images as well as images of precipitates or lattice defects in alloys. The acquisition time for elemental mapping with core-loss electrons is one order in magnitude shorter than with energy-dispersive X-ray spectroscopy. The removal of inelastically scattered electrons enables us to observe weak lines in convergent-beam electron diffraction patterns from a thicker specimen with a probe size 1–2 nm in diameter. A combination of the field emission gun and sensitive recording media such as an imaging plate and a slow-scan CCD camera makes the energy filtering more powerful.     

Experimental investigation of phase contrast formed by inelastically scattered electrons

Phase contrast formed by inelastically scattered electrons in a crystal has been investigated using spatially resolved EELS, which enables simultaneous observation of lattice fringes formed by electrons of various energy losses. Lattice fringes produced by low-loss electrons overlap on an elastic TEM image like Fourier images. This means that the exit wave is preserved in low-loss scattering. Similar Fourier images occur for electrons suffering core-losses in the range 50-400 eV, which indicates delocalization and spatial coherence in those core-loss scattering events. The spatial coherence of inelastically scattered electrons is estimated from the focus dependence of energy-filtered lattice fringe contrast. Spatial coherence widths shorten with increasing energy-loss, and their energy-loss dependence is similar to diffraction errors derived from the characteristic angle for inelastic scattering.     

Size effects in glass fragment identification by micro-x-ray fluorescence analysis

Energy-dispersive x-ray fluorescence (EDXRF) analysis with a lateral resolution of 300 μm has been used in scanning electron microscopy to carry out model experiments for the identification of small glass fragments. Small sample dimensions can produce size effects which cause intensity changes in the EDXRF spectra as compared with bulk specimen spectra. These effects can be analysed by means of the inelastically scattered Mo Kα source line as long as the x-ray spot size is smaller than the specimen dimension.     

Dynamical effects of anisotropic inelastic scattering in electron backscatter diffraction

We present a model which describes the appearance of excess and deficiency features in electron backscatter diffraction (EBSD) patterns and we show how to include this effect in many-beam dynamical simulations of EBSD. The excess and deficiency features appear naturally if we take into account the anisotropy of the internal source of inelastically scattered electrons which are subsequently scattered elastically to produce the EBSD pattern. The results of simulations applying this model show very good agreement with experimental patterns. The amount of the excess-deficiency asymmetry of the Kikuchi bands depends on their relative orientation with respect to the incident beam direction. In addition, higher order Laue zone rings are also influenced by the same effect.     

The scanning low-energy electron microscope: First attainment of diffraction contrast in the scanning electron microscope

Using small Pb crystals deposited in situ on a partially contaminated Si (100) crystal, we demonstrate that a commercial scanning electron microscope (SEM) can easily be converted into a scanning low-energy electron microscope (SLEEM). Although the contrast mechanism is much more complicated than that in nonscanning LEEM because not only one diffracted monochromatic beam and its close environment are used for imaging, but several diffracted beams and a wide energy spectrum of electrons of different origin (secondary electrons, inelastically andelastically scattered electrons) are used, SLEEM is a valuable addition to the standard SEM because it provides an additional structure- and orientation-sensitive contrast mechanism in crystalline materials, a low sampling depth, and high intensity at low energies.     

A method for the improvement of the visibility of transmission electron microscope images

A method is presented of improving the visibility of transmission electron microscope images in any situation in which a high resolution in only one chosen direction is of interest. The technique is based on the use of slot shaped objective apertures. Such apertures are of reduced area relative to a circular aperture giving the same all round resolution. The background intensity due to inelastically scattered electrons is thus reduced. The aperture device developed is described, while the value of the method is demonstrated by its application to the observation of dislocations. Further possible applications are indicated.