Lattice-resolution contrast from a focused coherent electron probe. Part I

To develop a Bloch wave framework for lattice-resolution contrast derived from coherent or incoherent scattering of an electron probe focused onto a crystal, boundary conditions which influence the propagation of an arbitrarily distorted coherent electron probe are addressed. These boundary conditions are particularly relevant for a probe focused within a unit cell, and lead to a general theory which hinges on Bloch wave excitation amplitudes being written as a function of beam position and focus. Whereas antisymmetric Bloch states are not excited for an incident plane wave at an exact zone axis orientation, these states may be strongly excited depending on probe focus and position within the unit cell. Equations for both coherent and incoherent lattice image contrast in scanning transmission electron microscopy are derived for any detector configuration in the Bloch wave framework. An equivalent expression amenable to evaluation via multislice techniques is also described. It is shown explicitly how mixed dynamic form factors for incoherent scattering should be taken into account for annular dark field or backscattered electron detectors, as well as for characteristic losses detected by X-ray emissions or by electron energy loss spectroscopy. A background contribution from "absorbed" electrons is included in the theory. The contribution of cross-talk from neighbouring columns to incoherent contrast is examined within the context of this theoretical framework.     

Optimal strategies for imaging thick biological specimens: exit wavefront reconstruction and energy-filtered imaging

In transmission electron microscopy (TEM) of thick biological specimens, the relationship between the recorded image intensities and the projected specimen mass density is distorted by incoherent electron–specimen interactions and aberrations of the objective lens. It is highly desirable to develop a strategy for maximizing and extracting the coherent image component, thereby allowing the projected specimen mass density to be directly related to image intensities. For this purpose, we previously used exit wavefront reconstruction to understand the nature of image formation for thick biological specimens in conventional TEM. Because electron energy-loss filtered imaging allows the contributions of inelastically scattered electrons to be removed, it is potentially advantageous for imaging thick, biological samples. In this paper, exit wavefront reconstruction is used to quantitatively analyse the imaging properties of an energy-filtered microscope and to assess its utility for thick-section microscopy. We found that for imaging thick biological specimens (> 0.5 μm) at 200 keV, only elastically scattered electrons contribute to the coherent image component. Surprisingly little coherent transfer was seen when using energy-filtering at the most probable energy loss (in this case at the first plasmon energy-loss peak). Furthermore, the use of zero-loss filtering in combination with exit wavefront reconstruction is considerably more effective at removing the effects of multiple elastic and inelastic scattering and microscope objective lens aberrations than either technique by itself. Optimization of the zero-loss signal requires operation at intermediate to high primary voltages (> 200 keV). These results have important implications for the accurate recording of images of thick biological specimens as, for instance, in electron microscope tomography.     

Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy

We report a local crystal structure analysis with a high precision of several picometers on the basis of scanning transmission electron microscopy (STEM). Advanced annular dark-field (ADF) imaging has been demonstrated using software-based experimental and data-processing techniques, such as the improvement of signal-to-noise ratio, the reduction of image distortion, the quantification of experimental parameters (e.g., thickness and defocus) and the resolution enhancement by maximum-entropy deconvolution. The accuracy in the atom position measurement depends on the validity of the incoherent imaging approximation, in which an ADF image is described as the convolution between the incident probe profile and scattering objects. Although the qualitative interpretation of ADF image contrast is possible for a wide range of specimen thicknesses, the direct observation of a crystal structure with deep-sub-angstrom accuracy requires a thin specimen (e.g., 10 nm), as well as observation of the structure image by conventional high-resolution transmission electron microscopy.     

Fundamental problems of imaging subsurface structures in the backscattered electron mode in scanning electron microscopy

In‐depth imaging of subsurface structures in scanning electron microscopy (SEM) is usually obtained by detecting backscattered electrons (BSE). For a layer‐by‐layer imaging in BSE microtomography, it is preferable to use an energy filtering of BSE. A simple approach is used to estimate the contrast by using backscattering coefficients of bulk materials and the maximum escape depths of the BSE. The contrast obtained by BSE energy filtering is about twice that of the standard BSE method by varying the acceleration voltage. The contrast decreases with increasing information depth. The information depth is about four times smaller than the electron range. The transmission of the spectrometer influences the minimum current of the order of 10^?8 A that is needed to get a contrast of 1%, for example.     

Diffraction effects and inelastic electron transport in angle‐resolved microscopic imaging applications

We analyse the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolour orientation imaging using multiple, angle‐resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in‐depth theoretical modelling of the energy‐ and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channelling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocations.     

A real-time optical image projection system for electron microscopy

The Hughes liquid crystal light valve has been coupled to a transmission electron microscope using a fibre optics plate and transmission phosphor. This system makes it possible to reconstruct in real time, electron images in coherent or incoherent light of arbitrary intensity outside the vacuum. The experimental results reported are used to estimate the design parameters of an on-line coherent optical diffractometer for high resolution work.     

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.     

Lattice-resolution contrast from a focused coherent electron probe. Part II

In the previous paper, boundary conditions matching the probe to the crystal wave function in scanning transmission electron microscopy were applied by matching the whole wave function across the boundary. It is shown here how that approach relates to previous Bloch wave formulations using (phase-linked) plane wave boundary conditions for wave vectors implied by the range of transverse momentum components in the incident probe. Matching the whole wave function across the boundary, and including a suitably fine mesh in the reciprocal space associated with the crystal to allow matching of transverse momentum components within the probe, leads to a structure matrix A containing many elements which would normally be excluded for plane wave incidence. For perfect crystals, the A-matrix may be block diagonalised. This leads to a considerable increase in the computational efficiency of the model and yields important insights into the physics of convergent probes in perfect crystals-reciprocity in coherent imaging and the small aperture limit for coherent and incoherent contrast are considered. The numerical equivalence of the incoherent lattice contrast calculated in this Bloch wave method and the multislice method using mixed dynamic form factors will be demonstrated. Comparison between both these methods and the frozen phonon model, a prevalent multislice method for annular dark field simulation which has the theoretical advantage of handling double channelling, will be made.     

Nanoscale scanning transmission electron tomography

Electron tomography enables the study of complex three‐dimensional objects with nanometre resolution. In materials science, scanning transmission electron microscopy provides images with minimal coherent diffraction effects and with high atomic number contrast that makes them ideal for electron tomographic reconstruction. In this study, we reviewed the topic of scanning transmission electron microscopy‐based tomography and illustrated the power of the technique with a number of examples with critical dimensions at the nanoscale.     

Extracting physically interpretable data from electron energy-loss spectra

Principal component analysis is routinely applied to analyze data sets in electron energy-loss spectroscopy (EELS). We show how physically meaningful spectra can be obtained from the principal components using a knowledge of the scattering of the probe electron and the geometry of the experiment. This approach is illustrated by application to EELS data for the carbon K edge in graphite obtained using a conventional transmission electron microscope. The effect of scattering of the probe electron is accounted for, yielding spectra which are equivalent to experiments using linearly polarized X-rays. The approach is general and can also be applied to EELS in the context of scanning transmission electron microscopy.     

Focused ion beam scanning electron microscopy in biology

Since the end of the last millennium, the focused ion beam scanning electron microscopy (FIB‐SEM) has progressively found use in biological research. This instrument is a scanning electron microscope (SEM) with an attached gallium ion column and the 2 beams, electrons and ions (FIB) are focused on one coincident point. The main application is the acquisition of three‐dimensional data, FIB‐SEM tomography. With the ion beam, some nanometres of the surface are removed and the remaining block‐face is imaged with the electron beam in a repetitive manner. The instrument can also be used to cut open biological structures to get access to internal structures or to prepare thin lamella for imaging by (cryo‐) transmission electron microscopy. Here, we will present an overview of the development of FIB‐SEM and discuss a few points about sample preparation and imaging.     

Coherence in inelastic electron scattering

The origin of dynamical effects in the inelastic scattering of fast electrons is discussed with reference to an (e, 2e) model for ionization and an Einstein model for TDS. The development of Kikuchi lines and bands from these localized interactions is discussed and related to current density. It is shown why the coherent preservation of amplitude and phase relationships between partial waves in a dynamical framework is of fundamental importance. Analytic expressions, related to the “mixed dynamic form factor” S(Q₁, Q₂, E), are written for K-shell ionization and for TDS. Diffraction of fast electrons emitted from a coherent point source on the top surface of a crystal is also discussed from the unified model presented for localized inelastic scattering.     

Application of channel electron multipliers in an electron detector for low‐voltage scanning electron microscopy

An electron detector containing channel electron multipliers was built and tested in the range of low‐voltage scanning electron microscopy as a detector of topographic contrast. The detector can detect backscattered electrons or the sum of backscattered electrons and secondary electrons, with different amount of secondary electrons. As a backscattered electron detector it collects backscattered electrons emitted in a specific range of take‐off angles and in a large range of azimuth angles enabling to obtain large solid collection angle and high collection efficiency. Two arrangements with different channel electron multipliers were studied theoretically with the use of the Monte Carlo method and one of them was built and tested experimentally. To shorten breaks in operation, a vacuum box preventing channel electron multipliers from an exposure to air during specimen exchanges was built and placed in the microscope chamber. The box is opened during microscope observations and is moved to the side of the scanning electron microscope chamber and closed during air admission and evacuation cycles enabling storing channel electron multipliers under vacuum for the whole time. Experimental tests of the detector included assessment of the type of detected electrons (secondary or backscattered), checking the tilt contrast, imaging the spatial collection efficiency, measuring the noise coefficient and recording images of different specimens.     

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.     

Low-energy electron microscopy (LEEM) and mirror electron microscopy (MEM) of biological specimens: Preliminary results with a novel beam separating system

Low-energy electron microscopy (LEEM) and mirror electron microscopy (MEM) utilize a parallel beam of slow-moving electrons backscattered from the specimen surface to form an image. If the electrons strike the surface an LEEM image is produced and if they are turned back just before reaching the surface an MEM image results. The applications thus far have been in surface physics. In the present study, applications of LEEM and MEM in the biological sciences are discussed. The preliminary results demonstrate the feasibility of forming images of uncoated cultured cells and cellular components using electrons in the threshold region (i.e. 0–10 V). The results also constitute a successful test of a novel beam-separating system for LEEM and MEM.     

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.     

Scanning electron microscope electron detector with a radial type discrete dynode electron multiplier

A discrete dynode electron multiplier with radial flux of electrons was built and tested in the range of low‐voltage scanning electron microscopy as a backscattered electron detector of topographic contrast. The multiplier collects backscattered electron emitted in a specific range of take‐off angles and over the whole azimuth angular range enabling large solid collection angle. Multipliers with different dynode shapes were studied theoretically with the use of the software for particle optics and three assemblies were built and tested experimentally. The gain estimation, assessment of the type of detected electrons (secondary electron or backscattered electron), imaging the spatial collection efficiency and signal‐to‐noise measurements were performed.     

Imaging of high-angle annular dark-field scanning transmission electron microscopy and observations of GaN-based violet laser diodes

The first part of this paper is devoted to physics, to explain high‐angle annular dark‐field scanning transmission electron microscopy (HAADF‐STEM) imaging and to interpret why HAADF‐STEM imaging is incoherent, instructing a strict definition of interference and coherence of electron waves. Next, we present our recent investigations of InGaN/GaN multiple quantum wells and AlGaN/GaN strained‐layer superlattice claddings in GaN‐based violet laser diodes, which have been performed by HAADF‐STEM and high‐resolution field‐emission gun scanning electron microscopy.     

Effects of electron channeling in HAADF-STEM intensity in La2CuSnO6

Atomic resolution imaging using the high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) can be applied to analyze the atomic structures of materials directly. This technique provides incoherent Z-contrast with the atomic number of the constituent elements. In the present work, unique contrasts that make intuitively interpreting the HAADF-STEM image in double perovskite oxide La₂CuSnO₆ difficult were observed. Multislice simulation confirmed that this occurred as an effect of the channeling process of electrons in combination with the effect of Debye–Waller factors. This was confirmed because in the La₂CuSnO₆ crystal, two independent Sn atoms and four independent La atoms in the unit cell had different Debye–Waller factors, and the La columns consisted of pairs of columns with a small separation, whereas the Sn atoms were arranged straight.