Coherent nano-area electron diffraction

We describe the new coherent nano-area electron diffraction (NED) and its application for structure determination of individual nanostructures. The study is motivated by the challenge and the general lack of analytical techniques for characterizing nanometer-sized, heterogeneous phases. We show that by focusing electrons on the focal plane of the pre-objective lens using a 3rd condenser lens and a small condense aperture, it is possible to achieve a nanometer-sized highly parallel illumination or probe. The high angular resolution of diffraction pattern from the parallel illumination allows over-sampling and consequently the solution of phase problem based on the recently developed ab initio phase retrieval technique. From this, a high-contrast and high-resolution image can be reconstructed at resolution beyond the performance limit of the image-forming objective lens. The significance of NED for nanostructure characterization will be exemplified by single-wall carbon nanotubes and small metallic clusters. Imaging from diffraction patterns, or diffractive imaging, will be demonstrated using double-wall carbon nanotubes.     

Position averaged convergent beam electron diffraction: Theory and applications

A finely focused angstrom-sized coherent electron probe produces a convergent beam electron diffraction pattern composed of overlapping orders of diffracted disks that sensitively depends on the probe position within the unit cell. By incoherently averaging these convergent beam electron diffraction patterns over many probe positions, a pattern develops that ceases to depend on lens aberrations and effective source size, but remains highly sensitive to specimen thickness, tilt, and polarity. Through a combination of experiment and simulation for a wide variety of materials, we demonstrate that these position averaged convergent beam electron diffraction patterns can be used to determine sample thicknesses (to better than 10%), specimen tilts (to better than 1 mrad) and sample polarity for the same electron optical conditions and sample thicknesses as used in atomic resolution scanning transmission electron microscopy imaging. These measurements can be carried out by visual comparison without the need to apply pattern-matching algorithms. The influence of thermal diffuse scattering on patterns is investigated by comparing the frozen phonon and absorptive model calculations. We demonstrate that the absorptive model is appropriate for measuring thickness and other specimen parameters even for relatively thick samples (>50 nm).     

Electron backscatter diffraction of grain and subgrain structures — resolution considerations

Characterization of microstructures containing small grains or low-angle grain boundaries by electron backscattered diffraction (EBSD) is limited by the spatial and angular resolution limits of the technique. It was found that the best effective spatial resolution (60 nm) for aluminium alloys in a tungsten-filament scanning electron microscope (SEM) was obtained for an intermediate probe current which provided a compromise between pattern quality and specimen interaction volume. The same specimens and EBSD equipment when used with a field-emission gun SEM showed an improvement in spatial resolution by a factor of 2–3. For characterizing low-angle boundary microstructures, the precision of determining relative orientations is a limiting factor. It was found that the orientation noise was directly related to the probe current and this was interpreted in terms of the effect of probe current on the quality of the diffraction patterns.     

Subject index to volume 10

The scanning transmission electron microscope with a field emission electron source operated at 100 kV allows X-ray microanalysis using electron probes as small as 1 to 2 nm. Measurements of the probe in a Vacuum Generators HB-501 STEM show that spherical aberration in the objective lens controls the probe size and shape at beam convergence half-angles of 10 mrad and greater typically used for X-ray microanalysis. A virtual objective aperture eliminates X-ray contributions from the probe-forming system, but must be aligned exactly to avoid asymmetrical broadening of the probe by spherical aberration. It is estimated that 5 nm X-ray spatial resolution can be achieved in low to medium atomic number materials. Even at this resolution however, probe broadening in the specimen controls the resolution; the main limitation is one of specimen preparation and a knowledge of the final specimen thickness. Determination of composition profiles near voids, dislocations and other individual defects in thin foils also requires a knowledge of the defect depth position and deconvolution of the probe and composition profiles.     

Aberration-compensated large-angle rocking-beam electron diffraction

The application of convergent beam electron diffraction (CBED) to determine symmetry, refine structure factors, and measure specimen thickness requires rather thick specimen and is very difficult or even impossible in the case of large unit cell materials. The large-angle rocking-beam electron diffraction (LARBED) technique introduced in this paper gives access to the kind of experimental data contained in CBED patterns but over a much larger angular range. In addition to symmetry determination and thickness measurement even for thin samples this technique also allows, in principle, very accurate measurements of structure factors. Similar to precession electron diffraction (PED), LARBED uses the illumination tilt coils to sequentially change the angle of incidence of the electron beam over a very large range. I will present results obtained by a recently developed self-calibrating acquisition software which compensates for aberration-induced probe shifts during the acquisition of LARBED patterns and keeps the probe within a few nm, while covering a tilt range from 0 to 100 mrad. This paper is dedicated to Prof. John C. H. Spence on the occasion of his 65th birthday.     

Multi-chord fiber-coupled interferometer with a long coherence length laser

This paper describes a 561 nm laser heterodyne interferometer that provides time-resolved measurements of line-integrated plasma electron density within the range of 10(15)-10(18) cm(-2). Such plasmas are produced by railguns on the plasma liner experiment, which aims to produce μs-, cm-, and Mbar-scale plasmas through the merging of 30 plasma jets in a spherically convergent geometry. A long coherence length, 320 mW laser allows for a strong, sub-fringe phase-shift signal without the need for closely matched probe and reference path lengths. Thus, only one reference path is required for all eight probe paths, and an individual probe chord can be altered without altering the reference or other probe path lengths. Fiber-optic decoupling of the probe chord optics on the vacuum chamber from the rest of the system allows the probe paths to be easily altered to focus on different spatial regions of the plasma. We demonstrate that sub-fringe resolution capability allows the interferometer to operate down to line-integrated densities of the order of 5 × 10(15) cm(-2).     

Computer simulation and analysis of high-resolution electron microscope images and diffraction patterns with partial coherence,hollow cone illumination,and virtual apertures

A general method for computing high-resolution conventional transmission electron microscope images and diffraction patterns, when there are different types of partially coherent illumination conditions, is described. Examples of convergent beam, hollow cone, and virtual aperture illumination conditions are given in the context of interpreting image features. A comparison of real and computed diffraction patterns shows that, in practice, many innovative imaging modes are possible, which can be verified prior to real microscope experiments.     

Optimization of EBSD parameters for ultra-fast characterization

Ultra-fast pattern acquisition of electron backscatter diffraction and offline indexing could become a dominant technique over online electron backscatter diffraction to investigate the microstructures of a wide range of materials, especially for in situ experiments or very large scans. However, less attention has been paid to optimize the parameters related to ultra-fast electron backscatter diffraction. The present results show that contamination on a clean and unmounted specimen is not a problem even at step sizes as small as 1 nm at a vacuum degree of 6.1 × 10(-5) Pa. There exists an optimum step size at about 50 data acquisition board units. A new and easy method to calculate the effective spatial resolution is proposed. Effective spatial resolution tends to increase slightly as the probe current increases from 10 to 100 nA. The fraction of indexed points decreases slightly as the frame rate increases from 128 patterns per second (pps) to 835 pps by compensating the probe current at the same ratio. The value 96 × 96 is found to be the optimum pattern resolution to obtain optimum speed and image quality. For a fixed position of electron backscatter diffraction detector, the fraction of indexed points as a function of working distance has a maximum value and drops sharply by shortening the working distance and it decreases slowly with increasing the working distance.     

Köhler illumination in the TEM: Fundamentals and advantages

Köhler illumination is the most favourable design for the illumination path of an electron microscope with a condenser objective lens. The new illumination system of the EM 910 and EM 912 OMEGA allows both wide area (Köhler) illumination for TEM operation and spot illumination for analytical investigations. Compared to conventional systems and objective lenses with a condenser mini lens, this system offers many advantages. In addition to the homogeneous, highly coherent and parallel illumination of every point in the specimen, it offers advantages for selected area diffraction and spot scan mode. Combined with the electron optical selection of a condenser aperture, this illumination system provides the flexibility necessary to achieve optimum illumination for the specimen.     

Influence of the elliptical illumination on acquisition and correction of coherent aberrations in high-resolution electron holography

In high-resolution off-axis electron holography, the interpretable lateral resolution is extended up to the information limit of the electron microscope by means of a correcting phase plate in Fourier space. A plane illuminating electron wave is generally assumed. However, in order to improve spatial coherence, which is essential for holography, the object under investigation is illuminated with an elliptically shaped electron source. This special illumination imposes a variation of beam directions over the field of view. Therefore, due to the interaction of beam tilt and coherent wave aberration, the effective aberrations vary over the field of view yielding a loss of isoplanicity. Consequently, in the past the aberrations were only corrected successfully for a small part of the field of view. However, a thorough analysis of the holographic imaging process shows that the imaging artifacts introduced by the elliptical illumination can be corrected under reconstruction by means of a phase curvature, which models the illuminating wave front. Applied in real space, this phase curvature is seamlessly incorporated into the correction process for coherent wave aberration resulting in an improvement of interpretable lateral resolution up to the information limit for the whole field of view.     

An in-vacuum x-ray diffraction microscope for use in the 0.7-2.9 keV range

A dedicated in-vacuum coherent x-ray diffraction microscope was installed at the 2-ID-B beamline of the Advanced Photon Source for use with 0.7-2.9 keV x-rays. The instrument can accommodate three common implementations of diffractive imaging; plane wave illumination; defocused-probe (Fresnel diffractive imaging) and scanning (ptychography) using either a pinhole, focused or defocused probe. The microscope design includes active feedback to limit motion of the optics with respect to the sample. Upper bounds on the relative optics-to-sample displacement have been measured to be 5.8 nm(v) and 4.4 nm(h) rms/h using capacitance micrometry and 27 nm/h using x-ray point projection imaging. The stability of the measurement platform and in-vacuum operation allows for long exposure times, high signal-to-noise and large dynamic range two-dimensional intensity measurements to be acquired. Finally, we illustrate the microscope's stability with a recent experimental result.     

Applications of modern microdiffraction to materials science

Modern experimental techniques for static convergent beam electron microdiffraction in transmission electron microscopes are discussed and compared to the better known selected area electron microdiffraction methods. The effects of probe coherence are qualitatively discussed. Some recent applications of convergent beam microdiffraction to microstructural characterization of small particles, various lattice defects and amorphous solids are described.     

Determination of mean free path for energy loss and surface oxide film thickness using convergent beam electron diffraction and thickness mapping: a case study using Si and P91 steel

Determining transmission electron microscope specimen thickness is an essential prerequisite for carrying out quantitative microscopy. The convergent beam electron diffraction method is highly accurate but provides information only on the small region being probed and is only applicable to crystalline phases. Thickness mapping with an energy filter is rapid, maps an entire field of view and can be applied to both crystalline and amorphous phases. However, the thickness map is defined in terms of the mean free path for energy loss (λ), which must be known in order to determine the thickness. Convergent beam electron diffraction and thickness mapping methods were used to determine λ for two materials, Si and P91 steel. These represent best‐ and worst‐case scenario materials, respectively, for this type of investigation, owing to their radically different microstructures. The effects of collection angle and the importance of dynamical diffraction contrast are also examined. By minimizing diffraction contrast effects in thickness maps, reasonably accurate (±15%) values of λ were obtained for P91 and accuracies of ±5% were obtained for Si. The correlation between the convergent beam electron diffraction‐derived thickness and the log intensity ratios from thickness maps also permits estimation of the thickness of amorphous layers on the upper and lower surfaces of transmission electron microscope specimens. These estimates were evaluated for both Si and P91 using cross‐sectional transmission electron microscopy and were found to be quite accurate.     

Performance and applications of electron energy loss spectroscopy in stem

When coupled in the image mode to a VG-HB501 microscope, the spectrometer designed by O. Krivanek and manufactured by Gatan Inc. is well suited for resolving analytical problems with a high spatial resolution. It actually records energy loss spectra from areas as small as 0.5 nm with a typical energy resolution of 1 eV over the energy loss range and with a good efficiency in collecting inelastic electrons. During the last few months, this high performance combination of microscope and spectrometer has been used to investigate (a) detection limits in EELS which are presently estimated of the order of ten atoms in a test situation such as metallic clusters deposited on a very thin carbon layer; (b) quantitative chemical analysis of representative nanovolumes of complex oxide specimens, emphasizing several aspects of elemental segregation in the neighborhood of grain boundaries and within vitreous areas; (c) changes of fine structures close to the K-oxygen threshold, due to different bonding states; and (d) efficient Z-contrast imaging modes on sections of embedded biological material without metallic staining.     

Resolution enhancing using cantilevered tip-on-aperture silicon probe in scanning near-field optical microscopy

Scanning near-field optical microscopy (SNOM) achieves a resolution beyond the diffraction limit of conventional optical microscopy systems by utilizing subwavelength aperture probe scanning. A problem associated with SNOM is that the light throughput decreases markedly as the aperture diameter decreases. Apertureless scanning near-field optical microscopes obtain a much better resolution by concentrating the light field near the tip apex. However, a far-field illumination by a focused laser beam generates a large background scattering signal. Both disadvantages are overcome using the tip-on-aperture (TOA) approach, as presented in previous works. In this study, a finite difference time domain analysis of the degree of electromagnetic field enhancement is performed to verify the efficiency of TOA probes. For plasmon enhancement, silver is deposited on commercially available cantilevered SNOM tips with 20nm thicknesses. To form the aperture and TOA in the probes, electron beam-induced deposition and focused ion beam machining were applied at the end of the sharpened tip. The results show that cantilevered TOA probes were highly efficient for improvements of the resolution of optical and topological measurement of nanostructures.     

First experimental test of a new monochromated and aberration-corrected 200 kV field-emission scanning transmission electron microscope

The first 200 kV scanning transmission electron microscope (STEM) with an imaging energy filter, a monochromator and a corrector for the spherical aberration (Cs-corrector) of the illumination system has been built and tested. The STEM/TEM concept with Koehler illumination allows to switch easily between STEM mode for analytical and TEM mode for high-resolution or in situ studies. The Cs-corrector allows the use of large illumination angles for retaining a sufficiently high beam current despite the intensity loss in the monochromator. With the monochromator on and a 3 microm slit in the dispersion plane that gives 0.26 eV full-width at half-maximum (FWHM) energy resolution we have obtained so far an electron beam smaller than 0.20 nm in diameter (FWHM as measured by scanning the spot quickly over the CCD) which contains 7 pA current and, according to simulations, should be around 0.12 nm in true size. A high-angle annular dark field (ADF) image with isotropic resolution better than 0.28 nm has been recorded with the monochromator in the above configuration and the Cs-corrector on. The beam current is still somewhat low for electron energy-loss spectroscopy (EELS) but is expected to increase substantially by optimising the condenser set-up and using a somewhat larger condenser aperture.     

Optimum condition of convergent beam illumination for observation of local structure by high resolution transmission electron microscopy

We propose the convergent beam illumination as a technique for the local structural analysis by high resolution transmission electron microscopy. The image contrast is lower in the convergent beam illumination than in the parallel beam illumination because of the lower coherency. However the intensity oscillation around an atom image, which appears due to interference effect, is much reduced with the convergent beam illumination, and pseudo-images do not appear at termination of crystal periodicity. The convergent beam illumination, rather than parallel beam illumination, precisely reveals non-periodic local structures, such as interfaces, surfaces and fine particles, which are even embedded in a crystal. From theoretical analysis the optimum condition is derived as divergence of q(s )* = 0.44 and focus of delta(z)* = 1.35 in generalized coordinates. Using the convergent beam illumination the point resolution is improved by 20% compared to conventional parallel beam illumination.     

Measuring the PSF from aperture images of arbitrary shape--an algorithm

A new algorithm for determining the point spread function (PSF) of digital imaging systems is presented. The input is an image of an aperture whose shape need not be regular. The aperture shape is refined to an effective sub-pixel resolution and the PSF of the system is determined by de-convolution, assuming uniform illumination and a step function edge. The method has been tested on theoretical aperture images of varying shape and PSF, with and without noise. Depending on the degree of noise, a known PSF can be recovered to an accuracy of between 0.2 and 0.8%. Some typical results are given for a Gatan Image Filter with a 794 YAG multiscan camera on a Philips EM 430 transmission electron microscope at 200 and 300 kV. An example of a de-convoluted convergent beam electron diffraction pattern is included. The algorithm tolerates a small amount of de-focus.     

The measurement and calculation of the X-ray spatial resolution obtained in the analytical electron microscope

The X-ray microanalytical spatial resolution is determined experimentally in various analytical electron microscopes by measuring the degradation of an atomically discrete composition profile across an interphase interface in a thin-foil of Ni-Cr-Fe. The experimental spatial resolutions are then compared with calculated values. The calculated spatial resolutions are obtained by the mathematical convolution of the electron probe size with an assumed beam-broadening distribution and the single-scattering model of beam broadening. The probe size is measured directly from an image of the probe in a TEM/STEM and indirectly from dark-field signal changes resulting from scanning the probe across the edge of an MgO crystal in a dedicated STEM. This study demonstrates the applicability of the convolution technique to the calculation of the microanalytical spatial resolution obtained in the analytical electron microscope. It is demonstrated that, contrary to popular opinion, the electron probe size has a major impact on the measured spatial resolution in foils < 150 nm thick.     

Nanometric crystal defects in transmission electron microscopy

Transmission electron microscopy (TEM) is revisited in order to define methods for the identification of nanometric defects. Nanometric crystal defects play an important role as they influence, generally in a detrimental way, physical properties. For instance, radiation-induced damage in metals strongly degrades mechanical properties, rendering the material stronger but brittle. The difficulty in using TEM to identify the nature and size of such defects resides in their small size. TEM image simulations are deployed to explore limits and possible ways to improve on spatial resolution and contrast. The contrast of dislocation loops, cavities, and a stacking fault tetrahedra (SFT) are simulated in weak beam, interfering reflections (HRTEM), and scanned condensed electron probe (STEM) mode. Results indicate that STEM is a possible way to image small defects. In addition, a new objective aperture is proposed to improve resolution in diffraction contrast. It is investigated by simulations of the weak beam imaging of SFT and successfully applied in experimental observations.