Analysis of Kikuchi band contrast reversal in electron backscatter diffraction patterns of silicon

We analyze the contrast reversal of Kikuchi bands that can be seen in electron backscatter diffraction (EBSD) patterns under specific experimental conditions. The observed effect can be reproduced using dynamical electron diffraction calculations. Two crucial contributions are identified to be at work: First, the incident beam creates a depth distribution of incoherently backscattered electrons which depends on the incidence angle of the beam. Second, the localized inelastic scattering in the outgoing path leads to pronounced anomalous absorption effects for electrons at grazing emission angles, as these electrons have to go through the largest amount of material. We use simple model depth distributions to account for the incident beam effect, and we assume an exit angle dependent effective crystal thickness in the dynamical electron diffraction calculations. Very good agreement is obtained with experimental observations for silicon at 20 keV primary beam energy.     

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 channelling based crystallography

Electron channelling occurs when the incident electron beam is parallel to the atom columns of an object, such as a crystal or a particular crystal defect. Then, the electrons are trapped in the electrostatic potential of an atom column in which they scatter dynamically. This picture provides physical insight and explains why a one-to-one correspondence is maintained between the exit wave and the projected structure, even in case of strong dynamical scattering. Moreover, the theory is very useful to invert the dynamical scattering, that is, to derive the projected structure from the exit wave. Finally, it can be used to determine the composition of an atom column with single atom sensitivity or to explain dynamical electron diffraction effects. In this paper, an overview of the channelling theory will be given together with some recent applications.     

Method for determination of the displacement field in patterned nanostructures by TEM/CBED analysis of split high-order Laue zone line profiles

A method to extract accurate information on the displacement field distribution from split high‐order Laue zones lines in a convergent‐beam electron diffraction pattern of nanostructures has been developed. Starting from two‐dimensional many beam dynamical simulation of HOLZ patterns, we assembled a recursive procedure to reconstruct the displacement field in the investigated regions of the sample, based on the best fit of a parametrized model. This recursive procedure minimizes the differences between simulated and experimental patterns, taken in strained regions, by comparing the corresponding rocking curves of a number of high‐order Laue zone reflections. Due to its sensitivity to small displacement variations along the electron beam direction, this method is able to discriminate between different models, and can be also used to map a strain field component in the specimen. We tested this method in a series of experimental convergent‐beam electron diffraction patterns, taken in a shallow trench isolation structure. The method presented here is of general validity and, in principle, it can be applied to any sample where not negligible strain gradients along the beam direction are present.     

Coherence and sampling requirements for diffractive imaging

Coherent Diffractive Imaging (CDI) allows images to be reconstructed from diffraction patterns by solving the non-crystallographic phase problem for isolated nanostructures. We show that the Shannon sampling of diffraction intensities needed in CDI requires a coherence width about twice the lateral dimensions of the object, and that the linear number of detector pixels fixes the energy spread needed in the beam. The Shannon sampling, defined by the transform of the periodically repeated autocorrelation of the object, is related to Bragg scattering from an equivalent crystal, and shown to be consistent with the sampling of Young's fringes established by scattering from extreme points in the object. The results are relevant to the design of diffraction cameras for CDI and plans for femotosecond X-ray diffraction from individual proteins.     

Structure determination at the atomic level from dynamical electron diffraction data under systematic row conditions.

We discuss a method to obtain structural information on crystals at the atomic level in high-resolution transmission electron microscopy from dynamical diffraction data under systematic row conditions. Working at a fixed incident energy and within an N-beam approximation, data is required at a well defined set of N incident beam orientations to determine the scattering matrix, one orientation for each column in the matrix. At each orientation the corresponding column of the scattering-matrix is obtained by Fourier transformation of the exit surface wave function. Thus, in addition to each exit surface image, we must recover the phase of the wave function for that orientation in the image plane. We show that retrieval of the phase using algorithms based on conservation of flux, which assume continuity of the phase, can yield incorrect solutions for the phase. This is because singularities can occur in the phase of the wave field at points where the intensity is zero, which can lead to edge dislocations in the phase. We demonstrate, using a model example, how these edge dislocations arise. We will show that phase retrieval from a through focal series of measurements or using the Gerchberg-Saxton algorithm (starting from measurements of an image and the corresponding diffraction pattern), correctly retrieves the phase and hence the exit surface wave function for all the orientations required to obtain the scattering-matrix. The dynamical (multiple) scattering can then be inverted to uniquely obtain the projected potential.     

Novel carbon nanosheets as support for ultrahigh-resolution structural analysis of nanoparticles

The resolution in transmission electron microscopy (TEM) has reached values as low as 0.08 nm. However, these values are not accessible for very small objects in the size range of a few nanometers or lower, as they have to be placed on some support, which contributes to the overall electron-scattering signal, thereby blurring the contrast. Here, we report on the use of nanosheets made from cross-linked aromatic self-assembled monolayers as TEM sample supports. When transferred onto a copper grid, a single 1.6-nm-thick nanosheet can cover the grid and is free standing within the micron-sized openings. Despite its thinness, the sheet is stable under the impact of the electron beam. Micrographs taken from nanoclusters onto these nanosheets show highly increased contrast in comparison to the images taken from amorphous carbon supports. In scanning transmission electron microscopy with nanosheet support, a size analysis of sub-nanometer Au clusters was performed and single Au atoms were resolved.     

Plasmon-Enhanced Near-Field Optical Spectroscopy of Multicomponent Semiconductor Nanostructures

Multicomponent semiconductor nanostructures were studied by local spectral analysis based on surface-enhanced Raman scattering by semiconductor nanostructures located on the surface of an array of Au nanoclusters near the metallized tip of an atomic force microscope. In the gap between the metal nanoclusters and the tip, where a semiconductor nanostructure is located, there is a strong increase in the local electric field (hot spot), resulting in a dramatic enhancement of the Raman scattering signal. An unprecedented enhancement of the Raman scattering signal by two-dimensional (over 108 for MoS2) and zero-dimensional (106 for CdSe nanocrystals) semiconductor nanostructures was achieved. The use of the method for mapping the Raman scattering response of a multicomponent system of MoS2 and CdSe made it possible to identify components with a spatial resolution far exceeding the diffraction limit.     

Precession technique and electron diffractometry as new tools for crystal structure analysis and chemical bonding determination

We have developed a new fast electron diffractometer working with high dynamic range and linearity for crystal structure determinations. Electron diffraction (ED) patterns can be scanned serially in front of a Faraday cage detector; the total measurement time for several hundred ED reflections can be tens of seconds having high statistical accuracy for all measured intensities (1-2%). This new tool can be installed to any type of TEM without any column modification and is linked to a specially developed electron beam precession "Spinning Star" system. Precession of the electron beam (Vincent-Midgley technique) reduces dynamical effects allowing also use of accurate intensities for crystal structure analysis. We describe the technical characteristics of this new tool together with the first experimental results. Accurate measurement of electron diffraction intensities by electron diffractometer opens new possibilities not only for revealing unknown structures, but also for electrostatic potential determination and chemical bonding investigation. As an example, we present detailed atomic bonding information of CaF(2) as revealed for the first time by precise electron diffractometry.     

Effect of sample bending on diffracted intensities observed in CBED patterns of plan view strained samples

Convergent beam electron diffraction is used to study the effect of the sample bending on diffracted intensities as observed in transmission electron microscopy (TEM). Studied samples are made of thin strained semiconductor Ga(1-)(x)In(x)As epitaxial layers grown on a GaAs substrate and observed in plan view. Strong variations of the diffracted intensities are observed depending on the thinning process used for TEM foil preparation. For chemically thinned samples, strong bending of the substrate occurs, inducing modifications of both kinematical and dynamical Bragg lines. For mechanically thinned samples, bending of the substrate is negligible. Kinematical lines are unaffected whereas dynamical lines have slightly asymmetric intensities. We analyse these effects using finite element modelling to calculate the sample strain coupled with dynamical multibeam simulations for calculating the diffracted intensities. Our results correctly reproduce the qualitative features of experimental patterns, clearly demonstrating that inhomogeneous displacement fields along the electron beam within the substrate are responsible for the observed intensity modifications.     

A quantitative analysis of the cone-angle dependence in precession electron diffraction

Precession electron diffraction (PED) is a technique which is gaining increasing interest due to its ease of use and reduction of the dynamical scattering problem in electron diffraction. To further investigate the usefulness of this technique, we have performed a systematic study of the effect of precession angle on the mineral andalusite where the semiangle was varied from 6.5 to 32 mrad in five discrete steps. The purpose of this study was to determine the optimal conditions for the amelioration of kinematically forbidden reflections, and the measurement of valence charge density. We show that the intensities of kinematically forbidden reflections decay exponentially as the precession semiangle () is increased. We have also determined that charge density effects are best observed at moderately low angles (6.5–13 mrad) even though PED patterns become more kinematical in nature as the precession angle is increased further.     

001] zone-axis bright-field diffraction contrast from coherent Ge(Si) islands on Si(001)

Coherent Ge(Si)/Si(001) quantum dot islands grown by solid source molecular beam epitaxy at a growth temperature of 700 degrees C were investigated using transmission electron microscopy working at 300kV. The [001] zone-axis bright-field diffraction contrast images of the islands show strong periodicity with the change of the TEM sample substrate thickness and the period is equal to the effective extinction distance of the transmitted beam. Simulated images based on finite element models of the displacement field and using multi-beam dynamical diffraction theory show a high degree of agreement. Studies for a range of electron energies show the power of the technique for investigating composition segregation in quantum dot islands.     

A precession electron diffraction study of α, β phases and Dauphiné twin in quartz

Precession electron diffraction is used to distinguish between the hexagonal β high-temperature and the trigonal α low-temperature phases of SiO₂ quartz. The structures just differ by a kink of the SiO₄ tetrahedra arranged along spiraling chains, which induces a loss of the two-fold axis and subsequent twinning in the low-temperature phase. Conventional selected-area electron diffraction (SAED) does not enable the phases distinction since only the intensity of reflections is different. It becomes possible with precession that reduces the dynamical interactions between reflections and makes their intensity very sensitive to small variations of the electron structure factors. Distinction between the twinned individuals in the low-temperature phase is then easily made and the twin law is characterized using stereographic projections. The actual symmetry of precessed zone axis patterns is also examined in detail. Using dynamical intensity simulations, it is shown that under certain thickness conditions, the diffraction class symmetry can be observed on selected area patterns that are to be used in the case of beam sensitive materials such as quartz.     

New approach for the dynamical simulation of CBED patterns in heavily strained specimens

A new method for the dynamical simulation of convergent beam electron diffraction (CBED) patterns is proposed. In this method, the three-dimensional stationary Schrödinger equation is replaced by a two-dimensional time-dependent equation, in which the direction of propagation of the electron beam, variable z, stands as a time. We demonstrate that this approach is particularly well-suited for the calculation of the diffracted intensities in the case of a z-dependent crystal potential. The corresponding software has been developed and implemented for simulating CBED patterns of various specimens, from perfect crystals to heavily strained cross-sectional specimens. Evidence is given for the remarkable agreement between simulated and experimental patterns.     

Diffracted phase and amplitude measurements by energy-filtered convergent-beam holography (CHEF)

Interference between transmitted and diffracted disks in convergent-beam electron diffraction (CBED) patterns using the CBED+EBI method proposed by Herring et al. is explored using different optical configurations on a spherical aberration corrected transmission electron microscope equipped with a biprism and imaging energy filter: the SACTEM-Toulouse. We will relate the amplitude and phase of these interference patterns, which we call convergent-beam holography (CHEF), to microscope transfer theory and the complex amplitudes of the diffracted beams. Experimental CHEF patterns recorded in the absence of aberration correction will be compared with simulations to validate the theory concerning the effect of microscope aberrations and current instabilities. Then, using aberration correction, we propose a scheme for eliminating the effect of the microscope, so that the diffracted amplitudes and phase due to dynamical scattering within the specimen can be studied. Experimental results are compared with simulations performed using the full dynamical theory. The potential for studying diffracted amplitudes and phases using CHEF analysis is discussed.     

Determination of absolute configurations of crystal structures using electron diffraction patterns by means of least-squares refinement

A simple method is reported to determine the absolute configuration of the crystal structure from electron diffraction patterns taken from very small areas. The method is based on the differences in the Friedel reflections, which are in general much larger than for X-rays due to the dynamical behaviour of the electron scattering. We express the absolute configuration with a parameter similar to the one Flack (Acta Cryst. A 39 (1983) 876) introduced in X-ray crystallography. This parameter is added to a refinement procedure that uses a multi-slice calculation to calculate diffraction patterns. The validity and strength of the method are shown with simulated and experimental data sets of GaN in the [0 1 0]-zone and a more complex compound, Ce5Cu19P12 in the [0 0 1] zone.     

Dynamical simulations of zone axis electron channelling patterns of cubic silicon carbide

We have observed and simulated energy-dependent intensity distributions in electron channelling patterns (ECP) of cubic silicon carbide (3C SiC) which were recorded close to the (111) zone axis. The kinetic energies used were in the range from 4 to 8 keV, covering the low-energy region of the ECP technique. We explain the observed patterns by dynamical many beam simulations using a bloch wave approach for the diffraction of the incoming beam and the forward-backward-approximation for the backscattering of the electrons. The dynamical simulations reproduce the experimental patterns very well. It is found that higher-order Laue zone reflections are responsible for the strong energy sensitivity of the intensity distributions.     

Refinement of the 200 structure factor for GaAs using parallel and convergent beam electron nanodiffraction data

We present a new method to measure structure factors from electron spot diffraction patterns recorded under almost parallel illumination in transmission electron microscopes. Bloch wave refinement routines have been developed to refine the crystal thickness, its orientation and structure factors by comparison of experimentally recorded and calculated intensities. Our method requires a modicum of computational effort, making it suitable for contemporary personal computers. Frozen lattice and Bloch wave simulations of GaAs diffraction patterns are used to derive optimised experimental conditions. Systematic errors are estimated from the application of the method to simulated diffraction patterns and rules for the recognition of physically reasonable initial refinement conditions are derived. The method is applied to the measurement of the 200 structure factor for GaAs. We found that the influence of inelastically scattered electrons is negligible. Additionally, we measured the 200 structure factor from zero loss filtered two-dimensional convergent beam electron diffraction patterns. The precision of both methods is found to be comparable and the results agree well with each other. A deviation of more than 20% from isolated atom scattering data is observed, whereas close agreement is found with structure factors obtained from density functional theory [A. Rosenauer, M. Schowalter, F. Glas, D. Lamoen, Phys. Rev. B 72 (2005), 085326-1], which account for the redistribution of electrons due to chemical bonding via modified atomic scattering amplitudes.     

Determination of crystal polarity from bend contours in transmission electron microscope images

A new method for determining the polarity of crystals with sphalerite structure (GaAs, GaSb, InP, etc.) within the transmission electron microscope (TEM) is presented. The method is derived from an established convergent beam electron diffraction (CBED) method (J. Appl. Crystallogr. 15 (1982) 60) and exploits the effects of the dynamical scattering on the contrast of bend contour crossings in conventional TEM images. In contrast to the CBED method, the bend contour method is performed in the image mode of the TEM. The sample can, therefore, be viewed while performing the polarity analysis. Furthermore, in the presence of strong foil bending, the bend contour method has some advantages for practical work. A general contrast rule for the bend contour intersections is stated which allows to readily obtain the crystal polarity by comparing the contrast in experimental images with the prediction of the rule. Exemplarily, the polarity of GaAs in TEM samples prepared for investigation in the two frequently used projections < 001 > and < 110 > is determined. The validity of the rule for the cases studied is confirmed by simulations of the dynamical scattering process. Furthermore, an independent analysis of the crystal polarity by making use of a long-range-ordered (GaIn)P layer grown on top of the GaAs confirms the results obtained with the bend contour method. As an example, the usefulness of the method is demonstrated in an analysis of the alpha/beta-character of misfit dislocations at the interface between the GaAs substrate and the (GaIn)P layer.     

Aperture contrast in thick amorphous specimens using scanning transmission electron microscopy

The contrast observed in thick amorphous specimens using a scanning transmission electron microscope (STEM) can be considerably improved by the use of an optimum collector aperture angle. The size of this angle can be calculated by considering the variation of electron current transmitted through the specimen as a function both of the specimen thickness and of the angle of collection subtended at the specimen. Typically these calculations predict optimum angles to be several times the half-width of the elastic scattering distribution, often 10(-1) rad or more. Observations of biological sections of up to 2 micron in thickness using scanning attachments of commercial transmission microscopes have verifie these results at beam voltages of 50, 100 and 200 kV. Wide angle convergent beam diffraction patterns were used to give accurate values of the effective angles represented by the various collector apertures. Once the linearity of the detector-amplifier system had been established, operation in a line modulation mode enabled quantitative measurements to be made of the image contrast. Such measurements also offer a quick effective method of comparing electron beam penetrations.