Zone-axis back-scattered electron contrast for fast electrons

Kikuchi pattern simulations of backscattered and transmitted electrons

We discuss a refined simulation approach which treats Kikuchi diffraction patterns in electron backscatter diffraction (EBSD) and transmission Kikuchi diffraction (TKD). The model considers the result of two combined mechanisms: (a) the dynamical diffraction of electrons emitted coherently from point sources in a crystal and (b) diffraction effects on incoherent diffuse intensity distributions. Using suitable parameter settings, the refined simulation model allows to reproduce various thickness- and energy-dependent features which are observed in experimental Kikuchi diffraction patterns. Excess-deficiency features are treated by the effect of gradients in the incoherent background intensity. Based on the analytical two-beam approximation to dynamical electron diffraction, a phenomenological model of excess-deficiency features is derived, which can be used for pattern matching applications. The model allows to approximate the effect of the incident beam geometry as a correction signal for template patterns which can be reprojected from pre-calculated reference data. As an application, we find that the accuracy of fitted projection centre coordinates in EBSD and TKD can be affected by changes in the order of 10 - 3 - 10 - 2 if excess-deficiency features are not considered in the theoretical model underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer from biases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.

Inelastic Scattering in Electron Backscatter Diffraction and Electron Channeling Contrast Imaging

Electron backscatter diffraction (EBSD) and electron channeling contrast imaging (ECCI) are used to extract crystallographic information from bulk samples, such as their crystal structure and orientation as well as the presence of any dislocation and grain boundary defects. These techniques rely on the backscattered electron signal, which has a large distribution in electron energy. Here, the influence of plasmon excitations on EBSD patterns and ECCI dislocation images is uncovered by multislice simulations including inelastic scattering. It is shown that the Kikuchi band contrast in an EBSD pattern for silicon is maximum at small energy loss (i.e., few plasmon scattering events following backscattering), consistent with previous energy-filtered EBSD measurements. On the other hand, plasmon excitation has very little effect on the ECCI image of a dislocation. These results are explained by examining the role of the characteristic plasmon scattering angle on the intrinsic contrast mechanisms in EBSD and ECCI.

Dictionary Indexing of Electron Channeling Patterns

The dictionary-based approach to the indexing of diffraction patterns is applied to electron channeling patterns (ECPs). The main ingredients of the dictionary method are introduced, including the generalized forward projector (GFP), the relevant detector model, and a scheme to uniformly sample orientation space using the "cubochoric" representation. The GFP is used to compute an ECP "master" pattern. Derivative free optimization algorithms, including the Nelder-Mead simplex and the bound optimization by quadratic approximation are used to determine the correct detector parameters and to refine the orientation obtained from the dictionary approach. The indexing method is applied to poly-silicon and shows excellent agreement with the calibrated values. Finally, it is shown that the method results in a mean disorientation error of 1.0° with 0.5° SD for a range of detector parameters.

Kikuchi pattern analysis of noncentrosymmetric crystals

Different models of Kikuchi pattern formation are compared with respect to their applicability to noncentrosymmetric crystals, and the breakdown of Friedel's rule in experimental electron backscatter diffraction (EBSD) patterns is discussed. DifferentAIIIBVsemiconductor materials are used to evaluate the resulting asymmetry of Kikuchi band profiles for polar lattice planes. By comparison with the characteristic etch pit morphology on a single-crystal surface, the polar character of the measured lattice planes can be assigned absolutely. The presented approach enables point-group-resolved orientation mapping, which goes beyond the commonly applied Laue group analysis in EBSD.

Dynamical electron backscatter diffraction patterns. Part I: pattern simulations

A new approach for the simulation of dynamic electron backscatter diffraction (EBSD) patterns is introduced. The computational approach merges deterministic dynamic electron-scattering computations based on Bloch waves with a stochastic Monte Carlo (MC) simulation of the energy, depth, and directional distributions of the backscattered electrons (BSEs). An efficient numerical scheme is introduced, based on a modified Lambert projection, for the computation of the scintillator electron count as a function of the position and orientation of the EBSD detector; the approach allows for the rapid computation of an individual EBSD pattern by bi-linear interpolation of a master EBSD pattern. The master pattern stores the BSE yield as a function of the electron exit direction and exit energy and is used along with weight factors extracted from the MC simulation to obtain energy-weighted simulated EBSD patterns. Example simulations for nickel yield realistic patterns and energy-dependent trends in pattern blurring versus filter window energies are in agreement with experimental energy-filtered EBSD observations reported in the literature.

Site-specific recoil diffraction of backscattered electrons in crystals

A novel diffraction effect in high-energy electron backscattering is demonstrated: the formation of element-specific diffraction patterns via nuclear recoil. For sapphire (Al(2)O(3)), the difference in recoil energy allows us to determine if an electron scattered from aluminum or from oxygen. The angular electron distribution obtained in such measurements is a strong function of the recoiling lattice site. These element-specific recoil diffraction features are explained using the dynamical theory of electron diffraction. Our observations open up new possibilities for local, element-resolved crystallographic analysis using quasielastically backscattered electrons in scanning electron microscopy.

Many-beam dynamical simulation of electron backscatter diffraction patterns

We present an approach for the simulation of complete electron backscatter diffraction (EBSD) patterns where the relative intensity distributions in the patterns are accurately reproduced. The Bloch wave theory is applied to describe the electron diffraction process. For the simulation of experimental patterns with a large field of view, a large number of reflecting planes has to be taken into account. This is made possible by the Bethe perturbation of weak reflections. Very good agreement is obtained for simulated and experimental patterns of gallium nitride GaN{0001} at 20kV electron energy. Experimental features like zone-axis fine structure and higher-order Laue zone rings are accurately reproduced. We discuss the influence of the diffraction of the incident beam in our experiment.

Modelling high-resolution electron microscopy based on core-loss spectroscopy

There are a number of factors affecting the formation of images based on core-loss spectroscopy in high-resolution electron microscopy. We demonstrate unambiguously the need to use a full nonlocal description of the effective core-loss interaction for experimental results obtained from high angular resolution electron channelling electron spectroscopy. The implications of this model are investigated for atomic resolution scanning transmission electron microscopy. Simulations are used to demonstrate that core-loss spectroscopy images formed using fine probes proposed for future microscopes can result in images that do not correspond visually with the structure that has led to their formation. In this context, we also examine the effect of varying detector geometries. The importance of the contribution to core-loss spectroscopy images by dechannelled or diffusely scattered electrons is reiterated here.

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.

Channelling effects in atomic resolution STEM

A Bloch wave theory for incoherent scattering of an incident plane wave has proved successful in predicting the fine detail in 2-D zone axis channelling patterns formed by ADF, BSE and characteristic X-ray detection in beam rocking mode. A previously published example of polarity determination of GaAs by channelling contrast is compared with simulations in order to illustrate the applicability of the theory. Modification of boundary conditions for a focused coherent probe allows lattice-resolution incoherent contrast based on ADF and EELS detection as well as X-ray emissions to be catered for within a similar theoretical framework. Mixed dynamic form factors constitute an integral part of this theory, where quantum-mechanical phase is a core issue. Simulations of lattice-resolution ADF and EELS are discussed with reference to various zone axis projections of GaAs. Issues of single versus double channelling conditions, and local versus nonlocal interactions, are discussed in relation to X-ray, ADF and EELS detection.

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.

Detection of Au precipitates in a Mg-based alloy using electronically simulated hollow cone illumination

Images from electronically simulated hollow cone illumination (or rotating dark field) conditions, obtained under plane wave (or weak) diffraction conditions, are generally assumed to approximate to the compositionally weighted sum of atomic number squared for sufficiently large momentum transfers. However, even for large momentum transfer encountered with a semi-angle of 5 degrees and 300keV electrons, appropriate numerical integration over condenser and objective aperture configurations indicates that some thermal scattering component is still present. A Mg-Al alloy with minor additions of Zn and Mn, and to which 0.1at.% Au has been added, is shown to provide a good system for the detection of high Z (atomic number) precipitates within a low Z matrix and on which semi-quantitative calculations may be based. Correlation of absolute rather than relative intensities from small precipitates (3-10nm diameter) with calculations based on an Einstein model for (incoherent) thermal diffuse scattering show that the small precipitates consist predominantly of Au, a conclusion subsequently supported by EDX analysis and electron diffraction measurements. It is also demonstrated that this incoherent contrast mechanism is ideal for stereographic imaging in the TEM.