Modelling dynamical 3D electron diffraction intensities. II. The role of inelastic scattering

The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave-Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.

A "Phase Scrambling" Algorithm for Parallel Multislice Simulation of Multiple Phonon and Plasmon Scattering Configurations

Multislice simulations of 4D scanning transmission electron microscopy (4D STEM) data are computationally demanding due to the large number of STEM probe positions that must be calculated. For accurate analysis, inelastic scattering from phonons and plasmons must also be included. However, current frozen phonon and Monte Carlo plasmon techniques require a separate calculation for each different phonon/plasmon configuration, and are therefore not suitable for scaling up to 4D STEM. Here a phase scrambling algorithm (PSA) is proposed, which treats all phonon/plasmon configurations simultaneously. A random phase is introduced to maintain incoherence between the different inelastic scattering events; this is the phase scrambling part of the algorithm. While for most applications, a few tens of frozen phonon iterations are sufficient for convergence, in the case of plasmon scattering as many as tens of thousands of iterations may be required. A PSA is statistically more representative of inelastic scattering, and achieves significant savings in computation time for plasmons. The increase in speed is a pre-requisite for 4D STEM inelastic scattering simulations.

Towards Electron Energy Loss Compton Spectra Free From Dynamical Diffraction Artifacts

The Compton signal in electron energy loss spectroscopy (EELS) is used to determine the projected electron momentum density of states for the solid. A frequent limitation however is the strong dynamical scattering of the incident electron beam within a crystalline specimen, i.e. Bragg diffracted beams can be additional sources of Compton scattering that distort the measured profile from its true shape. The Compton profile is simulated via a multislice method that models dynamical scattering both before and after the Compton energy loss event. Simulations indicate the importance of both the specimen illumination condition and EELS detection geometry. Based on this, a strategy to minimize diffraction artifacts is proposed and verified experimentally. Furthermore, an inversion algorithm to extract the projected momentum density of states from a Compton measurement performed under strong diffraction conditions is demonstrated. The findings enable a new route to more accurate electron Compton data from crystalline specimens.

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.