Inelastic Scattering in Electron Backscatter Diffraction and Electron Channeling Contrast Imaging

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.

Modelling Electron Channeling Contrast Intensity of Stacking Fault and Twin Boundary Using Crystal Thickness Effect

In a scanning electron microscope, the backscattered electron intensity modulations are at the origin of the contrast of like-Kikuchi bands and crystalline defects. The Electron Channeling Contrast Imaging (ECCI) technique is suited for defects characterization at a mesoscale with transmission electron microscopy-like resolution. In order to achieve a better comprehension of ECCI contrasts of twin-boundary and stacking fault, an original theoretical approach based on the dynamical diffraction theory is used. The calculated backscattered electron intensity is explicitly expressed as function of physical and practical parameters controlling the ECCI experiment. Our model allows, first, the study of the specimen thickness effect on the channeling contrast on a perfect crystal, and thus its effect on the formation of like-Kikuchi bands. Then, our theoretical approach is extended to an imperfect crystal containing a planar defect such as twin-boundary and stacking fault, clarifying the intensity oscillations observed in ECC micrographs.