Angular dependence of fast-electron scattering from materials

Abstract

Angular resolved scanning transmission electron microscopy is an important tool for investigating the properties of materials. However, several recent studies have observed appreciable discrepancies in the angular scattering distribution between experiment and theory. In this paper we discuss a general approach to lowloss inelastic scattering which, when incorporated in the simulations, resolves this problem and also closely reproduces experimental data taken over an extended angular range. We also explore the role of ionic bonding, temperature factors, amorphous layers on the surfaces of the specimen, and static displacements of atoms on the angular scattering distribution. The incorporation of low-loss inelastic scattering in simulations will improve the quantitative usefulness of techniques such as low-angle annular dark-field imaging and position-averaged convergent beam electron diffraction, especially for thicker specimens.

Inelastic Scattering in Electron Backscatter Diffraction and Electron Channeling Contrast Imaging

“…θ E can be calculated from E p /(2E o ), where E p is the plasmon energy [17 eV for silicon (Mendis, 2019)] and E o is the primary beam energy. Barthel et al (2020) obtained values of λ p = 1000 Å and θ c = 15 mrad by fitting simulations to experimental PACBED patterns of [110]-Si at 300 kV. Extrapolating to 5 kV, the beam voltage used for the present simulations, we obtain λ p = 16.7 Å and θ c = 132 mrad.…”

“…In this section, the Monte Carlo method for simulating plasmon excitations is summarized. The plasmon scattering depth ( s ), polar ( θ ), and azimuthal ( ϕ ) scattering angles are estimated using the following formulas (Mendis, 2019; Barthel et al, 2020):where R 1 , R 2 , and R 3 are computer-generated linear random variables within the range [0,1], λ p is the plasmon mean free path, and θ E and θ c are the characteristic and critical plasmon scattering angles, respectively (Egerton, 1996). θ E can be calculated from E p /(2 E o ), where E p is the plasmon energy [17 eV for silicon (Mendis, 2019)] and E o is the primary beam energy.…”

“…In this section, the Monte Carlo method for simulating plasmon excitations is summarized. The plasmon scattering depth (s), polar (θ), and azimuthal (ϕ) scattering angles are estimated using the following formulas (Mendis, 2019;Barthel et al, 2020):…”

“…Recently, Monte Carlo methods have been used to include plasmon excitations in multislice simulations (Mendis, 2019(Mendis, , 2020Barthel et al, 2020). The underlying principle is that plasmon excitations are highly delocalized (Muller & Silcox, 1995) and are, therefore, not significantly affected by electron beam channeling.…”

“…This process is repeated for many plasmon “configurations” and the results incoherently summed to give a statistically averaged result. Plasmon multislice simulations have been shown to reproduce experimental energy-filtered diffraction patterns (Mendis, 2019), as well as the angular distribution of scattering in position averaged convergent beam electron diffraction (PACBED) patterns (Barthel et al, 2020). These calculations were, however, for high-energy electron diffraction in transmission geometry.…”