- Poster
- IM5.P001

Florian Fritz Krause

Bremen / DE

Florian Fritz Krause (Bremen / DE), Tim Grieb (Bremen / DE), Marco Schowalter (Bremen / DE), Andreas Beyer (Marburg / DE), Saleh Firoozabadi (Marburg / DE), Pirmin Kükelhan (Marburg / DE), Hoel Laurent Robert (Jülich / DE), Knut Müller-Caspary (Jülich / DE; Munich / DE), Kerstin Volz (Marburg / DE), Andreas Rosenauer (Bremen / DE)

Abstract text (incl. figure legends and references)

The use of multislice simulations of the electron beam propagating through the specimen as reference data to evaluate experimental STEM images is a well-established technique for quantitative evaluation. Using the frozen phonon method to include inelastic phonon scattering, the simulations include thermal diffuse scattering (TDS) and Bragg diffraction, the two major scattering mechanisms. Especially for micrographs acquired from HAADF scattering such simulations have been proven to allow accurate precise evaluation of thickness or composition at atomic resolution.

The transfer of these successes into the medium- and low-angle regime however, has proven difficult: The measured intensity at low scattering angles is found to be higher than expected from frozen phonon simulations. This can be largely attributed to plasmon scattering, as energy filtered, angle resolved experiments confirm that plasmon loss diffraction patterns show an elevated intensity between semi-convergence angle and ~40 mrad [1].

The inclusion of plasmon scattering into multislice simulations is hence of high interest to restore the possibility for accurate evaluations in the low-angle regime. This work presents the implementation of the inelastic plasmon scattering events by inclusion of transition-potentials into the multislice routine. Because the energy loss due to a plasmon excitation is more than four magnitudes smaller than the probe electron energy, the characteristic scattering angle that mainly determines the shape of the transition potentials is only of few µrad. Simultaneously it is necessary to have a reciprocal space extent of several hundred mrad to accurately model TDS. As computational limitations limit the numerical grid size to few thousands of pixels in each direction, the plasmon transition potential is usually undersampled. This can cause a severe overestimation of lowest-angle scattering resulting in an underestimation of the influence of plasmons in the simulation. An integration scheme is proposed to mend this for the simulation of diffraction intensities.

Beyond the characteristic angle, the Lorentzian-shaped transition potential drops quickly to very small values, which has led other authors to the proposal of introducing a critical cuttoff angle, which has been shown to work accurately for conventional energy filtered TEM simulations [2]. In the present work it is shown, that plasmon scattering from the central beam to angles up to ~45 mrad even though improbable is the main contribution to the difference between simulations with and without the inclusion of plasmons. This is due to the very large intensity disparity between central beam and the outer diffraction pattern. It is thus of utmost importance to fully model the transition potentials without a cutoff to high angles, where they are dominated by a term derived from the plasmon dispersion relation.

When the simulation results including plasmon effects are compared to energy filtered experimental diffraction patterns of silicon, they are generally able to reproduce the amount and angle distribution of the plasmon scattering. Remaining discrepancies can be attributed to other effects as is discussed [3].

[1] A. Beyer *et al.*, Scientific Reports **10** (2020), p. 1

[2] J. Verbeeck et al., Ultramicroscopy **102** (2005), p. 239

[3] F. Krause* et al.*, Ultramicroscopy **161** (2016), p. 146