Abstract
Scanning transmission electron microscopy (STEM) allows to gain quantitative information on the atomic-scale structure and composition of materials, satisfying one of todays major needs in the development of novel nanoscale devices. The aim of this study is to quantify the impact of inelastic, i.e. plasmon excitations (PE), on the angular dependence of STEM intensities and answer the question whether these excitations are responsible for a drastic mismatch between experiments and contemporary image simulations observed at scattering angles below sim 40 mrad. For the two materials silicon and platinum, the angular dependencies of elastic and inelastic scattering are investigated. We utilize energy filtering in two complementary microscopes, which are representative for the systems used for quantitative STEM, to form position-averaged diffraction patterns as well as atomically resolved 4D STEM data sets for different energy ranges. The resulting five-dimensional data are used to elucidate the distinct features in real and momentum space for different energy losses. We find different angular distributions for the elastic and inelastic scattering, resulting in an increased low-angle intensity (sim 10–40 mrad). The ratio of inelastic/elastic scattering increases with rising sample thickness, while the general shape of the angular dependency is maintained. Moreover, the ratio increases with the distance to an atomic column in the low-angle regime. Since PE are usually neglected in image simulations, consequently the experimental intensity is underestimated at these angles, which especially affects bright field or low-angle annular dark field imaging. The high-angle regime, however, is unaffected. In addition, we find negligible impact of inelastic scattering on first-moment imaging in momentum-resolved STEM, which is important for STEM techniques to measure internal electric fields in functional nanostructures. To resolve the discrepancies between experiment and simulation, we present an adopted simulation scheme including PE. This study highlights the necessity to take into account PE to achieve quantitative agreement between simulation and experiment. Besides solving the fundamental question of missing physics in established simulations, this finally allows for the quantitative evaluation of low-angle scattering, which contains valuable information about the material investigated.
Highlights
High sampling of both real and reciprocal space simultaneously, referred to as “four-dimensional Scanning transmission electron microscopy (STEM)” (4D STEM)
The experimental findings will be compared to simulations, in order to approach the impact of plasmon excitations from the theoretical point of view
The impact of the plasmon excitations on low scattering angles will be highlighted by employing simulated as well as experimental atomic resolution ADF images generated for different angular regimes
Summary
High sampling of both real and reciprocal space simultaneously, referred to as “four-dimensional STEM” (4D STEM). Besides enabling efficient STEM phase contrast imaging[13,14,15], employing momentum-resolved STEM for an angular multi-range analysis to simultaneously measure, e.g., the local content of multiple chemical elements, lattice strain and the specimen thickness was envisaged[12] This relies on the assumptions that a certain set of specimen parameters yields a unique diffraction pattern within the boundary of available casespecific prior knowledge, and that simulation methods exist which resemble the experimental conditions and scattering physics accurately at all scattering angles. The capability of approaches to incorporate inelastic processes into frozen-phonon multislice simulations is investigated, balancing computational effort and accuracy This leads to possible routes forward to enable the quantitative interpretation of low-angle scattering so as to unfold the full potential of momentum-resolved STEM for materials analysis
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