Understanding the use of scattering cross‐sections in quantitative ADF STEM

Abstract

Quantitative scanning transmission electron microscopy (STEM) using an annular dark field (ADF) detector has become a widely used technique for the characterization of materials at the atomic level. The quantification process involves the comparison of experimental data with image simulations, the use of statistical tools in a parameter estimation framework or a combination of both [1]. These methods have been developed using different measures for comparison, like peak intensities at the atom column position [2], image contrast variations [3] or so‐called scattering cross‐sections [4, 5]. The latter correspond to the total scattered intensity integrated over the atom column area. They have been shown to be very sensitive to the number of atoms in a column and its composition [1, 4, 6, 7]. Figure 1a shows the increase in peak intensity (green axis) and cross‐section (black axis) versus increase in number of atoms for a Pt column in [110] zone axis. As it can be observed, the peak intensity saturates after around 8 atoms meanwhile the cross‐section monotonically increases. In this work, we perform an analysis of how the electron wave propagates inside the crystal for the probe positions that conform the scattering cross‐section. With this, we analyse how the signal is generated for different detector collection angle regimes. Then, the analysis allows to identify the origin of the scattered signal and why scattering cross‐sections are more sensitive for composition and number of atoms as compared to peak intensities. In Figure 1b, we show a simulated image of a unit cell of a Pt crystal in [110] zone axis with a color‐edited version indicating the labels of the probe positions that form the scattering cross‐section and their respective distance to the atom column position. Figure 2 shows the probability amplitude of the electron wave as it propagates through the crystal for probe position r0 (a), which corresponds to the peak intensity, and for the sum of all the probe positions that conform the scattering cross‐section (b). From this, we observe that the atom column is excited deeper in the column when analyzing the cross‐sections. The off‐column probe positions carry more rich information about the scattering process for different thickness and collection regimes, which explains the increased sensitivity of this measure to the number of atoms and its composition. We then discuss the contribution to the scattered intensity for different detector collection angle regimes, such as LAADF, MAADF and HAADF.