Probe integrated scattering cross sections in the analysis of atomic resolution HAADF STEM images

The physical basis for using a probe-position integrated cross section (PICS) for a single column of atoms as an effective way to compare simulation and experiment in high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) is described, and the use of PICS in order to make quantitative use of image intensities is evaluated. It is based upon the calibration of the detector and the measurement of scattered intensities. Due to the predominantly incoherent nature of HAADF STEM, it is found to be robust to parameters that affect probe size and shape such as defocus and source coherence. The main imaging parameter dependencies are on detector angle and accelerating voltage, which are well known. The robustness to variation in other parameters allows for a quantitative comparison of experimental data and simulation without the need to fit parameters. By demonstrating the application of the PICS to the chemical identification of single atoms in a heterogeneous catalyst and in thin, layered-materials, we explore some of the experimental considerations when using this approach.