Simplifying Electron Beam Channeling in Scanning Transmission Electron Microscopy (STEM)

Sub-angstrom scanning transmission electron microscopy (STEM) allows quantitative column-by-column analysis of crystalline specimens via annular dark-field images. The intensity of electrons scattered from a particular location in an atomic column depends on the intensity of the electron probe at that location. Electron beam channeling causes oscillations in the STEM probe intensity during specimen propagation, which leads to differences in the beam intensity incident at different depths. Understanding the parameters that control this complex behavior is critical for interpreting experimental STEM results. In this work, theoretical analysis of the STEM probe intensity reveals that intensity oscillations during specimen propagation are regulated by changes in the beam's angular distribution. Three distinct regimes of channeling behavior are observed: the high-atomic-number (Z) regime, in which atomic scattering leads to significant angular redistribution of the beam; the low-Z regime, in which the probe's initial angular distribution controls intensity oscillations; and the intermediate-Z regime, in which the behavior is mixed. These contrasting regimes are shown to exist for a wide range of probe parameters. These results provide a new understanding of the occurrence and consequences of channeling phenomena and conditions under which their influence is strengthened or weakened by characteristics of the electron probe and sample.