HAADF-STEM imaging with sub-angstrom probes: a full Bloch wave analysis

A full coherent Bloch wave calculation is presented to investigate high-angle annular dark-field image formation for sub-angstrom probes in scanning transmission electron microscopy (STEM). With increasing illumination angle, the contribution of the Is bound state increases to a maximum at an optimum probe angle, after which we find increasing contributions from high-angle plane wave states around the periphery of the objective aperture. Examination of image contributions from different depths within a crystal shows an oscillatory behavior due to the beating between Is and non-Is states. The oscillation period reduces with decreasing probe size, while the relative contribution from a specific depth increases. This signifies a changeover from a projection mode of imaging to a depth-slicing mode of imaging. This new mode appears capable of resolving three-dimensional atomic structures in future generation aberration-corrected STEM.