Electron beam-specimen interactions and their effect on high-angle annular dark-field imaging of dopant atoms within...

A Bloch wave model based on perturbation theory is used to analyse high-angle annular dark-field (HAADF) imaging of a substitutional and interstitial W atom in [111]-oriented body-centred-cubic Fe. For the substitutional atom the 1s Bloch state is scattered to high angles thereby producing HAADF dopant atom contrast. Intraband scattering of the 1s state is the strongest individual Bloch wave transition but collective interband scattering of the non-1s states to the 1s state leads to variations in the high-angle scattering with depth of the dopant atom. The non-1s states are Coulomb attracted towards the W atom thereby giving rise to an 'atom focusing' effect similar to channelling. For the interstitial atom, which in the [111] orientation does not overlap with an atom column of the host lattice, high-angle scattering and Coulomb attraction takes place through the non-1s states. Scattering of the 1s state is, however, negligible.