Multiple scattering events of primary electrons in directional elastic peak electron spectroscopy

Abstract

The application of multiple scattering (MS) calculations is presented in order to describe the scattering process of the primary electron beam in crystalline samples and obtain theoretical directional elastic peak electron spectroscopy (DEPES) profiles. Succeeding scattering orders were considered in MS calculations. The contribution of particular sample layers to the calculated intensities is discussed considering forward focusing, attenuation, and defocusing of primary electrons in the crystalline sample. The calculations were performed for a single $[110]$ chain of Al, Cu, Ag, and Au atoms. The results show the importance of multiple scattering events in DEPES profiles. A reduction of the calculated intensities for the $[110]$ direction was observed when the multiple scattering of primaries was considered. Convergence of the recursion method of MS evaluations for the increasing scattering order was ensured by means of $1∕\sqrt{N}$ normalization factor, where $N$ is the number of cluster atoms taken into account. Above the fourth scattering order, no significant changes of the calculated intensities were observed for all the considered kinds of atoms. Theoretical DEPES profiles obtained for the $\mathrm{Au}(111)$ crystal show a similar reduction of intensities for the $[110]$ atomic row as was observed for a single $\mathrm{Au}[110]$ chain. The consideration of MS events in calculations improve the correspondence between experimental and theoretical DEPES scans for $\mathrm{Cu}(111)$ at ${E}_{P}=1.2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$.