Low-energy-electron-diffraction analysis of the atomic geometry of ZnO (10¯10)

Abstract

An analysis of measured elastic low-energy-electron diffraction intensities from ZnO (10\ifmmode\bar\else\textasciimacron\fi{}10) is performed using a dynamical multiple-scattering methodology in which the scattering of the electrons from the individual Zn-O layers is evaluated exactly but the scattering between the layers is treated using a self-consistent version of perturbation theory. These analyses were carried out for six independent beams [i.e., $(hk)=(00), (01), (0\overline{1}), (10), (11), \mathrm{and} (1\overline{1})$] at three angles of incidence [$\ensuremath{\theta}=0,5,10\ifmmode^\circ\else\textdegree\fi{}$] along the azimuth such that the ($hk$) and ($\overline{h}k$) beams are identical by symmetry. This analysis reveals that the most probable structure of ZnO (10\ifmmode\bar\else\textasciimacron\fi{}10) is one in which the oxygen anions in the uppermost layer have relaxed vertically by $\ensuremath{\Delta}{d}_{\ensuremath{\perp}}(\mathrm{O})=\ensuremath{-}0.1\ifmmode\pm\else\textpm\fi{}0.05$ \AA{} and the zinc cations by $\ensuremath{\Delta}{d}_{\ensuremath{\perp}}(\mathrm{Zn})=\ensuremath{-}0.3\ifmmode\pm\else\textpm\fi{}0.1$ \AA{}. The lateral displacements of these species are less precisely defined with $\ensuremath{\Delta}{d}_{\ensuremath{\parallel}}(\mathrm{O})<0.1$ \AA{} and $\ensuremath{\Delta}{d}_{\ensuremath{\parallel}}(\mathrm{Zn})=0.2\ifmmode\pm\else\textpm\fi{}0.2$ \AA{}.