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

An analysis of measured elastic low-energy-electron diffraction intensities from ZnO (10¯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., $\left(hk\right)=\left(00\right), \mathrm{}\left(01\right), \left(0\mathrm{}\overline{1}\right), \mathrm{}\left(10\right), \mathrm{}\left(11\right), \mathrm{and} \left(1\mathrm{}\overline{1}\right)$] at three angles of incidence [$\theta =0,5,10\mathrm{}°$] 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¯10) is one in which the oxygen anions in the uppermost layer have relaxed vertically by $\Delta d_{\perp }\left(\mathrm{O}\right)=-0.1\mathrm{}\pm 0.05$ Å and the zinc cations by $\Delta d_{\perp }\left(\mathrm{Zn}\right)=-0.3\mathrm{}\pm 0.1$ Å. The lateral displacements of these species are less precisely defined with $\Delta d_{\parallel }\left(\mathrm{O}\right)<\mathrm{}0.1\mathrm{}$ Å and $\Delta d_{\parallel }\left(\mathrm{Zn}\right)=0.2\mathrm{}\pm 0.2$ Å.