Calculation of low-energy-electron-diffraction intensities fromZnO(101¯0). II. Influence of calculational procedure, model potential, and second-layer structural distortions

Abstract

Dynamical calculations of the intensities of normally-incident low-energy electrons diffracted from $\mathrm{ZnO}(10\overline{1}0)$, performed using an "exact" matrix-inversion method, are compared both with earlier calculations based on the renormalized-forward-scattering (RFS) method and with measured intensities. The sensitivity of the calculated intensities to the choice of model potential and the magnitude of thermal atomic vibrations is displayed within the context of examining the implications of uncertainties in nonstructural model parameters on surface-structure determinations via elastic low-energy-electron diffraction (ELEED) intensity analyses. We extend our earlier analysis of the surface structure of $\mathrm{ZnO}(10\overline{1}0)$ by utilizing the matrix inversion rather than RFS method, a recently revised bulk geometry for ZnO, an improved model potential, and a consideration of second-as well as top-layer structural distortions. The combination of these four improvements lead to the selection of the most probable surface structure for $\mathrm{ZnO}(10\overline{1}0)$ as one in which the top-layer oxygen is displaced vertically downward by $\ensuremath{\Delta}{d}_{\ensuremath{\perp}}(\mathrm{O})=\ensuremath{-}0.05\ifmmode\pm\else\textpm\fi{}0.1$ \AA{} and the top-layer zinc likewise by $\ensuremath{\Delta}{d}_{\ensuremath{\perp}}(\mathrm{Zn})=\ensuremath{-}0.45\ifmmode\pm\else\textpm\fi{}0.1$ \AA{}. No compelling evidence either for lateral distortions within the top layer or for second-layer distortions is obtained, although small improvements in the agreement between the calculated and observed intensities can be achieved by considering them. Our major conclusion is that given the limitations in the available ELEED intensity data and the uncertainties in the model potential and surface atomic vibrations, the vertical distortion cited above constitute the maximum structural information that can be extracted unambiguously via ELEED intensity analysis at the present time.