Phase diagrams of polar surface reconstructions of zinc oxide

Abstract

Due to the formation of surface dipoles the truncated-bulk like {0001} surfaces of zinc oxide (ZnO) are electrostatically unstable. These dipoles can neither be compensated by the formation of surface dimers nor by a relaxation of near surface layers. Hence, the driving force for the reconstruction of ZnO must be a deviation of the surface stoichiometry. To study this stabilization effect, we have performed density functional theory calculations on (2×2) and (3×3) periodic non-stoichiometric reconstructions of the ZnO polar surfaces. Among the 24 possible (2×2) periodic structures that preserve bulk symmetry, a class of ad-atom reconstructions shows the lowest energy of formation. To facilitate comparability with experimental conditions we calculate the Gibbs free energy of each reconstruction as a function of temperature and chemical conditions. However, the established calculation method is ambiguous in case of non-stoichiometric surfaces and must be extended by taking into account the temperature dependence of the ZnO enthalpy of formation. From the resulting data phase diagrams of the stable reconstructions of ZnO polar surfaces are constructed which are discussed in terms of epitaxial growth.