Self-consistent electronic-structure calculations of the (101-bar0) surfaces of the wurtzite compounds ZnO and CdS.

Abstract

We report ab initio calculations of the surface electronic structure of the hexagonal wurtzite semiconductors ZnO and CdS. The calculations are carried out self-consistently in the local-density approximation employing separable norm-conserving pseudopotentials. Localized Gaussian orbitals are used in the basis set for an efficient description of the strongly localized wave functions. The Zn 3d and Cd 4d electrons are explicitly taken into account as valence electrons since they are important for a quantitative description of the structural as well as the electronic properties, as our investigations of bulk ZnO and CdS have shown. Cationic d-d repulsion, p-d and s-d interactions, and orthogonalization effects are, therefore, included in our calculations of the ZnO and CdS (101\ifmmode\bar\else\textasciimacron\fi{}0) surfaces. The nonpolar cleavage face is described in a supercell geometry with eight atomic and four vacuum layers in each cell. The surface atomic structure is determined by elimination of the forces. For ZnO, we find a rotation relaxation, in which both the Zn and O surface atoms move inward towards the substrate. The calculated surface-perpendicular displacements of the Zn atoms relative to the O atoms in the top layer turn out to be slightly smaller than those determined experimentally by low-energy electron diffraction. The surface electronic structure exhibits an oxygen-derived dangling-bond band in the fundamental gap which is essentially unaffected by the calculated surface relaxation.This is in marked contrast to the results of previous studies using an empirical tight-binding approach which either find no surface states in the gap at all or one band of surface states that is shifted down into the projected bulk valence bands by the surface relaxation. For CdS(101\ifmmode\bar\else\textasciimacron\fi{}0) we find a surface structure that nicely agrees in general with the relaxation model experimentally determined for the related CdSe(101\ifmmode\bar\else\textasciimacron\fi{}0) surface. The surface electronic structure is compared with the results of polarization- and angle-resolved photoemission experiments. With the help of selection rules we are able to identify two occupied surface states at the top of the projected bulk valence bands in very good agreement with experiment.