Electronic structure of ideal and relaxed surfaces of ZnO: A prototype ionic wurtzite semiconductor and its surface properties

We report the results of a detailed theoretical investigation of electronic properties of unrelaxed and relaxed ZnO surfaces. The surface electronic structure is evaluated using the scattering theoretical method on the basis of an accurately fit empirical tight-binding Hamiltonian for bulk ZnO. Surface band structures and wave-vector-resolved as well as wave-vector-integrated layer densities of states for the polar Zn- and O-terminated ($\frac{0001}{000\overline{1}}$) surfaces and for the nonpolar ($10\overline{1}0$) and ($11\overline{2}0$) surfaces are fully discussed. In agreement with experiment, we find no bound surface states in the gap energy region. Instead of anion- and cation-derived dangling-bond surface states—familiar from more covalent zinc-blende semiconductors—at the ZnO surface ionic resonances occur which lie well within the projections of the bulk valence and conduction bands. In addition, covalent back-bond surface states are found which are derived from Zn $4s-\mathrm{O} 2p$ mixed bulk states. Finally we find surface states near the top of the projected conduction bands which are the antibonding counterparts of the covalent back-bond states. The nature and origins of all these surface features are discussed in detail. We have studied, as well, the relaxed ($10\overline{1}0$) surface using the relaxation model proposed by Duke et al. in order to identify characteristic relaxation-induced effects. We find that surface relaxation affects the ionic resonances only marginally while the more covalent back-bond and anti-backbond states are stronger influenced. Comparing our results with ultraviolet-photoelectron and electron-energy-loss spectroscopy data we find very good agreement. In the course of the discussion of our results we develop a very general picture of typical surface electronic properties of tetrahedrally coordinated, ionic semiconductors which is found to be in good accord with the experimentally observed trends.