Theoretical modelling of steps on the CaF2(111)surface

Abstract

The atomic and electronic structure and relaxation of the perfect(111) surface and several low-index surfaces of CaF2 arecalculated using an ab initio Hartree-Fock method. We findmarked differences between the bulk and surface valence bandstructures; however, the band gap is reduced by only 0.5 eV for thestepped surface. The (111) surface is found to exhibit nosignificant relaxation and we obtain a surface energy of0.47 J m-2. The atomic structure of two types of steppedsurface both having 0.32 nm high steps aligned along the [110]crystallographic direction is determined and the step energies arefound to be 0.25 and 0.35 nJ m-1, respectively. Stepenergies for configurations involving other orientations of stepsare considerably higher. The formation of double-height steps along[110], however, is found to be energetically favourable. Aconsiderable amount of relaxation is found for stepped surfaces andwe explain qualitatively why it results in a roughening of thesurface in some cases. The energetic position of gap electronicstates induced by steps on the (111) surface is found to be verysimilar to that for surface states of the perfect (111) surface;i.e. such states do not yield a significant density of states morethan 0.5 eV above the bulk valence band maximum. We discuss how thestep formation energies found here might explain surfacetopographical features found on cleaved and grown CaF2(111) surfaces.