Theoretical modelling of steps on the CaF2(111) surface

The atomic and electronic structure and relaxation of the perfect (111) surface and several low-index surfaces of CaF2 are calculated using an ab initio Hartree-Fock method. We find marked differences between the bulk and surface valence band structures; however, the band gap is reduced by only 0.5 eV for the stepped surface. The (111) surface is found to exhibit no significant relaxation and we obtain a surface energy of 0.47 J m(-2). The atomic structure of two types of stepped surface both having 0.32 nm high steps aligned along the [110] crystallographic direction is determined and the step energies are found to be 0.25 and 0.35 nJ m(-1), respectively. Step energies for configurations involving other orientations of steps are considerably higher. The formation of double-height steps along [110], however, is found to be energetically favourable. A considerable amount of relaxation is found for stepped surfaces and we explain qualitatively why it results in a roughening of the surface in some cases. The energetic position of gap electronic states induced by steps on the (111) surface is found to be very similar to that for surface states of the perfect (111) surface; i.e. such states do not yield a significant density of states more than 0.5 eV above the bulk valence band maximum. We discuss how the step formation energies found here might explain surface topographical features found on cleaved and grown CaF2(111) surfaces.