Hartree–Fock study of near-edge gap states in CaF2 with Na+, Cl− or Sr2+ impurities

The energy of formation and electronic structure of Na+, Cl− and Sr2+ impurity centers in CaF2 have been computed using ab initio Hartree–Fock theory and the supercell approach. The work extends and complements recent results [Solid State Commun. 118 (2001) 569] for Mg2+ as a substitutional impurity in CaF2. For Na+ substituting for Ca2+ [S(Na)], charge compensation by an F− vacancy [V(F)] or by a second, interstitial Na+ [I(Na)] are both considered. In all cases, geometry optimization is done by relaxing the positions of nearest- and next-nearest-neighbors to minimize the total energy. After correction for electron correlation, the energies of formation increase in the order Mg2+<Sr2+<Cl−<S(Na)+I(Na)<S(Na)+V(F), and the Na+ results are in agreement with previous Mott–Littleton formation energies. Ion charges, charge density maps and Mulliken bond populations are obtained to show the nature of bonding in the vicinity of the defect. Na+ leads to states just above the CaF2 valence band maximum (VBM), and Na+ (and also Mg2+) produce states just below the conduction band minimum. The results are in qualitative agreement with available optical data for Na+ and Mg2+ impurity effects on CaF2 near-edge absorption but show that gap states are important in addition to perturbed excitons. A Cl− impurity yields a narrow band of states above the VBM which may significantly affect the deep-ultraviolet transmission of CaF2. Sr2+ does not appear to produce states in the CaF2 gap.