First-principles simulations of H centers in CaF₂

H center, a hole trapped at an interstitial anion site, placed in the bulk and the (1 1 1) surface of calcium fluoride CaF₂, has been studied by using density functional theory (DFT) with hybrid exchange potentials, namely DFT-B3PW. The H center orients the (1 1 1) direction for the bulk case and the (1 0 0) direction for the surface case, and the hole is mainly localized on the interstitial fluorine. The surface H center leads to a remarkable XY-translation of the surface atoms. Spin and hyperfine coupling calculations show a considerable interaction between the unpaired spin and the spin of neighboring nuclei, and the surface effect strengthens the spin polarization and hyperfine structure. The hole induces an empty level in the β-spin band gap, located 2.88 eV above the valence band (VB) top, corresponding to the first optical absorption band, and the surface effect heightens the hole level considerably. Density of states (DOS) calculations reveal that the hole band mainly consists of the H-center p-orbitals, and the interstitial fluorine does the major contribution. Further study regarding the electron-hole pair, named FH pair in this paper, shows that the geometrical structure is similar to an F center and an H center paired together, whereas the hole localized on the H center in the isolated H-center case, moves to the fluorine vacancy (^VF) site. The electron-hole pair induces seven defect levels in the VB-CB (conduction band) gap, three of them located near the Fermi energy, being occupied, and four of them located above the Fermi level, forming the hole bands. The p-orbitals of the interstitial fluorine form the three electron bands and the four hole bands are composed of the s- and p-orbitals of the ^VF.