Electronic structure of theFcenter in CaO

Abstract

A theoretical model for calculating the electronic structure of the $F$ center in the alkaline-earth oxides is described; it is a modification of a similar model previously used for the alkali halides. The model emphasizes the importance of (a) electronic structure on the ions neighboring the defect, (b) electronic and ionic polarization of the lattice, and (c) lattice distortion and its effects on the energy levels and wave functions of the defect. Absorption and emission states of the $F$ center in CaO have been calculated using this model. The electron-lattice interaction for $A_{1g}$, $E_g$, and $T_{2g}$ displacements of the nearest-neighbor ions has been calculated and used to interpret the absorption and luminescence bands of the $F$ center. The calculated energy-level scheme as a function of lattice relaxation gives substantial agreement with published experimental data. It indicates that the ${}_{}{}^1{}_{}{}^{}T_{1u}^{}{}_{}{}^{}\to {}_{}{}^1{}_{}{}^{}A_{1g}^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}T_{1u}^{}{}_{}{}^{}\to {}_{}{}^1{}_{}{}^{}A_{1g}^{}{}_{}{}^{}$ transitions should occur at roughly 2.0 eV and give rise to two emission bands with different temperature dependence. The ${}_{}{}^3{}_{}{}^{}T_{1u}^{}{}_{}{}^{}$ relaxed excited state is predominantly coupled to the $E_g$ vibrational modes. Unlike the other states its wave function is a rapidly varying function of $A_{1g}$ lattice distortion. The calculations suggest that an absorption band associated with the ${}_{}{}^3{}_{}{}^{}T_{1u}^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}A_{1g}^{}{}_{}{}^{}$ transition may be observable at roughly 0.7 eV using techniques for excited-state spectroscopy.