The Refinement of Self-Trapped Excitons Structure in CaF$_{2}$ and SrF$_{2}$ Crystals: An Ab Initio Study

We present the results of ab initio calculations of self-trapped excitons (STE) in CaF
₂
and SrF
₂
crystals performed with BHHLYP density functional in embedded cluster approach. As a motivation for this theoretical study, we also report some previously unpublished experimental results on STE luminescence. They concern new luminescence bands of STE approximately 1 eV higher then the main band. The new bands have much lower intensities in pure crystals, however they remain almost unaffected by impurity doping while the main band is quenched by impurities. As possible candidates for excitonic configuration responsible for these high-energy bands, four possible configurations of the off-center STE are considered and rejected. For the on-center STE, i.e., V
_K
+ e, stable configuration has been found. The calculated luminescence energy of on-center STE is 6.57 eV in CaF
₂
and 6.31 eV in SrF
₂
crystal. On the basis of these energies (much higher than energies of new excitonic luminescence bands) and low stability of on-center STE, it is also rejected as a candidate for new bands. Finally, the hypothesis of electron self-trapping is considered. We have found electron self trapping in CaF
₂
and SrF
₂
crystals to be energetically favorable, however the value of energy gain lies within the possible calculation error. It was also found that there is a barrier about 0.3 eV for electron self-trapping. Self-trapped electron is a center with trigonal symmetry and can be considered as perturbed F-center. Calculated isotropic hyperfine couplings of self-trapped electron are given. On the basis of these results, we tentatively suggest that self-trapped electrons are the precursors of yet unknown excitonic configuration responsible for the new luminescence bands.