Study of Charge Transition Levels of Intrinsic Defect, Band Gab, and Formation Energy in Barium Fluoride and Calcium Fluoride

Abstract

This Thesis study semi local and hybrid density functional analysis of charge transition levels of native defects in BaF2 and CaF2 structures. The transition levels was calculated from the formation energies corresponding to two defect charge states. The errors arising from the small super cell size effects have been relieved through extrapolating the formation energies to the limit of infinite super cell size. The reliability of the extrapolation method has been verified through the application of two correction factors: the Makov-Payine factor to correct for the unwanted interaction between image charges in periodic super cell simulations, and the potential-alignment factor to align the valence band edges in defective and bulk super cells. The common error in the band gap inherited to semi local density functional has been accounted for by incorporating the hybrid density functional method, leading to a correct placement of the transition levels within the band gap. The band gap size from hybrid calculation is validated using the full potential, Lineralized Augmented Plane wave method with the Modified-Becke-Johnson exchange potential. The calculated transition level for the anion vacancy was (2.77 eV) below the conduction band, agreeing well with the experimental optical absorption band of (3.3eV) associated with the electron transition from the ground state F-center to the conduction band in CaF2. The most stable native defect was the charged cation in BaF2 with formation energy( -9.82 eV). The order of defect stabilities in our calculation was compatible with recent first-principle report, however, our formation energies are more accurate. Interestingly the cation and anion defect stability order in BaF2 matches that of CaF2. Our results are sufficiently accurate and, thus, significant for direct comparison with experiments. All the calculations and simulations in this thesis were done using Quantum Espresso Simulations Package.