First principles simulations of F centers in cubic SrTiO ₃

Abstract

Atomic and electronic structure of regular and O-deficient SrTiO 3 have been studied. Several types of first principles atomistic simulations: Hartree-Fock method, Density Functional Theory, and hybrid HF-DFT functionals, have been applied to periodic models that consider supercells of different sizes (ranging between 40 and 240 atoms). We confirm the ionic character of the Sr-O bonds and the high covalency of the Ti-O 2 substructure. For the stoichiometric cubic crystal; the lattice constant and bulk modulus correctly reproduce the experimental data whereas the band gap is only properly obtained by the B3PW functional. The relaxed geometry around the F center shows a large expansion of the two nearest Ti ions. Moreover, the vacancy formation energy is extremely sensitive to the size and the shape of the supercell as well as the calculation method. The electronic density map indicates the redistribution of two electrons of the missing O atom between the vacancy and 3d atomic orbitals of the two nearest Ti ions, in contrast to the F centers in ionic oxides where the charge centroid does not change.

First-principles calculations of the atomic and electronic structure ofFcenters in the bulk and on the (001) surface ofSrTiO3

“…A need in such large supercells comes from recent studies, which show a considerable dependence of vacancy formation energy and lattice relaxation on the supercell size, or equivalently on the vacancy concentration. 13,19 This is also in agreement with a recent study on Fe impurity in SrTiO 3 suggesting that the interaction of periodically repeated defects can be quite considerable even for supercells containing 160 atoms. 43 The corresponding local geometry has been determined by total energy minimization with respect to the coordinates of atoms lying in spheres of increasing radius surrounding the vacancy or all atoms in the supercell.…”

“…It exhibits a mixed ionic-covalent chemical bonding since the Sr-O bonds are quite ionic while the Ti-O substructure is partly covalently bound. 12,13 This particular nature of the chemical bonding leads also to a rather unique electronic structure with a band gap of 3.3 eV only. 12 Hence, as it simultaneously exhibits a strong chemical stability, SrTiO 3 continues to attract considerable attention as a model electroceramic material.…”

“…7,[20][21][22][23] For perovskite oxides such as SrTiO 3 , the electronic structure of the F-type defects is a subject of a long debate. 24 Several theoretical studies have suggested major and identical contributions from the 3d orbitals of the two Ti ions on both sides of O vacancy to the electron density of the F center, 13,19,26 although others indicate a partial or total localization of the electrons in the vacancy. 27 The position of the F center level in the optical band gap is also somewhat controversial 19,25 although indirect experimental data based on conductivity measurements suggest that the neutral F center is a quite shallow defect.…”

“…Hence, a number of theoretical studies dealing with the atomic and electronic structure of the F center in SrTiO 3 , based on first principles calculations, mainly relying on density functional theory ͑DFT͒ and using either cluster or periodic models, have appeared in the last few years. 13,19,25,26,29,30 Concerning the surface F centers, only two studies are available in the literature, one based on semiempirical methods 31 and another using ab initio methods but for small supercells. 32 No first principles calculations of the activation energy for the F center migration have been reported so far.…”

“…Recently it has been shown that the above mentioned supercell sizes are too small to screen the strong interaction of the periodically repeated F centers. 13,19 Also, it is well known that the GGA typically predicts underestimated values of the band gap of many oxides. 33,34 On the other hand, the selfconsistent-field Hartree-Fock ͑SCF-HF͒ method correctly predicts the insulating character of these compounds but typically overestimates the band gap 35 as also shown for SrTiO 3 .…”