Abstract:The behavior of holes in the valence band of BaTiO 3 is investigated using hybrid densityfunctional calculations. We find that holes tend to self-trap, localizing on individual O atoms and causing local lattice distortions, forming small hole-polarons. This takes place even in the absence of intrinsic defects or impurities. The self-trapped hole (STH) is more energetically favorable than the delocalized hole in the valence band. The calculated emission peak energy corresponding to the recombination of a conduc… Show more
“…O is not increased so high and consequently imposes the lower limit of the Fermi level. Furthermore, we have found the self-trapped hole (STH) is also stable by 0.25 eV and 0.29 eV in the R and C D phases, respectively, which are close to the previously reported self-trapping energy of 0.2 eV in highly symmetric cubic BTO [42]. Thus, it seems difficult to achieve the p-type BTO even if shallow acceptor dopants exist and V O is well suppressed by a growth technique.…”
Section: O and Ti −supporting
confidence: 88%
“…Calculated recombination energies of the electron polarons (Ti − Ti , V + O , V 0 O , H 0 O , and H 0 i ) with a hole at the VBM are 2.1-2.3 eV and 2.0-2.3 eV for the R and C D models, respectively, which are close to the experimental values of 2.4-2.5 eV [7][8][9]. Recently, Traiwattanapong et al have reported recombination energy of a STH and an electron at the CBM to be 2.17 eV [42], which is close to our calculated 2.33 and 2.04 eV in the R and C D phases, respectively. Therefore, the electron polarons, hole polarons, or both may be the origin of the green luminescences in BTO.…”
Small polarons and point defects in BaTiO 3 are investigated using hybrid functional calculations. Based on the experimentally-confirmed order-disorder-type phase transitions, Ti displacements along 111 directions are included in the cubic model. We reveal that the self-trapped electrons at Ti sites are stable in both rhombohedral and cubic BaTiO 3 and the Ti off-centering, which introduces antibonding hybridization between lowest-lying Ti-3d and O-2p orbitals at the conduction band minimum, is essential for stabilizing the self-trapped electrons. Our calculations are in contrast to previous theoretical studies, even qualitatively, but reasonably consistent with the long-standing experimentally-observed small polarons in BaTiO 3. This finding may explain why self-trapped electrons are not stable in SrTiO 3 but are in BaTiO 3 from the symmetry viewpoint.
“…O is not increased so high and consequently imposes the lower limit of the Fermi level. Furthermore, we have found the self-trapped hole (STH) is also stable by 0.25 eV and 0.29 eV in the R and C D phases, respectively, which are close to the previously reported self-trapping energy of 0.2 eV in highly symmetric cubic BTO [42]. Thus, it seems difficult to achieve the p-type BTO even if shallow acceptor dopants exist and V O is well suppressed by a growth technique.…”
Section: O and Ti −supporting
confidence: 88%
“…Calculated recombination energies of the electron polarons (Ti − Ti , V + O , V 0 O , H 0 O , and H 0 i ) with a hole at the VBM are 2.1-2.3 eV and 2.0-2.3 eV for the R and C D models, respectively, which are close to the experimental values of 2.4-2.5 eV [7][8][9]. Recently, Traiwattanapong et al have reported recombination energy of a STH and an electron at the CBM to be 2.17 eV [42], which is close to our calculated 2.33 and 2.04 eV in the R and C D phases, respectively. Therefore, the electron polarons, hole polarons, or both may be the origin of the green luminescences in BTO.…”
Small polarons and point defects in BaTiO 3 are investigated using hybrid functional calculations. Based on the experimentally-confirmed order-disorder-type phase transitions, Ti displacements along 111 directions are included in the cubic model. We reveal that the self-trapped electrons at Ti sites are stable in both rhombohedral and cubic BaTiO 3 and the Ti off-centering, which introduces antibonding hybridization between lowest-lying Ti-3d and O-2p orbitals at the conduction band minimum, is essential for stabilizing the self-trapped electrons. Our calculations are in contrast to previous theoretical studies, even qualitatively, but reasonably consistent with the long-standing experimentally-observed small polarons in BaTiO 3. This finding may explain why self-trapped electrons are not stable in SrTiO 3 but are in BaTiO 3 from the symmetry viewpoint.
“…One could expect intuitively holes localized on O ions nearest to the cation what happens often for the hole polarons in oxides, e.g. MgO:Li [35] and perovskites [13,36]. In addition, analysis of the electronic density of states (DOS) for (Ce,Tb)O2 ( fig.…”
Section: A Comparison Of Parent Oxides and Delocalization Of Holesmentioning
The atomic and electronic structure of CeO2 doped with Tb has been calculated from first principles with inclusion of strong correlation effects on the basis of Hubbard model (GGA+U). The two values of Hubbard U-parameter were applied separately on Ce and Tb ions, in order to treat correctly two oxidation states of Tb (3+ and 4+). Crystal structure distortion is also discussed for Tb3+ ions in ceria without oxygen vacancies. The corresponding total energy difference between the 3+ and 4+ states is very small and, thus, these states can co-exist without oxygen vacancy formation (unlike Gd doping). Multiple configurations have been obtained with localization of electrons on different number of cations, if the Tb ion has an oxygen vacancy nearby. A site symmetry approach has been successfully applied to identify the ground state configuration. Gibbs formation energy of oxygen vacancy due to Tb doping is reduced by almost a factor of four, in comparison with the pure CeO2. The dependence of Gibbs formation energy on the temperature and oxygen partial pressure is discussed. It has been also shown that the lowest formation energy for the small polaron occurs when the Ce 3+ and Tb 3+ ions are located as nearest neighbors to oxygen vacancy. The results obtained are compared with the existing literature data from the electrical conductivity and optical measurements.
“…Examples of STHs are found in TiO 2 , β-Ga 2 O 3 , CdWO 4 , and Y 3 Al 5 O 12 crystals [3][4][5][6] and also amorphous SiO 2 [7,8]. Firstprinciples calculations have predicted that STHs will be stable at low temperature in SrTiO 3 and BaTiO 3 crystals [9,10]. Self-trapping occurs in a crystal when the lattice surrounding the hole relaxes and forms a shallow potential well.…”
Density functional theory is used to establish the ground-state structure of the self-trapped hole (STH) in KH 2 PO 4 crystals. The STHs in this nonlinear optical material are free small polarons, a fundamental intrinsic point defect. They are produced with ionizing radiation in the low-temperature orthorhombic structure of KH 2 PO 4 and are only stable (i.e. longlived) below approximately 70 K. A large 129-atom cluster, K 19 H 40 P 14 O 56 , is constructed to model the STH. The ωB97XD functional with the 6−31+G * basis set is used and geometry optimization is performed. Our results show that two of the oxygen ions in a PO 4 unit relax toward each other and equally share the hole. These two oxygen ions do not initially have close hydrogen neighbors. This equal sharing of the hole is related to the presence of isolated, slightly distorted, PO 4 units and is significantly different from the small-polaron behavior often observed in other oxide crystals where the hole is localized on only one oxygen ion. The computational results provide a detailed description of the lattice relaxation occurring during formation of the STH. Characteristic spectral features of this defect are a larger hyperfine interaction with one 31 P nucleus and equal, but smaller, hyperfine interactions with two 1 H nuclei. The computed values for these isotropic and anisotropic hyperfine coupling constants are in excellent agreement with results obtained from electron paramagnetic resonance experiments.
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