Electronic structure of oxygen vacancies in ${\mathrm{SrTiO}}_3$ and ${\mathrm{LaAlO}}_3$

The electronic structure of oxygen vacancies in bulk perovskite oxides SrTiO${}_3$ and LaAlO${}_3$ is studied using the Heyd, Scuseria, Ernzerhof (HSE) hybrid density functional. In SrTiO${}_3$ the oxygen vacancy defect introduces a localized state comprised of $3d_{z^2}$ and $4p_z$ orbitals of the adjacent Ti atoms. This results in a bound state 0.7 eV below the conduction band edge. For LaAlO${}_3$, the oxygen vacancy creates a deep state 2.19 eV below the conduction band edge. The defect state is a hybrid of the adjacent La 5$d$ and the Al 3$p$ states. We compute the formation energies of the neutral oxygen vacancy defect V${}^0$ in bulk SrTiO${}_3$ and LaAlO${}_3$ to be 6.0 and 8.3 eV, respectively.

Figure 1

(a) Orbital-projected DOS (LDA) of titanium (Ti) states in STO. (b) Orbital-projected DOS (HSE) of titanium (Ti) states in STO. (c) Orbital-projected DOS (HSE) of oxygen (O) states in STO. Zero energy is set at the top of the valence band.

Figure 2

(a) Orbital projected DOS (HSE) of Lanthanum (La) states in LAO. (b) Orbital projected DOS (HSE) of O states in LAO. (c) Orbital projected DOS (HSE) of Al states in LAO Zero energy is set at the top of the valence band.

Figure 3

STO supercell containing oxygen vacancy.

Figure 4

LDA orbital projected DOS of Ti atom close to the vacancy site. The Fermi level is indicated by the dashed line showing the highest occupied state. Ti $d_z^2$ peaks (blue) around 0.8 eV and 2.8 eV correspond to the bonding and antibonding states, respectively.

Figure 5

Orbital-decomposed DOS (HSE) of a Ti atom (marked A in Fig. 2) contributing to the defect state. The Fermi level is indicated by the dashed line showing the highest occupied state. Ti $d_z^2$ peaks around $-$0.4 and 1.8 eV correspond to the bonding and antibonding states, respectively.

Figure 6

Energy levels of V${}_0$, V${}^{+}$, and V${}^{++}$ in STO (HSE) with respect to VBM and CBM.

Figure 7

(a) Contribution to the defect state (HSE) from one of the neighboring La atoms. (b) Contribution to the defect state (HSE) from one of the neighboring Al atoms.

Figure 8

Defect levels (HSE) in LAO.

Figure 9

(a) Formation energy of neutral and charged oxygen vacancy defects in STO as a function of supercell size (LDA). The formation energy of the charged defects shown in the plot correspond to $E_F=0$ eV. (b) Formation energy of neutral and charged oxygen vacancy defects in STO as a function of supercell size (HSE). The formation energy of the charged defects shown in the plot correspond to $E_F=0$ eV.

Figure 10

(a) Formation energy of an oxygen vacancy in various charged states in STO (HSE). (b) Formation energy of an oxygen vacancy in various charged states in STO (LDA).

Figure 11

(a) Formation energy of an oxygen vacancy in various charged states in LAO (HSE). (b) Formation energy of an oxygen vacancy in various charged states in LAO (LDA).