First-principles calculations of atomic and electronic structure of ${\text{SrTiO}}_3$ (001) and (011) surfaces

We present and discuss the results of the calculations of surface relaxation and rumpling on ${\text{SrTiO}}_3$ (001) and (011) surfaces. We consider both SrO and ${\text{TiO}}_2$ terminations of the (001) surface, and three terminations (Sr, TiO, and O) of the polar (011) surface. The calculations are based on hybrid Hartree–Fock and density-functional theory exchange functionals by using Becke’s three-parameter method combined with the nonlocal correlation functionals of Perdew and Wang. We find that all top-layer atoms for ${\text{TiO}}_2$ and SrO-terminated ${\text{SrTiO}}_3$ (001) surfaces relax inward, with the exception of SrO-terminated surface O atoms, whereas all second-layer atoms relax outward. The surface rumpling for the TiO-terminated ${\text{SrTiO}}_3$ (011) surface, which is 11.28% of the bulk lattice constant, is considerably larger than the relevant surface rumplings for SrO and ${\text{TiO}}_2$-terminated (001) surfaces. The surface rumplings for the SrO and ${\text{TiO}}_2$-terminated (001) surfaces are in excellent agreement with relevant low-energy electron diffraction and reflection high-energy electron diffraction experimental data, and the surface relaxation energies on both surfaces are similar. In contrast, the different terminations of the (011) surface lead to large differences in relaxation energies. The O-terminated (011) surface has the lowest surface relaxation energy $\left(-1.32\text{eV}\right)$. The TiO-terminated (011) surface has a much higher surface relaxation energy of $-1.55\text{eV}$, while the Sr-terminated (011) surface has the highest surface relaxation energy $\left(-1.95\text{eV}\right)$. Our calculations indicate a considerable increase in the Ti-O bond covalency $\left(0.130e\right)$ near the TiO-terminated (011) surface relative to the bulk $\left(0.088e\right)$, which is much larger than that for the (001) surface $\left(0.118e\right)$. The Ti-O bond populations are considerably larger in the direction perpendicular to the TiO-terminated (011) surface $\left(0.188e\right)$ than in the plane $\left(0.130e\right)$.

Figure 1

(Color online) Side view of ${\text{SrTiO}}_3$ (001) surfaces. (a) SrO-terminated surface. (b) ${\text{TiO}}_2$-terminated surface, with definitions of surface rumpling $s$ and the near-surface interplanar separations $d_{12}$ and $d_{23}$.

Figure 2

(Color online) Sketch of the cubic ${\text{SrTiO}}_3$ perovskite structure showing two (011) cleavage planes that give rise to charged SrTiO and ${\text{O}}_2$ (011) surfaces.

Figure 3

(Color online) Possible (011) surface slab models considered in the text. [(a)–(c)] Slabs obtained by simple cleavage, yielding mixed, O-terminated, and SrTiO-terminated polar surfaces, respectively. [(d)–(f)] Slabs with nonpolar TiO-terminated, Sr-terminated, and O-terminated surfaces, respectively.