$\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)(2\times 1)$ reconstructions: First-principles calculations of surface energy and atomic structure compared with scanning tunneling microscopy images

$(1\times 1)$ and $(2\times 1)$ reconstructions of the (001) $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ surface were studied using the first-principles full-potential linear muffin-tin orbital method. Surface energies were calculated as a function of $\mathrm{Ti}{\mathrm{O}}_2$ chemical potential, oxygen partial pressure $p_{{\mathrm{O}}_{}2}$and temperature. The $(1\times 1)$ unreconstructed surfaces were found to be energetically stable for many of the conditions considered. Under conditions of very low oxygen partial pressure the $(2\times 1)$ ${\mathrm{Ti}}_2{\mathrm{O}}_3$ reconstruction [Martin R. Castell, Surf. Sci. 505, 1 (2002)] is stable. The question as to why STM images of the $(1\times 1)$ surfaces have not been obtained was addressed by calculating charge densities for each surface. These suggest that the $(2\times 1)$ reconstructions would be easier to image than the $(1\times 1)$ surfaces. The possibility that the presence of oxygen vacancies would destabilise the $(1\times 1)$ surfaces was also investigated. If the $(1\times 1)$ surfaces are unstable then there exists the further possibility that the $(2\times 1)$ DL-$\mathrm{Ti}{\mathrm{O}}_2$ reconstruction [Natasha Erdman et al. Nature (London) 419, 55 (2002)] is stable in a $\mathrm{Ti}{\mathrm{O}}_2$-rich environment and for $p_{{\mathrm{O}}_2}>{10}^{-18}$ atm.

Figure 1

(a) $(1\times 1)$ unreconstructed $\mathrm{Ti}{\mathrm{O}}_2$ and SrO surfaces. (b) $(2\times 1)$ ${\mathrm{Ti}}_2{\mathrm{O}}_3$ reconstruction. (c) $(2\times 1)$ $\mathrm{Ti}{\mathrm{O}}_2$ reconstruction. (d) $(2\times 1)$ DL-$\mathrm{Ti}{\mathrm{O}}_2$ reconstruction. Ti atoms are darkest and O are lightest.

Figure 2

FP-LMTO band structure of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$.

Figure 3

Vertical slices through (a) $\mathrm{Ti}{\mathrm{O}}_2$ layer and (b) SrO layer to show atom positions and labels for the $(2\times 1)$ DL-$\mathrm{Ti}{\mathrm{O}}_2$ reconstruction.

Figure 4

Surface energies as a function of ${\mu }_{\mathrm{Ti}{\mathrm{O}}_2}$ at $T=1000\mathrm{K}$ and $p^0$.

Figure 5

Surface energies as a function of $p_{{\mathrm{O}}_2}$ at $T=1000\mathrm{K}$ (a) in equilibrium with $\mathrm{Ti}{\mathrm{O}}_2$ and (b) in equilibrium with SrO.

Figure 6

STM image ($2\mathrm{V}$ sample bias, $0.5\mathrm{nA}$ tunneling current) of the $(2\times 1)$ reconstructed surface. The two unit cell separation of the rows can be seen, but the single unit cell periodicity along the rows is not resolved. The $(2\times 1)$ surface unit cell is shown in the image. By averaging vertically through the image a plot of the average row heights is created as shown in the lower panel. The typical corrugation height is between 0.4 and $0.5\mathrm{\AA }$.

Figure 7

(Color online) Charge densities for the $(1\times 1)$ SrO terminated surface for slices through the SrO and $\mathrm{Ti}{\mathrm{O}}_2$ planes in two different energy windows above the conduction band.

Figure 8

(Color online) Charge densities for the $(1\times 1)$ $\mathrm{Ti}{\mathrm{O}}_2$ terminated surface for slices through the SrO and $\mathrm{Ti}{\mathrm{O}}_2$ planes in two different energy windows above the conduction band.

Figure 9

(Color online) Charge densities for the $(2\times 1)$ ${\mathrm{Ti}}_2{\mathrm{O}}_3$ terminated surface for slices through the SrO and $\mathrm{Ti}{\mathrm{O}}_2$ planes in two different energy windows above the conduction band.

Figure 10

(Color online) Charge densities for the $(2\times 1)$ DL-$\mathrm{Ti}{\mathrm{O}}_2$ terminated surface for slices through the SrO and $\mathrm{Ti}{\mathrm{O}}_2$ planes in two different energy windows above the conduction band.