Ab initio study of the two-dimensional metallic state at the surface of SrTiO${}_3$: Importance of oxygen vacancies

Motivated by recent angle-resolved photoemission spectroscopy observations of a highly metallic two-dimensional electron gas (2DEG) at the (001) vacuum-cleaved surface of SrTiO${}_3$ and the subsequent discussion on the possible role of oxygen vacancies for the appearance of such a state [Santander-Syro et al., Nature (London) 469, 189 (2011)], we analyze by means of density functional theory the electronic structure of various oxygen-deficient SrTiO${}_3$ surface slabs. We find a significant surface reconstruction after introducing oxygen vacancies and we show that the charges resulting from surface-localized oxygen vacancies—independent of the oxygen concentration—redistribute in the surface region and deplete rapidly within a few layers from the surface suggesting the formation of a 2DEG. We discuss the underlying model emerging from such observations.

Figure 1

Optimized structures of $2\times 2\times 6$ SrTiO${}_3$ slabs with oxygen vacancy in (a) the SrO and (b) the TiO${}_2$ surface layers.

Figure 2

Band structure with band weights of Ti for bulk STO.

Figure 3

Total and partial density of states for bulk STO and cleaved slab with oxygen vacancy normalized to STO formula units. (a) bulk STO; (b) $2\times 2\times 6$ with SrO termination; (c) $2\times 2\times 6$ with TiO${}_2$ termination. The inset figures are the zoom in of the bottom of the conduction band.

Figure 4

Band structure obtained within GGA for a $1\times 1\times 12$ slab ($x=0.0833$) with TiO${}_2$ termination. (a) Unrelaxed structure; (b) relaxed structure.

Figure 5

Band structure obtained within GGA and GGA+$U$ for a $2\times 2\times 4$ slab ($x=0.0625$). (a) GGA for SrO termination; (b) GGA for TiO${}_2$ termination; (c) GGA+$U$ for SrO termination; (d) GGA+$U$ for TiO${}_2$ termination.

Figure 6

Calculated band weights of Ti $3d$ for the $2\times 2\times 6$ slab with oxygen vacancy. (a) SrO termination; (b) TiO${}_2$ termination.

Figure 7

Calculated band structures for different (relaxed) slabs $2\times 2\times 4$, $2\times 2\times 6$, and $3\times 3\times 4$ with SrO termination (left panels) and TiO${}_2$ termination (right panels). (a) $2\times 2\times 4$ slab with SrO termination; (b) $2\times 2\times 4$ slab with TiO${}_2$ termination; (c) $2\times 2\times 6$ slab with SrO termination; (d) $2\times 2\times 6$ slab with TiO${}_2$ termination; (e) $3\times 3\times 4$ with SrO termination.

Figure 8

DOS filling of gap states for layer decomposed PDOS of SrO and TiO${}_2$ terminated slabs.

Figure 9

Ti $3d$ occupations for the SrO terminated $3\times 3\times 4$ slab.

Figure 10

Total DOS for $2\times 2\times 4$, $2\times 2\times 6$, and $3\times 3\times 4$ slabs with SrO and TiO${}_2$ termination, normalized to STO formula units.

Figure 11

Calculated Fermi surface for (a) SrO terminated $2\times 2\times 4$ slab, (b) TiO${}_2$ terminated $2\times 2\times 4$ slab, (c) SrO terminated $2\times 2\times 6$ slab, (d) TiO${}_2$ terminated $2\times 2\times 6$ slab, and (e) SrO terminated $3\times 3\times 4$ slab.

Figure 12

Calculated carrier density for the SrO and TiO${}_2$ terminated slabs; (a) carrier density per surface area; (b) carrier density per volume.

Figure 13

Calculated band weights of Ti $3d$ for the $2\times 2\times 6$ slab with oxygen vacancy and SrO termination. The contribution of each Ti in the two topmost TiO${}_2$ layers is shown separately.

Figure 14

Calculated band weights of Ti $3d$ for the $2\times 2\times 6$ slab with oxygen vacancy and TiO${}_2$ termination. The contribution of each Ti in the two topmost TiO${}_2$ layers is shown separately.