Formation of oxygen vacancies and charge carriers induced in the $n$-type interface of a LaAlO${}_3$ overlayer on SrTiO${}_3$(001)

We investigate the formation mechanism of oxygen vacancies and the properties of charge carriers induced in the $n$-type interface of a LaAlO${}_3$ (LAO) overlayer on SrTiO${}_3$(001) (STO) by carrying out density-functional-theory (DFT) calculations. We find that the formation of a low concentration of oxygen vacancies is dominated by the coupling between oxygen vacancies and the polar electric field in LAO. Oxygen vacancies on the LAO surface, which maximally reduce the electrostatic energy in LAO, are energetically the most stable, and most of the charge carriers induced by the surface vacancies are confined to the interface, forming a two-dimensional electron gas. We also verify that a high concentration of oxygen vacancies in the STO substrate could give rise to a three-dimensional electron gas. In addition, we demonstrate that the band profile at the interface is mainly determined by the concentration of the surface oxygen vacancies.

Figure 1

(2 $\times$ 2) supercells to model the $n$-type interface of an LAO overlayer on STO(001) (a) without oxygen vacancy and (b) with one oxygen vacancy (black circle) on the LAO surface.

Figure 2

Formation energies of oxygen vacancies at different atomic layers in the LAO/STO interface structure. The legend of 1Vo@(LAO)2/STO-2$\times$2 stands for one oxygen vacancy in a (2$\times$2) supercell containing two LAO layers, others follow the same convention. For the (2$\times$2) supercell containing two oxygen vacancies, one is fixed on the LAO surface and the other varies at different atomic layers. Atomic layers of SrO, TiO${}_2$, LaO, and AlO${}_2$ are denoted as Sr, Ti, La, and Al, respectively.

Figure 3

Formation energies of one oxygen vacancy on the LAO surface of (2$\times$2) supercells as a function of the chemical potential of the oxygen atom. The LAO thicknesses vary from 2 to 5 unit-cell layers. The ideal structure is the reference.

Figure 4

(a) Layer-projected density of states of (3$\times$3) supercell with one oxygen vacancy on the LAO surface. The arrow points to the oxygen-vacancy state. (b) Top view of the spatial distribution of the oxygen-vacancy state at the surface. (c) Side view of the top three LAO layers. The arrows and horizontal lines denote the ionic displacement in LAO.

Figure 5

Layer-projected DOSs for (2$\times$2) supercells (a) with one oxygen vacancy on the LAO surface and (b) with one oxygen vacancy in STO-1 layer.

Figure 6

Layer-projected DOSs for (2$\times$2) supercells (a) with two oxygen vacancies on the LAO surface and (b) with one vacancy on the LAO surface and the other in the LAO-3 layer.

Figure 7

Layer-resolved density and spatial distribution of charge carriers in the (LAO)${}_3$/(STO)${}_{17}$-(2$\times$1) supercell with oxygen vacancies. (a), (b) For one oxygen vacancy on the LAO surface; (c), (d) for one oxygen vacancy in the middle of STO; (e), (f) for one oxygen vacancy on the LAO surface and another in the middle of STO. LAO at right side of STO is omitted. The unit of carrier density is electron per unit cell.

Figure 8

Band diagrams of the LAO/STO interface with oxygen vacancies on the LAO surface for (a) $n_V<0.25$, (b) $n_V=0.25$, (c) $n_V>0.25$, (d) $n_V>0.25$ but oxygen vacancies in both the LAO surface layer and the STO substrate. Dashed line stands for Fermi level, and shade area for electron occupied states.