First-principles study of polar LaAlO (001) surface stabilization by point defects

We use density functional theory to investigate the influence of surface vacancies on the surface stability of a stoichiometric freestanding LaAlO${}_3$ (001) thin film. Defect-free three- and five-unit-cell-thick LaAlO${}_3$ (001) thin films show macroscopic electric fields of 0.28 and 0.22 V/Å, respectively. The built-in electric field is sufficiently strong for the five-unit-cell-thick film to undergo a dielectric breakdown in the local density approximation. We show that the electric field can be effectively compensated by La vacancies on the LaO surface, O vacancies on the AlO${}_2$ surface, or both types of vacancy present at the same time. Comparing surface Gibbs free energies we show that several surface vacancy structures are thermodynamically stable.

Figure 1

(a) Rhombohedral unit cell of LaAlO${}_3$. The unit-cell vectors are designated as ${\vec{a}}_1$, ${\vec{a}}_2,$ and ${\vec{a}}_3$. α $=$ 60° is used and the corresponding cubic perovskite cells are shown with black boxes. [001] and [111] indicate the crystallographic directions of the cubic cell. (b) Total energy versus octahedral tilting angle in LaAlO${}_3$. The lowest total energy is set to 0 eV.

Figure 2

The simulation cell: two five-u.c.-thick LAO (001) slabs in the cell are mirror symmetric.

Figure 3

(a) Layer-projected density of states of the three-u.c.-thick LAO film before (dashed line) and after (solid line) relaxation. The Fermi level is located at 0 eV. Planar-averaged local electrostatic potential energy of the three-u.c. LAO film before relaxation (b) and after relaxation (c), respectively. The vacuum level between the AlO${}_2$ surfaces is set to 0 eV. The macroscopically averaged potential energies are shown by blue curves.

Figure 4

Side views of the relaxed structure of the three-u.c. LAO film (a), and the relaxed structure of the five-u.c. LAO film (b). (c) Relative displacements of the ions with respect to the La and Al (001) planes in the bulk LAO.

Figure 5

Bader charges before (open circles) and after (filled squares) relaxation of LaO and AlO${}_2$ layers in the three-u.c.-thick LAO film (a), and in the five-u.c.- thick LAO film (b).

Figure 6

(a) Layer-projected density of states of the five-u.c.-thick LAO film before (dashed line) and after (solid line) relaxation. The Fermi level is located at 0 eV. Planar-averaged local electrostatic potential energy of the five-u.c.-thick LAO film before relaxation (b) and after relaxation (c), respectively. The vacuum level between the AlO${}_2$ surfaces is set to 0 eV. The macroscopically averaged potential energies are shown by blue curves.

Figure 7

Schematic of the surface vacancies.

Figure 8

Planar-averaged electrostatic potential of the five-u.c.-thick LAO films with 1/4 ML of La vacancies (a), 1/8 ML of O vacancies (b), and mixed vacancies (c).

Figure 9

Layer-projected density of states of the five-u.c.-thick LAO film with 1/4 ML of La vacancies (a), 1/8 ML of O vacancies (b), and mixed vacancies (c). The Fermi energy is located at 0 eV. Gray dotted lines show the projected density of states before relaxation and black lines show the projected density of states after relaxation.

Figure 10

Bader charges before (open circles) and after (open triangles) relaxation of LaO and AlO${}_2$ layers in the five-u.c.-thick LAO film with 1/4 ML of La vacancies (a), 1/8 ML of O vacancies (b), and mixed vacancies (c).

Figure 11

Relative displacements of atoms in the five-u.c.-thick LAO (001) slab with 1/4 ML of La vacancies (a), 1/8 ML of O vacancies (b), and mixed vacancies (c) with respect to the La and Al (001) planes in the bulk LAO structure.

Figure 12

Phase diagram for the LAO (001) surface as a function of La and O chemical potentials.