Evolution of the Interfacial Structure of ${\mathrm{LaAlO}}_3$ on ${\mathrm{SrTiO}}_3$

The evolution of the atomic structure of ${\mathrm{LaAlO}}_3$ grown on ${\mathrm{SrTiO}}_3$ was investigated using surface x-ray diffraction in conjunction with model-independent, phase-retrieval algorithms between two and five monolayers film thickness. A depolarizing buckling is observed between cation and oxygen positions in response to the electric field of polar ${\mathrm{LaAlO}}_3$, which decreases with increasing film thickness. We explain this in terms of competition between elastic strain energy, electrostatic energy, and electronic reconstructions. Based on these structures, the threshold for formation of a two-dimensional electron system at a film thickness of 4 monolayers is quantitatively explained. The findings are also qualitatively reproduced by density-functional-theory calculations.

Figure 1

Refined cation occupation for all four film thicknesses depicted as blocks. Intermixing of more than approximately 5% extends across 3 ML at the interface for all films, which also exhibit the same apparent partial occupation of the top two MLs of approximately 80 and 20%. The horizontal line at 0 marks the nominal interface.

Figure 2

(a) Cumulative displacement out of plane of the atomic positions relative to a reference grid defined by bulk STO. For reasons of clarity, only the average of the $A$-site (upper panels) and $B$-site (lower panels) atomic layer positions are shown. (b) and (c) show the buckling of the $A$-site and $B$-site atomic planes from the refined structure and the DFT calculations, respectively, shown on the same scale. Positive values indicate movements of the cation relative to the oxygen ions towards the surface. In (c) the filled and open circles mark the abrupt and intermixed DFT models, respectively. The dotted lines represent the nominal interface.

Figure 3

The influence of buckling on the valence band edge (VBE) and conduction band edge (CBE) relative to the Fermi level ($E_F$) for the 3-ML- and 4-ML-LAO films. Without buckling, the electric field is constant across the film. Buckling results in a zigzag motif, shown for the VBE. Negative buckling in the STO and the partial occupation at the surface were taken into account, but are not shown for the sake of clarity. Since from our “ionic” model, we cannot determine band bending in STO, this was neglected.