The predictions of the polar catastrophe scenario to explain the occurrence of a metallic interface in heterostructures of the solid solution(LaAlO$_3$)$_{x}$(SrTiO$_3$)$_{1-x}$ (LASTO:x) grown on (001) SrTiO$_3$ were investigated as a function of fi
lm thickness and $x$. The films are insulating for the thinnest layers, but above a critical thickness, $t_c$, the interface exhibits a constant finite conductivity which depends in a predictable manner on $x$. It is shown that $t_c$ scales with the strength of the built-in electric field of the polar material, and is immediately understandable in terms of an electronic reconstruction at the nonpolar-polar interface. These results thus conclusively identify the polar-catastrophe model as the intrinsic origin of the doping at this polar oxide interface.
The evolution of the atomic structure of LaAlO3 grown on SrTiO3 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 LaAlO3, which decreases with increasing film thickness. We explain this in terms of competition between elastic strain energy, electrostatic energy, and electronic reconstructions. The findings are qualitatively reproduced by density-functional theory calculations. Significant cationic intermixing across the interface extends approximately three monolayers for all film thicknesses. The interfaces of films thinner than four monolayers therefore extend to the surface, which might affect conductivity.
