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The predictions of the polar catastrophe scenario to explain the occurrenceof a metallic interface in heterostructures of the solidsolution(LaAlO$_3$)$_{x}$(SrTiO$_3$)$_{1-x}$ (LASTO:x) grown on (001) SrTiO$_3$were investigated as a function of film thickness and $x$. The films areinsulating for the thinnest layers, but above a critical thickness, $t_c$, theinterface exhibits a constant finite conductivity which depends in apredictable manner on $x$. It is shown that $t_c$ scales with the strength ofthe built-in electric field of the polar material, and is immediatelyunderstandable in terms of an electronic reconstruction at the nonpolar-polarinterface. These results thus conclusively identify the polar-catastrophe modelas the intrinsic origin of the doping at this polar oxide interface.

Intrinsic origin of the two-dimensional electron gas at polar oxide interfaces