Figure 1 - The polar catastrophe illustrated for atomically abrupt (001) interfaces between LaAlO3 and SrTiO3.

From the following article

Why some interfaces cannot be sharp

Naoyuki Nakagawa, Harold Y. Hwang and David A. Muller

Nature Materials 5, 204 - 209 (2006)


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a, The unreconstructed interface has neutral (001) planes in SrTiO3, but the (001) planes in LaAlO3 have alternating net charges (rho). If the interface plane is AlO2/LaO/TiO2, this produces a non-negative electric field (E), leading in turn to an electric potential (V) that diverges with thickness. b, If the interface is instead placed at the AlO2/SrO/TiO2 plane, the potential diverges negatively. c, The divergence catastrophe at the AlO2/LaO/TiO2 interface can be avoided if half an electron is added to the last Ti layer. This produces an interface dipole that causes the electric field to oscillate about 0 and the potential remains finite. The upper free surface is not shown, but in this simple model the uppermost AlO2 layer would be missing half an electron, which would bring the electric field and potential back to zero at the upper surface. The actual surface reconstruction is more complicated21. d, The divergence for the AlO2/SrO/TiO2 interface can also be avoided by removing half an electron from the SrO plane in the form of oxygen vacancies.