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The origin of the 2-dimensional electron system (2DES) appearing at the (001)interface of band insulators $\rm SrTiO_3$ and $\rm LaAlO_3$ has beenrationalized in the framework of a polar catastrophe scenario. This implies theexistence of a critical thickness of polar $\rm LaAlO_3$ overlayer ($4~\rmu.c.$) for the appearance of the 2DES: polar catastrophe for thick $\rmLaAlO_3$ overlayer is avoided either through a Zener breakdown or astabilization of donor defects at the $\rm LaAlO_3$ surface, both providingelectrons to dope the substrate. The observation of a critical thickness isobserved in experiments, supporting these hypotheses. Yet, there remains anopen debate about which of these possible mechanisms actually occurs first.Using hybrid functional Density Functional Theory, we re-examine thesemechanisms at the same level of approximation. Particularly, we clarify therole of donor defects in these heterostructures, and argue that, under usualgrowth conditions, electric-field driven stabilization of oxygen vacancies andhydrogen adsorbates at the LAO surface occur at a smaller LAO thickness thanrequired for Zener breakdown.

Polarity-field driven conductivity in SrTiO$_3$/LaAlO$_3$: a hybrid functional study