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Polarity-induced oxygen vacancies at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>LaAlO</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:mo>โ</mml:mo><mml:msub><mml:mrow><mml:mtext>SrTiO</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>interfaces
Using first-principles density-functional-theory calculations, we find a strong position and thickness dependence of the formation energy of oxygen vacancies in ${\text{LaAlO}}_{3}\ensuremath{\mid}{\text{SrTiO}}_{3}$ $(\text{LAO}\ensuremath{\mid}\text{STO})$ multilayers and interpret this with an analytical capacitor model. Oxygen vacancies are preferentially formed at $p$-type $\text{SrO}\ensuremath{\mid}{\text{AlO}}_{2}$ rather than at $n$-type $\text{LaO}\ensuremath{\mid}{\text{TiO}}_{2}$ interfaces; the excess electrons introduced by โฆ