Abstract
We investigate the formation mechanism of oxygen vacancies and the properties of charge carriers induced in the $n$-type interface of a LaAlO${}_{3}$ (LAO) overlayer on SrTiO${}_{3}$(001) (STO) by carrying out density-functional-theory (DFT) calculations. We find that the formation of a low concentration of oxygen vacancies is dominated by the coupling between oxygen vacancies and the polar electric field in LAO. Oxygen vacancies on the LAO surface, which maximally reduce the electrostatic energy in LAO, are energetically the most stable, and most of the charge carriers induced by the surface vacancies are confined to the interface, forming a two-dimensional electron gas. We also verify that a high concentration of oxygen vacancies in the STO substrate could give rise to a three-dimensional electron gas. In addition, we demonstrate that the band profile at the interface is mainly determined by the concentration of the surface oxygen vacancies.
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