Time domain electric pulse measurements were conducted on a capacitor consisting of a Pt film as the top electrode, atomic-layer-deposited 6.5-nm-thick amorphous Al2O3 as the dielectric layer, and two-dimensional electron gas (2DEG) at the interface between Al2O3 and SrTiO3 as the bottom electrode. The sample showed highly useful current-voltage characteristics as the selector in cross-bar array resistance switching random access memory. The long-term (order of second) variation in the leakage current when the Pt electrode was positively biased was attributed to the field-induced migration of oxygen vacancies between the interior of the Al2O3 and the 2DEG region. Relaxation of the vacancy concentration occurred even at room temperature.