## 3 Results and Discussion
It shows that the areal quasistatic capacitance of the MIM devices annealed at 250 or 300 \({}^{\circ}\)C is much higher than those measured at 1 kHz, while there is no much difference between the areal quasistatic capacitance and the areal capacitance at 1 kHz for the one annealed at 350 \({}^{\circ}\)C. The strong frequency-dependent capacitance of the MIM devices annealed at 250 or 300 \({}^{\circ}\)C is attributed to relaxation polarization of the weakly bound ions in the incompletely decomposed AlO\({}_{\rm x}\) films. Especially, the protons (H\({}^{+}\)), which can move in the whole AlO\({}_{\rm x}\) film, move to the ITO/AlO\({}_{\rm x}\) interface and form an electric double layer (EDL) that has ultrahigh capacitance at very low frequency [24,25]. To further investigate the effect of mobile hydrogen-related ions on the low-frequency capacitance of the AlO\({}_{\rm x}\) films, the surface of the bottom electrode (ITO) was treated by water before spin-coating the AlO\({}_{\rm x}\) precursor on it. The water treatment can introduce large amounts of the adsorbed water molecules at the ITO/AlO\({}_{\rm x}\) interface that would  
Figure 3: (**a**) Capacitance-frequency curves and (**b**) quasistatic capacitance-voltage curves of the AlO\({}_{\rm x}\) dielectrics without water treatment; (**c**) Capacitance-frequency curves; and (**d**) quasistatic capacitance-voltage curves of the AlO\({}_{\rm x}\) dielectrics with water treatment. further form hydrogen and OH groups. Figure 3c shows the frequency dependence of capacitance of the MIM devices with water treatment. It can be seen that the capacitance of all devices (even annealed at 350 \({}^{\circ}\)C) depends on the frequency seriously. The areal capacitances at 1 kHz of the MIM devices annealed at 250, 300, and 350 \({}^{\circ}\)C are 387.9, 295.3, and 268.9 nF/cm\({}^{2}\), respectively. However, the areal quasi-static capacitances of the MIM devices annealed at 250, 300, and 350 \({}^{\circ}\)C are as high as 1520, 846, and 647 nF/cm\({}^{2}\) (see Figure 3d). The extremely high quasistatic capacitance is most probably attributed to H\({}^{+}\) ions which are small and easy to be driven by the electric field. The H\({}^{+}\) ions in oxide films are generally associated with oxygen atoms to form a three-coordinate oxygen center (M-OH+-M), and the motion of H\({}^{+}\) ions is relied on \"a sequence of hops\" from one bridging oxygen atom to another [13, 24, 26]. When a voltage is applied to the MIM device, the H\({}^{+}\) ions migrate to the AlO\({}_{\rm x}\)/ITO interface by a sequence of hops and form a very thin EDL with an extremely large capacitance. Under an electric field of 0.3 MV/cm (2 V), the leakage current density (\(J\)) of the MIM devices without water treatment annealed at 250, 300, and 350 \({}^{\circ}\)C are 3.2 \(\times\) 10\({}^{-8}\), 2.4 \(\times\) 10\({}^{-8}\), and 1.4 \(\times\) 10\({}^{-8}\) A/cm\({}^{2}\), respectively, corresponding to much higher \(J\) of 5.5 \(\times\) 10\({}^{-7}\), 4.5 \(\times\) 10\({}^{-7}\), and 2.6 \(\times\) 10\({}^{-7}\) A/cm\({}^{2}\) for the water-treated ones (not shown). The breakdown field of the MIM devices without water treatment annealed at 250, 300, and 350 \({}^{\circ}\)C are 1.9, 2.9, and 3.2 MV/cm, respectively (not shown). Interestingly, the leakage current for the water-treated MIM devices increases greatly at -0.3 MV, but there are not apparent breakdown points. The difference may be attributed to the large amount of movable H\({}^{+}\) ions in the water-treated AlO\({}_{\rm x}\) samples, which form leakage current paths. To verify the existence of H\({}^{+}\) ions in the AlO\({}_{\rm x}\) films, TOF-SIMS experiments were carried out. Figure 4 shows the depth-profile element distribution of the water-treated AlO\({}_{\rm x}\)/ITO sample annealed at 350 \({}^{\circ}\)C. The intensities for the carbon signal are very weak, revealing little carbon-related residuals. By contrast, there are a number of hydrogens in the whole AlO\({}_{\rm x}\) dielectric.