With the highest brilliance synchrotron radiation X-ray (SPring-8) and TEM observations, Cu oxides ranged 2-nm to 10-nm in thickness formed on sputtered Cu has been evaluated. For the plasma-assisted Cu oxide, weak Cu2O and/or CuO X-ray diffraction pattern is observed, while no diffraction pattern in native and thermally (170°C) grown oxides. Those native and thermal oxides show Cu2O coordination observed by XANES (X-ray Absorption Near Edge Structure) method. This suggests that Cu oxide formed at low temperatures consists of stoichiometric Cu2O in an amorphous structure. According to the Fowler-Nordheim (F-N) current emission model, the current emission taking place at Cu2O decreases with increasing of the oxide thickness and its mean barrier height (φB) in the MIM band structure. In case of current density at 106A/cm2 of 1V, it is estimated that the allowable thickness of Cu oxides is approximately 1.5-nm at 1 eV of barrier height.