The physical origin of the ferroelectric-like character-istics in metal-insulator-metal (MIM) structures with amorphous (a-) dielectric enabled by oxygen ions (O2-) and vacancies (Vo2+) migration are systematically inves-tigated by modulating the metal-insulator interface and dielectric thickness. It is found that O2- and Vo2+ origi-nate from the interface between metal nitride and a-ZrO2 film, drifting through the path in a-ZrO2 film un-der the applied electric field to form the long-range movement induced polarization. Furthermore, the po-larization has a thickness-dependent saturation due to ions pinning.