The presence of oxygen vacancies is considered to be the cause of various phenomena in ferroelectric thin films. In this work, the role of oxygen vacancies is theoretically modeled. Various properties are numerically simulated using the two-dimensional Ising model. In the presence of an oxygen vacancy in a perovskite cell, the octahedral cage formed by oxygen ions is distorted so that the potential energy profile for the displacement of the titanium ion becomes asymmetric. It requires additional energy to move from the lower minimum position to the higher one. Moreover, space charges are also developed by trapping charge carriers into these vacancies. The combination of the pinning effect induced by the distorted octahedral cage and the screening of the electric field in the presence of space charges results in phenomena such as fatigue and imprint.
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