Simulation of thickness dependent coercive field in PZT thin films

The thickness-dependent coercive field in perovskite-type ferroelectric thin films has been simulated using the four-state Potts model. In this model, four mutually perpendicular dipole orientations result in four different kinds of domains in a film of tetragonal phase. In order to simulate the switching due to the domain wall movement, only those dipoles in the domain boundaries are allowed to rotate. Each rotation is restricted only to 90°, either clockwise or counter-clockwise. The influence of space charge is also included. For large thickness, the simulation result agrees with the trend observed in most experiments that the coercive field decreases with thickness. On the other hand, when the thickness is smaller than a critical value, the coercive field increases with thickness. The intrinsic influence governed by the domain-wall movement and the extrinsic effect induced by oxygen vacancies are discussed. This result not only reflects the two different regimes for polarization switching but also imp...