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Abstract
A mathematical model with a simple log-time dependence has been developed using a theoretical approach to describe the complicated depolarization effect (ΔP) observed in ferroelectric thin films. The model includes two driving forces responsible for ΔP. One is the depolarization field due to incomplete compensation of ferroelectric polarization at the interfaces. This leads to the polarity independent depolarization effect characterized by a symmetric ΔP. Another one is the internal bias which can be parallel or antiparallel to the applied field, leading to a polarity dependent or asymmetric ΔP. The model successfully predicts the changing ΔP with time. Two important parameters are estimated by analyzing the results of the model. One is the internal bias field, responsible for asymmetric retention of polarization. Another one is the size of back switched domains. The values obtained are comparable to the field near the surface and the surface layer thickness predicted by earlier models. The model provides an excellent fit to experimental data for two different types of PZT films, and is expected to be generally applicable to all thin film ferroelectrics.
