A model for the electric displacement hysteresis and strain butterfly loops of ferroelectric films under electrical loading is proposed based on an improved Preisach model for nonlinear remanent polarization. Our model shows improved displacement and strain versus electric field loops that agree reasonably well with the experimental data. Compared to the previous model, the current model, including the history-dependent electric field effect, which is always neglected in the conventional model, provides electric displacement and strain loops with a full and symmetric shape. In addition, both the loops of electric displacement and strain under intrinsic defects and injected charges have also been investigated by our model.
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Yang et al. (2009) studied this question.
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