Simulation of polarization and butterfly hysteresis loops in bismuth layer-structured ferroelectric thin films

Modeling of the hysteresis loop of ferroelectric thin films has been thought very difficult owing to its nonlinear and history-dependent electric field effects. Here we extend the Preisach model [Z. Phys. 94, 277 (1935)] by using the distribution function integral and superposition method. The model shows improved hysteresis loop that agrees reasonably well with the experimental data measured from the bismuth layer-structured ferroelectric thin films. Compared with the previous model, the current model provides polarization-field (P-E) loop with full and symmetric shape, suitable coercive field (Ec), and few undesirable parameters. The butterfly loop of perovskite-type ferroelectric thin films is also simulated. Additionally, the approach is able to describe the unsaturated loops obtained under various ac electric fields, which is very useful in circuit simulation of ferroelectric field effect transistor or ferroelectric capacitor.