A nucleation-growth model for ferroelectric hysteresis loops with complete and partial switching

This work proposes a two-dimensional lattice model based on a discrete Landau–Devonshire-type potential for calculating hysteresis loops of ferroelectric thin films in switching and sub-switching regimes, yielding good agreement with experimental data. Such a model is valuable for simulating the electric response of nonvolatile memory cells based on ferroelectric film capacitors. Setting the electric field below the nominal coercive field of Landau theory and placing nucleation seeds randomly in the lattice, switching proceeds with a nucleation-growth mechanism. Interactions with neighbors have also been taken into account. We have been able to qualitatively reproduce the shapes of experimental hysteresis loops measured on two types of PZT films in both switching and sub-switching regimes, as the negative susceptibility regions of minor loops are eliminated in our model. Snapshots of domain patterns associated to various points of hysteresis loops help understanding the nature of switching in time dependent electric field and may establish a link to modeling approaches based on ferroelectric property distributions.