Modeling saturated and unsaturated ferroelectric hysteresis loops : an analytical approach

Abstract

In ferroelectric materials, hysteresis behavior is very difficult to model due to its nonlinear and history-dependent characteristics. Among approaches that are able to describe unsaturated loops, many of them are either very complicated (numerical procedures must be employed) or the resulting loops contain some undesirable or defective features. In this work, a simple hysteresis model based on a special construction of the Preisach function is proposed. Explicit expressions for the polarization-field (P-E) responses under increasing and decreasing applied fields have been derived. The saturated and unsaturated P-E loops can be conveniently calculated by piecing together such responses. The technique is widely applicable to the modeling of ferroelectric hysteresis behavior of ceramics and polymers. As examples we study the applied field dependence of dielectric permittivity of a ferroelectric film and the remanent polarization of ferroelectric composites after ac poling. We find that the model predictions agree well with the experimental results.