On the Modeling of Polycrystalline Ferroelectric Thin Films: Landau-Based Models Versus Monte Carlo-Based Models Versus Experiment

Due to the potential for technological application, there has been an explosion of interest in heavily polycrystalline ferroelectric nanofilms, such as those of doped hafnium oxide. However, the heavily polycrystalline nature of these materials invalidates conventional modeling approaches as the dynamics have been found to be: 1) nucleation-limited; 2) involve grains of ferroelectric material interspersed among grains of alternative, nonferroelectric material; and 3) the direct interaction between these grains is observed to be minimal. In this article, we consider seven separate compact or "0-D" models of such polycrystalline films. Four of these models are based on a Landau paradigm and two are based on a Monte Carlo (MC) paradigm. The seventh is the traditional Preisach model. Although all of these models have been used in the literature to model novel polycrystalline ferroelectric nanofilms, here we compare and contrast the accuracy and physical appropriateness of each model by comparing both their static and dynamic properties against experimental data. We then find that although all models except single-grain models are capable of reproducing the static properties, only the MC models replicate the long-time dynamical properties. Thus, it is demonstrated that not all models are equally valid for the accurate modeling of such films.