Modeling and Simulation of Ferroelectric Materials at Multiple Length Scales

The presence of spontaneous and switchable polarization is a defining property of ferroelectric materials, making them indispensable in numerous industrial and scientific applications. Ferroelectric materials contain domains of ordered electric dipoles separated by domain walls, which can undergo polarization switching under externally applied electric fields. The domain-switching dynamics is crucial for the application of ferroelectric materials in electronic and electro-optic devices. Enhancing ferroelectric properties at reduced dimensions is essential for advancements in nanoelectronic applications. For this reason, ferroelectric phenomena are studied using an atomistic point of view. Previous studies indicate that the switching primarily occurs through domain wall motion, explained by statistical physics as the behavior of a pinned elastic interface. In one of the first studies of this work, molecular dynamics simulations are performed to investigate the domain-switching process in ferroelectric, tetragonal barium titanate perfect single crystals at room temperature using the core-shell model. Simulation results highlight the significance of domain nucleations during the ferroelectric switching process. They reveal that the domain-switching speed increases non-linearly due to domain nucleations within the switching domain. The strength of the electric field required to induce nucleation of new domains is also quantified. Continuing the atomistic studies, ferroelectric properties are investigated at reduced dimensions. More specifically, in this work, the onset of out-of-plane ferroelectricity in open-circuited stress-free barium titanate ultrathin films is investigated through molecular dynamics simulations. Findings indicate that the out-of-plane ferroelectricity is suppressed in ultrathin films with a thickness of 10 or fewer unit cells, suggesting a critical thickness for the emergence of out-of-plane ferroelectricity in such films. Moreover, asymmetrical hysteresis loops in ultrathin films slightly above the critical thickness are observed, highlighting the complexity of ferroelectric behavior at reduced dimensions. Atomistic studies of certain ferroelectric behaviors involve working with significantly large system sizes, necessitating the use of supercomputers or saving the state of the simulation at checkpoints and restarting the simulation, making it tedious and time- consuming. In some cases, it is even worse because it is not possible at all due to the sheer computational costs. This is typically addressed by using multiscale methods, which attempt to reduce the overall computational complexity while allowing for reasonable accuracy. A challenge to use multiscale methods for simulating ferroelectric materials is the following. The atomic interactions in a large class of functional materials, including all dielectrics, polarizable solids, and ionic solids, involve long-range Coulomb interactions. But atomistic-to-continuum multiscale methods, such as the QC method, currently employ summation rules that limit its applicability to short-ranged atomic interactions. This presents the difficulty of using the QC method to study the ferroelectric materials. To overcome this issue, in this work, the suitability of a cutoff-based method is evaluated to coarse-grain the Coulomb interactions within atomistic-to-continuum multiscale methods. Findings indicate that the cutoff-based method can be applied if the atomistic system has charge ordering; otherwise, the error in the accumulation of Coulomb interactions could be significant. Another challenge in using the QC method to dielectric crystals is that the kinematic response of different atoms to interactions within the crystals (as well as interactions with an external electric field) should be accounted accurately. With this in mind, the present work proposes an extension to the QC method for modeling and simulating ionic crystals on multiple length scales, enabling a seamless transition from atomistic to continuum descriptions. This approach includes a new method for imposing kinematic constraints on all basis atoms of a unit cell and uses a cutoff-based method for coarse-graining Coulomb interactions in ionic crystals. The proposed method is employed to simulate the surface effects of a ferroelectric nanocube and a nanopillar, modeling the region near surfaces with atomistic resolution and the interior with coarse-grained resolution. The implementation is also equipped with automatic mesh refinement ability using the gradient of electric polarization as an indicator. Results show the electric polarization structure in both the nanocube and nanopillar for the first time in a QC setting.