08-19 finite element modeling ferroelectric nanoparticles

[Image above] (a) Side view and (b) vertical cross-section of a parallelepiped-shape nanoparticle consisting of a uniaxial ferroelectric core sandwiched between two dielectric layers. The direction of the uniaxial polarization is shown by the blue arrow. Credit: Morozovska et al., Acta Materialia (CC BY-NC-ND 4.0)

While much discussion concerning pandemic-induced electronic shortages has focused on the semiconductor supply chain, semiconductors are not the only electronic component facing shortages in recent years.

Multilayer ceramic capacitors (MLCCs) have experienced recurring shortages since 2017, with concerns swelling once again in mid-2021 due to COVID-19-related supply chain issues.

MLCCs are the largest industrial use of a material type known as ferroelectric. Ferroelectric materials exhibit spontaneous electric polarization that can be reversed through application of an external electric field. Since the first reported observation of ferroelectricity more than 100 years ago, ferroelectric materials now are ubiquitous in our electrical and electromechanical components and systems.

While much is known about the bulk behavior of ferroelectric materials, much less is known about their surface behavior despite there being a known irregular phenomenon that occurs in this area.

“Indeed, since the early days of ferroelectricity, it has been recognized that the discontinuities of polarization at surfaces and interfaces [of ferroelectric materials] create a bound charge as a consequence of fundamental Maxwell electrostatics,” researchers write in a 2018 review article.

They explain that this bound charge gives rise to a depolarization field opposite to the polarization direction. To reduce the energy of the depolarization field and stabilize the ferroelectric phase, charge-compensating processes need to be implemented, such as creating 180° domain structures with antiparallel polarization stripes or surface-compensating free charges that counteract the polarization bound charges.

When determining the behavior of ferroelectric materials, these screening charges traditionally are excluded from consideration and analysis because they are assumed to be (a) always present and (b) irrelevant to the material’s macroscopic physics.

“This assumption is well justified for bulk ferroelectrics close to equilibrium, where the role of surface effects can be expected to be minor. This postulate, however, is no longer true on the nanoscale, when the free energies of surface ionic and electronic screening become comparable to the bulk free energy of the ferroelectric,” the researchers write.

Scientists have observed a range of highly unusual phenomena in nanoscale ferroelectric systems since the 1990s, such as hot electron and X-ray emission and fusion. However, it is only with the advancement of nanoscale probing techniques that scientists began describing the role of surface-charge dynamics in these phenomena.

Knowledge of these surface-charge-driven mechanisms is essential as researchers push development of new and emerging applications for nanoscale ferroelectrics, for example, nonvolatile ferroelectric random access memory and ferroelectric field-effect transistors.

In a recent open-access paper, researchers from the United States and Ukraine used finite element modeling to fill the gap in knowledge concerning the behavior of ferroelectric nanoparticles dispersed within highly polarized nonlinear media.

The dispersion of ferroelectric nanoparticles within highly polarized nonlinear media, such as liquid crystals, is viewed as a promising way to design advanced and tunable electro-optical devices and nonlinear optical elements. While there are many examples of these systems being realized experimentally, more theoretical studies are needed to help explain the experimental observations.

To set up their finite element model, the researchers used constitutive equations for relevant order parameter fields based on the Landau-Ginzburg-Devonshire phenomenological approach, along with electrostatic equations and elasticity theory.

For geometry, they considered a parallelepiped-shaped nanoparticle consisting of a uniaxial ferroelectric core sandwiched between two dielectric layers of either same or different physical natures (e.g., gaseous, soft matter, liquid).

The model revealed that polarization and susceptibility in these systems is very sensitive to the concentrations, formation energies, and relaxation times of the screening charges. As a result, the researchers could continuously switch the state of the ferroelectric core between paraelectric-like, ferroionic, antiferroionic, mixed antiferroionic–ferroionic, and ferroelectric-like ferroionic states by modifying the above properties.

“Obtained results are not only promising for advanced applications of ferroelectric nanoparticles in nanoelectronics and optoelectronics, they also offer strategies for experimental verification,” they conclude.

The open-access paper, published in Acta Materialia, is “Dynamic control of ferroionic states in ferroelectric nanoparticles” (DOI: 10.1016/j.actamat.2022.118138).