Thickness and grain-size dependence of ferroelectric properties in columnar-grained BaTiO₃ thin films

In this work, we investigated the association between the microstructural characteristics and the size-dependent properties in columnar-grained BaTiO₃ thin films. Based on the phase-field method, we devised a two-dimensional thin-film model with vertically aligned columnar grains and low-permittivity grain boundaries in between. The size dependence is referring to two aspects: the grain-size dependence and the film-thickness dependence. The calculations for the grain-size dependence (200 down to 20 nm) with a constant thickness of 160 nm showed that the reduction of the grain size results in a continuous decrease in the coercive field, remnant polarization, dielectric constant, and piezoelectric constant. With a constant grain size of 60 nm, the reduction of the film thickness (380 down to 80 nm) leads to decreasing coercive field, remnant polarization, piezoelectric constant, and actuation strain as well as an increasing dielectric constant. We found that the presence of the low-permittivity grain boundaries plays a crucial role in the observed size dependence. The dilution effect due to its low permittivity is the leading cause for the grain-size dependence, whereas the underlying domain-switching dynamics affected by the grain boundaries takes the lead for the film-thickness dependence. The relation between the grain-boundary influence and the observed size dependence of ferroelectric properties was discussed.