Thickness and strain dependence of piezoelectric coefficient in BaTiO3 thin films

Abstract

We explore the thickness dependence of the converse piezoelectric coefficient (${d}_{33}$) in epitaxial thin films of ${\mathrm{BaTiO}}_{3}$ (BTO) grown on (001) ${\mathrm{SrTiO}}_{3}$ substrates. Piezoresponse force microscope was performed using an atomic force microscope equipped with an interferometric displacement sensor allowing direct quantification of electromechanical coupling coefficients in BTO free from unwanted background contributions. We find that 80-nm-thick films exhibit a ${d}_{33}$ of $\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}20.5\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V}$, but as the thickness is reduced, the ${d}_{33}$ reduces to less than 2 pm/V for a 10 nm film. To explain the atomistic origin of the effect, we performed molecular dynamics simulations with a recently developed ab initio-derived reactive force field, constructed using the ReaxFF framework. Simulations predict that under applied electric fields thin films of ${\mathrm{BaTiO}}_{3}$ show an increasing thickness, with compressive strain, of the region screening the depolarization-field. This study confirms quantitatively the drop in piezoelectric performance in BTO ultrathin films and again highlights the importance of the screening mechanisms when films approach the ultrathin limits in dictating the functional behaviors.