A study of flexoelectric coupling associated internal electric field and stress in thin film ferroelectrics

Abstract

By discussions in the framework of tensor representations and phenomenological theory, general piezoelectricity equations that incorporate direct and inverse flexoelectric effects were analyzed and interlink between direct and inverse flexoelectricity discovered. Due to flexoelectric coupling, mechanical strain gradient is equivalent to internal electric field. In ferroelectrics above the Curie temperature, it was shown theoretically that strain gradient associated electric field leads to nonzero polarization without external electric field. It was also shown theoretically that polarization (or electric field) gradient is an extra source of internal stress. Magnitudes of flexoelectricity associated internal electric field and stress were analyzed for heteroepitaxial thin films of barium strontium titanate. Flexoelectric coupling is expected to intensify with reducing lateral dimensions and thickness and get large enough at nanoscale to modify ferroelectric phase transitions and functional response. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.