Large built-in electric fields due to flexoelectricity in compositionally graded ferroelectric thin films

We investigate the origin of large built-in electric fields that have been reported in compositionally graded ferroelectric thin films using PbZr₁-ₗTiₗO₃ (0. 2<x<0. 8) as a model system. We show that the built-in electric fields that cause a voltage offset in the hysteresis loops are dependent on strain relaxation (through misfit dislocation formation) and the accompanying polarization distribution within the material. Using a Ginzburg-Landau-Devonshire phenomenological formalism that includes the effects of compositional gradients, mechanical strain relaxation, and flexoelectricity, we demonstrate that the flexoelectric coupling between the out-of-plane polarization and the gradient of the epitaxial strain throughout the thickness of the film, not other inhomogeneities (i. e. , composition or polarization), is directly responsible for the observed voltage offsets. This work demonstrates the importance of flexoelectricity in influencing the properties of ferroelectric thin films and provides a powerful mechanism to control their properties.