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 PbZr sub(1-x)Ti sub(x)O sub(3) (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.