Hysteresis offset and dielectric response of compositionally graded ferroelectric materials

Ferroelectrics with a spatial variation in the polarization exhibit behavior and properties that are not routinely observed from homogenous bulk or thin film ferroelectrics. A systematic spatial variation in the polarization in a ferroelectric material can be achieved by variations in the composition of the material, impressing temperature gradients across the structure, or by imposing non-uniform external stress fields. In this article, a Landau-Ginzburg thermodynamic model is used to develop a methodology for analyzing compositionally graded ferroelectric materials. The composition gradient is shown to give rise to a corresponding polarization gradient. The misfit due to variations in the self-strain tends to flatten the polarization gradient and leads to the bending of the ferroelectric. The polarization gradients result in asymmetric hysteresis responses with "up" or "down" charge offsets which are strong functions of composition. Analysis shows that the compositional grading results in a broadening in the dielectric response as a function of temperature.