Electrical domain morphologies in compositionally graded ferroelectric films.

We present a nonlinear thermodynamic formalism coupled with an electrostatic analysis of uniaxial n-layered compositionally graded heteroepitaxial ferroelectric films and extend this formalism to continuously graded ferroelectric films. We show that the domain morphology and its subsequent evolution in the presence of an electric field are determined by the spontaneous polarisation of the film induced through the compositional grading. The results for compositionally graded epitaxial (001) (Ba,Sr)TiO(3) and (001) Pb(Zr,Ti)O(3) films on (001)SrTiO(3) demonstrate that, while the domain morphologies in these two films are different in appearance, the dielectric displacement and the dielectric permittivity of such graded ferroelectric films exhibit a strong nonlinear behaviour which results in a high dielectric tunability. These findings indicate that it is possible to design specific domain structures that will yield desirable dielectric properties by controlling the strength of the compositional grading in the films.