Slater model applied to polarization graded ferroelectrics

Ferroelectric thin films of ${\mathrm{Ba}}_x{\mathrm{Sr}}_{\text{1−x}}{\mathrm{TiO}}_3$ with compositional gradients normal to the growth surface have been formed by the successive deposition and annealing of films having step-variable Ba to Sr ratios. By suitably tailoring the magnitude and sense of the gradient in Ba to Sr ratio, directional potentials can be built into the structures yielding a new, but controllable, hysteresis phenomenon. Slater’s empirical model for ferroelectric materials has been extended to also describe thin films with polarization gradients normal to the growth surface, i.e., graded ferroelectric devices. This model accounts for several aspects of these structures, including: the broadness of the permittivity plots with temperature, the formation of a spontaneous potential upon oscillatory field excitation, offsets in the hysteresis graphs along the displacement axis with directions which are gradient dependent, and the electric field dependence of that offset.