Dynamic response of the dielectric and electro-optic properties of epitaxial-ferroelectric thin films

An analysis of the dynamic dielectric and electro-optic relaxation response of thin-film ferroelectrics is presented. The analysis is based upon the relaxation of ferroelectric domains with a continuous distribution of sizes given by percolation theory. The resulting temporal response is described by the expression $\ensuremath{\Phi}(t)\ensuremath{\propto}{t}^{\ensuremath{-}m}\mathrm{exp}[\ensuremath{-}(t/\ensuremath{\tau}{)}^{\ensuremath{\beta}}].$ The analysis was applied to ${\mathrm{KNbO}}_{3}$ thin films. Measurements of the polarization, birefringence, and dielectric transients show qualitative agreement with the model over 11 orders of magnitude in time.