Physical Approach to Ferroelectric Impedance Spectroscopy: The Rayleigh Element

The Rayleigh law describes the linear dependence of the permittivity of a ferroelectric on the applied ac electric field amplitude due to irreversible motions of domain walls. We show that this gives rise to a new equivalent-circuit element predestined to fit the impedance spectra of ferroelectrics based on an accepted physical model. Such impedance spectroscopy is a powerful tool to obtain a dielectric and resistive representation of the entire sample structure. The superiority of the Rayleigh analysis based on impedance spectroscopy compared to the common single-frequency approach is demonstrated for a ferroelectric Si : HfO2 thin film.