Impedance spectroscopy of ferroelectrics: The domain wall pinning element

Abstract

We introduce an equivalent-circuit element based on the theory of interface pinning in random systems to analyze the contribution of domain wall motion below the coercive field to the impedance of a ferroelectric, as a function of amplitude [Formula: see text] and frequency [Formula: see text] of an applied ac electric field. We demonstrate our model on a bulk [Formula: see text] (PZT) reference sample and then investigate capacitor stacks, containing ferroelectric [Formula: see text]–[Formula: see text] (BCZT) thin films, epitaxially grown by pulsed laser deposition on Nb-doped [Formula: see text] single crystal substrates and covered with Au electrodes. Impedance spectra from [Formula: see text] Hz to 1 MHz were collected at different [Formula: see text]. Deconvolution of the spectra is achieved by fitting the measured impedance with an equivalent-circuit model of the capacitor stacks, and we extract for [Formula: see text] kV/cm, a frequency-dependent permittivity of [Formula: see text] for the BCZT films from the obtained fit parameters. From an extended Rayleigh analysis, we obtain a coupling strength of 0.187 cm/kV between dielectric nonlinearity and dielectric dispersion in the BCZT films and identify different domain-wall-motion regimes. Finally, we construct a schematic diagram of the different domain-wall-motion regimes and discuss the corresponding domain-wall dynamics. Our approach can be utilized to replace purely phenomenological constant phase elements (CPEs) in modeling the impedance response of ferroelectrics and extracting material properties.