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 E0 and frequency f of an applied ac electric field. We demonstrate our model on a bulk PbZrxTi1−xO3 (PZT) reference sample and then investigate capacitor stacks, containing ferroelectric 0.5(Ba0.7Ca0.3)TiO3–0.5Ba(Zr0.2Ti0.8)O3 (BCZT) thin films, epitaxially grown by pulsed laser deposition on Nb-doped SrTiO3 single crystal substrates and covered with Au electrodes. Impedance spectra from f=10 Hz to 1 MHz were collected at different E0. Deconvolution of the spectra is achieved by fitting the measured impedance with an equivalent-circuit model of the capacitor stacks, and we extract for E0=2.5 kV/cm, a frequency-dependent permittivity of εr′(f)=458+7.3ln⁡(1Hz/2πf) 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.