On the capacitance versus voltage response and tunability of ferroelectrics: A microscopic model

Abstract

The dielectric permittivity is one of the most important properties of ferroelectrics and is strongly dependent upon the measuring conditions (electric field strength and frequency, external stress, among others). The electric field dependence of the dielectric permittivity is modeled considering ferroelectrics in which domain walls act as a stretched membrane under a homogeneous external electric field E(t)=E0+E1 sin ωt. Considering that the applied field is uniaxial and that the deformed membrane remains plane, it is possible to formulate the membrane vibration problem as a linear boundary value problem, which can be solved analytically. Real and imaginary dependence of the permittivity as a function of the frequency are derived from the analytic solution. By choosing an appropriate relationship between the membrane tension and the applied field, it is possible to describe the observed nonlinear hysteretic dependence of the permittivity under a bias electric field (CV response or tunability). The model was tested via fitting of experimental data from PbZr0.2Ti0.8O3 and PbZr0.53Ti0.43O3 ferroelectrics thin films, with excellent correspondence between model predictions and experimental results. Saturation polarization, coercive field, and remanent polarization, calculated from the CV curve quantitatively agree with the values found from the experimental hysteresis loop. Details about the hysteresis loop reconstruction and membrane characteristic relaxation frequency estimation obtained from CV curve are discussed.