Modeling of hysteresis curves of ferroelectric capacitor with inhomogeneous charged defect density and polarization parameters in the ferroelectric thin film

Abstract

A method for the modeling of polarization-electric field (P-E) hysteresis curves of the inhomogeneous ferroelectric thin film capacitor was developed, considering the local electric field histories. With the present modeling method, P-E hysteresis curves can be obtained from the ferroelectric film with any distributions of inhomogeneous charged defect density N(x) and local polarization parameters such as P-s(x), P-r(x), E-c(x) and epsilon(f)(x), and the separate or combined effect of the parameters on the P-E hysteresis curve can be investigated. It was found that microscopic variations of the charged defect density in the ferroelectric film induce asymmetry and voltage shift in the hysteresis curve. How much and in which direction the voltage shift occurs are determined by the concentration distribution of the charged defects and their signs. Inhomogeneity of the other local polarization parameters in the ferroelectric film has no effects on the voltage shift of the P-E hysteresis curves. However, when they combined with the inhomogeneity of the charged defect density, the voltage shift induced by the inhomogeneous charged defect is generally enhanced. The effects of the model parameters on the apparent P-s and P-r values were also investigated.