Explicit expressions for the dynamic polarization behavior in ferroelectrics with symmetric/asymmetric electrical conductivity

Abstract

We model the dynamic polarization behavior of ferroelectric films by an analytical approach. Using a parallelogramlike P-E hysteresis model, explicit expressions were obtained for describing the D-E loops of ferroelectric films as would be measured from a Sawyer-Tower circuit. By introducing the consideration of electrical conduction, resistive losses inflate the ferroelectric loop to some extent. In addition, an asymmetric conduction will result in polarization offsets with the magnitude and direction depending on the asymmetric conductivities of the materials. The inflated loop, as well as the offset phenomena, which have been observed experimentally [e.g., L. Zheng, C. Lin, W.-P. Xu, and M. Okuyama, J. Appl. Phys. 79, 8634 (1996)], will be discussed by means of our modeled results. Some simple exact formulas have been derived and the effects of electric, dielectric, and ferroelectric parameters, as well as the applied field on the “apparent” polarization were also examined.