Exact Expressions for Some Dielectric Properties of Ferroelectric Thin Films Based on the Tilley–Zeks Model

Abstract

The extrapolation length adopted in the Tilley–Zeks model of ferroelectric thin films plays a substantial role in governing the dielectric properties of thin films through the boundary conditions. The boundary conditions under an applied field are reexamined. The exact formulas for the transition temperature, the dielectric susceptibility, and the Curie constant are obtained for the Tilley–Zeks model of ferroelectric thin films, where various combinations of the extrapolation length are taken into account. The polarization profiles obtained under the applied field may be considered to approximately represent the soft mode.