Thickness transitions of ferroelectricity in thin films: II

The exact expressions for defining the critical point of ferroelectric thin films as a function of temperature, film thickness and some other parameters are obtained on the basis of the Tilley-Zeks model. The cases of symmetric and asymmetric extrapolation lengths at the two surfaces of films are investigated. The transition temperature of a ferroelectric thin film will increase or decrease, compared with that of the bulk, according to the sign of two extrapolation lengths. But in the mixed-sign case, it is governed by the relative effectiveness, i.e., by the absolute values of the two.