Theory of the size effect of the properties of the relaxor ferroelectric films

TL;DR

This paper develops a statistical model for relaxor ferroelectric film properties considering misfit strain and surface effects, revealing how film thickness influences phase transition smearing, critical thickness, and dielectric behavior.

Contribution

It introduces the first model based on random field theory that accounts for misfit strain and surface piezoelectric effects in relaxor ferroelectric films.

Findings

Mean field decreases with film thickness

Smearing of phase transition increases as film gets thinner

Susceptibility maximum shifts with frequency following Vogel-Fulcher law

Abstract

For the first time we proposed the model for the calculations of the relaxor ferroelectrics films properties in the framework of the random field theory. We took into account the misfit strain between film and substrate as well as surface piezoelectric effect that causes built-in electric field in the strained films. In the statistical theory framework we calculated random field distribution function with the electric dipoles and monopoles as the field sources. It was shown that with thickness decrease the mean field decreases, while the width of the distribution function increases. This leads to the additional smearing of the phase transition in the films in comparison to the bulk relaxors. As an example the dependence of the order parameter and dielectric susceptibility on the film thickness, temperature and random fields distribution function parameters was obtained. For free standing film the existence of critical thickness of relaxor state transformation into glassy state was predicted. Contrary to this the appearance of misfit strain induced ferroelectric phase appeared to be possible for some pairs film-substrate. We have shown that susceptibility temperature maximum shift with frequency in relaxor ferroelectric thin films obeys Vogel-Fulcher law with parameters dependent on film thickness. For the first time the analytical dependences of freezing temperature decreases and activation energy on the thickness was obtained, namely freezing temperature decreases and activation energy increases with film thickness decrease. Obtained results quantitatively agree with the available experimental data for PbMg1/3Nb2/3O3 relaxor thin films.