Theoretical investigation of polarization scaling in ultrathin epitaxial PbZrxTi1−xO3 films

JOURNAL OF APPLIED PHYSICS 102, 104113 2007
Q. Y. Qiu and V. Nagarajana
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
Received 21 August 2007; accepted 27 September 2007; published online 29 November 2007

We present a theoretical analysis of the scaling of the polarization and the static dielectric susceptibility through a mean-polarization approach for ultrathin epitaxial PbZrxTi1−xO3 thin films. We use the traditional Euler-Lagrangian framework applied to a Landau-Ginzburg-Devonshire LGD nonlinear thermodynamic treatment. The novelty of our approach is that the model hinges on using experimentally measured correlation lengths and temperature scaling relationships to give the size-dependent expansion parameters of the nonlinear thermodynamic potential. These are then used in a Taylor series expansion of the polarization at the center of the film. We show that this method is able to correctly predict experimentally observed scaling without the need for the so-called extrapolation length which is impossible to measure experimentally . Furthermore, as no implicit correlation between the correlation length and the coefficient of the gradient term in the LGD potential g11 is assumed, the model thus involves fully experimentally measurable parameters and their systematic temperature dependence rather than implicit assumptions. The model finds that the Curie temperature in ultrathin films is more sensitive to epitaxial strain as compared to the polarization and that the critical thickness is strongly dependent on the “temperature-epitaxial strain” parameter space. Interestingly, while it finds that at lower temperatures the depolarization field does play a strong role in the thickness dependence as well as spatial profile of the polarization, with increasing temperature, a significant weakening of the role of depolarization fields occurs. Consequently the interface-induced suppression is lower and, as a result, the polarization profile is more homogenous at higher temperatures. This indicates that systematic temperature dependent studies are fundamental to further understanding of size effects i ferroelectrics.
© 2007 American Institute of Physics. DOI: 10.1063/1.2809334