Misfit strain–film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films

Acta Materialia 58 (2010) 823–835
Q.Y. Qiu , R. Mahjoub, V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
S.P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
Received 19 March 2009; received in revised form 7 August 2009; accepted 29 September 2009
Available online 24 October 2009
Abstract
The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization
field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities e11 and e33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.
2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Ferroelectricity; Thin films; Phase transformations; Electroceramics; Dielectrics