Film thickness versus misfit strain phase diagrams for epitaxial PbTiO3 ultrathin ferroelectric films

PHYSICAL REVIEW B 78, 064117 2008
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 1 June 2008; revised manuscript received 14 July 2008; published 27 August 2008
We present a full scale nonlinear thermodynamic model based on a Landau-Ginzburg-Devonshire formalism and the theory of dense polydomain structures in a multiparameter space to predict the phase stability of 001 oriented PbTiO3 epitaxial thin films as a function of film thickness and epitaxial strain. The developed methodology, which accounts for electrostatic boundary conditions as well as the formation of misfit dislocations and polydomain structures, produces a thickness-strain phase stability diagram where it finds that the rotational phases the so-called r and ac phases in epitaxial PbTiO3 are possible only in a very small window. We find that for experimentally used thickness or strains or both that often fall outside this window, the film is in either single phase tetragonal c phase or in a c/a/c/a polydomain state; this explains why rotational polar domains are rarely observed in epitaxial ferroelectric thin films.
DOI: 10.1103/PhysRevB.78.064117
PACS number s : 77.80.Bh, 77.84.Dy