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

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.