Film thickness versus misfit strain phase diagrams for epitaxialPbTiO3ultrathin ferroelectric films

Abstract

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 ${\text{PbTiO}}_{3}$ 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 ${\text{PbTiO}}_{3}$ 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.