Size effects in ultra-thin ferroelectric films: a theoretical mean field study

摘要

The question of size-effect in ultra-thin ferroelectrics and strain-engineering of ferroelectrics thin films has now become an intensely debated topic. Despite the various contradicting experimental and theoretical results, there is unanimous consent that the mechanical and electrical boundary conditions control the ultimate phase stability in epitaxial ferroelectric thin films. Distinctly, the theoretical models reported so far treat these boundary and the system's geometric conditions as almost independent parameters with no one work that lakes into account the entire possible parameters. We present a full-scale non-linear Landau-Ginzburg-Devonshire thermodynamic model that is able to account for both thickness-induced depolarization field effects as well as the real strain at the interface taking into account dislocation formation to predict the phase stability of (001) oriented PbZr1-xTix03 (PZT) epitaxial thin films for both isotropic and anisotropic cases. We compute a universal free energy function and find out the most stable phase (i.e. minimum free energy) for an epitaxial ferroelectrics film that is sandwiched between electrodes. in a multiparameter (temperature, film thickness, effective misfit strain, critical thickness for dislocation formations, real misfit strain, interface-induced polarization gradients and electrode-screening length) space. Ultimately the model is able to produce a thickness-strain phase stability diagram where it finds that the rotational phase (the so-called "r" and "ac" phase) in PZT films are possible in a much smaller window than the previous predictions. We find that for experimentally used thickness or strain (or both) that often fall outside this window, the film is in the c-or ferroelastic polydomain state. It is also shown that this self-consistent theoretical approach provides a description of dielectric and ferroelectric properties epitaxial PZT ferroelectric films.