Domain pattern formation in epitaxial ferroelectric films

Abstract

In this talk we treat domain patterns that develop in epitaxial ferroelectric (FE) films. The models are applicable to ferroelectric films grown epitaxially in their paraelectric cubic state (PE) on single crystal substrates. We explicitly treat misfit strain relaxation by both misfit dislocations and by domain pattern formation. We have developed temperature dependent stability maps that predict the energetically favorable domain structure that will form at the PE → FE transition. The stability maps incorporate the role of: (i) the substrate lattice parameter; (ii) differential thermal expansion; (iii) cooling rate; (iv) depolarizing fields and electrode geometry; and (v) applied electric fields. We treat the formal defect description both the … a1/a2/a1/a2… and the …a1/c/a1/c… domain patterns and show rigorous mechanics solutions for the elastic energy of both configurations. As a result of the PE → FE transition, the crystal axes of individual domain are rotated in the far-field. The concepts of the domain stability map, the relative coherency strain, and far field rotation of crystals axes in the domain are verified by three independent measurements (integrated x-ray peak intensity, partitioning of crystals tilts, and domain volume fraction by TEM) for MOCVD PbTiO₃ films grown on MgO(001), SrTiO₃(001), LaAlO₃(001) and SrRuO₃/SrTiO₃(001).