Domain pattern formation in epitaxial rhombohedral ferroelectric films. II. Interfacial defects and energetics

Abstract

The coherency defect technique is developed for the domain pattern energetics in rhombohedral (001) epitaxial ferroelectric films. The coherency defects that are necessary to maintain the epitaxy during the ferroelectric phase transition are considered to be the only sources of elastic strains and stresses (and, correspondingly energy) in the film/substrate system. The coherency defects include: (i) a uniform distribution of edge dislocations which are responsible for the in-plane tension or compression and have Burgers vectors parallel to the interface; and two kinds of mesoscale defects: (ii) Somigliana screw dislocations which are responsible for in-plane shear; and (iii) wedge disclinations which are responsible for the out of plane rotations in neighboring domains. Using this approach, analytical expressions were found for the elastic energy in the film/substrate system for both the {101}-ri/rj and the {100}-ri/rj domain patterns. These two configurations differ by the orientation of domain walls, coherency defect content, and also the morphology of the free surface (flat versus puckered surfaces). Calculations are performed for screened mesoscale coherency defect configurations that represent a single embedded domain pattern and multidomain patterns. The following mesoscale defect configurations are used for these calculations: Somigliana dislocation dipoles, wedge disclination dipoles, Somigliana dislocation quadrupoles, and disclination quadrupoles. It is predicted that there is no critical thickness for domain pattern formation in rhombohedral ferroelectric epitaxial films. Agreement is shown between experimentally observed domain widths and theoretically predicted values.