Domain Patterns in (111) Oriented Tetragonal Ferroelectric Films

Abstract

The possible domain patterns are developed for (111) oriented epitaxial tetragonal ferroelectric (FT) films. The domain patterns in the film form as the result of phase transition from the paraelectric to ferroelectric state to minimize the elastic energy of the system at the expense of creating of domain boundaries and developing non-uniform elastic fields near the film/substrate interface. Six possible domain variants may form, half of which are related by the inversion of the polarization vector. The possible domain walls arising between pairs of variants can be derived from the conditions of the mechanical and charge compatibility. These walls are {101} boundaries (pseudocubic indexing) and can either be inclined or normal to film/substrate interface. The domain patterns with inclined boundaries have a flat free film surface and possess non-zero net polarization in the direction normal to the film surface, i.e., they correspond to the poled film state. The domain patterns with normal boundaries lead to ‘puckering’ of the film surface, simultaneously they are related to the unpoled state of ferroelectric films. The coherency defect technique is developed for domain pattern energetics for (111) oriented FT films. The coherency defects include (i) a cross-grid of edge dislocations with unbalanced densities (which lead to in-plane biaxial strain field), (ii) Somigliana screw dislocations (which produce alternating sense of shear in neighboring domains), and (iii) wedge disclinations (which are related to out-of-plane rotations in neighboring domains). Analytical calculations of the pattern energy are performed for single embedded domain and multidomain patterns. These calculations are based on the use of screened configurations for representative coherency elements: disclination and Somigliana screw dislocation dipoles and quadrupoles. It is predicted that there is no critical thickness for domain pattern formation in (111) oriented epitaxial tetragonal ferroelectric films. Tiling of different domain patterns in complex mesoscopic structures is also discussed and supported by experimental observations.