Epitaxial films, crystal symmetry

The limited number of high quality substrates suitable for oxide epitaxy, together with the wide range of structural properties exhibited by oxides, may require the use of a substrate with a different crystal symmetry than the film material. If the crystal symmetries are sufficiently different, antiphase boundaries (ABPs) may result during nucleation of the initial monolayers. Such APBs tend to be very stable and thus typically become permanently ingrained in the film structure. The question we address here is the effect that APBs in the bulk of the film have on the surface structure. 

Epitaxy is a kind of interface between a thin film and a substrate. Epitaxial growth refers to the formatiOTi of crystals of one material on the crystal face of another or the same material. The lattice structure and orientation or lattice symmetry of the thin-film material is identical to that of the substrate on which it is deposited. 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

---