Effect of substrate orientation on lattice relaxation of epitaxial $BiFeO3$ thin films

We have investigated detailed structural properties of epitaxial $BiFeO3$ thin films grown on (001), (110), and (111) $SrTiO3$ substrates in thicknesses up to $1μm$⁠. X-ray reciprocal space mappings reveal that the fabricated films have crystal structures and the strain relaxation dictated by the substrate orientation. The rhombohedral structure, which is observed in the bulk form, is maintained only when the film is grown on the (111)-oriented substrate. The films grown on the (001) and (110)-oriented substrates have a lower structural symmetry than the rhombohedral one, namely a monoclinic structure. Two different processes are observed for the relaxation of the epitaxial strain from the substrate: they are (1) changes in lattice constants and (2) changes in the distortion angle in the $BiFeO3$ lattice. In the presence of a biaxial strain along the {100} axis, the relaxation in the distortion angle is inhibited, causing a gradual change in the lattice constants. As the number of the {100} axes on the substrate surface is decreased, the distortion angle relaxation becomes the dominant process, making the lattice parameters fully relaxed. We also find that the tilting of the crystallographic domain structures takes place concomitant with the angle relaxation process. These results indicate the strong influence of the substrate orientation on the structural properties of epitaxially-grown $BiFeO3$ thin films.