Misfit strain relaxation in (Ba _0.60Sr _0.40)TiO ₃ epitaxial thin films on orthorhombic NdGaO ₃ substrates

Strain relaxation in (Ba _0.60Sr _0.40)TiO ₃ (BST) thin films on (110) orthorhombic NdGaO ₃ substrates is investigated by x-ray diffractometry. Pole figure analysis indicates a [010] _BST||[1̄10] _NGO and [001] _BST||[001] _NGO in-plane and [100] _BST||[100] _NGO out-of-plane epitaxial relationship. The residual strains are relaxed at h ∼ 200 nm, and for h > 600 nm, films are essentially strain free. Two independent dislocations mechanisms operate to relieve the anisotropic misfit strains along the principal directions. The critical thickness for misfit dislocation formation along [001] and [010] are 11 and 15 nm, respectively. Stress analysis indicates deviation from linear elasticity for h < 200. The films with 10<h<25 nm are of monoclinic symmetry due to a finite principal shear stress along [110] of the initial orthorhombic cell.