Anisotropic strain relaxation in (Ba _0.6 Sr _0.4) TiO ₃ epitaxial thin films

We have studied the evolution of anisotropic epitaxial strains in 〈110〉-oriented (Ba0.60 Sr0.40) TiO3 paraelectric (m3m) thin films grown on orthorhombic (mm2) 〈100〉-oriented NdGaO3 by high-resolution x-ray diffractometry. All the six independent components of the three-dimensional strain tensor were measured in films with 25-1200-nm thickness, from which the principal stresses and strains were obtained. Pole figure analysis indicated that the epitaxial relations are [001]m3m∥[001] mm2 and [1- 10]m3m∥[010]mm2 in the plane of the film, and [110]m3m∥[100]mm2 along the growth direction. The dislocation system responsible for strain relief along [001] has been determined to be ∫b∫(001)=34 ∫b∫. Strain relief along the [1- 10] direction, on the other hand, has been determined to be due to a coupled mechanism given by ∫b∫ (1- 10)= ∫b∫ and ∫b∫ (1- 10)=34 ∫b∫. Critical thicknesses, as determined from nonlinear regression using the Matthews-Blakeslee equation, for misfit dislocation formation along [001] and [1- 10] direction were found to be 5 and 7 nm, respectively. The residual strain energy density was calculated as ~2.9×106 Jm3 at 25 nm, which was found to relax an order of magnitude by 200 nm. At 200 nm, the linear dislocation density along [001] and [1- 10] are ~6.5×105 and ~6×105 cm-1, respectively. For films thicker than 600 nm, additional strain relief occurred through surface undulations, indicating that this secondary strain-relief mechanism is a volume effect that sets in upon cooling from the growth temperature.