Anisotropic strain relaxation in (Ba0.6Sr0.4)TiO3 epitaxial thin films

We have studied the evolution of anisotropic epitaxial strains in ⟨110⟩-oriented (Ba0.60Sr0.40)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)=3∕4∣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)=3∕4∣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 ∼2.9×106J∕m3 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 ∼6×105cm−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.