A new method for the determination of strain profiles in epitaxic thin films using X-ray diffraction

A new and versatile method is proposed for the determination of strain profiles in epitaxic thin films. It is based on the simulation of the X-ray diffraction (XRD) profiles using cubic B-spline functions to model the vertical lattice displacement profile. The lattice displacement profile, and consequently the strain profile, directly results from a least-square fit of the model to the experimental XRD profiles. Noa prioriassumption is made regarding the shape of the strain profile. Moreover, as spline functions are used, the recovered lattice displacement profile is smooth and exhibits a minimum curvature, thus avoiding oscillating or saw-toothed unphysical solutions. The potential of this method is illustrated with (100) yttria-stabilized zirconia epitaxic thin films deposited onto (11\bar{2}0) sapphire substrates by sol–gel processing.