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. No a priori assumption 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 (110) sapphire substrates by sol-gel processing.