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 ( 11 (2) over bar0) sapphire substrates by sol - gel processing.