Strain depth profiles in thin films extracted from in-plane X-ray diffraction

Abstract

Thin films generally contain depth-dependent residual stress gradients, which influence their functional properties and stability in harsh environments. An understanding of these stress gradients and their influence is crucial for many applications. Standard methods for thin-film stress determination only provide average strain values, thus disregarding possible variation in strain/stress across the film thickness. This work introduces a new method to derive depth-dependent strain profiles in thin films with thicknesses in the submicrometre range by laboratory-based in-plane grazing X-ray diffraction, as applied to magnetron-sputtering-grown polycrystalline Cu thin films with different thicknesses. By performing in-plane grazing diffraction analysis at different incidence angles, the in-plane lattice constant depth profile of the thin film can be resolved through a dedicated robust data processing procedure. Owing to the underlying intrinsic difficulties related to the inverse Laplace transform of discrete experimental data sets, four complementary procedures are presented to reliably extract the strain depth profile of the films from the diffraction data. Surprisingly, the strain depth profile is not monotonic and possesses a complex shape: highly compressive close to the substrate interface, more tensile within the film and relaxed close to the film surface. The same strain profile is obtained by the four different data evaluation methods, confirming the validity of the derived depth-dependent strain profiles as a function of the film thickness. Comparison of the obtained results with the average in-plane stresses independently derived by the standard stress analysis method in the out-of-plane diffraction geometry validates the solidity of the proposed method.