A Novel Technique to Determine Elastic Constants of Thin Films

AbstractA new X-ray diffraction technique to determine elastic moduli of polycrystalline thin films deposited on monocrystalline substrates is demonstrated. The technique is based on the combination of sin2ψ and X-ray diffraction wafer curvature techniques which are used to characterize X-ray elastic strains and macroscopic stress in thin film. The strain measurements must be performed for various hkl reflections. The stresses are determined from the substrate curvature applying the Stoney's equation. The stress and strain values are used to calculate hkl reflection dependent X-ray elastic moduli. The mechanical elastic moduli can be then extrapolated from X-ray elastic moduli considering film macroscopic elastic anisotropy. The derived approach shows for which reflection and corresponding value of the X-ray anisotropic factor Γ the X-ray elastic moduli are equal to their mechanical counterparts in the case of fibre textured cubic polycrystalline aggregates. The approach is independent of the crystal elastic anisotropy and depends on the fibre texture type, the texture sharpness, the amount of randomly oriented crystallites and on the supposed grain interaction model. The new method is demonstrated on a fiber textured Cu thin film deposited on monocrystalline Si(100) substrate. The advantage of the new technique remains in the fact that moduli are determined non-destructively, using a static diffraction experiment and represent volume averaged quantities.