Determination of depth gradients of grain interaction and stress in Cu thin films

Grain‐interaction and residual stress depth gradients in a sputter‐deposited Cu thin film (thickness 4 µm) were determined by employing X‐ray diffraction stress measurements at constant information depths in the range between 200 and about 1500 nm. A novel procedure, which allows the determination of an effective grain‐interaction parameter on the basis of the f (ψ, hkl ) method and the Voigt and Reuss models of elastic grain interaction, was used. The range of accessible penetration depths was maximized by employing different photon energies using a laboratory diffractometer with Cu  K α radiation and a diffractometer at a synchrotron beamline. The variation of grain interaction with depth could be successfully related to the microstructure of the specimen. The tensile residual stress in the film parallel to its surface decreases with decreasing depth. By measuring the lattice spacing for several reflections at one penetration depth with two different photon energies ( i.e. using small and large incident beam angles) it was found that the surface roughness of the specimen counteracts the effect of beam refraction to some degree. As a consequence, irrespective of whether a refraction correction is applied or neglected for the low‐incidence angle measurement, erroneous results are obtained for lattice spacings derived from reflections at small incidence angles; reliable grain‐interaction and stress analysis requires measurements at high incidence angle.