Depth dependence of residual strains in polycrystalline Mo thin films using high-resolution x-ray diffraction

The magnitude of the stress in a thin film can be obtained by measuring the curvature of the film–substrate couple. Crystal curvature techniques yield the average stress throughout the film thickness. On a microscopic level, the details of the strain distribution, as a function of depth through the thickness of the film, can have important consequences in governing film quality and ultimate morphology. A new method, using high-resolution x-ray diffraction to determine the depth dependence of strain in polycrystalline thin films, is described. The technique requires an analysis of the diffraction peak shifts of at least six independent {hkl} scattering vectors, at a variety of penetration depths from the free surface of the film. The data are then used to determine the magnitude and directions of the strain eigenvalues in a laboratory reference frame for each penetration depth from the free surface of the film. A linear elastic model was used to determine the strains in successive slabs of the film. Results are reported for two Mo films, with nominal thicknesses of 50 and 100 nm, which were deposited by planar magnetron sputtering onto Si (100) substrates. This technique can provide quantitative insight into the depth variation of residual strains (stresses) in thin films and should work with a wide variety of materials.