Dependence of growth stress on microstructure in periodic nanometer layered thin-film coatings

Sputtered x-ray multilayer coatings usually exhibit the presence of intrinsic stress in the structures. Stress in the coatings are undesirable in many x-ray optical applications where flat mirrors, or precise control of curved mirrors, are designed. Controlling of the stress in these multilayers requires understanding of stress and microstructural evolution in multilayers and thin films.Stress in thin films can be determined by the amount of bending or curvature of the substrate caused by the films. For a film deposited on a flat substrate, stress in the film is measured by using the laser scanning technique. The change in the curvature of the film and substrate is determined fromthe reflection profile fo the incident laser.For the usual case of a substrate that is elastically isotropic in the plane of the film, the expression of the biaxial stress in the film is given by the Stoney equation:for the case in which the thickness of the films is usually much less than that of the substrate, where E and γ are the substrate biaxial modulus and Poison ratio, ts and tare the substrate and film thicknesses, and K is the substrate curvature.