Normal and Interfacial Stresses in Thin-Film coated Optics: The Case of Diamond-Coated Zinc Sulfide Windows

摘要

Optical components such as mirrors or windows consisting of a substrate and a coating made up of thin films created at elevated temperatures exhibit substantial residual stresses induced by growth strains as well as thermoelastic strains that develop during the cool-down phase. A comprehensive description of these streses must include not only the only the normal stresses in the film layers and the substrate but also the nterfacial shearing stresses, which may cause delamination to occur. The primary purpose of this paper is to take advantage of recent progress in describing elastic interactions in multialyered laminates for obtaining conceptually correct formulas for the residual stresses and the substrate's curvature of thin-film coated optics. Available analytical solutions for the normal stresses of elastically isotropic structures make no assumptions regarding layer thicknesses but disregard the ptential impact of edge effects. For circular structures such as caoted optics, we show that recent work by Suhir (J. Appl. Phys. 88, 2363 (2000)) now allows us to describe the distribution of both normal and interfacial stresses, on assuming that the "thin-film" conditions are satified. The task of evaluating the deflection turns out to be fairly straitforward and leads to the conclusion that edge effects do not alter the bow of large and/or compliant structurs. The case of diamond-coated ZnS windows illustrates how thermal expansion mismatches can give rise to compressive film stresses of gigapascal intensity, which cause substrate deformations that are unacceptable in terms of the optical performance. Since the deflection of a multialyer-coated substrate reflects the sum of the contributions (positive or negative) induced by each film, the deflection can be minimized by properly designing the film stack. For a diamond-coated ZnS window, this means that a suitable buffer must be in tension; in principle, a buffer made of calcium lanthanum sulfide, about 300 mum thick, can mitigate the bending force exerted by a 50-mum thick diamond film and suppress the shear at the substrate/coating interface, thus enhancing the adhesion.