Mechanical elastic and inelastic properties of thin coatings are often studied by means of the curvature measurement technique in combination with the Stoney formula. It is then implicitly assumed that the elastic substrate is initially flat which implies that the curvatures theoretically remain constant over the substrate. If the substrate has a slight initial curvature, a different situation arises. In this case, the curvatures will vary over the substrate. It has recently been shown that in spite of this, the stresses that appear in the thin coating will remain constant over the surface of the substrate. Therefore, measured curvatures can generally not be used to extract layer stresses without a proper compensation for the initial curvature. A general method for the extraction of mechanical properties from curvature measurements on non-planar substrates is outlined. The method is valid for linear as well as non-linear shell theories. The compensation needed to evaluate a coating on a circular substrate with spherical initial curvature is studied for all relevant parameters. The results are particularly discussed in relation to curvature measurements on silicon wafers.
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Wikström, A., Gudmundson, P. Stresses in Thin Coatings from Curvature Measurements on Non-Planar Substrates. MRS Online Proceedings Library 653, 1041 (2000). https://doi.org/10.1557/PROC-653-Z10.4