Stoney Formula: Investigation of Curvature Measurements by Optical Profilometer

Abstract

Thin films’ residual stress is often determined by the Stoney formula, using the measurements of the substrate curvature, even if the required hypotheses are not completely respected. In this study, a 2.2 µm titanium nitride coating was deposited by reactive sputtering on a silicon substrate. The Stoney formula was used in order to calculate the residual stress of the film. The radius of curvature was measured, before and after coating by optical profilometer, considering the whole surface of the sample. The effect of the substrate shape (square and rectangular) with various dimensions was investigated. We showed that the shape of the substrate influence strongly the deformation. Moreover, it was highlighted that the choice of the radius (maximum value, minimum value, mean value, with or without initial curvature correction) is critical to the determination of the stress.