The effects of film thickness variations on the residual stress distributions in coated Cr thin films

Generally, the residual stress of thin film coatings is calculated using Stoney's equation. However, variables in the manufacturing of the coated film, such as crystalline particle size and the unevenness of the thickness of the film, cause the radius of curvature of the beam to vary all over the beam. The cantilever beam curves not only in the axial direction but also in the transverse direction. Therefore, the residual stress in a film coating comprises not only axial residual stress but also transverse residual stress, and its distribution is also not uniform. Under such conditions, Stoney's equation must be modified. In this study, Si was used as a substrate in the production of cantilever beam specimens. Chromium thin films of various thicknesses were coated onto the Si substrates. The 3D digital image correlation technique was used to measure the out-of-plane displacement of the specimens at various positions. Then the modified Stoney's equation was used to obtain the axial and transverse residual stress at each measurement point to study the effect of variations in the thickness of the thin film on the magnitude and uniformity of the distribution of the residual stresses. Three thin film thicknesses 1, 2, and 3 μm were studied, and three specimens for each thickness were used. For each specimen, axial and transverse residual stresses were obtained at nine test points, and the equivalent residual stress was calculated. The results of this study reveal that as the difference between the thicknesses of the coating increased, average equivalent residual stress decreased and the distribution of stresses became more uniform. By comparing the corresponding results for the 1- and 3-μm-thick films revealed that the confidence levels in the average value and uniformity of the equivalent residual stress distribution, which increased with thickness, were 92.81% and 80.57%, respectively.