Comment on “The multilayer-modified Stoney’s formula for laminated polymer composites on a silicon substrate” [J. Appl. Phys. 86, 5474 (1999)]

There is a vast amount of literature dealing with the strains, the stresses, and the curvature induced by thermal cycling of multilayered laminates, but much of the published work fails to provide proper derivations of the applicable formulas. For example, Kim et al. recently proposed [J. Appl. Phys. 86, 5474 (1999)] a formula — the multilayer-modified Stoney’s formula — for estimating the bow of structures consisting of thin films mounted on a thick substrate, which they validate on the basis of experimental data. In this communication, it is shown that the formula can be derived from available closed-form solutions for the curvature of elastically isotropic multilayer laminates and has no conceptual connection with Stoney’s formula.