Enhancing accuracy to Stoney equation

This paper proposes a three-dimensional system for modelling stress in thin films deposited on plane substrates much thicker than the film itself. The approach is the minimization of the deformation energy of the sample (substrate + film), considering the deformed substrate as a small spherical surface with large curvature radius. Results of the model show the validity limits of the well-established Stoney equation that satisfy the upper theoretical limit of Poisson ratio (ν) for isotropic materials. Our main result is that the stress values obtained in general literature using Stoney equation are underestimated when considering a typical Poisson ratio for substrates in the range of 0.25 ≤ νs ≤ 0.4.