Extensions of the Stoney formula for substrate curvature to configurations with thin substrates or large deformations

Abstract

Two main assumptions which underlie the Stoney formula relating substrate curvature to mismatch strain in a bonded thin film are that the film is very thin compared to the substrate, and the deformations are infinitesimally small. Expressions for the curvature–strain relationship are derived for cases in which these assumptions are relaxed, thereby providing a basis for interpretation of experimental observations for a broader class of film–substrate configurations.