Elastic flexure of bilayered beams subject to strain differentials

Abstract

The residual stresses present in a thin film and the curvature formed at its substrate during deposition have been a great concern to electrochemists and process engineers. Here a new hybrid analytical method is presented to reanalyze the flexural problem subjected to a strain differential in the general case. It was shown that the present solutions for ultrathin films agree with Stoney's equation. Moreover, single or dual neutral axes resulted, depending on materials and thickness ratios between the film and the substrate. Quantitative differences with others in the solutions of deformed curvature and residual stress are discussed in a representative case of GaAs top coat/Si substrate wafers.