Governing equation for the measurement of nonuniform stress distributions in thin films using a substrate deformation technique

Abstract

Determination of stress in thin films deposited on substrates is a basic and essential requirement in micronanotechnology. Most often local measurements of the induced substrate curvature are related to local stress using the Stoney equation. However, it is well known that this method gives incorrect results if the stress distribution is nonuniform. Here a general governing equation for the evaluation of nonuniform stress distributions in thin films is derived, which has the new feature of being able to treat the cases of anisotropic stress and also the effect on substrate deformation of a large in-plane thin film tension.