On the mechanics of a double thin film on a finite thickness substrate

Abstract

The single edge loading problem of a double thin film deposited on a finite thickness substrate is considered. The films and the substrate are assumed to be homogeneous and isotropic. The membrane analogy is adopted for the films and two dimensional elasticity is applied to the substrate. The compatibility of the tangential strain between the film and the substrate yields the governing singular integral equation in terms of the interfacial shear stress. The numerical solution is provided using the Gauss–Chebyshev discretization method. The sensitivity of the interfacial shear and the normal stresses to several effective parameters are examined. The results of current study are compatible with the finite element simulations. The lowest interfacial shear stress pertains to a substrate with a free edge boundary condition. The results of current study are applicable to the debonding failure assessment of the multi-layer joints and semiconductors which are susceptible to the interfacial shear stresses near the film edges.