Elastic and elastic-plastic analysis of multilayer thin films filled with heterogeneous materials

Due to the mismatch between the coefficients of thermal expansion (CTE) of two adjacent films, the residual stress was growing up during thermal cycling. The aim of this work is to extend the Stoney equation for the multilayer thin films with heterostructure (voids filled with gas or other solids) or unsmooth interface. The general theoretical models were built for elastic and elastic-plastic deformation in the multilayer films with void region filled with other solid or gas. The proposed closed solution (CS) was simplified for analyzing the micro/nano devices with the micromachined multilayered multilayer films structure that thin films locate on a much thicker substrate. One model of through silicon via (TSV) has been built and analyzed. Based on the finite element method (FEM) and the initial CS, a modified CS is built up. The influence of the location and thickness of void, CTE and Young’s modulus (YM) on the normal stress of the thin films was analyzed by the simplified CS and FEM. Based on the FEM and CS the linear and coupled relationship has been set up. With the FEM analysis, the equivalent CTE and YM influenced by the void can be described by equation. The difference of critical temperature for the film from elastic deformation to plastic deformation was studied.