Identification of multilayered thin-film stress from nonlinear deformation of substrate

Due to the enlargement of wafer size and the increase of product integrity, thin-film stress problems inevitably get into the range of geometric nonlinearity and are found in multilayered thin-film materials.In this work, multilayered thin-film materials are modeled as a large-deflection multilayered composite plate in the framework of geometrically nonlinear plate theory.Based on the principle of virtual work for a thin-film material plate with thin-film stresses of multiple layers as driving forces, a nonlinear plate finite element system for kinematic fields of thin-film materials, which includes in-plane displacements, cross section rotations, and out-of-plane deflection, is established.The least squares method with regularization applied for total or partial kinematic fields obtained by the finite element method solution versus those given by experiments leads to an iterative procedure for identification of the nonlinear multilayered thin-film stresses.