Full-field optical measurement of curvatures in ultra-thin-film-substrate systems in the range of geometrically nonlinear deformations

This article describes coherent gradient sensing (CGS) as an optical, full- field, real-time, nonintrusive, and noncontact technique for the measuremen t of curvatures and nonuniform curvature changes in film-substrate systems. The technique is applied to the study of curvature fields in thin Al films (6 mum) deposited on thin circular silicon wafers (105 mum) of "large" in- plane dimensions (50.8 mm in diameter) subjected to thermal loading histori es. The loading and geometry is such that the system experiences deformatio ns that are clearly within the nonlinear range. The discussion is focused o n investigating the limits of the range of the linear relationship between the thermally induced mismatch strain and the substrate curvature, on the d egree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and finally, on the bifurcati on of deformation mode from axial symmetry to asymmetry with increasing mis match strain. Results obtained on the basis of both simple models and more- detailed finite-element simulations are compared with the full-field CGS me asurements with the purpose of validating the analytical and numerical mode ls. (C) 2001 American Institute of Physics.