The GALCIT-developed "Coherent Gradient Sensor (CGS)" method is an optical shearing interferometer sensitive to surface slope changes of plates undergoing deformations and was initially used in conjunction with high-speed photography for the study of dynamic failure of opaque structural materials.
In the first section of this lecture we describe an entirely different application of CGS of relevance to the microelectronics and opto-electronics industry. Here we present CGS as a unique inspection and reliability tool used for the rapid, full-field, and in-situ measurement of deformation states (slopes and curvature components) in thin film-wafer substrate systems and for the subsequent inference of non- uniform stresses in thin films and thin film structures deposited on such substrates. We also demonstrate the unique ability of CGS to produce curvature maps in large, 300mm patterned wafers during various stages of processing.
In the second part of the lecture we describe how classical analytical approaches (e.g. the classical Stoney formula), relating local stresses to local curvatures in such systems fail in the presence of misfit stain, temperature and thin film thickness, non-uniformities. To mitigate this we present a series of new analytical models (developed in collaboration with Northwestern University and MIT colleagues) capable of relating non-uniform curvature components to arbitrarily non-uniform stress states resulting from the presence of geometrical, misfit strain and temperature non-uniformities. A striking outcome of the entire class of such models is that film stresses, in the presence of such non- uniformities, are found to always depend non-locally on system curvatures thus necessitating full field wafer curvature recording rather than point-wise measurements. This remarkable fact makes CGS (a full field rather than a point-wise method of measuring curvatures) a perfect optical technique to be used, in conjunction with the analytical models presented here, for accurate film stress inference and for stress management in realistic cases involving the various processing steps of large, 300mm Wafers.