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Modification of curvature-based thin-film residual stress measurement for MEMS applications

Wafer level thin-film residual stress characterization is crucial for the structural reliability of many semiconductor and microelectromechanical systems (MEMS) devices. Because of its simplistic nature, the curvature measurement scheme is traditionally the most widely acknowledged method. Film stress is determined by converting the measured curvatures using Stoney's formula. However, this equation is based on linear beam theory and exhibits considerable errors if the rigidity of films cannot be neglected. This presents a problem for many MEMS related applications, where thicker films are usually required. In this paper, an assumed shaped energy-based approach is proposed to improve the curvature/stress conversion by simultaneously considering the effects of geometrical nonlinearity and mid-plane offsets. Solutions obtained by this method agree very well with those produced by nonlinear finite element simulations. Parametric studies show that for stiffer films, such as thick silicon carbide on silicon, this improved conversion model can provide a much more accurate curvature to stress conversion while the traditional conversion results in significant errors.