DETERMINING MEAN AND GRADIENT RESIDUAL-STRESSES IN THIN-FILMS USING MICROMACHINED CANTILEVERS

A technique that provides a first approximation to the mean, sigma(0), and gradient, sigma(1), components of residual stress in a thin-film material is discussed. In this method, measurements are made on a sing le micromachined cantilever, as opposed to an array of structures as u sed in the related critical-length buckling approach, to find tensile, compressive and gradient stresses. The measured deflection profile of a cantilever is reduced to rotation and curvature components, which a re shown to derive independently from sigma(0) and sigma(1), respectiv ely. Essential to this method is the observation that a micromachined structure with a 'nominally-clamped' boundary undergoes subtle rotatio n at its junction with the portion of the thin film that remains bonde d to the substrate but is contiguous with the structure. This boundary rotation effect occurs through in-plane expansion or contraction of t he bonded film following relief of residual stress. Thus, the deformat ion of the micromachined cantilevers considered here and of more gener al bulk- or surface-micromachined devices, can be strongly influenced by the state of stress in the still-bonded film.