Determining mean and gradient residual stresses in thin films using micromachined cantilevers

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Abstract
A technique that provides a first approximation to the mean, , and gradient, , components of residual stress in a thin-film material is discussed. In this method, measurements are made on a single micromachined cantilever, as opposed to an array of structures as used 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 are shown to derive independently from and , respectively. Essential to this method is the observation that a micromachined structure with a `nominally-clamped' boundary undergoes subtle rotation at its junction with the portion of the thin film that remains bonded to the substrate but is contiguous with the structure. This boundary rotation effect occurs through in-plane expansion or contraction of the bonded film following relief of residual stress. Thus, the deformation of the micromachined cantilevers considered here and of more general bulk- or surface-micromachined devices, can be strongly influenced by the state of stress in the still-bonded film.