Integrated measurement-modeling approaches for evaluating residual stress using micromachined fixed-fixed beams

Two methodologies have been developed to determine the biaxial residual stress value in thin films using electrostatically actuated fixed-fixed beam test structures. In the first, we determine the compliance matrix of the support posts using 3-D finite-element analysis. The residual stress value is then found from the best fit between the measured and modeled deflection curves, with the residual stress as the only free parameter in the model. An accuracy of ±0.5 MPa for the average biaxial residual stress level is evaluated from the reproducibility of independent measurements over a wide range of loadings. The key to the second methodology lies in the recognition that for a given value of residual stress, there exists a unique family of deflection curves associated with two adjacent beams of different lengths. Therefore, compliance information can be extracted directly from the deflection curves. We proceed to show that essentially the same values of residual stress are found by the two methodologies, while the latter allows much more rapid extraction of the residual stress. With the second methodology established, we find that residual stress values vary across a quarter of a six-inch diameter wafer by 2.5 MPa for three structural levels of polycrystalline silicon in our five-level surface micromachining technology.