Interferometry of actuated microcantilevers to determine material properties and test structure nonidealities in MEMS

Abstract

By integrating interferometric deflection data from electrostatically actuated microcantilevers with a numerical finite difference model, we have developed a step-by-step procedure to determine values of Young's modulus while simultaneously quantifying nonidealities. The central concept in the methodology is that nonidealities affect the long-range deflections of the beams, which can be determined to near nanometer accuracy. Beam take-off angle, curvature and support post compliance are systematically determined. Young's modulus is then the only unknown parameter, and is directly found. We find an average value of Young's modulus for polycrystalline silicon of 164.3 GPa and a standard deviation of 3.2 GPa (/spl plusmn/2%), reflecting data from three different support post designs. Systematic errors were assessed and may alter the average value by /spl plusmn/5%. An independent estimate from grain orientation measurements yielded 163.4-164.4 GPa (the Voigt and Reuss bounds), in agreement with the step-by-step procedure. Other features of the test procedure include that it is rapid, nondestructive, verifiable and requires only a small area on the test chip.