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

• Published in: Journal of microelectromechanical systems 2001-09, Vol.10 (3), p.336-346
• Main Authors: Jensen, B.D., de Boer, M.P., Masters, N.D., Bitsie, F., LaVan, D.A.
• Format: Article
• Language: English
• Subjects: Applied sciences; Beams (structural); Crystal orientation; Curvature; Deflection; Elastic moduli; Exact sciences and technology; Finite difference method; Fluid dynamics; Fundamental areas of phenomenology (including applications); Industrial metrology. Testing; Instrumentation for fluid dynamics; Interferometry; Laboratories; Material properties; Materials testing; Mathematical analysis; Mathematical models; Mechanical engineering. Machine design; Mechanical factors; Microelectromechanical systems; Micromechanical devices; Modulus of elasticity; Nondestructive testing; Physics; Polysilicon; Precision engineering, watch making; Silicon; Standard deviation; Statistical methods; Substrates; Thin films; Transistors
• ISSN: 1057-7157; 1941-0158
• DOI: 10.1109/84.946779

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.