A simple method for extracting material parameters of multilayered MEMS structures using resonance frequency measurements

Multilayered structures are increasingly used in MEMS. Based on the resonant frequency of the doubly-clamped multilayered beam, the Young's modulus and residual stress for an individual layer have been measured by designing beam test structures for each layer with different widths. Taking into account the buckling or no buckling problem of the multilayered beam, this paper introduces a model for the resonant frequency of the beam. An approach to extract the Young's modulus and residual stress for the individual layer is developed. The validity of this approach has been studied using finite element modeling. As a multilayered example, test structures for a gold/polysilicon bilayer beam were fabricated. A scanning laser Doppler vibrometer system was used to measure the resonant frequency of the beam. The extracted parameters are that the average value of Young's modulus of polysilicon and gold are 133.7 GPa and 78.6 GPa with standard deviation being 4.2 GPa and 11.5 GPa, respectively; the average value of residual stress of polysilicon and gold are 13.9 MPa (compressive) and 19.7 MPa (tensile) with standard deviation being 0.47 MPa and 4.4 MPa, respectively.