A Simple Extraction Method of Young?￠????s Modulus for Multilayer Films in MEMS Applications

摘要

Based on the first resonance frequency measurement of multilayer beams, a simple extraction method has been developed to extract the Young?￠????s modulus of individual layers. To verify this method, the double-layer cantilever, as a typical example, is analyzed to simplify the situation and finite element modeling (FEM) is used in consideration of the buckling and unbuckling situation of cantilevers. The first resonance frequencies, which are obtained by ANSYS (15.0, ANSYS Inc., Pittsburgh, PA, USA) with a group of thirteen setting values of Young?￠????s modulus in the polysilicon layer are brought into the theoretical formulas to obtain a new group of Young?￠????s modulus in the polysilicon layer. The reliability and feasibility of the theoretical method are confirmed, according to the slight differences between the setting values and the results of the theoretical model. In the experiment, a series of polysilicon-metal double-layer cantilevers were fabricated. Digital holographic microscopy (DHM) (Lync????e Tech, Lausanne, Switzerland) is used to distinguish the buckled from the unbuckled. A scanning laser Doppler vibrometer (LDV) (Polytech GmbH, Berlin, Germany) system is used to measure the first resonance frequencies of them. After applying the measurement results into the theoretical modulus, the average values of Young?￠????s modulus in the polysilicon and gold layers are 151.78 GPa and 75.72 GPa, respectively. The extracted parameters are all within the rational ranges, compared with the available results.