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

Abstract

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) (Lyncée 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.

A Novel Measurement Method of Mechanical Properties for Individual Layers in Multilayered Thin Films

“…Assuming that the cantilever beam has a uniform curvature radius, z m is the maximum deflection of cantilever beam, l 2 is the length of the unbuckled cantilever beam, a simplified equation can be obtained to fit out its curvature radius R=l22/false(2zmfalse) [12]. This is suitable for obtaining the curvature radius R from FEA results.…”

“…This is significantly helpful, considering the mechanical parameters in the micromachined film depends on not only the process conditions but also the fabrication processes. Therefore, an in situ extraction method of material properties for multilayered films is expected [8,9,10,11,12]. During the past several years, some methods have been presented for extracting mechanical parameters [10,11,12].…”

“…Therefore, an in situ extraction method of material properties for multilayered films is expected [8,9,10,11,12]. During the past several years, some methods have been presented for extracting mechanical parameters [10,11,12]. The method based on the resonant frequency of doubly-clamped multilayered beams is relatively complex and the inaccuracy from the iterative computation is a little high, because four-element nonlinear equations need to be solved [10,11].…”

“…This significantly limits its practicability. An approach using multilayered cantilever beams has been presented based on the first resonance frequency measurement, but only the Young’s modulus of each layer for multilayered films can be extracted [12].…”

Optical direct detection of thermal vibrations of ultralow stiffness micro-nano structures.

“…There are numerous techniques to measure the elastic properties including elastic modulus. Numerical calculation [151][152][153] and finite element analysis [154][155][156] are used as a preliminary step to predict the elastic properties of unknown/new synthetic materials in order to choose a proper instrument for actual measurements. Experimental techniques include scattering, tensile (Force-elongation), AFM/indentation and spectral resonance measurements.…”