A practical method for simultaneous determination of Poisson’s ratio and Young’s modulus of elasticity of thin films

Sun, Jun‐Yi; Jianli, HU; Zheng, Zhao; He, Xiao‐Ting; Geng, Huan-huan

doi:10.1007/s12206-011-1002-y

Cited by 20 publications

(13 citation statements)

References 46 publications

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“…Compared with our early works about Hencky problem [4,7,17], it may easily be seen that all the expressions obtained here for displacements, strains and stresses have the same form as those in Hencky solution. But the boundary conditions, under which Eqs.…”

Section: Resultssupporting

confidence: 50%

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Closed‐form solution of elastic circular membrane with initial stress under uniformly‐distributed loads: Extended Hencky solution

Sun

Lian

et al. 2015

Z Angew Math Mech

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The well‐known Hencky solution is only applicable to the problem of deformation of the elastic circular membrane without initial stress under transverse uniformly‐distributed loads. The problem considered here is a more general case: an initial tensile or compressive stress has been present in the initially flat circular membrane before the membrane is subjected to the transverse loads. The closed‐form solution of the considered problem was presented and all the expressions obtained here for displacements, strains and stresses have the same form as those in the well‐known Hencky solution. The initial stress plays an important role in the determination of numerical value of the integral constant controlling membrane equation. The solution obtained here can be regressed into the well‐known Hencky solution when the initial stress is equal to zero, and it is therefore called extended Hencky solution.

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Section: Resultssupporting

confidence: 50%

“…Elastic circular membrane structures and structural components have found a variety of applications [1][2][3][4][5][6][7]. They often exhibit large deflections.…”

Section: Introductionmentioning

confidence: 99%

Closed‐form solution of elastic circular membrane with initial stress under uniformly‐distributed loads: Extended Hencky solution

Sun

Lian

et al. 2015

Z Angew Math Mech

Self Cite

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“…To make results more intuitive, the paper sets exact values to the Poisson’s ratio in each layer. The way to extract the Poisson’ ratio ν i is introduced in [20,21,22]. The Poisson’s ratio of each layer in a certain rational range has little effect on the results of the Young’s modulus [12].…”

Section: Theory Of the Test Structurementioning

confidence: 99%

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

et al. 2019

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Various multilayered thin films are extensively used as the basic component of some micro-electro-mechanical systems, requiring an efficient measurement method for material parameters, such as Young’s modulus, residual stress, etc. This paper developed a novel measurement method to extract the Young’s moduli and residual stresses for individual layers in multilayered thin films, based on the first resonance frequency measurements of both cantilever beams and doubly-clamped beams. The fabrication process of the test structure, the corresponding modeling and the material parameter extraction process are introduced. To verify this method, the test structures with gold/polysilicon bilayer beams are fabricated and tested. The obtained Young’s moduli of polysilicon films are from 151.38 GPa to 154.93 GPa, and the obtained Young’s moduli of gold films are from 70.72 GPa to 75.34 GPa. The obtained residual stresses of polysilicon films are from −14.86 MPa to −13.11 MPa (compressive stress), and the obtained residual stresses of gold films are from 16.27 to 23.95 MPa (tensile stress). The extracted parameters are within the reasonable ranges, compared with the available results or the results obtained by other test methods.

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“…To make results more intuitive, the paper sets exact values to the Poisson’s ratio in each layer. The way to obtain Poisson’ ratio ν i is shown in [ 21 , 22 , 23 ]. The Poisson’s ratio of each layer in a certain rational range has little effect on the results of the Young’s modulus.…”

Section: Theorymentioning

confidence: 99%

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

et al. 2017

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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.

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A practical method for simultaneous determination of Poisson’s ratio and Young’s modulus of elasticity of thin films

Cited by 20 publications

References 46 publications

Closed‐form solution of elastic circular membrane with initial stress under uniformly‐distributed loads: Extended Hencky solution

Closed‐form solution of elastic circular membrane with initial stress under uniformly‐distributed loads: Extended Hencky solution

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

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

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