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Research Papers

A Renewal Weakest-Link Model of Strength Distribution of Polycrystalline Silicon MEMS Structures

[+] Author and Article Information
Zhifeng Xu

Department of Civil,
Environmental, and Geo-Engineering,
University of Minnesota,
500 Pillsbury Dr. S.E.,
Minneapolis, MN 55455
e-mail: xuxx0877@umn.edu

Roberto Ballarini

Department of Civil and Environmental Engineering,
University of Houston,
N127, Engineering Building 1,
4726 Calhoun Road,
Houston, TX 77204
e-mail: rballari@Central.UH.EDU

Jia-Liang Le

Department of Civil,
Environmental, and Geo-Engineering,
University of Minnesota,
500 Pillsbury Dr. S.E.,
Minneapolis, MN 55455
e-mail: jle@umn.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received February 20, 2019; final manuscript received April 8, 2019; published online May 17, 2019. Assoc. Editor: Yonggang Huang.

J. Appl. Mech 86(8), 081005 (May 17, 2019) (10 pages) Paper No: JAM-19-1087; doi: 10.1115/1.4043440 History: Received February 20, 2019; Accepted April 08, 2019

Experimental data have made it abundantly clear that the strength of polycrystalline silicon (poly-Si) microelectromechanical systems (MEMS) structures exhibits significant variability, which arises from the random distribution of the size and shape of sidewall defects created by the manufacturing process. Test data also indicated that the strength statistics of MEMS structures depends strongly on the structure size. Understanding the size effect on the strength distribution is of paramount importance if experimental data obtained using specimens of one size are to be used with confidence to predict the strength statistics of MEMS devices of other sizes. In this paper, we present a renewal weakest-link statistical model for the failure strength of poly-Si MEMS structures. The model takes into account the detailed statistical information of randomly distributed sidewall defects, including their geometry and spacing, in addition to the local random material strength. The large-size asymptotic behavior of the model is derived based on the stability postulate. Through the comparison with the measured strength distributions of MEMS specimens of different sizes, we show that the model is capable of capturing the size dependence of strength distribution. Based on the properties of simulated random stress field and random number of sidewall defects, a simplified method is developed for efficient computation of strength distribution of MEMS structures.

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Figures

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Fig. 1

(a) Uniaxial tensile MEMS specimen with sidewall defects idealized by V-notches and (b) schematic of the renewal weakest-link model for failure of a sidewall

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Fig. 8

Probability distributions of the number of V-nocthes for different specimen lengths

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Fig. 9

Size effect on the mean structural strength

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Fig. 10

Comparison of the strength distributions of MEMS specimens predicted by the renewal weakest-link model and the simplified model

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Fig. 11

Plot of relative error Δ1(σN) defined in Eq. (35)

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Fig. 12

Plot of relative error Δ2(σN, L) defined in Eq. (39)

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Fig. 2

Analysis of a notched segment

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Fig. 3

Calculated pdf of segment length

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Fig. 7

Predicted strength distributions of MEMS specimens of different lengths presented in (a) Weibull distribution paper and (b) Gaussian distribution paper

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Fig. 4

Joint pdf fzl(z, l) of the dimensionless stress field

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Fig. 5

Optimum fits of the measured strength histograms (data set 1) by the present model

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Fig. 6

Optimum fits of the measured strength histograms (data set 2) by the present model

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