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Research Papers

Onset of Wiggling in a Microscopic Patterned Structure Induced by Intrinsic Stress During the Dry Etching Process

[+] Author and Article Information
Hiro Tanaka

Department of Mechanical Engineering,
The University of Tokyo,
Tokyo 113, Japan
e-mail: tanaka.hiro@fml.t.u-tokyo.ac.jp

Takahiro Hidaka, Satoshi Izumi, Shinsuke Sakai

Department of Mechanical Engineering,
The University of Tokyo,
Tokyo 113, Japan

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 30, 2014; final manuscript received June 24, 2014; accepted manuscript posted June 26, 2014; published online July 10, 2014. Assoc. Editor: Xue Feng.

J. Appl. Mech 81(9), 091009 (Jul 10, 2014) (8 pages) Paper No: JAM-14-1143; doi: 10.1115/1.4027914 History: Received March 30, 2014; Revised June 24, 2014; Accepted June 26, 2014

In semiconductor devices, fine patterning can cause structural instability because of intrinsic compressive stress. We studied one such instability phenomenon, out-of-plane wiggling of a patterned structure with mask–dielectric ridges, to improve the yield of these highly miniaturized devices. Our simple continuum approach uses dimensionless parameters to control the bifurcation threshold of ridge wiggling. Coupled with modeling the etching process, our approach revealed the onset of buckling, agreeing well with experimental data. To study the influence of the ridge width and the elastic substrate on buckling stress and deformation, we performed numerical analyses using a finite element method (FEM).

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Figures

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Fig. 1

Processing schematics for the patterned structure with mask–dielectric ridges

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Fig. 2

Tilted SEM images of the patterned structures with or without ridge wiggling: (a) Exp. 2, (b) Exp. 6, and (c) Exp. 8

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Fig. 3

Schematics of the bilayer model, considering a single ridge fixed at a substrate: (a) an overview of the model and (b) two side-views of the model

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Fig. 4

Schematics of the dry-etching model

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Fig. 5

Stability diagram of the bilayer model, showing the change in κ, with the Λc-curve superimposed on the qc2–curve

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Fig. 6

Comparison of Λc-curve and Λetch-curve with change in κ, calculated using the etching conditions listed in Table 3. The dashed curves indicate the calculated Λc-curve with identical conditions as shown in Fig. 5. The filled circles are the observation points that correspond to the experimental data in Table 3.

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Fig. 7

Shifting of the onset of buckling for Exp. 6: (a) the increase in Ed and (b) the increase in rm/rd

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Fig. 8

Cross-sectional drawing of a FEM model. The profile of the patterned structure corresponds to Exp. 2.

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Fig. 9

Center view of the computed buckling modes of the two ridges on a elastic substrate: (a) coordinate-phase for the two ridges, φ0 degap and φ90 degap, and (b) antiphase for the two ridges, φ0 degap and φ90 degap. Each contour figure shows the y-displacements of the substrate surface (z–x plane). The dashed curves superposed on each contour figure show the upper undulations of the two ridges. The threshold of each contour bar is normalized to the maximum displacement amplitude of each dashed undulation.

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Fig. 10

(a) and (b) schematics of the wiggling patterns of two parallel ridges on an elastic substrate, expressed by Eq. (29). The wiggling patterns in the insets correspond to changes in (a) θ0 = 0,π/8,π/4,3π/8,π/2 at θ1 = θ2 = 0, and (b) θ1 = 0,π/4,π/2,3π/4,π at θ0 = π/4 and θ2 = 0. (c) The y-displacements of the substrate surface for the superposition of the two buckling modes, φ0 degcp and φ0 degap (see Fig. 9), which corresponds to the case of θ0 = π/4 and θ1 = θ2 = 0 in Eq. (29). The range of values in the contour bar is consistent with that in Fig. 9(a).

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