• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.621-633
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• 2023

The major objective of this paper is to study the receding contact problem between two functional graded layers under a flat indenter. The gravity is assumed negligible, and the shear moduli of both layers are assumed to vary exponentially along the thickness direction. In the absence of body forces, the problem is reduced to a system of Fredholm singular integral equations with the contact pressure and contact size as unknowns via Fourier integral transform, which is transformed into an algebraic one by the Gauss-Chebyshev quadratures and polynomials of both the first and second kinds. Then, an iterative speediest descending algorithm is proposed to numerically solve the system of algebraic equations. Both semi-analytical and finite element method, FEM solutions for the presented problem validate each other. To improve the accuracy of the numerical result of FEM, a graded FEM solution is performed to simulate the FGM mechanical characteristics. The results reveal the potential links between the contact stress/size and the indenter size, the thickness, as well as some other material properties of FGM.

• Proceedings of the Korean Vacuum Society Conference
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• 1998.02a
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• pp.77-77
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• 1998

Present silicon dioxide (SiOz) 떠m as intennetal dielectridIMD) layers will result in high parasitic c capacitance and crosstalk interference in 비gh density devices. Low dielectric materials such as f f1uorina뼈 silicon oxide(SiOF) and f1uoropolymer IMD layers have been tried to s이ve this problem. I In the SiOF ftlm, as fluorine concentration increases the dielectric constant of t뼈 film decreases but i it becomes unstable and wa않r absorptivity increases. The dielectric constant above 3.0 is obtain어 i in these ftlms. Fluoropolymers such as polyte$\sigma$따luoroethylene(PTFE) are known as low dielectric c constant (>2.0) materials. However, their $\alpha$)Or thermal stability and low adhesive fa$\pi$e have h hindered 야1리ru뚱 as IMD ma따"ials. 1 The concept of a plasma processing a찌Jaratus with 비gh density plasma at low pressure has r received much attention for deposition because films made in these plasma reactors have many a advantages such as go여 film quality and gap filling profile. High ion flux with low ion energy in m the high density plasma make the low contamination and go어 $\sigma$'Oss피lked ftlm. Especially the h helicon plasma reactor have attractive features for ftlm deposition 야~au똥 of i앙 high density plasma p production compared with other conventional type plasma soun:es. I In this pa야Jr, we present the results on the low dielectric constant fluorocarbonated-SiOF film d밑JOsited on p-Si(loo) 5 inch silicon substrates with 00% of 0dFTES gas mixture and 20% of Ar g gas in a helicon plasma reactor. High density 띠asma is generated in the conventional helicon p plasma soun:e with Nagoya type ill antenna, 5-15 MHz and 1 kW RF power, 700 Gauss of m magnetic field, and 1.5 mTorr of pressure. The electron density and temperature of the 0dFTES d discharge are measUI벼 by Langmuir probe. The relative density of radicals are measured by optic허 e emission spe따'Oscopy(OES). Chemical bonding structure 3I피 atomic concentration 따'C characterized u using fourier transform infrared(FTIR) s야3띠"Oscopy and X -ray photonelectron spl:’따'Oscopy (XPS). D Dielectric constant is measured using a metal insulator semiconductor (MIS;AVO.4 $\mu$ m thick f fIlmlp-SD s$\sigma$ucture. A chemical stoichiome$\sigma$y of 야Ie fluorocarbina$textsc{k}$영-SiOF film 따~si야영 at room temperature, which t the flow rate of Oz and FTES gas is Isccm and 6sccm, res야~tvely, is form려 야Ie SiouFo.36Co.14. A d dielec$\sigma$ic constant of this fIlm is 2.8, but the s$\alpha$'!Cimen at annealed 5OOt: is obtain려 3.24, and the s stepcoverage in the 0.4 $\mu$ m and 0.5 $\mu$ m pattern 킹'C above 92% and 91% without void, res야~tively. res야~tively.