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Research Papers: Contact Mechanics

The Effects of Interfacial Particles on the Contact of an Elastic Sphere With a Rigid Flat Surface

[+] Author and Article Information
Dinçer Bozkaya, Sinan Müftü

Department of Mechanical Engineering, Northeastern University, Boston, MA 02115

J. Tribol 130(4), 041401 (Aug 04, 2008) (13 pages) doi:10.1115/1.2958073 History: Received October 01, 2007; Revised June 16, 2008; Published August 04, 2008

In chemical mechanical polishing (CMP), a rigid wafer is forced on a rough elastomeric polishing pad, while a slurry containing abrasive particles flows through the interface. One of the important factors that influence the material removal rate in CMP is the magnitude of contact force transmitted to the abrasive particles trapped at the contact interface. The total push-down force is distributed to the direct contact between the wafer and the pad, and to the three-body contact between the wafer, the pad, and the abrasive particles. The presence of the abrasive particles alters the asperity contact, which otherwise can be described by Hertz contact relationships. In this study, the effect of the interfacial particles on the single asperity contact is investigated. An approach used by Greenwood and Tripp (1967, “The Elastic Contact of Rough Spheres  ,” ASME J. Appl. Mech., 34, pp. 153–160) to study the contact of rough spheres is utilized since the presence of the particles provides a rough character to the contact. The results show that the contact behavior becomes non-Hertzian with decreasing contact force and increasing elastic modulus, particle size, and particle concentration. The role of the interfacial particles is to spread the contact over a larger area while lowering the maximum contact pressure at the center of contact predicted by Hertz contact. The conditions required to transfer the contact force on the particles effectively are also described.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cross-sectional view of the wafer-pad interface at different scales of contact

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Figure 2

Single particle model

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Figure 3

Particle contact force in pure particle, fpp*, and mixed, fpm*, contact regimes obtained by the FE model

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Figure 4

(a) Variation of the direct contact pressure, pd*, along the contact interface for different penetration depths, δp*, obtained by FEA. (b) Influence radius, ri*, and (c) maximum direct contact pressure, pdmax*, as a function of pad compression, εs, defined by Eqs. 4,5, respectively.

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Figure 5

Multiparticle model

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Figure 6

The variation of direct contact area, Ad, and influence factor, if, with pad compression, εp.

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Figure 7

(a) Top view of a particle and its six neighbors. (b)–(d) Different levels of influence factor if.

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Figure 8

(a) The contact pressure P̃c in pure particle (P̃pp) and mixed (P̃pm+P̃d) contact regimes for different particle concentrations, ηw=1.25%, 2.5%, and 5%, and (b) particle contact pressure ratio P̃pm∕P̃c

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Figure 9

The direct contact area, Ad, and influence factor, if, in mixed contact regime for different particle concentrations, ηw=1.25%, 2.5%, and 5%

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Figure 10

Single asperity model

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Figure 11

The error between the predicted maximum contact pressure with respect to the Hertz model (p̃0=(3F̃cs∕(2π3R̃b2))1∕3) utilizing different layer thicknesses t̃s

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Figure 12

The number of active particles, nas, as a function of the total contact force, F̃cs, for different particle concentrations, ηw

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Figure 13

The effect of the particle concentration, ηw, on the contact pressure, p̃c, distribution in the contact interface for contact force values of (a) F̃cs=104 and (b) F̃cs=105

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Figure 14

The effects of the particle concentration, ηw, on the distribution of ratio of the particle contact pressure to the total contact pressure, p̃p∕p̃c, and the direct contact area, Ad, in the contact zone for contact force values of (a) F̃cs=104 and (b) F̃cs=105

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Figure 15

The variation of the particle contact force as a fraction of the total contact force, F̃ps∕F̃cs, and the direct contact area, Ads, with the total contact force, F̃cs, for different particle concentrations, ηw

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Figure 16

The variation of the total contact force, F̃cs, with the penetration at the center of contact, δ̃0s, for different particle concentrations ηw

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Figure 17

The effect of the asperity radius, R̃b, on the contact pressure, p̃c, distribution along the contact zone, for contact force values of (a) F̃cs=104 and (b) F̃cs=105

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Figure 18

The variation of the particle contact force as a fraction of the total contact force, F̃ps∕F̃cs, and the direct contact area, Ads, with the total contact force, F̃cs, for different asperity radii, R̃b

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Figure 19

Numerical algorithm for the solution of the single asperity model

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