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SPECIAL ISSUE ON NANOMANUFACTURING

A Quasi-Static Mechanics Analysis of Three-Dimensional Nanoscale Surface Polishing

[+] Author and Article Information
H. Xu

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

K. Komvopoulos1

Department of Mechanical Engineering, University of California, Berkeley, CA 94720kyriakos@me.berkeley.edu

1

Corresponding author.

J. Manuf. Sci. Eng 132(3), 030912 (Jun 03, 2010) (10 pages) doi:10.1115/1.4001582 History: Received June 21, 2009; Revised April 07, 2010; Published June 03, 2010; Online June 03, 2010

A quasi-static mechanics analysis of nanoscale surface polishing that provides insight into the surface topography evolution and the removal of material at the asperity level is presented. The analysis is based on a three-dimensional stochastic model that accounts for multiscale (fractal) surface roughness and elastic, elastic-plastic, and fully plastic asperity deformation by hard abrasive nanoparticles embedded in the soft surface layer of a rigid polishing plate. Numerical results of the steady-state roughness of the polished surface, material removal rate, and wear coefficient are presented in terms of the apparent contact pressure, polishing speed, original topography and mechanical properties of the polished surface, average size and density of nanoparticles, and surface roughness of the polishing plate. Simulation trends are associated with elastic-plastic and fully plastic asperity contacts, responsible for irreversible topography changes (roughening effect) and material removal (smoothening effect), respectively. Analytical trends and predictions of the steady-state roughness of the polished surface and material removal rate are shown to be in good agreement with experimental results of nanoscale surface polishing (lapping) of magnetic recording ceramic heads.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Cross section schematic and (b) kinematics of the polishing process

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Figure 2

Schematic illustration of the polishing process with pertinent nomenclature

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Figure 3

(a) Schematic representation of asperity-nanoparticle interaction and (b) equivalent model of asperity truncation by a nanoparticle

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Figure 4

Schematic of surface modification at an elastic-plastic contact due to plowing by a nanoparticle

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Figure 5

(a) Roughness of the sample surface Rq and (b) material removal rate dh1/dt versus polishing time t (pa=356 kPa, υ=133 mm/s, Rq=1 nm (polishing plate), R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 6

(a) Initial (Rqi=0.96 nm), (b) transient (Rqt=0.59 nm), and (c) steady-state (Rqss=0.15 nm) topographies of the polished surface (pa=356 kPa, υ=133 mm/s, Rq=1 nm (polishing plate), R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 7

Power spectral density function P(ω) of the initial (Rqi=0.96 nm), transient (Rqt=0.59 and 0.27 nm), and steady-state (Rqss=0.15 nm) topographies of the polished surface (pa=356 kPa, υ=133 mm/s, Rq=1 nm (polishing plate), R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 8

Power spectral density function P(ω) of the polished surface topography obtained at steady-state polishing for initial roughness of the polished surface Rqi=0.96 nm, 0.50 nm, and 0.10 nm (pa=356 kPa, υ=133 mm/s, Rq=1 nm (polishing plate), R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 9

Asperity-nanoparticle contact fractions at steady-state polishing versus apparent contact pressure pa (Nc=number of total contacts, Ncep=number of elastic-plastic contacts, Ncfp=number of fully plastic contacts, N=number of nanoparticles existing in the analysis area, υ=133 mm/s, Rq=5 nm (polishing plate), R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 10

(a) Roughness of the polished surface Rqss, (b) material removal rate dh1/dt, and (c) wear coefficient K versus apparent contact pressure pa at steady-state polishing (υ=133 mm/s, Rq=5 nm (polishing plate), R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 11

Asperity-nanoparticle contact fractions versus roughness Rq of the polishing plate at steady-state polishing (Nc=number of total contacts, Ncep=number of elastic-plastic contacts, Ncfp=number of fully plastic contacts, N=number of nanoparticles existing in the analysis area, pa=356 kPa, υ=133 mm/s, R=50 nm, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 12

(a) Roughness of the polished surface Rqss, (b) material removal rate dh1/dt, and (c) wear coefficient K versus roughness Rq of the polishing plate at steady-state polishing (R=25 nm(pa=89 kPa), 50 nm (pa=356 kPa), and 75 nm (pa=356 kPa), υ=133 mm/s, np=9 μm−2, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 13

(a) Roughness of the polished surface Rqss, (b) material removal rate dh1/dt, and (c) wear coefficient K versus roughness Rq of the polishing plate at steady-state polishing (np=5 μm−2, 9 μm−2, and 15 μm−2, pa=356 kPa, υ=133 mm/s, R=50 nm, E=390 GPa, Y=7.3 GPa, H=20 GPa, and Hl=45 MPa)

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Figure 14

(a) Roughness of the polished surface Rqss, (b) material removal rate dh1/dt, and (c) wear coefficient K versus elastic modulus E of the polished surface with Y=7.3 GPa; (d) roughness of the polished surface Rqss, (e) material removal rate dh1/dt, and (f) wear coefficient K versus yield strength of the polished surface with E=390 GPa (pa=356 kPa, υ=133 mm/s, Rq=5 nm (polishing plate), R=50 nm, np=9 μm−2, and Hl=45 MPa)

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