Research Papers: Other (Seals, Manufacturing)

A Particle-Augmented Mixed Lubrication Modeling Approach to Predicting Chemical Mechanical Polishing

[+] Author and Article Information
Elon J. Terrell1

Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213

C. Fred Higgs2

Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213higgs@andrew.cmu.edu


Currently at Columbia University.


Corresponding author.

J. Tribol 131(1), 012201 (Dec 02, 2008) (10 pages) doi:10.1115/1.2991173 History: Received February 06, 2008; Revised August 05, 2008; Published December 02, 2008

Chemical mechanical polishing (CMP) is a manufacturing process that is commonly used to planarize integrated circuits and other small-scale devices during fabrication. Although a number of models have been formulated, which focus on specific aspects of the CMP process, these models typically do not integrate all of the predominant mechanical aspects of CMP into a single framework. Additionally, the use of empirical fitting parameters decreases the generality of existing predictive CMP models. Therefore, the focus of this study is to develop an integrated computational modeling approach that incorporates the key physics behind CMP without using empirical fitting parameters. CMP consists of the interplay of four key tribological phenomena—fluid mechanics, particle dynamics, contact mechanics, and resulting wear. When these physical phenomena are all actively engaged in a sliding contact, the authors call this particle-augmented mixed lubrication (PAML). By considering all of the PAML phenomena in modeling particle-induced wear (or material removal), this model was able to predict wear-in silico from a measured surface topography during CMP. The predicted material removal rate (MRR) was compared with experimental measurements of copper CMP. A series of parametric studies were also conducted in order to predict the effects of varying slurry properties such as solid fraction and abrasive particle size. The results from the model are promising and suggest that a tribological framework is in place for developing a generalized first-principle PAML modeling approach for predicting CMP.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 2

(a) Sample topography of the copper wafer that was used for the PAML simulations, measured using contact profilometry; (b) sample wafer surface topography represented as voxels (Nx=Ny=16)

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Figure 3

Diagram of the wafer/pad domain in one of the PAML simulations

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Figure 14

PAML prediction of MRR with varied inputs for abrasive particle radius

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Figure 4

Flowchart of the PAML computational model

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Figure 5

Diagram of the fluid boundary conditions that were implemented in the Chorin fluid flow solver

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Figure 6

Diagram of the cell division of the PAML domain, which was used in the Chorin solver to solve the slurry flowfield

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Figure 7

Diagram showing the basis of the wear formulation in this study, wherein a slurry particle digs a wear trench between the two contacting surfaces

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Figure 8

Sample step height measurement of copper film wafer—(a) contour plot, and (b) line plot across the center of the plot

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Figure 9

PAML simulation at a given instance in time

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Figure 10

PAML prediction of the instantaneous wear of the wafer surface for the base case (W=6 psi, X=0.04, ap=0.15 μm)

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Figure 11

PAML prediction of the cumulative wear of the wafer surface for the base case (W=6 psi, X=0.04, ap=0.15 μm)

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Figure 12

Comparison between predicted and measured MRRs

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Figure 13

PAML prediction of MRR with varied inputs for particle solid fraction




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