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Mathematical modeling of material removal rate in roll-type linear CMP (roll-CMP) process: Effect of polishing pad

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Abstract

Recently, a roll-type linear chemical mechanical polishing (Roll-CMP) process was developed for fabricating large flexible substrates such as flexible printed circuit boards (FPCBs). The major difference between the Roll-CMP and the conventional CMP is the type of contact between the polishing pad and the substrate. Roll-CMP uses line contact for material removal of the Cu film on FPCBs. Many researchers have studied mathematical models to understand the conventional CMP process. In this paper, a mathematical model on the material removal rate (MRR) of Roll-CMP is proposed based on Hertzian contact theory and previously studied models on conventional CMP to understand the effect of the polishing pad. Two kinds of polishing pads were prepared to investigate their effect on the material removal of copper clad laminate (CCL). The increase in the average radius of pad asperities over the standard deviation of pad asperities increases MRR. The slurry loading capacity of the polishing pad impacts the MRR of Cu as well. The proposed model may offer a theoretical understanding for the Roll-CMP process.

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Abbreviations

a :

half of contact width

L :

length of roller

d :

diameter of roller

E p :

elastic modulus of polishing pad

v p :

Poisson’s ratio of polishing pad

E s :

elastic modulus of substrate

v s :

Poisson’s ratio of substrate

F :

down force

A :

apparent area of contact

A r :

real area of contact

E ps :

composite elastic modulus of pad and substrate

R p :

average radius of pad asperities

Δ p :

standard deviation of pad asperities

F m (b):

parabolic cylinder function

b :

dimensionless separation (h/Δ p )

q :

area density of particles in a slurry

N a :

number of active particles

χ:

volume concentration of particles in a slurry

C a :

weight concentration of particles in a slurry

D a :

diameter of particle

ω a :

weight of single particle

ρ s :

density of slurry

ρ a :

density of particle

H s :

hardness of substrate

E ap :

composite elastic modulus of particle and pad

δ p :

indentation depth of particle into pad

δ s :

indentation depth of particle into substrate

ζ:

2δ p /D a

S :

cross-sectional removal area

K :

Rabinowicz’s wear constant

MRR :

material removal rate

V :

relative velocity

A s :

total polished area of substrate

k :

constant representing the effect of the slurry loading capacity of the polishing pad

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  1. Department of Mechanical Engineering, Tongmyong University, 428, Sinseon-ro, Nam-gu, Busan, 48520, South Korea

    Hyunseop Lee

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Lee, H. Mathematical modeling of material removal rate in roll-type linear CMP (roll-CMP) process: Effect of polishing pad. Int. J. Precis. Eng. Manuf. 17, 495–501 (2016). https://doi.org/10.1007/s12541-016-0062-4

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  • DOI: https://doi.org/10.1007/s12541-016-0062-4

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