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
References
Lee, H., Park, Y., Lee, S., and Jeong, H., “Preliminary Study on the Effect of Spray Slurry Nozzle in CMP for Environmental Sustainability, Int. J. Precis. Eng. Manuf., Vol. 15, No. 6, pp. 995–1000, 2014.
Lee, H., Guo, Y., and Jeong, H., “Temperature Distribution in Polishing Pad during CMP Process: Effect of Retaining Ring, Int. J. Precis. Eng. Manuf., Vol. 13, No. 1, pp. 25–31, 2012.
Lee, H., Dornfeld, D. A., and Jeong, H., “Mathematical Modelbased Evaluation Methodology for Environmental Burden of Chemical Mechanical Planarization Process, Int. J. Precis. Eng. Manuf.-Green Tech., Vol. 1, No. 1, pp. 11–15, 2014.
Wang, H., Lee, H., and Jeong, H., “Statistical Analysis on Process Variables in Linear Roll-CMP, Journal of the Korean Society of Tribologists and Lubrication Engineers, Vol. 30, No. 3, pp. 139–145, 2014.
Lee, H., Wang, H., Park, J., and Jeong, H., “Experimental Investigation of Process Parameters for Roll-Type Linear Chemical Mechanical Polishing (Roll-CMP) System, Precision Engineering, Vol. 38, No. 4, pp. 928–934, 2014.
Preston, F., “The Theory and Design of Plate Glass Polishing Machines, Journal of the Soc Glass Technology, Vol. 11, pp. 214–256, 1927.
Tseng, W. T., Chin, J. H., and Kang, L. C., “A Comparative Study on the Roles of Velocity in the Material Removal Rate during Chemical Mechanical Polishing, Journal of the Electrochemical Society, Vol. 146, No. 5, pp. 1952–1959, 1999.
Guo, L. and Subramanian, R. S., “Mechanical Removal in CMP of Copper using Alumina Abrasives, Journal of The Electrochemical Society, Vol. 151, No. 2, pp. G104–G108, 2004.
Homma, Y., “Dynamical Mechanism of Chemical Mechanical Polishing Analyzed to Correct Preston’s Empirical Model, Journal of the Electrochemical Society, Vol. 153, No. 6, pp. G587–G590, 2006.
Qin, K., Moudgil, B., and Park, C.-W., “A Chemical Mechanical Polishing Model Incorporating both the Chemical and Mechanical Effects, Thin Solid Films, Vol. 446, No. 2, pp. 277–286, 2004.
Johnson, K. L., “Contact Mechanics, Cambridge University, p. 406, 1985.
Zhao, Y. and Chang, L., “A Micro-Contact and Wear Model for Chemical-Mechanical Polishing of Silicon Wafers, Wear, Vol. 252, No. 3, pp. 220–226, 2002.
Wang, Y., Zhao, Y.-W., and Gu, J., “A New Nonlinear-Micro-Contact Model for Single Particle in the Chemical-Mechanical Polishing with Soft Pad, Journal of Materials Processing Technology, Vol. 183, No. 2, pp. 374–379, 2007.
Jiang, J.-Z., Zhao, Y.-W., Wang, Y.-G., and Luo, J.-B., “A Chemical Mechanical Polishing Model based on the Viscous Flow of the Amorphous Layer, Wear, Vol. 265, No. 7, pp. 992–998, 2008.
Chen, X., Zhao, Y., and Wang, Y., “Modeling the Effects of Particle Deformation in Chemical Mechanical Polishing, Applied Surface Science, Vol. 258, No. 22, pp. 8469–8474, 2012.
Lee, H. S., Jeong, H. D., and Dornfeld, D. A., “Semi-Empirical Material Removal Rate Distribution Model for SiO2 Chemical Mechanical Polishing (CMP) Processes, Precision Engineering, Vol. 37, No. 2, pp. 483–490, 2013.
Lee, H., Park, Y., Lee, S., and Jeong, H., “Effect of Wafer Size on Material Removal Rate and Its Distribution in Chemical Mechanical Polishing of Silicon Dioxide Film, Journal of Mechanical Science and Technology, Vol. 27, No. 10, pp. 2911–2916, 2013.
Park, K. H., Kim, H. J., Chang, O. M., and Jeong, H. D., “Effects of Pad Properties on Material Removal in Chemical Mechanical Polishing, Journal of Materials Processing Technology, Vol. 187, No. pp. 73–76, 2007.
Oliver, M. R., “Chemical-Mechanical Planarization of Semiconductor Materials, Springer, p. 172, 2004.
Wang, H., “Effect of Pad Viscoelastic Behavior on Polishing Characteristics in Roll-CMP Process, M.Sc. Thesis, Department of Mechanical Engineering, Pusan National University, 2015.
Budynas, R. G. and Nisbett, K. J., “Shigley's Mechanical Engineering Design, McGraw-Hill, p. 124, 2011.
Greenwood, J. A. and Williamson, J. B. P., “Contact of Nominally Flat Surfaces, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 95, pp. 300–319, 1966.
Bhushan, B., “Principles and Applications of Tribology, John Wiley & Sons, 2nd Ed., pp. 234–236, 2013.
Rabinowicz, E., “Friction and Wear of Materials, 2nd Ed., Wiley, 1995.
Xu, G., Liang, H., Zhao, J., and Li, Y., “Investigation of Copper Removal Mechanisms during CMP, Journal of The Electrochemical Society, Vol. 151, No. 10, pp. G688–G692, 2004.
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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