By keeping a pad moving relative to a wafer along a circular path without rotation, we developed a polishing technique called circular-translational-moving polishing (CTMP), which permits multidirectional polishing of the work piece and thus bears the advantage of isotropic polishing and a potential increase of material removal rate (MRR) on the wafer. To illuminate the mechanisms of CTMP and determine the optimum process variables in a CTMP process, a three-dimensional hydrodynamic lubrication model for CTMP with a smooth and rigid pad under a quasi-stable state is established in a polar coordinate system. The model equations are further calculated numerically by the finite difference method. The instantaneous distribution of fluid pressure is obtained, which shows that a negative pressure exists. The reason for negative pressure in CTMP and its effect on polishing is discussed. Moreover, the nominal clearance of the fluid film, roll, and pitch angles under different working conditions are obtained in terms of the applied load, moments, and polishing velocity. The obtained numerical analysis can be used as guidance for choosing operation parameters in a practical CTMP application.
ZHAI Wenjie, LIU Changxiong, LIANG Yingchun
. Numerical analysis of hydrodynamic process of
circular-translational-moving polishing (CTMP)[J]. Frontiers of Mechanical Engineering, 2008
, 3(4)
: 441
-448
.
DOI: 10.1007/s11465-008-0074-6
1. Preston F . Thetheory and design of plate glass polishing machines. J So Glass Technol, 1927, 11: 214–256
2. Yu T K, Yu C, Orlowski M . Combined asperity contact and fluid flow model for chemical-mechanicalpolishing. IEEE International Workshopon Numerical Modeling of Processes and Devices for Integrated Circuits,New York, 1994 : 29–32
3. Runnels S R, Eyman L M . Tribology analysis of chemicalmechanical polishing. J Electrochem Soc, 1994, 141(6): 698–701. doi:10.1149/1.2054985
4. Wang D, Lee J, Holland K, Bibby T, et al.. Vonmises stress in chemical-mechanical polishing process. J Electrochem Soc, 1999, 146: 253–255
5. Tichy J, Levert J A, Shan L, Danyluk S . Contactmechanics and lubrication hydrodynamics of chemical mechanical polishing. J Electrochem Soc, 1999, 146: 1523–1528. doi:10.1149/1.1391798
6. Shan L, Zhou C H, Danyluk S . Mechanical interactions and their effects on chemicalmechanical polishing. IEEE Trans on SemiconducManuf, 2001, 14(3): 207. doi: 10.1109/66.939815
7. Lin J F, Chen S C, Ouyang Y L, et al.. Analysis of the tribological mechanisms arisingin the chemical mechanical polishing of copper-film wafers when usinga pad with concentric grooves. J of Tribology,ASME Trans, 2006, 128: 445–459. doi:10.1115/1.2194913
8. Hocheng H, Tsai H Y, Tsai B . Effects of kinematic variables on nonuniformity in chemicalmechanical planarization. InternationalJournal of Machine Tools & Manufacture, 2000, 40: 1651–1669. doi:10.1016/S0890-6955(00)00013-4
9. Nannaji S, Lai J Y, Chun J H, Suh N P . Mechanismsof the chemical mechanical polishing (CMP) process in integrated circuitfabrication. Annals of the CIRP, 2001, 50(1): 233–238
10. Saikko V . AMultidirectional motion pin-on-disk wear test method for prostheticjoint materials. J Biomed Mater Res, 1998, 41: 58–64. doi:10.1002/(SICI)1097-4636(199807)41:1<58::AID-JBM7>3.0.CO;2-P
11. Zhai W J, Wang Y L, Liu C X . Characteristic analysis of circular-translational-grindingof plane. Harbin Institute of Technology, 2006, (Suppl): 95–97 (in Chinese)
12. Sundararajan S, Thakurta D G, Schwendeman D W, et al.. Two-dimensional wafer-scale mechanical planarizationmodel based on lubrication theory and mass transport. J Electrochem Soc, 1999, 146(2): 761–766. doi:10.1149/1.1391678
13. Park S S, Cho C H, Ahn Y . Hydrodynamic analysis of chemical mechanical polishingprocess. Tribology International, 2000, 33: 723–730. doi:10.1016/S0301-679X(00)00114-6
14. Chen J M, Fang Y C . Hydrodynamic Characteristicsof the thin fluid film in chemical–mechanical polishing. IEEE Trans on Semiconduc Manuf, 2002, 15(1): 39–44. doi:10.1109/66.983442
15. Levert J A, Baker A R, Mess F M, et al.. Mechanisms of chemical-mechanical polishingof sio2 dielectric on integrated circuits. STLE Tribol Trans, 1998, 41(4): 593–599. doi:10.1080/10402009808983787
16. Shan L, Levert J, Meade L, et al.. Interfacial fluid mechanics and pressure predictionin chemical mechanical polishing. ASMEJ Tribol, 2000, 122: 539–543. doi:10.1115/1.555398
17. Levert J A, Danyluk S, Tichy J . Mechanism for subambient interfacial pressure while polishingwith liquids. ASME J Tribol, 2000, 122: 450–457. doi:10.1115/1.555381
18. Zhou C H, Shan L, Hight J R, et al.. Fluid pressure and its effects on chemical mechanicalpolishing. Wear, 2002, 253: 430–437. doi:10.1016/S0043-1648(02)00155-2
19. Ng S H, Borucki L, Higgs F C, et al.. Tilt and interfacial fluid pressure measurementsof a disk sliding on a polymeric pad. ASMEJ Tribol, 2005, 127: 198–205. doi:10.1115/1.1829718
20. Higgs F C, Ng S H, Borucki L, et al.. A mixed-lubrication approach to predicting CMPfluid pressure modeling and experiments. J Electrochem Soc, 2005, 152(3): 193–198. doi:10.1149/1.1855834
21. Hamrock B J . Fundamentals of Fluid Film Lubrication, New York: McGraw-Hill, 1994