Physics of the Coefficient of Friction in CMP

Physics of the Coefficient of Friction in CMP

Physics of the Coefficient of Friction in CMP

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action <strong>of</strong> particles should f<strong>in</strong>d an <strong>in</strong>terest<strong>in</strong>g place with<strong>in</strong> <strong>the</strong> context <strong>of</strong> nanolubrication <strong>the</strong>ory.AcknowledgementsThe authors would like to thank C.P. Please, T. Witelski, C. Breward, D. Schwendeman, M. Gratton, J.Evans, A. Bhattacharya, M. Nichols and M. Surles for stimulat<strong>in</strong>g discussions on <strong>the</strong> implications <strong>of</strong>nanolubrication at <strong>the</strong> 2005 Ma<strong>the</strong>matical Problems <strong>in</strong> Industry workshop held at WorcesterPolytechnic Institute on 13-17 June, 2005.References[1] F. Preston, J. <strong>of</strong> <strong>the</strong> Society. <strong>of</strong> Glass Technology, 11, pp. 214-256, (1927).[2] S.R. Runnels, J. Electrochem. Soc., 141(7), pp. 1900-1904 (1994).[3] J. Sorooshian, L. Borucki, D. Ste<strong>in</strong>. R. Timon, D. He<strong>the</strong>r<strong>in</strong>gton, A. Philipossian, Trans. ASMEJ. Tribology, 127(3), pp. 639-651 (2005).[4] L. Borucki, J. Sorooshian, Z. Li, Y. Sampurno, Y. Zhuang, A. Philipossian, Proc. 9th International<strong>CMP</strong>-MIC, Fremont, CA, Feb. 23-25, 2005, pp. 168-175.[5] L. Borucki, D. Rosales-Yeomans, A. Philipossian, Proc. 10th CAMP <strong>CMP</strong> Symposium, LakePlacid, NY, August 14-17, 2005.[6] Y. Sampurno, L. Borucki, A. Philipossian, J. Electrochem. Soc. 152(11), 2005.[7] G.P. Muldowney, Proc. Pac RIM-<strong>CMP</strong> Conference, Tokyo, Japan, Dec. 6, 2004, pp 33-44.[8] S. Gold and V. A. Burrows, Electrochem. and Solid State Letters, 7(12), G295-G298 (2004).[9] L.J. Borucki, T. Witelski, C.P. Please, P.R. Kramer, D. Schwendeman, J. Eng<strong>in</strong>eer<strong>in</strong>gMa<strong>the</strong>matics, Vol. 50, 1-24 (2004).[10] L. Borucki, H. Lee, Y. Zhuang, A. Philipossian, Proc. AIChE Annual Meet<strong>in</strong>g, Aust<strong>in</strong> TX, Nov. 8,2004.[11] J. Luo and D. Dornfeld, IEEE Trans. on Semiconductor Manufactur<strong>in</strong>g, 14(2), pp. 112-133(2001).[12] X. Xia and G. Ahmadi, Particulate Science and Technology, 20(3), 187-196.[13] C. Zhou, L.Shan. J.R. Hight, S.-H. Ng and S. Danyluk, Mat. Res. Soc. Symp. Proc. Vol. 671, pp.M1.6.1-M1.6.7, Materials Research Society, San Francisco, CA (2001).[14] S.-H. Ng, doctoral dissertation, Georgia Institute <strong>of</strong> Technology, Atlanta, GA, 2004.[15] A.Z. Szeri, Fluid Film Lubrication Theory and Design, Cambridge U. Press, Ch. 8 (1998).[16] G. Muldowney, C.L. Elmufdi, R. Palaparthi, Proc. 10th CAMP <strong>CMP</strong> Symposium, Lake Placid,NY, August 14-17, 2005.[17] K. L. Johnson, Contact Mechanics, Cambridge U. Press, 1985.[18] B.J. Hamrock and D. Dowson, Trans. ASME J. Lubrication Technology, 100, 236-245 (1978).[19] L. Borucki, L. Charns and A. Philipossian, J. <strong>of</strong> <strong>the</strong> Electrochemical Soc., 151(12), G809 (2004).[20] Z. Li, doctoral dissertation, <strong>the</strong> University <strong>of</strong> Arizona, Tucson, AZ, 2005.[21] P.A. Thompson, G.S. Grest and M.O. Robb<strong>in</strong>s, “Phase Transitions and Universal Dynamics <strong>in</strong>Conf<strong>in</strong>ed Films,” Phys. Rev. Lett. 68, 3448-3451 (1992).

FiguresFigure 1: High accuracy fit <strong>of</strong> a model to<strong>the</strong>rmal oxide polish<strong>in</strong>g data (RMS error52 A/m<strong>in</strong>) [3].Figure 2: <strong>Coefficient</strong> <strong>of</strong> friction vs. padflatness ratio (PFR) [10].Figure 3: Cross section <strong>of</strong> a lubricatedelastic l<strong>in</strong>e contact at steady state [15].Figure 4: Computed viscous contributionto <strong>the</strong> COF as a function <strong>of</strong> E and R.Figure 5: Correlation <strong>of</strong> COF withtemperature <strong>in</strong> an ILD polish<strong>in</strong>gexperiment [19].Figure 6: Variation <strong>of</strong> COF with velocity<strong>in</strong> a copper polish<strong>in</strong>g experiment [20].experiment [19].

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