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Feature-Scale Simulations of Particulate Slurry Flows in Chemical Mechanical Polishing by Smoothed Particle Hydrodynamics

Published online by Cambridge University Press:  03 June 2015

Dong Wang ,
Sihong Shao ,
Changhao Yan ,
Wei Cai  and
Xuan Zeng
Dong Wang
Affiliation:
State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China
Sihong Shao*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
Changhao Yan
Affiliation:
State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China
Wei Cai
Affiliation:
State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Xuan Zeng*
Affiliation:
State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China
*
Corresponding author.Email:[email protected]
Corresponding author.Email:[email protected]
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Abstract

In this paper, the mechanisms of material removal in chemical mechanical polishing (CMP) processes are investigated in detail by the smoothed particle hydrodynamics (SPH) method. The feature-scale behaviours of slurry flow, rough pad, wafer defects, moving solid boundaries, slurry-abrasive interactions, and abrasive collisions are modelled and simulated. Compared with previous work on CMP simulations, our simulations incorporate more realistic physical aspects of the CMP process, especially the effect of abrasive concentration in the slurry flows. The preliminary results on slurry flow in CMP provide microscopic insights on the experimental data of the relation between the removal rate and abrasive concentration and demonstrate that SPH is a suitable method for the research of CMP processes.

Keywords

76M2874F1070E1835Q30Chemical mechanical polishingsmoothed particle hydrodynamicsparticulate flowrough padwafer defectsabrasive concentration
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 5 , November 2014 , pp. 1389 - 1418
Copyright
Copyright © Global Science Press Limited 2014

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References

[1]Zantye, P. B., Kumar, A., Sikder, A. K., Chemical mechanical planarization for microelectronics applications, Mat. Sci. Eng. R 45 (2004) 89–220.Google Scholar
[2]Bielmann, M., Mahajan, U., Singh, R. K., Effect of particle size during tungsten chemical mechanical polishing, Electrochem. Solid State Lett. 2 (8) (1999) 401–403.Google Scholar
[3]Basim, G. B., Adler, J. J., Mahajan, U., Singh, R. K., Moudgil, B. M., Effect of particle size of chemical mechanical polishing slurries for enhanced polishing with minimal defects, J. Elec-trochem. Soc. 147 (9) (2000) 3523–3528.Google Scholar
[4]Zhou, C., Shan, L., Hight, J. R., Danyluk, S., Ng, S. H., Paszkowskic, A. J., Influence of colloidal abrasive size on material removal rate and surface finish in SiO2 chemical mechanical polishing, Tribol. Trans. 45 (2) (2002) 232–238.Google Scholar
[5]Matijević, E., Babu, S. V., Colloid aspects of chemical-mechanical planarization, J. Colloid Interface Sci. 320 (2008) 219–237.Google Scholar
[6]Preston, F. W., The theory and design of plate glass polishing machines, J. Soc. Glass Technol. 11 (1927) 214–257.Google Scholar
[7]Runnels, S. R., Eyman, L. M., Tribology analysis of chemical-mechanical polishing, J. Electrochem. Soc. 141 (6) (1994) 1698–1701.Google Scholar
[8]Tichy, J., Levert, J. A., Shan, L., Danyluk, S., Contact mechanics and lubrication hydrodynamics of chemical mechanical polishing, J. Electrochem. Soc. 146 (4) (1999) 1523–1528.Google Scholar
[9]Sundararajan, S., Thakurta, D. G., Schwendeman, D. W., Murarka, S. P., Gill, W. N., Two-dimensional wafer-scale chemical mechanical planarization models based on lubrication theory and mass transport, J. Electrochem. Soc. 146 (2) (1999) 761–766.Google Scholar
[10]Runnels, S. R., Freature-scale fluid-based erosion modeling for chemical-mechanical polish-ing, J. Electrochem. Soc. 141 (7) (1994) 1900–1904.CrossRefGoogle Scholar
[11] C.-Yao, H., Feke, D. L., Robinson, K. M., Meikle, S., Contact mechanics and lubrication hydrodynamics of chemical mechanical polishing, J. Electrochem. Soc. 147 (4) (2000) 1502–1512.Google Scholar
[12]Arbelaez, D., Zohdi, T. I., Dornfeld, D. A., Modeling and simulation of material removal with particulate flows, Comput. Mech. 42 (5) (2008) 749–759.Google Scholar
[13]Zhou, C., Shan, L., Hight, J. R., Ng, S. H., Danyluk, S., Fluid pressure and its effects on chemical mechanical polishing, Wear 253 (2002) 430–437.Google Scholar
[14]Mueller, N., Rogers, C., Manno, V. P., White, R., Moinpour, M., In situ investigation of slurry flow fields during CMP, J. Electrochem. Soc. 156 (12) (2009) H908–H912.Google Scholar
[15]Zhao, D., He, Y., Lu, X., In situ measurement of fluid pressure at the wafer-pad interface during chemical mechanical polishing of 12-inch wafer, J. Electrochem. Soc. 159 (1) (2012) H22–H28.Google Scholar
[16]Terrell, E. J., Higgs III, C. F., Hydrodynamics of slurry flow in chemical mechanical polishing, J. Electrochem. Soc. 153 (6) (2006) K15–K22.Google Scholar
[17]Park, S.-S., Cho, C.-H., Ahn, Y., Hydrodynamic analysis of chemical mechanical polishing process, Tribol. Int. 33 (2000) 723–730.Google Scholar
[18]Ng, S. H., Measurement and Modeling of Fluid Pressures in Chemical Mechanical Polishing, Ph.D. thesis, Georgia Institute of Technology (2005).Google Scholar
[19]Cooper, K., Cooper, J., Groschopf, J., Flake, J., Solomentsev, Y., Farkas, J., Effects of particle concentration on chemical mechanical planarization, Electrochem. Solid State Lett. 5 (12) (2002) G109–G112.Google Scholar
[20]Tamboli, D., Banerjee, G., Waddell, M., Novel interpretations of CMP removal rate depen-dencies on slurry particle size and concentration, Electrochem. Solid State Lett. 7 (10) (2004) F62–F65.Google Scholar
[21]Zhang, Z., Liu, W., Song, Z., Effect of abrasive particle concentration on preliminary chemical mechanical polishing of glass substrate, Microelectron. Eng. 87 (2010) 2168–2172.Google Scholar
[22]Paul, E., A model of chemical mechanical polishing, J. Electrochem. Soc. 148 (6) (2001) G355– G358.Google Scholar
[23]Jeng, Y.-R., Huang, P.-Y., A material removal rate model considering interfacial micro-contact wear behaviour for chemical mechanical polishing, J. Tribol.-Trans. ASME 127 (2005) 190–197.Google Scholar
[24]Wang, Y., Zhao, Y., An, W., Ni, Z., Wang, J., Modeling effects of abrasive particle size and concentration on material removal at molecular scale in chemical mechanical polishing, Appl. Surf. Sci. 257 (2010) 249–253.Google Scholar
[25]Ye, Y. Y., Biswas, R., Morris, J. R., Bastawros, A., Chandra, A., Molecular dynamics simulation of nanoscale machining of copper, Nanotechnology 14 (10) (2003) 390–396.Google Scholar
[26]Chagarov, E., Adams, J. B., Molecular dynamics simulations of mechanical deformation of amorphous silicon dioxide during chemical-mechanical polishing, J. Appl. Phys. 94 (6) (2003) 3853–3861.Google Scholar
[27]Agrawal, P. M., Raff, L. M., Bukkapatnam, S., Komanduri, R., Molecular dynamics investigations on polishing of a silicon wafer with a diamond abrasive, Appl. Phys. A-Mater. Sci. Process. 100 (1) (2010) 89–104.Google Scholar
[28]Lucy, L. B., A numerical approach to the testing of the fission hypothesis, Astron. J. 82 (12) (1977) 1013–1024.Google Scholar
[29]Gingold, R. A., Monaghan, J. J., Smoothed particle hydrodynamics: Theory and application to non-spherical stars, Mon. Not. Roy. Astron. Soc. 181 (1977) 375–389.Google Scholar
[30]Monaghan, J. J., Smoothed particle hydrodynamics and its diverse applications, Annu. Rev. Fluid Mech. 44 (1) (2012) 323–346.Google Scholar
[31]Takano, K., Yamada, K., Takezawa, N., Suzuki, T., Inamura, T., SPH-based flow simulation of polishing slurry including polished debris in CMP, J. Jpn. Soc. Precis. Eng. 73 (1) (2007) 90–95, in Japanese.Google Scholar
[32]Adami, S., Hu, X. Y., Adams, N. A., A generalized wall boundary condition for smoothed particle hydrodynamics, J. Comput. Phys. 231 (2012) 7057–7075.Google Scholar
[33]Wang, D., Zhou, Y. S., Shao, S. H., Effcient implementation of smoothed particle hydrodynamics (SPH) with plane sweep algorithm, preprint (2013).Google Scholar
[34]Liu, G. R., Liu, M. B., Smoothed Particle Hydrodynamics: A Meshfree Particle Method, World Scientific Publishing Co. Pte. Ltd., Singapore, 2003.Google Scholar
[35]Dehnen, W., Aly, H., Improving convergence in smoothed particle hydrodynamics simulations without pairing instability, Mon. Not. Roy. Astron. Soc. 425 (2) (2012) 1068–1082.Google Scholar
[36]Morris, J. P., Fox, P. J., Zhu, Y., Modeling low Reynolds number incompressible flows using SPH, J. Comput. Phys. 136 (1997) 214–226.Google Scholar
[37]Monaghan, J. J., Smoothed particle hydrodynamics, Rep. Prog. Phys. 68 (8) (2005) 1703–1759.Google Scholar
[38]Price, D. J., Smoothed particle hydrodynamics and magnetohydrodynamics, J. Comput. Phys. 231 (2012) 759–794.Google Scholar
[39]Hu, X. Y., Adams, N. A., A multi-phase SPH method for macroscopic and mesoscopic flows, J. Comput. Phys. 213 (2006) 844–861.Google Scholar
[40]Marrone, S., Antuono, M., Colagrossi, A., Colicchio, G., Touzé, D. Le, Grazianni, G., ¿-SPH model for simulating violent impact flows, Comput. Methods Appl. Mech. Engrg. 200 (2011) 1526–1542.Google Scholar
[41]Monaghan, J. J., Simulating free surface flows with SPH, J. Comput. Phys. 110 (1994) 399–406.Google Scholar
[42]Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.Google Scholar
[43]Monaghan, J. J., SPH without a tensile instability, J. Comput. Phys. 159 (2) (2000) 290–311.Google Scholar
[44]Adami, S., Hu, X. Y., Adams, N. A., A transport-velocity formulation for smoothed particle hydrodynamics, J. Comput. Phys. 241 (2013) 292–307.Google Scholar
[45]Molteni, D., Colagrossi, A., A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH, Comput. Phys. Commun. 180 (6) (2009) 861–872.Google Scholar
[46]Bonet, J., Lok, T.-S., Variational and momentum preservation aspects of smooth particle hydrodynamic formulations, Comput. Methods Appl. Mech. Engrg. 180 (1999) 97–115.Google Scholar
[47]Lu, J., Rogers, C., Manno, V. P., Philipossian, A., Anjur, S., Moinpour, M., Measurements of slurry film thickness and wafer drag during CMP, J. Electrochem. Soc. 151 (4) (2004) G241–G247.Google Scholar
[48]Lortz, W., Menzel, F., Brandes, R., Klaessig, F., Knothe, T., Shibasaki, T., News from the M in CMP-viscosity of CMP slurries, a constant?, MRS Proc. 767 (2003) 47–56.Google Scholar
[49]Fan, X.-J., Tanner, R. I., Zheng, R., Smoothed particle hydrodynamics simulation of non-Newtonian moulding flow, J. Non-Newton. Fluid Mech. 165 (2010) 219–226.Google Scholar
[50]Monaghan, J. J., Kos, A., Issa, N., Fluid motion generated by impact, J. Waterw. Port Coast. Ocean Eng.-ASCE 129 (6) (2003) 250–260.Google Scholar
[51]Bouscasse, B., Colagrossi, A., Marrone, S., Antuono, M., Nonlinear water wave interaction with floating bodies in SPH, J. Fluids Struct. 42 (2013) 112–129.Google Scholar
[52]Glowinski, R., Pan, T. W., Hesla, T. I., Joseph, D. D., Periaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow, J. Comput. Phys. 169 (2001) 363–426.Google Scholar
[53]Monaghan, J. J., Particle methods for hydrodynamics, Comput. Phys. Rep. 3 (2) (1985) 71124.Google Scholar
[54]Hernquist, L., Katz, N., TreeSPH: A unification of SPH with the hierarchical tree method, Astrophys. J. Suppl. Ser. 70 (1989) 419–446.Google Scholar
[55]Courant, R., Friedrichs, K., Lewy, H., On the partial difference equations of mathematical physics, IBM J. Res. Dev. 11 (2) (1967) 215–234.Google Scholar
[56]Monaghan, J. J., Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys. 30 (1992) 543–574.Google Scholar
[57]Kaufman, F. B., Thompson, D. B., Broadie, R. E., Jaso, M. A., Guthrie, W. L., Pearson, D. J., Small, M. B., Chemical-mechanical polishing for fabricating patterned W metal features as chip interconnects, J. Electrochem. Soc. 138 (11) (1991) 3460–3465.Google Scholar
[58]Zhao, Y., Chang, L., Kim, S. H., A mathematical model for chemical-mechanical polishing based on formation and removal of weakly bonded molecular species, Wear 254 (2003) 332–339.Google Scholar
[59]Chang, L., On the CMP material removal at the molecular scale, J. Tribol.-Trans. ASME 129 (2) (2007) 436–437.Google Scholar
[60]Hocheng, H., Tsai, H. Y., Su, Y. T., Modeling and experimental analysis of the material removal rate in the chemical mechanical planarization of dielectric films and bare silicon wafers, J. Electrochem. Soc. 148 (10) (2001) G581–G586.Google Scholar
[61]Xin, J., Cai, W., Tichy, J. A., A fundamental model proposed for material removal in chemical-mechanical polishing, Wear 268 (2010) 837–844.Google Scholar
[62]Feng, C., Yan, C., Tao, J., Zeng, X., Cai, W., A contact-mechanics-based model for general rough pads in chemical mechanical polishing processes, J. Electrochem. Soc. 156 (7) (2009) H601– H611.Google Scholar
[63]Antoci, C., Gallati, M., Sibilla, S., Numerical simulation of fluid-structure interaction by SPH, Comput. Struct. 85 (2007) 879–890.Google Scholar
[64]Hamrock, B. J., Schmid, S. R., Jacobson, B. O., Fundamentals of Fluid Film Lubrication, 2nd Edition, Marcel Dekker, Inc., New York, USA, 2004.Google Scholar
[65]Fortes, A. F., Joseph, D. D., Lundgren, T. S., Nonlinear mechanics of fluidization of beds of spherical particles, J. Fluid Mech. 177 (1987) 467–483.Google Scholar
[66]Hu, H. H., Joseph, D. D., Crochet, M. J., Direct simulation of fluid particle motions, Theor. Comput. Fluid Dyn. 3 (1992) 285–306.Google Scholar
[67]Feng, Z.-G., Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys. 195 (2004) 602–628.Google Scholar
[68]Uhlmann, M., An immersed boundary method with direct forcing for the simulation of par-ticulate flows, J. Comput. Phys. 209 (2005) 448–476.Google Scholar
[69]Qin, K., Multi-scale Modeling of the Slurry Flow and the Material Removal in Chemical Mechanical Polishing, Ph.D. thesis, The University of Florida (2003).Google Scholar
[70]White, R. D., Mueller, A. J., Shin, M., Gauthier, D., Manno, V. P., Rogers, C. B., Measurement of microscale shear forces during chemical mechanical planarization, J. Electrochem. Soc. 158 (10) (2011) H1041–H1051.Google Scholar
[71]Ilie, F., Models of nanoparticles movement, collision, and friction in chemical mechanical polishing (CMP), J. Nanopart. Res. 14 (3) (2012) 752.Google Scholar
[72]Singh, R. K., Lee, S.-M., Choi, K.-S., Bahar Basim, G., Choi, W., Chen, Z., Moudgil, B. M., Funda-mentals of slurry design for CMP of metal and dielectric materials, MRS Bull. 27 (10) (2002) 752–760.Google Scholar