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RESEARCH PAPERS

Revisiting the Removal Rate Model for Oxide CMP

[+] Author and Article Information
Jamshid Sorooshian

Department of Chemical and Environmental Engineering, University of Arizona, Tucson, Arizona 85721

Leonard Borucki

Intelligent Planar, 3831 East Ivy Street, Mesa, Arizona 85205

David Stein, Robert Timon, Dale Hetherington

Sandia National Laboratories, MS 1084, Albuquerque, New Mexico 87185

Ara Philipossian

Department of Chemical and Environmental Engineering, University of Arizona, Tuscon, Arizona 85721

J. Tribol 127(3), 639-651 (Jun 13, 2005) (13 pages) doi:10.1115/1.1866168 History: Received May 14, 2004; Revised January 03, 2005; Online June 13, 2005
Copyright © 2005 by ASME
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References

Preston,  F., 1927, “The Theory and Design of Plate Glass Polishing Machines,” J. Soc. Glass Technol., 11, pp. 214–256.
Cook,  L. M., 1990, “Chemical Processes in Glass Polishing,” J. Non-Cryst. Solids, 120, pp. 152–170.
Tomozawa,  M., 1997, “Oxide CMP Mechanisms,” Solid State Technol., pp. 169–175.
Zhang,  F., and Busnaina,  A., 1998, “The Role of Particle Adhesion and Surface Deformation in Chemical Mechanical Polishing Processes,” Electrochem. Solid-State Lett., 1, pp. 184–187.
Tseng,  W., and Wang,  Y., 1997, “Re-Examination of Pressure and Speed Dependencies of Removal Rate During Chemical Mechanical Polishing Processes,” J. Electrochem. Soc., 144, pp. L15–L17.
Shi,  F., and Zhao,  B., 1998, “Modeling of Chemical Mechanical Polishing With Soft Pads,” Appl. Phys. A: Mater. Sci. Process., 67, pp. 249–252.
Zhao,  B., and Shi,  F., 1999, “Chemical Mechanical Polishing—Threshold Pressure and Mechanism,” Electrochem. Solid-State Lett., 2, pp. 145–147.
Zhao, B., and Shi, F., 1999, “Chemical Mechanical Polishing in IC Processes: New Fundamental Insights,” Proc. of 4th CMP-MIC, Santa Clara, CA, pp. 13–22.
Stein, D., and Hetherington, D., 2002, “Review and Experimental Analysis of Oxide CMP Models,” Chemical Mechanical Planarization in IC Device Manufacturing III, R. Opila et al., eds., The Electrochemical Society Proceedings Series, Pennington, NJ, PV 99-37 , pp. 217–233.
Borst,  C., Thakurta,  D., Gill,  W., and Gutmann,  R., 2002, “Surface Kinetics Model for SiLK Chemical Mechanical Polishing,” J. Electrochem. Soc., 149, pp. G118–G127.
Borst, C., Thakurta, D., Gill, W., and Gutmann, R., 2002, Chemical-Mechanical Polishing of Low Dielectric Constant Polymers and Organosilicate Glasses, Kluwer Academic, Boston, MA.
Patrick,  W. J., Guthrie,  W. L., Standley,  C. L., and Schiable,  P. M., 1991, “Applications of Chemical Mechanical Polishing to the Fabrication of VLSI Circuit Interconnections,” J. Electrochem. Soc., 138, p. 1778.
Sorooshian,  J., DeNardis,  D., Charns,  L., Li,  Z., Shadman,  F., Boning,  D., Hetherington,  D., and Philipossian,  A., 2004, “Arrhenius Characterization of ILD and Copper CMP Processes,” J. Electrochem. Soc., 151, pp. G85–G88.
Lim,  S. C., and Ashby,  M. F., 1987, “Wear Mechanism Maps,” Acta Metall., 35, pp. 1–24.
Williams,  J. A., 1999, “Wear Modeling: Analytical, Computational and Mapping: A Continuum Mechanics Approach,” Wear, 225–229, pp. 1–17.
Lefevre, P., Rader, W. S., Van Calcer, P., Poutasse, C., Ina, K., Sakai, K., and Tamai, K., 2002, “Fujimi Planarite First Slurry for a Three Slurries Low K CMP Process,” Proc. 7th International Symposium on Chemical-Mechanical Planarization (CAMP), Lake Placid, NY.
Borucki, L., Jindal, A., Cale, T., Gutmann, R., Tichy, J., Ng, S. H., and Danyluk, S., 2004, “Experimental and Theoretical Analysis of Non-Rotating Copper Wafer Polishing,” Proc. of 9th CMP-MIC, Marina Del Ray, CA, pp. 106–113.
Press, W. H., Teulkolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in C, 2nd ed., Cambridge University Press, New York.
Cowan, R. S., and Winer, W. O., ASM Handbook: Vol. 18 Friction, Lubrication and Wear Technology, ASM International, OH.
Borucki, L., Ng, S.-H., and Danyluk, D., 2004, “Fluid Pressures and Pad Topograpy in Chemical-Mechanical Polishing,” submitted to ASME J. Tribology.
Elmufdi, C. L., Paesano, A., Muldowney, G. P., and James, D. B., 2004, “Solid Mechanics of Grooved CMP Pads: Modeling and Experiments,” Proc. 9th International Symposium on Chemical-Mechanical Planarization (CAMP), Lake Placid, NY, 8–11 August.
Shan, L., 2000, “Mechanical Interactions at the Interface of Chemical Mechanical Polishing,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.

Figures

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Thermal silicon dioxide removal rate data from Stein and Hetherington 9 grouped by pad-wafer rotation rate. The circled region contains four replicates, three of which are indistinguishable.
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Room temperature removal rates for thermal oxide (a) and PE-TEOS (b). Note the accuracy in measurement replication.
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Lim-Ashby contour plot of the PE-TEOS removal rates in Fig. 2(b). The contour interval is 500 Å/min. The gray lines show a triangulation of the individual (p,V) pairs used in the experiment in Fig. 2(b). The triangles are used for linear interpolation of the measured rates.
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PE-TEOS removal rate as a function of pV and platen temperature set point. Data were not obtained at 41 and 52 kW/m2 at a platen set point of 13°C.
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PE-TEOS removal rates (see Fig. 4) versus the inverse of the mean pad temperature (i.e., the average recorded IR pad temperature over the entire duration of a polish) rather than the platen set point. Data are separated by pV. Adjacent pairs of points at each pV are replicates.
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Thermal silicon dioxide removal rate as a function of pV and platen temperature set point. Data were not obtained at 41 and 52 kW/m2 for a platen set point of 13°C.
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(a) Least squares fitting error of the augmented Langmuir-Hinshelwood model to the PE-TEOS data in Fig. 2. (b) The temperature model velocity exponent, a.
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(a) The mechanical removal rate coefficient cp and (b) the reaction rate preexponential A of the model in this work
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Comparison of the model with PE-TEOS data at different platen temperatures using E from polishing condition pV3 (∼31 kW/m2 ). Only means of data replicates are shown for clarity.
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(a) Plot of the model estimate of the ratio k1/k2 of the chemical rate to the mechanical rate as a function of E for each pV condition used in the PE-TEOS data in Fig. 2(b). (b) Plot of the measured and calculated apparent activation energies for the PE-TEOS data from Fig. 5 as a function of the mean of the ratio k1/k2 at each pV condition.
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(a) The temperature increase proportionality constant β and (b) the required reaction temperature rise for the six pV conditions in the PE-TEOS data
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Comparison of the fit of the model of Eqs. (7) and (8) with room temperature PE-TEOS data at the largest and smallest values of E considered
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Map of the ratio of chemical rate k1 to mechanical rate k2 derived from the best fit of the Langmuir-Hinshelwood model to the data from 9 [see Figs. 14 and 15(a)]. Material removal is severely mechanically limited in the upper left hand corner of the map. Toward the right side of the map, chemical and mechanical rates are more equally balanced.
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Apparent pressure threshold behavior at constant V and sublinear velocity behavior at constant p in the PE-TEOS data from Fig. 2(b) compared with extrapolations from the current model. The upper model extrapolation is performed at constant pressure (7 PSI) and variable speed. The lower model extrapolation is at constant speed (90 RPM) and variable pressure. The isolated point at pV∼44 kW/m2 (6 PSI, 60 RMP) lies on neither extrapolation because the removal rate depends on p and V individually rather than just on the product pV. At any fixed pV, a range of rates is possible.
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(a) Coordinate system and notation used in the flash-heating model in Appendix A. (b) Polishing pad scanning profilometry data showing evidence of an exponential right hand tail 20.
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Preston plot of thermal oxide polishing data from 9 (open circles and squares). A theoretical fit to the data with the current model is also shown (solid triangles). See also Table 1. The fit was performed using a randomly selected subset of the data (circles)—the match with the remaining data (squares) provides a measure of predictive capability.
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(a) Lim-Ashby plot of the thermal oxide polishing data in Fig. 14. The gray lines show a triangulation of the individual (p,V) pairs used in the experiment in Fig. 14. (b) Lim-Ashby wear plot showing how the data from (a) would have looked had the removal rate been perfectly Prestonian (i.e., if all points had been on the regression line with no scatter). The contour lines are linear approximations to hyperbolic arcs of the form pV=const. The triangles are used for linear interpolation of the measured rates. Contour interval: 500 Å/min.
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Comparison of the model in this work (solid symbols) with thermal oxide removal rate data at different platen temperature set points (see Fig. 6) using the activation energy at the most thermally limited condition (pV3)
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(a) Pad heat partition factors as a function of sliding velocity and asperity contact dimension. (b) Pad heat partition factor proportionality constant and velocity exponent.

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