Revisiting the Removal Rate Model for Oxide CMP

Jamshid Sorooshian; Leonard Borucki; David Stein; Robert Timon; Dale Hetherington; Ara Philipossian

doi:10.1115/1.1866168

Journal of Tribology | Volume 127 | Issue 3 | Research Paper

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RESEARCH PAPERS

Revisiting the Removal Rate Model for Oxide CMP

Jamshid Sorooshian, Leonard Borucki, David Stein, Robert Timon, Dale Hetherington and Ara Philipossian

[+] 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

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Figures

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.

View Large | Save Figure | Download Slide (.ppt)

(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 c_p and (b) the reaction rate preexponential A of the model in this work

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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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(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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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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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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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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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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(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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Sorooshian J, Borucki L, Stein D, Timon R, Hetherington D, Philipossian A. Revisiting the Removal Rate Model for Oxide CMP. ASME. J. Tribol. 2005;127(3):639-651. doi:10.1115/1.1866168.

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Revisiting the Removal Rate Model for Oxide CMP

References

Figures

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.

Room temperature removal rates for thermal oxide (a) and PE-TEOS (b). Note the accuracy in measurement replication.

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.

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.

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.

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.

(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.

(a) The mechanical removal rate coefficient c_p and (b) the reaction rate preexponential A of the model in this work

(a) The temperature increase proportionality constant β and (b) the required reaction temperature rise for the six pV conditions in the PE-TEOS data

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

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.

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)

(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.

(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.

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

Revisiting the Removal Rate Model for Oxide CMP

References

Figures

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.

Room temperature removal rates for thermal oxide (a) and PE-TEOS (b). Note the accuracy in measurement replication.

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.

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.

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.

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.

(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.

(a) The mechanical removal rate coefficient cp and (b) the reaction rate preexponential A of the model in this work

(a) The temperature increase proportionality constant β and (b) the required reaction temperature rise for the six pV conditions in the PE-TEOS data

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

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.

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)

(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.

(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.

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

(a) The mechanical removal rate coefficient c_p and (b) the reaction rate preexponential A of the model in this work