Abstract

Silica nanospheres with diameters ranging from 60 nm to 269 nm are investigated as an alternative to polystyrene spheres for calibrating laser-scattering-based wafer surface inspection systems, since they are less susceptible to changes upon ultraviolet exposure. Polystyrene and silica spheres were classified by differential mobility analysis before being deposited onto bare silicon wafers, and scattered signals were measured by two commercial tools using 488 nm and 355 nm laser light. The instrument signals were modeled by integrating a theoretically-determined differential cross section over the collection geometry of each tool, and the predicted signals were compared to the measured signals. The resulting calibrations, whether performed using the polystyrene spheres, the silica spheres, or both, were found to be equivalent and to meet industry requirements, provided the index of refraction of the silica spheres was allowed to be a floating parameter. The indices were found to be 1.413 and 1.421 at 488 nm and 355 nm, respectively, consistent with a void fraction of 11.4%.

© 2008 Optical Society of America

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References

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  1. E. Marx and G. W. Mulholland, "Size and refractive index determination of single polystyrene spheres," J. Res. Natl. Bur. Stand. 88, 321-338 (1983).
  2. G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).
  3. G. W. Mulholland, N. P. Bryner, and C. Croarkin, "Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis," Aerosol Sci. and Technol. 31, 39-55 (1999).
    [CrossRef]
  4. SEMI Standard M53, "Practice for Calibrating Scanning Surface Inspection Systems using Certified Depositions of Monodisperse Polystyrene Latex Spheres on Unpatterned Semiconductor Wafer Surfaces," available from Semiconductor Equipment and Materials International, 3081 Zanker Road, San Jose, CA 95134, http://www.semi.org.
  5. P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica 137A, 209-242 (1986).
  6. P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica 137A, 243-257 (1986).
  7. T. A. Germer, "Modeled Integrated Scatter Tool (MIST)," available from http://physics.nist.gov/scatmech.
  8. T. A. Germer, "SCATMECH: Polarized Light Scattering C++ Class Library," available from http://physics.nist.gov/scatmech.
  9. J. H Kim, G. W. Mulholland, S. H. Ehrman, and T. A. Germer, "Polarized light scattering from dielectric and metallic spheres on silicon wafers," Appl. Opt. 41, 5405-5412 (2002).
    [CrossRef] [PubMed]
  10. J. H. Kim, S. H. Ehrman, G. W. Mulholland, and T. A. Germer, "Polarized light scattering by dielectric and metallic spheres on oxidized silicon surfaces," Appl. Opt. 43, 585-591 (2004).
    [CrossRef] [PubMed]
  11. J. H. Kim, S. H. Ehrman, and T. A. Germer, "Influence of particle oxide coating on light scattering by submicron metal particles on silicon wafers," Appl. Phys. Lett. 84, 1278-1280 (2004).
    [CrossRef]
  12. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
    [CrossRef]
  13. Styrene, Its Polymers , Copolymers, and Derivatives, R. H. Boundy and R. F. Boyer, eds., (Reinhold, New York, 1952).
  14. E. D. Palik, Handbook of Optical Constants of Solids, (Academic, San Diego, 1985).
  15. E. O. Knutson and K. T. Whitby, "Aerosol classification by electric mobility: apparatus, theory, and applications," J. Aerosol Sci. 6, 443-451 (1975).
    [CrossRef]
  16. P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).
  17. Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.
  18. SEMI Standard M52, "Guide for Specifying Scanning Surface Inspection Systems for Silicon Wafers for the 130 nm, 90 nm, 65 nm, and 45 nm Technology Generations," available from Semiconductor Equipment and Materials International, 3081 Zanker Road, San Jose, CA 95134, http://www.semi.org.
  19. H. G. TompkinsA User’s Guide to Ellipsometry, (Academic, San Diego, 1993).
  20. The uncertainties quoted in this article were obtained by estimating the standard uncertainty u for the measurement and multiplying by a coverage factor of k = 2. These values correspond to a confidence level of 95%.

2004 (2)

J. H. Kim, S. H. Ehrman, and T. A. Germer, "Influence of particle oxide coating on light scattering by submicron metal particles on silicon wafers," Appl. Phys. Lett. 84, 1278-1280 (2004).
[CrossRef]

J. H. Kim, S. H. Ehrman, G. W. Mulholland, and T. A. Germer, "Polarized light scattering by dielectric and metallic spheres on oxidized silicon surfaces," Appl. Opt. 43, 585-591 (2004).
[CrossRef] [PubMed]

2002 (1)

1999 (1)

G. W. Mulholland, N. P. Bryner, and C. Croarkin, "Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis," Aerosol Sci. and Technol. 31, 39-55 (1999).
[CrossRef]

1998 (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

1991 (1)

P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).

1986 (2)

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica 137A, 209-242 (1986).

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica 137A, 243-257 (1986).

1985 (1)

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

1983 (1)

E. Marx and G. W. Mulholland, "Size and refractive index determination of single polystyrene spheres," J. Res. Natl. Bur. Stand. 88, 321-338 (1983).

1975 (1)

E. O. Knutson and K. T. Whitby, "Aerosol classification by electric mobility: apparatus, theory, and applications," J. Aerosol Sci. 6, 443-451 (1975).
[CrossRef]

Bobbert, P. A.

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica 137A, 209-242 (1986).

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica 137A, 243-257 (1986).

Bryner, N. P.

G. W. Mulholland, N. P. Bryner, and C. Croarkin, "Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis," Aerosol Sci. and Technol. 31, 39-55 (1999).
[CrossRef]

P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).

Croarkin, C.

G. W. Mulholland, N. P. Bryner, and C. Croarkin, "Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis," Aerosol Sci. and Technol. 31, 39-55 (1999).
[CrossRef]

Ehrman, S. H.

Germer, T. A.

Greef, R.

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica 137A, 243-257 (1986).

Hartman, A. W.

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

Hembree, G. G.

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Johs, B.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Kim, J. H

Kim, J. H.

J. H. Kim, S. H. Ehrman, and T. A. Germer, "Influence of particle oxide coating on light scattering by submicron metal particles on silicon wafers," Appl. Phys. Lett. 84, 1278-1280 (2004).
[CrossRef]

J. H. Kim, S. H. Ehrman, G. W. Mulholland, and T. A. Germer, "Polarized light scattering by dielectric and metallic spheres on oxidized silicon surfaces," Appl. Opt. 43, 585-591 (2004).
[CrossRef] [PubMed]

Kinney, P. D.

P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).

Knutson, E. O.

E. O. Knutson and K. T. Whitby, "Aerosol classification by electric mobility: apparatus, theory, and applications," J. Aerosol Sci. 6, 443-451 (1975).
[CrossRef]

Lettieri, T. R.

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

Marx, E.

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

E. Marx and G. W. Mulholland, "Size and refractive index determination of single polystyrene spheres," J. Res. Natl. Bur. Stand. 88, 321-338 (1983).

McGahan, W. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Mulholland, G. W.

J. H. Kim, S. H. Ehrman, G. W. Mulholland, and T. A. Germer, "Polarized light scattering by dielectric and metallic spheres on oxidized silicon surfaces," Appl. Opt. 43, 585-591 (2004).
[CrossRef] [PubMed]

J. H Kim, G. W. Mulholland, S. H. Ehrman, and T. A. Germer, "Polarized light scattering from dielectric and metallic spheres on silicon wafers," Appl. Opt. 41, 5405-5412 (2002).
[CrossRef] [PubMed]

G. W. Mulholland, N. P. Bryner, and C. Croarkin, "Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis," Aerosol Sci. and Technol. 31, 39-55 (1999).
[CrossRef]

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

E. Marx and G. W. Mulholland, "Size and refractive index determination of single polystyrene spheres," J. Res. Natl. Bur. Stand. 88, 321-338 (1983).

Mulholland, G.W.

P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).

Paulson, W.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Pui, D. Y. H.

P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).

Vlieger, J.

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica 137A, 209-242 (1986).

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica 137A, 243-257 (1986).

Whitby, K. T.

E. O. Knutson and K. T. Whitby, "Aerosol classification by electric mobility: apparatus, theory, and applications," J. Aerosol Sci. 6, 443-451 (1975).
[CrossRef]

Woollam, J. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Aerosol Sci. and Technol. (1)

G. W. Mulholland, N. P. Bryner, and C. Croarkin, "Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis," Aerosol Sci. and Technol. 31, 39-55 (1999).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. H. Kim, S. H. Ehrman, and T. A. Germer, "Influence of particle oxide coating on light scattering by submicron metal particles on silicon wafers," Appl. Phys. Lett. 84, 1278-1280 (2004).
[CrossRef]

J. Aerosol Sci. (1)

E. O. Knutson and K. T. Whitby, "Aerosol classification by electric mobility: apparatus, theory, and applications," J. Aerosol Sci. 6, 443-451 (1975).
[CrossRef]

J. Appl. Phys. (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

J. Res. Natl. Bur. Stand. (2)

E. Marx and G. W. Mulholland, "Size and refractive index determination of single polystyrene spheres," J. Res. Natl. Bur. Stand. 88, 321-338 (1983).

G. W. Mulholland, A. W. Hartman, G. G. Hembree, E. Marx, and T. R. Lettieri, "Development of a onemicrometer-diameter particle size standard reference material," J. Res. Natl. Bur. Stand. 90, 3-26 (1985).

J. Res. Natl. Inst. Stand. Technol. (1)

P. D. Kinney, D. Y. H. Pui, G.W. Mulholland, and N. P. Bryner, "Use of the electrostatic classification method to size 0.1 μm SRM particles-a feasibility study," J. Res. Natl. Inst. Stand. Technol. 96, 147-176 (1991).

Physica (2)

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica 137A, 209-242 (1986).

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica 137A, 243-257 (1986).

Other (9)

T. A. Germer, "Modeled Integrated Scatter Tool (MIST)," available from http://physics.nist.gov/scatmech.

T. A. Germer, "SCATMECH: Polarized Light Scattering C++ Class Library," available from http://physics.nist.gov/scatmech.

SEMI Standard M53, "Practice for Calibrating Scanning Surface Inspection Systems using Certified Depositions of Monodisperse Polystyrene Latex Spheres on Unpatterned Semiconductor Wafer Surfaces," available from Semiconductor Equipment and Materials International, 3081 Zanker Road, San Jose, CA 95134, http://www.semi.org.

Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

SEMI Standard M52, "Guide for Specifying Scanning Surface Inspection Systems for Silicon Wafers for the 130 nm, 90 nm, 65 nm, and 45 nm Technology Generations," available from Semiconductor Equipment and Materials International, 3081 Zanker Road, San Jose, CA 95134, http://www.semi.org.

H. G. TompkinsA User’s Guide to Ellipsometry, (Academic, San Diego, 1993).

The uncertainties quoted in this article were obtained by estimating the standard uncertainty u for the measurement and multiplying by a coverage factor of k = 2. These values correspond to a confidence level of 95%.

Styrene, Its Polymers , Copolymers, and Derivatives, R. H. Boundy and R. F. Boyer, eds., (Reinhold, New York, 1952).

E. D. Palik, Handbook of Optical Constants of Solids, (Academic, San Diego, 1985).

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Figures (4)

Fig. 1.
Fig. 1.

The measured signal as a function of predicted signal measured for PS spheres (solid squares) and silica spheres (open triangles). The index assumed for the silica spheres is that of bulk silica. The straight line is a least-squares best fit of a straight line to the PS sphere data.

Fig. 2.
Fig. 2.

The residual fractional diameter error determined from calibrations at 488 nm. The closed symbols and open symbols represent the fractional residual error for PS and silica particles, respectively. The squares, triangles, and circles represent the results when the system was calibrated with PS, silica, and both particles, respectively.

Fig. 3.
Fig. 3.

Results of applying the calibration to the silica spheres at 488 nm: (open symbols, left scale) the PS-equivalent diameter of the silica particles and (solid symbols, right scale) the ratio of that diameter to the actual diameter.

Fig. 4.
Fig. 4.

The apparent FWHM of the size distribution of the (solid squares) PS and (open triangles) silica particles measured at 488 nm.

Tables (3)

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Table 1. Optical constants used for the modeling.

Tables Icon

Table 2. Particle diameters deposited on wafers.

Tables Icon

Table 3. Summary of the calibration results.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

( D ) = d θ   d ϕ sin θ σ Ω ( θ , ϕ , D ) ,
Δ D i D i = silica 1 { g 1 [ S ( D i ) ] } D i D i
U = 2 [ ( σ + u dep ) ( N M ) ] 1 2 ,
D = PS 1 [ g 1 ( S ) ] .
D = j 1 [ g k 1 ( S ) ] ,
n eff 2 = n h 2 ( 1 2 n h 2 ( x 1 ) + 2 x ) 1 x + n h 2 ( x + 2 ) .
x = 2 n h 4 2 n eff 2 n h 2 + n eff 2 ( n h 2 1 ) ( 2 n h 2 + n eff 2 )

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