Abstract

I model variations in the profile of a silicon grating consisting of parallel lines or trenches by calculating the reflectance of a superstructure in which the profiles are randomly modulated about the nominal profile. I vary the edge positions, the edge profiles, the line heights, and the trench depths and find that the Stokes reflectance can be modified from its nominal value by a relatively large amount, especially in the case of linewidth variations. I find that the reflected field can be approximated by the mean field reflected by a distribution of periodic gratings and that the field does not represent the field from the average profile. In fitting results to more than one modeled parameter, the changes that are observed can be enough to shift the deduced parameter in some cases by more than the rms variation of that parameter. The diffuse reflectance (the nonspecular diffraction efficiency) is found to increase with the variance of the fluctuations.

© 2007 Optical Society of America

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  1. W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2006 (1)

V. A. Ukraintsev, "A comprehensive test of optical scatterometry readiness for 65nm technology production," in Metrology, Inspection, and Process Control for Microlithography XX, C. N. Archie, ed., Proc. SPIE 6152, 61521G-1 (2006).

2004 (1)

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

2003 (1)

2001 (2)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, "Specular spectroscopic scatterometry," IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

H.-T. Huang, W. Kong, and F. L. Terry, Jr., "Normal-incidence spectroscopic ellipsometry for critical dimension monitoring," Appl. Phys. Lett. 78, 3983-3985 (2001).
[CrossRef]

1998 (2)

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures," Appl. Opt. 37, 5112-5115 (1998).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

1997 (1)

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

1996 (1)

1995 (3)

Bao, J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, "Specular spectroscopic scatterometry," IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Coulombe, S. A.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures," Appl. Opt. 37, 5112-5115 (1998).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

Evans, M. S.

Farmiga, N. O.

Gaylord, T. K.

Grann, E. B.

Hirsh, J. I.

Hosch, J. W.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

Hu, J.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Huang, H.-T.

H.-T. Huang, W. Kong, and F. L. Terry, Jr., "Normal-incidence spectroscopic ellipsometry for critical dimension monitoring," Appl. Phys. Lett. 78, 3983-3985 (2001).
[CrossRef]

Jakatdar, N.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, "Specular spectroscopic scatterometry," IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Kong, W.

H.-T. Huang, W. Kong, and F. L. Terry, Jr., "Normal-incidence spectroscopic ellipsometry for critical dimension monitoring," Appl. Phys. Lett. 78, 3983-3985 (2001).
[CrossRef]

Korlahalli, R.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Lalanne, P.

Liu, W.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Lowe-Webb, R.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Marciante, J. R.

McNeil, J. R.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures," Appl. Opt. 37, 5112-5115 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, "Metrology of subwavelength photoresist gratings using optical scatterometry," J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

Minhas, B. K.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures," Appl. Opt. 37, 5112-5115 (1998).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Mui, D. S. L.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Murnane, M. R.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, "Metrology of subwavelength photoresist gratings using optical scatterometry," J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

Naqvi, H.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

Naqvi, S. S. H.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures," Appl. Opt. 37, 5112-5115 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, "Metrology of subwavelength photoresist gratings using optical scatterometry," J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

Niu, X.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, "Specular spectroscopic scatterometry," IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Pommet, D. A.

Prins, S. L.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

Raymond, C. J.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, "Metrology of subwavelength photoresist gratings using optical scatterometry," J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

Sasano, H.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Shivaprasad, D.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Sohail, S.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

Spanos, C. J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, "Specular spectroscopic scatterometry," IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Ta, H. T.

Terry, F. L.

H.-T. Huang, W. Kong, and F. L. Terry, Jr., "Normal-incidence spectroscopic ellipsometry for critical dimension monitoring," Appl. Phys. Lett. 78, 3983-3985 (2001).
[CrossRef]

Ukraintsev, V. A.

V. A. Ukraintsev, "A comprehensive test of optical scatterometry readiness for 65nm technology production," in Metrology, Inspection, and Process Control for Microlithography XX, C. N. Archie, ed., Proc. SPIE 6152, 61521G-1 (2006).

Yang, W.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H.-T. Huang, W. Kong, and F. L. Terry, Jr., "Normal-incidence spectroscopic ellipsometry for critical dimension monitoring," Appl. Phys. Lett. 78, 3983-3985 (2001).
[CrossRef]

IEEE Trans. Semicond. Manuf. (2)

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. L. Mui, "Line-profile and critical-dimension monitoring using a normal incidence optical CD metrology," IEEE Trans. Semicond. Manuf. 17, 564-572 (2004).
[CrossRef]

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, "Specular spectroscopic scatterometry," IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Vac. Sci. Technol. B (3)

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, "Multiparameter grating metrology using optical scatterometry," J. Vac. Sci. Technol. B 15, 361-368 (1997).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, "Metrology of subwavelength photoresist gratings using optical scatterometry," J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. Sohail, H. Naqvi, and J. R. McNeil, "Scatterometry measurement of sub-0.1μm linewidth gratings," J. Vac. Sci. Technol. B 16, 80-87 (1998).
[CrossRef]

Proc. SPIE (1)

V. A. Ukraintsev, "A comprehensive test of optical scatterometry readiness for 65nm technology production," in Metrology, Inspection, and Process Control for Microlithography XX, C. N. Archie, ed., Proc. SPIE 6152, 61521G-1 (2006).

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Figures (7)

Fig. 1
Fig. 1

Illustration of the four different profile perturbations considered in this study: (a) line edge variation, (b) sidewall roughness, (c) line height variation, and (d) trench depth variation. The gray scale represents the refractive index in the x z plane; the profiles are independent of the y direction. The profiles shown here are exaggerated, having twice the maximum modulation considered in the simulations. In both (a) and (b), the case of random edge variation is shown.

Fig. 2
Fig. 2

Specular reflectance Stokes parameters calculated as functions of rms variation σ for normal incidence and for (open symbols) MC-simulated line edge variation, (solid symbols) MC-simulated sidewall roughness and (curves) the simplified mean-field model. Three cases are shown: (a) random edge variation, (b) linewidth variation, and (c) line position variation. The symbols and curves represent (squares, solid curves) R 0 , (circles, dashed curves) R 1 , (upward triangles, dotted curves) R 2 , and (downward triangles, dash-dot curves) R 3 .

Fig. 3
Fig. 3

Same as Fig. 2, except for an incident angle of 70°.

Fig. 4
Fig. 4

Specular reflectance Stokes parameters calculated as functions of rms variation σ for normal incidence and for (a) line height variation and (b) trench depth variation. The data represent (symbols) the MC simulations and (curves) the simplified mean-field model. The symbols and curves represent (squares, solid curves) R 0 , (circles, dashed curves) R 1 , (upward triangles, dotted curves) R 2 , and (downward triangles, dash-dot curves) R 3 .

Fig. 5
Fig. 5

Same as Fig. 4, except for an incident angle of 70°.

Fig. 6
Fig. 6

Integrated nonspecular diffraction efficiency found from MC simulation for normal incidence as a function of rms variation σ for (open symbols) line edge variation, (solid symbols) sidewall roughness. Three cases are shown: (squares) random edge variation, (circles) linewidth variation, and (triangles) line position variation.

Fig. 7
Fig. 7

Normal incidence Stokes reflectance as a function of wavelength for (symbols) MC-simulated random line edge variation with σ = 10 nm , (solid curve) unperturbed profile, (dashed curve) the mean-field model, and (dotted curve) the result of a best fit to a simple profile with a nonvertical sidewall, as described in the text.

Tables (1)

Tables Icon

Table 1 Average Fraction of Power Diffracted into Different Orders for Normal Illumination Calculated for Line Edge Variation

Equations (10)

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sin θ i = sin θ + i λ Λ 0 ,
Δ x ( z ) = Re 1 π 2 d k d z g ( z ) exp [ i ϕ ( k ) + i k ( z z ) ] ,
g ( z ) = A exp [ ( z τ ) 2 2 ]
A = σ π 1 4 ( L τ ) 1 2 erf ( L 2 τ ) .
R 0 = 1 2 r TE 2 + 1 2 r TM 2 ,
R 1 = 1 2 r TE 2 1 2 r TM 2 ,
R 2 = Re r TE * r TM ,
R 3 = Im r TE * r TM ,
E a = 1 σ a 2 π d a E ( a ) exp [ ( a a 0 ) 2 2 σ a 2 ] ,
E ( h ) = E ( d ) exp ( 2 i k z d ) ,

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