Abstract

Phase-modulation scatterometry is a metrology technique for determining, by means of a phase modulator as a key device, the parameters of gratings. The main source of error to be dealt with are the fluctuations of the phase-modulation amplitude. The grating zeroth-order reflectance modulated by the phase modulator is converted into a signal by the photodetector. The measurables are the direct term and the first two harmonics of the signal. For experimental data fitting, we used the ratio of the harmonics over the direct term because it significantly improves the accuracy. A sensitivity analysis was performed for two samples, one real and one theoretical, to find the measurement configuration that insures optimum determination precision for the grating parameters. For the real sample, comparison of the theoretical predictions for sensitivity with the actual values showed a good agreement. For both samples the sensitivity analysis indicated subnanometric precision for the critical dimension (grating linewidth).

© 2002 Optical Society of America

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References

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  1. J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.
  2. B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
    [CrossRef]
  3. S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
  4. P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).
  5. P. C. Logofatu, Sensitivity Optimized Scatterometry, Ph.D. dissertation (University of New Mexico, Albuquerque, N. Mex., 2000).
  6. P. C. Logofatu, “Sensitivity analysis of grating parameter estimation,” Appl. Opt. 41, 7179–7186 (2002).
    [CrossRef] [PubMed]
  7. S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
    [CrossRef]
  8. O. Acher, E. Bigan, B. Drevillon, “Improvements of phase modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
    [CrossRef]
  9. D. W. Mills, R. L. Allen, W. M. Duncan, “Spectral ellipsometry on patterned wafers,” in Process, Equipment, and Materials Control in Integrated Circuit Manufacturing, A. G. Sabnis, I. J. Raaijmakers, eds., Proc. SPIE2637, 194–203 (1995).
  10. M. G. Moharram, E. B. Grann, D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  11. M. G. Moharram, D. A. Pommet, E. B. Grann, “Stable implementation of the rigorous coupled-wave theory for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  12. T. C. Oakberg, “Modulated interference effects: use of photoelastic modulators with lasers,” Opt. Eng. 34, 1545–1550 (1995).
    [CrossRef]
  13. R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
    [CrossRef]
  14. S. Wolfram, Mathematica, a System for Doing Mathematics by Computer (Addison-Wesley, Reading, Mass., 1992).

2002 (1)

1998 (1)

1995 (3)

1989 (1)

O. Acher, E. Bigan, B. Drevillon, “Improvements of phase modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

1972 (1)

1969 (1)

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Acher, O.

O. Acher, E. Bigan, B. Drevillon, “Improvements of phase modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Allen, R. L.

D. W. Mills, R. L. Allen, W. M. Duncan, “Spectral ellipsometry on patterned wafers,” in Process, Equipment, and Materials Control in Integrated Circuit Manufacturing, A. G. Sabnis, I. J. Raaijmakers, eds., Proc. SPIE2637, 194–203 (1995).

Azzam, R. M. A.

Bashara, N. M.

Bigan, E.

O. Acher, E. Bigan, B. Drevillon, “Improvements of phase modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Coulombe, S. A.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, 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, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).

Drevillon, B.

O. Acher, E. Bigan, B. Drevillon, “Improvements of phase modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Duncan, W. M.

D. W. Mills, R. L. Allen, W. M. Duncan, “Spectral ellipsometry on patterned wafers,” in Process, Equipment, and Materials Control in Integrated Circuit Manufacturing, A. G. Sabnis, I. J. Raaijmakers, eds., Proc. SPIE2637, 194–203 (1995).

Gaspar, S. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.

Grann, E. B.

Hickman, K. C.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.

Jasperson, S. N.

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Logofatu, P. C.

P. C. Logofatu, “Sensitivity analysis of grating parameter estimation,” Appl. Opt. 41, 7179–7186 (2002).
[CrossRef] [PubMed]

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).

P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).

P. C. Logofatu, Sensitivity Optimized Scatterometry, Ph.D. dissertation (University of New Mexico, Albuquerque, N. Mex., 2000).

McNeil, J. R.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, 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, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).

P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.

Mills, D. W.

D. W. Mills, R. L. Allen, W. M. Duncan, “Spectral ellipsometry on patterned wafers,” in Process, Equipment, and Materials Control in Integrated Circuit Manufacturing, A. G. Sabnis, I. J. Raaijmakers, eds., Proc. SPIE2637, 194–203 (1995).

Minhas, B. K.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, 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, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).

Moharram, M. G.

Naqvi, S. S. H.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, 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, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.

Oakberg, T. C.

T. C. Oakberg, “Modulated interference effects: use of photoelastic modulators with lasers,” Opt. Eng. 34, 1545–1550 (1995).
[CrossRef]

Pommet, D. A.

Schnatterly, S. E.

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Wilson, S. R.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.

Wolfram, S.

S. Wolfram, Mathematica, a System for Doing Mathematics by Computer (Addison-Wesley, Reading, Mass., 1992).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

T. C. Oakberg, “Modulated interference effects: use of photoelastic modulators with lasers,” Opt. Eng. 34, 1545–1550 (1995).
[CrossRef]

Rev. Sci. Instrum. (2)

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

O. Acher, E. Bigan, B. Drevillon, “Improvements of phase modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Other (6)

D. W. Mills, R. L. Allen, W. M. Duncan, “Spectral ellipsometry on patterned wafers,” in Process, Equipment, and Materials Control in Integrated Circuit Manufacturing, A. G. Sabnis, I. J. Raaijmakers, eds., Proc. SPIE2637, 194–203 (1995).

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric-scatterometry for sub-0.1 mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).

P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).

P. C. Logofatu, Sensitivity Optimized Scatterometry, Ph.D. dissertation (University of New Mexico, Albuquerque, N. Mex., 2000).

S. Wolfram, Mathematica, a System for Doing Mathematics by Computer (Addison-Wesley, Reading, Mass., 1992).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. R. Brundle, C. A. Evans, S. Wilson, eds. (Manning, Boston, Mass., 1992), pp. 711–722.

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Figures (5)

Fig. 1
Fig. 1

Experimental arrangement of the phase-modulator scatterometer.

Fig. 2
Fig. 2

Empirical error function for the phase-modulator scatterometer. (a) I 0: σ2= 10-6 + 3.2 × 10-4 I 0, (b) I s : σ2 = 10-6 + 2.0 × 10-4 I s , (c) I c : σ2 = 10-6 + 1.4 × 10-4 I c . The measurements were performed with the XL6 sample at ϕ = 0° and λ = 632.8 nm.

Fig. 3
Fig. 3

Example of fitting data from the phase-modulator scatterometer for sample XL6 at ϕ = 90° and λ = 632.8 nm. The results of the fitting were lw = 1493.1 ± 1.2 Å, h g = 5568.4 ± 3.3 Å, and h 1 = 1604.3 ± 1.9 Å.

Fig. 4
Fig. 4

Sensitivity map from the SAF scan for the phase-modulator scatterometer, sample XL6, at λ = 632.8 nm. Here the color code is as follows: white means large σ (bad sensitivity), black means small σ (good sensitivity).

Fig. 5
Fig. 5

Sensitivity map from the SAF scan for the phase-modulator scatterometer, sample P200, at λ = 632.8 nm. The color code is the same as in Fig. 4.

Tables (2)

Tables Icon

Table 1 Numerical Results of the Sensitivity Analysis of Sample XL6a

Tables Icon

Table 2 Numerical Results of the Sensitivity Analysis of Sample P200a

Equations (18)

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

Eout=ÂrˆMˆPˆEin,
Â= cos2 Acos A sin Asin A cos Asin2 A,
rˆ=rpprpsrsprss,
Mˆ=cos M-sin Msin Mcos M exp-jδt001×cos Msin M-sin Mcos M,
δt= A sinωt,
r=Eout/EP= =cosP-MrP cos M+rs sin M+sin P-M-rP sin M+rs cos Mexp-jδt,
rp=rpp cos A+rsp sin A,
rs=rps cos A+rss sin A,
Eout=EoutcosAsinA,
EP=Epin cos P+Esin sin P cosPsinP =EPcosPsinP.
It=I0+Is sin δt+Ic cos δt,
I0=|rp|2+|rs|2+cos 2P-Mcos 2M|rp|2-|rs|2+2 sin 2M Rerprs*,
Is=2 sin 2P-MImrprs*,
Ic=sin 2P-M-sin 2M|rp|2-|rs|2+2 cos 2M Rerprs*.
S0SωS2ω=10J0A02J1A0002J2A I0IsIc.
Rω=Sω2J1A0S0,
R2ω=S2ω2J2A0S0.
σ2=10-6+5.0×10-4I2.

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