Abstract

Spectroscopic ellipsometry is one of the most important measurement schemes used in the optical nano-metrology for not only thin film measurement but also nano pattern 3D structure measurement. In this paper, we propose a novel snap shot phase sensitive normal incidence spectroscopic ellipsometic scheme based on a double-channel spectral carrier frequency concept. The proposed method can provide both Ψ(λ) and Δ(λ) only by using two spectra acquired simultaneously through the double spectroscopic channels. We show that the proposed scheme works well experimentally by measuring a binary grating with nano size 3D structure. We claim that the proposed scheme can provide a snapshot spectroscopic ellipsometric parameter measurement capability with moderate accuracy.

©2011 Optical Society of America

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References

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  1. H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).
    [Crossref]
  2. X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
    [Crossref]
  3. B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000).
    [Crossref]
  4. H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
    [Crossref]
  5. W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. Mui, “Line-profile and critical dimension measurements using a normal incidence optical metrology system ,” in Advanced Semiconductor Manufacturing 2002 IEEE/SEMI Conference and Workshop (IEEE, 2002), pp. 119–124.
  6. A. Sezginer, “Scatterometry by phase sensitive reflectometer,” U.S. Patent no. 6,985,232 B2 (Jan. 10, 2006).
  7. M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
    [Crossref]
  8. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
    [Crossref]
  9. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [Crossref]
  10. Y. Ohtsuka and K. Oka, “Contour mapping of the spatiotemporal state of polarization of light,” Appl. Opt. 33(13), 2633–2636 (1994).
    [Crossref] [PubMed]
  11. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24(5), 291–293 (1999).
    [Crossref] [PubMed]
  12. D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50(19), 3360–3368 (2011).
    [Crossref] [PubMed]
  13. L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24(18), 1314–1316 (1999).
    [Crossref] [PubMed]
  14. D. Kim, S. Kim, H. J. Kong, and Y. Lee, “Measurement of the thickness profile of a transparent thin film deposited upon a pattern structure with an acousto-optic tunablefilter,” Opt. Lett. 27(21), 1893–1895 (2002).
    [Crossref] [PubMed]
  15. K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24(21), 1475–1477 (1999).
    [Crossref] [PubMed]
  16. The Levenberg-Marquardt algorithm is available as lsqnonlin function by a commercial S/W MATLAB.

2011 (1)

2004 (1)

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).
[Crossref]

2002 (1)

2001 (2)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

2000 (1)

B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000).
[Crossref]

1999 (3)

1995 (2)

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
[Crossref]

M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
[Crossref]

1994 (1)

1982 (1)

Abdelsalam, D. G.

Bao, J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Bevilacqua, F.

Cuche, E.

Depeursinge, C.

Gallmann, L.

Gaylord, T. K.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
[Crossref]

M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
[Crossref]

Grann, E.

Grann, E. B.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
[Crossref]

Huang, H.

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).
[Crossref]

H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000).
[Crossref]

Iaconis, C.

Ina, H.

Jakatdar, N.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Kato, T.

Keller, U.

Kim, D.

Kim, S.

Kobayashi, S.

Kong, H. J.

Kong, W.

H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

Lee, Y.

Magnusson, R.

Matuschek, N.

Moharam, M. G.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
[Crossref]

M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
[Crossref]

Niu, X.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Ohtsuka, Y.

Oka, K.

Pommet, D.

Pommet, D. A.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
[Crossref]

Spanos, C. J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Steinmeyer, G.

Stutzman, B. S.

B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000).
[Crossref]

Sutter, D. H.

Takeda, M.

Terry, F. L.

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).
[Crossref]

H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000).
[Crossref]

Walmsley, I. A.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

IEEE Trans. Semicond. Manuf. (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

J. Opt. Soc. Am. (2)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
[Crossref]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1086 (1995).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (1)

B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000).
[Crossref]

Opt. Lett. (4)

Thin Solid Films (1)

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).
[Crossref]

Other (3)

The Levenberg-Marquardt algorithm is available as lsqnonlin function by a commercial S/W MATLAB.

W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. Mui, “Line-profile and critical dimension measurements using a normal incidence optical metrology system ,” in Advanced Semiconductor Manufacturing 2002 IEEE/SEMI Conference and Workshop (IEEE, 2002), pp. 119–124.

A. Sezginer, “Scatterometry by phase sensitive reflectometer,” U.S. Patent no. 6,985,232 B2 (Jan. 10, 2006).

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Figures (9)

Fig. 1
Fig. 1 (a) Specular scatterometry configuration for analyzing periodic binary grating and (b)trapezoidal modeling of nano-pattern grating for the RCWA.

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Fig. 2
Fig. 2 Schematic diagram of the proposed snapshot phase sensitive scatterometric system.

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Fig. 3
Fig. 3 Spectrum intensity data for the (a) TE mode and the (b) TM mode, (c) & (d) are amplitude data in the spectral frequency domain obtained after the FFT for the two spectrum intensity data shown in (a) and (b), respectively.

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Fig. 4
Fig. 4 Inverse FFT data: (a) the TE mode reflection coefficient and TM mode reflection coefficient (b) represents the unwrapped phase function ϕTE(k,pattern) and ϕTM(k,pattern).

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Fig. 5
Fig. 5 Comparison results for (a) Ψ(k) and (b) Δ(k): the solid blue lines are calculated by using the RCWA and the dotted red lines are measured by the proposed snapshot phase sensitive scatterometry based on double-channel spectral carrier frequency concept.

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Fig. 6
Fig. 6 The SEM image of the manufactured binary nano pattern grating and its 3D shape unknown factor description.

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Fig. 7
Fig. 7 (a)The dual spectrum data ITE and ITM measured simultaneously from the proposed snapshot scheme and (b) the spectral frequency distribution after the FFT step [TE mode: red dotted line, and TM mode: blue solid line].

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Fig. 8
Fig. 8 Inverse FFT data: (a) the TE mode reflection coefficient and TM mode reflection coefficient and (b) the wrapped phase function ϕTE(k,pattern) and ϕTM(k,pattern) (TE mode: red dotted line, and TM mode: blue solid line).

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Fig. 9
Fig. 9 Comparison results for (a) Ψ(k) and (b) Δ(k): the solid blue lines represent the measured data and the dotted red lines are modeled data by using RCWA.

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Equations (7)

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ε(x)= ∑ h ε h exp( j 2πh L x )
E I,y = E inc,y + ∑ i R i exp[−j( k xi x− k I,zi z)] , E II,y = ∑ i T i exp{−j[ k xi x+ k II,zi (z−d)]} ,
k xi = k 0 [ n I sinθ−i( λ 0 /L)]
k l,zi ={ k 0 [ n l 2 − ( k xi / k 0 ) 2 ] 1/2          k 0 n l > k xi , −j k 0 [( k xi / k 0 )− n l 2 ]           k xi > k 0 n l                                                                                       l=I,II.
ρ= R p R s = R TE R TM =| R TE R TM | e i( δ TE − δ TM ) =tanΨ​​ e iΔ
I TE (k,h,pattern)= | E r,TE (k)+ E t,TE (k,h,pattern) | 2 = i 0,TE (k,pattern)[1+ γ TE (k,pattern)cos{ Φ TE (k,h,pattern​)}] where   Φ TE (k,h,pattern)=2kh+φ (k,pattern) TE
I TM (k,h,pattern)= | E r,TM (k)+ E t,TM (k,h,pattern) | 2 = i 0,TM (k,pattern)[1+ γ TM (k,pattern)cos{ Φ TM (k,h,pattern​)}] where   Φ TM (k,h,pattern)=2kh+φ (k,pattern) TM

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