Accurate characterization of nanoimprinted resist patterns using Mueller matrix ellipsometry

Xiuguo Chen; Shiyuan Liu; Chuanwei Zhang; Hao Jiang; Zhichao Ma; Tangyou Sun; Zhimou Xu

doi:10.1364/OE.22.015165

Accurate characterization of nanoimprinted resist patterns using Mueller matrix ellipsometry

Xiuguo Chen, Shiyuan Liu, Chuanwei Zhang, Hao Jiang, Zhichao Ma, Tangyou Sun, and Zhimou Xu

Optics Express
Vol. 22,
Issue 12,
pp. 15165-15177
(2014)
•https://doi.org/10.1364/OE.22.015165

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Xiuguo Chen, Shiyuan Liu, Chuanwei Zhang, Hao Jiang, Zhichao Ma, Tangyou Sun, and Zhimou Xu, "Accurate characterization of nanoimprinted resist patterns using Mueller matrix ellipsometry," Opt. Express 22, 15165-15177 (2014)

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Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction gratings (050.1950)
- Instrumentation, measurement, and metrology (120.0120)
- Ellipsometry and polarimetry (120.2130)
- Inverse scattering (290.3200)

About this Article
History
- Original Manuscript: April 14, 2014
- Revised Manuscript: May 31, 2014
- Manuscript Accepted: June 4, 2014
- Published: June 12, 2014

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Open Access

Abstract

In order to control nanoimprint lithography processes to achieve good fidelity, accurate characterization of structural parameters of nanoimprinted resist patterns is highly desirable. Among the possible techniques, optical scatterometry is relatively ideal due to its high throughput, low cost, and minimal sample damage. Compared with conventional optical scatterometry, which is usually based on reflectometry and ellipsometry and obtains at most two ellipsometric angles, Mueller matrix ellipsometry (MME) based scatterometry can provide up to 16 quantities of a 4 × 4 Mueller matrix in each measurement and can thereby acquire much more useful information about the sample. In addition, MME has different measurement accuracy in different measurement configurations. It is expected that much more accurate characterization of nanoimprinted resist patterns can be achieved by choosing appropriate measurement configurations and fully using the rich information hidden in the measured Mueller matrices. Accordingly, nanoimprinted resist patterns were characterized using an in-house developed Mueller matrix ellipsometer in this work. We have experimentally demonstrated that not only more accurate quantification of line width, line height, sidewall angle, and residual layer thickness of nanoimprinted resist patterns can be achieved, but also the residual layer thickness variation over the illumination spot can be directly determined, when performing MME measurements in the optimal configuration and meanwhile incorporating depolarization effects into the optical model. The comparison of MME-extracted imprinted resist profiles has also indicated excellent imprint pattern fidelity.

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References

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Publication

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nm resolution,” Science 272(5258), 85–87 (1996).
[Crossref]
S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]
H.-J. Lee, C. L. Soles, H. W. Ro, R. L. Jones, E. K. Lin, W. Wu, and D. R. Hines, “Nanoimprint pattern transfer quality from specular x-ray reflectivity,” Appl. Phys. Lett. 87(26), 263111 (2005).
[Crossref]
R. L. Jones, T. Hu, C. L. Soles, E. K. Lin, R. M. Reano, S. W. Pang, and D. M. Casa, “Real-time shape evolution of nanoimprinted polymer structures during thermal annealing,” Nano Lett. 6(8), 1723–1728 (2006).
[Crossref] [PubMed]
D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]
R. M. Al-Assaad, S. Regonda, L. Tao, S. W. Pang, and W. Hu, “Characterizing nanoimprint profile shape and polymer flow behavior using visible light angular scatterometry,” J. Vac. Sci. Technol. B 25(6), 2396–2401 (2007).
[Crossref]
H. J. Patrick, T. A. Germer, Y. Ding, H. W. Ro, L. J. Richter, and C. L. Soles, “Scatterometry for in situ measurement of pattern reflow in nanoimprinted polymers,” Appl. Phys. Lett. 93(23), 233105 (2008).
[Crossref]
C. J. Raymond, “Scatterometry for semiconductor metrology,” in Handbook of Silicon Semiconductor Metrology, A. C. Diebold, ed. (CRC, 2001), Chap. 18, pp. 477–514.
X. G. Chen, S. Y. Liu, C. W. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52(27), 6726–6734 (2013).
[Crossref] [PubMed]
R. Silver, T. A. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[Crossref]
B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]
T. Novikova, A. De Martino, S. Ben Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45(16), 3688–3697 (2006).
[Crossref] [PubMed]
M. Foldyna, A. De Martino, E. Garcia-Caurel, R. Ossikovski, C. Licitra, F. Bertin, K. Postava, and B. Drévillon, “Critical dimension of bioperiodic gratings determined by spectral ellipsometry and Mueller matrix polarimetry,” Eur. Phys. J. Appl. Phys. 42(3), 351–359 (2008).
[Crossref]
X. G. Chen, S. Y. Liu, C. W. Zhang, and H. Jiang, ““Measurement configuration optimization for accurate grating reconstruction by Mueller matrix polarimetry,” J. Micro/Nanolith. MEMS MOEMS 12(3), 033013 (2013).
[Crossref]
Z. Q. Dong, S. Y. Liu, X. G. Chen, and C. W. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014), doi:.
[Crossref]
T. Novikova, A. De Martino, P. Bulkin, Q. Nguyen, B. Drévillon, V. Popov, and A. Chumakov, “Metrology of replicated diffractive optics with Mueller polarimetry in conical diffraction,” Opt. Express 15(5), 2033–2046 (2007).
[Crossref] [PubMed]
T. Novikova, P. Bulkin, V. Popov, B. Haj Ibrahim, and A. De Martino, “V. Popov, B. Haj Ibrahim, and A. De Martino, “Mueller polarimetry as a tool for detecting asymmetry in diffraction grating profiles,” J. Vac. Sci. Technol. B 29(5), 051804 (2011).
[Crossref]
J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]
X. G. Chen, C. W. Zhang, and S. Y. Liu, “Depolarization effects from nanoimprinted grating structures as measured by Mueller matrix polarimetry,” Appl. Phys. Lett. 103(15), 151605 (2013).
[Crossref]
M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
[Crossref]
L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
[Crossref]
S. Y. Liu, Y. Ma, X. G. Chen, and C. W. Zhang, “Estimation of the convergence order of rigorous coupled-wave analysis for binary gratings in optical critical dimension metrology,” Opt. Eng. 51(8), 081504 (2012).
[Crossref]
R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).
[Crossref]
H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
T. A. Germer and H. J. Patrick, “Effect of bandwidth and numerical aperture in optical scatterometry,” Proc. SPIE 7638, 76381F (2010).
[Crossref]
H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).
R. W. Collins and J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films,” J. Opt. Soc. Am. A 16(8), 1997–2006 (1999).
[Crossref]
S. Y. Liu, X. G. Chen, and C. W. Zhang, “Mueller matrix polarimetry: A powerful tool for nanostructure metrology,” ECS Trans. 60(1), 237–242 (2014).
[Crossref]
C. H. 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, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]
A. R. Forouhi and I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics,” Phys. Rev. B Condens. Matter 38(3), 1865–1874 (1988).
[Crossref] [PubMed]
X. G. Chen, S. Y. Liu, H. G. Gu, and C. W. Zhang, “Formulation of error propagation and estimation in grating reconstruction by a dual-rotating compensator Mueller matrix polarimeter,” Thin Solid Films (2014), doi:.
[Crossref]

2014 (2)

Z. Q. Dong, S. Y. Liu, X. G. Chen, and C. W. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014), doi:.
[Crossref]

S. Y. Liu, X. G. Chen, and C. W. Zhang, “Mueller matrix polarimetry: A powerful tool for nanostructure metrology,” ECS Trans. 60(1), 237–242 (2014).
[Crossref]

2013 (4)

X. G. Chen, S. Y. Liu, C. W. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52(27), 6726–6734 (2013).
[Crossref] [PubMed]

X. G. Chen, C. W. Zhang, and S. Y. Liu, “Depolarization effects from nanoimprinted grating structures as measured by Mueller matrix polarimetry,” Appl. Phys. Lett. 103(15), 151605 (2013).
[Crossref]

X. G. Chen, S. Y. Liu, C. W. Zhang, and H. Jiang, ““Measurement configuration optimization for accurate grating reconstruction by Mueller matrix polarimetry,” J. Micro/Nanolith. MEMS MOEMS 12(3), 033013 (2013).
[Crossref]

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

2012 (1)

S. Y. Liu, Y. Ma, X. G. Chen, and C. W. Zhang, “Estimation of the convergence order of rigorous coupled-wave analysis for binary gratings in optical critical dimension metrology,” Opt. Eng. 51(8), 081504 (2012).
[Crossref]

2011 (1)

T. Novikova, P. Bulkin, V. Popov, B. Haj Ibrahim, and A. De Martino, “V. Popov, B. Haj Ibrahim, and A. De Martino, “Mueller polarimetry as a tool for detecting asymmetry in diffraction grating profiles,” J. Vac. Sci. Technol. B 29(5), 051804 (2011).
[Crossref]

2010 (2)

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

T. A. Germer and H. J. Patrick, “Effect of bandwidth and numerical aperture in optical scatterometry,” Proc. SPIE 7638, 76381F (2010).
[Crossref]

2008 (2)

H. J. Patrick, T. A. Germer, Y. Ding, H. W. Ro, L. J. Richter, and C. L. Soles, “Scatterometry for in situ measurement of pattern reflow in nanoimprinted polymers,” Appl. Phys. Lett. 93(23), 233105 (2008).
[Crossref]

M. Foldyna, A. De Martino, E. Garcia-Caurel, R. Ossikovski, C. Licitra, F. Bertin, K. Postava, and B. Drévillon, “Critical dimension of bioperiodic gratings determined by spectral ellipsometry and Mueller matrix polarimetry,” Eur. Phys. J. Appl. Phys. 42(3), 351–359 (2008).
[Crossref]

2007 (3)

R. M. Al-Assaad, S. Regonda, L. Tao, S. W. Pang, and W. Hu, “Characterizing nanoimprint profile shape and polymer flow behavior using visible light angular scatterometry,” J. Vac. Sci. Technol. B 25(6), 2396–2401 (2007).
[Crossref]

R. Silver, T. A. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[Crossref]

T. Novikova, A. De Martino, P. Bulkin, Q. Nguyen, B. Drévillon, V. Popov, and A. Chumakov, “Metrology of replicated diffractive optics with Mueller polarimetry in conical diffraction,” Opt. Express 15(5), 2033–2046 (2007).
[Crossref] [PubMed]

2006 (2)

T. Novikova, A. De Martino, S. Ben Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45(16), 3688–3697 (2006).
[Crossref] [PubMed]

R. L. Jones, T. Hu, C. L. Soles, E. K. Lin, R. M. Reano, S. W. Pang, and D. M. Casa, “Real-time shape evolution of nanoimprinted polymer structures during thermal annealing,” Nano Lett. 6(8), 1723–1728 (2006).
[Crossref] [PubMed]

2005 (2)

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

H.-J. Lee, C. L. Soles, H. W. Ro, R. L. Jones, E. K. Lin, W. Wu, and D. R. Hines, “Nanoimprint pattern transfer quality from specular x-ray reflectivity,” Appl. Phys. Lett. 87(26), 263111 (2005).
[Crossref]

1999 (1)

R. W. Collins and J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films,” J. Opt. Soc. Am. A 16(8), 1997–2006 (1999).
[Crossref]

1998 (1)

C. H. 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, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

1997 (2)

L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
[Crossref]

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

1996 (1)

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nm resolution,” Science 272(5258), 85–87 (1996).
[Crossref]

1995 (1)

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

1988 (1)

A. R. Forouhi and I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics,” Phys. Rev. B Condens. Matter 38(3), 1865–1874 (1988).
[Crossref] [PubMed]

1986 (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).
[Crossref]

Al-Assaad, R. M.

Allgair, J.

Attota, R.

Barnes, B. M.

Ben Hatit, S.

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).
[Crossref]

Bertin, F.

Bloomer, I.

A. R. Forouhi and I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics,” Phys. Rev. B Condens. Matter 38(3), 1865–1874 (1988).
[Crossref] [PubMed]

Bulkin, P.

Bunday, B.

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

Casa, D. M.

Cepler, A.

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

Chen, X. G.

S. Y. Liu, X. G. Chen, and C. W. Zhang, “Mueller matrix polarimetry: A powerful tool for nanostructure metrology,” ECS Trans. 60(1), 237–242 (2014).
[Crossref]

X. G. Chen, S. Y. Liu, H. G. Gu, and C. W. Zhang, “Formulation of error propagation and estimation in grating reconstruction by a dual-rotating compensator Mueller matrix polarimeter,” Thin Solid Films (2014), doi:.
[Crossref]

Chou, S. Y.

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nm resolution,” Science 272(5258), 85–87 (1996).
[Crossref]

Chumakov, A.

Collins, R. W.

Cordes, A.

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

De Martino, A.

Ding, Y.

Dong, Z. Q.

Drévillon, B.

Farys, V.

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

Foldyna, M.

Forouhi, A. R.

A. R. Forouhi and I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics,” Phys. Rev. B Condens. Matter 38(3), 1865–1874 (1988).
[Crossref] [PubMed]

Fuard, D.

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

Garcia-Caurel, E.

Gaylord, T. K.

Germer, T. A.

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

T. A. Germer and H. J. Patrick, “Effect of bandwidth and numerical aperture in optical scatterometry,” Proc. SPIE 7638, 76381F (2010).
[Crossref]

Gil, J. J.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).
[Crossref]

Gourgon, C.

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

Grann, E. B.

Gu, H. G.

Guo, L.

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

Haj Ibrahim, B.

Herzinger, C. H.

Hines, D. R.

Hu, J.

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

Hu, T.

Hu, W.

Hwu, J. J.

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

Jiang, H.

Johs, B.

Jones, R. L.

Jun, J.

Koh, J.

Krauss, P. R.

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nm resolution,” Science 272(5258), 85–87 (1996).
[Crossref]

Lee, H.-J.

Li, J.

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

Li, L.

L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
[Crossref]

Licitra, C.

Lin, E. K.

Liu, S. Y.

S. Y. Liu, X. G. Chen, and C. W. Zhang, “Mueller matrix polarimetry: A powerful tool for nanostructure metrology,” ECS Trans. 60(1), 237–242 (2014).
[Crossref]

Liu, Y.

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

Liu, Z.

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

Ma, Y.

Marx, E.

McGahan, W. A.

Moharam, M. G.

Nguyen, Q.

Novikova, T.

Ossikovski, R.

Pang, S. W.

Patrick, H. J.

T. A. Germer and H. J. Patrick, “Effect of bandwidth and numerical aperture in optical scatterometry,” Proc. SPIE 7638, 76381F (2010).
[Crossref]

Paulson, W.

Perret, C.

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

Pommet, D. A.

Popov, V.

Postava, K.

Rabello, S.

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

Reano, R. M.

Regonda, S.

Renstrom, P. J.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nm resolution,” Science 272(5258), 85–87 (1996).
[Crossref]

Richter, L. J.

Ro, H. W.

Schiavone, P.

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

Settens, C.

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

Silver, R.

Soles, C. L.

Tao, L.

Vartanian, V.

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

Woollam, J. A.

Wu, W.

Zhang, C. W.

S. Y. Liu, X. G. Chen, and C. W. Zhang, “Mueller matrix polarimetry: A powerful tool for nanostructure metrology,” ECS Trans. 60(1), 237–242 (2014).
[Crossref]

Zhang, W.

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

Zhuang, L.

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

ECS Trans. (1)

S. Y. Liu, X. G. Chen, and C. W. Zhang, “Mueller matrix polarimetry: A powerful tool for nanostructure metrology,” ECS Trans. 60(1), 237–242 (2014).
[Crossref]

Eur. Phys. J. Appl. Phys. (1)

J. Appl. Phys. (1)

J. Micro/Nanolith MEMS MOEMS (1)

J. Li, J. J. Hwu, Y. Liu, S. Rabello, Z. Liu, and J. Hu, “Mueller matrix measurement of asymmetric gratings,” J. Micro/Nanolith MEMS MOEMS 9(4), 041305 (2010).
[Crossref]

J. Micro/Nanolith. MEMS MOEMS (1)

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

L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
[Crossref]

J. Vac. Sci. Technol. B (4)

D. Fuard, C. Perret, V. Farys, C. Gourgon, and P. Schiavone, “Measurement of residual thickness using scatterometry,” J. Vac. Sci. Technol. B 23(6), 3069–3074 (2005).
[Crossref]

S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, “Sub-10 nm imprint lithography and applications,” J. Vac. Sci. Technol. B 15(6), 2897–2904 (1997).
[Crossref]

Nano Lett. (1)

Opt. Acta (Lond.) (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).
[Crossref]

Opt. Eng. (1)

Opt. Express (1)

Phys. Rev. B Condens. Matter (1)

A. R. Forouhi and I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics,” Phys. Rev. B Condens. Matter 38(3), 1865–1874 (1988).
[Crossref] [PubMed]

Proc. SPIE (3)

T. A. Germer and H. J. Patrick, “Effect of bandwidth and numerical aperture in optical scatterometry,” Proc. SPIE 7638, 76381F (2010).
[Crossref]

B. Bunday, T. A. Germer, V. Vartanian, A. Cordes, A. Cepler, and C. Settens, “Gaps analysis for CD metrology beyond the 22 nm node,” Proc. SPIE 8681, 86813B (2013).
[Crossref]

Science (1)

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nm resolution,” Science 272(5258), 85–87 (1996).
[Crossref]

Thin Solid Films (1)

Other (5)

C. J. Raymond, “Scatterometry for semiconductor metrology,” in Handbook of Silicon Semiconductor Metrology, A. C. Diebold, ed. (CRC, 2001), Chap. 18, pp. 477–514.

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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Fig. 1 Representation of polarized light incidence for a one-dimensional grating structure.

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Fig. 2 Principle and prototype of the dual rotating-compensator Mueller matrix ellipsometer.

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Fig. 3 XSEM micrograph and geometric model of the nanoimprinted grating sample with an imprint pressure of 20 bar.

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Fig. 4 The maximal norms of the configuration error propagating matrix

‖ {\tilde{J}}_{p}^{+} {\tilde{J}}_{a} ‖

calculated in different measurement configurations. The incidence angle was fixed at 65°.

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Fig. 5 The norms of systematic errors in the structural parameters of different nanoimprinted grating samples extracted in different measurement configurations without considering any depolarization effect. The corresponding imprint pressures are 10, 15 and 20 bar, respectively. The incidence angle was fixed at 65°.

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Fig. 6 Depolarization index spectra of the measured and calculated best-fit Mueller matrix spectra of the nanoimprinted grating sample with an imprint pressure of 20 bar. The depolarization index spectrum DI corresponds to the measured Mueller matrix spectrum. The depolarization index spectrum DI₁ corresponds to the calculated best-fit Mueller matrix spectrum when only considering the depolarization effects induced by finite spectral bandwidth and NA. The depolarization index spectrum DI₂ corresponds to the calculated best-fit Mueller matrix spectrum when considering the depolarization effects induced by finite spectral bandwidth, NA, and residual layer thickness nonuniformity. Data analysis was performed in the optimal measurement configuration.

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Fig. 7 Fitting result of the measured and calculated best-fit Mueller matrix spectra of the nanoimprinted grating sample with an imprint pressure of 20 bar. The fit1 and fit2 corresponds to their counterparts in Tables 1 and 2, which are the calculated best-fit Mueller matrix spectra achieved when ignoring depolarization effects and when considering the depolarization effects induced by finite spectral bandwidth, NA, and residual layer thickness nonuniformity, respectively. Data analysis was also performed in the optimal measurement configuration.

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Tables (2)

Table 1 Comparison of fitting parameters obtained from the MME and XSEM measurements. Data analysis was performed in the optimal measurement configuration (θ = 65°, ϕ = 15°).

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Table 2 Comparison of fitting errors between the ellipsometer-measured and the calculated best-fit Mueller matrix spectra with and without depolarization effects taking into account. Data analysis was performed in the optimal measurement configuration.

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Equations (8)

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[\begin{array}{l} E_{r p} \\ E_{r s} \end{array}] = J [\begin{array}{l} E_{i p} \\ E_{i s} \end{array}] = [\begin{matrix} r_{p p} & r_{p s} \\ r_{s p} & r_{s s} \end{matrix}] [\begin{array}{l} E_{i p} \\ E_{i s} \end{array}],

M = [\begin{matrix} M_{11} & M_{12} & M_{13} & M_{14} \\ M_{21} & M_{22} & M_{23} & M_{24} \\ M_{31} & M_{32} & M_{33} & M_{34} \\ M_{41} & M_{42} & M_{43} & M_{44} \end{matrix}] = A (J \otimes J^{*}) A^{- 1},

A = [\begin{matrix} 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & - 1 \\ 0 & 1 & 1 & 0 \\ 0 & i & - i & 0 \end{matrix}] .

(θ_{o p t}, ϕ_{o p t}) = \arg \min_{θ \in Θ, ϕ \in Φ} [\max_{p \in Ω} (‖ {\tilde{J}}_{p}^{+} {\tilde{J}}_{a} ‖)],

D I = {[\frac{T r (M M^{T}) - M_{11}^{2}}{3 M_{11}^{2}}]}^{1 / 2}, 0 \leq D I \leq 1,

M^{D} = \int ρ (x) M^{N D} (x) d x,

χ_{r}^{2} = \frac{1}{15 N - K} \sum_{k = 1}^{N} \sum_{i, j = 1}^{4} {[\frac{m_{i j, k}^{meas} - m_{i j, k}^{calc} (p, a)}{σ (m_{i j, k})}]}^{2},

S_{o u t} = [M_{A} R (A)] [R (- C_{2}) M_{C 2} (δ_{2}) R (C_{2})] M_{S} [R (- C_{1}) M_{C 1} (δ_{1}) R (C_{1})] [R (- P) M_{P}] S_{i n},

Parameter	Sample 1 (10 bar)			Sample 2 (15 bar)			Sample 3 (20 bar)
Parameter	fit1	fit2	SEM	fit1	fit2	SEM	fit1	fit2	SEM
p₁ [nm]	352.34 ± 0.970	350.12 ± 0.816	350.9	351.65 ± 0.869	350.19 ± 0.719	350.3	350.57 ± 0.921	349.65 ± 0.783	350.1
p₂ [nm]	469.41 ± 0.555	470.21 ± 0.475	470.8	468.81 ± 0.533	470.08 ± 0.433	470.6	468.38 ± 0.584	469.94 ± 0.492	470.9
p₃ [deg]	87.33 ± 0.148	87.00 ± 0.127	87.2	87.23 ± 0.132	87.04 ± 0.112	87.2	87.05 ± 0.135	86.90 ± 0.121	86.9
p₄ [nm]	56.81 ± 0.330	55.71 ± 0.296	55.7	49.73 ± 0.336	48.34 ± 0.287	48.6	40.74 ± 0.402	39.09 ± 0.347	39.1
p₅ [nm]	68.08 ± 2.765	71.83 ± 2.380	−	64.60 ± 2.785	70.35 ± 2.186	−	51.67 ± 3.743	57.72 ± 2.873	−
σ_t [nm]	−	3.53 ± 0.365	−	−	3.78 ± 0.350	−	−	3.03 ± 0.565	−

	Sample 1 (10 bar)		Sample 2 (15 bar)		Sample 3 (20 bar)
	fit1	fit2	fit1	fit2	fit1	fit2
$χ_{r}^{2}$ value	63.30	36.52	57.10	30.54	67.44	37.85

Parameter	Sample 1 (10 bar)			Sample 2 (15 bar)			Sample 3 (20 bar)
Parameter	fit1	fit2	SEM	fit1	fit2	SEM	fit1	fit2	SEM
p₁ [nm]	352.34 ± 0.970	350.12 ± 0.816	350.9	351.65 ± 0.869	350.19 ± 0.719	350.3	350.57 ± 0.921	349.65 ± 0.783	350.1
p₂ [nm]	469.41 ± 0.555	470.21 ± 0.475	470.8	468.81 ± 0.533	470.08 ± 0.433	470.6	468.38 ± 0.584	469.94 ± 0.492	470.9
p₃ [deg]	87.33 ± 0.148	87.00 ± 0.127	87.2	87.23 ± 0.132	87.04 ± 0.112	87.2	87.05 ± 0.135	86.90 ± 0.121	86.9
p₄ [nm]	56.81 ± 0.330	55.71 ± 0.296	55.7	49.73 ± 0.336	48.34 ± 0.287	48.6	40.74 ± 0.402	39.09 ± 0.347	39.1
p₅ [nm]	68.08 ± 2.765	71.83 ± 2.380	−	64.60 ± 2.785	70.35 ± 2.186	−	51.67 ± 3.743	57.72 ± 2.873	−
σ_t [nm]	−	3.53 ± 0.365	−	−	3.78 ± 0.350	−	−	3.03 ± 0.565	−

	Sample 1 (10 bar)		Sample 2 (15 bar)		Sample 3 (20 bar)
	fit1	fit2	fit1	fit2	fit1	fit2
$χ_{r}^{2}$ value	63.30	36.52	57.10	30.54	67.44	37.85