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.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  30. 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).
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    [CrossRef]

2014

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

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]

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]

2012

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

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

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

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

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]

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]

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]

2006

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]

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]

2005

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

1998

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

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

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

1995

1988

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

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.

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]

Allgair, J.

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]

Attota, R.

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]

Barnes, B. M.

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]

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.

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]

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.

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]

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]

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]

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]

Casa, D. M.

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]

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.

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]

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]

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]

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]

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.

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]

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]

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, 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]

Ding, Y.

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]

Dong, Z. Q.

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]

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.

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]

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.

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]

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]

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]

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]

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.

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]

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.

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]

Herzinger, C. H.

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]

Hines, D. R.

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]

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.

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]

Hu, W.

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]

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.

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, 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]

Johs, B.

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]

Jones, R. L.

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]

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]

Jun, J.

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]

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.

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]

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.

Licitra, C.

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]

Lin, E. K.

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]

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]

Liu, S. Y.

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]

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]

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]

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]

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]

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.

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]

Marx, E.

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]

McGahan, W. A.

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]

Moharam, M. G.

Nguyen, Q.

Novikova, T.

Ossikovski, R.

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]

Pang, S. W.

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. 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]

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]

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]

Paulson, W.

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]

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.

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]

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]

Postava, K.

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]

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.

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]

Regonda, S.

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]

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.

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]

Ro, H. W.

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]

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]

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.

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]

Soles, C. L.

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]

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]

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]

Tao, L.

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]

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.

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]

Wu, W.

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]

Zhang, C. W.

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]

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]

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]

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]

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]

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.

Appl. Phys. Lett.

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]

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]

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]

ECS Trans.

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.

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]

J. Appl. Phys.

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]

J. Micro/Nanolith MEMS MOEMS

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

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]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

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]

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]

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.

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]

Opt. Acta (Lond.)

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.

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]

Opt. Express

Phys. Rev. B Condens. Matter

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

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

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

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

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]

Other

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).

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]

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Figures (7)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

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

Fig. 4
Fig. 4

The maximal norms of the configuration error propagating matrix J ˜ p + J ˜ a calculated in different measurement configurations. The incidence angle was fixed at 65°.

Fig. 5
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°.

Fig. 6
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.

Fig. 7
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.

Tables (2)

Tables Icon

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°).

Tables Icon

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.

Equations (8)

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

[ E rp E rs ]=J[ E ip E is ]=[ r pp r ps r sp r ss ][ E ip E is ],
M=[ 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 ]=A( J J * ) A 1 ,
A=[ 1 0 0 1 1 0 0 1 0 1 1 0 0 i i 0 ].
( θ opt , ϕ opt )=arg min θΘ,ϕΦ [ max pΩ ( J ˜ p + J ˜ a ) ],
DI= [ Tr(M M T ) M 11 2 3 M 11 2 ] 1/2 ,0DI1,
M D = ρ(x) M ND (x)dx ,
χ r 2 = 1 15NK k=1 N i,j=1 4 [ m ij,k meas m ij,k calc (p,a) σ( m ij,k ) ] 2 ,
S out =[ M A R(A)][R( C 2 ) M C2 ( δ 2 )R( C 2 )] M S [R( C 1 ) M C1 ( δ 1 )R( C 1 )][R(P) M P ] S in ,

Metrics