Abstract

In order to efficiently extract the sample Mueller matrix by dual rotating–retarder ellipsometry, it is critical for the data reduction technique to achieve a minimal data processing burden while considering the ease of retarder control. In this paper, we propose an unevenly spaced sampling strategy to reach a globally optimal measurement matrix with minimum sampling points for continuous measurements. Taking into account the robustness to both systematic errors and detection noise, we develop multi-objective optimization models to identify the optimal unevenly spaced sampling points. A combined global search algorithm based on the multi-objective genetic algorithm is subsequently designed to solve our model. Finally, simulations and experiments are conducted to validate our approach as well as to provide near-optimal schemes for different design scenarios. The results demonstrate that significant improvement on error immunity performance can be achieved by applying an unevenly sampled measurement strategy compared to an evenly sampled one for our ellipsometer scenario.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2018 (1)

X. Chen, H. Gu, H. Jiang, C. Zhang, and S. Liu, “Probing optimal measurement configuration for optical scatterometry by the multi-objective genetic algorithm,” Meas. Sci. Technol. 29(4), 045014 (2018).
[Crossref]

2017 (2)

2016 (3)

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise,” Opt. Express 24(26), 29691–29704 (2016).
[Crossref] [PubMed]

B. Bunday, “HVM metrology challenges towards the 5nm node,” Proc. SPIE 9778, 97780E (2016).
[Crossref]

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

2015 (3)

2014 (4)

H. Dai and C. Yan, “Measurement errors resulted from misalignment errors of the retarder in a rotating-retarder complete Stokes polarimeter,” Opt. Express 22(10), 11869–11883 (2014).
[Crossref] [PubMed]

X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using Mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
[Crossref] [PubMed]

D. E. Aspnes, “Spectroscopic ellipsometry — Past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

L. M. S. Aas, D. G. Skåre, P. G. Ellingsen, P. A. Letnes, and M. Kildemo, “Design, optimization and realization of a ferroelectric liquid crystal based Mueller matrix ellipsometer using a genetic algorithm,” Thin Solid Films 571, 522–526 (2014).
[Crossref]

2013 (4)

L. M. S. Aas, P. G. Ellingsen, B. E. Fladmark, P. A. Letnes, and M. Kildemo, “Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms,” Opt. Express 21(7), 8753–8762 (2013).
[Crossref] [PubMed]

J. C. Vap, S. E. Nauyoks, and M. A. Marciniak, “Optimization of a dual-rotating-retarder polarimeter as applied to a tunable infrared Mueller-matrix scatterometer,” Meas. Sci. Technol. 24(5), 055901 (2013).
[Crossref]

W. Du, S. Liu, C. Zhang, and X. Chen, “Optimal configuration for the dual rotating-compensator Mueller matrix ellipsometer,” Proc. SPIE 8759, 875925 (2013).
[Crossref]

A. Peinado, A. Lizana, and J. Campos, “Optimization and tolerance analysis of a polarimeter with ferroelectric liquid crystals,” Appl. Opt. 52(23), 5748–5757 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

J. Li, B. Ramanujam, and R. W. Collins, “Dual rotating compensator ellipsometry: Theory and simulations,” Thin Solid Films 519(9), 2725–2729 (2011).
[Crossref]

2010 (3)

2009 (2)

2008 (3)

2007 (2)

J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

P. Lemaillet, F. Pellen, S. Rivet, B. Le Jeune, and J. Cariou, “Optimization of a dual-rotating-retarder polarimeter designed for hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 24(3), 609–614 (2007).
[Crossref]

2006 (1)

2003 (1)

2002 (2)

2000 (3)

1999 (1)

1997 (1)

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21(2), 109–151 (1997).
[Crossref]

1978 (2)

R. M. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2(6), 148–150 (1978).
[Crossref] [PubMed]

P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. A 68(11), 1519–1528 (1978).
[Crossref]

Aas, L. M. S.

Anna, G.

Aspnes, D. E.

D. E. Aspnes, “Spectroscopic ellipsometry — Past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

Azzam, R. M.

Bozdog, C.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Bunday, B.

B. Bunday, “HVM metrology challenges towards the 5nm node,” Proc. SPIE 9778, 97780E (2016).
[Crossref]

Campos, J.

Cariou, J.

Cepler, A.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Chao, R.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Chen, X.

Chen, Z.

Chipman, R. A.

Cohen, O.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Collins, R. W.

J. Li, B. Ramanujam, and R. W. Collins, “Dual rotating compensator ellipsometry: Theory and simulations,” Thin Solid Films 519(9), 2725–2729 (2011).
[Crossref]

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]

Dai, H.

De Martino, A.

Dereniak, E. L.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

Descour, M. R.

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Drévillon, B.

Du, W.

W. Du, W. Jia, Z. Zhang, and C. Wang, “Optimization of the infrared Stokes imaging polarimeter,” Proc. SPIE 10461, 104611Q (2017).
[Crossref]

S. Liu, W. Du, X. Chen, H. Jiang, and C. Zhang, “Mueller matrix imaging ellipsometry for nanostructure metrology,” Opt. Express 23(13), 17316–17329 (2015).
[Crossref] [PubMed]

W. Du, S. Liu, C. Zhang, and X. Chen, “Optimal configuration for the dual rotating-compensator Mueller matrix ellipsometer,” Proc. SPIE 8759, 875925 (2013).
[Crossref]

Ellingsen, P. G.

Felix, N.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Fischer, J.

Fladmark, B. E.

Garcia, J. P.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Garcia-Caurel, E.

Gaudiello, J.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Goudail, F.

Gu, H.

X. Chen, H. Gu, H. Jiang, C. Zhang, and S. Liu, “Probing optimal measurement configuration for optical scatterometry by the multi-objective genetic algorithm,” Meas. Sci. Technol. 29(4), 045014 (2018).
[Crossref]

Guillorn, M.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Hatit, S. B.

Hauge, P. S.

P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. A 68(11), 1519–1528 (1978).
[Crossref]

Hingerl, K.

M. Losurdo and K. Hingerl, Ellipsometry at the Nanoscale (Springer Verlag, 2013).

Hollstein, A.

Hoover, B. G.

Hu, H.

Iemmi, C.

Jia, W.

W. Du, W. Jia, Z. Zhang, and C. Wang, “Optimization of the infrared Stokes imaging polarimeter,” Proc. SPIE 10461, 104611Q (2017).
[Crossref]

Jiang, H.

Johnson, S. J.

Kalkandjiev, T. K.

Kemme, S. A.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

Kildemo, M.

L. M. S. Aas, D. G. Skåre, P. G. Ellingsen, P. A. Letnes, and M. Kildemo, “Design, optimization and realization of a ferroelectric liquid crystal based Mueller matrix ellipsometer using a genetic algorithm,” Thin Solid Films 571, 522–526 (2014).
[Crossref]

L. M. S. Aas, P. G. Ellingsen, B. E. Fladmark, P. A. Letnes, and M. Kildemo, “Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms,” Opt. Express 21(7), 8753–8762 (2013).
[Crossref] [PubMed]

P. A. Letnes, I. S. Nerbø, L. M. S. Aas, P. G. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express 18(22), 23095–23103 (2010).
[Crossref] [PubMed]

J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

Kim, Y. K.

Klare, M.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Koh, J.

Ladstein, J.

J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

Lara, D.

Laude, B.

Le Jeune, B.

Le Roy-Brehonnet, F.

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21(2), 109–151 (1997).
[Crossref]

Lemaillet, P.

Letnes, P. A.

Li, J.

J. Li, B. Ramanujam, and R. W. Collins, “Dual rotating compensator ellipsometry: Theory and simulations,” Thin Solid Films 519(9), 2725–2729 (2011).
[Crossref]

Li, X.

Liang, R.

Liu, S.

Liu, T.

Lizana, A.

Locke, A. M.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Losurdo, M.

M. Losurdo and K. Hingerl, Ellipsometry at the Nanoscale (Springer Verlag, 2013).

Loubet, N.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Lund, P.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Ma, Z.

Marciniak, M. A.

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[Crossref]

Mompart, J.

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R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Nauyoks, S. E.

J. C. Vap, S. E. Nauyoks, and M. A. Marciniak, “Optimization of a dual-rotating-retarder polarimeter as applied to a tunable infrared Mueller-matrix scatterometer,” Meas. Sci. Technol. 24(5), 055901 (2013).
[Crossref]

Nerbø, I. S.

P. A. Letnes, I. S. Nerbø, L. M. S. Aas, P. G. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express 18(22), 23095–23103 (2010).
[Crossref] [PubMed]

J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

Novikova, T.

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R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
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[Crossref] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Preusker, R.

Ramanujam, B.

J. Li, B. Ramanujam, and R. W. Collins, “Dual rotating compensator ellipsometry: Theory and simulations,” Thin Solid Films 519(9), 2725–2729 (2011).
[Crossref]

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D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

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R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Skåre, D. G.

L. M. S. Aas, D. G. Skåre, P. G. Ellingsen, P. A. Letnes, and M. Kildemo, “Design, optimization and realization of a ferroelectric liquid crystal based Mueller matrix ellipsometer using a genetic algorithm,” Thin Solid Films 571, 522–526 (2014).
[Crossref]

Smith, M. H.

Stabo-Eeg, F.

J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

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J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

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D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

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J. C. Vap, S. E. Nauyoks, and M. A. Marciniak, “Optimization of a dual-rotating-retarder polarimeter as applied to a tunable infrared Mueller-matrix scatterometer,” Meas. Sci. Technol. 24(5), 055901 (2013).
[Crossref]

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Vidal, J.

Wang, C.

W. Du, W. Jia, Z. Zhang, and C. Wang, “Optimization of the infrared Stokes imaging polarimeter,” Proc. SPIE 10461, 104611Q (2017).
[Crossref]

Wang, Z.

Wolfling, S.

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

Wu, L.

Xu, Z.

Yan, C.

Zhang, C.

Zhang, Z.

W. Du, W. Jia, Z. Zhang, and C. Wang, “Optimization of the infrared Stokes imaging polarimeter,” Proc. SPIE 10461, 104611Q (2017).
[Crossref]

Zhu, J.

Appl. Opt. (6)

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

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

Meas. Sci. Technol. (2)

J. C. Vap, S. E. Nauyoks, and M. A. Marciniak, “Optimization of a dual-rotating-retarder polarimeter as applied to a tunable infrared Mueller-matrix scatterometer,” Meas. Sci. Technol. 24(5), 055901 (2013).
[Crossref]

X. Chen, H. Gu, H. Jiang, C. Zhang, and S. Liu, “Probing optimal measurement configuration for optical scatterometry by the multi-objective genetic algorithm,” Meas. Sci. Technol. 29(4), 045014 (2018).
[Crossref]

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H. Dai and C. Yan, “Measurement errors resulted from misalignment errors of the retarder in a rotating-retarder complete Stokes polarimeter,” Opt. Express 22(10), 11869–11883 (2014).
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A. Peinado, A. Lizana, A. Turpín, C. Iemmi, T. K. Kalkandjiev, J. Mompart, and J. Campos, “Optimization, tolerance analysis and implementation of a Stokes polarimeter based on the conical refraction phenomenon,” Opt. Express 23(5), 5636–5652 (2015).
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T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise,” Opt. Express 24(26), 29691–29704 (2016).
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D. Lara and C. Paterson, “Stokes polarimeter optimization in the presence of shot and Gaussian noise,” Opt. Express 17(23), 21240–21249 (2009).
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A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, “Optimization and performance criteria of a Stokes polarimeter based on two variable retarders,” Opt. Express 18(10), 9815–9830 (2010).
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G. Anna and F. Goudail, “Optimal Mueller matrix estimation in the presence of Poisson shot noise,” Opt. Express 20(19), 21331–21340 (2012).
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X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
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K. M. Twietmeyer and R. A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16(15), 11589–11603 (2008).
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L. M. S. Aas, P. G. Ellingsen, B. E. Fladmark, P. A. Letnes, and M. Kildemo, “Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms,” Opt. Express 21(7), 8753–8762 (2013).
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S. Liu, W. Du, X. Chen, H. Jiang, and C. Zhang, “Mueller matrix imaging ellipsometry for nanostructure metrology,” Opt. Express 23(13), 17316–17329 (2015).
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X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using Mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
[Crossref] [PubMed]

P. A. Letnes, I. S. Nerbø, L. M. S. Aas, P. G. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express 18(22), 23095–23103 (2010).
[Crossref] [PubMed]

Opt. Lett. (6)

Proc. SPIE (6)

W. Du, W. Jia, Z. Zhang, and C. Wang, “Optimization of the infrared Stokes imaging polarimeter,” Proc. SPIE 10461, 104611Q (2017).
[Crossref]

R. Muthinti, N. Loubet, R. Chao, J. Ott, M. Guillorn, N. Felix, J. Gaudiello, P. Lund, A. Cepler, M. Sendelbach, O. Cohen, S. Wolfling, C. Bozdog, and M. Klare, “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc. SPIE 9778, 977810 (2016).
[Crossref]

B. Bunday, “HVM metrology challenges towards the 5nm node,” Proc. SPIE 9778, 97780E (2016).
[Crossref]

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

J. Ladstein, M. Kildemo, G. K. Svendsen, I. S. Nerbø, and F. Stabo-Eeg, “Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers,” Proc. SPIE 6587, 65870D (2007).
[Crossref]

W. Du, S. Liu, C. Zhang, and X. Chen, “Optimal configuration for the dual rotating-compensator Mueller matrix ellipsometer,” Proc. SPIE 8759, 875925 (2013).
[Crossref]

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[Crossref]

J. Li, B. Ramanujam, and R. W. Collins, “Dual rotating compensator ellipsometry: Theory and simulations,” Thin Solid Films 519(9), 2725–2729 (2011).
[Crossref]

L. M. S. Aas, D. G. Skåre, P. G. Ellingsen, P. A. Letnes, and M. Kildemo, “Design, optimization and realization of a ferroelectric liquid crystal based Mueller matrix ellipsometer using a genetic algorithm,” Thin Solid Films 571, 522–526 (2014).
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Figures (7)

Fig. 1
Fig. 1 Schematic of a typical DRR-MME.
Fig. 2
Fig. 2 Condition number (log(O1)) distribution under different polarizer/analyzer combinations.
Fig. 3
Fig. 3 Pareto fronts of Model1-S1 obtained by (a) rough search and (b) fine local search
Fig. 4
Fig. 4 Optimal retarder positions for a perfect calibration scenario (Model 1 S1-S3, free space)
Fig. 5
Fig. 5 Measurement errors of each element in the SMM under perfect calibration scenarios
Fig. 6
Fig. 6 Tolerance comparison of 16 and 30 measurements with optimal uneven sampling (sample 4)
Fig. 7
Fig. 7 Experimental setup

Tables (10)

Tables Icon

Table 2 Combined search strategy based on multi-objective genetic algorithm

Tables Icon

Table 3 Test-bed design

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Table 5 Comparison on detection noise propagation

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Table 6 Comparison on detection noise propagation

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Table 7 Comparisons on instrumental errors propagation of different samples

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Table 8 Experimental results

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Table 9 Results of Model 1 tests obtained by combined search strategy

Tables Icon

Table 10 Results of Model 2 tests obtained by combined search strategy

Equations (28)

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

I i = V o A i M 0 G i S in = P i M
M= P 0 1 I 0
M ^ = P ^ 1 I r = P ^ 1 ( P r M+Δ I ^ r )= P ^ 1 [( P ^ + δ P )M+Δ I ^ r ]
ΔM= P ^ 1 δ P M+ P ^ 1 Δ I ^ r
||ΔM|| ||M|| κ( P ^ )( || δ P || || P 0 || + ||Δ I ^ r || || I 0 || )
κ( P ^ )=|| P ^ | | 2 || P ^ 1 | | 2
O 1 = min κ( P 0 ( x 1 , x 2 x n ))
Δ M i 2 = ( k Q ik ) 2 σ Ik 2
O 2 =min i ( k Q ik ( x 1 , x 2 x n )) 2
ΔM=QΔ P 0 M+QΔ I ^ r
Δ P 0, ij P 0,ij θ 1 | θ 1,i Δ θ 1,i + P 0,ij θ 2 | θ 2,i Δ θ 2,i = f ij Δ θ 1,i + g ij Δ θ 2,i
E( (Δ M i ) 2 )= σ 2 k Q i,k 2 [ ( j M j f kj ) 2 + ( j M j g kj ) 2 ]
E(||ΔM| | F 2 )= i σ 2 k Q i,k 2 [ ( j M j f kj ) 2 + ( j M j g kj ) 2 ]
O 3 =min i k Q i,k 2 [( j f kj 2 ) +( j g kj 2 )]
O 4 = O 2 =min i ( k Q ik ) 2
Model 1: min { O 1 =κ( P 0 ), O 2 = ( i ( k Q ik ) 2 ) 1/2 }
Model 2: min { O 3 = i k Q i,k 2 ( j f kj 2 ) +( j g kj 2 )) , O 4 = ( i ( k Q ik ) 2 ) 1/2 }
s.t.det| P 0 |0
0 x 1 < x 2 < x n T
S( O t )= O t ( x 1 , x 2 x n ) k=1 n [ O t ( x k +Δ x k ) O t ( x k )]
S * = argmin i { η i = t ω t ( O t +S( O t )) }
||ΔM|||| P ^ 1 δ P M+ P ^ 1 Δ I ^ r |||| P ^ 1 |||| δ P ||||M||+|| P ^ 1 ||||Δ I ^ r ||
||ΔM|| ||M|| || P ^ 1 |||| δ P ||||M|| 1 ||M|| +|| P ^ 1 ||||Δ I ^ r || || P 0 || || I 0 ||
||ΔM|| ||M|| κ( P ^ )( || δ P || || P ^ || + ||Δ I ^ r || || I 0 || || P 0 || || P ^ || )κ( P ^ )( || δ P || || P ^ || + ||Δ I ^ r || || I 0 || )
Δ M i = j k Q ik ( f kj Δ θ 1,k + g kj Δ θ 2,k ) M j =Δ M i f +Δ M i g
Δ M i f = Q i1 j M j f 1j Δ θ 1,1 + Q i2 j M j f 2,j Δ θ 1,2 + Q i,16 j M j f 16,j Δ θ 1,16
E( (Δ M i f ) 2 )= σ 1 2 k Q i,k 2 ( j M j f kj ) 2
E( (Δ M i ) 2 )= σ 2 k Q i,k 2 [ ( j M j f kj ) 2 + ( j M j g kj ) 2 ]

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