Abstract

A two-axis Lloyd’s mirrors interferometer based optical fabrication system was theoretically investigated and constructed for patterning high-uniformity nanoscale crossed grating structures over a large area with a high throughput. The current interferometer was configured with two reflected mirrors and a grating holder, which are placed edge by edge and orthogonal with each other. In such a manner, the two beams reflected from the two mirrors interfere with the incident beam, respectively, forming a crossed grating patterns with only one exposure. Differing from the conventional solution for elimination of unexpected interference between the two reflected beams, a systematical analysis, that is based on the proposed index indicating the non-orthogonality between the two beams at different incident angles, was conducted by using a spatial full polarization tracing method. Without polarization modulation to eliminate the additional interference, an optimal exposure condition with small non-orthogonality between reflected beams was found at a certain incident angle range, while the two required interferences to construct cross grating still remain high. A pattern period of ∼1 µm-level crossed grating structure could be obtained through balancing the structure area and the non-orthogonality. Finally, the exposure setup with orthogonal two-axis Lloyd’s mirrors interferometer is established, and the crossed grating structure with the periods of 1076 nm along X-direction and 1091 nm along Y-direction was successfully fabricated on a silicon substrate via microfabrication technology over a large area of 400 mm2. The uniformity of crossed grating array over the whole area was evaluated by an atomic force microscope, and the standard deviations of structure periods along X- and Y-directions smaller than 0.3% are achieved. It is demonstrated that the orthogonal two-axis Lloyd’s mirrors interferometer based on single-beam single-exposure scheme with non-orthogonality systematic analysis is an effective approach to fabricate crossed grating patterns of 1 µm-level period with high uniformity over a large area.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

G. Liang, X. Chen, Z. Wen, G. Chen, and L. Guo, “Super-resolution photolithography using dielectric photonic crystal,” Opt. Lett. 44(5), 1182–1185 (2019).
[Crossref]

X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
[Crossref]

2018 (4)

X. Mao and L. Zeng, “Design and fabrication of crossed gratings with multiple zero-reference marks for planar encoders,” Meas. Sci. Technol. 29(2), 025204 (2018).
[Crossref]

Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
[Crossref]

X. Chen, Y. Shimizu, C. Chen, Y. Chen, and W. Gao, “Generalized method for probing ideal initial polarization states in multibeam Lloyd’s mirror interference lithography of 2D scale gratings,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(2), 021601 (2018).
[Crossref]

X. Li, H. Lu, Q. Zhou, G. Wu, K. Ni, and X. Wang, “An Orthogonal Type Two-Axis Lloyd’s Mirror for Holographic Fabrication of Two-Dimensional Planar Scale Gratings with Large Area,” Appl. Sci. 8(11), 2283 (2018).
[Crossref]

2017 (3)

X. Chen, Z. Ren, Y. Shimizu, Y. Chen, and W. Gao, “Optimal polarization modulation for orthogonal two-axis Lloyd’s mirror interference lithography,” Opt. Express 25(19), 22237–22252 (2017).
[Crossref]

C. Lin, S. Yan, and F. You, “Fabrication and characterization of short-period double-layer cross-grating with holographic lithography,” Opt. Commun. 383, 17–25 (2017).
[Crossref]

D. R. Lincoln, J. J. Charlton, N. A. Hatab, B. Skyberg, N. V. Lavrik, I. I. Kravchenko, J. A. Bradshaw, and M. J. Sepaniak, “Surface Modification of Silicon Pillar Arrays To Enhance Fluorescence Detection of Uranium and DNA,” ACS Omega 2(10), 7313–7319 (2017).
[Crossref]

2016 (4)

D. Yang, C. Li, C. Wang, Y. Ji, and Q. Quan, “High Figure of Merit Fano Resonance in 2-D Defect-Free Pillar Array Photonic Crystal for Refractive Index Sensing,” IEEE Photonics J. 8(6), 1–14 (2016).
[Crossref]

X. Chen, F. Yang, C. Zhang, J. Zhou, and L. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016).
[Crossref]

H. Zhou and L. Zeng, “Method to fabricate orthogonal crossed gratings based on a dual Lloyd’s mirror interferometer,” Opt. Commun. 360, 68–72 (2016).
[Crossref]

Y. Shimizu, R. Aihara, Z. Ren, Y. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref]

2015 (1)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015).
[Crossref]

2014 (2)

M. Vala and J. Homola, “Flexible method based on four-beam interference lithography for fabrication of large areas of perfectly periodic plasmonic arrays,” Opt. Express 22(15), 18778–18789 (2014).
[Crossref]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two dimensional diffraction gratings,” CIRP Ann. 63(1), 461–464 (2014).
[Crossref]

2013 (1)

X. Li, W. Gao, H. S. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

2012 (2)

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

P. Senanayake, C.-H. Hung, J. Shapiro, A. Scofield, A. Lin, B. S. Williams, and D. L. Huffaker, “3D Nanopillar optical antenna photodetectors,” Opt. Express 20(23), 25489–25496 (2012).
[Crossref]

2011 (1)

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and Functional Materials Fabricated by Interferometric Lithography,” Adv. Mater. 23(2), 147–179 (2011).
[Crossref]

2010 (2)

I. Byun and J. Kim, “Cost-effective laser interference lithography using a 405 nm AlInGaN semiconductor laser,” J. Micromech. Microeng. 20(5), 055024 (2010).
[Crossref]

H. Korre, C. P. Fucetola, J. A. Johnson, and K. K. Berggren, “Development of a simple, compact, low-cost interference lithography system,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 28(6), C6Q20–C6Q24 (2010).
[Crossref]

2009 (1)

J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80(1), 015401 (2009).
[Crossref]

2007 (1)

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56(1), 529–532 (2007).
[Crossref]

2005 (1)

S. R. J. Brueck, “Optical and interferometric lithography - Nanotechnology enablers,” Proc. IEEE 93(10), 1704–1721 (2005).
[Crossref]

2004 (1)

D. Xia, A. Biswas, D. Li, and S. R. J. Brueck, “Directed self-assembly of silica nanoparticles into nanometer-scale patterned surfaces using spin-coating,” Adv. Mater. 16(16), 1427–1432 (2004).
[Crossref]

2003 (2)

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Y. Xia, Y. Yin, Y. Lu, and J. McLellan, “Template-assisted self-assembly of spherical colloids into complex and controllable structures,” Adv. Funct. Mater. 13(12), 907–918 (2003).
[Crossref]

2001 (1)

G. A. Ozin and S. M. Yang, “The race for the photonic chip: Colloidal crystal assembly in silicon wafers,” Adv. Funct. Mater. 11(2), 95–104 (2001).
[Crossref]

1989 (1)

C. J. Richard, “Introduction to Microelectronic fabrication: Volume 5 of modular series on solid state devices,” Am. Scientist 77(3), 301–302 (1989).

Abelmann, L.

H. Wolferen and L. Abelmann, Lithography: Principles, Processes and Materials (Nova Science, 2011).

Aihara, R.

Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
[Crossref]

Y. Shimizu, R. Aihara, Z. Ren, Y. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref]

Araki, T.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Berggren, K. K.

H. Korre, C. P. Fucetola, J. A. Johnson, and K. K. Berggren, “Development of a simple, compact, low-cost interference lithography system,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 28(6), C6Q20–C6Q24 (2010).
[Crossref]

Biswas, A.

D. Xia, A. Biswas, D. Li, and S. R. J. Brueck, “Directed self-assembly of silica nanoparticles into nanometer-scale patterned surfaces using spin-coating,” Adv. Mater. 16(16), 1427–1432 (2004).
[Crossref]

Bosse, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015).
[Crossref]

Bradshaw, J. A.

D. R. Lincoln, J. J. Charlton, N. A. Hatab, B. Skyberg, N. V. Lavrik, I. I. Kravchenko, J. A. Bradshaw, and M. J. Sepaniak, “Surface Modification of Silicon Pillar Arrays To Enhance Fluorescence Detection of Uranium and DNA,” ACS Omega 2(10), 7313–7319 (2017).
[Crossref]

Brueck, S. R. J.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and Functional Materials Fabricated by Interferometric Lithography,” Adv. Mater. 23(2), 147–179 (2011).
[Crossref]

S. R. J. Brueck, “Optical and interferometric lithography - Nanotechnology enablers,” Proc. IEEE 93(10), 1704–1721 (2005).
[Crossref]

D. Xia, A. Biswas, D. Li, and S. R. J. Brueck, “Directed self-assembly of silica nanoparticles into nanometer-scale patterned surfaces using spin-coating,” Adv. Mater. 16(16), 1427–1432 (2004).
[Crossref]

Byun, I.

I. Byun and J. Kim, “Cost-effective laser interference lithography using a 405 nm AlInGaN semiconductor laser,” J. Micromech. Microeng. 20(5), 055024 (2010).
[Crossref]

Charlton, J. J.

D. R. Lincoln, J. J. Charlton, N. A. Hatab, B. Skyberg, N. V. Lavrik, I. I. Kravchenko, J. A. Bradshaw, and M. J. Sepaniak, “Surface Modification of Silicon Pillar Arrays To Enhance Fluorescence Detection of Uranium and DNA,” ACS Omega 2(10), 7313–7319 (2017).
[Crossref]

Chen, C.

Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
[Crossref]

X. Chen, Y. Shimizu, C. Chen, Y. Chen, and W. Gao, “Generalized method for probing ideal initial polarization states in multibeam Lloyd’s mirror interference lithography of 2D scale gratings,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(2), 021601 (2018).
[Crossref]

Chen, G.

Chen, L.

X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
[Crossref]

Chen, S.

X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
[Crossref]

Chen, X.

G. Liang, X. Chen, Z. Wen, G. Chen, and L. Guo, “Super-resolution photolithography using dielectric photonic crystal,” Opt. Lett. 44(5), 1182–1185 (2019).
[Crossref]

Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
[Crossref]

X. Chen, Y. Shimizu, C. Chen, Y. Chen, and W. Gao, “Generalized method for probing ideal initial polarization states in multibeam Lloyd’s mirror interference lithography of 2D scale gratings,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(2), 021601 (2018).
[Crossref]

X. Chen, Z. Ren, Y. Shimizu, Y. Chen, and W. Gao, “Optimal polarization modulation for orthogonal two-axis Lloyd’s mirror interference lithography,” Opt. Express 25(19), 22237–22252 (2017).
[Crossref]

X. Chen, F. Yang, C. Zhang, J. Zhou, and L. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016).
[Crossref]

Chen, Y.

X. Chen, Y. Shimizu, C. Chen, Y. Chen, and W. Gao, “Generalized method for probing ideal initial polarization states in multibeam Lloyd’s mirror interference lithography of 2D scale gratings,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(2), 021601 (2018).
[Crossref]

Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
[Crossref]

X. Chen, Z. Ren, Y. Shimizu, Y. Chen, and W. Gao, “Optimal polarization modulation for orthogonal two-axis Lloyd’s mirror interference lithography,” Opt. Express 25(19), 22237–22252 (2017).
[Crossref]

Y. Shimizu, R. Aihara, Z. Ren, Y. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref]

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015).
[Crossref]

Chua, J. K.

J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80(1), 015401 (2009).
[Crossref]

Deng, M.

X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
[Crossref]

Dian, S.

X. Li, W. Gao, H. S. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Estler, W. T.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015).
[Crossref]

Fucetola, C. P.

H. Korre, C. P. Fucetola, J. A. Johnson, and K. K. Berggren, “Development of a simple, compact, low-cost interference lithography system,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 28(6), C6Q20–C6Q24 (2010).
[Crossref]

Gao, W.

Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
[Crossref]

X. Chen, Y. Shimizu, C. Chen, Y. Chen, and W. Gao, “Generalized method for probing ideal initial polarization states in multibeam Lloyd’s mirror interference lithography of 2D scale gratings,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(2), 021601 (2018).
[Crossref]

X. Chen, Z. Ren, Y. Shimizu, Y. Chen, and W. Gao, “Optimal polarization modulation for orthogonal two-axis Lloyd’s mirror interference lithography,” Opt. Express 25(19), 22237–22252 (2017).
[Crossref]

Y. Shimizu, R. Aihara, Z. Ren, Y. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
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X. Li, W. Gao, H. S. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
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Hung, C.-H.

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X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two dimensional diffraction gratings,” CIRP Ann. 63(1), 461–464 (2014).
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D. Xia, A. Biswas, D. Li, and S. R. J. Brueck, “Directed self-assembly of silica nanoparticles into nanometer-scale patterned surfaces using spin-coating,” Adv. Mater. 16(16), 1427–1432 (2004).
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X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
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X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
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[Crossref]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two dimensional diffraction gratings,” CIRP Ann. 63(1), 461–464 (2014).
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X. Li, W. Gao, H. S. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
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D. R. Lincoln, J. J. Charlton, N. A. Hatab, B. Skyberg, N. V. Lavrik, I. I. Kravchenko, J. A. Bradshaw, and M. J. Sepaniak, “Surface Modification of Silicon Pillar Arrays To Enhance Fluorescence Detection of Uranium and DNA,” ACS Omega 2(10), 7313–7319 (2017).
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X. Li, H. Lu, Q. Zhou, G. Wu, K. Ni, and X. Wang, “An Orthogonal Type Two-Axis Lloyd’s Mirror for Holographic Fabrication of Two-Dimensional Planar Scale Gratings with Large Area,” Appl. Sci. 8(11), 2283 (2018).
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W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015).
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X. Li, H. Lu, Q. Zhou, G. Wu, K. Ni, and X. Wang, “An Orthogonal Type Two-Axis Lloyd’s Mirror for Holographic Fabrication of Two-Dimensional Planar Scale Gratings with Large Area,” Appl. Sci. 8(11), 2283 (2018).
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W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
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D. Yang, C. Li, C. Wang, Y. Ji, and Q. Quan, “High Figure of Merit Fano Resonance in 2-D Defect-Free Pillar Array Photonic Crystal for Refractive Index Sensing,” IEEE Photonics J. 8(6), 1–14 (2016).
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Shi, L.

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
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Y. Shimizu, R. Aihara, K. Mano, C. Chen, Y. Chen, X. Chen, and W. Gao, “Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings,” Precis. Eng. 52, 138–151 (2018).
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X. Chen, Z. Ren, Y. Shimizu, Y. Chen, and W. Gao, “Optimal polarization modulation for orthogonal two-axis Lloyd’s mirror interference lithography,” Opt. Express 25(19), 22237–22252 (2017).
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Y. Shimizu, R. Aihara, Z. Ren, Y. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two dimensional diffraction gratings,” CIRP Ann. 63(1), 461–464 (2014).
[Crossref]

X. Li, W. Gao, H. S. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
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T. Kan, K. Matsumoto, and I. Shimoyama, “Nano-pillar structure for sensitivity enhancement of SPR sensor,” presented at the 15th International Conference on Solid-State Sensors, Actuators and Microsystems. Transducers 2009, Denver, CO, USA, 21-25 June 2009.

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D. R. Lincoln, J. J. Charlton, N. A. Hatab, B. Skyberg, N. V. Lavrik, I. I. Kravchenko, J. A. Bradshaw, and M. J. Sepaniak, “Surface Modification of Silicon Pillar Arrays To Enhance Fluorescence Detection of Uranium and DNA,” ACS Omega 2(10), 7313–7319 (2017).
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D. Yang, C. Li, C. Wang, Y. Ji, and Q. Quan, “High Figure of Merit Fano Resonance in 2-D Defect-Free Pillar Array Photonic Crystal for Refractive Index Sensing,” IEEE Photonics J. 8(6), 1–14 (2016).
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X. Li, H. Lu, Q. Zhou, G. Wu, K. Ni, and X. Wang, “An Orthogonal Type Two-Axis Lloyd’s Mirror for Holographic Fabrication of Two-Dimensional Planar Scale Gratings with Large Area,” Appl. Sci. 8(11), 2283 (2018).
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W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015).
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D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and Functional Materials Fabricated by Interferometric Lithography,” Adv. Mater. 23(2), 147–179 (2011).
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Y. Xia, Y. Yin, Y. Lu, and J. McLellan, “Template-assisted self-assembly of spherical colloids into complex and controllable structures,” Adv. Funct. Mater. 13(12), 907–918 (2003).
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X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
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W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

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C. Lin, S. Yan, and F. You, “Fabrication and characterization of short-period double-layer cross-grating with holographic lithography,” Opt. Commun. 383, 17–25 (2017).
[Crossref]

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D. Yang, C. Li, C. Wang, Y. Ji, and Q. Quan, “High Figure of Merit Fano Resonance in 2-D Defect-Free Pillar Array Photonic Crystal for Refractive Index Sensing,” IEEE Photonics J. 8(6), 1–14 (2016).
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X. Chen, F. Yang, C. Zhang, J. Zhou, and L. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016).
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G. A. Ozin and S. M. Yang, “The race for the photonic chip: Colloidal crystal assembly in silicon wafers,” Adv. Funct. Mater. 11(2), 95–104 (2001).
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X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
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Y. Xia, Y. Yin, Y. Lu, and J. McLellan, “Template-assisted self-assembly of spherical colloids into complex and controllable structures,” Adv. Funct. Mater. 13(12), 907–918 (2003).
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C. Lin, S. Yan, and F. You, “Fabrication and characterization of short-period double-layer cross-grating with holographic lithography,” Opt. Commun. 383, 17–25 (2017).
[Crossref]

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X. Mao and L. Zeng, “Design and fabrication of crossed gratings with multiple zero-reference marks for planar encoders,” Meas. Sci. Technol. 29(2), 025204 (2018).
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X. Chen, F. Yang, C. Zhang, J. Zhou, and L. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016).
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X. Chen, F. Yang, C. Zhang, J. Zhou, and L. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016).
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Zhou, L.

X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
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Zhou, Q.

X. Li, H. Lu, Q. Zhou, G. Wu, K. Ni, and X. Wang, “An Orthogonal Type Two-Axis Lloyd’s Mirror for Holographic Fabrication of Two-Dimensional Planar Scale Gratings with Large Area,” Appl. Sci. 8(11), 2283 (2018).
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X. Yin, H. Zhu, H. Guo, M. Deng, T. Xu, Z. Gong, X. Li, Z. Hang, C. Wu, H. Li, S. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13(1), 1800081 (2019).
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ACS Nano (1)

X. Chen, F. Yang, C. Zhang, J. Zhou, and L. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016).
[Crossref]

ACS Omega (1)

D. R. Lincoln, J. J. Charlton, N. A. Hatab, B. Skyberg, N. V. Lavrik, I. I. Kravchenko, J. A. Bradshaw, and M. J. Sepaniak, “Surface Modification of Silicon Pillar Arrays To Enhance Fluorescence Detection of Uranium and DNA,” ACS Omega 2(10), 7313–7319 (2017).
[Crossref]

Adv. Funct. Mater. (2)

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Figures (7)

Fig. 1.
Fig. 1. Schematics of exposure system (a) and orthogonal two-axis Lloyd’s mirrors (b).
Fig. 2.
Fig. 2. Polarization tracing model of orthogonal two-axis Lloyd’s mirrors.
Fig. 3.
Fig. 3. Curve of non-orthogonality of polarization vector with the incident angle.
Fig. 4.
Fig. 4. Experiment setup of exposure system with amplified two-axis Lloyd’s mirrors.
Fig. 5.
Fig. 5. Optical image of finally fabricated 2D grating substrate (a) and orientation of 2D grating substrate in two-axis Lloyd’s mirrors configuration with 16 identified positions measured by AFM (b).
Fig. 6.
Fig. 6. AFM images of the fabricated 2D grating: 16 images from (a) to (p) corresponding to the scanning positions with equal distance located in the whole 20×20 mm2 2D grating.
Fig. 7.
Fig. 7. Scanning data graph of grating pillar-structure and schematic of pillar duty circle measurement standard.

Tables (3)

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Table 1. Parameters of ICP-RIE with Bosch-process.

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Table 2. 2D grating periods analysis in X-axis and Y-axis directions.

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Table 3. Pillar duty cycle analysis in 20×20 mm2 2D grating.

Equations (23)

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e ( r , t ) = A E Re { exp [ i ( k k r ) ω t + δ ] } ,
e ( r , t ) = m  = 1 3 A m E m Re { exp [ i ( k k m r ) ω t + δ m ] } ,
I ( r ) = m = 1 3 A m 2 + 2 m = 1 2 m < n Re { e m ( r , t ) [ e n ( r , t ) ] } ,
I ( r ) = m = 1 3 A m 2 + 2 m = 1 2 m < n A m A n E m E n cos [ ( k m k n ) r + ( δ m δ n ) ] ,
D n m = | E n E m | ,
D n m = | E n E m | = | E m E n | = 0 ,
s m  =  s m  =  k 1 × k m | k 1 × k m | ,
p m = s m × k 1 ,
p m = s m × k m .
k 1  =  ( cos θ cos φ cos θ sin φ sin θ ) ,
k 2  =  ( cos θ cos φ cos θ sin φ sin θ ) ,
k 3  =  ( cos θ cos φ cos θ sin φ sin θ ) .
g 12 = g 13 = 2 π | k 1 k 2 | = 2 π | k 1 k 3 |  =  λ 2 cos θ ,
s 1 = (  -  sin ϕ cos ϕ 0 ) ,
p 1 = ( sin θ cos ϕ sin θ sin ϕ cos θ ) .
O 1 -  o u t = ( p 1 s 1 k 1 ) = ( p 1 -  x s 1 -  x k 1 -  x p 1 -  y s 1 -  y k 1 -  y p 1 -  z s 1 -  z k 1 -  z ) = ( sin θ cos ϕ sin ϕ cos θ cos φ sin θ sin ϕ cos ϕ cos θ sin φ cos θ 0 sin θ ) .
E 1  =  O 1 -  o u t E 1  -  i n .
O 2 -  i n 1 = ( p 2 s 2 k 1 ) T = ( cos 2 θ sin φ cos φ sin 2 θ  +  cos 2 θ cos 2 φ sin 2 θ  +  cos 2 θ cos 2 φ sin θ cos θ sin φ sin 2 θ  +  cos 2 θ cos 2 φ sin θ sin 2 θ  +  cos 2 θ cos 2 φ 0 cos θ cos φ sin 2 θ  +  cos 2 θ cos 2 φ cos θ cos φ cos θ sin φ sin θ ) ,
O 2 -  o u t = ( p 2 s 2 k 2 )  =  ( cos 2 θ sin φ cos φ sin 2 θ  +  cos 2 θ cos 2 φ sin θ sin 2 θ  +  cos 2 θ cos 2 φ cos θ cos φ sin 2 θ  +  cos 2 θ cos 2 φ 0 cos θ sin φ sin θ cos θ sin φ sin 2 θ  +  cos 2 θ cos 2 φ cos θ cos φ sin 2 θ  +  cos 2 θ cos 2 φ sin θ ) .
E 2 = O 2  -  o u t J r  -  X O 2 -  i n 1 O 1 -  o u t E 2 -  i n .
J r  -  X = ( r p  -  X 0 0 0 r s  -  X 0 0 0 1 ) ,
E 3 = O 3  -  o u t J r  -  Y O 3 -  i n 1 O 1 -  o u t E 3 -  i n ,
D 23 = | E 2 E 3 | .

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