Abstract

We present the concept of spectral sorting using normalized optical efficiency and systematically study the dielectric based multilayer structure for spectral sorting of visible light with silicon as the absorbing material. We show that by using grating structures, the spectral sorter structures are more efficient when the detector size is less than 1µm, enabling the shrinking of the detector size to the wavelength scale. A comprehensive design strategy is derived that could be used as a design guideline to achieve the sorting of visible light. We show that for pixel size as small as 0.5µm, optical efficiency as high as 80% could be achieved using dielectric based sorting structures.

© 2017 Optical Society of America

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References

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  1. Y. Huo, C. C. Fesenmaier, and P. B. Catrysse, “Microlens performance limits in sub-2µm pixel CMOS image sensors,” Opt. Express 18(6), 5861–5872 (2010).
    [PubMed]
  2. A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electro. Rev. 12(2), 221–245 (2004).
  3. A. Rogalski, “Progress in focal plane array technologies,” Prog. Quantum Electron. 36(2), 342–473 (2012).
  4. H. Iwai, “Roadmap for 22nm and beyond,” Microelectron. Eng. 86, 1520–1528 (2009).
  5. A. Theuwissen, “CMOS image sensors: State-of-the-art and future perspectives,” in Proc. 33rd European Solid-State Circuits Conf. (ESSCIRC, 2007), pp. 21 −27.
  6. T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).
  7. R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).
  8. A. Rogalski, “Infrared detectors: status and trends,” Prog. Quantum Electron. 27(59), 59–210 (2003).
  9. J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).
  10. H. Dammann, “Color Separation Gratings,” Appl. Opt. 17(15), 2273–2279 (1978).
    [PubMed]
  11. K. Knop, “Diffraction gratings for color filtering in the zero diffraction order,” Appl. Opt. 17(22), 3598–3603 (1978).
    [PubMed]
  12. M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).
  13. B. Layet, I. G. Cormack, and M. R. Taghizadeh, “Stripe color separation with diffractive optics,” Appl. Opt. 38(35), 7193–7201 (1999).
    [PubMed]
  14. S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).
  15. T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).
  16. R. Marinelli and E. Palange, “Optical performances of lensless sub-2micron pixel for application in image sensors,” Prog. Electromagnetics Res. B 31, 1–14 (2011).
  17. C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16(25), 20457–20470 (2008).
    [PubMed]
  18. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  19. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).
  20. R. C. Tyan, A. A. Salvekar, H. P. Chou, C. C. Cheng, A. Scherer, P. C. Sun, F. Xu, and Y. Fainman, “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14(7), 1627–1636 (1997).
  21. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53 (1997).
  22. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
    [PubMed]
  23. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Phys. JETP-USSR 2(3), 466–475 (1956).

2013 (1)

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

2012 (1)

A. Rogalski, “Progress in focal plane array technologies,” Prog. Quantum Electron. 36(2), 342–473 (2012).

2011 (1)

R. Marinelli and E. Palange, “Optical performances of lensless sub-2micron pixel for application in image sensors,” Prog. Electromagnetics Res. B 31, 1–14 (2011).

2010 (1)

2009 (2)

H. Iwai, “Roadmap for 22nm and beyond,” Microelectron. Eng. 86, 1520–1528 (2009).

R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).

2008 (2)

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16(25), 20457–20470 (2008).
[PubMed]

T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

2006 (1)

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

2004 (1)

A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electro. Rev. 12(2), 221–245 (2004).

2003 (1)

A. Rogalski, “Infrared detectors: status and trends,” Prog. Quantum Electron. 27(59), 59–210 (2003).

2000 (1)

T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).

1999 (2)

1997 (2)

1983 (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).

1978 (2)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Phys. JETP-USSR 2(3), 466–475 (1956).

Ahn, J. C.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Bhan, R. K.

R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).

Catrysse, P.

T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).

Catrysse, P. B.

Chen, T.

T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).

Cheng, C. C.

Choi, C. H.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Choi, S.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Chou, H. P.

Cormack, I. G.

Dammann, H.

Ebbesen, T. W.

T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

Fainman, Y.

Fesenmaier, C. C.

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).

Fujii, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

Gamal, A. E.

T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).

Genet, C.

T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

Hane, K.

Hiramoto, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

Hiroshige, G.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Huo, Y.

Iwai, H.

H. Iwai, “Roadmap for 22nm and beyond,” Microelectron. Eng. 86, 1520–1528 (2009).

Jalwania, C. R.

R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).

Jeong, H.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Kanamori, Y.

Kim, B.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Kim, H.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Klaus, W.

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

Knop, K.

Kodate, K.

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

Komai, Y.

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

Lalanne, P.

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53 (1997).

Laux, E.

T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

Layet, B.

Lee, D.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Lee, K.

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

Lomash, S. K.

R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).

Marinelli, R.

R. Marinelli and E. Palange, “Optical performances of lensless sub-2micron pixel for application in image sensors,” Prog. Electromagnetics Res. B 31, 1–14 (2011).

Morris, G. M.

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53 (1997).

Nagayoshi, M.

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

Nakamura, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

Nishiwaki, S.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

Oka, K.

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

Palange, E.

R. Marinelli and E. Palange, “Optical performances of lensless sub-2micron pixel for application in image sensors,” Prog. Electromagnetics Res. B 31, 1–14 (2011).

Rogalski, A.

A. Rogalski, “Progress in focal plane array technologies,” Prog. Quantum Electron. 36(2), 342–473 (2012).

A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electro. Rev. 12(2), 221–245 (2004).

A. Rogalski, “Infrared detectors: status and trends,” Prog. Quantum Electron. 27(59), 59–210 (2003).

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Phys. JETP-USSR 2(3), 466–475 (1956).

Salvekar, A. A.

Sasaki, M.

Saxena, R. S.

R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).

Scherer, A.

Skauli, T.

T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

Sun, P. C.

Suzuki, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

Taghizadeh, M. R.

Tyan, R. C.

Wandell, B.

T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).

Xu, F.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).

Def. Sci. J. (1)

R. K. Bhan, R. S. Saxena, C. R. Jalwania, and S. K. Lomash, “Uncooled Infrared Microbolometer Arrays and their Characterisation Techniques,” Def. Sci. J. 59, 580–590 (2009).

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

Jpn. J. Appl. Phys. (1)

M. Nagayoshi, K. Oka, W. Klaus, Y. Komai, and K. Kodate, “Design and Evaluation of Color Separation Grating Using rigorous Coupled Wave Analysis,” Jpn. J. Appl. Phys. 45, 6670 (2006).

Microelectron. Eng. (1)

H. Iwai, “Roadmap for 22nm and beyond,” Microelectron. Eng. 86, 1520–1528 (2009).

Nanotechnology (1)

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53 (1997).

Nat. Photonics (2)

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7, 240–246 (2013).

T. Skauli, E. Laux, C. Genet, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

Opt. Express (2)

Opt. Lett. (1)

Opto-Electro. Rev. (1)

A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electro. Rev. 12(2), 221–245 (2004).

Proc. SPIE (1)

T. Chen, P. Catrysse, A. E. Gamal, and B. Wandell, “How small should pixel size be?” Proc. SPIE 3965, 451–459 (2000).

Prog. Electromagnetics Res. B (1)

R. Marinelli and E. Palange, “Optical performances of lensless sub-2micron pixel for application in image sensors,” Prog. Electromagnetics Res. B 31, 1–14 (2011).

Prog. Quantum Electron. (2)

A. Rogalski, “Progress in focal plane array technologies,” Prog. Quantum Electron. 36(2), 342–473 (2012).

A. Rogalski, “Infrared detectors: status and trends,” Prog. Quantum Electron. 27(59), 59–210 (2003).

Soviet Phys. JETP-USSR (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Phys. JETP-USSR 2(3), 466–475 (1956).

Other (3)

J. C. Ahn, B. Kim, K. Lee, S. Choi, H. Jeong, H. Kim, G. Hiroshige, C. H. Choi, and D. Lee, “SNR Metric and Crosstalk in Color Image Sensor of Small Size Pixel,” Proc. VLSI-TSA(1–2), (2013).

A. Theuwissen, “CMOS image sensors: State-of-the-art and future perspectives,” in Proc. 33rd European Solid-State Circuits Conf. (ESSCIRC, 2007), pp. 21 −27.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

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Figures (8)

Fig. 1
Fig. 1 (a) Reduction of dimension of square shaped pixel (or detector), (b) Incidence area considered for calculating NOE over two pixels.
Fig. 2
Fig. 2 (a) Two layer dielectric structure on top of silicon, with individual thickness of 100nm. Reflection as a function of wavelength and refractive index of top layer ( n gt ) with index of second layer (b) n IL =1.5 and (c) n IL =2.0, (d) reflection of two layer system with index of first layer n gt :2.1.
Fig. 3
Fig. 3 (a) Unit cell of the periodic arrangement of layered structures designed to minimize reflection at different wavelengths. Absorption spectra of silicon under the layered system with first- and second- layer made of material with indices (b) n gt :2.1 and n IL1 :2.0, (c) n gt :2.1 and n IL2 :1.5 for different sizes (Px) of the structure.
Fig. 4
Fig. 4 (a) Homogenization of grating with subwavelength period. The effective index of homogenous layer is calculated using effective medium theory. (b) Effective index as a function of wavelength for different grating widths with grating refractive index of 2.5 and period 250nm.
Fig. 5
Fig. 5 (a) Unit cell of periodic arrangement of two layered structure with groove in junction of two antireflecting structures (configuration C1). Absorption as a function of wavelength in silicon under (b) n IL1 :1.5 and (c) n IL2 :2.0 for configuration C1. (d) Unit cell of periodic arrangement of two layered structure with grating stub in junction of two antireflecting structures (configuration C2). Absorption as a function of wavelength in silicon under, (e) n IL1 :1.5 and (f) n IL2 :2.0 for configuration C2.
Fig. 6
Fig. 6 Electromagnetic power dissipation in silicon as a function of spatial position for configuration C2 at wavelength of (a) 520nm and (b) 420nm. The red arrow indicates the power flow time average in the structure.
Fig. 7
Fig. 7 (a) Three layer structure for selective antireflection of colored light. (b) Reflection as a function of wavelength of the three layer antireflection structure (B1-G1) designed for blue-green light, with d 1 : 60nm, d 2 : 100nm and d 3 :50nm and n 1 : 2.1, n 2 : 1.5 for blue, n 2 : 2.0 for green light and n 3 : 1.5 (c) Reflection as a function of wavelength of the three layer antireflection structure (G2-R1) designed for green-red light, with d 1 : 90nm, d 2 : 100nm and d 3 :50nm and n 1 : 2.1, n 2 : 1.5 for green, n 2 : 2.0 for red light and n 3 : 1.5. (d) Unit cell of periodic arrangement of three layered structure with grating stub in junction between the two antireflecting structures, (e) Absorption spectra of B1-G1 structure, and (f) Absorption spectra of G2-R1 structure.
Fig. 8
Fig. 8 Absorption as a function of the incident angle θ, for configuration C2 with Px = 0.5µm, for (a) n IL1 :1.5 and (b) n IL2 :2.0; Region of spectral sorting is delimited by a dashed line.

Equations (3)

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NO E B (or G) = P DB (or G) P inc =  FF× A 1 A 1 + A 2 η B(or G)
n eff (2) = [ ( n TE (0) ) 2 + 1 3 ( P λ ) 2 π 2 f 2 ( 1f ) 2 ( n g 2 n 0 2 ) 2 ] 1/2
n TE (0) = [ ( 1f ) n 0 2 +f n g 2 ] 1/2

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