Abstract

In this paper, we propose a method to analyze the light extraction efficiency (LEE) enhancement of a nanopatterned sapphire substrates (NPSS) light-emitting diode (LED) by comparing wave optics software with ray optics software. Finite-difference time-domain (FDTD) simulations represent the wave optics software and Light Tools (LTs) simulations represent the ray optics software. First, we find the trends of and an optimal solution for the LEE enhancement when the 2D-FDTD simulations are used to save on simulation time and computational memory. The rigorous coupled-wave analysis method is utilized to explain the trend we get from the 2D-FDTD algorithm. The optimal solution is then applied in 3D-FDTD and LTs simulations. The results are similar and the difference in LEE enhancement between the two simulations does not exceed 8.5% in the small LED chip area. More than 104 times computational memory is saved during the LTs simulation in comparison to the 3D-FDTD simulation. Moreover, LEE enhancement from the side of the LED can be obtained in the LTs simulation. An actual-size NPSS LED is simulated using the LTs. The results show a more than 307% improvement in the total LEE enhancement of the NPSS LED with the optimal solution compared to the conventional LED.

© 2013 Optical Society of America

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2012

2011

C. C. Sun, S. Y. Tsai, and T. X. Lee, “Enhancement of angular flux utilization based on implanted micro pyramid array and lens encapsulation in GaN LEDs,” J. Disp. Technol. 7, 289–294 (2011).
[CrossRef]

J. W. Pan and C. W. Fan, “The high luminance hybrid light guide plate for backlight module application,” Opt. Express 19, 20079–20087 (2011).
[CrossRef]

2010

J. W. Pan, S. H. Tu, W. S. Sun, C. M. Wang, and J. Y. Chang, “Integration of non-Lambertian LED and reflective optical element as efficient street lamp,” Opt. Express 18, A221–A230 (2010).
[CrossRef]

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

C. C. Kao, Y. K. Su, C. L. Lin, and J. J. Chen, “The aspect ratio effects on the performances of GaN-based light-emitting diodes with nanopatterned sapphire substrates,” Appl. Phys. Lett. 97, 023111 (2010).
[CrossRef]

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron. 46, 1456–1463 (2010).
[CrossRef]

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46, 714–720 (2010).
[CrossRef]

2009

C. Weisman, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs—designing light extraction,” Laser Photon. Rev. 3, 262–286 (2009).
[CrossRef]

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Quantum Electron. 15, 1257–1263(2009).
[CrossRef]

2008

H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

2007

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

T. X. Lee, K. F. Gao, W. T. Chien, and C. C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express 15, 6670–6676 (2007).
[CrossRef]

2006

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

2005

2004

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

2001

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

1999

Abe, Y.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Bao, K.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Bergenek, K.

C. Weisman, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs—designing light extraction,” Laser Photon. Rev. 3, 262–286 (2009).
[CrossRef]

Chang, J. Y.

Chen, J. J.

C. C. Kao, Y. K. Su, C. L. Lin, and J. J. Chen, “The aspect ratio effects on the performances of GaN-based light-emitting diodes with nanopatterned sapphire substrates,” Appl. Phys. Lett. 97, 023111 (2010).
[CrossRef]

Chen, Y.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Chien, W. T.

Craford, M. G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

Dai, T.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Deguchi, K.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

DenBaars, S. P.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

Fan, C. W.

Fu, Q.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Fujii, H.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Fujii, T.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

Gao, H.

H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

Gao, K. F.

Gao, Y.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

Gardner, N. F.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Academic, 2005).

Harbers, G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

Hu, E. L.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

Hwang, I. K.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Quantum Electron. 15, 1257–1263(2009).
[CrossRef]

Jin, X.

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron. 46, 1456–1463 (2010).
[CrossRef]

Juan, T. K.

Kang, X. N.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Kannaka, M.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Kao, C. C.

C. C. Kao, Y. K. Su, C. L. Lin, and J. J. Chen, “The aspect ratio effects on the performances of GaN-based light-emitting diodes with nanopatterned sapphire substrates,” Appl. Phys. Lett. 97, 023111 (2010).
[CrossRef]

Kern, R. S.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Krames, M. R.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Lee, R. K.

Lee, T. X.

Li, B.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Li, J.

H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

Lian, G. J.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Lin, C. L.

C. C. Kao, Y. K. Su, C. L. Lin, and J. J. Chen, “The aspect ratio effects on the performances of GaN-based light-emitting diodes with nanopatterned sapphire substrates,” Appl. Phys. Lett. 97, 023111 (2010).
[CrossRef]

Lin, C. Y.

Lin, S. F.

Linder, N.

C. Weisman, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs—designing light extraction,” Laser Photon. Rev. 3, 262–286 (2009).
[CrossRef]

Long, D. H.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Quantum Electron. 15, 1257–1263(2009).
[CrossRef]

Ludowise, M. J.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Ma, S. H.

Matsumoto, H.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Mueller, G. O.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

Mueller-Mach, R.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

Mukai, T.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

Murakami, K.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Nakamura, S.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

Narita, J.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

Narukawa, Y.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

O’Shea, J. J.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Okada, N.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Okuno, T.

T. Okuno, “Development of subwavelength structure coating (SWC) and its application to imaging lenses,” in International Optical Design Conference, Vol. 7652 of 2010 SPIE-OSA Technical Digest Series (Optical Society of America, 2010), paper IMA2.

Painter, O. J.

Pan, J. W.

Ryu, H. Y.

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46, 714–720 (2010).
[CrossRef]

Ryu, S. W.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Quantum Electron. 15, 1257–1263(2009).
[CrossRef]

Sakamoto, T.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

Scherer, A.

Schwarz, U. T.

C. Weisman, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs—designing light extraction,” Laser Photon. Rev. 3, 262–286 (2009).
[CrossRef]

Sharma, R.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

Shchekin, O. B.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

Shim, J. I.

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46, 714–720 (2010).
[CrossRef]

Shinagawa, T.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Steigerwald, D. A.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Stockman, S. A.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Su, Y. K.

C. C. Kao, Y. K. Su, C. L. Lin, and J. J. Chen, “The aspect ratio effects on the performances of GaN-based light-emitting diodes with nanopatterned sapphire substrates,” Appl. Phys. Lett. 97, 023111 (2010).
[CrossRef]

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Sun, W. S.

Sun, Y. J.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Tadatomo, K.

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

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A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Academic, 2005).

Trieu, S. S.

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron. 46, 1456–1463 (2010).
[CrossRef]

Tsai, S. Y.

C. C. Sun, S. Y. Tsai, and T. X. Lee, “Enhancement of angular flux utilization based on implanted micro pyramid array and lens encapsulation in GaN LEDs,” J. Disp. Technol. 7, 289–294 (2011).
[CrossRef]

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Vuckovic, J. S.

Wang, C. M.

Wang, C. S.

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H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

Weisman, C.

C. Weisman, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs—designing light extraction,” Laser Photon. Rev. 3, 262–286 (2009).
[CrossRef]

Wierer, J. J.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

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K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

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Yamada, T.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

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H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

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Zeng, Y.

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[CrossRef]

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K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Zhang, G. Y.

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

Zhang, Y.

H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

Zhou, L.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

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T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855–857 (2004).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O’Shea, M. J. Ludowise, N. F. Gardner, R. S. Kern, and S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

K. Bao, X. N. Kang, B. Zhang, T. Dai, Y. J. Sun, Q. Fu, G. J. Lian, G. C. Xiong, G. Y. Zhang, and Y. Chen, “Improvement of light extraction from GaN-based thin-film light-emitting diodes by patterning undoped GaN using modified laser lift-off,” Appl. Phys. Lett. 92, 141104 (2008).
[CrossRef]

C. C. Kao, Y. K. Su, C. L. Lin, and J. J. Chen, “The aspect ratio effects on the performances of GaN-based light-emitting diodes with nanopatterned sapphire substrates,” Appl. Phys. Lett. 97, 023111 (2010).
[CrossRef]

IEEE J. Quantum Electron.

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron. 46, 1456–1463 (2010).
[CrossRef]

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[CrossRef]

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Quantum Electron. 15, 1257–1263(2009).
[CrossRef]

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H. Gao, F. Yan, Y. Zhang, J. Li, Y. Zeng, and G. Wang, “Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale,” J. Appl. Phys. 103, 014314 (2008).
[CrossRef]

J. Disp. Technol.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
[CrossRef]

C. C. Sun, S. Y. Tsai, and T. X. Lee, “Enhancement of angular flux utilization based on implanted micro pyramid array and lens encapsulation in GaN LEDs,” J. Disp. Technol. 7, 289–294 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

Y. Narukawa, J. Narita, T. Sakamoto, K. Deguchi, T. Yamada, and T. Mukai, “Ultra-high efficiency white light emitting diodes,” Jpn. J. Appl. Phys. 45, L1084–L1086 (2006).
[CrossRef]

Laser Photon. Rev.

C. Weisman, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs—designing light extraction,” Laser Photon. Rev. 3, 262–286 (2009).
[CrossRef]

Opt. Express

Phys. Status Solidi C

T. Shinagawa, Y. Abe, H. Matsumoto, B. Li, K. Murakami, N. Okada, K. Tadatomo, M. Kannaka, and H. Fujii, “Light-emitting diodes fabricated on nanopatterned sapphire substrates by thermal lithography,” Phys. Status Solidi C 7, 2165–2167 (2010).
[CrossRef]

Other

T. Okuno, “Development of subwavelength structure coating (SWC) and its application to imaging lenses,” in International Optical Design Conference, Vol. 7652 of 2010 SPIE-OSA Technical Digest Series (Optical Society of America, 2010), paper IMA2.

Lumerical, http://www.lumerical.com .

Optial Research Associates (ORA), http://www.opticalres.com .

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Academic, 2005).

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Figures (10)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the NPSS LED in the FDTD simulation and (b) thickness and refractive index of each layer in the FDTD simulation.

Fig. 2.
Fig. 2.

Schematic diagram of three kinds of dipole sources located in the x-y plane: center of D, center of P, and center of diagonal line between adjacent patterns on the NPSS.

Fig. 3.
Fig. 3.

LEE enhancement results as a function of the aspect ratio (H/D) with the rectangular patterned NPSS (a) from the top monitor and (b) from the bottom monitor.

Fig. 4.
Fig. 4.

LEE enhancement as a function of the fill factor (D/P) with the rectangular NPSS (a) from the top monitor and (b) from the bottom monitor.

Fig. 5.
Fig. 5.

LEE enhancement as a function of the aspect ratio (H/D) with the triangular patterned NPSS (a) from the top monitor and (b) from the bottom monitor.

Fig. 6.
Fig. 6.

LEE enhancement as a function of the fill factor (D/P) with the triangular patterned NPSS (a) from the top monitor and (b) from the bottom monitor.

Fig. 7.
Fig. 7.

(a1)–(a4) show the different diffraction order and angle when the incident angle is 0, 30, 45, and 60 deg. The dashed line represents the escape angle range. (b) Shows the diffraction efficiency calculated within the escape angle range as a function of the period with different AR.

Fig. 8.
Fig. 8.

(a) Top LEE enhancement and computational memory as a function of the LED chip area and (b) top LEE enhancement as a function of the LED chip area.

Fig. 9.
Fig. 9.

Schematic diagram of the sapphire substrate model with (a) PML and (b) reflective boundary at the bottom surface of the sapphire substrate.

Fig. 10.
Fig. 10.

Reflectance as a function of (a) d and w and (b) d with a constant d/w.

Tables (2)

Tables Icon

Table 1. Kinds of Dipole Source State

Tables Icon

Table 2. LEE Enhancement in the Three Cases

Equations (3)

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

ε=[i=1N12surface(P)da]/N,
γ=εNPSSLED/εConventionalLED.
Reflectance(%)=PReflectionPPMLPPML×100%.

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