Abstract

The light extraction efficiency of a light-emitting element with microstructured surface is analyzed with a rigorous grating diffraction theory. The grating theory reveals an improvement of extraction efficiency due to diffraction of light by the surface microstructure. The simulation results show that the improvement of extraction efficiency is due mainly to the reflected diffraction rather than to the transmitted diffraction. A part of total-internal-reflection light is diffracted into directions at less than the critical angle. Extraction efficiency is improved by multiple reflection and diffraction of light in a high-refractive-index layer. We propose a simple design method for an efficient surface microstructure from the viewpoint of reflected diffraction.

© 2006 Optical Society of America

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  1. M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
    [CrossRef]
  2. Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
    [CrossRef]
  3. T.-X. Lee, C.-Y. Lin, S.-H. Ma, and C.-C. Sun, "Analysis of position dependent light extraction GaN-based LEDs," Opt. Express 13, 4175-4179 (2005).
    [CrossRef] [PubMed]
  4. K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
    [CrossRef]
  5. Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
    [CrossRef]
  6. M. G. Moharam and T. K. Gaylord, "Three dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 73, 1105-1112 (1983).
    [CrossRef]
  7. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).
    [CrossRef]
  8. P. Vincent, "A finite-difference method for dielectric and conducting crossed gratings," Opt. Commun. 26, 293-296 (1978).
    [CrossRef]
  9. H. Rigneault, F. Lemarchand, and A. Sentenac, "Dipole radiation into grating structure," J. Opt. Soc. Am. A 17, 1048-1058 (2000).
    [CrossRef]
  10. D. Delbeke, P. Bienstman, R. Bockstaele, and R. Baets, "Rigorous electromagnetic analysis of dipole emission in periodically corrugated layers: the grating-assisted resonant-cavity light-emitting diode," J. Opt. Soc. Am. A 19, 871-880 (2002).
    [CrossRef]
  11. See, for example, Principles of Optics, 6th ed. (Pergamon, 1989), pp. 615-617.

2005 (1)

2004 (2)

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

2003 (1)

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

2002 (2)

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

D. Delbeke, P. Bienstman, R. Bockstaele, and R. Baets, "Rigorous electromagnetic analysis of dipole emission in periodically corrugated layers: the grating-assisted resonant-cavity light-emitting diode," J. Opt. Soc. Am. A 19, 871-880 (2002).
[CrossRef]

2000 (1)

1995 (1)

1989 (1)

See, for example, Principles of Optics, 6th ed. (Pergamon, 1989), pp. 615-617.

1983 (1)

1978 (1)

P. Vincent, "A finite-difference method for dielectric and conducting crossed gratings," Opt. Commun. 26, 293-296 (1978).
[CrossRef]

Baets, R.

Bienstman, P.

Bockstaele, R.

Cho, S.-H.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Deguchi, K.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Delbeke, D.

Do, Y. R.

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Huh, J.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Kim, G.-H

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Kim, S.-H.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Kim, Y.-C.

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Lee, T.-X.

Lee, Y.-H.

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Lee, Y.-J.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

Lemarchand, F.

Lin, C.-Y.

Ma, S.-H.

Mitani, T.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Moharam, M. G.

Mukai, T.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Narukawa, Y.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Niki, I.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Orita, K.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Pommet, D. A.

Rigneault, H.

Sano, M.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Sentenac, A.

Shioji, S.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Song, Y.-W.

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

Sonobe, A.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Sun, C.-C.

Takigawa, S.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Takizawa, T.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Tamura, S.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Ueda, D.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Ueda, T.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Vincent, P.

P. Vincent, "A finite-difference method for dielectric and conducting crossed gratings," Opt. Commun. 26, 293-296 (1978).
[CrossRef]

Yamada, M.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Yuri, M.

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, "A high-extraction-efficiency nanopatternd organic light-emitting diode," Appl. Phys. Lett. 82, 3779-3781 (2003).
[CrossRef]

J. Appl. Phys. (1)

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emittingdiodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys., Part 1 (2)

K. Orita, S. Tamura, T. Takizawa, T. Ueda, M. Yuri,S. Takigawa, and D. Ueda, "High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal," Jpn. J. Appl. Phys., Part 1 , 43, 5809-5813 (2004).
[CrossRef]

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, A. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high extractional quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J. Appl. Phys., Part 1 , 41, L1431-L1433 (2002).
[CrossRef]

Opt. Commun. (1)

P. Vincent, "A finite-difference method for dielectric and conducting crossed gratings," Opt. Commun. 26, 293-296 (1978).
[CrossRef]

Opt. Express (1)

Other (1)

See, for example, Principles of Optics, 6th ed. (Pergamon, 1989), pp. 615-617.

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Figures (8)

Fig. 1
Fig. 1

Simple structure of a GaN light-emitting diode. The GaN layer is covered by epoxy resin. The bottom layer is aluminum, acting as a reflective electrode.

Fig. 2
Fig. 2

Schematic diagram of diffraction of light from the two dimensionally periodic structured surface.

Fig. 3
Fig. 3

Transmittance and reflectance of diffraction orders, η m , n and ξ m , n . The transmittance of (0, 0) means η 0 , 0 ( θ t , ϕ t ) , and the reflectance of ( ± 1 , ± 1 ) expresses the sum of reflectance, ξ 1 , 1 + ξ 1 , 1 + ξ 1 , 1 + ξ 1 , 1 . The center of each figure is the origin of the diffraction angle, which means θ t = ϕ t = 0 or θ r = ϕ r = 0 . The radius is angle θ t or θ r , and the argument is azimuth ϕ t or ϕ r .

Fig. 4
Fig. 4

Sums of transmittance and reflectance, η ( θ t , ϕ t ) and ξ ( θ r , ϕ r ) , for the structured surface. The right column shows calculation results for the flat surface. The center of each figure is the origin of the diffraction angle, which means θ t = ϕ t = 0 or θ r = ϕ r = 0 . The radius is angle θ t or θ r , and the argument is azimuth ϕ t or ϕ r .

Fig. 5
Fig. 5

Schematic diagram of the multiple reflection and diffraction in the high-refractive-index layer.

Fig. 6
Fig. 6

Extraction efficiency η ̃ as a function of the number of incidences k. “Structured” and “flat” are the efficiencies for the structured surface and the flat surface, respectively. “3% absorb.” is for the structured surface, and the active layer absorbs light energy by 3% for each passing the active layer at the normal incidence.

Fig. 7
Fig. 7

Angular radiation pattern after the multiple reflection of the structured and flat surfaces.

Fig. 8
Fig. 8

Extraction efficiency and sum of diffraction efficiencies with respect to the projection height. A and B are the indices based on the reflected diffraction efficiencies, which are defined by Eqs. (21, 22), respectively. C and D are the indices based on the transmitted diffraction efficiencies.

Tables (1)

Tables Icon

Table 1 Transmittance and Reflectance of Each Diffraction Order, η ¯ m , n and ξ ¯ m , n

Equations (22)

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

n 2 λ sin θ t ( cos ϕ t , sin ϕ t ) = n 1 λ ( sin θ i ) ( cos ϕ i , sin ϕ i ) + ( m Λ x , n Λ y )
n 1 λ sin θ r ( cos ϕ r , sin ϕ r ) = n 1 λ ( sin θ i ) ( cos ϕ i , sin ϕ i ) + ( m Λ x , n Λ y )
1 2 π 0 2 π 0 π 2 T m , n ( θ i , ϕ i ) sin θ i d θ i d ϕ i = 1 2 π 0 2 π 0 π 2 T m , n ( θ t , ϕ t ) U m , n ( θ t , ϕ t ) J t , m , n d θ t d ϕ t = 1 2 π 0 2 π 0 π 2 η m , n ( θ t , ϕ t ) sin θ t d θ t d ϕ t .
η m , n ( θ t , ϕ t ) = T m , n ( θ t , ϕ t ) U m , n ( θ t , ϕ t ) J t , m , n sin θ t .
1 2 π 0 2 π 0 π 2 R m , n ( θ i , ϕ i ) sin θ i d θ i d ϕ i = 1 2 π 0 2 π 0 π 2 R m , n ( θ r , ϕ r ) V m , n ( θ r , ϕ r ) J r , m , n d θ r d ϕ r = 1 2 π 0 2 π 0 π 2 ξ m , n ( θ r , ϕ r ) sin θ r d θ r d ϕ r ,
ξ m , n ( θ r , ϕ r ) = R m , n ( θ r , ϕ r ) V ( θ r , ϕ r ) J r , m , n sin θ r .
η ( θ t , ϕ t ) = m n η m , n ( θ t , ϕ t ) ,
ξ ( θ r , ϕ r ) = m n ξ m , n ( θ r , ϕ r ) .
η ¯ = 1 2 π 0 2 π 0 π 2 η ( θ t , ϕ t ) sin θ t d θ t d ϕ t ,
ξ ¯ = 1 2 π 0 2 π 0 π 2 ξ ( θ r , ϕ r ) sin θ r d θ r d ϕ r .
η ¯ m , n = 0 2 π 0 π 2 η m , n ( θ t , ϕ t ) sin θ t d θ t d ϕ t ,
ξ ¯ m , n = 0 2 π 0 π 2 ξ m , n ( θ r , ϕ r ) sin θ r d θ r d ϕ r .
η ¯ = m n η ¯ m , n ,
ξ ¯ = m n ξ ¯ m , n .
I ( 1 ) ( θ i , ϕ i ) = 1 2 [ 1 + R B ( θ i , ϕ i ) ] ,
η ̃ 1 = 1 2 π m n 0 2 π 0 π 2 T m , n ( θ i , ϕ i ) I ( 1 ) ( θ i , ϕ i ) sin θ i d θ i d ϕ i ;
η ( 1 ) ( θ t , ϕ t ) = 1 2 π m n T m , n ( θ t , ϕ t ) I ( 1 ) ( θ t , ϕ t ) U m , n ( θ t , ϕ t ) J t , m , n sin θ t .
ξ ( 1 ) ( θ r , ϕ r ) = 1 2 π m n R m , n ( θ r , ϕ r ) I ( 1 ) ( θ r , ϕ r ) V m , n ( θ r , ϕ r ) J r , m , n sin θ r .
I ( 2 ) ( θ r , ϕ r ) = R B ( θ r , ϕ r ) ξ ( 1 ) ( θ r , ϕ r ) .
η ̃ = k = 1 η ̃ ( k ) ,
A = 0 π 2 m , n 0 , 0 R m , n ( θ i , 0 ) d θ i + 0 π 2 m , n 0 , 0 R m , n ( θ i , π 4 ) d θ i ,
B = 0 π 2 m , n 0 , 0 R m , n ( θ i , 0 ) sin θ i d θ i + 0 π 2 m , n 0 , 0 R m , n ( θ i , π 4 ) sin θ i d θ i .

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