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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25373–25380
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Size-controllable nanopyramids photonic crystal selectively grown on p-GaN for enhanced light-extraction of light-emitting diodes

Chengxiao Du, Tongbo Wei, Haiyang Zheng, Liancheng Wang, Chong Geng, Qingfeng Yan, Junxi Wang, and Jinmin Li  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25373-25380 (2013)
http://dx.doi.org/10.1364/OE.21.025373


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Abstract

Size-controllable p-GaN hexagonal nanopyramids (HnPs)-photonic crystal (PhC) structures were selectively grown on flat p-GaN layer for the elimination of total internal reflection of light-emitting diodes (LEDs). The LEDs with HnPs-PhC of 46.3% bottom fill factor (PhC lattice constant is 730 nm) showed an improved light output power by 99.9% at forward current of 350 mA compared to the reference LEDs with flat p-GaN layer. We confirmed the effect of HnPs-PhC with different bottom fill factors and the effect of nanopyramid-shaped and nanocolumn-shaped PhC on the light-extraction of LEDs was also investigated by using three-dimensional finite-difference time-domain simulations.

© 2013 Optical Society of America

1. Introduction

GaN-based light-emitting diodes (LEDs) are becoming an increasingly attractive alternative to conventional light sources due to their compact structures, high efficiency and long lifetime. Ongoing research is dedicated to improving their performance through the use of more efficient light-generating and light-extracting structures [1

1. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009). [CrossRef]

]. As a consequence of the total internal reflection (TIR) caused by the large discrepancy of the refractive index between the GaN (n = 2.52) and the air (n = 1.0), a large amount of light emitted from the active region is trapped inside the LEDs, resulting in low light-extraction efficiency (LEE) for LED devices [2

2. A. I. Zhmakin, “Enhancement of light extraction from light emitting diodes,” Phys. Rep. 498(4-5), 189–241 (2011). [CrossRef]

]. To solve this problem, many methods have been used to model the propagation of emitted light by the surface/interface morphology modification, including the use of surface texturing [3

3. 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(6), 855–857 (2004). [CrossRef]

,4

4. T. B. Wei, Q. F. Kong, J. X. Wang, J. Li, Y. P. Zeng, G. H. Wang, J. M. Li, Y. X. Liao, and F. T. Yi, “Improving light extraction of InGaN-based light emitting diodes with a roughened p-GaN surface using CsCl nano-islands,” Opt. Express 19(2), 1065–1071 (2011). [CrossRef] [PubMed]

], sapphire substrates patterning [5

5. K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato, and T. Taguchi, “High output power InGaN ultraviolet light-emitting diodes fabricated on patterned substrates using metalorganic vapor phase epitaxy,” Jpn. J. Appl. Phys. 40(Part 2, No. 6B), L583–L585 (2001). [CrossRef]

,6

6. H. Y. Gao, F. W. Yan, Y. Zhang, J. M. Li, Y. P. Zeng, and G. H. 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(1), 014314 (2008). [CrossRef]

], LED chips shaping [7

7. C.-F. Lin, Z.-J. Yang, B.-H. Chin, J.-H. Zheng, J.-J. Dai, B.-C. Shieh, and C.-C. Chang, “Enhanced light output power in InGaN light-emitting diodes by fabricating inclined undercut structure,” J. Electrochem. Soc. 153(12), G1020–G1024 (2006). [CrossRef]

], graded-refractive-index (GRIN) layer coating [8

8. J. K. Kim, S. Chhajed, M. F. Schubert, E. F. Schubert, A. J. Fischer, M. H. Crawford, J. Cho, H. Kim, and C. Sone, “Light-extraction enhancement of GaInN light-emitting diodes by graded-refractive-index indium tin oxide anti-reflection contact,” Adv. Mater. 20(4), 801–804 (2008). [CrossRef]

,9

9. J. K. Kim, A. N. Noemaun, F. W. Mont, D. Meyaard, E. F. Schubert, D. J. Poxson, H. Kim, C. Sone, and Y. Park, “Elimination of total internal reflection in GaInN light-emitting diodes by graded-refractive-index micropillars,” Appl. Phys. Lett. 93(22), 221111 (2008). [CrossRef]

], and two-dimensional (2D) photonic crystal (PhC) structures integrating [1

1. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009). [CrossRef]

,10

10. A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012). [CrossRef] [PubMed]

17

17. T. B. Wei, K. Wu, D. Lan, Q. F. Yan, Y. Chen, C. X. Du, J. X. Wang, Y. P. Zeng, and J. M. Li, “Selectively grown photonic crystal structures for high efficiency InGaN emitting diodes using nanospherical-lens lithography,” Appl. Phys. Lett. 101(21), 211111 (2012). [CrossRef]

].

In this letter, we developed a simple and effective method to grow size-controllable p-GaN hexagonal nanopyramids (HnPs) through selective area growth (SAG) [18

18. A. Lundskog, U. Forsberg, P. O. Holtz, and E. Janzén, “Morphology control of hot-wall MOCVD selective area grown hexagonal GaN pyramids,” Cryst. Growth Des. 12(11), 5491–5496 (2012). [CrossRef]

] on the flat p-GaN layer for high LEE. The GaN HnPs were grown from patterned SiO2 mask fabricated by nanosphere lithography (NSL) technology [17

17. T. B. Wei, K. Wu, D. Lan, Q. F. Yan, Y. Chen, C. X. Du, J. X. Wang, Y. P. Zeng, and J. M. Li, “Selectively grown photonic crystal structures for high efficiency InGaN emitting diodes using nanospherical-lens lithography,” Appl. Phys. Lett. 101(21), 211111 (2012). [CrossRef]

,19

19. W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007). [CrossRef]

], which is simple and low-cost. We studied the growth characteristics of GaN HnPs in order to easily control their size. The LEE enhancement factor as a function of HnPs GaN bottom fill factor (f) of LEDs was first investigated in details. We further compared the effect of the HnPs-PhC and the hexagonal nanocolums (HnCs)-PhC on the LEE of LEDs in order to study if the details of the shape of the PhC modify the light-extraction.

2. Experiments

The blue LEDs with conventional InGaN/GaN multiple quantum wells (MQWs) were grown on c-plane sapphire substrates via metalorganic chemical vapor deposition (MOCVD). In our recipe, the 80-nm-thick p-GaN layer was grown under 950 °C and 130 Torr for 10.5 min using 15 sccm (sccm denotes standard cubic centimeters per minute) trimethylgallium (TMG), 6 slm (slm denotes standard liters per minute) ammonia (NH3) as precursors and bis-cyclopentadienyl magnesium (Cp2Mg) as the Mg-source. The p-GaN HnPs were regrown to fabricate HnPs-PhC LEDs [Fig. 1
Fig. 1 Schematic illustration of process for growth of GaN HnPs on p-GaN layer.
]. Firstly, 30-nm-thick SiO2 layer was deposited on p-GaN layer by using plasma enhanced chemical vapor deposition system. Next, 500-nm-thick photoresist was spun on the SiO2 layer. And then, monolayer of self-assembly polystyrene (PS) spheres was transferred onto the photoresist followed by developing-exposure process using the focusing nature of PS spheres developed by our group previously. Detailed exposure and development process can be seen in our early work [17

17. T. B. Wei, K. Wu, D. Lan, Q. F. Yan, Y. Chen, C. X. Du, J. X. Wang, Y. P. Zeng, and J. M. Li, “Selectively grown photonic crystal structures for high efficiency InGaN emitting diodes using nanospherical-lens lithography,” Appl. Phys. Lett. 101(21), 211111 (2012). [CrossRef]

]. The nano holes pattern was transferred onto the SiO2 layer through an inductively coupled plasma etching process. Finally, the photoresist was removed, leaving circular window openings in SiO2 mask and the wafer was cleaned for regrowth of p-GaN HnPs. SAG performed on these circular window openings and gallium polar (0001)-oriented p-GaN templates as substrates resulted in uniform HnPs with six smooth semipolar {1-101} facets, which is stable under 950 °C and 500 Torr, ensuring low loss of photons during the modulation of light flow from the LEDs.

3. Results and discussion

Figure 2(a)
Fig. 2 Bird view SEM images of (a) nano holes array in photoresist. The inset of (a) is the cross-section view of nano holes. (b) and (c) are HnPs GaN. The insets of (b) and (c) are the truncated pyramids GaN.(d) Tilted high resolution images of the HnPs GaN.
is the scanning electron microscopy (SEM) images of nanoholes with a diameter of ~400 nm which were developed thoroughly using 900-nm-diameter (also the lattice constant: Λ) PS spheres in the photoresist and the cross-section view is illustrated in the inset of it. We also used 730-nm-diameter PS spheres to develop nanopatterns in photoresist. We found that the diameters of nanoholes generated by 900-nm-diameter PS spheres are almost the same to the ones generated by 730-nm-diamter PS spheres under modified exposure-develop condition. This is because the little difference of the beam waist of 900 and 730-nm-diamter PS spheres under 365-nm-wavelength laser exposure [19

19. W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007). [CrossRef]

].

After removing SiO2 mask by hydrofluoric acid solution, the HnPs (H = 400 nm, f = 26.3%, Λ = 900 nm) LED wafer (PhC1-LED), the HnPs (H = 430 nm, f = 46.3%, Λ = 730 nm) LED wafer (PhC2-LED) and a reference LED (R-LED) wafer with regrown flat p-GaN layer in the same run with PhC1-LED wafer were fabricated with a conventional mesa area of 1 × 1mm2 using indium tin oxide (ITO) deposited on p-GaN layer as transparent conductive layer and Cr/Pt/Au as n- and p-electrodes by e-beam evaporation.

Compared to R-LEDs, the light output power (LOP) of PhC1- and PhC2-LEDs measured by an integrating sphere is improved by 55.0% and 99.9% at an injection current of 350 mA duo to the effective PhC Bragg scattering effect, respectively [Fig. 4(a)
Fig. 4 (a) LOP-I-V curves of the LEDs. (b) Far field radiation patterns of the LEDs.
]. The forward voltage of PhC1-LEDs and R-LEDs is similar at an injection current of 350 mA [Fig. 4(a)], which implies that the ITO ohmic contacts with the semipolar {10-10} facets are similar to the polar (0001) facet. However, the forward voltage of PhC2-LEDs is a little larger than R- and PhC1-LEDs for the elevated bulk resistance of thicker p-GaN. The angular far-field emissionpatterns of PhCs LEDs show omnidirectional enhancement in the overall integrated intensity due to the Bragg scattering of the PhCs [Fig. 4(b)]. The full-width-at-half maximum (FWHM) of emission divergence for the PhC1-LEDs and PhC2-LEDs are 148.7° and 145.1°, respectively, which is a little smaller compared to that of 149.6° for R-LEDs. This implies that the PhC’s directional characteristic on the light emission in our experiment isn’t strong because the period of embedded-PhCis large enough to have many diffraction orders in the blue light regime resulting in light leakage along many directions. These slightly smaller emission divergence may be caused by partial side emission of the conventional LEDs is redirected to the top and bottom (has a metal reflector) escape-cone by the PhCs effect [12

12. J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84(19), 3885–3887 (2004). [CrossRef]

].

We used the 3D FDTD solutions tools (Lumerical Solutions, Inc.) to quantitatively investigate the LEE enhancement factor as a function of HnPs GaN f at Λ = 900 nm of the HnPs-PhC LEDs. The simplified simulated LED structure consisted of 200-nm-thick ITO layer, 150-nm-thick p-GaN layer, 120-nm-thick active region, 2-μm-thick n-GaN layer, and 1-μm-thick sapphire. The simulation area was 7 × 7 μm2. The mesh size and the time step size are 0.25 nm and 0.035 femtosecond, respectively. The simulation area is much smaller than actual size of LEDs. In order to truncate the lateral dimension of actual LED structure, we used four perfect mirrors at the edges of the LED. A silver reflector under the sapphire substrate was used for the simulations. We also used symmetry to reduce the number of simulations to reduce the calculation time and two point dipoles polarized along the x and y directions was used as a radiating source and placed in the middle of the MQW layer [19

19. W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007). [CrossRef]

]. The light source wavelength was set to 460 nm. The light extraction was calculated from the top surface only. Figure 5(a)
Fig. 5 (a) Schematic of the 3D FDTD simulation domain for the HnPs-PhC LED. (b) Calculated LEE enhancement factor of the HnPs-PhC and the HnCs-PhC LED with different f. (c) Radiation profiles of the horizontal dipole source (dx) and (dy) in the R-LED and HnPs-PhC LED with f = 50%, respectively.
shows the simplified HnPs-PhC LED structures for theoretical calculation. The simulation results clearly show that, when f < 70%, the enhancement of LEE is increasing with the f of HnPs GaN [Fig. 5(b)]. This is because large f leading to more opportunity for the strong interaction between the guided modes and the HnPs-PhC. The radiation profiles of the horizontal dipole sources along the x-axis (dx) and the y-axis (dy) for the R-LED and PhC1-LED with f = 50% was illustrated in Fig. 5(c). It was found that most ofthe radiation from the dx and dy dipoles of the R LED is propagating inside the GaN epitaxial layer and the sapphire layer and cannot escape to the air, resulting in serious light absorption. However, emission from HnPs-PhC LED is significantly extracted into the air. Interestingly, one may wonder if the details of the shape of the scattering feature modify this result. So, we compared the effect of HnCs-PhC with the same f to HnPs-PhC on the LEE of LEDs [Fig. 5(b)]. It can be clearly seen that the LEE enhancement factor of both kind of PhC is similar at f < 50%. This is not surprising since it is governed by the average index of the scattering layer and not on the details of its geometry [10

10. A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012). [CrossRef] [PubMed]

]. When the f is large than 70% for HnCs-PhC, significantly decreasing of LEE enhancement factor is shown. We believe that the average index of the HnCs-PhC with large f is almost the same as the index of flat p-GaN layer, resulting in insufficient light-extraction.

4. Conclusions

In summary, size-controllable p-GaN HnPs-PhC for high light-extraction by suppression of the TIR has been fabricated via SAG method based on NSL technology. The size of GaN HnPs can be controlled by changing the size of the mask patterns and the growth time in MOCVD. The LOP of PhC2-LEDs (f = 50%) has been improved significantly by 99.9% due to the sufficient PhC Bragg scattering effect, which was confirmed by using 3D FDTD simulations. We also compared the effect of HnCs-PhC and HnPs-PhC on the LEE of LEDs. We find that when f < 50%, the LEE enhancement is not sensitive to the details of the shape of PhC. However, the effect on the LEE of LEDs is strongly affected by the shape of the PhC when it has large f.

Acknowledgments

This work was supported by the National Natural Sciences Foundation of China under Grant Nos. 61274040 and 61274008, by the National Basic Research Program of China under Grant No. 2011CB301902, and by the National High Technology Program of China under Grant No. 2011AA03A103. The authors are grateful for the FDTD solutions tools from Lumerical Solutions, Inc.

References and links

1.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009). [CrossRef]

2.

A. I. Zhmakin, “Enhancement of light extraction from light emitting diodes,” Phys. Rep. 498(4-5), 189–241 (2011). [CrossRef]

3.

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(6), 855–857 (2004). [CrossRef]

4.

T. B. Wei, Q. F. Kong, J. X. Wang, J. Li, Y. P. Zeng, G. H. Wang, J. M. Li, Y. X. Liao, and F. T. Yi, “Improving light extraction of InGaN-based light emitting diodes with a roughened p-GaN surface using CsCl nano-islands,” Opt. Express 19(2), 1065–1071 (2011). [CrossRef] [PubMed]

5.

K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato, and T. Taguchi, “High output power InGaN ultraviolet light-emitting diodes fabricated on patterned substrates using metalorganic vapor phase epitaxy,” Jpn. J. Appl. Phys. 40(Part 2, No. 6B), L583–L585 (2001). [CrossRef]

6.

H. Y. Gao, F. W. Yan, Y. Zhang, J. M. Li, Y. P. Zeng, and G. H. 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(1), 014314 (2008). [CrossRef]

7.

C.-F. Lin, Z.-J. Yang, B.-H. Chin, J.-H. Zheng, J.-J. Dai, B.-C. Shieh, and C.-C. Chang, “Enhanced light output power in InGaN light-emitting diodes by fabricating inclined undercut structure,” J. Electrochem. Soc. 153(12), G1020–G1024 (2006). [CrossRef]

8.

J. K. Kim, S. Chhajed, M. F. Schubert, E. F. Schubert, A. J. Fischer, M. H. Crawford, J. Cho, H. Kim, and C. Sone, “Light-extraction enhancement of GaInN light-emitting diodes by graded-refractive-index indium tin oxide anti-reflection contact,” Adv. Mater. 20(4), 801–804 (2008). [CrossRef]

9.

J. K. Kim, A. N. Noemaun, F. W. Mont, D. Meyaard, E. F. Schubert, D. J. Poxson, H. Kim, C. Sone, and Y. Park, “Elimination of total internal reflection in GaInN light-emitting diodes by graded-refractive-index micropillars,” Appl. Phys. Lett. 93(22), 221111 (2008). [CrossRef]

10.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012). [CrossRef] [PubMed]

11.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004). [CrossRef]

12.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84(19), 3885–3887 (2004). [CrossRef]

13.

D.-H. Kim, C.-O. Cho, Y.-G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C. Sone, Y. Park, W. J. Choi, and Q.-H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87(20), 203508 (2005). [CrossRef]

14.

A. David, T. Fujii, R. Sharma, K. McGroddy, S. Nakamura, S. P. DenBaars, E. L. Hu, C. Weisbuch, and H. Benisty, “Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

15.

E. Matioli, E. Rangel, M. Iza, B. Fleury, N. Pfaff, J. Speck, E. Hu, and C. Weisbuch, “High extraction efficiency light-emitting diodes based on embedded air-gap photonic-crystals,” Appl. Phys. Lett. 96(3), 031108 (2010). [CrossRef]

16.

H. Kitagawa, M. Fujita, T. Suto, T. Asano, and S. Noda, “Green GaInN photonic-crystal light-emitting diodes with small surface recombination effect,” Appl. Phys. Lett. 98(18), 181104 (2011). [CrossRef]

17.

T. B. Wei, K. Wu, D. Lan, Q. F. Yan, Y. Chen, C. X. Du, J. X. Wang, Y. P. Zeng, and J. M. Li, “Selectively grown photonic crystal structures for high efficiency InGaN emitting diodes using nanospherical-lens lithography,” Appl. Phys. Lett. 101(21), 211111 (2012). [CrossRef]

18.

A. Lundskog, U. Forsberg, P. O. Holtz, and E. Janzén, “Morphology control of hot-wall MOCVD selective area grown hexagonal GaN pyramids,” Cryst. Growth Des. 12(11), 5491–5496 (2012). [CrossRef]

19.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007). [CrossRef]

OCIS Codes
(230.0250) Optical devices : Optoelectronics
(230.3670) Optical devices : Light-emitting diodes
(220.4241) Optical design and fabrication : Nanostructure fabrication
(230.5298) Optical devices : Photonic crystals

ToC Category:
Optical Devices

History
Original Manuscript: June 21, 2013
Revised Manuscript: September 28, 2013
Manuscript Accepted: October 7, 2013
Published: October 17, 2013

Citation
Chengxiao Du, Tongbo Wei, Haiyang Zheng, Liancheng Wang, Chong Geng, Qingfeng Yan, Junxi Wang, and Jinmin Li, "Size-controllable nanopyramids photonic crystal selectively grown on p-GaN for enhanced light-extraction of light-emitting diodes," Opt. Express 21, 25373-25380 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25373


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References

  1. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics3(3), 163–169 (2009). [CrossRef]
  2. A. I. Zhmakin, “Enhancement of light extraction from light emitting diodes,” Phys. Rep.498(4-5), 189–241 (2011). [CrossRef]
  3. 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(6), 855–857 (2004). [CrossRef]
  4. T. B. Wei, Q. F. Kong, J. X. Wang, J. Li, Y. P. Zeng, G. H. Wang, J. M. Li, Y. X. Liao, and F. T. Yi, “Improving light extraction of InGaN-based light emitting diodes with a roughened p-GaN surface using CsCl nano-islands,” Opt. Express19(2), 1065–1071 (2011). [CrossRef] [PubMed]
  5. K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato, and T. Taguchi, “High output power InGaN ultraviolet light-emitting diodes fabricated on patterned substrates using metalorganic vapor phase epitaxy,” Jpn. J. Appl. Phys.40(Part 2, No. 6B), L583–L585 (2001). [CrossRef]
  6. H. Y. Gao, F. W. Yan, Y. Zhang, J. M. Li, Y. P. Zeng, and G. H. 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(1), 014314 (2008). [CrossRef]
  7. C.-F. Lin, Z.-J. Yang, B.-H. Chin, J.-H. Zheng, J.-J. Dai, B.-C. Shieh, and C.-C. Chang, “Enhanced light output power in InGaN light-emitting diodes by fabricating inclined undercut structure,” J. Electrochem. Soc.153(12), G1020–G1024 (2006). [CrossRef]
  8. J. K. Kim, S. Chhajed, M. F. Schubert, E. F. Schubert, A. J. Fischer, M. H. Crawford, J. Cho, H. Kim, and C. Sone, “Light-extraction enhancement of GaInN light-emitting diodes by graded-refractive-index indium tin oxide anti-reflection contact,” Adv. Mater.20(4), 801–804 (2008). [CrossRef]
  9. J. K. Kim, A. N. Noemaun, F. W. Mont, D. Meyaard, E. F. Schubert, D. J. Poxson, H. Kim, C. Sone, and Y. Park, “Elimination of total internal reflection in GaInN light-emitting diodes by graded-refractive-index micropillars,” Appl. Phys. Lett.93(22), 221111 (2008). [CrossRef]
  10. A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys.75(12), 126501 (2012). [CrossRef] [PubMed]
  11. T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett.84(4), 466–468 (2004). [CrossRef]
  12. J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett.84(19), 3885–3887 (2004). [CrossRef]
  13. D.-H. Kim, C.-O. Cho, Y.-G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C. Sone, Y. Park, W. J. Choi, and Q.-H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett.87(20), 203508 (2005). [CrossRef]
  14. A. David, T. Fujii, R. Sharma, K. McGroddy, S. Nakamura, S. P. DenBaars, E. L. Hu, C. Weisbuch, and H. Benisty, “Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution,” Appl. Phys. Lett.88(6), 061124 (2006). [CrossRef]
  15. E. Matioli, E. Rangel, M. Iza, B. Fleury, N. Pfaff, J. Speck, E. Hu, and C. Weisbuch, “High extraction efficiency light-emitting diodes based on embedded air-gap photonic-crystals,” Appl. Phys. Lett.96(3), 031108 (2010). [CrossRef]
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