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Energy Express

  • Editor: Bernard Kippelen
  • Vol. 19, Iss. S5 — Sep. 12, 2011
  • pp: A1104–A1108

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GaN-based light-emitting diodes with photonic crystals structures fabricated by porous anodic alumina template

XingXing Fu, Bei Zhang, XiangNing Kang, JunJing Deng, Chang Xiong, Tao Dai, XianZhe Jiang, TongJun Yu, ZhiZhong Chen, and Guo Yi Zhang  »View Author Affiliations


Optics Express, Vol. 19, Issue S5, pp. A1104-A1108 (2011)
http://dx.doi.org/10.1364/OE.19.0A1104


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Abstract

In this paper, we propose and demonstrate a convenient and flexible approach for preparation large-area of photonic crystals (PhCs) structures on the GaN-based LED chip. The highly-ordered porous anodic alumina (AAO) with pitch of wavelength scale was adopted as a selective dry etching mask for PhCs-pattern transfer. The PhCs with different pore depths were simultaneously formed on the entire surfaces of GaN-based LED chip including ITO, GaN surrounding contacts and the sidewall of the mesa by one-step reactive ion etching (RIE). The light output power improvement of PhCs-based GaN LED was achieved as high as 94% compared to that of the conventional GaN-based LED.

© 2011 OSA

1. Introduction

Gallium nitride (GaN)-based light-emitting diodes (LED), which are now being widely used, have greatly promoted the development of solid state lighting. However, the light extraction efficiency of a planar LED is still limited by total internal reflection (TIR) resulting from the large index contrast between the GaN film (n=2.5) and air (n=1) [1

E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, Cambridge, 2003), pp. 89–91.

]. The formation of shallow etching microstructures including PhCs on the surfaces of GaN-based LED is an effective approach to suppress the limitations of TIR by coupling guided modes trapped inside GaN layers [2

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs-designing light extraction,” Laser Photon. Rev. 1, 1–25 (2008).

–9

Y. M. Song, E. S. Choi, J. S. Yu, and Y. T. Lee, “Light-extraction enhancement of red AlGaInP light-emitting diodes with antireflective subwavelength structures,” Opt. Express 17(23), 20991–20997 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-23-20991. [CrossRef] [PubMed]

]. Patterning or roughening an indium tin oxide (ITO) contact layer without disturbing the p-GaN layer can improve light extraction efficiency remarkably [10

T. K. Kim, S. H. Kim, S. S. Yang, J. K. Son, K. H. Lee, Y. G. Hong, K. H. Shim, J. W. Yang, K. Y. Lim, S. J. Bae, and G. M. Yang, “GaN-based light-emitting diode with textured indium tin oxide transparent layer coated with Al2O3 powder,” Appl. Phys. Lett. 94(16), 161107 (2009). [CrossRef]

]. In addition, texturing the sidewall could result in 10%~20% enhancement of light output power [11

Y. W. Cheng, K. M. Pan, C. Y. Wang, H. H. Chen, M. Y. Ke, C. P. Chen, M. Y. Hsieh, H. M. Wu, L. H. Peng, and J. J. Huang, “Enhanced light collection of GaN light emitting devices by redirecting the lateral emission using nanorod reflectors,” Nanotechnology 20(3), 035202 (2009). [CrossRef] [PubMed]

]. Therefore, patterning all the surfaces including the ITO surface, p-GaN layer around the edge of the mesa, the sidewall and the n-GaN layer would induce most of different order guided modes to couple with PhCs to obtain higher light extraction [12

T. Dai, B. Zhang, X. N. Kang, K. Bao, D. S. Xu, G. Y. Zhang, and Z. Z. Gan, “Light Extraction Improvement From GaN-based Light-Emitting Diodes With Nano-Patterned Surface Using Anodic Aluminum Oxide Template,” IEEE Photon. Technol. Lett. 20(23), 1974–1976 (2008). [CrossRef]

]. Furthermore, from our previous work on PhCs, we have found that the lattice constant of PhCs with wavelength-scale is benefit to the light extraction of GaN based blue LED [13

X. X. Fu, B. Zhang, X. N. Kang, C. Xiong, and G. Y. Zhang, “Lattice Constant Effects of Photonic Crystal on the Extraction of Guided Modes of GaN-based Light-Emitting Diodes,” Sci. China Tech. Sci. 54(1), 1–5 (2011). [CrossRef]

]. Nevertheless, most ways of incorporating PhCs into LED is realized by electron-beam lithography [4

K. McGroddy, A. David, E. Matioli, M. Iza, S. Nakamura, S. DenBaars, J. S. Speck, C. Weisbuch, and E. L. Hu, “Directional emission control and increased light extraction in GaN photonic crystal light emitting diodes,” Appl. Phys. Lett. 93(10), 103502 (2008). [CrossRef]

–6

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94(12), 123106 (2009). [CrossRef]

], focused ion beam milling [7

T. Dai, B. Zhang, Z. S. Zhang, D. Liu, X. Wang, K. Bao, X. N. Kang, J. Xu, and X. Zhu, “Surface light extraction mapping from two-dimensional array of 12-fold photonic quasicrystal on current injected GaN-based LEDs,” Chin. Phys. Lett. 24(4), 979–982 (2007). [CrossRef]

], and laser holographic lithography [8

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]

] which are limited by expensive equipment and low yield. Nano-imprint lithography can be applicable for large-scale production, however, the stamp used for imprinting process is very expensive and the technique is still in development. A practical application of PhCs with wavelength-scale on a large-area of LED chips is still a big challenge. Fortunately, AAO has unique properties to be self-organized in spatially regular, hexagonally order which is suitable to form large-area two-dimensional PhCs with low-cost and high throughout [14

T. Yanagishita, K. Nishio, and H. Masuda, “Two-Dimensional Photonic Crystal Composed of Ordered Polymer Nanopillar Arrays with High Aspect Ratios Using Anodic Porous Alumina Templates,” Appl. Phys. Express 1(1), 012002 (2008). [CrossRef]

]. Recently, we have fabricated two inch large AAO template with the lattice pitch of about 460 nm successfully, and obtained their optical transmission diffraction properties for the application on GaN-based LEDs [15

X. X. Fu, X. N. Kang, B. Zhang, C. Xiong, X. Z. Jiang, D. S. Xu, W. M. Du, and G. Y. Zhang, “Light transmission from the large-area highly ordered epoxy conical pillar arrays and application to GaN-based light emitting diodes,” J. Mater. Chem. 21(26), 9576–9581 (2011). [CrossRef]

].

In this paper, we propose a preparation of large-area PhCs structures with pitch of wavelength scale on the GaN-based LED. By adopting AAO as a pattern transfer and selective etching mask of reactive ion etching (RIE), the PhCs structures with different pore depths have been obtained at the entire surfaces of GaN-based LED. The scanning electron microscopy (SEM) and microscopic electroluminescence (EL) were used to investigate the formation of PhCs and the light extraction improvement.

2. Experimental procedures

The GaN wafers used in this work were emitting at 445 nm which were grown on C-plane sapphire substrate by low-pressure metal-organic chemical vapor deposition (MOCVD). The 300 μm×300 μm LEDs were prepared by conventional fabrication processes. A 230 nm thick ITO transparent layer was evaporated on the p-GaN layer to form p-type Ohmic contact and current spreading layer.

The AAO sample was obtained by a conventional two-step anodization [14

T. Yanagishita, K. Nishio, and H. Masuda, “Two-Dimensional Photonic Crystal Composed of Ordered Polymer Nanopillar Arrays with High Aspect Ratios Using Anodic Porous Alumina Templates,” Appl. Phys. Express 1(1), 012002 (2008). [CrossRef]

]. The anodization was performed in 0.1 M phosphoric acid solution at 195 V during 0°C to obtain highly and hexagonally ordered nanopore arrays with the pitch of about 460 nm. The though-pore AAO membrane as a PhCs transfer module of dry etching mask was therefore obtained by peeling off from Al foil and removing barrier layer using chemical etching in sequence. During the RIE dry etching procedure, a gas mixture of Cl2, BCl3 and Ar was employed.

For the purpose of application on the device, the AAO membrane was attached on the surfaces of two-inch diameter of GaN-based LED chips as a selective etching mask of PhCs-pattern transfer template during RIE process. By well adjusting the etching parameters of gas mixture ratio under the inductive power of 150 W, the etching rates of ITO and GaN are about 30 nm per minute and 90 nm per minute, respectively. Thus, a desirable etching rate selectivity of ITO to GaN is obtained to be 1:3 by using this simplified one-step dry etching. Additionally, the thin AAO membrane also shows good advantages of flexible to make compact contact on the whole chip even though the surface of the mesa and n-GaN of the LED chip have a height difference up to 1 μm.

3. Results and discussion

Figure 1(a) shows the photograph image of a typical two-inch diameter large AAO template with highly-ordered PhCs structures under white light illumination. It is obvious that the gradually color changes revealed a uniform feature of the AAO. Figure 1(b) and 1(c) display the top view of SEM images of the original PhCs on AAO template and GaN, respectively. The lattice pitch and the diameter of pores on AAO template are 460±10 nm and 300±15 nm, while the corresponding dimensions of PhCs are 460±10 nm and 295±10 nm on GaN, respectively. Apparently, the transfer of PhCs pattern from the AAO membrane is well satisfied. The equilateral hexagon shape of GaN-based pores is mainly caused by the hexagonal crystal anisotropy of the GaN epitaxial layers.

Fig. 1 Two-inch diameter large-area AAO template; (b) Top view of AAO PhCs structures; (c) The corresponding PhCs structures of the GaN

Figure 2(a) shows the schematic diagram of the light trace emitting from PhCs structures on the different surfaces of GaN-based LED. As shown, the shallow etching PhC on ITO layer (I region) with a residual ITO layer to avoid the electrical properties degradation of LED can effectively diffract the guided modes which trapped inside the ITO layer before the PhCs formation. Moreover, the deep etching PhC on p-GaN layer around the edge of the mesa (II region) can block the propagation of the guided modes along the junction and scatter the trapped modes out from the device surface. Additionally, the originally trapped guided modes propagating to n-GaN layer and sapphire substrate modes can also be scattered by the PhC on n-GaN layer (III region) to further improve the light extraction. Therefore, it is reasonable to design the PhCs LED model to obtain high improvement of the light extraction of GaN based LED.

Fig. 2 The PhC structures on the surfaces of GaN-based LED. (a) Schematic diagram of light traces emitting from the PhCs-based LED; (b) The side view SEM image of PhCs on the ITO surface of GaN-based LED; (c) the side view SEM image of PhCs on the surfaces of p-GaN layer, side-wall and n-GaN layer, respectively.

Considering the thickness of ITO layer is about 230 nm, we have strictly controlled the etching time to reach the average depths to be 200 nm. Consequently, about 30 nm thick residual thin layer of ITO on p-type GaN can still play the role of Ohmic contact and current spreading layer as well, as shown in Fig. 2(b). On the other hand, the corresponding PhCs on the p-GaN and n-GaN region in Fig. 2(c) exhibited deeper depths of about 630 nm. It is essential to note that, since the deep PhCs structures are located outside the current injection region, they did not seriously affect the I-V characteristic. Furthermore, the tapered pores’ wall has the advantage of introducing a graded refractive index profile which will further increase the transmission by reducing Fresnel reflection.

The light output power of the GaN based LED devices was measured using an integrating sphere system. Figure 3 shows the typical light output power-current-voltage (L-I-V) characteristics of the LED with PhCs structures (PhCs-LED) compared to that of the conventional LED (C-LED). As shown, light output powers of PhCs-LED is obvious higher than that of the C-LED. The integrated light output power of the PhCs-LED is 12.2 mW which is enhanced as high as about 94% compared to that of 6.3 mW of the C-LED under an injection current of 20 mA measured by integrating sphere system. It is essential to note that, the light output power of both LEDs can be further improved by thinning sapphire substrate combined with Ag or Al reflector. The increase of forward voltage is only about 0.03V at 20 mA while the increase of reverse current at a bias of −5 V is only 50 pA for the PhC-LED compared to that of the C-LED. The series resistance for the PhC-LED has increased by 1-2 Ω compared to that of the C-LED. These results reveal the slight influence on the PhC-LED electrical performance which is acceptable.

Fig. 3 Typical L-I-V curves of conventional GaN-based LED and surface-patterned GaN-based LED with PhC structures.

We acquired the microscopic EL images of the LED chips. Figure 4 directly illustrates the obvious different brightness of the surface EL emission between C-LED and PhC-LED at the injection current of 0.5 mA. It is reasonable to believe that, in addition to the PhCs on the ITO emitting surface, the PhCs on GaN and sidewall of mesa are all benefit to scattering effect on guided modes in the LED.

Fig. 4 The typical surface EL images of (a) C-LED and (b) PhC-LED at the injection current of 0.5 mA, respectively.

To get better insight into the light extraction improvement, we have also measured the wavelength-resolved angular EL spectrum of PhCs-LED and C-LED. As shown in Fig. 5 , the light emission spectrum of C-LED is weakly modulated by the Fabry-Perot (F-P) interferences. However, the F-P interferences have disappeared for the PhCs-LED due to scattering effect of the concave ITO surface with PhCs structures. Moreover, the EL intensity of PhCs-LED is much higher than that of C-LED, we attribute to the PhCs’ diffraction and scattering effect that play a major role in out-coupling guided modes above the light line and hence improves the light extraction efficiency.

Fig. 5 Measured wavelength-resolved angular EL spectrum for PhC-LED and C-LED

4. Conclusion

In summary, we have successfully demonstrated a feasible, low cost method to enhance light extraction by producing PhCs structures on LED surfaces with large area of chip level. By using an AAO template as a selective dry etching mask for PhCs-pattern transfer, PhC structures were simultaneously formed on the entire surface of the device including ITO and GaN surfaces surrounding the p-type and n-type contacts with different pore depths by one-step of RIE etching. The improvement of light output power of the PhCs based LED are achieved up to 94% compared to that of the C-LED at injection current of 20 mA. The improvement is attributed to the diffraction and scattering effects of guided modes by the PhCs on the whole emitting surface of the device.

Acknowledgements

This work was supported by National key Basic Research Special Foundation of China under Grant No. TG2011CB301905, TG2007CB307004, TG2011CB301904, and Science and Technology Project of Beijing under Grant No.Z101103050410003, and Natural Science Foundation of China under Grant Nos. 61076012, 60876063, 60676032.

References and links

1.

E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, Cambridge, 2003), pp. 89–91.

2.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs-designing light extraction,” Laser Photon. Rev. 1, 1–25 (2008).

3.

C. Xiong, B. Zhang, X. N. Kang, T. Dai, and G. Y. Zhang, “Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals,” Opt. Express 17(26), 23684–23689 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23684. [CrossRef] [PubMed]

4.

K. McGroddy, A. David, E. Matioli, M. Iza, S. Nakamura, S. DenBaars, J. S. Speck, C. Weisbuch, and E. L. Hu, “Directional emission control and increased light extraction in GaN photonic crystal light emitting diodes,” Appl. Phys. Lett. 93(10), 103502 (2008). [CrossRef]

5.

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]

6.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94(12), 123106 (2009). [CrossRef]

7.

T. Dai, B. Zhang, Z. S. Zhang, D. Liu, X. Wang, K. Bao, X. N. Kang, J. Xu, and X. Zhu, “Surface light extraction mapping from two-dimensional array of 12-fold photonic quasicrystal on current injected GaN-based LEDs,” Chin. Phys. Lett. 24(4), 979–982 (2007). [CrossRef]

8.

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]

9.

Y. M. Song, E. S. Choi, J. S. Yu, and Y. T. Lee, “Light-extraction enhancement of red AlGaInP light-emitting diodes with antireflective subwavelength structures,” Opt. Express 17(23), 20991–20997 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-23-20991. [CrossRef] [PubMed]

10.

T. K. Kim, S. H. Kim, S. S. Yang, J. K. Son, K. H. Lee, Y. G. Hong, K. H. Shim, J. W. Yang, K. Y. Lim, S. J. Bae, and G. M. Yang, “GaN-based light-emitting diode with textured indium tin oxide transparent layer coated with Al2O3 powder,” Appl. Phys. Lett. 94(16), 161107 (2009). [CrossRef]

11.

Y. W. Cheng, K. M. Pan, C. Y. Wang, H. H. Chen, M. Y. Ke, C. P. Chen, M. Y. Hsieh, H. M. Wu, L. H. Peng, and J. J. Huang, “Enhanced light collection of GaN light emitting devices by redirecting the lateral emission using nanorod reflectors,” Nanotechnology 20(3), 035202 (2009). [CrossRef] [PubMed]

12.

T. Dai, B. Zhang, X. N. Kang, K. Bao, D. S. Xu, G. Y. Zhang, and Z. Z. Gan, “Light Extraction Improvement From GaN-based Light-Emitting Diodes With Nano-Patterned Surface Using Anodic Aluminum Oxide Template,” IEEE Photon. Technol. Lett. 20(23), 1974–1976 (2008). [CrossRef]

13.

X. X. Fu, B. Zhang, X. N. Kang, C. Xiong, and G. Y. Zhang, “Lattice Constant Effects of Photonic Crystal on the Extraction of Guided Modes of GaN-based Light-Emitting Diodes,” Sci. China Tech. Sci. 54(1), 1–5 (2011). [CrossRef]

14.

T. Yanagishita, K. Nishio, and H. Masuda, “Two-Dimensional Photonic Crystal Composed of Ordered Polymer Nanopillar Arrays with High Aspect Ratios Using Anodic Porous Alumina Templates,” Appl. Phys. Express 1(1), 012002 (2008). [CrossRef]

15.

X. X. Fu, X. N. Kang, B. Zhang, C. Xiong, X. Z. Jiang, D. S. Xu, W. M. Du, and G. Y. Zhang, “Light transmission from the large-area highly ordered epoxy conical pillar arrays and application to GaN-based light emitting diodes,” J. Mater. Chem. 21(26), 9576–9581 (2011). [CrossRef]

OCIS Codes
(230.3670) Optical devices : Light-emitting diodes
(160.5298) Materials : Photonic crystals

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: May 16, 2011
Revised Manuscript: July 16, 2011
Manuscript Accepted: July 19, 2011
Published: August 1, 2011

Citation
XingXing Fu, Bei Zhang, XiangNing Kang, JunJing Deng, Chang Xiong, Tao Dai, XianZhe Jiang, TongJun Yu, ZhiZhong Chen, and Guo Yi Zhang, "GaN-based light-emitting diodes with photonic crystals structures fabricated by porous anodic alumina template," Opt. Express 19, A1104-A1108 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S5-A1104


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References

  1. E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, Cambridge, 2003), pp. 89–91.
  2. C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs-designing light extraction,” Laser Photon. Rev. 1, 1–25 (2008).
  3. C. Xiong, B. Zhang, X. N. Kang, T. Dai, and G. Y. Zhang, “Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals,” Opt. Express 17(26), 23684–23689 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23684 . [CrossRef] [PubMed]
  4. K. McGroddy, A. David, E. Matioli, M. Iza, S. Nakamura, S. DenBaars, J. S. Speck, C. Weisbuch, and E. L. Hu, “Directional emission control and increased light extraction in GaN photonic crystal light emitting diodes,” Appl. Phys. Lett. 93(10), 103502 (2008). [CrossRef]
  5. 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]
  6. C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94(12), 123106 (2009). [CrossRef]
  7. T. Dai, B. Zhang, Z. S. Zhang, D. Liu, X. Wang, K. Bao, X. N. Kang, J. Xu, and X. Zhu, “Surface light extraction mapping from two-dimensional array of 12-fold photonic quasicrystal on current injected GaN-based LEDs,” Chin. Phys. Lett. 24(4), 979–982 (2007). [CrossRef]
  8. 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]
  9. Y. M. Song, E. S. Choi, J. S. Yu, and Y. T. Lee, “Light-extraction enhancement of red AlGaInP light-emitting diodes with antireflective subwavelength structures,” Opt. Express 17(23), 20991–20997 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-23-20991 . [CrossRef] [PubMed]
  10. T. K. Kim, S. H. Kim, S. S. Yang, J. K. Son, K. H. Lee, Y. G. Hong, K. H. Shim, J. W. Yang, K. Y. Lim, S. J. Bae, and G. M. Yang, “GaN-based light-emitting diode with textured indium tin oxide transparent layer coated with Al2O3 powder,” Appl. Phys. Lett. 94(16), 161107 (2009). [CrossRef]
  11. Y. W. Cheng, K. M. Pan, C. Y. Wang, H. H. Chen, M. Y. Ke, C. P. Chen, M. Y. Hsieh, H. M. Wu, L. H. Peng, and J. J. Huang, “Enhanced light collection of GaN light emitting devices by redirecting the lateral emission using nanorod reflectors,” Nanotechnology 20(3), 035202 (2009). [CrossRef] [PubMed]
  12. T. Dai, B. Zhang, X. N. Kang, K. Bao, D. S. Xu, G. Y. Zhang, and Z. Z. Gan, “Light Extraction Improvement From GaN-based Light-Emitting Diodes With Nano-Patterned Surface Using Anodic Aluminum Oxide Template,” IEEE Photon. Technol. Lett. 20(23), 1974–1976 (2008). [CrossRef]
  13. X. X. Fu, B. Zhang, X. N. Kang, C. Xiong, and G. Y. Zhang, “Lattice Constant Effects of Photonic Crystal on the Extraction of Guided Modes of GaN-based Light-Emitting Diodes,” Sci. China Tech. Sci. 54(1), 1–5 (2011). [CrossRef]
  14. T. Yanagishita, K. Nishio, and H. Masuda, “Two-Dimensional Photonic Crystal Composed of Ordered Polymer Nanopillar Arrays with High Aspect Ratios Using Anodic Porous Alumina Templates,” Appl. Phys. Express 1(1), 012002 (2008). [CrossRef]
  15. X. X. Fu, X. N. Kang, B. Zhang, C. Xiong, X. Z. Jiang, D. S. Xu, W. M. Du, and G. Y. Zhang, “Light transmission from the large-area highly ordered epoxy conical pillar arrays and application to GaN-based light emitting diodes,” J. Mater. Chem. 21(26), 9576–9581 (2011). [CrossRef]

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