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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 22 — Oct. 22, 2012
  • pp: 25058–25063
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Light-extraction enhancement and directional emission control of GaN-based LEDs by self-assembled monolayer of silica spheres

Hee Kwan Lee, Yeong Hwan Ko, Ganji Seeta Rama Raju, and Jae Su Yu  »View Author Affiliations


Optics Express, Vol. 20, Issue 22, pp. 25058-25063 (2012)
http://dx.doi.org/10.1364/OE.20.025058


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Abstract

The light extraction of 1 × 1 mm2 GaN-based blue light-emitting diodes (LEDs) was enhanced by a self-assembled monolayer (SAM) of silica submicron spheres. The silica spheres were synthesized with various spherical sizes via the ammonia-catalyzed hydrolysis and condensation of tetraethyl orthosilicate in water/ethanol solutions. Hexagonal closely-packed (HCP) silica sphere monolayer was formed onto the indium tin oxide layer of the LED by a spin coating process. The size effect of silica spheres on the light-extraction efficiency (LEE) of GaN-based LEDs was theoretically studied and their optimum size was determined. The simulation results showed that the use of silica spheres can improve the LEE by 1.1-1.32 times compared to the conventional LEDs. The light output power of the LED with 650-nm-thick SAM of HCP silica spheres was experimentally enhanced by 1.28 and 1.23 times under the injection currents of 100 and 350 mA, respectively. By employing the SAM of HCP silica spheres, the directional emission pattern was relatively converged, indicating a reasonable consistency with the simulation result.

© 2012 OSA

1. Introduction

High-efficiency and high-power gallium nitride (GaN)-based light-emitting diodes (LEDs) have attracted much attention due to their promising applications, such as traffic signals, back light units in liquid crystal displays, outdoor/indoor lightings, and general illuminations [1

1. F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A 194(2), 380–388 (2002). [CrossRef]

]. However, external quantum efficiency is still limited by the total internal reflection at the interface between the semiconductor and air due to its large refractive index difference. Only a few percent of photons are escaped from LEDs and most of light trapped within the device is eventually converted to heat. Furthermore, poor directional emission profiles of LEDs limit the use in a wider variety of applications because they exhibited a broad radiation pattern from both the surface and sidewalls. Thus, the directional emission property should be adequately controlled, together with the large enhancement of light-extraction efficiency (LEE). The LEE has been enhanced by using various approaches, such as micro- and nano-patterned surface texturing, and antireflective coating layers [2

2. R. H. Horng, S. H. Huang, C. C. Yang, and D. S. Wuu, “Efficiency improvement of GaN-based LEDs with ITO texturing window layers using natural lithography,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1196–1201 (2006). [CrossRef]

7

7. S. J. Tu, J. K. Sheu, M. L. Lee, C. C. Yang, K. H. Chang, Y. H. Yeh, F. W. Huang, and W. C. Lai, “Enhanced output power of GaN-based LEDs with embedded AlGaN pyramidal shells,” Opt. Express 19(13), 12719–12726 (2011). [CrossRef] [PubMed]

]. Although these approaches resulted in an efficient light-extraction enhancement, the directional emission property has not been controlled. There were few reports on the light-propagation control through the self-aligned nanorod array or photonic crystals [8

8. K. McGroddy, A. David, E. Matioli, M. Lza, S. Nakamura, S. DenBaars, J. D. Dpeck, 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]

10

10. 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]

]. These methods often involve complex and damage-induced processes (e.g., plasma dry etching), thereby, inducing severe electrical degradation. Meanwhile, the employment of SiO2/polystyrene on GaN surface improved the LEE and it modified the directionality of light [11

11. Y. K. Ee, P. Kumnorkaew, R. A. Arif, H. Tong, H. Zhao, J. F. Gilchrist, and N. Tansu, “Optimization of light extraction efficiency of III-nitride LEDs with self-assembled colloidal-based microlenses,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1218–1225 (2009). [CrossRef]

,12

12. X. H. Li, R. Song, Y. K. Ee, P. Kumnorkaew, J. F. Gilchrist, and N. Tansu, “Light extraction efficiency and radiation patterns of III-nitride light-emitting diodes with colloidal microlens arrays with various aspect ratios,” IEEE Photon. J. 3(3), 489–499 (2011). [CrossRef]

]. This is a simple, large-area, and low-cost process. For GaN-based lateral LEDs, however, indium tin oxide (ITO) layer as a transparent conducting electrode is generally used for more uniform current spreading because the p-GaN layer has high resistivity and low hole concentration [13

13. M. V. Bogdanov, K. A. Bulashevich, O. V. Khokhlev, I. Yu. Evstratov, M. S. Ramm, and S. Yu. Karpov, “Effect of ITO spreading layer on performance of blue light-emitting diodes,” Phys. Status Solidi C 7(7–8), 2127–2129 (2010). [CrossRef]

]. The design and fabrication of silica spheres on the ITO layer of LEDs have not been studied. Also, the theoretical analysis is important to understand the light extraction mechanism of LEDs.

In this work, we studied the effect of self-assembled monolayer (SAM) of hexagonal closely-packed (HCP) silica spheres on the optical characteristics of GaN-based LEDs, together with a theoretical analysis. The silica spheres were synthesized via the ammonia-catalyzed hydrolysis and condensation of tetraethyl orthosilicate (TEOS) in water/ethanol solutions, and they were deposited on the ITO surface of lateral LEDs by a spin coating method [14

14. W. Stöber, A. Fink, and E. Bohn, “Controlled growth of monodisperse silica spheres in the micron size range,” J. Colloid Interface Sci. 26(1), 62–69 (1968). [CrossRef]

]. The optical and electrical properties were evaluated and discussed for the fabricated LEDs with SAM of HCP silica spheres in comparison with the conventional LEDs. To investigate the size effect of silica spheres on the optical properties of LEDs, a finite-difference time-domain (FDTD) simulation was performed.

2. Fabrication and characterization

The SAM of HCP silica spheres was covered on the GaN-based LEDs emitting at λ~450 nm. Figure 1
Fig. 1 Schematic diagrams of the GaN-based blue LEDs with SAM of silica spheres.
shows the schematic diagram of GaN-based LEDs with SAM of HCP silica spheres. The LEDs were fabricated into a mesa size of 1 × 1 mm2 by conventional LED fabrication processes. The device structure consisted of an undoped GaN layer, a Si-doped n-type GaN layer, five pairs of InGaN/GaN multiple quantum wells (MQWs), a Mg-doped p-type GaN layer, and a ITO layer. The Cr/Au layers were used as n- and p-metal electrodes. To form the SAM on the ITO electrode surface, the silica spheres were synthesized via the ammonia-catalyzed hydrolysis and condensation of TEOS in water/ethanol solutions. First, mixtures of 40 ml de-ionized water, 20 ml ethanol, and ammonia (NH4OH) were stirred at room temperature for 15 min. Then, 20 ml TEOS was added, and it was additionally stirred for 2 h. The monolayer of silica spheres was formed on LEDs by using the spin coating process. The sodium dodecyl sulfate was added into the silica colloidal suspension as a surfactant. The hydrophilicity enhances the adhesion ability of surface. Initially, the silica colloidal suspension with an optimum average size of 650 nm was dropped onto the samples, and it was rotated with three different rotation speed steps of 250 rpm for 60 s, 300 rpm for 60 s, and 800 rpm for 200 s. The morphologies of as-synthesized silica spheres were characterized by using a field-emission scanning electron microscope (FE-SEM). The optical and electrical properties of the fabricated LEDs were analyzed, and the directional property of the emitted light was analyzed by measuring the far-field radiation pattern.

3. Results and discussion

Figure 2
Fig. 2 FE-SEM images of the as-synthesized silica spheres with different sizes: (a) 450 nm, (b) 540 nm, (c) 650 nm, and (d) 700 nm.
shows the FE-SEM images of the as-synthesized silica spheres with different sizes. The size of spheres was controlled by the amount of NH4OH. As shown in Fig. 2, the silica spheres exhibited a good spherical structure and the size distributions were almost uniform. The average size became larger with increasing the amount of NH4OH. At 15 ml of NH4OH, the sphere size was approximately 450 nm and it increased to 700 nm at 30 ml. The silica spheres also had good uniformity and reproducibility. This indicates that the submicron scale silica spherical particles can be easily formed with a suitable size by a simple procedure.

To investigate the size effect of silica spheres on the light-extraction of GaN-based LEDs, the FDTD simulation was carried out. Figure 3(a)
Fig. 3 (a) Calculated light-extraction enhancement of GaN-based LEDs as a function of the size of silica spheres, and (b) FDTD simulation results of wave propagation for LEDs with and without SAM of silica spheres.
shows the calculated light-extraction enhancement of LEDs as a function of the size of silica spheres. The simulated LED structure consisted of 0.2-μm-thick ITO, 0.2-μm-thick p-GaN, MQWs, 4-μm-thick n-GaN, 3.5-μm-thick undpoed GaN, and 430-μm-thick sapphire. The monolayer of the HCP silica spheres with different sizes between 300 and 900 nm was modeled. The refractive indices of ITO, GaN, sapphire, and silica spheres were set to 2, 2.5, 1.77 and 1.54, respectively. The simulations were conducted at an emission wavelength of 450 nm. From the simulation results, the light-extraction was increased by the monolayer of the HCP silica spheres. The LEE was improved with the increased size of silica spheres. The optimum silica size was found to be ~650 nm and the LEE was enhanced by 1.32 times compared to the conventional LED. When the size of silica spheres was increased above 650 nm, the LEE was reduced. As the sphere size increases largely, the effect of silica sphere becomes less pronounced because its geometrical dimensions are much larger than the wavelength of emitted light. Figure 3(b) shows the FDTD simulation results of wave propagation for LEDs with and without SAM of silica spheres with a size of 650 nm. In FDTD simulations, the y-polarized electric field was taken into consideration. When the light passed through silica spheres, the strong light interference patterns were observed and the light was more focused. These results means that the incorporation of the silica spheres can efficiently improve the LEE and directional emission properties of LEDs.

Figure 4(a)
Fig. 4 (a) L-I-V curves of GaN-based LEDs with and without SAMs of HCP silica spheres, (b) normalized far-field radiation patterns of the corresponding LEDs. The inset of (a) shows the FE-SEM image of SAM of HCP silica spheres integrated on LED.
shows the light-current-voltage (L-I-V) curves of GaN-based LEDs with and without SAM of HCP silica spheres. The silica sphere integrated LED was prepared with an optimum average size of 650 nm. The SAM of HCP silica spheres integrated on LED is illustrated in the inset of Fig. 4(a). The integrated silica sphere indicated a good adhesion property on the ITO surface. The forward voltage was not distinctly affected by the formation of the silica sphere monolayer. For all samples, the forward voltage indicated almost the same value of ~3.34 V at an injection current of 100 mA. At 350 mA, the forward voltage of the conventional LED was 4.40 V and it was slightly increased to 4.44 V for LED with SAM of silica spheres. The light output power has been measured by using a Si-photodiode placed at 1 cm apart from the LED surface. As shown in Fig. 4, the light output power was improved by employing the silica spheres. Compared to the conventional LED, the light output power of LED with SAM of silica spheres was enhanced by 28% at an injection current of 100 mA. At a high injection current of 350 mA, the enhancement of the output power by 23% was obtained. Figure 4(b) shows the normalized far-field radiation patterns of the conventional LED and the LED with SAM of silica spheres under an injection current of 350 mA at 298 K. The emission was measured in the angular range of 0-90°. The far-field radiation pattern of LED integrated silica spheres was slightly converged compared to that of the conventional LED. This results from the focusing effect by the spherical lens shapes through the SAM of silica spheres.

The increased LEE and the directionally focused light are mainly due to the formation of SAM of HCP silica spheres on the ITO surface of LEDs. To make a deeper understanding of the effect of silica spheres on the LEE and the directionally focused light, the wave-like behavior of light should be considered because the geometrical dimensions of spheres are of order of wavelength. Figure 5
Fig. 5 Light-ray dynamics for the plane ITO layer and for the ITO layer with silica spheres: (a) light-ray traces in the plane ITO layer, and (b)-(c) light-ray traces in the ITO layer with silica spheres.
shows the light-ray dynamics for plane ITO surface and for ITO surface with silica spheres. The critical angle and incident angle are represented as θc and θ0, respectively. When the light passes into the plane surface of ITO layer, it is only transmitted through the escape cone of 30° with a photon escape probability of only 6.2%. Figure 5(b) shows the ray of light passing into silica sphere with the incident angle of θ0 from the ITO layer. In this case, the light rays can vary with the incident angle. At an incident angle between π/6 < θ0 < θc, the light is guided in silica sphere. For θc < θ0, the light is also guided in LEDs. When the light passes into silica sphere with an incident angle between 0 < θ0 < π/6, it is transmitted into air through the lens-like medium of silica spheres. Moreover, the light extraction can be improved because the light undergoes the increased photon escape probability by the formation of a graded refractive index profile at the interfaces in ITO/air. The light is transmitted through the escape cone of 40.5ο with a photon escape probability of 10.5%. At normal incidence, also, the silica sphere with an optimum size act as antireflective coating layer (d=(2ni1)λ/4n, d: thickness of a coating layer, ni: positive integer, n: refractive index), which minimizes the reflection of light. Thus, the LEE of LEDs can be efficiently enhanced by the use of silica sphere with an optimum size.

0<θ0<π/6:Focusedlightπ/6<θ0<θc:Guidedlightinsilicasphereθc<θ0:GuidedlightinLEDs

Figure 5(c) shows the two arbitrary rays of light passing into silica sphere with incident angles of θ0 through the air from the ITO layer. The light always passes through the silica spheres except for the light with the normal incidence at the boundary between two silica spheres. When the light passes into silica spheres with an incident angle between 0 < θ0 < π/2, it is transmitted into air and refracted to the same angle with the incident light. For this reason, the light can be more focused compared to the light passing through the planar ITO layer.
0<θ0<π/2:Focusedlight
As mentioned above, the silica spheres with an optimum size provide the increased photon escape cone and the reduced Fresnel reflection loss with forming the graded refractive index between the ITO and air. Thus, the more photon can be propagated into air from the LEDs. Additionally, the directional emission properties are modified by the spherical lens shape of silica spheres. When the light passes into the silica spheres with special incident angles, it is probably focused by their convex lens-like shape and then transmitted into air. We believe that the SAM of HCP silica spheres with an optimum size is a suitable method to lead to the enhanced light-extraction and directional light emission properties of LEDs.

4. Conclusion

The effect of silica spheres on the LEE of LEDs was experimentally and theoretically investigated. The large-area GaN-based LEDs of 1 × 1 mm2 with SAM of HCP silica spheres were fabricated. The silica spheres were coated onto the ITO surface of LED by a simple spin coating process. It was found that the total internal reflection can be efficiently reduced by the use of the monolayer of silica spheres with an optimum size of 650 nm. Compared to the conventional LED, the fabricated LED with 650-nm-thick SAM of HCP silica spheres resulted in the enhancement of 1.28 and 1.23 times at the injection currents of 100 and 350 mA, respectively. Also, the incorporation of silica spheres improved the directional emission property. As results, this is a simple and cost-effective method for high-brightness LEDs and directional light applications.

Acknowledgment

This work was supported by Basic Science Research Program through the NRF funded by the MEST (No. 2011-0026393).

References and links

1.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A 194(2), 380–388 (2002). [CrossRef]

2.

R. H. Horng, S. H. Huang, C. C. Yang, and D. S. Wuu, “Efficiency improvement of GaN-based LEDs with ITO texturing window layers using natural lithography,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1196–1201 (2006). [CrossRef]

3.

C. Huh, K. S. Lee, E. J. Kang, and S. J. Park, “Improved light-output and electrical performance of InGaN-based light emitting diode by microroughening of the p-GaN surface,” J. Appl. Phys. 93(11), 9383–9385 (2003). [CrossRef]

4.

Y. M. Song, E. S. Choi, G. C. Park, C. Y. Park, S. J. Jang, and Y. T. Lee, “Disordered antireflective nanostructures on GaN-based light-emitting diodes using Ag nanoparticles for improved light extraction efficiency,” Appl. Phys. Lett. 97(9), 093110 (2010). [CrossRef]

5.

S. L. Ou, D. S. Wuu, S. P. Liu, Y. C. Fu, S. C. Huang, and R. H. Horng, “Pulsed laser deposition of ITO/AZO transparent contact layers for GaN LED applications,” Opt. Express 19(17), 16244–16251 (2011). [CrossRef] [PubMed]

6.

Z. Yin, X. Liu, Y. Wu, X. Hao, and X. Xu, “Enhancement of light extraction in GaN-based light-emitting diodes using rough beveled ZnO nanocone arrays,” Opt. Express 20(2), 1013–1021 (2012). [CrossRef] [PubMed]

7.

S. J. Tu, J. K. Sheu, M. L. Lee, C. C. Yang, K. H. Chang, Y. H. Yeh, F. W. Huang, and W. C. Lai, “Enhanced output power of GaN-based LEDs with embedded AlGaN pyramidal shells,” Opt. Express 19(13), 12719–12726 (2011). [CrossRef] [PubMed]

8.

K. McGroddy, A. David, E. Matioli, M. Lza, S. Nakamura, S. DenBaars, J. D. Dpeck, 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]

9.

K. H. Li and H. W. Choi, “InGaN light-emitting diodes with indium-tin-oxide photonic crystal current-spreading layer,” J. Appl. Phys. 110(5), 053104 (2011). [CrossRef]

10.

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]

11.

Y. K. Ee, P. Kumnorkaew, R. A. Arif, H. Tong, H. Zhao, J. F. Gilchrist, and N. Tansu, “Optimization of light extraction efficiency of III-nitride LEDs with self-assembled colloidal-based microlenses,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1218–1225 (2009). [CrossRef]

12.

X. H. Li, R. Song, Y. K. Ee, P. Kumnorkaew, J. F. Gilchrist, and N. Tansu, “Light extraction efficiency and radiation patterns of III-nitride light-emitting diodes with colloidal microlens arrays with various aspect ratios,” IEEE Photon. J. 3(3), 489–499 (2011). [CrossRef]

13.

M. V. Bogdanov, K. A. Bulashevich, O. V. Khokhlev, I. Yu. Evstratov, M. S. Ramm, and S. Yu. Karpov, “Effect of ITO spreading layer on performance of blue light-emitting diodes,” Phys. Status Solidi C 7(7–8), 2127–2129 (2010). [CrossRef]

14.

W. Stöber, A. Fink, and E. Bohn, “Controlled growth of monodisperse silica spheres in the micron size range,” J. Colloid Interface Sci. 26(1), 62–69 (1968). [CrossRef]

OCIS Codes
(220.2740) Optical design and fabrication : Geometric optical design
(230.3670) Optical devices : Light-emitting diodes
(310.1210) Thin films : Antireflection coatings
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: May 7, 2012
Revised Manuscript: August 29, 2012
Manuscript Accepted: October 9, 2012
Published: October 18, 2012

Citation
Hee Kwan Lee, Yeong Hwan Ko, Ganji Seeta Rama Raju, and Jae Su Yu, "Light-extraction enhancement and directional emission control of GaN-based LEDs by self-assembled monolayer of silica spheres," Opt. Express 20, 25058-25063 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-25058


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References

  1. F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A194(2), 380–388 (2002). [CrossRef]
  2. R. H. Horng, S. H. Huang, C. C. Yang, and D. S. Wuu, “Efficiency improvement of GaN-based LEDs with ITO texturing window layers using natural lithography,” IEEE J. Sel. Top. Quantum Electron.12(6), 1196–1201 (2006). [CrossRef]
  3. C. Huh, K. S. Lee, E. J. Kang, and S. J. Park, “Improved light-output and electrical performance of InGaN-based light emitting diode by microroughening of the p-GaN surface,” J. Appl. Phys.93(11), 9383–9385 (2003). [CrossRef]
  4. Y. M. Song, E. S. Choi, G. C. Park, C. Y. Park, S. J. Jang, and Y. T. Lee, “Disordered antireflective nanostructures on GaN-based light-emitting diodes using Ag nanoparticles for improved light extraction efficiency,” Appl. Phys. Lett.97(9), 093110 (2010). [CrossRef]
  5. S. L. Ou, D. S. Wuu, S. P. Liu, Y. C. Fu, S. C. Huang, and R. H. Horng, “Pulsed laser deposition of ITO/AZO transparent contact layers for GaN LED applications,” Opt. Express19(17), 16244–16251 (2011). [CrossRef] [PubMed]
  6. Z. Yin, X. Liu, Y. Wu, X. Hao, and X. Xu, “Enhancement of light extraction in GaN-based light-emitting diodes using rough beveled ZnO nanocone arrays,” Opt. Express20(2), 1013–1021 (2012). [CrossRef] [PubMed]
  7. S. J. Tu, J. K. Sheu, M. L. Lee, C. C. Yang, K. H. Chang, Y. H. Yeh, F. W. Huang, and W. C. Lai, “Enhanced output power of GaN-based LEDs with embedded AlGaN pyramidal shells,” Opt. Express19(13), 12719–12726 (2011). [CrossRef] [PubMed]
  8. K. McGroddy, A. David, E. Matioli, M. Lza, S. Nakamura, S. DenBaars, J. D. Dpeck, 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]
  9. K. H. Li and H. W. Choi, “InGaN light-emitting diodes with indium-tin-oxide photonic crystal current-spreading layer,” J. Appl. Phys.110(5), 053104 (2011). [CrossRef]
  10. 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,” Nanotechnology20(3), 035202 (2009). [CrossRef] [PubMed]
  11. Y. K. Ee, P. Kumnorkaew, R. A. Arif, H. Tong, H. Zhao, J. F. Gilchrist, and N. Tansu, “Optimization of light extraction efficiency of III-nitride LEDs with self-assembled colloidal-based microlenses,” IEEE J. Sel. Top. Quantum Electron.15(4), 1218–1225 (2009). [CrossRef]
  12. X. H. Li, R. Song, Y. K. Ee, P. Kumnorkaew, J. F. Gilchrist, and N. Tansu, “Light extraction efficiency and radiation patterns of III-nitride light-emitting diodes with colloidal microlens arrays with various aspect ratios,” IEEE Photon. J.3(3), 489–499 (2011). [CrossRef]
  13. M. V. Bogdanov, K. A. Bulashevich, O. V. Khokhlev, I. Yu. Evstratov, M. S. Ramm, and S. Yu. Karpov, “Effect of ITO spreading layer on performance of blue light-emitting diodes,” Phys. Status Solidi C7(7–8), 2127–2129 (2010). [CrossRef]
  14. W. Stöber, A. Fink, and E. Bohn, “Controlled growth of monodisperse silica spheres in the micron size range,” J. Colloid Interface Sci.26(1), 62–69 (1968). [CrossRef]

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