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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6148–6155
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Azimuthally isotropic irradiance of GaN-based light-emitting diodes with GaN microlens arrays

Mount-Learn Wu, Yun-Chih Lee, Shih-Pu Yang, Po-Shen Lee, and Jenq-Yang Chang  »View Author Affiliations


Optics Express, Vol. 17, Issue 8, pp. 6148-6155 (2009)
http://dx.doi.org/10.1364/OE.17.006148


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Abstract

In this paper, the irradiance-modifying concept is proposed by introducing a microlens array on the p-GaN layer of GaN-based light-emitting diode (LED). Every microlens can locally modulate photons emitting from a micro-scaled active region of multiple quantum wells (MQWs) just beneath the microlens. The azimuthally isotropic irradiance from the GaN-based LED with microlens arrays is demonstrated numerically and experimentally. To realize such a novel LED, one-dimensional GaN microlens array with a period of 1.6 μm and a filling factor of 0.64 are fabricated by using dry etching. According to experimental results, the azimuthally isotropic light emission of proposed LED is observed. By using the angular-resolved photoluminescence, its intensity variation corresponding to the azimuth angles is as low as 10% within the angle region of ±50°.

© 2009 Optical Society of America

1. Introduction

Various LED array configurations designed to achieve the uniform illumination on a target plane by optimizing LED-to-LED spacing [14

14. Ivan Moreno, Maximino Avendano-Alejo, and Rumen I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45, 2265–2272 (2006). [CrossRef] [PubMed]

] and arranging the LED array on a spherical surface [15

15. I. Moreno, J. Munoz, and R. Ivanov, “Uniform illumination of distant targets using a spherical light-emitting diode array,” Opt. Eng. 46, 033001 (2007). [CrossRef]

] have been proposed. As considering compact lighting systems, directly modulating the emitting light pattern of a LED chip by adjusting its geometric parameters is important in applications such as projection TV light engines and direct flat panel display illumination. Several light-pattern modulation schemes have been reported, including theoretical demonstrations of etching photonic crystals [16

16. H. T. Hsueh, J. -F. T. Wang, C. H. Chao, W. Y. Yeh, C. F. Lai, H. C. Kuo, T. C. Lu, and S. C. Wang, “Azimuthal Anisotropy of Light Extraction from Photonic Crystal Light-emitting Diodes,” in Conference on Lasers and Electro-Optics/Pacific Rim 2007, (Optical Society of America, 2007), paper ThF1_4. [CrossRef]

] and photonic quasi-crystals [17

17. M.D.B. Charlton, M.E. Zoorob, and T. Lee, “Photonic Quasi-Crystal LEDs Design, modeling, and optimization,” Proc. SPIE 6486, 64860R-1–64860R-10 (2007).

] into the top emitting surfaces of LEDs or the experimental demonstration of monolithically integrated microlenses into sapphire substrates of LEDs [18

18. H. W. Choi, C. Liu, E. Gu, G. McConnell, J. M. Girkin, I. M. Watson, and M. D. Dawson, “GaN micro-Light Emitting Diode Arrays with Monolithically-integrated Sapphire micro-lenses,” Appl. Phys. Lett. 84, 2253–2255 (2004). [CrossRef]

]. Among these approaches, the ordered surface patterning of photonic (quasi-)crystals can be applied to design various azimuthally anisotropic irradiances from LEDs [16

16. H. T. Hsueh, J. -F. T. Wang, C. H. Chao, W. Y. Yeh, C. F. Lai, H. C. Kuo, T. C. Lu, and S. C. Wang, “Azimuthal Anisotropy of Light Extraction from Photonic Crystal Light-emitting Diodes,” in Conference on Lasers and Electro-Optics/Pacific Rim 2007, (Optical Society of America, 2007), paper ThF1_4. [CrossRef]

, 17

17. M.D.B. Charlton, M.E. Zoorob, and T. Lee, “Photonic Quasi-Crystal LEDs Design, modeling, and optimization,” Proc. SPIE 6486, 64860R-1–64860R-10 (2007).

]. The GaN micro-LEDs with monolithically integrated microlenses on the sapphire rear face can improve the directionality of the light emitted [18

18. H. W. Choi, C. Liu, E. Gu, G. McConnell, J. M. Girkin, I. M. Watson, and M. D. Dawson, “GaN micro-Light Emitting Diode Arrays with Monolithically-integrated Sapphire micro-lenses,” Appl. Phys. Lett. 84, 2253–2255 (2004). [CrossRef]

]. Unfortunately, the scheme of tailoring geometric parameters of LED chips to demonstrate azimuthally isotropic irradiances is not yet realized.

In this paper, the local modulation of photons within a micro-scaled region of MOWs just beneath the GaN microlens is proposed. We present the first experimental demonstration of the azimuthally isotropic irradiance from GaN-based LEDs. The azimuthally isotropic light emission with an intensity variation less than 10% is observed within the emitting angles of ±50° by using the angular-resolved photoluminescence.

2. Numerical simulation of GaN-based LEDs with microlens arrays

The proposed structure of LED grown on a sapphire substrate, as illustrated in Fig. 1, includes an n-GaN layer, multiple quantum wells (MQWs), and a p-GaN layer with microlens arrays. The microlenses fabricated on the p-GaN layer plays a role to modulate the emitting photons just beneath the microlenses. As illustrated in this figure, the structure parameters given in the numerical analysis include period of microlens array Λ = 1.6 μm, filling factor of microlens F = 0 - 1, p-GaN layer thickness hpGaN = 0.3 μm, MQWs thickness hMQWS = 0.01 μm, n-GaN layer thickness hnGaN = 4 μm, p-GaN reflective index npGaN = 2.5, MQWs reflective index nMQWS= 2.4, n-GaN reflective index nnGaN = 2.5, microstructure etching depth hm = 0.185 μm, and microstructure slanted angle θ = 27.4°. The finite-difference time-domain (FDTD) analysis is used to study the irradiance behaviour of the proposed LED with microlens arrays. In order to describe the random propagation of unpolarized photons trapped within or escaping from LEDs, multiple TE and TM-polarized point sources with the wavelength of 460 nm are arranged within the MQWs region with an interval of 100 nm. In one identical period of the microlens, the average number of point sources is 16. As shown in Fig. 1, there are 17 points (S1 – S17) uniformly located in the MQWs region underneath one identical period of microlens array. Two outer point sources are shared with neighboring microlenses. To facilitate the numerical simulation, the computation window of 160 × 80 μm2 with a spatial discretization of 20 nm is employed under the limitation of computer memory. Figure 2 shows the simulated angular radiation patterns emitting from the proposed LEDs with microlens arrays of various filling factors, including F = 0, 0.4, 0.64, and 1. The four emission patterns are normalized to unity intensity at their maximum values. Among these four cases, the filling factor of 1 is the planar type with the p-GaN layer thickness of 0.3 μm. The filling factor of 0 means the p-GaN layer of the planar type is etched down to 0.115 μm. Two different filling factors F = 0.4 and 0.64 are applied to demonstrate the modulation effect of microlens with different sizes. As shown in this figure, a Lambertian light pattern emitting from the planar LED is agreed with the theoretical prediction. The angular radiation patterns are varied with the filling factors of microlenses. As indicated in this figure, the azimuthally isotropic light emission with an intensity variation less than 10% is observed within the emitting angles of ±50° for the case of F = 0.64.

Fig. 1. Schematic diagram of the proposed GaN-based LED. The microlens patterns are employed on the top surface of the p-GaN layer.
Fig. 2. Angular radiation patterns emitting from the proposed LEDs with microlens arrays of filling factors F = 0, 0.4, 0.64, and 1.

3. Light extraction of single point-source under modulation of microlens

In order to understand the azimuthally isotropic irradiance of the proposed GaN-based LED with a filling factor of 0.64 for the microlens array, the spatial modulation due to a microlens on a single point source is demonstrated by using the FDTD method. The single point source is chosen for providing a good resolution for clearly observing the spatial modulation caused by the microlens. According to specific positions of single point sources arranged in the MQWs beneath one identical period of the microlens array, the spatial modulation of microlens can be classified into three categories including the case A of full modulation, the case B of partial modulation, and the case C of non-modulation.

Figure 3(a) demonstrates light emits from the proposed LED of the case A with the single point-source arranged in the MQWs just beneath the central part of microlens. As shown in this figure, most of photons escape from two slanted surface due to their larger light-escape cones. It is notable that the radiation pattern as shown in Fig. 3(b) possesses three peak intensities at θ = 0° and ±50°. It means that the two-lobe near-field radiation pattern of the case A gradually converts into the three-peak far-field pattern. The total intensity integration of angular radiation pattern of the case A is 58.74.

Fig. 3. The case A of full modulation. (a) Poynting intensity distribution of the proposed LED with the single point-source arranged in the MQWs beneath the central part of microlens. (b) Radiation pattern.

Figure 4(a) demonstrates light emits from the proposed LED of the case B with the single point-source arranged in the MQWs just beneath the right corner of microlens. In this figure, most of photons escape from the right slanted surface and form a single-lobe radiation pattern as illustrated in Fig. 4(b). The total intensity integration of angular radiation pattern of the case B is 12.58. It means that the laterally shift of a point-source corresponding to the central position of microlens would degrade the coupling effect of microlens.

Figure 5(a) demonstrates light emits from the proposed LED of the case C with the single point-source arranged in the MQWs just beneath the planar p-GaN layer between two microlenses. In this figure, photons directly escape from the planar p-GaN surface and form a bat-wing radiation pattern as illustrated in Fig. 5(b). The total intensity integration of angular radiation pattern of the case C is 27.47. As compared with the case A, it is almost 2-fold reduction in the light extraction from the planar p-GaN surface. Moreover, the bat-wing radiation pattern reveals that the microlenses still modulate the emitting light pattern into that with two peak intensities at θ = ±30° although almost photons penetrate into the air from the planar interface.

Fig. 4. The case B of partial modulation. (a) Poynting intensity distribution of the proposed LED with the single point-source arranged in the MQWs beneath the right corner of microlens. (b) Radiation pattern.
Fig. 5. The case C of non-modulation. (a) Poynting intensity distribution of the proposed LED with the single point-source arranged in the MQWs beneath the planar p-GaN layer between two microlenses. (b) Radiation pattern.

Fig. 6. The combinations of case A, B, and C. (a) Poynting intensity distribution of the proposed LED with five point sources arranged in the MQWs beneath one identical period of the microlens. (b) Radiation pattern.
Fig. 7. Combinations of case A, B, and C with dense point-source. (a) Poynting intensity distribution of the proposed LED with seventeen point-source arranged in the MQWs beneath one identical period of the microlens. (b) Radiation pattern of seventeen point-sources (green line).

4. Experimental results

The microlens array is constructed on the p-GaN layer to investigate the feasibility of modulating the emitting light patterns of LEDs. Initially, intended microlens profile with a period of 1.6 μm is defined in PMMA by e-beam lithography. Then, the patterned PMMA on the p-GaN surface is developed in a solution of methylisobutyl ketone and isopropyl alcohol. Finally, a following inductive-coupled plasma (ICP) dry etching process is used to transfer the patterned structure to the p-GaN layer. Figures 8(a) and 8(b) show pictures of fabricated microlens array observed by scanning electron microscope (SEM) and atomic force microscope (AFM), respectively. The microlens is observed with an average period close to 1.6 μm. The filling factor F corresponding to the average period is around 0.64. The lateral size of the area of fabricated microlens is over 1 mm × 1 mm.

In order to confirm the modulation in azimuthally isotropic irradiance of one-dimensional GaN microlens, the irradiance measurement of proposed LED is carried out by using an angular-resolved photoluminescence (PL) configuration. It is not an electroluminescencen (active operation) of a LED. As illustrated in Fig. 9, the measurement setup consists of He-Cd laser of 325 nm, a monochromator, a photomultiplier tube, a lock-in amplifier, a laser-line bandpass filter, a long-pass filter, an object lens of 20X magnification, and a fiber with a collimator. For showing the modulation of proposed structures clearly, the measured irradiance plane is perpendicular to the direction of one-dimensional microslens. With inserting a laser-line bandpass filter in the optical path of measurement system, the GaN-based LED can be pumped by using He-Cd laser of 325 nm only. The focusing beam of He-Cd laser with a diameter smaller than 1 mm is obliquely incident to the fabricated microlens region on the p-GaN surface. The most part of emitting light radiated from the inner of chip would couple into the air through the proposed structure surface. The fiber with a collimator in an angular-resolved irradiance measurement is adopted to collect the spatial emitting light. Under geometric arrangement of these optical components as shown in Fig. 9, an angular resolution of 4.4° can be obtained in the system. This angular-resolved irradiance measurement system is convenient to get the emitting light pattern of LEDs for photoluminescence configuration.

Fig. 8. Images of fabricated microlens array by (a) SEM and (b) AFM.

Figure 10 shows the measured angular radiation patterns emitting from the proposed LED and the planar LED. For comparison, the simulated angular radiation patterns emitting from microlens LEDs is illustrated in this figure. As shown in this figure, the theoretical model can be used to precisely predict the irradiance of both LEDs. An azimuthally isotropic light emission with an intensity variation less than 10% within the emitting angles of ±50° is observed. It also means that a great amount of photons with higher spatial frequencies emit from the proposed LED as compared with the planar one. With the assistance of the microlens array, more photons induced in GaN-based LED can be effectively coupled into the air.

Fig. 9. Angular-resolved photoluminescence measurement setup.

The deviation between the experimental and simulated results may result from the spatial resolution of angular PL system. However, the main feature of the uniform light pattern still agrees with the results obtained in the simulation. Moreover, it is referred that the surface roughness of microlens, as shown in Fig. 8(b), also induce the inevitable scattering that would degrade the uniformity of irradiance in certain degree. However, such surface roughness of microlens would enhance the light extraction efficiency. As compared with the planar one, the improvement of light extraction from proposed LEDs is about 250%.

Fig. 10. Measured angular radiation patterns of microlens and planar LEDs.

5. Conclusion

The microlens array has been applied to a p-GaN surface of LED for purpose of modulating the light pattern uniformly within a cone of 100°. Through the simulation of FDTD and the measurement of PL angular-resolved, the proposed structure reveals the strong modulation effect in uniformity light pattern of LED light source. As a concluding remark, the proposed microlens-like structure provides modulation for LEDs as a spatial intensity uniformity device integrated with GaN-LEDs structure. The further work would be in designing the functional radiation pattern to increase the applications of LEDs light source. And we expect that further optimization of the angular-resolved irradiance measurement system such as the angular resolution and co-plane stability will promise high accuracy radiation pattern of LEDs.

Acknowledgment

This work was supported by National Science Council of the Republic of China under Grant number NSC97-2221-E-008-024.

References and links

1.

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

2.

S. I. Na, G. Y. Ha, D. S. Han, S. S. Kim, J. Y. Kim, J. H. Lim, D. J. Kim, K. I. Min, and S. J. Park, “Selective wet etching of p-GaN for efficient GaN-based light-emitting diodes,” IEEE Photon. Technol. Lett. 18, 1512–1514 (2006). [CrossRef]

3.

C. H. Kuo, C. C. Lin, S. J. Chang, Y. P. Hsu, J. M. Tsai, W. C. Lai, and P. T. Wang, “Nitride-based light-emitting diodes with p-AlInGaN surface layers,” IEEE Tran. Electron. Dev. 52, 2346–2349 (2005). [CrossRef]

4.

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

5.

C. H. Chao, S. L. Chung, and T. L. Wu, “Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals,” Appl. Phys. Lett. 89, 091116 (2006). [CrossRef]

6.

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

7.

H. W. Choi, C. W. Jeon, and M. D. Dawson, “InGaN microring light-emitting diodes,” IEEE Photon. Technol. Lett. 16, 33–35 (2004). [CrossRef]

8.

K. H. Kim, J. Li, S. X. Jin, J. Y. Lin, and H. X. Jiang, “III-nitride ultraviolet light-emitting diodes with delta doping,” Appl. Phys. Lett. 83, 566–568 (2003). [CrossRef]

9.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J Appl. Phys. 41, 1431–1433 (2002). [CrossRef]

10.

S. J. Chang, W.S. Chen, S. C. Shei, T. K. Ko, C. F. Shen, Y. P. Hsu, C. S. Chang, J. M. Tsai, W. C. Lai, and A. J. Lin, “Highly Reliable High-Brightness GaN-Based Flip Chip LEDs,” IEEE Tran. Advanced Packaging 30, (2007).

11.

I. Moreno and U. Contreras, “Color distribution from multicolor LED arrays,” Opt. Express 15, 3607–3618 (2007) [CrossRef] [PubMed]

12.

A. Borbely and S. G. Johnson, “Performance of phosphor-coated light-emitting diode optics in ray-trace simulations,” Opt. Eng. 44, 111308 (2005). [CrossRef]

13.

C. Deller, G. Smith, and J. Franklin, “Colour mixing LEDs with short microsphere doped acrylic rods,” Opt. Express 12, 3327–3333 (2004) [CrossRef] [PubMed]

14.

Ivan Moreno, Maximino Avendano-Alejo, and Rumen I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45, 2265–2272 (2006). [CrossRef] [PubMed]

15.

I. Moreno, J. Munoz, and R. Ivanov, “Uniform illumination of distant targets using a spherical light-emitting diode array,” Opt. Eng. 46, 033001 (2007). [CrossRef]

16.

H. T. Hsueh, J. -F. T. Wang, C. H. Chao, W. Y. Yeh, C. F. Lai, H. C. Kuo, T. C. Lu, and S. C. Wang, “Azimuthal Anisotropy of Light Extraction from Photonic Crystal Light-emitting Diodes,” in Conference on Lasers and Electro-Optics/Pacific Rim 2007, (Optical Society of America, 2007), paper ThF1_4. [CrossRef]

17.

M.D.B. Charlton, M.E. Zoorob, and T. Lee, “Photonic Quasi-Crystal LEDs Design, modeling, and optimization,” Proc. SPIE 6486, 64860R-1–64860R-10 (2007).

18.

H. W. Choi, C. Liu, E. Gu, G. McConnell, J. M. Girkin, I. M. Watson, and M. D. Dawson, “GaN micro-Light Emitting Diode Arrays with Monolithically-integrated Sapphire micro-lenses,” Appl. Phys. Lett. 84, 2253–2255 (2004). [CrossRef]

OCIS Codes
(230.3670) Optical devices : Light-emitting diodes
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Optical Devices

History
Original Manuscript: January 15, 2009
Revised Manuscript: March 21, 2009
Manuscript Accepted: March 31, 2009
Published: April 1, 2009

Citation
Mount-Learn Wu, Yun-Chih Lee, Shih-Pu Yang, Po-Shen Lee, and Jenq-Yang Chang, "Azimuthally isotropic irradiance of GaN-based light-emitting diodes with GaN microlens arrays," Opt. Express 17, 6148-6155 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6148


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References

  1. T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, "Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening," Appl. Phys. Lett. 84, 855-857 (2004). [CrossRef]
  2. S. I. Na, G. Y. Ha, D. S. Han, S. S. Kim, J. Y. Kim, J. H. Lim, D. J. Kim, K. I. Min, and S. J. Park, "Selective wet etching of p-GaN for efficient GaN-based light-emitting diodes," IEEE Photon. Technol. Lett. 18, 1512-1514 (2006). [CrossRef]
  3. C. H. Kuo, C. C. Lin, S. J. Chang, Y. P. Hsu, J. M. Tsai, W. C. Lai, and P. T. Wang, "Nitride-based light-emitting diodes with p-AlInGaN surface layers," IEEE Tran. Electron. Dev. 52, 2346-2349 (2005). [CrossRef]
  4. A. David, T. Fuji, R. Sharma, K. McGroddy, S. Nakamura, S. P. DenBaars, E. L. Hu, and C. Weisbuch, "Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution," Appl. Phys. Lett. 88, 061124 (2006). [CrossRef]
  5. C. H. Chao, S. L. Chung, and T. L. Wu, "Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals," Appl. Phys. Lett. 89, 091116 (2006). [CrossRef]
  6. A. David, T. Fuji, B. Moran, S. Nakamura, S. P. DenBaars, R. Sharma, K. McGroddy, E. L. Hu, and C. Weisbuch, "Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution," Appl. Phys. Lett. 88, 061124 (2006). [CrossRef]
  7. H. W. Choi, C. W. Jeon, and M. D. Dawson, "InGaN microring light-emitting diodes," IEEE Photon. Technol. Lett. 16, 33-35 (2004). [CrossRef]
  8. K. H. Kim, J. Li, S. X. Jin, J. Y. Lin, and H. X. Jiang, "III-nitride ultraviolet light-emitting diodes with delta doping," Appl. Phys. Lett. 83, 566-568 (2003). [CrossRef]
  9. M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, "InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode," Jpn. J Appl. Phys. 41, 1431-1433 (2002). [CrossRef]
  10. S. J. Chang, W.S. Chen, S. C. Shei, T. K. Ko, C. F. Shen, Y. P. Hsu, C. S. Chang, J. M. Tsai, W. C. Lai, and A. J. Lin, "Highly Reliable High-Brightness GaN-Based Flip Chip LEDs," IEEE Tran. Adv. Packaging 30, (2007).
  11. I. Moreno and U. Contreras, "Color distribution from multicolor LED arrays," Opt. Express 15, 3607-3618 (2007) [CrossRef] [PubMed]
  12. A. Borbely, S. G. Johnson, "Performance of phosphor-coated light-emitting diode optics in ray-trace simulations," Opt. Eng. 44, 111308 (2005). [CrossRef]
  13. C. Deller, G. Smith, and J. Franklin, "Colour mixing LEDs with short microsphere doped acrylic rods," Opt. Express 12, 3327-3333 (2004) [CrossRef] [PubMed]
  14. I. Moreno, M. Avendano-Alejo, and R. I. Tzonchev, "Designing light-emitting diode arrays for uniform near-field irradiance," Appl. Opt. 45, 2265-2272 (2006). [CrossRef] [PubMed]
  15. I. Moreno, J. Munoz, and R. Ivanov, "Uniform illumination of distant targets using a spherical light-emitting diode array," Opt. Eng. 46, 033001 (2007). [CrossRef]
  16. H. T. Hsueh, J. -F. T. Wang, C. H. Chao, W. Y. Yeh, C. F. Lai, H. C. Kuo, T. C. Lu, and S. C. Wang, "Azimuthal Anisotropy of Light Extraction from Photonic Crystal Light-emitting Diodes," in Conference on Lasers and Electro-Optics/Pacific Rim 2007, (Optical Society of America, 2007), paper ThF1_4. [CrossRef]
  17. M. D. B. Charlton, M. E. Zoorob, and T. Lee, "Photonic Quasi-Crystal LEDs Design, modeling, and optimization," Proc. SPIE 6486, 64860R-1-64860R-10 (2007).
  18. H. W. Choi, C. Liu, E. Gu, G. McConnell, J. M. Girkin, I. M. Watson, and M. D. Dawson, "GaN micro-Light Emitting Diode Arrays with Monolithically-integrated Sapphire micro-lenses," Appl. Phys. Lett. 84, 2253-2255 (2004). [CrossRef]

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