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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 14566–14572
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Coherent vertical beaming using Bragg mirrors for high-efficiency GaN light-emitting diodes

Sun-Kyung Kim and Hong-Gyu Park  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14566-14572 (2013)
http://dx.doi.org/10.1364/OE.21.014566


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Abstract

We propose a dielectric Bragg mirror that utilizes coherent coupling with multiple quantum wells (MQWs) to significantly enhance light extraction from GaN light-emitting diode (LED). Full vectorial electromagnetic simulation showed that, under constructive interference conditions, the Bragg mirror consisting of two dielectric (SiO2/TiO2) stacks and a silver layer led to >30% enhancement in light extraction, as compared to a single silver mirror. Such significant enhancement by a pre-designed Bragg/metal mirror was ascribed to the vertically oriented radiation pattern and reduced plasmonic metal loss. In addition, the gap distance between the MQWs and a Bragg mirror at which the constructive interference takes place could be controlled by modulating the thickness of the first low-refractive-index layer. Moreover, a two-dimensional periodic pattern was incorporated into an upper GaN layer with the designed Bragg mirror and it was shown that a lattice constant of ~800 nm was optimal for light extraction. We believe that tailoring the radiation profile of light emitters by coherent coupling with designed high-reflectivity mirrors will be a promising route to overcome the efficiency limit of current semiconductor LED devices.

© 2013 OSA

1. Introduction

High-efficiency GaN light-emitting diodes (LEDs) are environmentally friendly energy-saving devices, thus making their development highly desirable [1

1. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007). [CrossRef]

,2

2. A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based Light Emitters,” IEEE Electron. Lett. 57, 79–87 (2010).

]. Over the past decade, most GaN LED chips have been used in mobile backlights units or small-sized light bulbs. Recently, the market trend has shifted to high-output applications such as TV backlight and general illumination, and this has resulted in rapid expansion of the market size. However, to replace conventional lighting with LEDs, the efficiency of LEDs must be improved. The efficiency of GaN LEDs is primarily determined by heteroepitaxial growth techniques, and the extraction efficiency can be improved as long as all photons generated from multiple quantum wells (MQWs) are not extracted into an ambient medium [3

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

].

Thus far, several strategies for enhancing the light extraction efficiency of GaN LED devices have been proposed and demonstrated. The most common method for significantly increasing the light extraction efficiency is the introduction of random surface texturing [4

4. C. C. Kao, J. T. Chu, H. C. Kuo, S. C. Wang, and C. C. Yu, “Improvement of InGaN-GaN light-emitting diode performance with a nano-roughened p-GaN surface,” IEEE Photon. Technol. Lett. 17(5), 983–985 (2005). [CrossRef]

,5

5. Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys. 43(No. 5A), L637–L639 (2004). [CrossRef]

] or periodic patterning into a GaN layer [3

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

,6

6. H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express 14(19), 8654–8660 (2006). [CrossRef] [PubMed]

,7

7. A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007). [CrossRef]

], bottom reflector [8

8. S.-K. Kim, H.-S. Ee, K.-D. Song, and H.-G. Park, “Design of out-coupling structures with metal-dielectric surface relief,” Opt. Express 20(15), 17230–17236 (2012). [CrossRef]

,9

9. H. W. Huang, H. C. Kuo, C. F. Lai, C. E. Lee, C. W. Chiu, T. C. Lu, S. C. Wang, C. H. Lin, and K. M. Leung, “Enhanced performance of an InGaN–GaN light-emitting diode by roughening the undoped-GaN surface and applying a mirror coating to the sapphire substrate,” IEEE Photon. Technol. Lett. 19, 181117 (2007).

], or substrate [10

10. Y. C. Yang, J.-K. Sheu, M.-L. Lee, C. H. Yen, W.-C. Lai, S. J. Hon, and T. K. Ko, “Vertical InGaN light-emitting diode with a retained patterned sapphire layer,” Opt. Express 20(S6), A1019–A1025 (2012). [CrossRef]

]. The non-periodic or periodic patterns can even diffract light waves whose wave vectors are outside the light cone (e.g. θ~23.6° for air as an ambient medium) [11

11. 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 mode distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

]. Thus, light trapped inside a medium with high refractive index can be extracted until it is completely absorbed [13

13. S.-K. Kim, H. D. Song, H.-S. Ee, H. M. Choi, H. K. Cho, Y.-H. Lee, and H.-G. Park, “Metal mirror assisting light extraction from patterned AlGaInP light-emitting diodes,” Appl. Phys. Lett. 94(10), 101102 (2009). [CrossRef]

]. Another important strategy is to exploit coherent coupling between MQWs and a high-reflectivity mirror [14

14. Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221–2223 (2003). [CrossRef]

,15

15. S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010). [CrossRef] [PubMed]

]. The distribution of wave vectors of radiation generated from MQWs can be controlled by different interference conditions. When the condition of constructive interference holds for a normal direction, most of the wave vectors steer nearby the normal direction. Vertically oriented radiation by coherent coupling with a mirror does not undergo total internal reflection or does not require diffraction of low-order guided modes [3

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

,11

11. 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 mode distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

]. In order to harness this vertical beaming effect, thus far, only a metallic (e.g. silver) mirror has been used in LED structures [14

14. Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221–2223 (2003). [CrossRef]

,15

15. S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010). [CrossRef] [PubMed]

].

2. Coherent coupling with a single dielectric layer

In our FDTD simulation, MQWs were modeled as an appropriately combined set of electric dipole sources with orthogonal polarization. As an electric dipole is placed close to an interface across which the refractive index changes, an imaginary dipole is created in an opposite plane (Fig. 1(a)
Fig. 1 (A) Schematic of electric dipoles and their image dipoles with polarization normal (left) or parallel (right) to a mirror plane. (B) Extraction efficiency of a GaN structure with a bottom substrate composed of air (solid red) or sapphire (solid black), as a function of distance, d, between random electric dipole sources and the substrate. Right: schematic of the calculated GaN structure.
). Then, a real dipole interferes with its corresponding imaginary dipole and such interference can modulate the radiation’s profile as well as the spontaneous emission rate [16

16. J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999). [CrossRef]

].

3. Coherent coupling with Bragg mirrors

As a high-reflectivity mirror we have considered a system of distributed Bragg reflectors (DBRs) that were composed of two different dielectrics (Fig. 2(a)
Fig. 2 (A) Schematic of a GaN structure with a bottom DBR. (B) Reflectance of 2- (solid red) and 4-pairs (solid brown) of SiO2/TiO2 DBRs and a silver mirror (solid gray), as a function of incident angle. (C) Extraction efficiency of a GaN structure with 2- (solid red) and 4-pairs (solid brown) of SiO2/TiO2 DBRs and a silver mirror (solid gray), as a function of distance, d, between random electric dipole sources and the mirrors. The dashed red curve denotes the values from the GaN structure with 2-pairs of modified SiO2/TiO2 DBR. (D, E) Electric field intensity profiles of the GaN structure with 2-pairs of DBR (D) and a silver mirror (E) when d is 10 (upper, D), 100 (bottom, D), 70 (upper, E) and 120 nm (bottom, E), respectively.
). In the DBR, a quarter-wave SiO2 (n = 1.5) and TiO2 (n = 2.5) were stacked in an alternating way over a specific period [18

18. K. H. Baik, B. K. Min, J. Y. Kim, H. K. Kim, C. Sone, Y. Park, and H. Kim, “Light output enhancement of GaN-based flip-chip light-emitting diodes fabricated with SiO2/TiO2 distributed Bragg reflector coated on mesa sidewall,” J. Appl. Phys. 108(6), 063105 (2010). [CrossRef]

]. The DBR can be used in thin-film flip chip [19

19. O. B. Shchekin, J. E. Epler, T. A. Trottier, T. Margalith, D. A. Steigerwald, M. O. Holcomb, P. S. Martin, and M. R. Krames, “High performance thin-film flip-chip InGaN–GaN light-emitting diodes,” Appl. Phys. Lett. 89(7), 071109 (2006). [CrossRef]

] or vertical slab GaN LEDs [3

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

,5

5. Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys. 43(No. 5A), L637–L639 (2004). [CrossRef]

,10

10. Y. C. Yang, J.-K. Sheu, M.-L. Lee, C. H. Yen, W.-C. Lai, S. J. Hon, and T. K. Ko, “Vertical InGaN light-emitting diode with a retained patterned sapphire layer,” Opt. Express 20(S6), A1019–A1025 (2012). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

] where the sapphire substrate is removed by laser lift-off technique. First, we calculated the reflectivity of 2-pairs and 4-pairs of DBRs as a function of incident angle, and we also calculated the reflectivity of a silver mirror as a reference (Fig. 2(b)). For this reflectivity calculation, an analytical transfer-matrix method was used [20

20. E. Hecht, Optics, 4th ed. (Addison-Wesley Longman, 2002).

]. The results of reflectivity calculation showed that the reflectivity of the DBRs had a local maximum at normal incidence and reached unity beyond a critical angle which was determined by the two materials, GaN and SiO2, a low refractive index layer in the DBRs [21

21. S.-K. Kim, H. K. Cho, K. K. Park, J. Jang, J. S. Lee, K. W. Park, Y. Park, J.-Y. Kim, and Y.-H. Lee, “Angle-tuned, evanescently-decoupled reflector for high-efficiency red light-emitting diode,” Opt. Express 16(9), 6026–6032 (2008). [CrossRef] [PubMed]

]. The overall reflectivity was proportional to the number of the pairs of dielectrics. On the other hand, a silver mirror exhibited a slight gradual increase in reflectivity with increasing incident angle.

To quantitatively investigate the interference effect between the random dipole sources and the DBR or a silver mirror [22

22. D. R. Lide, CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 88th ed. (CRC Press, 2008).

], we calculated the extraction efficiency of a GaN structure using FDTD simulation while varying the gap distance, d (Fig. 2(c)). The calculated result showed that the extraction efficiency was greatly enhanced following the introduction of high-reflectivity mirrors, as compared to a single dielectric layer (Fig. 1(b)). For the DBRs, the extraction efficiency increased as the number of the dielectric stacks increased, which was in accord with the results obtained for the reflectivity (Fig. 2(b)). The local maxima in extraction efficiencies of 2-pairs and 4-pairs DBRs were found at gap distances of d = 10, 90 and 180 nm. Because for each dielectric, a DBR is composed of a quarter-wave stack, the phase change that light undergoes at the reflection of each layer is always zero. Therefore, the extraction efficiency in DBR becomes maximized as the distance d approaches zero. Specifically, in-plane dipoles, which are responsible for vertical radiation, satisfy the lowest order requirement of constructive interference condition at d = 0 nm. As the order of constructive interference increases, the extraction efficiency at the local maximum decreases gradually, because additional constructive interference takes place at other off-angles. In the case of a metal mirror, the phase change for reflected light is given by π + 2α, where α = 2πl/λ and l is the skin depth of a metal [14

14. Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221–2223 (2003). [CrossRef]

,15

15. S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010). [CrossRef] [PubMed]

]. This illustrates that the extraction efficiency in a silver mirror is minimized close to d = 0 nm and is maximized at d = 40 and 120 nm. We note that the maximal extraction efficiency of 2-pairs and 4-pairs DBRs surpassed that of a silver mirror.

The interference effect becomes much clearer after the radiation profiles of dipole sources in a GaN structure are calculated. We considered the 2-pairs of SiO2/TiO2 DBR (Fig. 2(d)) and a silver mirror (Fig. 2(e)). Under constructive (destructive) conditions, for both mirrors, the radiation pattern had an intensity anti-node (node) in the vertical direction. However, it was clearly observed that, under constructive conditions, the vertical radiation pattern of the DBR had less angular spreading, compared to that of the silver mirror. We postulate that higher efficiency from the DBRs is achieved due to the narrow beam divergence along with the absence of plasmonic metal loss that becomes severe when dipoles are located nearby a metal surface [23

23. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]

]. Lastly, we studied the possibility of tuning a gap distance at which constructive interference occurs. Although extraction efficiency of the DBRs at d = 10 nm was larger than that of a silver mirror at d = 120 nm, a gap distance of 10 nm would not be acceptable in real GaN LED devices because current spreading is very poor at such a small gap distance. To resolve this issue, we reduced the thickness of the first SiO2 layer in the DBR from a quarter-wave length (75 nm) to 25 nm [21

21. S.-K. Kim, H. K. Cho, K. K. Park, J. Jang, J. S. Lee, K. W. Park, Y. Park, J.-Y. Kim, and Y.-H. Lee, “Angle-tuned, evanescently-decoupled reflector for high-efficiency red light-emitting diode,” Opt. Express 16(9), 6026–6032 (2008). [CrossRef] [PubMed]

]. In this modified DBR, the first maximum of extraction efficiency was observed at d = 30 nm (Fig. 2(c), dashed red), while the extraction efficiency remained almost unchanged. Taken together, a designed dielectric DBR mirror exhibits enhanced vertical beaming effect as compared to a metallic mirror, resulting in the increased extraction efficiency of a DBR. Significantly, an optimal condition that promises the maximal extraction efficiency can be controlled by the rational design of each one of the dielectric layers in the DBR [24

24. R. Sharma, E. D. Haberer, C. Meier, E. L. Hu, and S. Nakamura, “Vertically oriented GaN-based air-gap distributed Bragg reflector structure fabricated using band-gap-selective photoelectrochemical etching,” Appl. Phys. Lett. 87(5), 051107 (2005). [CrossRef]

].

To further improve the vertical beaming effect and its resultant extraction efficiency, we designed a SiO2/TiO2 DBR combined with an underlying silver mirror (Fig. 3(a)
Fig. 3 (A) Reflectance of 1- (solid black), 2- (solid red), 3- (solid blue) and 4-pairs (solid green) of SiO2/TiO2 DBRs combined with a silver mirror, which were calculated as a function of incident angle. Inset: schematic of the calculated DBR/silver mirror. (B) Extraction efficiency of a GaN structure with 2-pairs of SiO2/TiO2 DBRs with a silver mirror, calculated as a function of the number of dielectric stacks in the DBR. Inset: schematic of the calculated GaN structure with a bottom DBR/silver mirror.
, inset). Although Bragg/metal mirrors have been explored in prior works [25

25. H. Chen, H. Guo, P. Zhang, X. Zhang, H. Liu, S. Wang, and Y. Cui, “Enhanced performance of GaN-based light-emitting diodes by using Al mirror and atomic layer deposition-TiO2/Al2O3 distributed Bragg reflector backside reflector with patterned sapphire substrate,” Appl. Phys. Express 6(2), 022101 (2013). [CrossRef]

,26

26. N.-M. Lin, S.-C. Shei, and S.-J. Chang, “Nitride-based LEDs with high-reflectance and wide-angle Ag mirror+SiO2/TiO2 DBR backside reflector,” J. Lightwave Technol. 29(7), 1033–1038 (2011). [CrossRef]

], the mirrors positioned far away from MQWs were used only for improving the reflectivity. First, we calculated the angular reflectance of the DBR/silver mirror as a function of the number of dielectric stacks in the DBR (Fig. 3(a)). The calculated result showed that the reflectance nearby 0° was enhanced noticeably compared to the system that had only a DBR or a silver mirror (Fig. 2(b)). However, multiple dips emerged at off-axis angles in the angular reflectance, which stems from amplified optical absorption on the silver mirror by optical resonances. The optical resonances were observed more clearly with increasing the number of dielectric stacks. Next, we calculated the extraction efficiency of the DBR/silver mirror at the first constructive interference condition (d = 10 nm) as a function of the number of dielectric stacks in the DBR (Fig. 3(b)). The result showed that the extraction efficiency was maximized when 2-pairs of SiO2/TiO2 dielectric stacks were used for the DBR. More importantly, the extraction efficiency of 18.5% was obtained, which constituted ~30% improvement over the maximal value that could be obtained from a silver mirror (Fig. 2(c)). We infer that the gradual decrease of DBRs in extraction efficiency with increasing number of dielectric stacks is attributed to the multiple dips in angular reflectance (Fig. 3(a)). Consequently, a dielectric DBR combined with a metallic mirror provides excellent reflectivity nearby the normal direction, which leads to significant enhancement in extraction efficiency as a result of the interference effect. The DBR/silver mirror can be further tailored toward higher extraction efficiency by the vertical beaming effect. For example, the SiO2 layer used as a low index layer can be replaced by air in order to further increase the contrast in refractive index between the two layers [24

24. R. Sharma, E. D. Haberer, C. Meier, E. L. Hu, and S. Nakamura, “Vertically oriented GaN-based air-gap distributed Bragg reflector structure fabricated using band-gap-selective photoelectrochemical etching,” Appl. Phys. Lett. 87(5), 051107 (2005). [CrossRef]

,27

27. J. H. Ryu, H. Y. Kim, H. K. Kim, Y. S. Katharria, N. Han, J. H. Kang, Y. J. Park, M. Han, B. D. Ryu, K. B. Ko, E.-K. Suh, and C.-H. Hong, “High performance of InGaN light-emitting diodes by air-gap/GaN distributed Bragg reflectors,” Opt. Express 20(9), 9999–10003 (2012). [CrossRef] [PubMed]

].

4. Two-dimensional periodic pattern with a designed Bragg mirror

In a semiconductor LED device, introduction of random texturing [4

4. C. C. Kao, J. T. Chu, H. C. Kuo, S. C. Wang, and C. C. Yu, “Improvement of InGaN-GaN light-emitting diode performance with a nano-roughened p-GaN surface,” IEEE Photon. Technol. Lett. 17(5), 983–985 (2005). [CrossRef]

,5

5. Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys. 43(No. 5A), L637–L639 (2004). [CrossRef]

] or periodic patterning into a dielectric [3

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

,6

6. H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express 14(19), 8654–8660 (2006). [CrossRef] [PubMed]

,7

7. A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007). [CrossRef]

,10

10. Y. C. Yang, J.-K. Sheu, M.-L. Lee, C. H. Yen, W.-C. Lai, S. J. Hon, and T. K. Ko, “Vertical InGaN light-emitting diode with a retained patterned sapphire layer,” Opt. Express 20(S6), A1019–A1025 (2012). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

] or metallic [8

8. S.-K. Kim, H.-S. Ee, K.-D. Song, and H.-G. Park, “Design of out-coupling structures with metal-dielectric surface relief,” Opt. Express 20(15), 17230–17236 (2012). [CrossRef]

,9

9. H. W. Huang, H. C. Kuo, C. F. Lai, C. E. Lee, C. W. Chiu, T. C. Lu, S. C. Wang, C. H. Lin, and K. M. Leung, “Enhanced performance of an InGaN–GaN light-emitting diode by roughening the undoped-GaN surface and applying a mirror coating to the sapphire substrate,” IEEE Photon. Technol. Lett. 19, 181117 (2007).

] surface is essential to extract light trapped by total internal reflection. To investigate how surface patterning interacts with the vertical beaming effect, we incorporated a two-dimensional square-lattice pattern into a GaN medium with a bottom DBR/silver mirror (Fig. 4(a)
Fig. 4 (A) Schematic of a GaN patterned structure with a bottom DBR/silver mirror. (B) Extraction efficiency of the GaN structure with the DBR/silver (solid red) and single silver mirror (solid gray), as a function of propagation distance, r. Inset: extraction efficiency of the GaN structure with the DBR/silver (solid red) and a single silver mirror (solid gray), as a function of lattice constant, a. For the DBR, 2-pairs of SiO2/TiO2 stacks were used.
). The 2-pairs of SiO2/TiO2 dielectric stacks were used for the DBR onto a silver mirror. Randomly polarized dipole sources were generated at a certain gap distance (d) to induce the vertical beaming effect (d = 10 nm for the DBR/silver mirror and d = 120 nm for a single silver mirror). Then, using the FDTD simulation, we calculated the extraction efficiency of the periodically patterned GaN structures with the DBR/silver mirror (Fig. 4(b), solid red) and a single silver mirror (Fig. 4(b), solid gray) as a function of propagation distance r. Here, propagation distance denotes the distance to which the photons, generated by the MQWs, can travel inside the GaN medium. The lattice constant a and the depth of the periodic pattern were fixed at 800 and 600 nm, respectively. No material absorption except for silver mirror was accounted. The details on the FDTD calculation are described elsewhere [6

6. H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express 14(19), 8654–8660 (2006). [CrossRef] [PubMed]

,8

8. S.-K. Kim, H.-S. Ee, K.-D. Song, and H.-G. Park, “Design of out-coupling structures with metal-dielectric surface relief,” Opt. Express 20(15), 17230–17236 (2012). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

,13

13. S.-K. Kim, H. D. Song, H.-S. Ee, H. M. Choi, H. K. Cho, Y.-H. Lee, and H.-G. Park, “Metal mirror assisting light extraction from patterned AlGaInP light-emitting diodes,” Appl. Phys. Lett. 94(10), 101102 (2009). [CrossRef]

,21

21. S.-K. Kim, H. K. Cho, K. K. Park, J. Jang, J. S. Lee, K. W. Park, Y. Park, J.-Y. Kim, and Y.-H. Lee, “Angle-tuned, evanescently-decoupled reflector for high-efficiency red light-emitting diode,” Opt. Express 16(9), 6026–6032 (2008). [CrossRef] [PubMed]

]. The calculated result showed that extraction efficiencies for the DBR/silver and single silver bottom mirrors increased steadily with the increasing propagation distance. However, for all propagation distances, the LED structure with the DBR/silver mirror was characterized by a more significant light extraction than the structure with single silver mirror. In addition, we calculated the extraction efficiencies for both LED structures while varying the lattice constant of the periodic pattern (Fig. 4(b), inset). In this calculation, we set a cut-off propagation distance as 300 μm to define the extraction efficiency [11

11. 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 mode distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

]. In a real LED device, the cut-off propagation distance is determined by interior optical absorption such as material absorption, free carrier absorption or inter-band absorption [13

13. S.-K. Kim, H. D. Song, H.-S. Ee, H. M. Choi, H. K. Cho, Y.-H. Lee, and H.-G. Park, “Metal mirror assisting light extraction from patterned AlGaInP light-emitting diodes,” Appl. Phys. Lett. 94(10), 101102 (2009). [CrossRef]

,28

28. C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev. 3(3), 262–286 (2009). [CrossRef]

]. The result showed that both structures had their maximal efficiency at a = 800 nm. Such a lattice constant is much larger than λ/n that provides the phase-matching condition to the fundamental guided mode, and is favorable for diffraction of light if the wave-vector is distributed in the vicinity of light cone [3

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

,11

11. 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 mode distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

]. Since high-order guided modes with wave vectors nearby light cone are diffracted more efficiently than low-order guided modes propagating horizontally [11

11. 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 mode distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

,12

12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

], the vertical beaming effect can boost the light extraction by a periodic surface pattern. At optimal a, the extraction efficiency of the structure with the DBR/silver mirror was ~15% higher than that of the structure with single silver mirror. The enhancement can be increased if real absorption is taken into account and thus, the propagation distance under consideration is shorter.

5. Conclusion

We studied the interference effect of dipole sources as they are placed close to a dielectric DBR at a distance of approximately one wavelength of light. Under the condition of constructive interference, the dipole sources generated radiation patterns with narrow beam divergence, which resulted in the improved extraction efficiency of a GaN LED structure. The vertical beaming effect and its resultant extraction efficiency were further improved when the dielectric DBR was combined with an underlying silver mirror. The maximal extraction efficiency of the GaN structure with a rationally designed DBR/silver mirror was enhanced by ~30% compared to that of the GaN structure that contained only a silver mirror. Considering that the reflectivity of a real silver mirror is degraded due to its surface roughness [29

29. S.-K. Kim, H.-S. Ee, W. Choi, S.-H. Kwon, J.-H. Kang, Y.-H. Kim, H. Kwon, and H.-G. Park, “Surface-plasmon-induced light absorption on a rough silver surface,” Appl. Phys. Lett. 98(1), 011109 (2011). [CrossRef]

], such an enhancement from the dielectric DBR mirror is likely to be more pronounced in experimental situations. In addition, the vertical beaming effect allowed for a relatively large lattice constant (a ~800 nm) for effective extraction of light trapped in a GaN medium. Our structure can be fully demonstrated in vertical GaN slab or thin-film GaN flip-chip structures where n-doped GaN layer is periodically patterned. Manipulating the wave vectors of light emitters by using rationally designed mirrors will provide a feasible and powerful strategy for the development of high-efficiency semiconductor LED devices.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (Grant No. 2013003115).

References and links

1.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007). [CrossRef]

2.

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based Light Emitters,” IEEE Electron. Lett. 57, 79–87 (2010).

3.

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

4.

C. C. Kao, J. T. Chu, H. C. Kuo, S. C. Wang, and C. C. Yu, “Improvement of InGaN-GaN light-emitting diode performance with a nano-roughened p-GaN surface,” IEEE Photon. Technol. Lett. 17(5), 983–985 (2005). [CrossRef]

5.

Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys. 43(No. 5A), L637–L639 (2004). [CrossRef]

6.

H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express 14(19), 8654–8660 (2006). [CrossRef] [PubMed]

7.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007). [CrossRef]

8.

S.-K. Kim, H.-S. Ee, K.-D. Song, and H.-G. Park, “Design of out-coupling structures with metal-dielectric surface relief,” Opt. Express 20(15), 17230–17236 (2012). [CrossRef]

9.

H. W. Huang, H. C. Kuo, C. F. Lai, C. E. Lee, C. W. Chiu, T. C. Lu, S. C. Wang, C. H. Lin, and K. M. Leung, “Enhanced performance of an InGaN–GaN light-emitting diode by roughening the undoped-GaN surface and applying a mirror coating to the sapphire substrate,” IEEE Photon. Technol. Lett. 19, 181117 (2007).

10.

Y. C. Yang, J.-K. Sheu, M.-L. Lee, C. H. Yen, W.-C. Lai, S. J. Hon, and T. K. Ko, “Vertical InGaN light-emitting diode with a retained patterned sapphire layer,” Opt. Express 20(S6), A1019–A1025 (2012). [CrossRef]

11.

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 mode distribution,” Appl. Phys. Lett. 88(6), 061124 (2006). [CrossRef]

12.

S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]

13.

S.-K. Kim, H. D. Song, H.-S. Ee, H. M. Choi, H. K. Cho, Y.-H. Lee, and H.-G. Park, “Metal mirror assisting light extraction from patterned AlGaInP light-emitting diodes,” Appl. Phys. Lett. 94(10), 101102 (2009). [CrossRef]

14.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221–2223 (2003). [CrossRef]

15.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010). [CrossRef] [PubMed]

16.

J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999). [CrossRef]

17.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008). [CrossRef]

18.

K. H. Baik, B. K. Min, J. Y. Kim, H. K. Kim, C. Sone, Y. Park, and H. Kim, “Light output enhancement of GaN-based flip-chip light-emitting diodes fabricated with SiO2/TiO2 distributed Bragg reflector coated on mesa sidewall,” J. Appl. Phys. 108(6), 063105 (2010). [CrossRef]

19.

O. B. Shchekin, J. E. Epler, T. A. Trottier, T. Margalith, D. A. Steigerwald, M. O. Holcomb, P. S. Martin, and M. R. Krames, “High performance thin-film flip-chip InGaN–GaN light-emitting diodes,” Appl. Phys. Lett. 89(7), 071109 (2006). [CrossRef]

20.

E. Hecht, Optics, 4th ed. (Addison-Wesley Longman, 2002).

21.

S.-K. Kim, H. K. Cho, K. K. Park, J. Jang, J. S. Lee, K. W. Park, Y. Park, J.-Y. Kim, and Y.-H. Lee, “Angle-tuned, evanescently-decoupled reflector for high-efficiency red light-emitting diode,” Opt. Express 16(9), 6026–6032 (2008). [CrossRef] [PubMed]

22.

D. R. Lide, CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 88th ed. (CRC Press, 2008).

23.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]

24.

R. Sharma, E. D. Haberer, C. Meier, E. L. Hu, and S. Nakamura, “Vertically oriented GaN-based air-gap distributed Bragg reflector structure fabricated using band-gap-selective photoelectrochemical etching,” Appl. Phys. Lett. 87(5), 051107 (2005). [CrossRef]

25.

H. Chen, H. Guo, P. Zhang, X. Zhang, H. Liu, S. Wang, and Y. Cui, “Enhanced performance of GaN-based light-emitting diodes by using Al mirror and atomic layer deposition-TiO2/Al2O3 distributed Bragg reflector backside reflector with patterned sapphire substrate,” Appl. Phys. Express 6(2), 022101 (2013). [CrossRef]

26.

N.-M. Lin, S.-C. Shei, and S.-J. Chang, “Nitride-based LEDs with high-reflectance and wide-angle Ag mirror+SiO2/TiO2 DBR backside reflector,” J. Lightwave Technol. 29(7), 1033–1038 (2011). [CrossRef]

27.

J. H. Ryu, H. Y. Kim, H. K. Kim, Y. S. Katharria, N. Han, J. H. Kang, Y. J. Park, M. Han, B. D. Ryu, K. B. Ko, E.-K. Suh, and C.-H. Hong, “High performance of InGaN light-emitting diodes by air-gap/GaN distributed Bragg reflectors,” Opt. Express 20(9), 9999–10003 (2012). [CrossRef] [PubMed]

28.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev. 3(3), 262–286 (2009). [CrossRef]

29.

S.-K. Kim, H.-S. Ee, W. Choi, S.-H. Kwon, J.-H. Kang, Y.-H. Kim, H. Kwon, and H.-G. Park, “Surface-plasmon-induced light absorption on a rough silver surface,” Appl. Phys. Lett. 98(1), 011109 (2011). [CrossRef]

OCIS Codes
(230.1480) Optical devices : Bragg reflectors
(230.3670) Optical devices : Light-emitting diodes
(260.3160) Physical optics : Interference

ToC Category:
Optical Devices

History
Original Manuscript: May 14, 2013
Manuscript Accepted: June 3, 2013
Published: June 11, 2013

Citation
Sun-Kyung Kim and Hong-Gyu Park, "Coherent vertical beaming using Bragg mirrors for high-efficiency GaN light-emitting diodes," Opt. Express 21, 14566-14572 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14566


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References

  1. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech.3(2), 160–175 (2007). [CrossRef]
  2. A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based Light Emitters,” IEEE Electron. Lett.57, 79–87 (2010).
  3. J. J. Wierer, A. David, and M. M. Mergens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics3(3), 163–169 (2009). [CrossRef]
  4. C. C. Kao, J. T. Chu, H. C. Kuo, S. C. Wang, and C. C. Yu, “Improvement of InGaN-GaN light-emitting diode performance with a nano-roughened p-GaN surface,” IEEE Photon. Technol. Lett.17(5), 983–985 (2005). [CrossRef]
  5. Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys.43(No. 5A), L637–L639 (2004). [CrossRef]
  6. H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express14(19), 8654–8660 (2006). [CrossRef] [PubMed]
  7. A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech.3(2), 133–148 (2007). [CrossRef]
  8. S.-K. Kim, H.-S. Ee, K.-D. Song, and H.-G. Park, “Design of out-coupling structures with metal-dielectric surface relief,” Opt. Express20(15), 17230–17236 (2012). [CrossRef]
  9. H. W. Huang, H. C. Kuo, C. F. Lai, C. E. Lee, C. W. Chiu, T. C. Lu, S. C. Wang, C. H. Lin, and K. M. Leung, “Enhanced performance of an InGaN–GaN light-emitting diode by roughening the undoped-GaN surface and applying a mirror coating to the sapphire substrate,” IEEE Photon. Technol. Lett.19, 181117 (2007).
  10. Y. C. Yang, J.-K. Sheu, M.-L. Lee, C. H. Yen, W.-C. Lai, S. J. Hon, and T. K. Ko, “Vertical InGaN light-emitting diode with a retained patterned sapphire layer,” Opt. Express20(S6), A1019–A1025 (2012). [CrossRef]
  11. 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 mode distribution,” Appl. Phys. Lett.88(6), 061124 (2006). [CrossRef]
  12. S.-K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett.92(24), 241118 (2008). [CrossRef]
  13. S.-K. Kim, H. D. Song, H.-S. Ee, H. M. Choi, H. K. Cho, Y.-H. Lee, and H.-G. Park, “Metal mirror assisting light extraction from patterned AlGaInP light-emitting diodes,” Appl. Phys. Lett.94(10), 101102 (2009). [CrossRef]
  14. Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett.82(14), 2221–2223 (2003). [CrossRef]
  15. S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express18(11), 11025–11032 (2010). [CrossRef] [PubMed]
  16. J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B60(7), 4688–4695 (1999). [CrossRef]
  17. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett.92(5), 053502 (2008). [CrossRef]
  18. K. H. Baik, B. K. Min, J. Y. Kim, H. K. Kim, C. Sone, Y. Park, and H. Kim, “Light output enhancement of GaN-based flip-chip light-emitting diodes fabricated with SiO2/TiO2 distributed Bragg reflector coated on mesa sidewall,” J. Appl. Phys.108(6), 063105 (2010). [CrossRef]
  19. O. B. Shchekin, J. E. Epler, T. A. Trottier, T. Margalith, D. A. Steigerwald, M. O. Holcomb, P. S. Martin, and M. R. Krames, “High performance thin-film flip-chip InGaN–GaN light-emitting diodes,” Appl. Phys. Lett.89(7), 071109 (2006). [CrossRef]
  20. E. Hecht, Optics, 4th ed. (Addison-Wesley Longman, 2002).
  21. S.-K. Kim, H. K. Cho, K. K. Park, J. Jang, J. S. Lee, K. W. Park, Y. Park, J.-Y. Kim, and Y.-H. Lee, “Angle-tuned, evanescently-decoupled reflector for high-efficiency red light-emitting diode,” Opt. Express16(9), 6026–6032 (2008). [CrossRef] [PubMed]
  22. D. R. Lide, CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 88th ed. (CRC Press, 2008).
  23. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater.3(9), 601–605 (2004). [CrossRef] [PubMed]
  24. R. Sharma, E. D. Haberer, C. Meier, E. L. Hu, and S. Nakamura, “Vertically oriented GaN-based air-gap distributed Bragg reflector structure fabricated using band-gap-selective photoelectrochemical etching,” Appl. Phys. Lett.87(5), 051107 (2005). [CrossRef]
  25. H. Chen, H. Guo, P. Zhang, X. Zhang, H. Liu, S. Wang, and Y. Cui, “Enhanced performance of GaN-based light-emitting diodes by using Al mirror and atomic layer deposition-TiO2/Al2O3 distributed Bragg reflector backside reflector with patterned sapphire substrate,” Appl. Phys. Express6(2), 022101 (2013). [CrossRef]
  26. N.-M. Lin, S.-C. Shei, and S.-J. Chang, “Nitride-based LEDs with high-reflectance and wide-angle Ag mirror+SiO2/TiO2 DBR backside reflector,” J. Lightwave Technol.29(7), 1033–1038 (2011). [CrossRef]
  27. J. H. Ryu, H. Y. Kim, H. K. Kim, Y. S. Katharria, N. Han, J. H. Kang, Y. J. Park, M. Han, B. D. Ryu, K. B. Ko, E.-K. Suh, and C.-H. Hong, “High performance of InGaN light-emitting diodes by air-gap/GaN distributed Bragg reflectors,” Opt. Express20(9), 9999–10003 (2012). [CrossRef] [PubMed]
  28. C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(3), 262–286 (2009). [CrossRef]
  29. S.-K. Kim, H.-S. Ee, W. Choi, S.-H. Kwon, J.-H. Kang, Y.-H. Kim, H. Kwon, and H.-G. Park, “Surface-plasmon-induced light absorption on a rough silver surface,” Appl. Phys. Lett.98(1), 011109 (2011). [CrossRef]

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