We describe the fabrication of corrugated inorganic oxide surface via direct single step conformal nanoimprinting to achieve enhanced light extraction in light emitting diodes (LEDs). Nanoscale zinc oxide (ZnO) and indium tin oxide (ITO) corrugated layer were created on a nonplanar GaN LED surface including metal electrode using ultraviolet (UV) assisted conformal nanoimprinting and subsequent inductively coupled plasma reactive ion etching (ICP-RIE) treatment. The total output powers of the surface corrugated LEDs increased by 45.6% for the patterned sapphire substrate LED and 41.9% for the flat c-plane substrate LED without any degradation of the electrical characteristics. The role of the nanoscale corrugations on the light extraction efficiency enhancement was examined using 3-dimensional finite-difference time-domain (FDTD) analysis. It was found that light scattering by subwavelength scale surface corrugation plays important role to redirect the trapped light into radiative modes. This straightforward inorganic oxide imprint method with inherent flexibility provides an efficient way to generate nanoscale surface textures for the production of high power LEDs and optoelectronic devices.
© 2012 OSA
Light emitting diodes (LEDs) are attracting a lot of interest as candidates for next-generation lighting sources due to their low energy consumption and long lifetimes [1,2]. However, in order to realize the future LED-based solid-state lighting, the quantum efficiency of LEDs is needed to be improved further1. The external quantum efficiency of LEDs is mainly determined by the internal quantum efficiency (IQE) and the light extraction efficiency (LEE) . Recently, the IQE of a GaN LED was drastically increased due to the rapid development of growth techniques using metalorganic chemical vapor deposition (MOCVD) processes . In case of the LEE, although the use of a patterned sapphire substrate (PSS) can yield an LEE enhancement up to 80%, further enhancements in the LEE are strongly required for the continued development of high-power low-consumption LEDs . A variety of efforts have been applied toward increasing the LEEs of GaN LEDs  including chip shaping , surface texturing , photonic crystal structures [8,9], or surface plasmon coupling [10,11] etc. Among the various proposed techniques, photonic structures with submicron features have been incorporated into the devices in an approach that has been attracted wide attention over the past decade in addition to PSS. However it requires sophisticated multistep processes that frequently involve time-consuming focused ion beam (FIB) and e-beam lithography or other high-cost lithographic techniques followed by subtractive or additive pattern transfer [12,13]. Recently, nanoimprint lithography (NIL) has gained a lot of interest as a high-resolution, high-throughput, and cost-effective nanopatterning technology [14,15]. Unlike other lithographic techniques in which a minimum pattern resolution usually counterbalances the maximum patternable area, the recent remarkable development of NIL offers an opportunity for ultralarge-area nanopatterning across 8 inch wafer scale with a minimum feature size of less than 100 nm . Moreover, NIL using flexible mold can generate topographic patterns with stepwise variations in the pattern depths that are difficult to achieve using other lithographic techniques. Although several studies have combined NIL with LEDs for the preparation of large-area nanoscale surface textures, electrical degradation and non-uniformity often observed as a result of etching damage between the p-GaN and the ohmic metals [17–19]. To address this problem, selected-area patterning on the outside of an electrode has been proposed as an alternative approach; however, difficulties associated with the multi-step processes required to offset the low etching selectivity of a polymer mask pose formidable technological challenges .
In this work, we report the development of a highly efficient strategy for increasing the LEE using direct single step conformal nanoimprinting of high refractive index inorganic oxide corrugations on the top surfaces of LEDs. In general, the low LEE of GaN-based LEDs mainly results from the total internal reflection (TIR) of light at the GaN/indium tin oxide (ITO)/air interface due to the difference between the refractive indexes of GaN, ITO, and air. In this study, high refractive index zincoxide (ZnO) photonic nanostructures was fabricated because it can provide not only photonic crystal effects but also better index matching, which can significantly improve the LEE in LEDs . To avoid electrical degradation by plasma damage to the ITO and p-metal contact areas, a flexible perfluoropolyether (PFPE) mold was used to prepare ZnO conformal nanoimprint patterns on the uneven LED surfaces including p-metal electrode. We found that the LEE of LEDs with nanoscale corrugated ZnO/ITO patterns were significantly enhanced than the conventional LED with a planar ITO without any degradation in a forward voltage. The significant ZnO/ITO texturing effect in the GaN LEDs, which showed an enhancement in the total output power of more than 45%, is discussed in detail.
To fabricate the ZnO corrugations on the uneven LED surfaces including p-metal electrode, ultraviolet (UV) NIL of metal precursors was used in place of thermal NIL to ensure conformal pattern transfer and to prevent the formation of cracks and defects during the demolding process [22,23]. Photosensitive 2-nitrobenzaldehyde was introduced to the ZnO precursor as a photoinitiator for the photochemical reaction. During UV illumination, the aci-form from nitrobenzaldehyde (NBA) is rapidly produced through the intramolecular proton-transfer reaction and a proton is released to yield the nitronate anion. The nitronate anion is converted to 2-nitrosobenzoic anion. Consequently, metal ion in metal alkoxide formed by condensation reaction attracts to nitryl ligand and a cross-linked structure is formed [24–26]. The photosensitive precursor films were spin coated onto the LED surfaces at 3000-5000 rpm and baked on a hot plate at 75 °C for 1 min to remove residual solvent from the film. The film thickness was controlled by modulating the concentration of the sol and the spin coating speed. A flexible bi functional urethane methacrylate PFPE mold duplicated from a Ni master (Holotools GmbH) with photonic nanostructures was then pressed against the ZnO precursor film at a pressure of 3 bar for 5 min using a UV nanoimprinter. After demolding, UV illumination (52 mWcm−2 with a spectral peak at 365 nm) was applied to the ZnO pattern for 5 min. And the corrugated ZnO pattern was annealed at 300 °C for 1 h to remove any residual organic compounds. Subsequent annealing was performed to crystallize ZnO films after UV illumination. Refractive index of ZnO films were measured by using a spectroscopic ellipsometer (Model M2000D, Woollam) at an incidence angle of 70°. After direct UV imprinting and annealing, large-area nanoscale ZnO corrugations formed on the top of the LED. Conventional epi-up planar blue GaN LED structures grown on a PSS and flat c-plane substrate was used in this study (Epivalley, Korea). A 230 nm- thick transparent conductive ITO layer was deposited on the p-GaN layer as a current spreading layer, and a p-metal electrode of Au/Ni/Cr (300/25/20 nm) was deposited by e-beam evaporation onto the ITO layer. Note that, to improve the LEE without degrading the electrical characteristics of the LEDs, the imprint process was applied after the preparation of a p-metal contact on the ITO layer. The ZnO/ITO surface was modified with inductively coupled plasma reactive ion etching (ICP-RIE, Oxford Instruments Ltd.) with a gas mixture of BCl3/Cl2 by using the ZnO pattern as a shadow mask. Finally, ZnO pattern on the p-metal pad was removed during the PR process for mesa etching. In this process, the masking area on the p-metal was opened for removal of the ZnO residues by BOE (buffered oxide etch).
3. Result and discussion
Figure 1 shows a schematic diagram of the overall process used to form the inorganic oxide corrugations on the LED surfaces using direct substrate conformal NIL. After the preparation of p-metal contact, a photocurable Zn precursor was spin-coated onto the LED surface (Fig. 1(a) and 1(b)). The Zn precursor film was pressed with a flexible PFPE mold duplicated from a Ni master (Fig. 1(c)). Notably, although the imprinted areas were not flat due to the presence of the prepatterned p-metal electrode, the flexible mold made conformal contact on the LED surface (Fig. 1(d)). After UV illumination, the ZnO corrugation was fabricated on the top surfaces of the LEDs (Fig. 1(e) and 1(f)). The facility of the straightforward method of patterning a nonplanar, stepped substrate using a flexible soft mold presents a major advantage over other approaches.
Figure 2 shows SEM image of imprinted ZnO patterns on the uneven LED substrate including p-metal electrode. Note that the ZnO patterns were transferred very conformally even in the boundary between the substrate and electrode. Figures 2(a)-2(c) show SEM images of the plane, tilted and side views of a directly imprinted ZnO corrugation on the uneven LED surface including p-metal electrode. The images clearly show the 108 nm thick ZnO layer composed of a 35 nm thick residual layer and 75 nm thick corrugated nanostructures with a period of 270 nm. To investigate the surface texturing effects of LED, we modified the ZnO surface with ICP-RIE by using the ZnO pattern as a shadow mask. After 60 s etching, the ZnO layer was completely removed and the underlying ITO layer was textured with the same manner of ZnO layer except for variations in the corrugation depth. In Fig. 2(d), we demonstrate an SEM image of a corrugated ITO layer after 60 s etching. Figure 2(e) plots the corrugation depth (Rz) as a function of the etching time. Rz decreased linearly as the etching time increased due to the etching rate differences between the ZnO and ITO layers. The ZnO residual layer was removed in 30 s, and complete removal of the ZnO layer was achieved within 60 s. As the etching time increased, the ZnO was removed and the ITO became exposed. X-ray photoelectron spectroscopy (XPS) revealed the systematic changes in the Zn 2p and In 3d peaks according to the ICP RIE. Figures 2(f) and 2(g) show the corresponding 2D and 3D atomic force microscopy (AFM) images of the corrugated ZnO and ITO layers after the etching process.
The optical and electrical characteristics of the PSS LEDs (300 × 300 µm2) with different surface corrugations were investigated using the probe system (Model: LEOS OPI 150, WITHLIGHT Co). After ZnO patterns were formed on the LEDs, we prepared various samples by changing the ICP-RIE etching time from 0, 30, 60, and 90 s (denoted by PSS-0s, −30s, −60s, −90s), respectively. Maximum 90 s etching time was set to prevent the damage of the current spreading ITO layer. In addition, we prepared a GaN reference LED (PSS-Ref) with a planar ITO layer. Figure 3(a) shows the current-forward voltage (I-V) characteristics of the reference LED (PSS-Ref) and the sample LEDs prepared with various etching times. The turn-on voltage (Vf) of all devices was approximately 3 V at 20 mA. Significant degradation of the electrical properties was not observed because the p-metal electrode was deposited on ITO before the ZnO patterning process. Slight increases of Vf for PSS-0s and PSS-30s (about 0.2 V at 20 mA) are attributed to the deviation of epi wafer by considering the relatively small device size of 300 × 300 µm2. The light output power (L) was also measured as a function of the current (I) over the range 0-100 mA in steps of 1 mA. Figure 3(b) shows the L-I plot of the reference and sample LEDs. After the formation of ZnO corrugations on the reference LED (sample PSS-0s), it showed a 14.0% increase in the light output at an injection current of 20 mA, and a much larger light output was observed for longer etching time. Notably, the sample PSS-90s displayed a 45.6% greater light output compared with the reference LED at an injection current of 20 mA, as shown in the inset of Fig. 3(b).
The improvements in the light output characteristic shown in Fig. 3(b) were further clarified by repeating the same experiments for flat c-plane substrate LEDs. Similar to the PSS LED samples, we prepared samples by varying the ICP-RIE etching time from 0, 30, and 60 s (denoted by Flat-0s, −30s, −60s), and a reference LED (Flat-Ref) with a planar ITO layer. In Fig. 4 we summarized all the L-I plot for the flat c-plane LED samples together with those of the PSS LED samples. The LEE enhancement trend for the flat c-plane LED samples resembled that of the PSS LED samples. The LEE is increased with the etching time and the highest LEE enhancement of 41.9% was observed at an etch time of 60 s, as was observed for the PSS LED samples. Figure 5 shows the electroluminescence (EL) spectra of the GaN LEDs with or without surface corrugations for the flat substrate and the PSS. As expected, the EL intensities of the corrugated ZnO/ITO LEDs were much greater than those of the LEDs without surface patterns and the same enhancement trend could be observed. Therefore, it could be considered that the observed LEE enhancements are achieved by introducing the corrugated ZnO and ITO layer.
To elucidate the improved LEE of the corrugated-ZnO/ITO GaN LED, a three dimensional finite-difference time-domain (FDTD) calculation was performed to model the LED devices [27,28]. In this calculation, we used a perfectly matched layer and perfect mirror boundary conditions to deal with the finite-size effects and the reduced simulation area. The absorption coefficient of the GaN was assumed to be 300 cm−1, corresponding to a photo lifetime of 320 fs. A point dipole polarized in the x-y plane was used as a radiating source of the LED. The spectrum of the dipole was centered at a wavelength of 450 nm with a FWHM of 10 nm and the center time of the pulse was 150 fs. The refractive indexes of GaN, sapphire, ITO, and ZnO at a wavelength of 450 nm were 2.42, 1.77, 2.06, and 1.8, respectively. A grid size of 20 nm was used in this simulation after checking the convergence. The extracted light was then measured by computing the Poynting vectors at the detected surfaces surrounding all sides of the LED. Figure 6(a) demonstrates the time-dependent total energy emitted from the top surface of the LED devices. The surface corrugated PSS samples produced a long tail in the time-dependent emission energy indicating that the trapped light inside the LED device was extracted by the PSS mainly due to the multiple reflections. Even though the PSS effect is dominant in the light extraction, one can notice that the strength of the long tail is significantly enhanced for the nanoscale patterned samples. Figure 6(b) shows a plot of the integrated total energies obtained from Fig. 6(a). It clearly shows the enhancement of LEE by introducing the PSS and surface corrugated ZnO/ITO layers. Notably, the LEE calculated using the FDTD methods displayed the trend observed in the experimental results (Fig. 4) as the surface structure was varied from the planar ITO layer to the corrugated ZnO and ITO layers. At the extraction time of 470 fs, the output energies of the corrugated LEDs were 20% higher than those of the LED without corrugation. Figure 6(c) shows an electric field intensity distribution in the Flat-Ref. and PSS-60s LEDs at the various extraction times. Obvious enhancement of light extraction can be observed in the PSS-60s sample compared to the Flat-Ref. sample.
In general, the enhanced LEE by incorporating the subwavelength microstructures can be understood by photonic crystal effects and surface scattering effects [6,21,29]. The photonic crystal effects include the photonic bandgap (PBG) effect and diffraction effect of guided light. The effects of the PBG on the LEE enhancement can be checked simply by calculating the correlation length of the nanoscale patterns. The length scale of the PBG effects is about λ/n ~a/2, where a is the lattice constant and λ is the wavelength. By putting the values of refractive index of ITO (1.8) and center wavelength (440 nm), we can obtain the correlation length of 488 nm which is about 2 times larger than the period of our nanopatterns (270 nm). To clarify the LEE enhancement mechanism, we performed FDTD calculation for the disordered surface structures by introducing a disordering parameter σ. The disordering parameter σ corresponds to a random shift in position of the nanopatterns. Figure 7 shows the variation of the LEE enhancement by increasing σ from 0 to 90 nm. Note that the LEE changed only slightly with increased disordering parameter which implies that the LEE enhancements observed in Fig. 6 are not caused by photonic crystal effects [6,21]. Therefore, as a possible candidate for the enhanced LEE, we consider the light scattering effects from a rough surface. M. N.-Vesperinas et al. reported that the corrugated surface has a correlation length smaller than the wavelength can increase transmitted evanescent waves beyond the critical angle [21,29]. Since the introduction of the disordering in the nanoscale patterns does not detrimental to the light extraction, the improvements in the optical power were thought to be resulted from the increased extraction efficiency due to the radiative outcoupling of the trapped modes due to light scattering from the corrugated surface. From this point of view, the LEE enhancement dependence on the RIE etching time shown in Fig. 3(b) can be understood as well. Since the LEE enhancements are mainly related to the surface scattering caused by subwavelength scale corrugation, the ZnO/ITO interface embedded below the corrugation surface is not advantageous to the light extraction since it additionally causes TIR. Thus we consider the increase of extraction efficiency with respect to the etching time is related to the elimination of the ZnO/ITO interface rather than effect of corrugation depth.
In summary, we investigated the enhanced LEEs of GaN LEDs by introducing the direct single step conformal nanoimprint techniques. Large-area nanoscale ZnO corrugations could be generated using a single step process via conformal imprinting of a photosensitive ZnO precursor solution. This straightforward inorganic oxide imprint method provides an efficient way to avoid complicated repeated deposition or etching processes in the preparation of nanoscale surface corrugations. We fabricated high refractive index ZnO nanostructures on the ITO surfaces of GaN LEDs and prepared various surface textured samples using ICP-RIE. Compared with a LED sample without surface corrugations, the output power of the new LEDs were enhanced by 45.6% for the PSS LEDs and 41.9% for the flat substrate LEDs without the concomitant degradation of the electrical properties. The LEE enhancement due to the surface corrugations was further supported by FDTD calculations. The single step inorganic oxide nanoimprint method described here offers a novel means for enhancing the LEE of high power LEDs and optoelectronic devices by simply and effectively introducing nanoscale corrugations on the LED surface.
This work was supported by a National Platform Technology grant (10033636) from the Ministry of Knowledge Economy of Korea and Korea Institute of Machinery & Materials (KIMM) research program (SC0890). We also acknowledge support by the National Research Foundation of Korea and Korea Research Council for Industrial Science & Technology.
References and links
2. S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3, 180–182 (2009). [CrossRef]
3. D. Xiao, K. W. Kim, S. M. Bedair, and J. M. Zavada, “Design of white light-emitting diodes using InGaN/AlInGaN quantum-well structures,” Appl. Phys. Lett. 84, 672–674 (2004). [CrossRef]
4. S.-M. Kim, K. S. Kim, G. Y. Jung, J. H. Baek, H. Jeong, and M. S. Jeong, “Electroluminescence comparison of photonic crystal light-emitting diodes with random and periodic hole structure,” J. Phys. D Appl. Phys. 42, 152004 (2009). [CrossRef]
5. M. R. Krames, M. Ochiai-Holcomb, G. E. Höfler, C. Carter-Coman, E. I. Chen, I.-H. Tan, P. Grillot, N. F. Gardner, H. C. Chui, J.-W. Huang, S. A. Stockman, F. A. Kish, M. G. Craford, T. S. Tan, C. P. Kocot, M. Hueschen, J. Posselt, B. Loh, G. Sasser, and D. Collins, “High-power truncated-inverted-pyramid (AlxGa1−x)0.5In0.5P/GaP light emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 2365–2367 (1999). [CrossRef]
6. I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thinfilm light emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993). [CrossRef]
7. K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato, and T. Taguchi, “High output power InGaN ultraviolet light-emitting diodes fabricated on patterned substrates using metalorganic vapor phase epitaxy,” Jpn. J. Appl. Phys. 40, L583–L585 (2001). [CrossRef]
8. 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 nanoimprinted photonic crystal GaN-based blue light emitting diodes,” Opt. Express 14, 8654–8660 (2006).
9. Z.-Y. Kim, M.-K. Kwon, K.-W. Lee, S.-J. Park, S. H. Kim, and K.-D. Lee, “Enhanced light extraction from GaN-based green light-emitting diode with photonic crystal,” Appl. Phys. Lett. 91, 181109 (2007). [CrossRef]
10. 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, 601–605 (2004). [CrossRef] [PubMed]
11. S. G. Zhang, X. W. Zhang, Z. G. Yin, J. X. Wang, J. J. Dong, H. L. Gao, F. T. Si, S. S. Sun, and Y. Tao, “Localized surface plasmon-enhanced electroluminescence from ZnO based heterojunction light-emitting diodes,” Appl. Phys. Lett. 99, 181116 (2011). [CrossRef]
12. S. X. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaN-based two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006). [CrossRef]
13. L. Chen and A. V. Nurmikko, “Fabrication and performance of efficient blue light emitting III-nitride photonic crystals,” Appl. Phys. Lett. 85, 3663–3665 (2004). [CrossRef]
14. S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272, 85–87 (1996). [CrossRef]
15. E. A. Costner, M. W. Lin, W.-L. Jen, and C. G. Willson, “Nanoimprint lithography materials development for semiconductor device fabrication,” Annu. Rev. Mater. Res. 39, 155–180 (2009). [CrossRef]
16. G.-Y. Jung, E. Johnston-Halperin, W. Wu, Z. Yu, S.-Y. Wang, W. M. Tong, Z. Li, J. E. Green, B. A. Sheriff, A. Boukai, Y. Bunimovich, J. R. Heath, and R. S. Williams, “Circuit fabrication at 17 nm half-pitch by nanoimprint lithography,” Nano Lett. 6, 351–354 (2006). [CrossRef] [PubMed]
17. D.-H. Kim, C.-O. Cho, Y.-G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C. Sone, Y. Park, W. J. Choi, and Q.-H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005). [CrossRef]
18. K.-J. Byeon, E.-J. Hong, H. Park, J.-Y. Cho, S.-H. Lee, J. Jhin, J. H. Baek, and H. Lee, “Full wafer scale nanoimprint lithography for GaN-based light-emitting diodes,” Thin Solid Films 519, 2241–2246 (2011). [CrossRef]
19. K.-J. Byeon, J. Y. Cho, J. Kim, H. Park, and H. Lee, “Fabrication of SiNx-based photonic crystals on GaN-based LED devices with patterned sapphire substrate by nanoimprint lithography,” Opt. Express 20, 11423–11432 (2012). [CrossRef] [PubMed]
20. J.-Y. Kim, M.-K. Kwon, S.-J. Park, S. H. Kim, and K.-D. Lee, “Enhancement of light extraction from GaN-based green light-emitting diodes using selective area photonic crystal,” Appl. Phys. Lett. 96, 251103 (2010). [CrossRef]
21. J. Zhong, H. Chen, G. Saraf, Y. Lu, C. K. Choi, J. J. Song, D. M. Mackie, and H. Shen, “Integrated ZnO nanotips on GaN light emitting diodes for enhanced emission efficiency,” Appl. Phys. Lett. 90, 203515 (2007). [CrossRef]
22. H.-H. Park, D.-G. Choi, X. Zhang, S. Jeon, S.-J. Park, S.-W. Lee, S. Kim, K. D. Kim, J.-H. Choi, J. Lee, D. K. Yun, K. J. Lee, H.-H. Park, R. H. Hill, and J.-H. Jeong, “Photo-induced hybrid nanopatterning of titanium dioxide via direct imprint lithography,” J. Mater. Chem. 20, 1921–1926 (2010). [CrossRef]
23. H.-H. Park, X. Zhang, S.-W. Lee, K.-D. Kim, D.-G. Choi, J.-H. Choi, J. Lee, E.-S. Lee, H.-H. Park, R. H. Hill, and J.-H. Jeong, “Facile nanopatterning of zirconium dioxide films via direct ultraviolet-assisted nanoimprint lithography,” J. Mater. Chem. 21, 657–662 (2010). [CrossRef]
24. J. Choi and M. Terazima, “Photochemical reaction of 2-nitrobenzaldehyde by monitoring the diffusion coefficient,” J. Phys. Chem. B 107(35), 9552–9557 (2003). [CrossRef]
25. A. Diaspro, F. Federici, C. Viappiani, S. Krol, M. Pisciotta, G. Chirico, F. Cannone, and A. Gliozzi, “Two-photon photolysis of 2-nitrobenzaldehyde monitored by fluorescent-labeled nanocapsules,” J. Phys. Chem. B 107, 11008–11012 (2003). [CrossRef]
26. E. A. Meulenkamp, “Size dependence of the dissolution of ZnO nanoparticles,” J. Phys. Chem. B 102, 7764–7769 (1998). [CrossRef]
27. D. H. Long, I.-K. Hwang, and S.-W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Quantum Electron. 15, 1257–1263 (2009). [CrossRef]
28. R. Han-Youl, “Modification of the light extraction efficiency in micro-cavity vertical InGaN light-emitting diode structures,” J. Korean Phys. Soc. 55, 1267–1271 (2009). [CrossRef]
29. M. Nieto-Vesperinas and J. A. Sánchez-Gil, “Light scattering from a random rough interface with total internal reflection,” J. Opt. Soc. Am. A 9, 424–436 (1992). [CrossRef]