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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26507–26514
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Growth of highly bright-white silica nanowires as diffusive reflection coating in LED lighting

Shuang Xi, Tielin Shi, Lei Zhang, Dan Liu, Wuxing Lai, and Zirong Tang  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26507-26514 (2011)
http://dx.doi.org/10.1364/OE.19.026507


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Abstract

Large quantities of silica nanowires were synthesized through thermal treatment of silicon wafer in the atmosphere of N2/H2(5%) under 1200 °C with Cu as catalyst. These nanowires grew to form a natural bright-white mat, which showed highly diffusive reflectivity over the UV-visible range, with more than 60% at the whole range and up to 88% at 350 nm. The utilization of silica nanowires in diffusive coating on the reflector cup of LED is demonstrated, which shows greatly improved light distribution comparing with the specular reflector cup. It is expected that these nanowires can be promising coating material for optoelectronic applications.

© 2011 OSA

1. Introduction

One-dimensional (1-D) structures, such as nanowires, nanobelts and nanotubes, have intrigued considerable research enthusiasm for their unique properties and promising applications as building blocks in nanoscale electronics and optoelectronics, which is superior to their bulk counterparts [1

1. Y. N. Xia, P. D. Yang, Y. G. Sun, Y. Y. Wu, B. Mayers, B. Gates, Y. D. Yin, F. Kim, and H. Q. Yan, “One-dimensional nanostructures: synthesis, characterization, and applications,” Adv. Mater. (Deerfield Beach Fla.) 15(5), 353–389 (2003). [CrossRef]

,2

2. C. M. Lieber and Z. L. Wang, “Functional nanowires,” MRS Bull. 32(02), 99–108 (2007). [CrossRef]

]. Silicon based nanowires are especially attractive due to their valuable semiconducting, electrical, and optical properties, as well as their potential application in the fields of photonics, photovoltaics, and sensors [3

3. L. J. Chen, “Silicon nanowires: the key building block for future electronic devices,” J. Mater. Chem. 17(44), 4639–4643 (2007). [CrossRef]

5

5. Z. W. Pan, Z. R. Dai, L. Xu, S. T. Lee, and Z. L. Wang, “Temperature controlled growth of silicon-based nanostructures by thermal evaporation of SiO powders,” J. Phys. Chem. B 105(13), 2507–2514 (2001). [CrossRef]

]. As an excellent electrical insulator, silica is abundant in nature and possesses diverse phases [6

6. R. W. G. Wyckoff, Crystal Structures (Wiley-Interscience, NewYork, 1965).

]. Its 1-D structure, silica nanowires, have been recently designated for usage as high-intensity light sources, near-field optical microscopy probes, and interconnections in integrated optical systems [7

7. G. Bilalbegović, “Electronic properties of silica nanowires,” J. Phys. Condens. Matter 18(15), 3829–3836 (2006). [CrossRef]

]. Progress in the ability to fabricate silica nanowires with large quantity and high quality is in urgent demand to produce a new class of silica nanowire based devices.

With the rapidly increasing demand for high-bright lighting sources, the energy-saving LEDs have attracted more and more attentions for both experiment and commercialization [8

8. A. Mills, “LED 2005 illuminates,” III–Vs Rev. 18(9), 30–35 (2005–2006).

]. It has been well-known that LEDs offer a number of advantages compared to existing light source because of the increased lifetimes, reduced power, small size, higher brightness and better spectral purity [9

9. T. Taguchi, “Japanese semiconductor lighting project based on ultraviolet LED and phosphor system,” Proc. SPIE 4445, 5–12 (2001). [CrossRef]

12

12. A. E. Moe, S. Marx, N. Banani, M. Liu, B. Marquardt, and D. M. Wilson, “Improvements in LED-based fluorescence analysis systems,” Sens. Actuators B Chem. 111–112, 230–241 (2005). [CrossRef]

]. LED performance has improved by a factor of 10 per decade. However, the light extraction efficiency of LEDs is still quite low because of total internal reflection, Fennel reflection and absorption by inherent components [13

13. X. D. Wang, Y. Li, H. Yang, X. Y. Yi, L. C. Wang, G. H. Wang, F. H. Yang, and J. M. Li, “Design and optimization of dielectric optical coatings for GaN based high bright LEDs,” Proc. SPIE 6841, 68410E (2007). [CrossRef]

]. Moreover, the non-uniform illumination of LED light sources still remains an issue in practical applications. Until now, there are many techniques to improve the emitting performance of LEDs, such as chip shaping, surface roughing and high refractive index encapsulant materials [14

14. E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, and I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” Proc. SPIE 4776, 223–234 (2002).

,15

15. D. Fuhrmann, C. Netzel, U. Rossow, A. Hangleiter, G. Ade, and P. Hinze, “Optimization scheme for the quantum efficiency of GaInN-based green-light-emitting diodes,” Appl. Phys. Lett. 88(7), 071105 (2006). [CrossRef]

]. In this article, we introduced the novel idea of using silica nanowires as the optical coatings to the design and fabrication of high-bright LEDs and studied their influence on the lighting performance.

Herein, we have successfully fabricated a large scale of silica nanowires via vapor-liquid-solid (VLS) mechanism with Cu as the catalyst. These grown nanowires formed a brilliant white mat, which demonstrated high diffusive reflectivity at the UV-visible light range. They were applied in this work as diffusive coating material for the reflector cup of LED lamps, and the influence of nanowire coating on emitting intensity and uniformity was further explored.

2. Material and methods

The experimental procedure to synthesize the nanowire was presented in Fig. 1(a)
Fig. 1 (a) Process flow for synthesis of silica nanowires. (b) Schematic of tube-quartz furnace. (c) Temperature and atmosphere control curve.
, which mainly consisted of three steps. The first step was cleaning the Si wafer: the single-crystalline Si wafer [100] with a native oxidation layer (5 nm) was first dipped into acetone under ultrasonic agitation for 10 min to erase the surface contaminations, and then handled with SPM (H2SO4:H2O2 = 2:1) solution. The following metal deposition was conducted with radio frequency magnetron sputtering using a 99.9% copper target. A Cu film with 50 nm thickness would act as catalyst in later nanowire growth. The copper-coated silicon wafer was then loaded to a quartz crucible boat placed in the central region of an alumina tube furnace (GSL-1400X), shown as Fig. 1(b). Before the experiment, the furnace was evacuated to 10−3 Torr and then flushed with N2 (99.999%) several times to eliminate the oxygen and moisture in the chamber. The crucible was heated to 1200 °C at the heating rate of 15 °C/min under a N2 flow of 50 standard cubic centimeters per minute (sccm). When the temperature reached the preset value, the gas flux was switched to mixture gas flow of H2(5%)/N2 at a rate of 100 sccm, and the purity of H2 is 99.999%. Growth was carried out for 2 h at this temperature in the mixed atmosphere, and then the furnace was cooled to room temperature using N2 as the feed gas. The temperature control curve is presented in Fig. 1(c). When the furnace was naturally cooled down to room temperature, ultra-bright white products were observed on the wafer.

The structure and morphology of the products were characterized using a scanning electron microscope (SEM, JEOL JSM-5510LV) operated at 20 keV, high resolution transmission electron microscope (HRTEM, FEI-F20) equipped with energy-dispersive x-ray (EDX) and selected-area electron diffraction (SAED). UV-Vis spectrophotometer (Lambda 35, America PerkinElmer) was conducted to quantitatively characterize the reflectance of SiO2 nanowire mat on silicon wafer. The emitting spectra of displayed LED lamps were characterized with an optical spectrophotometer (Ocean Optics HR2000 +), where their total intensity was measured with an integrated sphere detector, and emitting intensity at different angles was obtained through a 1 mm probe (QR400-7-UV/VIS).

3. Results and discussion

3.1. Morphology and structure of nanowires

Figure 2(a)
Fig. 2 SEM micrographs of the as-grown SiO2 nanowires from (a) plan view, (b) cross-sectional view. (c) TEM image of the obtained nanowires, with the EDX spectrum as an inset; (d) HRTEM electron micrograph of a specific nanowire and the corresponding SAED patterns as an inset.
is the SEM image from plan view of the synthesized nanowires, showing that the nanowires are randomly distributed and dense enough to fully cover the silicon wafer. The cross-sectional view in Fig. 2(b) shows that these nanowires grew to form a disordered thick mat, with the thickness up to hundreds of micrometers. To pursue detailed structural and chemical information on a single nanowire, TEM and HRTEM investigation methods were applied. Figure 2(c) shows a TEM of the obtained nanowires with a diameter distribution ranging from 50 to 180 nm. EDX analyses shown as an inset revealed their chemical composition consisting of Si and O. Figure 2(d) shows a HRTEM image of a specific silica nanowire, indicating that the silica nanowire consists of amorphous phase throughout the whole structure. The corresponding SAED pattern shown as an inset confirms its amorphous structure.

It should be noted that there was no other silicon species introduced into the system, so the silicon wafer was the only silicon sources. At high temperature, the thin Cu layer might be melted and shrink into nano-sized droplets which would act as catalysts for nanowire growth. In the initial stage, the native oxide might react with the silicon substrate to generate SiO vapor, which would partly decompose into SiO2 vapor and Si vapor in return. Meanwhile, the silicon exposed to the environment could react with oxygen to generate more SiO vapor, or diffused into Cu droplets leading to the formation of Cu-Si alloys. The vapor consisting of O and Si would be absorbed by the alloy. When the concentrations of Si and O in the alloy were high enough, they would react to form SiO2 nanoparticle which acted as the nucleation site, and thus to initiate the growth of the SiO2 nanowires. By continuously supplying Si and O into the alloy droplets, the silica nanowires grew through VLS mechanism. Besides the decomposition of the native oxide layer, the oxygen source could also come from the residue oxygen in the reaction chamber, the trace amount of oxygen in feeding gas, and the leakage of our vacuum system. The dominant oxygen source could come from the leakage of our furnace vacuum system for the synthesis of large quantities of silica nanowires [16

16. Z. W. Pan, Z. R. Dai, C. Ma, and Z. L. Wang, “Molten gallium as a catalyst for the large-scale growth of highly aligned silica nanowires,” J. Am. Chem. Soc. 124(8), 1817–1822 (2002). [CrossRef] [PubMed]

].

3.2 Optical property of the nanowire mat

The optical reflection properties of disordered nanowire mats mainly arise from multiple scattering, which could be used as diffuse optical reflectors [17

17. O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. M. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8(9), 2638–2642 (2008). [CrossRef] [PubMed]

,18

18. R. A. Street, W. S. Wong, and C. Paulson, “Analytic model for diffuse reflectivity of silicon nanowire mats,” Nano Lett. 9(10), 3494–3497 (2009). [CrossRef] [PubMed]

]. Thick disorder-distributed nanowire mats have especially high diffuse reflectivity, due to light scattering from many nanowires unlike the ordered nanowires displaying very low reflectivity [19

19. R. A. Street, P. Qi, R. Lujan, and W. S. Wong, “Reflectivity of disordered silicon nanowires,” Appl. Phys. Lett. 93(16), 163109 (2008). [CrossRef]

]. Thus, the synthesized silica nanowire mat with the thickness up to hundreds of micrometers could have a diffusive surface. Visual inspection of the obtained sample shows no specular reflection and no obvious angular anisotropy. UV-Vis spectrophotometer with a 50mm integrated sphere detector was applied to quantitatively characterize the reflectance of silica nanowire mat on silicon wafer. The reflectivity of the sample at wavelength ranging from 350 nm to 800 nm is shown in Fig. 3(a)
Fig. 3 (a) Measured reflectivity of silica nanowire mat on silicon substrate. The inset shows the photographic image of silica nanowire mat on silicon wafer. (b) Chromaticity triangle depicting the coordinates of the SiO2 nanowires.
. At the whole measured range, the reflectivity of silica nanowire mat is maintained above 60% and up to 88% at 350 nm. The fabricated nanowire mat has the property of outstanding optical reflection especially in the UV range, indicating its potential application in UV lighting devices. To evaluate the performance of these nanowires on color luminescent emission, the Commission International Del’Eclairage (CIE) chromaticity coordinates of x and y were obtained for this material, shown in Fig. 3(b). For SiO2 nanowires, the CIE coordinates were found to be x = 0.42, y = 0.4, which lies just near the white point with the white point to be x = 0.35 and y = 0.35.

3.3 The application of silica nanowires in UV LED lamps

The specular reflector cup [shown as an inset in Fig. 4(a)
Fig. 4 (a) Reflectivity of the specular reflector at normal incident angle, with the photographic image of specular reflector cup as an inset. (b) The cross-sectional image of the diffusive reflector cup. (c) The SEM image of nanowire distribution taken from the local coating layer.
] is made from Low-Temperature Co-fired Ceramics coated with Ag, and its specular reflectivity taken at normal incident angle is shown in Fig. 4(a). Silica nanowires were affixed to the reflector cup through spin-coating of nanowire-containing silicone (OE6550, with a weight ratio of A:B = 1:1) onto cup surface. Firstly, the synthesized nanowires on the silicon substrate were collected and treated by the mixed solution of ethanol and silane coupling agent (KH-550) for improved dispersion in silicone; secondly, the nanowires were mixed with silicone with the weight ratio of 1:100 and the mixture was ultrasonic vibrated for 15 min, followed by vacuum-pumping for 10 min; then, the mixture was ready for spin-coating. The coating thickness and uniformity were controlled by the spinning speed. In our experiment, the speed was set to be 1000 rpm for 10 s and followed by 2000 rpm for 30 s. Finally, the coating was baked at 120 °C for 1 h and the diffusive reflector cup was prepared. The cross-sectional image of diffusive reflector cup [Fig. 4(b)] showed that the coating layer was well attached to the cup surface, with uniform thickness of around 50 μm. The corresponding SEM image [Fig. 4(c)] acquired at cross-section outlined by the rectangle in Fig. 4(b), indicated that the nanowires were evenly and disorderly distributed in silicone. Using specular and diffusive reflector cups, GaN-based specular and diffusive UV LED lamps (λ = 380 nm) were respectively fabricated with the following process. GaN chip was first die-bonded to the bottom of reñector cup by silver-containing adhesive and cured at 150 °C for 2 h; then, wire bonding was conducted for the chip followed by encapsulation of the same silicone; finally, an optical lens was attached onto the encapsulant through curing process.

The scheme of a LED lamp is shown as Fig. 5(a)
Fig. 5 (a) Schematic diagram of UV LED package. (b) and (c) are photographic images of LED lamps before and after energized, respectively, with the diffusive one at the left side and specular at the right side. (d) Total emission intensity measured on UV LED lamps employing a specular and a diffusive reflector cup.
. The photographic images of the LED lamps before and after energized are shown, respectively, in Figs. 5(b) and 5(c), with the diffusive one at the left side and specular at the right side. These two kinds of LEDs have almost the same appearance before and after charged. The emission spectra of the diffusive and specular LEDs [Fig. 5(d)] were measured using an optics characterization system with an integrated sphere detector and the integral time was set to be 500 ms. There is no obvious difference between the two measured spectra, where the LED with specular reflector cup is slightly higher in total emitting intensity.

To investigate the effect of silica nanowires on light extracting uniformity, a spectrometer with 1 mm probe was utilized to explore the emitting distribution at different angles. The probe was initially located at the top of lamp, defined as 0°, and then it was rotated by 10°, 20°, 30°. The light intensity distributions of specular and diffusive LED lamps from different angles are shown as Figs. 6(a)
Fig. 6 (a) and (b) are emitting spectra of specular and diffusive LED lamps, respectively, taken from different angles. (c) Measured angular dependence of peak intensity for a specular and a diffusive LED lamp.
and 6(b). The peak intensity of 0 degree in diffusive LED lamp was lower than in specular LED lamp. It was probably due to that the nanowires distributed in silica gel induced strong scattering in diffusive LED lamp, while the specular reflector cup had high reflectivity of 92% at 380 nm from 0 degree as shown in Fig. 4(a). It’s obvious that with the detection angle increasing, the light intensity of specular LED decreases more rapidly. Peak intensities varing with detection angles are plotted and compared in Fig. 6(c), in which the changing tendency can be more easily interpreted. Compared with the specular LED, the diffusive lamp shows a much slower decreasing rate, indicating that the diffusive LED has a more uniform light distribution. This improvement is attributed to SiO2 nanowire coating, which introduce a chaotic diffuse reflection pattern and scatter the emission from LED chip in each direction, and thus distribute the emitted light evenly.

4. Conclusion

In conclusion, we successfully fabricated a large quantity of SiO2 nanowires using a scalable and uncomplicated process. These nanowires formed highly bright-white mat displaying exceptional diffusive reflectance at the UV-visible light range. It has been demonstrated that the obtained nanowires could be an excellent candidate as coating materials over conventional specular reflector cup for a more uniform LED lighting, which may find wide applications in optoelectronic area.

Acknowledgments

This work is financially supported by National Science Foundation of China (No. 90923019, 50875103, 50975114).

References and links

1.

Y. N. Xia, P. D. Yang, Y. G. Sun, Y. Y. Wu, B. Mayers, B. Gates, Y. D. Yin, F. Kim, and H. Q. Yan, “One-dimensional nanostructures: synthesis, characterization, and applications,” Adv. Mater. (Deerfield Beach Fla.) 15(5), 353–389 (2003). [CrossRef]

2.

C. M. Lieber and Z. L. Wang, “Functional nanowires,” MRS Bull. 32(02), 99–108 (2007). [CrossRef]

3.

L. J. Chen, “Silicon nanowires: the key building block for future electronic devices,” J. Mater. Chem. 17(44), 4639–4643 (2007). [CrossRef]

4.

D. R. Kim, C. H. Lee, and X. Zheng, “Probing flow velocity with silicon nanowire sensors,” Nano Lett. 9(5), 1984–1988 (2009). [CrossRef] [PubMed]

5.

Z. W. Pan, Z. R. Dai, L. Xu, S. T. Lee, and Z. L. Wang, “Temperature controlled growth of silicon-based nanostructures by thermal evaporation of SiO powders,” J. Phys. Chem. B 105(13), 2507–2514 (2001). [CrossRef]

6.

R. W. G. Wyckoff, Crystal Structures (Wiley-Interscience, NewYork, 1965).

7.

G. Bilalbegović, “Electronic properties of silica nanowires,” J. Phys. Condens. Matter 18(15), 3829–3836 (2006). [CrossRef]

8.

A. Mills, “LED 2005 illuminates,” III–Vs Rev. 18(9), 30–35 (2005–2006).

9.

T. Taguchi, “Japanese semiconductor lighting project based on ultraviolet LED and phosphor system,” Proc. SPIE 4445, 5–12 (2001). [CrossRef]

10.

R. L. Woods, A. L. Rashed, J. M. Benavides, and R. H. Webb, “A low-power, LED-based, high-brightness anomaloscope,” Vision Res. 46(22), 3775–3781 (2006). [CrossRef] [PubMed]

11.

H. Iwanaga, A. Amano, F. Aiga, K. Harada, and M. Oguchi, “Development of ultraviolet LED devices containing europium (III) complexes in fluorescence layer,” J. Alloy. Comp. 408–412, 921–925 (2006). [CrossRef]

12.

A. E. Moe, S. Marx, N. Banani, M. Liu, B. Marquardt, and D. M. Wilson, “Improvements in LED-based fluorescence analysis systems,” Sens. Actuators B Chem. 111–112, 230–241 (2005). [CrossRef]

13.

X. D. Wang, Y. Li, H. Yang, X. Y. Yi, L. C. Wang, G. H. Wang, F. H. Yang, and J. M. Li, “Design and optimization of dielectric optical coatings for GaN based high bright LEDs,” Proc. SPIE 6841, 68410E (2007). [CrossRef]

14.

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, and I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” Proc. SPIE 4776, 223–234 (2002).

15.

D. Fuhrmann, C. Netzel, U. Rossow, A. Hangleiter, G. Ade, and P. Hinze, “Optimization scheme for the quantum efficiency of GaInN-based green-light-emitting diodes,” Appl. Phys. Lett. 88(7), 071105 (2006). [CrossRef]

16.

Z. W. Pan, Z. R. Dai, C. Ma, and Z. L. Wang, “Molten gallium as a catalyst for the large-scale growth of highly aligned silica nanowires,” J. Am. Chem. Soc. 124(8), 1817–1822 (2002). [CrossRef] [PubMed]

17.

O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. M. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8(9), 2638–2642 (2008). [CrossRef] [PubMed]

18.

R. A. Street, W. S. Wong, and C. Paulson, “Analytic model for diffuse reflectivity of silicon nanowire mats,” Nano Lett. 9(10), 3494–3497 (2009). [CrossRef] [PubMed]

19.

R. A. Street, P. Qi, R. Lujan, and W. S. Wong, “Reflectivity of disordered silicon nanowires,” Appl. Phys. Lett. 93(16), 163109 (2008). [CrossRef]

OCIS Codes
(160.4760) Materials : Optical properties
(160.6030) Materials : Silica
(230.3670) Optical devices : Light-emitting diodes
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Optical Devices

History
Original Manuscript: September 26, 2011
Revised Manuscript: November 22, 2011
Manuscript Accepted: November 22, 2011
Published: December 13, 2011

Citation
Shuang Xi, Tielin Shi, Lei Zhang, Dan Liu, Wuxing Lai, and Zirong Tang, "Growth of highly bright-white silica nanowires as diffusive reflection coating in LED lighting," Opt. Express 19, 26507-26514 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26507


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References

  1. Y. N. Xia, P. D. Yang, Y. G. Sun, Y. Y. Wu, B. Mayers, B. Gates, Y. D. Yin, F. Kim, and H. Q. Yan, “One-dimensional nanostructures: synthesis, characterization, and applications,” Adv. Mater. (Deerfield Beach Fla.) 15(5), 353–389 (2003). [CrossRef]
  2. C. M. Lieber and Z. L. Wang, “Functional nanowires,” MRS Bull. 32(02), 99–108 (2007). [CrossRef]
  3. L. J. Chen, “Silicon nanowires: the key building block for future electronic devices,” J. Mater. Chem. 17(44), 4639–4643 (2007). [CrossRef]
  4. D. R. Kim, C. H. Lee, and X. Zheng, “Probing flow velocity with silicon nanowire sensors,” Nano Lett. 9(5), 1984–1988 (2009). [CrossRef] [PubMed]
  5. Z. W. Pan, Z. R. Dai, L. Xu, S. T. Lee, and Z. L. Wang, “Temperature controlled growth of silicon-based nanostructures by thermal evaporation of SiO powders,” J. Phys. Chem. B 105(13), 2507–2514 (2001). [CrossRef]
  6. R. W. G. Wyckoff, Crystal Structures (Wiley-Interscience, NewYork, 1965).
  7. G. Bilalbegović, “Electronic properties of silica nanowires,” J. Phys. Condens. Matter 18(15), 3829–3836 (2006). [CrossRef]
  8. A. Mills, “LED 2005 illuminates,” III–Vs Rev. 18(9), 30–35 (2005–2006).
  9. T. Taguchi, “Japanese semiconductor lighting project based on ultraviolet LED and phosphor system,” Proc. SPIE 4445, 5–12 (2001). [CrossRef]
  10. R. L. Woods, A. L. Rashed, J. M. Benavides, and R. H. Webb, “A low-power, LED-based, high-brightness anomaloscope,” Vision Res. 46(22), 3775–3781 (2006). [CrossRef] [PubMed]
  11. H. Iwanaga, A. Amano, F. Aiga, K. Harada, and M. Oguchi, “Development of ultraviolet LED devices containing europium (III) complexes in fluorescence layer,” J. Alloy. Comp. 408–412, 921–925 (2006). [CrossRef]
  12. A. E. Moe, S. Marx, N. Banani, M. Liu, B. Marquardt, and D. M. Wilson, “Improvements in LED-based fluorescence analysis systems,” Sens. Actuators B Chem. 111–112, 230–241 (2005). [CrossRef]
  13. X. D. Wang, Y. Li, H. Yang, X. Y. Yi, L. C. Wang, G. H. Wang, F. H. Yang, and J. M. Li, “Design and optimization of dielectric optical coatings for GaN based high bright LEDs,” Proc. SPIE 6841, 68410E (2007). [CrossRef]
  14. E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, and I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” Proc. SPIE 4776, 223–234 (2002).
  15. D. Fuhrmann, C. Netzel, U. Rossow, A. Hangleiter, G. Ade, and P. Hinze, “Optimization scheme for the quantum efficiency of GaInN-based green-light-emitting diodes,” Appl. Phys. Lett. 88(7), 071105 (2006). [CrossRef]
  16. Z. W. Pan, Z. R. Dai, C. Ma, and Z. L. Wang, “Molten gallium as a catalyst for the large-scale growth of highly aligned silica nanowires,” J. Am. Chem. Soc. 124(8), 1817–1822 (2002). [CrossRef] [PubMed]
  17. O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. M. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8(9), 2638–2642 (2008). [CrossRef] [PubMed]
  18. R. A. Street, W. S. Wong, and C. Paulson, “Analytic model for diffuse reflectivity of silicon nanowire mats,” Nano Lett. 9(10), 3494–3497 (2009). [CrossRef] [PubMed]
  19. R. A. Street, P. Qi, R. Lujan, and W. S. Wong, “Reflectivity of disordered silicon nanowires,” Appl. Phys. Lett. 93(16), 163109 (2008). [CrossRef]

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