Abstract

Disordered GaN nanopillars of three different heights: 300, 550, and 720 nm are fabricated, and demonstrate broad angular and spectral anti-reflective characteristics, up to an incident angle of 60° and for the wavelength range of λ=300–1800nm. An algorithm based on a rigorous coupled-wave analysis (RCWA) method is developed to investigate the correlations between the reflective characteristics and the structural properties of the nanopillars. The broadband and omnidirectional antireflection arises mainly from the refractive-index gradient provided by nanopillars. Calculations show excellent agreement with the measured reflectivities for both s- and p- polarizations.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  11. Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
    [CrossRef]
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    [CrossRef]
  13. C.-C. Chen, P. Yu, J.-C. Yu, and H.-C. Kuo are preparing a manuscript to be called "Angular and Spectral Reflectivity Calculations of Silicon Nano-Textured Surfaces."

2007 (1)

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

2005 (1)

2004 (2)

A. Xing, M. Davanco, D. J. Blumenthal, and E. L. Hu, "Fabrication of. 2-D photonic crystal membrane structure," J. Vac. Sci. Tech. B 22, 70-73 (2004).
[CrossRef]

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

2003 (2)

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

Y. Kanamori, K.-I. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared wavelengths," Jpn. J. Appl. Phys. 42, 4020-4023 (2003).
[CrossRef]

2002 (2)

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

1999 (1)

1997 (1)

W. Q. Han, S. S. Fan, Q. Q. Li, and Y. D. Hu, "Synthesis of Gallium Nitride nanorods through a carbon nanotube-confined reaction," Science 277, 1287-1289 (1997).
[CrossRef]

1996 (1)

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Blumenthal, D. J.

A. Xing, M. Davanco, D. J. Blumenthal, and E. L. Hu, "Fabrication of. 2-D photonic crystal membrane structure," J. Vac. Sci. Tech. B 22, 70-73 (2004).
[CrossRef]

Chang, Y. C.

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

Chen, C.-C.

C.-C. Chen, P. Yu, J.-C. Yu, and H.-C. Kuo are preparing a manuscript to be called "Angular and Spectral Reflectivity Calculations of Silicon Nano-Textured Surfaces."

Cho, Y. H.

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

Chu, C. F.

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Chu, J. T.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

Chung, K. S.

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

Davanco, M.

A. Xing, M. Davanco, D. J. Blumenthal, and E. L. Hu, "Fabrication of. 2-D photonic crystal membrane structure," J. Vac. Sci. Tech. B 22, 70-73 (2004).
[CrossRef]

Du, Y.

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

Fan, S. S.

W. Q. Han, S. S. Fan, Q. Q. Li, and Y. D. Hu, "Synthesis of Gallium Nitride nanorods through a carbon nanotube-confined reaction," Science 277, 1287-1289 (1997).
[CrossRef]

Han, S.

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

Han, W. Q.

W. Q. Han, S. S. Fan, Q. Q. Li, and Y. D. Hu, "Synthesis of Gallium Nitride nanorods through a carbon nanotube-confined reaction," Science 277, 1287-1289 (1997).
[CrossRef]

Hane, K.

Y. Kanamori, K.-I. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared wavelengths," Jpn. J. Appl. Phys. 42, 4020-4023 (2003).
[CrossRef]

Y. Kanamori, M. Sasaki, and K. Hane, "Broadband antireflection gratings fabricated upon silicon substrates," Opt. Lett. 24, 1422-1424 (1999).
[CrossRef]

Hsueh, T. H.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Hu, E. L.

A. Xing, M. Davanco, D. J. Blumenthal, and E. L. Hu, "Fabrication of. 2-D photonic crystal membrane structure," J. Vac. Sci. Tech. B 22, 70-73 (2004).
[CrossRef]

Hu, Y. D.

W. Q. Han, S. S. Fan, Q. Q. Li, and Y. D. Hu, "Synthesis of Gallium Nitride nanorods through a carbon nanotube-confined reaction," Science 277, 1287-1289 (1997).
[CrossRef]

Huang, H. W.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Iwasa, N.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Jin, W.

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

Kanamori, Y.

Y. Kanamori, K.-I. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared wavelengths," Jpn. J. Appl. Phys. 42, 4020-4023 (2003).
[CrossRef]

Y. Kanamori, M. Sasaki, and K. Hane, "Broadband antireflection gratings fabricated upon silicon substrates," Opt. Lett. 24, 1422-1424 (1999).
[CrossRef]

Kang, T. W.

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

Kao, C. C.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

Kim, D. S.

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

Kim, H. M.

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

Kiyoku, H.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Kobayashi, K.-I.

Y. Kanamori, K.-I. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared wavelengths," Jpn. J. Appl. Phys. 42, 4020-4023 (2003).
[CrossRef]

Kuo, H. C.

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

Levi, A. F. J.

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

Li, Q. Q.

W. Q. Han, S. S. Fan, Q. Q. Li, and Y. D. Hu, "Synthesis of Gallium Nitride nanorods through a carbon nanotube-confined reaction," Science 277, 1287-1289 (1997).
[CrossRef]

Lin, C. F.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Lin, G. R.

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

Lin, H. S.

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

Liu, E. S.

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

Mao, G.

Matsushita, T.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Nagahama, S.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Nakamura, S.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Sasaki, M.

Senoh, M.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Sugimoto, Y.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Tsai, J. Y.

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Wang, J.

Wang, S. C.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Xing, A.

A. Xing, M. Davanco, D. J. Blumenthal, and E. L. Hu, "Fabrication of. 2-D photonic crystal membrane structure," J. Vac. Sci. Tech. B 22, 70-73 (2004).
[CrossRef]

Yamada, T.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Yu, C. C.

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Yu, J.-C.

C.-C. Chen, P. Yu, J.-C. Yu, and H.-C. Kuo are preparing a manuscript to be called "Angular and Spectral Reflectivity Calculations of Silicon Nano-Textured Surfaces."

Yu, P.

C.-C. Chen, P. Yu, J.-C. Yu, and H.-C. Kuo are preparing a manuscript to be called "Angular and Spectral Reflectivity Calculations of Silicon Nano-Textured Surfaces."

Yugami, H.

Y. Kanamori, K.-I. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared wavelengths," Jpn. J. Appl. Phys. 42, 4020-4023 (2003).
[CrossRef]

Zhao, Y.

Zhou, C.

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

Appl. Phys. Lett. (3)

H. M. Kim, D. S. Kim, T. W. Kang, Y. H. Cho, and K. S. Chung, "Growth and characterization of single-crystal GaN nanorods by hydride vapor phase epitaxy," Appl. Phys. Lett. 81, 2193-2195 (2002).
[CrossRef]

Y. Du, S. Han, W. Jin, C. Zhou, and A. F. J. Levi, "Polarization-dependent reflectivity from dielectric nanowires," Appl. Phys. Lett. 83, 996-998 (2003).
[CrossRef]

G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett. 90, 181923-181925 (2007).
[CrossRef]

J. Vac. Sci. Tech. B (1)

A. Xing, M. Davanco, D. J. Blumenthal, and E. L. Hu, "Fabrication of. 2-D photonic crystal membrane structure," J. Vac. Sci. Tech. B 22, 70-73 (2004).
[CrossRef]

Jpn. J. Appl. Phys. (3)

C. C. Yu, C. F. Chu, J. Y. Tsai, H. W. Huang, T. H. Hsueh, C. F. Lin, and S. C. Wang, "Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching," Jpn. J. Appl. Phys. 41, L910 -L912 (2002).
[CrossRef]

Y. Kanamori, K.-I. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared wavelengths," Jpn. J. Appl. Phys. 42, 4020-4023 (2003).
[CrossRef]

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes," Jpn. J. Appl. Phys. 35, L74-L76 (1996).
[CrossRef]

Mater. Sci. Eng. B (1)

H. W. Huang, C. C. Kao, T. H. Hsueh, C. C. Yu, C. F. Lin, J. T. Chu, H. C. Kuo, and S. C. Wang, "Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching," Mater. Sci. Eng. B 113, 125-129 (2004).

Opt. Lett. (2)

Science (1)

W. Q. Han, S. S. Fan, Q. Q. Li, and Y. D. Hu, "Synthesis of Gallium Nitride nanorods through a carbon nanotube-confined reaction," Science 277, 1287-1289 (1997).
[CrossRef]

Other (2)

C.-C. Chen, P. Yu, J.-C. Yu, and H.-C. Kuo are preparing a manuscript to be called "Angular and Spectral Reflectivity Calculations of Silicon Nano-Textured Surfaces."

D. S. Hobbs, B. D. MacLeod, and J. R. Riccobono, "Update on the development of high performance anti-reflecting surface relief micro-structures," Proc. SPIE 6545, 65450Y-1-14 (2007).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a). The schematics of n-GaN nanopillars fabricated using self-assembled Ni nano-masks and ICP-RIE process. Cross-sectional views of the FESEM graphs for fabricated nanopillar structures with heights of (b) 300 nm, (c) 550 nm, and (d) 720 nm.

Fig. 2.
Fig. 2.

Measured reflectivities of GaN nano-pillars with three different heights: h=350nm, 550nm, and 720nm, for (a) s-polarization and (b) p-polarization. The inset shows a schematic of the measurement setup.

Fig. 3.
Fig. 3.

The measured reflectivity ratio of polarizations, Is/Ip for nanopillars of h=300, 550, and 720 nm is plotted as a function the incident angle, while that for bulk GaN is simulated for reference. The reflectivities of nanopillar structures are polarization-insensitive compared to those of bulk.

Fig. 4.
Fig. 4.

The reflectivity spectroscopy for bulk GaN and the nanopillars with a height of 720 nm at an incident angle of 32°.

Fig. 5.
Fig. 5.

(a). The index profile consists of 7×7 random nanopillars with a height of 720 nm. Calculated reflectivities of GaN nanopillars are plotted as a function of the incident angle for three different heights: (b) h=300 nm, (c) h=550 nm, and (d) h=720 nm, for both s- and p-polarizations.

Fig. 6.
Fig. 6.

The reflectivities of nanopillars are calculated as a function of pillar height (a) with a fixed refractive-index gradient, and (b) with fixed fill factors for both s- and p-polarizations at an incident angle of 21°.

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