Abstract

Omnidirectional and broadband light harvesting is critical to photovoltaics due to the sun’s movement and its wide spectral range of radiation. In this work, we demonstrate distinctive indium-tin-oxide nanowhiskers that achieve superior angular and spectral characteristics for crystalline silicon solar cells using angle-resolved reflectance spectroscopy. The solar-spectrum weighted reflectance is well below 6% for incident angles of up to 70° and for the wavelength range between 400nm and 1000nm. As a result, the nanowhisker coated solar cell exhibits broadband quantum efficiency characteristics and enhanced short-circuit currents for large angles of incidence.

© 2011 OSA

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    [CrossRef]

2010 (2)

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

M. Y. Chiu, C. H. Chang, M. A. Tsai, F. Y. Chang, and P. Yu, “Improved optical transmission and current matching of a triple-junction solar cell utilizing sub-wavelength structures,” Opt. Express 18(S3Suppl 3), A308–A313 (2010).
[CrossRef] [PubMed]

2009 (3)

C. H. Chiu, P. Yu, C. H. Chang, C. S. Yang, M. H. Hsu, H. C. Kuo, and M. A. Tsai, “Oblique electron-beam evaporation of distinctive indium-tin-oxide nanorods for enhanced light extraction from InGaN/GaN light emitting diodes,” Opt. Express 17(23), 21250–21256 (2009).
[CrossRef] [PubMed]

C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
[CrossRef]

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

2008 (2)

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93(13), 133108 (2008).
[CrossRef]

2007 (4)

S. Takaki, Y. Aoshima, and R. Satoh, “Growth mechanisms of indium tin oxide whiskers prepared by sputtering,” Jpn. J. Appl. Phys. 46(No. 6A), 3537–3544 (2007).
[CrossRef]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

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, 65450Y-14 (2007).
[CrossRef]

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

2006 (1)

V. M. Aroutiounian, K. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D Appl. Phys. 39(8), 1623–1625 (2006).
[CrossRef]

2005 (1)

J. L. Balenzategui and F. Chenlo, “Measurement and analysis of angular response of bare and encapsulated silicon solar cells,” Sol. Energy Mater. Sol. Cells 86(1), 53–83 (2005).
[CrossRef]

2004 (2)

B. S. Richards, “Comparison of TiO2 and other dielectric coatings for buried contact solar cells: a review,” Prog. Photovolt. Res. Appl. 12(4), 253–281 (2004).
[CrossRef]

Y. Q. Chen, J. Jiang, B. Wang, and J. G. Hou, “Synthesis of tin-doped indium oxide nanowires by self-catalytic VLS growth,” J. Phys. D Appl. Phys. 37(23), 3319–3322 (2004).
[CrossRef]

2002 (1)

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

1999 (3)

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999).
[CrossRef]

1997 (2)

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[CrossRef]

C. Martinet, V. Paillard, A. Gagnaire, and J. Joseph, “Deposition of SiO2 and TiO2 thin films by plasma enhanced chemical vapor deposition for antireflection coating,” J. Non-Cryst. Solids 216, 77–82 (1997).
[CrossRef]

1983 (1)

1982 (1)

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta (Lond.) 29, 993–1009 (1982).
[CrossRef]

1973 (1)

P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature 244(5414), 281–282 (1973).
[CrossRef]

Aoshima, Y.

S. Takaki, Y. Aoshima, and R. Satoh, “Growth mechanisms of indium tin oxide whiskers prepared by sputtering,” Jpn. J. Appl. Phys. 46(No. 6A), 3537–3544 (2007).
[CrossRef]

Arafune, K.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Aroutiounian, V. M.

V. M. Aroutiounian, K. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D Appl. Phys. 39(8), 1623–1625 (2006).
[CrossRef]

Atwater, H. A.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Bagnall, D. M.

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93(13), 133108 (2008).
[CrossRef]

Balenzategui, J. L.

J. L. Balenzategui and F. Chenlo, “Measurement and analysis of angular response of bare and encapsulated silicon solar cells,” Sol. Energy Mater. Sol. Cells 86(1), 53–83 (2005).
[CrossRef]

Boden, S. A.

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93(13), 133108 (2008).
[CrossRef]

Boettcher, S. W.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Briggs, R. M.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Chang, C. H.

M. Y. Chiu, C. H. Chang, M. A. Tsai, F. Y. Chang, and P. Yu, “Improved optical transmission and current matching of a triple-junction solar cell utilizing sub-wavelength structures,” Opt. Express 18(S3Suppl 3), A308–A313 (2010).
[CrossRef] [PubMed]

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

C. H. Chiu, P. Yu, C. H. Chang, C. S. Yang, M. H. Hsu, H. C. Kuo, and M. A. Tsai, “Oblique electron-beam evaporation of distinctive indium-tin-oxide nanorods for enhanced light extraction from InGaN/GaN light emitting diodes,” Opt. Express 17(23), 21250–21256 (2009).
[CrossRef] [PubMed]

C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
[CrossRef]

Chang, F. Y.

Chang, Y. C.

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

Chang, Y. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Chattopadhyay, S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Chen, K. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Chen, L. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Chen, Y. Q.

Y. Q. Chen, J. Jiang, B. Wang, and J. G. Hou, “Synthesis of tin-doped indium oxide nanowires by self-catalytic VLS growth,” J. Phys. D Appl. Phys. 37(23), 3319–3322 (2004).
[CrossRef]

Chenlo, F.

J. L. Balenzategui and F. Chenlo, “Measurement and analysis of angular response of bare and encapsulated silicon solar cells,” Sol. Energy Mater. Sol. Cells 86(1), 53–83 (2005).
[CrossRef]

Chiu, C. H.

C. H. Chiu, P. Yu, C. H. Chang, C. S. Yang, M. H. Hsu, H. C. Kuo, and M. A. Tsai, “Oblique electron-beam evaporation of distinctive indium-tin-oxide nanorods for enhanced light extraction from InGaN/GaN light emitting diodes,” Opt. Express 17(23), 21250–21256 (2009).
[CrossRef] [PubMed]

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

Chiu, M. Y.

Clapham, P. B.

P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature 244(5414), 281–282 (1973).
[CrossRef]

Fujii, H.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Gagnaire, A.

C. Martinet, V. Paillard, A. Gagnaire, and J. Joseph, “Deposition of SiO2 and TiO2 thin films by plasma enhanced chemical vapor deposition for antireflection coating,” J. Non-Cryst. Solids 216, 77–82 (1997).
[CrossRef]

Gotoh, Y.

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

Hobbs, D. S.

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, 65450Y-14 (2007).
[CrossRef]

Hou, J. G.

Y. Q. Chen, J. Jiang, B. Wang, and J. G. Hou, “Synthesis of tin-doped indium oxide nanowires by self-catalytic VLS growth,” J. Phys. D Appl. Phys. 37(23), 3319–3322 (2004).
[CrossRef]

Hsu, C. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Hsu, J. W. P.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Hsu, M. H.

Hsu, S. H.

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

Hsu, Y. K.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Huang, Y. F.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Hutley, M. C.

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta (Lond.) 29, 993–1009 (1982).
[CrossRef]

P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature 244(5414), 281–282 (1973).
[CrossRef]

Jen, Y. J.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Jiang, J.

Y. Q. Chen, J. Jiang, B. Wang, and J. G. Hou, “Synthesis of tin-doped indium oxide nanowires by self-catalytic VLS growth,” J. Phys. D Appl. Phys. 37(23), 3319–3322 (2004).
[CrossRef]

Joseph, J.

C. Martinet, V. Paillard, A. Gagnaire, and J. Joseph, “Deposition of SiO2 and TiO2 thin films by plasma enhanced chemical vapor deposition for antireflection coating,” J. Non-Cryst. Solids 216, 77–82 (1997).
[CrossRef]

Kanamori, Y.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Kaneko, T.

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

Kelzenberg, M. D.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Kuo, H. C.

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

C. H. Chiu, P. Yu, C. H. Chang, C. S. Yang, M. H. Hsu, H. C. Kuo, and M. A. Tsai, “Oblique electron-beam evaporation of distinctive indium-tin-oxide nanorods for enhanced light extraction from InGaN/GaN light emitting diodes,” Opt. Express 17(23), 21250–21256 (2009).
[CrossRef] [PubMed]

Lalanne, P.

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[CrossRef]

Lee, C. S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Lee, Y. J.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Lewis, N. S.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Liu, T. A.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Liu, X.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Lo, H. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

MacLeod, B. D.

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, 65450Y-14 (2007).
[CrossRef]

Maddalena, P.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Martinet, C.

C. Martinet, V. Paillard, A. Gagnaire, and J. Joseph, “Deposition of SiO2 and TiO2 thin films by plasma enhanced chemical vapor deposition for antireflection coating,” J. Non-Cryst. Solids 216, 77–82 (1997).
[CrossRef]

Martirosyan, K.

V. M. Aroutiounian, K. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D Appl. Phys. 39(8), 1623–1625 (2006).
[CrossRef]

McKenzie, B. B.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Meng, G. W.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Morris, G. M.

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[CrossRef]

Nishiyama, K.

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

Ohshita, Y.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Paillard, V.

C. Martinet, V. Paillard, A. Gagnaire, and J. Joseph, “Deposition of SiO2 and TiO2 thin films by plasma enhanced chemical vapor deposition for antireflection coating,” J. Non-Cryst. Solids 216, 77–82 (1997).
[CrossRef]

Pan, C. L.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Parretta, A.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Peng, C. Y.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Peng, X. S.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Peters, D. W.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Petykiewicz, J. A.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Putnam, M. C.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Riccobono, J. R.

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, 65450Y-14 (2007).
[CrossRef]

Richards, B. S.

B. S. Richards, “Comparison of TiO2 and other dielectric coatings for buried contact solar cells: a review,” Prog. Photovolt. Res. Appl. 12(4), 253–281 (2004).
[CrossRef]

Ruby, D. S.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Sai, H.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Sako, T.

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

Sarno, A.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Satoh, R.

S. Takaki, Y. Aoshima, and R. Satoh, “Growth mechanisms of indium tin oxide whiskers prepared by sputtering,” Jpn. J. Appl. Phys. 46(No. 6A), 3537–3544 (2007).
[CrossRef]

Soukiassian, P.

V. M. Aroutiounian, K. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D Appl. Phys. 39(8), 1623–1625 (2006).
[CrossRef]

Southwell, W. H.

Spurgeon, J. M.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Srinivasarao, M.

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999).
[CrossRef]

Takaki, S.

S. Takaki, Y. Aoshima, and R. Satoh, “Growth mechanisms of indium tin oxide whiskers prepared by sputtering,” Jpn. J. Appl. Phys. 46(No. 6A), 3537–3544 (2007).
[CrossRef]

Tortora, P.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Tsai, M. A.

Turner-Evans, D. B.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Wang, A.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Wang, B.

Y. Q. Chen, J. Jiang, B. Wang, and J. G. Hou, “Synthesis of tin-doped indium oxide nanowires by self-catalytic VLS growth,” J. Phys. D Appl. Phys. 37(23), 3319–3322 (2004).
[CrossRef]

Wang, X. F.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Wang, Y. W.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Warren, E. L.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Wilson, S. J.

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta (Lond.) 29, 993–1009 (1982).
[CrossRef]

Yakubu, H.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Yamaguchi, M.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Yang, C. S.

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

C. H. Chiu, P. Yu, C. H. Chang, C. S. Yang, M. H. Hsu, H. C. Kuo, and M. A. Tsai, “Oblique electron-beam evaporation of distinctive indium-tin-oxide nanorods for enhanced light extraction from InGaN/GaN light emitting diodes,” Opt. Express 17(23), 21250–21256 (2009).
[CrossRef] [PubMed]

C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
[CrossRef]

Yu, J. C.

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

Yu, P.

M. Y. Chiu, C. H. Chang, M. A. Tsai, F. Y. Chang, and P. Yu, “Improved optical transmission and current matching of a triple-junction solar cell utilizing sub-wavelength structures,” Opt. Express 18(S3Suppl 3), A308–A313 (2010).
[CrossRef] [PubMed]

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
[CrossRef]

C. H. Chiu, P. Yu, C. H. Chang, C. S. Yang, M. H. Hsu, H. C. Kuo, and M. A. Tsai, “Oblique electron-beam evaporation of distinctive indium-tin-oxide nanorods for enhanced light extraction from InGaN/GaN light emitting diodes,” Opt. Express 17(23), 21250–21256 (2009).
[CrossRef] [PubMed]

Yugami, H.

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

Yumoto, H.

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

Zhang, J.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Zhang, L. D.

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Zhao, J.

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Adv. Mater. (Deerfield Beach Fla.) (1)

P. Yu, C. H. Chang, C. H. Chiu, C. S. Yang, J. C. Yu, H. C. Kuo, S. H. Hsu, and Y. C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective indium tin oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
[CrossRef]

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93(13), 133108 (2008).
[CrossRef]

Chem. Mater. (1)

X. S. Peng, G. W. Meng, X. F. Wang, Y. W. Wang, J. Zhang, X. Liu, and L. D. Zhang, “Synthesis of oxygen-deficient indium-tin-oxide (ITO) nanofibers,” Chem. Mater. 14(11), 4490–4493 (2002).
[CrossRef]

Chem. Rev. (1)

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999).
[CrossRef]

J. Cryst. Growth (1)

H. Yumoto, T. Sako, Y. Gotoh, K. Nishiyama, and T. Kaneko, “Growth mechanism of vapor-liquid-solid (VLS) grown indium tin oxide (ITO) whiskers along the substrate,” J. Cryst. Growth 203(1-2), 136–140 (1999).
[CrossRef]

J. Non-Cryst. Solids (1)

C. Martinet, V. Paillard, A. Gagnaire, and J. Joseph, “Deposition of SiO2 and TiO2 thin films by plasma enhanced chemical vapor deposition for antireflection coating,” J. Non-Cryst. Solids 216, 77–82 (1997).
[CrossRef]

J. Phys. D Appl. Phys. (2)

V. M. Aroutiounian, K. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D Appl. Phys. 39(8), 1623–1625 (2006).
[CrossRef]

Y. Q. Chen, J. Jiang, B. Wang, and J. G. Hou, “Synthesis of tin-doped indium oxide nanowires by self-catalytic VLS growth,” J. Phys. D Appl. Phys. 37(23), 3319–3322 (2004).
[CrossRef]

Jpn. J. Appl. Phys. (2)

H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. 46(No. 6A), 3333–3336 (2007).
[CrossRef]

S. Takaki, Y. Aoshima, and R. Satoh, “Growth mechanisms of indium tin oxide whiskers prepared by sputtering,” Jpn. J. Appl. Phys. 46(No. 6A), 3537–3544 (2007).
[CrossRef]

Nano Lett. (1)

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Nanotechnology (1)

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[CrossRef]

Nat. Mater. (1)

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef]

Nature (1)

P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature 244(5414), 281–282 (1973).
[CrossRef]

Opt. Acta (Lond.) (1)

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta (Lond.) 29, 993–1009 (1982).
[CrossRef]

Opt. Commun. (1)

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172(1-6), 139–151 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

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, 65450Y-14 (2007).
[CrossRef]

Prog. Photovolt. Res. Appl. (1)

B. S. Richards, “Comparison of TiO2 and other dielectric coatings for buried contact solar cells: a review,” Prog. Photovolt. Res. Appl. 12(4), 253–281 (2004).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

J. L. Balenzategui and F. Chenlo, “Measurement and analysis of angular response of bare and encapsulated silicon solar cells,” Sol. Energy Mater. Sol. Cells 86(1), 53–83 (2005).
[CrossRef]

Other (1)

ASTMG173–03, Standard tables for reference solar spectral irradiances, (ASTM International, West Conshohocken, Pennsylvania, 2005).

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Figures (5)

Fig. 1
Fig. 1

The schematic formation of ITO nanowhiskers undergoing three steps: nucleation, column growth, and branch development. The growth mechanism is possibly dominated by a self-catalytic vapor-liquid-solid mechanism in an oxygen-deficient ambience.

Fig. 2
Fig. 2

Scanning electron micrographs (SEM) for ITO nanowhiskers deposited on micro-grooved silicon solar cells. (a) The initial step shows nanorod structure. (b) The optimized ITO nanowhisker structure. (c) The 45° tilted and (d) cross-sectional views of the optimized ITO nanowhiskers on microgrooves.

Fig. 3
Fig. 3

(a) The current density-voltage curves of the solar cell with ITO nanowhiskers (the whisker cell) and the reference cell. (b) The external quantum efficiency (EQE) and reflectance (R) spectra at the normal incident angle for both whisker and reference cells.

Fig. 4
Fig. 4

Angle-resolved reflectance spectra for (a) reference cell and (b) ITO nanowhisker cell in the wavelength range of 400nm to 1000nm at the incident angle of 0 to 80 degree.

Fig. 5
Fig. 5

(a)The weighted reflectance <R> of both cells, calculated by the AM1.5g solar spectrum intensity and the measured angular reflectance spectra shown in Fig. 4. (b) The angular photocurrent characterization of the nanowhisker cell (red) and the reference cell (blue). The green triangle shows the corresponding enhancement factor at different incident angles, where the dashed curve represents an eye guide.

Equations (1)

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< R ( θ ) > = 400 n m 1000 n m R ( θ , λ ) I A M 1.5 g ( λ ) d λ 400 n m 1000 n m I A M 1.5 g ( λ ) d λ ,

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