Abstract

Depolarization of sub-μm-high Si nano-pillar/nano-rod surface reflectance with morphologically controlled anti-reflection spectrum is demonstrated. Extremely small reflectance dip of 1.5% at 400-450 nm for Si nano-pillars is extraordinary when comparing with Si nano-rods, in which the reflectance vs. L/λ for Si nano-pillars coincides well with the graded-index multilayer based modeling spectrum. Alternatively, Si nano-rods preserve its flattened reflectance spectrum up to 1700 nm, whereas the Si nano-pillar surface reflectance monotonically increases to approach that of bulk Si. The destructive interference is only induced on Si nano-pillar surface with larger aspect-ratio ≥15 and small sidewall slope <7 to suppress surface reflectance at blue-green wavelength region. Anomalous depolarization observed from disordered Si nano-pillar/nano-rod surface reflection indicates that TM-mode incidence interacts with more bound electrons than TE-mode to preserve its effective dielectric permittivity less deviated from the bulk Si. The degraded depolarization ratio observed under TE-mode incidence which correlates well with a simplified bounded-electron resonance model is elucidated.

© 2009 OSA

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    [CrossRef] [PubMed]
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2009 (1)

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

2008 (3)

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

H. J. Xu and X. J. Li, “Silicon nanoporous pillar array: a silicon hierarchical structure with high light absorption and triple-band photoluminescence,” Opt. Express 16(5), 2933–2941 (2008).
[CrossRef] [PubMed]

2007 (2)

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

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(18), 181923 (2007).
[CrossRef]

2005 (1)

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

2004 (1)

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

2003 (1)

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

2000 (1)

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

1998 (1)

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 (1998).
[CrossRef]

1980 (1)

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

1975 (1)

1972 (1)

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

Acet, M.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Agnello, S.

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

Bello, I.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Blanchard, A. J.

Boizot, B.

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

Carl, A.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Chang, Y. C.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[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(18), 181923 (2007).
[CrossRef]

Chen, C. F.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, K. H.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, L. C.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, Z. H.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Cheng, H. M.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Cong, H. T.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Dalton, W. A. J.

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

Das, D.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Elam, J. W.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Hadobas, K.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Hilfiker, J. N.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Hsu, C. H.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Hsu, S. H.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Hupp, J. T.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Hwang, J. S.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Kim, T. J.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Kim, Y. D.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Kirsch, S.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Kuo, H. C.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[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(18), 181923 (2007).
[CrossRef]

Leader, J. C.

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

Lee, C. S.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Lee, S. T.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Li, X. J.

Lin, C. J.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Lin, G.-R.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[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(18), 181923 (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(18), 181923 (2007).
[CrossRef]

Liu, E. S.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[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(18), 181923 (2007).
[CrossRef]

Lo, H. C.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Lowdermilk, W. H.

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

Martinson, A. B. F.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Meng, F. S.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

Milam, D.

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

Pai, Y. H.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

Pellin, M. J.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Peng, K. Q.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Rouse, J. W.

Skuja, L.

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 (1998).
[CrossRef]

Song, H. S.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Tang, Y. B.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Tsai, J.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Wassermann, E. F.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Wilhelmi, G. J.

Wu, C. T.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Wu, Y.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Xu, H. J.

Xu, Y.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Yan, Y. J.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Zhang, W. J.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Zhu, J.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

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(18), 181923 (2007).
[CrossRef]

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

J. Appl. Phys. (1)

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Figures (7)

Fig. 1
Fig. 1

The etching processes for preparing (a) Si nano-pillars (b) Si nano-rods.

Fig. 2
Fig. 2

SEM bird-eye-view (upper) and TEM cross-section-view (lower) images of Si nano-pillars (a and c) and Si nano-rods (b and d) with height of 210 nm.

Fig. 3
Fig. 3

Reflectance spectra of Si nano-rods and nano-pillars.

Fig. 4
Fig. 4

Schematic illustration of Si nano-pillars modeling by a multi-layered film with graded changed refractive index profile.

Fig. 5
Fig. 5

The measured and simulated reflectance spectra of Si nano-pillars and nano-rods as a function of L/λ (with L denoting the height).

Fig. 6
Fig. 6

Depolarization effects of Si Nano-pillars (blue) and Nano-rods (red) as compared to Si wafer (black) at TM-mode (a) and TE-mode (b) incidence.

Fig. 7
Fig. 7

Illustrations of the depolarized reflections under purely (a) TM-mode (b) TE-mode polarized incidences.

Equations (7)

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n ( x ) = ( 1 n s ( λ ) n 0 n s ( λ ) x L ) 1 ,
R = | r | 2 = ( 1 + sin 2 y | C | 2 sin 2 ( N + 1 ) y ) 1 ,
Φ = lim N N ϕ = 2 π λ 0 L n ( x ) d x = 2 π n 0 n s ( λ ) L λ ( n s ( λ ) n 0 ) ln n s ( λ ) n 0 .
| C | 1 2 N ln n s ( λ ) n 0 ,
y 1 N [ Φ 2 ( 1 2 ln n s ( λ ) n 0 ) 2 ] 1 / 2 .
R = ( 1 + Φ 2 Δ 2 Δ 2 sin 2 Φ 2 Δ 2 ) 1 with Δ 2 = 1 4 ln 2 n s ( λ ) n 0 .
ε r = 1 + P ε 0 E = 1 + N q 2 m ε 0 j f j ω j 2 ω 2 i γ j ω ,

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