Abstract

Quasi-ordered moth-eye arrays were fabricated in Si using a colloidal lithography method to achieve highly efficient, omni-directional transmission of mid and far infrared (IR) radiation. The effect of structure height and aspect ratio on transmittance and scattering was explored experimentally and modeled quantitatively using effective medium theory. The highest aspect ratio structures (AR = 9.4) achieved peak transmittance of 98%, with >85% transmission for λ = 7-30 μm. A detailed photon balance was constructed by measuring transmission, forward scattering, specular reflection and diffuse reflection to quantify optical losses due to near-field effects. In addition, angle-dependent transmission measurements showed that moth-eye structures provide superior anti-reflective properties compared to unstructured interfaces over a wide angular range (0-60° incidence). The colloidal lithography method presented here is scalable and substrate-independent, providing a general approach to realize moth-eye structures and anti-reflection in many IR-compatible material systems.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2014

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

F. L. Gonzalez, D. E. Morse, M. J. Gordon, “Importance of diffuse scattering phenomena in moth-eye arrays for broadband infrared applications,” Opt. Lett. 39(1), 13–16 (2014).
[CrossRef] [PubMed]

2013

Y. F. Huang, S. Chattopadhyay, “Nanostructure surface design for broadband and angle-independent antireflection,” J. Nanophoton. 7(1), 073594 (2013).
[CrossRef]

P. I. Stavroulakis, S. A. Boden, T. Johnson, D. M. Bagnall, “Suppression of backscattered diffraction from sub-wavelength ‘moth-eye’ arrays,” Opt. Express 21(1), 1–11 (2013).
[CrossRef] [PubMed]

2012

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

2011

H. Raut, V. Ganesh, A. Nair, S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energy Environ. Sci. 4(10), 3779–3804 (2011).
[CrossRef]

2010

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

2008

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

2006

2005

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

2002

1992

1986

1954

R. J. Collins, H. Y. Fan, “Infrared lattice absorption bands in germanium, silicon, and diamond,” Phys. Rev. 93(4), 674–678 (1954).
[CrossRef]

Arpin, K. A.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Asano, K.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Baca, A. J.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Bagnall, D. M.

Baier, V.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Boden, S. A.

Bowers, J. E.

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

Braun, P. V.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Chattopadhyay, S.

Y. F. Huang, S. Chattopadhyay, “Nanostructure surface design for broadband and angle-independent antireflection,” J. Nanophoton. 7(1), 073594 (2013).
[CrossRef]

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Chen, K. H.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Chen, L. C.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Collins, R. J.

R. J. Collins, H. Y. Fan, “Infrared lattice absorption bands in germanium, silicon, and diamond,” Phys. Rev. 93(4), 674–678 (1954).
[CrossRef]

Fan, H. Y.

R. J. Collins, H. Y. Fan, “Infrared lattice absorption bands in germanium, silicon, and diamond,” Phys. Rev. 93(4), 674–678 (1954).
[CrossRef]

Fowler, J.

Frey, B.

B. Frey, D. Leviton, T. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Friedman, D. J.

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

Ganesh, V.

H. Raut, V. Ganesh, A. Nair, S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energy Environ. Sci. 4(10), 3779–3804 (2011).
[CrossRef]

Ganguly, A.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Glaser, T.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Gonzalez, F. L.

Gordon, M. J.

Gunning, W. J.

Halpern, M.

Henry, R.

Huang, Y. F.

Y. F. Huang, S. Chattopadhyay, “Nanostructure surface design for broadband and angle-independent antireflection,” J. Nanophoton. 7(1), 073594 (2013).
[CrossRef]

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Ihring, A.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Imada, H.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Jen, Y. J.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Johnson, H. T.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Johnson, T.

Jones, B. F.

B. F. Jones, P. Plassmann, “Digital infrared thermal imaging of human skin,” IEEE Eng. Med. Biol. Mag. 21(6), 41–48 (2002).
[CrossRef] [PubMed]

Kamizuka, T.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Katsidis, C. C.

Lau, J.

Leong, J.

Leviton, D.

B. Frey, D. Leviton, T. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Lewis, J. A.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Lin, C.

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

Lin, F.

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Liu, Z.

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Madison, T.

B. Frey, D. Leviton, T. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Marriage, T.

Marsden, D.

Marsden, G.

McMahon, W. E.

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

Mihi, A.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Miyata, T.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Morgenroth, W.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Morse, D. E.

Motamedi, M. E.

Mu, S.

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Nair, A.

H. Raut, V. Ganesh, A. Nair, S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energy Environ. Sci. 4(10), 3779–3804 (2011).
[CrossRef]

Nakagawa, T.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Nakamura, T.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Nash, D. B.

Okada, K.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Onaka, T.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Page, L.

Perl, E. E.

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

Plassmann, P.

B. F. Jones, P. Plassmann, “Digital infrared thermal imaging of human skin,” IEEE Eng. Med. Biol. Mag. 21(6), 41–48 (2002).
[CrossRef] [PubMed]

Ramakrishna, S.

H. Raut, V. Ganesh, A. Nair, S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energy Environ. Sci. 4(10), 3779–3804 (2011).
[CrossRef]

Raut, H.

H. Raut, V. Ganesh, A. Nair, S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energy Environ. Sci. 4(10), 3779–3804 (2011).
[CrossRef]

Rogers, J. A.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Sako, S.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Sakon, I.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Schroter, S.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Seifert, N.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Siapkas, D. I.

Southwell, W. H.

Stavroulakis, P. I.

Uchiyama, M.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Wada, T.

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

Wishnow, E.

Wollack, E.

Xie, G.

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Zhang, G.

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Zhang, J.

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Adv. Mater.

K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, “Multidimensional architectures for functional optical devices,” Adv. Mater. 22(10), 1084–1101 (2010).
[CrossRef] [PubMed]

Appl. Opt.

Energy Environ. Sci.

H. Raut, V. Ganesh, A. Nair, S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energy Environ. Sci. 4(10), 3779–3804 (2011).
[CrossRef]

IEEE Eng. Med. Biol. Mag.

B. F. Jones, P. Plassmann, “Digital infrared thermal imaging of human skin,” IEEE Eng. Med. Biol. Mag. 21(6), 41–48 (2002).
[CrossRef] [PubMed]

IEEE J. Photovolt.

E. E. Perl, C. Lin, W. E. McMahon, D. J. Friedman, J. E. Bowers, “Ultrabroadband and wide-angle hybrid antireflection coatings with nanostructures,” IEEE J. Photovolt. 4(3), 962–967 (2014).

J. Nanophoton.

Y. F. Huang, S. Chattopadhyay, “Nanostructure surface design for broadband and angle-independent antireflection,” J. Nanophoton. 7(1), 073594 (2013).
[CrossRef]

Mater. Sci. Eng. Rep.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, L. C. Chen, “Anti-reflective and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Microsyst. Technol.

T. Glaser, A. Ihring, W. Morgenroth, N. Seifert, S. Schroter, V. Baier, “High temperature resistant antireflective moth-eye structures for infrared radiation sensors,” Microsyst. Technol. 11, 86–90 (2005).

Nanotechnology

G. Xie, G. Zhang, F. Lin, J. Zhang, Z. Liu, S. Mu, “The fabrication of subwavelength anti-reflective nanostructures using a bio-template,” Nanotechnology 19(9), 095605 (2008).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev.

R. J. Collins, H. Y. Fan, “Infrared lattice absorption bands in germanium, silicon, and diamond,” Phys. Rev. 93(4), 674–678 (1954).
[CrossRef]

Proc. SPIE

T. Kamizuka, T. Miyata, S. Sako, H. Imada, T. Nakamura, K. Asano, M. Uchiyama, K. Okada, T. Wada, T. Nakagawa, T. Onaka, I. Sakon, “Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy,” Proc. SPIE 8450, 845051 (2012).
[CrossRef]

B. Frey, D. Leviton, T. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Elsevier, 1985).

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Figures (7)

Fig. 1
Fig. 1

SEM images of a moth-eye showing the hexagonally-packed, quasi-ordered sinusoidal protuberances that give the moth eye its anti-reflective behavior.

Fig. 2
Fig. 2

Experimental configuration for transmission, reflection, and diffuse scattering measurements. Configuration 1: direct and angle-dependent transmission, 2: specular reflection at 8° from normal incidence, 3: diffuse reflectance, and 4: forward scattering. S = sample, MCT = HgCdTe detector, DTGS = La-doped deuterated triglycine sulfate detector, FM = flip mirror, PM = parabolic mirror, and AS = aperture stop. Schematic is not to scale.

Fig. 3
Fig. 3

(a) Relative transmission spectra of Si moth-eye arrays with different feature heights (h = 0.5 μm (purple), 1.5 μm (green) and 3.0 μm (red)), calculated with the effective medium approximation (EMA). The transmission increase in the mid- and far-IR is strongly dependent on the feature height. (b) Relative transmission spectra measured for Si moth-eye arrays fabricated with feature heights of 0.8 μm (purple, aspect ratio AR = 2.8), 1.7 μm (green, AR = 5.2) and 3.0 μm (red, AR = 9.4). The increase in transmission in the mid-IR qualitatively follows the trend predicted by the EMA. (insets) SEM images of the moth-eye arrays. Note: the black curve (Si*) in each panel is for an unstructured Si wafer surface, and data are normalized by the theoretical single-side transmission limit of 70%.

Fig. 4
Fig. 4

SEM image of aspect ratio 9.4 moth-eye structure in Si fabricated with a 320 nm mask. Feature height is approximately 3μm. Sidewall scalloping at the bases of the features is due to the Bosch etch process.

Fig. 5
Fig. 5

(a) As-measured transmission (ME, red), diffuse reflectance (DR, purple), forward scattering (FS, green), and photon balance (PB, orange) for the high aspect ratio (AR = 9.4) Si moth-eye structures shown in Fig. 3. Calculated transmission of the Si moth-eye structure (EMA, blue) and a bare Si wafer (Si*, black) are also shown. The EMA quantitatively predicts ME transmittance when the infinite wavelength limit is valid (λ>10 μm). (b) As-measured specular reflectance (ME, red) and calculated reflectance (EMA, blue) of the ME structure. The single-side perfect anti-reflective coating (SS limit, teal) and bare Si wafer (Si*, black) are also shown. The extremely low specular reflectance of the ME is due to DR and FS scattering losses rather than inherent anti-reflectivity due to a graded index profile.

Fig. 6
Fig. 6

Relative transmission of high aspect ratio ME structures (red) and a commercial, interference-based anti-reflective coating on Si (C-AR, green) for 3-5μm. Calculated (Si*, black) and measured (Si, cyan) spectra for a bare Si wafer is also shown. The commercial ARC achieves a peak transmission of ~95%, while the ME structure has a peak transmission of ~98%. (inset) Cross-sectional SEM image of the moth-eye array.

Fig. 7
Fig. 7

(a) Experimental angle-dependent direct transmission of high aspect ratio (AR = 9.4) moth-eye structures on Si at λ = 10 μm (ME, red) compared to a bare Si wafer (Si, black). The calculated single-side anti-reflective limit (SS limit, teal) is also shown. (b) Angle-dependent transmission of the moth-eye sample at different IR wavelengths (8, 10, 14 μm = blue pluses, black triangles and red squares, respectively). The incident angle is measured from the surface normal.

Equations (1)

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f 1 f n S i 2 n e f f 2 n S i 2 + 2 n e f f 2 = n e f f 2 1 2 n e f f 2 + 1 ,

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