Abstract

Two randomly rough surfaces are fabricated on a crystalline silicon substrate, exhibiting autocorrelation functions (ACFs) distinct from those of other rough surfaces. Such ACFs make surfaces named Bessel’s rough surfaces due to the fitting functions. Scattering patterns and reflectance from these surfaces are demonstrated both numerically and experimentally for 405-nm-wavelength light at an oblique angle of incidence. Patterns are dissimilar to those of a planar surface and other commonly-seen rough surfaces. Moreover, the reduced reflectance from Bessel’s rough surfaces offers a cost-effective way of absorbing solar energy.

© 2015 Optical Society of America

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References

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2014 (2)

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Y.-B. Chen, I.-C. Ho, F.-C. Chiu, and C.-S. Chang, “In-plane scattering patterns from a complex dielectric grating at the normal and oblique incidence,” J. Opt. Soc. Am. A 31(4), 879–885 (2014).
[Crossref] [PubMed]

2013 (2)

Z. M. Zhang and H. Ye, “Measurements of radiative properties of engineered micro-/nanostructures,” Annu. Rev. Heat Transfer 16(1), 345–396 (2013).
[Crossref]

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

2012 (3)

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering Gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37(23), 4868–4870 (2012).
[Crossref] [PubMed]

Y. M. Xuan, Y. G. Han, and Y. Zhou, “Spectral radiative properties of two-dimensional rough surfaces,” Int. J. Thermophys. 33(12), 2291–2310 (2012).
[Crossref]

2008 (1)

2007 (2)

2006 (3)

S. Koynov, M. S. Brandt, and M. Stutzmann, “Black nonreflecting silicon surfaces for solar cells,” Appl. Phys. Lett. 88(20), 203107 (2006).
[Crossref]

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

H. J. Lee, Y. B. Chen, and Z. M. Zhang, “Directional radiative properties of anisotropic rough silicon and gold surfaces,” Int. J. Heat Mass Transfer 49(23-24), 4482–4495 (2006).
[Crossref]

2005 (2)

C. Galiński and R. Zbikowski, “Insect-like flapping wing mechanism based on a double spherical Scotch yoke,” J. R. Soc. Interface 2(3), 223–235 (2005).
[Crossref] [PubMed]

H. J. Lee, B. J. Lee, and Z. M. Zhang, “Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings,” J. Quant. Spectrosc. Radiat. Transf. 93(1-3), 185–194 (2005).
[Crossref]

2004 (1)

Q. Z. Zhu and Z. M. Zhang, “Anisotropic slope distribution and bidirectional reflectance of a rough silicon surface,” J. Heat Transfer 126(6), 985–993 (2004).
[Crossref]

2003 (2)

W. G. Sawyer, K. I. Diaz, M. A. Hamilton, and B. Micklos, “Evaluation of a model for the evolution of wear in a scotch-yoke mechanism,” J. Tribol. - T. ASME 125(3), 678–681 (2003).
[Crossref]

C. G. Granqvist, “Solar energy materials,” Adv. Mater. 15(21), 1789–1803 (2003).
[Crossref]

2001 (1)

Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, “Bidirectional reflectance distribution function of rough silicon wafers,” Int. J. Thermophys. 22(4), 1311–1326 (2001).
[Crossref]

2000 (2)

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

A. G. Aberle, “Surface passivation of crystalline silicon solar cells: a review,” Prog. Photovolt. Res. Appl. 8(5), 473–487 (2000).
[Crossref]

1999 (1)

S. Strehlke, S. Bastide, and C. Levy-Clement, “Optimization of porous silicon reflectance for silicon photovoltaic cells,” Sol. Energy Mater. Sol. Cells 58(4), 399–409 (1999).
[Crossref]

1997 (1)

M. Imaizumi, T. Ito, M. Yamaguchi, and K. Kaneko, “Effect of grain size and dislocation density on the performance of thin film polycrystalline silicon solar cells,” J. Appl. Phys. 81(11), 7635–7640 (1997).
[Crossref]

1992 (1)

G. Willeke, H. Nussbaumer, H. Bender, and E. Bucher, “A simple and effective light trapping technique for polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26(4), 345–356 (1992).
[Crossref]

1984 (1)

E. S. Barr, “The Roberval balance,” Phys. Teach. 22(2), 121 (1984).
[Crossref]

1979 (2)

T. Huen, “Reflectance of thinly oxidized silicon at normal incidence,” Appl. Opt. 18(12), 1927–1932 (1979).
[Crossref] [PubMed]

J. I. Gittleman, E. K. Sichel, H. W. Lehmann, and R. Widmer, “Textured silicon: a selective absorber for solar thermal conversion,” Appl. Phys. Lett. 35(10), 742–744 (1979).
[Crossref]

1956 (1)

M. Rosenblatt, “A central limit theorem and a strong mixing condition,” Proc. Natl. Acad. Sci. U.S.A. 42(1), 43–47 (1956).
[Crossref] [PubMed]

Aberle, A. G.

A. G. Aberle, “Surface passivation of crystalline silicon solar cells: a review,” Prog. Photovolt. Res. Appl. 8(5), 473–487 (2000).
[Crossref]

Andreani, L. C.

Barr, E. S.

E. S. Barr, “The Roberval balance,” Phys. Teach. 22(2), 121 (1984).
[Crossref]

Bastide, S.

S. Strehlke, S. Bastide, and C. Levy-Clement, “Optimization of porous silicon reflectance for silicon photovoltaic cells,” Sol. Energy Mater. Sol. Cells 58(4), 399–409 (1999).
[Crossref]

Bender, H.

G. Willeke, H. Nussbaumer, H. Bender, and E. Bucher, “A simple and effective light trapping technique for polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26(4), 345–356 (1992).
[Crossref]

Bermel, P.

Brandt, M. S.

S. Koynov, M. S. Brandt, and M. Stutzmann, “Black nonreflecting silicon surfaces for solar cells,” Appl. Phys. Lett. 88(20), 203107 (2006).
[Crossref]

Bucher, E.

G. Willeke, H. Nussbaumer, H. Bender, and E. Bucher, “A simple and effective light trapping technique for polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26(4), 345–356 (1992).
[Crossref]

Carius, R.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Catchpole, K. R.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[Crossref]

Chanda, D.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Chang, C.-S.

Chen, Y. B.

H. J. Lee, Y. B. Chen, and Z. M. Zhang, “Directional radiative properties of anisotropic rough silicon and gold surfaces,” Int. J. Heat Mass Transfer 49(23-24), 4482–4495 (2006).
[Crossref]

Chen, Y.-B.

Chiu, F.-C.

Corcoran, C. J.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Cui, Y.

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

DeWitt, D. P.

Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, “Bidirectional reflectance distribution function of rough silicon wafers,” Int. J. Thermophys. 22(4), 1311–1326 (2001).
[Crossref]

Diaz, K. I.

W. G. Sawyer, K. I. Diaz, M. A. Hamilton, and B. Micklos, “Evaluation of a model for the evolution of wear in a scotch-yoke mechanism,” J. Tribol. - T. ASME 125(3), 678–681 (2003).
[Crossref]

Ding, X. M.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Fan, S.

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Finger, F.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Galinski, C.

C. Galiński and R. Zbikowski, “Insect-like flapping wing mechanism based on a double spherical Scotch yoke,” J. R. Soc. Interface 2(3), 223–235 (2005).
[Crossref] [PubMed]

Galli, M.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Gao, L.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Ge, J.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Gittleman, J. I.

J. I. Gittleman, E. K. Sichel, H. W. Lehmann, and R. Widmer, “Textured silicon: a selective absorber for solar thermal conversion,” Appl. Phys. Lett. 35(10), 742–744 (1979).
[Crossref]

Granqvist, C. G.

C. G. Granqvist, “Solar energy materials,” Adv. Mater. 15(21), 1789–1803 (2003).
[Crossref]

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[Crossref]

Gregorkiewicz, T.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Hamilton, M. A.

W. G. Sawyer, K. I. Diaz, M. A. Hamilton, and B. Micklos, “Evaluation of a model for the evolution of wear in a scotch-yoke mechanism,” J. Tribol. - T. ASME 125(3), 678–681 (2003).
[Crossref]

Han, Y. G.

Y. M. Xuan, Y. G. Han, and Y. Zhou, “Spectral radiative properties of two-dimensional rough surfaces,” Int. J. Thermophys. 33(12), 2291–2310 (2012).
[Crossref]

Hapke, P.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Ho, I.-C.

Hou, X. Y.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Houben, L.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Huen, T.

Imaizumi, M.

M. Imaizumi, T. Ito, M. Yamaguchi, and K. Kaneko, “Effect of grain size and dislocation density on the performance of thin film polycrystalline silicon solar cells,” J. Appl. Phys. 81(11), 7635–7640 (1997).
[Crossref]

Ito, T.

M. Imaizumi, T. Ito, M. Yamaguchi, and K. Kaneko, “Effect of grain size and dislocation density on the performance of thin film polycrystalline silicon solar cells,” J. Appl. Phys. 81(11), 7635–7640 (1997).
[Crossref]

Jiang, N.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Joannopoulos, J. D.

Kaneko, K.

M. Imaizumi, T. Ito, M. Yamaguchi, and K. Kaneko, “Effect of grain size and dislocation density on the performance of thin film polycrystalline silicon solar cells,” J. Appl. Phys. 81(11), 7635–7640 (1997).
[Crossref]

Kim, J. K.

Kim, Y. S.

Kimerling, L. C.

Kluth, O.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Kowalczewski, P.

Koynov, S.

S. Koynov, M. S. Brandt, and M. Stutzmann, “Black nonreflecting silicon surfaces for solar cells,” Appl. Phys. Lett. 88(20), 203107 (2006).
[Crossref]

Krauss, T. F.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Kuo, M. L.

Lambertz, A.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Lee, B. J.

H. J. Lee, B. J. Lee, and Z. M. Zhang, “Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings,” J. Quant. Spectrosc. Radiat. Transf. 93(1-3), 185–194 (2005).
[Crossref]

Lee, H. J.

H. J. Lee, Y. B. Chen, and Z. M. Zhang, “Directional radiative properties of anisotropic rough silicon and gold surfaces,” Int. J. Heat Mass Transfer 49(23-24), 4482–4495 (2006).
[Crossref]

H. J. Lee, B. J. Lee, and Z. M. Zhang, “Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings,” J. Quant. Spectrosc. Radiat. Transf. 93(1-3), 185–194 (2005).
[Crossref]

Lee, Y. R.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Lehmann, H. W.

J. I. Gittleman, E. K. Sichel, H. W. Lehmann, and R. Widmer, “Textured silicon: a selective absorber for solar thermal conversion,” Appl. Phys. Lett. 35(10), 742–744 (1979).
[Crossref]

Levy-Clement, C.

S. Strehlke, S. Bastide, and C. Levy-Clement, “Optimization of porous silicon reflectance for silicon photovoltaic cells,” Sol. Energy Mater. Sol. Cells 58(4), 399–409 (1999).
[Crossref]

Lin, S. Y.

Liscidini, M.

Liu, V.

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Lu, W.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Lu, X.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Luo, C.

Ma, L. L.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Micklos, B.

W. G. Sawyer, K. I. Diaz, M. A. Hamilton, and B. Micklos, “Evaluation of a model for the evolution of wear in a scotch-yoke mechanism,” J. Tribol. - T. ASME 125(3), 678–681 (2003).
[Crossref]

Mont, F. W.

Muck, A.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Nussbaumer, H.

G. Willeke, H. Nussbaumer, H. Bender, and E. Bucher, “A simple and effective light trapping technique for polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26(4), 345–356 (1992).
[Crossref]

Nuzzo, R. G.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Park, J. S.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[Crossref]

Poxson, D. J.

Priolo, F.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Rech, B.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Rogers, J. A.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Rosenblatt, M.

M. Rosenblatt, “A central limit theorem and a strong mixing condition,” Proc. Natl. Acad. Sci. U.S.A. 42(1), 43–47 (1956).
[Crossref] [PubMed]

Sawyer, W. G.

W. G. Sawyer, K. I. Diaz, M. A. Hamilton, and B. Micklos, “Evaluation of a model for the evolution of wear in a scotch-yoke mechanism,” J. Tribol. - T. ASME 125(3), 678–681 (2003).
[Crossref]

Schubert, E. F.

Shao, J.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Shen, Y. J.

Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, “Bidirectional reflectance distribution function of rough silicon wafers,” Int. J. Thermophys. 22(4), 1311–1326 (2001).
[Crossref]

Sichel, E. K.

J. I. Gittleman, E. K. Sichel, H. W. Lehmann, and R. Widmer, “Textured silicon: a selective absorber for solar thermal conversion,” Appl. Phys. Lett. 35(10), 742–744 (1979).
[Crossref]

Strehlke, S.

S. Strehlke, S. Bastide, and C. Levy-Clement, “Optimization of porous silicon reflectance for silicon photovoltaic cells,” Sol. Energy Mater. Sol. Cells 58(4), 399–409 (1999).
[Crossref]

Stutzmann, M.

S. Koynov, M. S. Brandt, and M. Stutzmann, “Black nonreflecting silicon surfaces for solar cells,” Appl. Phys. Lett. 88(20), 203107 (2006).
[Crossref]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[Crossref]

Tsai, B. K.

Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, “Bidirectional reflectance distribution function of rough silicon wafers,” Int. J. Thermophys. 22(4), 1311–1326 (2001).
[Crossref]

Vetterl, O.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Wagner, H.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

Wang, K. X. Z.

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Widmer, R.

J. I. Gittleman, E. K. Sichel, H. W. Lehmann, and R. Widmer, “Textured silicon: a selective absorber for solar thermal conversion,” Appl. Phys. Lett. 35(10), 742–744 (1979).
[Crossref]

Willeke, G.

G. Willeke, H. Nussbaumer, H. Bender, and E. Bucher, “A simple and effective light trapping technique for polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26(4), 345–356 (1992).
[Crossref]

Xuan, Y. M.

Y. M. Xuan, Y. G. Han, and Y. Zhou, “Spectral radiative properties of two-dimensional rough surfaces,” Int. J. Thermophys. 33(12), 2291–2310 (2012).
[Crossref]

Yamaguchi, M.

M. Imaizumi, T. Ito, M. Yamaguchi, and K. Kaneko, “Effect of grain size and dislocation density on the performance of thin film polycrystalline silicon solar cells,” J. Appl. Phys. 81(11), 7635–7640 (1997).
[Crossref]

Ye, H.

Z. M. Zhang and H. Ye, “Measurements of radiative properties of engineered micro-/nanostructures,” Annu. Rev. Heat Transfer 16(1), 345–396 (2013).
[Crossref]

Yu, K. J.

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Yu, Z.

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Zbikowski, R.

C. Galiński and R. Zbikowski, “Insect-like flapping wing mechanism based on a double spherical Scotch yoke,” J. R. Soc. Interface 2(3), 223–235 (2005).
[Crossref] [PubMed]

Zeng, L.

Zhang, Z. M.

Z. M. Zhang and H. Ye, “Measurements of radiative properties of engineered micro-/nanostructures,” Annu. Rev. Heat Transfer 16(1), 345–396 (2013).
[Crossref]

H. J. Lee, Y. B. Chen, and Z. M. Zhang, “Directional radiative properties of anisotropic rough silicon and gold surfaces,” Int. J. Heat Mass Transfer 49(23-24), 4482–4495 (2006).
[Crossref]

H. J. Lee, B. J. Lee, and Z. M. Zhang, “Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings,” J. Quant. Spectrosc. Radiat. Transf. 93(1-3), 185–194 (2005).
[Crossref]

Q. Z. Zhu and Z. M. Zhang, “Anisotropic slope distribution and bidirectional reflectance of a rough silicon surface,” J. Heat Transfer 126(6), 985–993 (2004).
[Crossref]

Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, “Bidirectional reflectance distribution function of rough silicon wafers,” Int. J. Thermophys. 22(4), 1311–1326 (2001).
[Crossref]

Zhou, Y.

Y. M. Xuan, Y. G. Han, and Y. Zhou, “Spectral radiative properties of two-dimensional rough surfaces,” Int. J. Thermophys. 33(12), 2291–2310 (2012).
[Crossref]

Zhou, Y. C.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

Zhu, Q. Z.

Q. Z. Zhu and Z. M. Zhang, “Anisotropic slope distribution and bidirectional reflectance of a rough silicon surface,” J. Heat Transfer 126(6), 985–993 (2004).
[Crossref]

Adv. Energy Mater. (1)

K. J. Yu, L. Gao, J. S. Park, Y. R. Lee, C. J. Corcoran, R. G. Nuzzo, D. Chanda, and J. A. Rogers, “Light trapping in ultrathin monocrystalline silicon solar cells,” Adv. Energy Mater. 3(11), 1401–1406 (2013).
[Crossref]

Adv. Mater. (1)

C. G. Granqvist, “Solar energy materials,” Adv. Mater. 15(21), 1789–1803 (2003).
[Crossref]

Annu. Rev. Heat Transfer (1)

Z. M. Zhang and H. Ye, “Measurements of radiative properties of engineered micro-/nanostructures,” Annu. Rev. Heat Transfer 16(1), 345–396 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

S. Koynov, M. S. Brandt, and M. Stutzmann, “Black nonreflecting silicon surfaces for solar cells,” Appl. Phys. Lett. 88(20), 203107 (2006).
[Crossref]

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, and X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[Crossref]

J. I. Gittleman, E. K. Sichel, H. W. Lehmann, and R. Widmer, “Textured silicon: a selective absorber for solar thermal conversion,” Appl. Phys. Lett. 35(10), 742–744 (1979).
[Crossref]

Int. J. Heat Mass Transfer (1)

H. J. Lee, Y. B. Chen, and Z. M. Zhang, “Directional radiative properties of anisotropic rough silicon and gold surfaces,” Int. J. Heat Mass Transfer 49(23-24), 4482–4495 (2006).
[Crossref]

Int. J. Thermophys. (2)

Y. M. Xuan, Y. G. Han, and Y. Zhou, “Spectral radiative properties of two-dimensional rough surfaces,” Int. J. Thermophys. 33(12), 2291–2310 (2012).
[Crossref]

Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, “Bidirectional reflectance distribution function of rough silicon wafers,” Int. J. Thermophys. 22(4), 1311–1326 (2001).
[Crossref]

J. Appl. Phys. (2)

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[Crossref]

M. Imaizumi, T. Ito, M. Yamaguchi, and K. Kaneko, “Effect of grain size and dislocation density on the performance of thin film polycrystalline silicon solar cells,” J. Appl. Phys. 81(11), 7635–7640 (1997).
[Crossref]

J. Heat Transfer (1)

Q. Z. Zhu and Z. M. Zhang, “Anisotropic slope distribution and bidirectional reflectance of a rough silicon surface,” J. Heat Transfer 126(6), 985–993 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transf. (1)

H. J. Lee, B. J. Lee, and Z. M. Zhang, “Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings,” J. Quant. Spectrosc. Radiat. Transf. 93(1-3), 185–194 (2005).
[Crossref]

J. R. Soc. Interface (1)

C. Galiński and R. Zbikowski, “Insect-like flapping wing mechanism based on a double spherical Scotch yoke,” J. R. Soc. Interface 2(3), 223–235 (2005).
[Crossref] [PubMed]

J. Tribol. - T. ASME (1)

W. G. Sawyer, K. I. Diaz, M. A. Hamilton, and B. Micklos, “Evaluation of a model for the evolution of wear in a scotch-yoke mechanism,” J. Tribol. - T. ASME 125(3), 678–681 (2003).
[Crossref]

Nano Lett. (1)

K. X. Z. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

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Phys. Teach. (1)

E. S. Barr, “The Roberval balance,” Phys. Teach. 22(2), 121 (1984).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. Rosenblatt, “A central limit theorem and a strong mixing condition,” Proc. Natl. Acad. Sci. U.S.A. 42(1), 43–47 (1956).
[Crossref] [PubMed]

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A. G. Aberle, “Surface passivation of crystalline silicon solar cells: a review,” Prog. Photovolt. Res. Appl. 8(5), 473–487 (2000).
[Crossref]

Sol. Energy Mater. Sol. Cells (3)

S. Strehlke, S. Bastide, and C. Levy-Clement, “Optimization of porous silicon reflectance for silicon photovoltaic cells,” Sol. Energy Mater. Sol. Cells 58(4), 399–409 (1999).
[Crossref]

G. Willeke, H. Nussbaumer, H. Bender, and E. Bucher, “A simple and effective light trapping technique for polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26(4), 345–356 (1992).
[Crossref]

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, and H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1-2), 97–108 (2000).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 The randomly rough surface maker and its two main components, Scotch yoke and Roberval balance. Arrowheads in the full view mark moving directions of components. A sample is placed on the upper platform of Roberval balance as specified with a square.
Fig. 2
Fig. 2 The average height along y-direction ( h y ¯ ) for three 10 μm × 10 μm scanned areas of: (a) Sample A; (b) Sample B. The inset in each sub-figure shows the original contour measured.
Fig. 3
Fig. 3 (a) The CDF of Sample A and the ideal CDF obtained with σ x ¯ , y ¯ = 58 nm. (b) The CDF of Sample B and the ideal CDF obtained with σ x ¯ , y ¯ = 35 nm.
Fig. 4
Fig. 4 (a) The ACF of Sample A, a Gauss surface, an Exponent surface, and numerically generated surfaces (Bessel_25 and Bessel_50). All surfaces have the same correlation length ζ x ¯ , y ¯ = 605 nm. (b) The ACF of Sample B, the Gauss surface, the Exponent surface, Bessel_25, and Bessel_50. All surfaces share ζ x ¯ , y ¯ = 566 nm.
Fig. 5
Fig. 5 Calibration results of the TAAS at λ = 405 nm for both TE and TM waves: (a) The reflectance R from a crystalline silicon substrate; (b) The zeroth order reflected diffraction efficiency η0 from a silicon grating.
Fig. 6
Fig. 6 The BRDF*cosθr of samples and that of a Gauss surface and Bessel_50 at the oblique (θi = 15°) incidence of linearly polarized light. Results at TE wave incidence are (a) and (b), while those at TM wave incidence are (c) and (d). σ x ¯ , y ¯ = 58 nm and ζ x ¯ , y ¯ = 605 nm are shared in (a) and (c); while σ x ¯ , y ¯ = 35 nm and ζ x ¯ , y ¯ = 566 nm are shared in (b) and (d).
Fig. 7
Fig. 7 The BRDF*cosθr of samples and that of a Gauss surface and Bessel_50 at the oblique (θi = 30°) incidence of linearly polarized light.
Fig. 8
Fig. 8 The BRDF*cosθr of samples and that of a Gauss surface and Bessel_50 at the oblique (θi = 60°) incidence of linearly polarized light.

Tables (2)

Tables Icon

Table 1 The hemispherical R from a generated Bessel’s rough surfaces (Bessel_50), a Gauss surface, a planar surface, and Sample A. The σ x ¯ , y ¯ = 58 nm and ζ x ¯ , y ¯ = 605 nm are shared by Bessel_50, the Gauss surface, and Sample A.

Tables Icon

Table 2 The hemispherical R from a generated Bessel’s rough surface, a Gauss surface, and Sample B. They all have σ x ¯ , y ¯ = 35 nm and ζ x ¯ , y ¯ = 566 nm.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

CDF ( h ) = 1 σ x ¯ 2 π h exp [ 1 2 ( s h x ¯ σ x ¯ ) 2 ] d s
f ( h ) = 1 σ x ¯ 2 π exp [ 1 2 ( h h x ¯ σ x ¯ ) 2 ]
ρ ( x 1 , x 2 ) = C ( x 1 , x 2 ) σ ( x 1 ) σ ( x 2 )
ρ G ( τ ) = exp [ ( τ ) 2 ]
ρ E ( τ ) = exp [ | τ | ]
ρ B ( τ )= j=1 c j J 0 ( α j τ R G )
c j = 0 R G τ ρ S ( τ ) J 0 ( α j τ R G )dτ R G 2 2 J 1 2 ( α j )
BRDF= d I r I i cos θ i d Ω i

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