Abstract

In this work, black silicon (BSi) structures including nanocones and nanowires are modeled using effective medium theory (EMT), where each structure is assumed to be a multilayer structure of varying effective index, and its optical scattering in the infrared range is studied in terms of its total reflectance, transmittance and absorptance using the transfer matrix method (TMM). The different mechanisms of the intrinsic absorption of silicon are taken into account, which translates into proper modeling of its complex refraction index, depending on several parameters including the doping level. The model validity is studied by comparing the results with the rigorous coupled wave analysis and is found to be in good agreement. The effect of the aspect ratio, the spacing between the structure features and the structure disordered nature are all considered. Moreover, the results of the proposed model are compared with reflectance measurements of a fabricated BSi sample, in addition to other measurements reported in the literature for Silicon Nanowires (SiNWs). The TMM along with EMT proves to be a convenient method for modeling BSi due to its simple implementation and computational speed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar cells,” IEEE Trans. Electron Dev. 38(8), 1925–1934 (1991).
    [Crossref]
  2. H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
    [Crossref] [PubMed]
  3. K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
    [Crossref]
  4. Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
    [Crossref]
  5. M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
    [Crossref]
  6. Y. M. Sabry, D. Khalil, T. E. Bourouina, and M. Anwar, “Structured silicon-based thermal emitter,” U.S. patent WO2017011269 A3 (2017).
  7. W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
    [Crossref]
  8. Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
    [Crossref]
  9. E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
    [Crossref] [PubMed]
  10. T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
    [Crossref]
  11. Y. J. Hung, S. L. Lee, K. C. Wu, Y. Tai, and Y. T. Pan, “Antireflective silicon surface with vertical-aligned silicon nanowires realized by simple wet chemical etching processes,” Opt. Express 19(17), 15792–15802 (2011).
    [Crossref] [PubMed]
  12. X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
    [Crossref]
  13. P. G. Maloney, P. Smith, V. King, C. Billman, M. Winkler, and E. Mazur, “Emissivity of microstructured silicon,” Appl. Opt. 49(7), 1065–1068 (2010).
    [Crossref] [PubMed]
  14. M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
    [Crossref]
  15. S. Hava and M. Auslender, “Theoretical dependence of infrared absorption in bulk-doped silicon on carrier concentration,” Appl. Opt. 32(7), 1122–1125 (1993).
    [Crossref] [PubMed]
  16. D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
    [Crossref]
  17. N. M. Ravindra, S. R. Marthi, and S. Sekhri, “Modeling of optical properties of black silicon/crystalline silicon,” Silicon. J. Sci. Ind. Metrol. 1(1), 100001 (2015).
  18. T. Rahman and S. A. Boden, “Optical modeling of black silicon for solar cells using effective index techniques,” IEEE J. Photovolt. 7(6), 1556–1562 (2017).
    [Crossref]
  19. D. Abi Saab, Black Silicon Optical Properties, Growth Mechanisms and Applications (PhD thesis), Université Paris-Est, (2015).
  20. 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. Mater. Sci. 205(4), 876–879 (2008).
    [Crossref]
  21. H. A. Macleod, Thin Film Optical Filters (CRC, 2010), Chap. 2.
  22. H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
    [Crossref]
  23. B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
    [Crossref]
  24. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2006), Chap. 5.
  25. G. E. Jellison and D. H. Lowndes, “Optical absorption coefficient of silicon at 1.152 μ at elevated temperatures,” Appl. Phys. Lett. 41(7), 594–596 (1982).
    [Crossref]
  26. G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
    [Crossref]
  27. J. C. Strum and C. M. Reaves, “Silicon temperature measurement by infrared absorption. Fundamental processes and doping effects,” IEEE Trans. Electron Dev. 39(1), 81–88 (1992).
    [Crossref]
  28. P. Vandenabeele and K. Maex, “Influence of temperature and backside roughness on the emissivity of Si wafers during rapid thermal processing,” J. Appl. Phys. 72(12), 5867–5875 (1992).
    [Crossref]
  29. A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
    [Crossref]
  30. Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
    [Crossref]
  31. K. Lichtenecker, “The dielectric constants of natural and synthetic mixtures,” Phys. Z. 27, 115 (1926).
  32. J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. A 203(359-371), 385–420 (1904).
    [Crossref]
  33. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. Dielektrizitätskonstanten und leitfähigkeiten der mischkörper aus isotropen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
    [Crossref]
  34. R. Zallen, The Physics of Amorphous Solids (John Wiley & Sons, 1983), Chap. 4.
  35. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981).
    [Crossref]
  36. M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Opt. Soc. Am. 12(5), 1068–1076 (1995).
    [Crossref]
  37. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. 13(4), 779–784 (1996).
    [Crossref]
  38. P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
    [Crossref]
  39. Y. A. Cengel, Heat and Mass Transfer: A Practical Approach (McGraw Hill, 2006), Chap. 11.
  40. J. P. Hugonin and P. Lalanne, (2005), Reticolo Software for Grating Analysis, Institut d'Optique, Orsay, France.
  41. V. Myroshnychenko and C. Brosseau, “Finite-element modeling method for the prediction of the complex effective permittivity of two-phase random statistically isotropic heterostructures,” J. Appl. Phys. 97(4), 044101 (2005).
    [Crossref]
  42. M. Khorasaninejad, N. Abedzadeh, J. Sun, J. N. Hilfiker, and S. S. Saini, “Polarization resolved reflection from ordered vertical silicon nanowire arrays,” Opt. Lett. 37(14), 2961–2963 (2012).
    [Crossref] [PubMed]
  43. S. Patchett, M. Khorasaninejad, N. O, and S. S. Saini, “Effective index approximation for ordered silicon nanowire arrays,” J. Opt. Soc. Am. B 30(2), 306–313 (2013).
    [Crossref]
  44. M. Khorasaninejad, S. Patchett, J. Sun, N. O, and S. S. Saini, “Polarization-resolved reflections in ordered and bunched silicon nanowire arrays,” J. Opt. Soc. Am. B 9(11), 3063–3068 (2012).
    [Crossref]

2017 (1)

T. Rahman and S. A. Boden, “Optical modeling of black silicon for solar cells using effective index techniques,” IEEE J. Photovolt. 7(6), 1556–1562 (2017).
[Crossref]

2016 (1)

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

2015 (2)

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

N. M. Ravindra, S. R. Marthi, and S. Sekhri, “Modeling of optical properties of black silicon/crystalline silicon,” Silicon. J. Sci. Ind. Metrol. 1(1), 100001 (2015).

2014 (3)

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

2013 (4)

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

S. Patchett, M. Khorasaninejad, N. O, and S. S. Saini, “Effective index approximation for ordered silicon nanowire arrays,” J. Opt. Soc. Am. B 30(2), 306–313 (2013).
[Crossref]

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

2012 (2)

M. Khorasaninejad, N. Abedzadeh, J. Sun, J. N. Hilfiker, and S. S. Saini, “Polarization resolved reflection from ordered vertical silicon nanowire arrays,” Opt. Lett. 37(14), 2961–2963 (2012).
[Crossref] [PubMed]

M. Khorasaninejad, S. Patchett, J. Sun, N. O, and S. S. Saini, “Polarization-resolved reflections in ordered and bunched silicon nanowire arrays,” J. Opt. Soc. Am. B 9(11), 3063–3068 (2012).
[Crossref]

2011 (2)

Y. J. Hung, S. L. Lee, K. C. Wu, Y. Tai, and Y. T. Pan, “Antireflective silicon surface with vertical-aligned silicon nanowires realized by simple wet chemical etching processes,” Opt. Express 19(17), 15792–15802 (2011).
[Crossref] [PubMed]

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

2010 (1)

2008 (1)

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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

2005 (1)

V. Myroshnychenko and C. Brosseau, “Finite-element modeling method for the prediction of the complex effective permittivity of two-phase random statistically isotropic heterostructures,” J. Appl. Phys. 97(4), 044101 (2005).
[Crossref]

2003 (1)

Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
[Crossref]

1999 (1)

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

1998 (3)

B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
[Crossref]

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

1996 (1)

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. 13(4), 779–784 (1996).
[Crossref]

1995 (1)

M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

1993 (1)

1992 (2)

J. C. Strum and C. M. Reaves, “Silicon temperature measurement by infrared absorption. Fundamental processes and doping effects,” IEEE Trans. Electron Dev. 39(1), 81–88 (1992).
[Crossref]

P. Vandenabeele and K. Maex, “Influence of temperature and backside roughness on the emissivity of Si wafers during rapid thermal processing,” J. Appl. Phys. 72(12), 5867–5875 (1992).
[Crossref]

1991 (1)

J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar cells,” IEEE Trans. Electron Dev. 38(8), 1925–1934 (1991).
[Crossref]

1982 (1)

G. E. Jellison and D. H. Lowndes, “Optical absorption coefficient of silicon at 1.152 μ at elevated temperatures,” Appl. Phys. Lett. 41(7), 594–596 (1982).
[Crossref]

1981 (1)

1980 (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

1958 (1)

G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
[Crossref]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. Dielektrizitätskonstanten und leitfähigkeiten der mischkörper aus isotropen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

1926 (1)

K. Lichtenecker, “The dielectric constants of natural and synthetic mixtures,” Phys. Z. 27, 115 (1926).

1904 (1)

J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. A 203(359-371), 385–420 (1904).
[Crossref]

Abedrabbo, S.

B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
[Crossref]

Abedzadeh, N.

Abi Saab, D.

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

Abramsona, A. R.

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

Alcubilla, R.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Angelescu, D.

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

Anwar, M.

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

Auslender, M.

Basset, P.

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

Baulin, V. A.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Billman, C.

Boden, S. A.

T. Rahman and S. A. Boden, “Optical modeling of black silicon for solar cells using effective index techniques,” IEEE J. Photovolt. 7(6), 1556–1562 (2017).
[Crossref]

Bourouina, T.

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

Brosseau, C.

V. Myroshnychenko and C. Brosseau, “Finite-element modeling method for the prediction of the complex effective permittivity of two-phase random statistically isotropic heterostructures,” J. Appl. Phys. 97(4), 044101 (2005).
[Crossref]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. Dielektrizitätskonstanten und leitfähigkeiten der mischkörper aus isotropen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

Calle, E.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Chang, Y.-C.

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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

Chen, D.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Chen, W.

B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
[Crossref]

Chen, Y.

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

Cole, J. M.

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

Coxon, P. R.

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

Crawford, R. J.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Deliwala, S.

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

Fan, Z.

Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
[Crossref]

Finlay, R. J.

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

Fray, D. J.

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

Garín, M.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Garnett, J. C. M.

J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. A 203(359-371), 385–420 (1904).
[Crossref]

Gartia, M. R.

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

Gaylord, T. K.

Gervinskas, G.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Grann, E. B.

M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

Green, M. A.

J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar cells,” IEEE Trans. Electron Dev. 38(8), 1925–1934 (1991).
[Crossref]

Hasan, J.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Hava, S.

Her, T.

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

Hilfiker, J. N.

M. Khorasaninejad, N. Abedzadeh, J. Sun, J. N. Hilfiker, and S. S. Saini, “Polarization resolved reflection from ordered vertical silicon nanowire arrays,” Opt. Lett. 37(14), 2961–2963 (2012).
[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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

Hoex, B.

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

Hsu, S.-H.

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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

Hung, Y. J.

Ivanova, E. P.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Jellison, G. E.

G. E. Jellison and D. H. Lowndes, “Optical absorption coefficient of silicon at 1.152 μ at elevated temperatures,” Appl. Phys. Lett. 41(7), 594–596 (1982).
[Crossref]

Jiang, J.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

Jiang, Y.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Juodkazis, S.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Jurek, M. P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

Kasebier, T.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Khalil, D.

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

Khorasaninejad, M.

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. Mater. Sci. 205(4), 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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

King, V.

Kley, E.-B.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Lalanne, P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. 13(4), 779–784 (1996).
[Crossref]

Lamb, R. N.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Lee, S. L.

Lehr, D.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Leprince-Wang, Y.

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

Li, F.

Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
[Crossref]

Li, H. H.

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

Li, S.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Lichtenecker, K.

K. Lichtenecker, “The dielectric constants of natural and synthetic mixtures,” Phys. Z. 27, 115 (1926).

Lin, C.-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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

Lin, G.-R.

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. Mater. Sci. 205(4), 876–879 (2008).
[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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

Liu, G. L.

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

Liu, W.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Liu, X.

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

Lowndes, D. H.

G. E. Jellison and D. H. Lowndes, “Optical absorption coefficient of silicon at 1.152 μ at elevated temperatures,” Appl. Phys. Lett. 41(7), 594–596 (1982).
[Crossref]

Macfarlane, G. G.

G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
[Crossref]

Maex, K.

P. Vandenabeele and K. Maex, “Influence of temperature and backside roughness on the emissivity of Si wafers during rapid thermal processing,” J. Appl. Phys. 72(12), 5867–5875 (1992).
[Crossref]

Mainwaring, D. E.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Maloney, P. G.

Marthi, S. R.

N. M. Ravindra, S. R. Marthi, and S. Sekhri, “Modeling of optical properties of black silicon/crystalline silicon,” Silicon. J. Sci. Ind. Metrol. 1(1), 100001 (2015).

Marty, F.

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

Mazur, E.

P. G. Maloney, P. Smith, V. King, C. Billman, M. Winkler, and E. Mazur, “Emissivity of microstructured silicon,” Appl. Opt. 49(7), 1065–1068 (2010).
[Crossref] [PubMed]

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

Mclean, T. P.

G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
[Crossref]

Miaoulis, I. N.

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

Ming, A.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Moharam, M. G.

M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981).
[Crossref]

Morris, G. M.

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. 13(4), 779–784 (1996).
[Crossref]

Mostarshedi, S.

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

Myroshnychenko, V.

V. Myroshnychenko and C. Brosseau, “Finite-element modeling method for the prediction of the complex effective permittivity of two-phase random statistically isotropic heterostructures,” J. Appl. Phys. 97(4), 044101 (2005).
[Crossref]

Nguyen, K. N.

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

Nieva, P.

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

O, N.

S. Patchett, M. Khorasaninejad, N. O, and S. S. Saini, “Effective index approximation for ordered silicon nanowire arrays,” J. Opt. Soc. Am. B 30(2), 306–313 (2013).
[Crossref]

M. Khorasaninejad, S. Patchett, J. Sun, N. O, and S. S. Saini, “Polarization-resolved reflections in ordered and bunched silicon nanowire arrays,” J. Opt. Soc. Am. B 9(11), 3063–3068 (2012).
[Crossref]

Ortega, P.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Ou, W.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Pan, Y. T.

Patchett, S.

S. Patchett, M. Khorasaninejad, N. O, and S. S. Saini, “Effective index approximation for ordered silicon nanowire arrays,” J. Opt. Soc. Am. B 30(2), 306–313 (2013).
[Crossref]

M. Khorasaninejad, S. Patchett, J. Sun, N. O, and S. S. Saini, “Polarization-resolved reflections in ordered and bunched silicon nanowire arrays,” J. Opt. Soc. Am. B 9(11), 3063–3068 (2012).
[Crossref]

Peters, M.

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

Pommet, D. A.

M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

Protat, S.

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

Quarrington, J. E.

G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
[Crossref]

Rahman, T.

T. Rahman and S. A. Boden, “Optical modeling of black silicon for solar cells using effective index techniques,” IEEE J. Photovolt. 7(6), 1556–1562 (2017).
[Crossref]

Ratzsch, S.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Ravindra, N. M.

N. M. Ravindra, S. R. Marthi, and S. Sekhri, “Modeling of optical properties of black silicon/crystalline silicon,” Silicon. J. Sci. Ind. Metrol. 1(1), 100001 (2015).

B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
[Crossref]

Reaves, C. M.

J. C. Strum and C. M. Reaves, “Silicon temperature measurement by infrared absorption. Fundamental processes and doping effects,” IEEE Trans. Electron Dev. 39(1), 81–88 (1992).
[Crossref]

Ren, Y.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Repo, P.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Richalot, E.

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

Roberts, V.

G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
[Crossref]

Sabry, Y.

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

Saini, S. S.

Savin, H.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Schrempel, F.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Sekhri, S.

N. M. Ravindra, S. R. Marthi, and S. Sekhri, “Modeling of optical properties of black silicon/crystalline silicon,” Silicon. J. Sci. Ind. Metrol. 1(1), 100001 (2015).

Smith, P.

Sopori, B. L.

B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
[Crossref]

Steglich, M.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Strum, J. C.

J. C. Strum and C. M. Reaves, “Silicon temperature measurement by infrared absorption. Fundamental processes and doping effects,” IEEE Trans. Electron Dev. 39(1), 81–88 (1992).
[Crossref]

Su, Y.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Sun, J.

M. Khorasaninejad, S. Patchett, J. Sun, N. O, and S. S. Saini, “Polarization-resolved reflections in ordered and bunched silicon nanowire arrays,” J. Opt. Soc. Am. B 9(11), 3063–3068 (2012).
[Crossref]

M. Khorasaninejad, N. Abedzadeh, J. Sun, J. N. Hilfiker, and S. S. Saini, “Polarization resolved reflection from ordered vertical silicon nanowire arrays,” Opt. Lett. 37(14), 2961–2963 (2012).
[Crossref] [PubMed]

Sun, X.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Tada, H.

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

Tai, Y.

Tan, Q.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Truong, V. K.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Tunnermann, A.

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Vandenabeele, P.

P. Vandenabeele and K. Maex, “Influence of temperature and backside roughness on the emissivity of Si wafers during rapid thermal processing,” J. Appl. Phys. 72(12), 5867–5875 (1992).
[Crossref]

von Gastrow, G.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Wang, W.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Watson, G. S.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Watson, J. A.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Webb, H. K.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Winkler, M.

Wong, P. Y.

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

Wu, A. H. F.

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Wu, C.

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

Wu, K. C.

Wu, Y.

Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
[Crossref]

Wu, Z.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Xiao, Z.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Xiong, J.

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

Xu, Z.

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

Yang, Y.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Zavracky, P.

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

Zhang, P.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Zhang, T.

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Zhao, J.

J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar cells,” IEEE Trans. Electron Dev. 38(8), 1925–1934 (1991).
[Crossref]

Zhao, X.

Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
[Crossref]

Ann. Phys. (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. Dielektrizitätskonstanten und leitfähigkeiten der mischkörper aus isotropen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

T. Her, R. J. Finlay, C. Wu, S. Deliwala, and E. Mazur, “Microstructuring of silicon with femtosecond laser pulses,” Appl. Phys. Lett. 73(12), 1673–1675 (1998).
[Crossref]

Z. Xu, Y. Chen, M. R. Gartia, J. Jiang, and G. L. Liu, “Surface plasmon enhanced broadband spectrophotometry on black silver substrates,” Appl. Phys. Lett. 98(24), 241904 (2011).
[Crossref]

G. E. Jellison and D. H. Lowndes, “Optical absorption coefficient of silicon at 1.152 μ at elevated temperatures,” Appl. Phys. Lett. 41(7), 594–596 (1982).
[Crossref]

Energy Environ. Sci. (1)

X. Liu, P. R. Coxon, M. Peters, B. Hoex, J. M. Cole, and D. J. Fray, “Black silicon: fabrication methods properties and solar energy applications,” Energy Environ. Sci. 7(10), 3223–3263 (2014).
[Crossref]

IEEE J. Photovolt. (1)

T. Rahman and S. A. Boden, “Optical modeling of black silicon for solar cells using effective index techniques,” IEEE J. Photovolt. 7(6), 1556–1562 (2017).
[Crossref]

IEEE Trans. Electron Dev. (2)

J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar cells,” IEEE Trans. Electron Dev. 38(8), 1925–1934 (1991).
[Crossref]

J. C. Strum and C. M. Reaves, “Silicon temperature measurement by infrared absorption. Fundamental processes and doping effects,” IEEE Trans. Electron Dev. 39(1), 81–88 (1992).
[Crossref]

J. Appl. Phys. (3)

P. Vandenabeele and K. Maex, “Influence of temperature and backside roughness on the emissivity of Si wafers during rapid thermal processing,” J. Appl. Phys. 72(12), 5867–5875 (1992).
[Crossref]

K. N. Nguyen, P. Basset, F. Marty, Y. Leprince-Wang, and T. Bourouina, “On the optical and morphological properties of microstructured Black Silicon obtained by cryogenic-enhanced plasma reactive ion etching,” J. Appl. Phys. 113(19), 194903 (2013).
[Crossref]

V. Myroshnychenko and C. Brosseau, “Finite-element modeling method for the prediction of the complex effective permittivity of two-phase random statistically isotropic heterostructures,” J. Appl. Phys. 97(4), 044101 (2005).
[Crossref]

J. Electroceram. (1)

Y. Wu, X. Zhao, F. Li, and Z. Fan, “Evaluation of mixing rules for dielectric constants of composite dielectrics by MC-FEM calculation on 3D cubic lattice,” J. Electroceram. 11(3), 227–239 (2003).
[Crossref]

J. Electron. Mater. (1)

B. L. Sopori, W. Chen, S. Abedrabbo, and N. M. Ravindra, “Modeling emissivity of rough and textured silicon wafers,” J. Electron. Mater. 27(12), 1341–1346 (1998).
[Crossref]

J. Mater. Res. (1)

A. R. Abramsona, P. Nieva, H. Tada, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Effect of doping level during rapid thermal processing of multilayer structures,” J. Mater. Res. 14(6), 2402–2410 (1999).
[Crossref]

J. Mod. Opt. (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

J. Opt. Soc. Am. (2)

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. 13(4), 779–784 (1996).
[Crossref]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981).
[Crossref]

J. Opt. Soc. Am. B (2)

S. Patchett, M. Khorasaninejad, N. O, and S. S. Saini, “Effective index approximation for ordered silicon nanowire arrays,” J. Opt. Soc. Am. B 30(2), 306–313 (2013).
[Crossref]

M. Khorasaninejad, S. Patchett, J. Sun, N. O, and S. S. Saini, “Polarization-resolved reflections in ordered and bunched silicon nanowire arrays,” J. Opt. Soc. Am. B 9(11), 3063–3068 (2012).
[Crossref]

J. Phys. Chem. Ref. Data (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

Laser Photonics Rev. (1)

M. Steglich, D. Lehr, S. Ratzsch, T. Kasebier, F. Schrempel, E.-B. Kley, and A. Tunnermann, “An ultra-black silicon absorber,” Laser Photonics Rev. 8(2), L13–L17 (2014).
[Crossref]

Mater. Res. Express (1)

D. Abi Saab, S. Mostarshedi, P. Basset, S. Protat, D. Angelescu, and E. Richalot, “Effect of black silicon disordered structures distribution on its wideband reduced reflectance,” Mater. Res. Express 1(4), 045045 (2014).
[Crossref]

Mater. Sci. Semicond. Process. (1)

Y. Su, S. Li, Z. Wu, Y. Yang, Y. Jiang, J. Jiang, Z. Xiao, P. Zhang, and T. Zhang, “High responsivity MSM black silicon photodetector,” Mater. Sci. Semicond. Process. 16(3), 619–624 (2013).
[Crossref]

Nat. Commun. (1)

E. P. Ivanova, J. Hasan, H. K. Webb, G. Gervinskas, S. Juodkazis, V. K. Truong, A. H. F. Wu, R. N. Lamb, V. A. Baulin, G. S. Watson, J. A. Watson, D. E. Mainwaring, and R. J. Crawford, “Bactericidal activity of black silicon,” Nat. Commun. 4, 2838 (2013).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Opt. Soc. Am. (1)

M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

Phil. Trans. R. Soc. A (1)

J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. A 203(359-371), 385–420 (1904).
[Crossref]

Phys. Rev. (1)

G. G. Macfarlane, T. P. Mclean, J. E. Quarrington, and V. Roberts, “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. 111(5), 1245–1254 (1958).
[Crossref]

Phys. Status Solidi., A Appl. Mater. Sci. (1)

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. Mater. Sci. 205(4), 876–879 (2008).
[Crossref]

Phys. Z. (1)

K. Lichtenecker, “The dielectric constants of natural and synthetic mixtures,” Phys. Z. 27, 115 (1926).

Proc. SPIE (1)

M. Anwar, Y. Sabry, P. Basset, F. Marty, T. Bourouina, and D. Khalil, “Black silicon-based infrared radiation source,” Proc. SPIE 9752, 97520E (2016).
[Crossref]

Silicon. J. Sci. Ind. Metrol. (1)

N. M. Ravindra, S. R. Marthi, and S. Sekhri, “Modeling of optical properties of black silicon/crystalline silicon,” Silicon. J. Sci. Ind. Metrol. 1(1), 100001 (2015).

Other (8)

D. Abi Saab, Black Silicon Optical Properties, Growth Mechanisms and Applications (PhD thesis), Université Paris-Est, (2015).

Y. M. Sabry, D. Khalil, T. E. Bourouina, and M. Anwar, “Structured silicon-based thermal emitter,” U.S. patent WO2017011269 A3 (2017).

W. Liu, A. Ming, Y. Ren, Q. Tan, W. Ou, X. Sun, W. Wang, D. Chen, and J. Xiong, “CMOS MEMS infrared source based on black silicon,” in Proceedings of IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (2016).
[Crossref]

R. Zallen, The Physics of Amorphous Solids (John Wiley & Sons, 1983), Chap. 4.

H. A. Macleod, Thin Film Optical Filters (CRC, 2010), Chap. 2.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2006), Chap. 5.

Y. A. Cengel, Heat and Mass Transfer: A Practical Approach (McGraw Hill, 2006), Chap. 11.

J. P. Hugonin and P. Lalanne, (2005), Reticolo Software for Grating Analysis, Institut d'Optique, Orsay, France.

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Figures (16)

Fig. 1
Fig. 1 Illustrations for different types of microstructured Si (a) BSi fabricated using cryogenic DRIE [3] (b) BSi fabricated using femto-second pulsed laser [13] (c) SiNWs fabricated using chemical etching [11].
Fig. 2
Fig. 2 Refractive index profile for (a) SiNWs (b) Nanocones.
Fig. 3
Fig. 3 An illustration for the assumed surface topography of the simulated BSi structures. The number of stacked layers is in the order of tens to hundreds but a smaller number is demonstrated here for convenience.
Fig. 4
Fig. 4 A multi-layer structure illustrating the TMM.
Fig. 5
Fig. 5 A comparison of the different absorption schemes in silicon at a donor concentration of 1015 cm−3 and temperature of (a) 300 K (b) 600 K.
Fig. 6
Fig. 6 Reflectance of BSi for unpolarized incident light simulated using the proposed TMM model and RCWA method. Two structures are simulated: the first has a maximum cone height of 1 μm, periodicity of 100 nm, base-spacing of 10 nm (labeled Structure 1), while the second has maximum cone height of 1.5 μm, periodicity of 150 nm, base-spacing of 15 nm (labeled Structure 2).
Fig. 7
Fig. 7 The total reflectance for a BSi structure with the base-spacing varied from 0 to 0.1 μm for the wavelengths 2, 4 and 6 μm. The results shown for unpolarized light.
Fig. 8
Fig. 8 The magnitude of the electric field components Ez for a BSi structure with no base-spacing (shown in the left figure) compared to a structure of 0.08 um base-spacing (shown in the right figure).
Fig. 9
Fig. 9 The total reflectance for a BSi structure calculated using RCWA and the proposed TMM model at different angles of incidence at λ = 1 μm for (a) S-polarized and (b) P-polarized light, and at λ = 5 μm for (c) S-polarized and (d) P-polarized light.
Fig. 10
Fig. 10 The reflectance of a BSi structure calculated using the proposed model for the wavelength range of 1-10 μm for (a) S-polarized and (b) P-polarized light.
Fig. 11
Fig. 11 (a) The total reflectance, transmittance and emissivity for a BSi structure with the height varied from 0.5 to 2 μm at wavelengths of 4, 5 and 6 m for unpolarized light. (b) The total reflectance, transmittance and emissivity for a BSi structure with the base-spacing varied from 0 to 0.4 m at wavelengths of 4, 5 and 6 m for unpolarized light.
Fig. 12
Fig. 12 Studying the effect of disorder of the BSi surface topology on the (a) reflectance and (b) emissivity using the proposed TMM model. Transmittance is zero for the assumed parameters hence not shown.
Fig. 13
Fig. 13 The setup used for measuring the reflectance of a BSi sample using an integrating sphere and an FTIR spectrometer.
Fig. 14
Fig. 14 SEM of the BSi sample used in the reflectance measurement.
Fig. 15
Fig. 15 The reflectance measurement for a BSi sample is compared to the result of proposed model simulation. The BSi sample has a height of about 0.75 μm, period of 0.3 μm, no base-spacing, and is fabricated on a lightly doped substrate of thickness 500 μm.
Fig. 16
Fig. 16 Comparing the results of the proposed model with reported reflectance measurements of SiNWs for different SiNWs structures for S-polarized light: (a) diameter = 38 nm, periodicity = 100 nm, height = 0.383 μm [‎42]; (b) diameter = 45 nm, periodicity = 100 nm, height = 0.383 μm [43] (c) diameter = 90 nm, periodicity = 400 nm, height = 1 μm [43]; (d) diameter = 105 nm, periodicity = 400 nm, height = 1 μm [44]

Equations (29)

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[ B C ]= [ E 0 E M H 0 E M ]= [ r=1 M [ cos( δ r ) isin( δ r ) η r η r isin( δ r ) cos( δ r ) ] ][ 1 η N ]
η r ={ ϒ  n r cos( θ r )for spolarization ( TM ) ϒ  n r /cos( θ r ) for ppolarization ( TE )
R= ( η o BC η o B+C ) ( η o BC η o B+C ) *
T=  4  η o  Re( η M ) ( η o B+C ) ( η o B+C ) *
n( λ, T )=  e r ( T )+b(λ, T)
e r ( T )=11.4445+2.7739* 10 4  T+1.705* 10 6   T 2 8.1347* 10 10   T 3
b( λ, T )=  L( T ) λ 2 ( A 0 + A 1 T+  A 2 T 2 )
A 0 =0.8948,  A 1 =4.3977* 10 4 ,  A 2 =7.38358x 10 8
L(  T )=exp( 3 ΔL( T ) L 293 )
ΔL(  T ) L 293 =7.1x 10 2 +1.887* 10 6  T+1.934* 10 9   T 2 4.544* 10 13   T 3
n d = n u N e 2 2 ω 2 ϵ o m n u
κ= αλ 4π 
α BG = i=1 4 l=1 2 (1) l   α i (E) exp( ( 1 ) l   θ i T ) 1  in c m 1
α 1 ( E )= { 0.504 E +392 ( E0.0055 ) 2 ,  for E0.0055 0.504 E ,  for 0E0.0055 0,  for E<0
α 2 ( E )= { 18.08 E +5760 (E0.0055) 2 ,  for E0.0055  18.08 E ,  for 0E0.0055 0,  for E<0
α 3 ( E )= { 536  E 2 ,  for E0 0,  for E<0
α 4 ( E )= { 988  E 2 ,  for E0 0,  for E<0
E= hν  E g ( T )+  (1) l   K B θ i
E g ( T )=  E g 0   A  T 2 B + T  in eV
α FC = n σ n ( T )+p σ p ( T ) in c m 1
σ n ( T )=1.01*  10 12  T  λ 2  in c m 2
σ p ( T )=0.51*  10 12  T  λ 2  in c m 2
α FC =4.15x 10 5 * λ 1.51 * T 2.95 exp( 7000 T )in c m 1
α LV =(19.75 + 0.0174T)*exp( 22.7 λ ) in c m 1
ϵ e α = V l ϵ l α + V h ϵ h α
ϵ e    ϵ m ϵ e +2 ϵ m =F  ϵ i    ϵ m ϵ i +2 ϵ m
V h ϵ h    ϵ e ϵ h  + A  ϵ e + V l ϵ l    ϵ e ϵ l  + A  ϵ e =0, with A=  1 V c V c
ϵ( x )=  m ϵ m exp(j 2πm Δ )
Emissivity=1RT

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