Abstract

We describe a radiative transfer (RT) equation for the simulation of optical scattering effects in a nanostructured semiconductor for spectroscopic ellipsometry (SE). As an example, we chose porous silicon (PS), whose pores are considered to act as light scatterers. We examined the effects of pore radius, slab thickness, and incident angle. The volume scattering effect in the internal morphology of the PS generates incoherent light, leading to depolarization. By simulating the four Stokes parameters through the RT equation, we could theoretically assess the degree of polarization that is essential for SE measurements of some nanostructured semiconductors.

© 2003 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]
  5. U. Richter, “Application of the degree of polarization to film thickness gradients,” Thin Solid Films 313-314, 102–107 (1998).
    [CrossRef]
  6. M. Kildemo, R. Ossikovski, M. Stchakovsky, “Measurement of the absorption edge of thick transparent substrates using the incoherent reflection model and spectroscopic UV-visible-near IR ellipsometry,” Thin Solid Films 313-314, 108–113 (1998).
    [CrossRef]
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    [CrossRef]
  8. S.-M. F. Nee, T. Cole, “Effects of depolarization of polarimetric components on null ellipsometry,” Thin Solid Films 313-314, 90–96 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
    [CrossRef]
  24. C. M. Lam, A. Ishimaru, “Mueller matrix calculation for a slab of random medium with both random rough surfaces and discrete particles,” IEEE Trans. Antennas Propag. 42, 145–156 (1994).
    [CrossRef]
  25. D. E. Aspnes, “Optical response of microscopically rough surfaces,” Phys. Rev. B 41, 10,334–10,343 (1990).
    [CrossRef]
  26. M. S. Hybertsen, “Absorption and emission of light in nanoscale silicon structures,” Phys. Rev. Lett. 72, 1514–1517 (1994).
    [CrossRef] [PubMed]
  27. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  28. R. L.-T. Cheng, A. Ishimaru, “Transmission, backscattering, and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
    [CrossRef]
  29. I. Mihalcescu, G. Lerondel, R. Romestain, “Porous silicon anisotropy investigated by guided light,” Thin Solid Films 297, 245–249 (1997).
    [CrossRef]
  30. K. H. Jun, R. Carius, H. Stiebig, “Optical characteristics of intrinsic microcrystalline silicon,” Phys. Rev. B 66, 115301-1–115301-11 (2002).
    [CrossRef]

2002

K. H. Jun, R. Carius, H. Stiebig, “Optical characteristics of intrinsic microcrystalline silicon,” Phys. Rev. B 66, 115301-1–115301-11 (2002).
[CrossRef]

2000

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

O. Bisi, S. Ossicini, L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

S. Strehlke, S. Bastide, O. Polgar, M. Fried, Lévy-Clément, “Characterization of thin porous silicon films formed on n+/p silicon junctions by spectroscopic ellipsometry,” J. Electrochem. Soc. 147, 636–641 (2000).
[CrossRef]

1999

G. Rothenberger, P. Comte, M. Grätzel, “A contribution to the optical design of dye-sensitized nanocrystalline solar cells,” Sol. Energy Mater. Sol. Cells 58, 321–336 (1999).
[CrossRef]

1998

J. Ferber, J. Luther, “Computer simulations of light scattering and absorption in dye-sensitized solar cells,” Sol. Energy Mater. Sol. Cells 54, 265–275 (1998).
[CrossRef]

S.-M. F. Nee, T. Cole, “Effects of depolarization of polarimetric components on null ellipsometry,” Thin Solid Films 313-314, 90–96 (1998).
[CrossRef]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33–39 (1998).
[CrossRef]

U. Rossow, “Depolarization/mixed polarization corrections of ellipsometry spectra,” Thin Solid Films 313-314, 97–101 (1998).
[CrossRef]

M. Forcht, A. Gombert, R. Joerger, M. Köhl, “Ellipsometric investigation of thick polymer films,” Thin Solid Films 313-314, 808–813 (1998).
[CrossRef]

U. Richter, “Application of the degree of polarization to film thickness gradients,” Thin Solid Films 313-314, 102–107 (1998).
[CrossRef]

M. Kildemo, R. Ossikovski, M. Stchakovsky, “Measurement of the absorption edge of thick transparent substrates using the incoherent reflection model and spectroscopic UV-visible-near IR ellipsometry,” Thin Solid Films 313-314, 108–113 (1998).
[CrossRef]

1997

I. Mihalcescu, G. Lerondel, R. Romestain, “Porous silicon anisotropy investigated by guided light,” Thin Solid Films 297, 245–249 (1997).
[CrossRef]

1996

S.-M. F. Nee, “Polarization of specular reflection and near-specular scattering by a rough surface,” Appl. Opt. 35, 3570–3582 (1996).
[CrossRef]

C. Brosseau, “Meuller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996).
[CrossRef]

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

1994

S. Krishnan, P. C. Nordine, “Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter: a study of depolarization effects,” Appl. Opt. 33, 4184–4192 (1994).
[CrossRef] [PubMed]

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

C. M. Lam, A. Ishimaru, “Mueller matrix calculation for a slab of random medium with both random rough surfaces and discrete particles,” IEEE Trans. Antennas Propag. 42, 145–156 (1994).
[CrossRef]

M. S. Hybertsen, “Absorption and emission of light in nanoscale silicon structures,” Phys. Rev. Lett. 72, 1514–1517 (1994).
[CrossRef] [PubMed]

1993

C. M. Lam, A. Ishimaru, “Calculation of Mueller matrices and polarization signatures for a slab of random medium using vector radiative transfer,” IEEE Trans. Antennas Propag. 41, 851–862 (1993).
[CrossRef]

1990

D. E. Aspnes, “Optical response of microscopically rough surfaces,” Phys. Rev. B 41, 10,334–10,343 (1990).
[CrossRef]

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experimental and application to microwave remote sensing and polarimetry,” IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[CrossRef]

1988

1987

1982

1981

R. T. Shin, J. A. Kong, “Radiative transfer theory for active remote sensing of a homogenous layer containing spherical scatterers,” J. Appl. Phys. 52, 4221–4230 (1981).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Optical response of microscopically rough surfaces,” Phys. Rev. B 41, 10,334–10,343 (1990).
[CrossRef]

Bastide, S.

S. Strehlke, S. Bastide, O. Polgar, M. Fried, Lévy-Clément, “Characterization of thin porous silicon films formed on n+/p silicon junctions by spectroscopic ellipsometry,” J. Electrochem. Soc. 147, 636–641 (2000).
[CrossRef]

Bensahel, D.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Bisi, O.

O. Bisi, S. Ossicini, L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

Brosseau, C.

C. Brosseau, “Meuller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996).
[CrossRef]

Campidellì, Y.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Carius, R.

K. H. Jun, R. Carius, H. Stiebig, “Optical characteristics of intrinsic microcrystalline silicon,” Phys. Rev. B 66, 115301-1–115301-11 (2002).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Cheng, R. L.-T.

Cole, T.

S.-M. F. Nee, T. Cole, “Effects of depolarization of polarimetric components on null ellipsometry,” Thin Solid Films 313-314, 90–96 (1998).
[CrossRef]

Collins, R. W.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Comte, P.

G. Rothenberger, P. Comte, M. Grätzel, “A contribution to the optical design of dye-sensitized nanocrystalline solar cells,” Sol. Energy Mater. Sol. Cells 58, 321–336 (1999).
[CrossRef]

Ding, K.-H.

L. Tsang, J. A. Kong, K.-H. Ding, in Scattering of Electromagnetic Waves, J. A. Kong, ed. (Wiley, New York, 2001), Vol. 1.

Ferber, J.

J. Ferber, J. Luther, “Computer simulations of light scattering and absorption in dye-sensitized solar cells,” Sol. Energy Mater. Sol. Cells 54, 265–275 (1998).
[CrossRef]

Ferlauto, A. S.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Ferrieu, F.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Forcht, M.

M. Forcht, A. Gombert, R. Joerger, M. Köhl, “Ellipsometric investigation of thick polymer films,” Thin Solid Films 313-314, 808–813 (1998).
[CrossRef]

Fried, M.

S. Strehlke, S. Bastide, O. Polgar, M. Fried, Lévy-Clément, “Characterization of thin porous silicon films formed on n+/p silicon junctions by spectroscopic ellipsometry,” J. Electrochem. Soc. 147, 636–641 (2000).
[CrossRef]

Fujiwara, H.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Glowacki, F.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Gombert, A.

M. Forcht, A. Gombert, R. Joerger, M. Köhl, “Ellipsometric investigation of thick polymer films,” Thin Solid Films 313-314, 808–813 (1998).
[CrossRef]

Grätzel, M.

G. Rothenberger, P. Comte, M. Grätzel, “A contribution to the optical design of dye-sensitized nanocrystalline solar cells,” Sol. Energy Mater. Sol. Cells 58, 321–336 (1999).
[CrossRef]

Halimaouì, A.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Hybertsen, M. S.

M. S. Hybertsen, “Absorption and emission of light in nanoscale silicon structures,” Phys. Rev. Lett. 72, 1514–1517 (1994).
[CrossRef] [PubMed]

Ishimaru, A.

C. M. Lam, A. Ishimaru, “Mueller matrix calculation for a slab of random medium with both random rough surfaces and discrete particles,” IEEE Trans. Antennas Propag. 42, 145–156 (1994).
[CrossRef]

C. M. Lam, A. Ishimaru, “Calculation of Mueller matrices and polarization signatures for a slab of random medium using vector radiative transfer,” IEEE Trans. Antennas Propag. 41, 851–862 (1993).
[CrossRef]

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experimental and application to microwave remote sensing and polarimetry,” IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[CrossRef]

R. L.-T. Cheng, A. Ishimaru, “Transmission, backscattering, and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
[CrossRef]

Jellison, G. E.

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33–39 (1998).
[CrossRef]

Joerger, R.

M. Forcht, A. Gombert, R. Joerger, M. Köhl, “Ellipsometric investigation of thick polymer films,” Thin Solid Films 313-314, 808–813 (1998).
[CrossRef]

Jun, K. H.

K. H. Jun, R. Carius, H. Stiebig, “Optical characteristics of intrinsic microcrystalline silicon,” Phys. Rev. B 66, 115301-1–115301-11 (2002).
[CrossRef]

Kildemo, M.

M. Kildemo, R. Ossikovski, M. Stchakovsky, “Measurement of the absorption edge of thick transparent substrates using the incoherent reflection model and spectroscopic UV-visible-near IR ellipsometry,” Thin Solid Films 313-314, 108–113 (1998).
[CrossRef]

Kim, K.

Koh, J.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Köhl, M.

M. Forcht, A. Gombert, R. Joerger, M. Köhl, “Ellipsometric investigation of thick polymer films,” Thin Solid Films 313-314, 808–813 (1998).
[CrossRef]

Kong, J. A.

R. T. Shin, J. A. Kong, “Radiative transfer theory for active remote sensing of a homogenous layer containing spherical scatterers,” J. Appl. Phys. 52, 4221–4230 (1981).
[CrossRef]

L. Tsang, J. A. Kong, K.-H. Ding, in Scattering of Electromagnetic Waves, J. A. Kong, ed. (Wiley, New York, 2001), Vol. 1.

Krishnan, S.

Lagendijk, A.

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

Lam, C. M.

C. M. Lam, A. Ishimaru, “Mueller matrix calculation for a slab of random medium with both random rough surfaces and discrete particles,” IEEE Trans. Antennas Propag. 42, 145–156 (1994).
[CrossRef]

C. M. Lam, A. Ishimaru, “Calculation of Mueller matrices and polarization signatures for a slab of random medium using vector radiative transfer,” IEEE Trans. Antennas Propag. 41, 851–862 (1993).
[CrossRef]

Larré, A.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Lerondel, G.

I. Mihalcescu, G. Lerondel, R. Romestain, “Porous silicon anisotropy investigated by guided light,” Thin Solid Films 297, 245–249 (1997).
[CrossRef]

Lévy-Clément,

S. Strehlke, S. Bastide, O. Polgar, M. Fried, Lévy-Clément, “Characterization of thin porous silicon films formed on n+/p silicon junctions by spectroscopic ellipsometry,” J. Electrochem. Soc. 147, 636–641 (2000).
[CrossRef]

Luther, J.

J. Ferber, J. Luther, “Computer simulations of light scattering and absorption in dye-sensitized solar cells,” Sol. Energy Mater. Sol. Cells 54, 265–275 (1998).
[CrossRef]

Mandel, L.

Messier, R.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Mihalcescu, I.

I. Mihalcescu, G. Lerondel, R. Romestain, “Porous silicon anisotropy investigated by guided light,” Thin Solid Films 297, 245–249 (1997).
[CrossRef]

Nee, S.-M. F.

Nordine, P. C.

Ossicini, S.

O. Bisi, S. Ossicini, L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

Ossikovski, R.

M. Kildemo, R. Ossikovski, M. Stchakovsky, “Measurement of the absorption edge of thick transparent substrates using the incoherent reflection model and spectroscopic UV-visible-near IR ellipsometry,” Thin Solid Films 313-314, 108–113 (1998).
[CrossRef]

Pavesi, L.

O. Bisi, S. Ossicini, L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

Polgar, O.

S. Strehlke, S. Bastide, O. Polgar, M. Fried, Lévy-Clément, “Characterization of thin porous silicon films formed on n+/p silicon junctions by spectroscopic ellipsometry,” J. Electrochem. Soc. 147, 636–641 (2000).
[CrossRef]

Richter, U.

U. Richter, “Application of the degree of polarization to film thickness gradients,” Thin Solid Films 313-314, 102–107 (1998).
[CrossRef]

Romestain, R.

I. Mihalcescu, G. Lerondel, R. Romestain, “Porous silicon anisotropy investigated by guided light,” Thin Solid Films 297, 245–249 (1997).
[CrossRef]

Rossow, U.

U. Rossow, “Depolarization/mixed polarization corrections of ellipsometry spectra,” Thin Solid Films 313-314, 97–101 (1998).
[CrossRef]

Rothenberger, G.

G. Rothenberger, P. Comte, M. Grätzel, “A contribution to the optical design of dye-sensitized nanocrystalline solar cells,” Sol. Energy Mater. Sol. Cells 58, 321–336 (1999).
[CrossRef]

Rovira, P. I.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Shin, R. T.

R. T. Shin, J. A. Kong, “Radiative transfer theory for active remote sensing of a homogenous layer containing spherical scatterers,” J. Appl. Phys. 52, 4221–4230 (1981).
[CrossRef]

Stchakovsky, M.

M. Kildemo, R. Ossikovski, M. Stchakovsky, “Measurement of the absorption edge of thick transparent substrates using the incoherent reflection model and spectroscopic UV-visible-near IR ellipsometry,” Thin Solid Films 313-314, 108–113 (1998).
[CrossRef]

Stiebig, H.

K. H. Jun, R. Carius, H. Stiebig, “Optical characteristics of intrinsic microcrystalline silicon,” Phys. Rev. B 66, 115301-1–115301-11 (2002).
[CrossRef]

Strehlke, S.

S. Strehlke, S. Bastide, O. Polgar, M. Fried, Lévy-Clément, “Characterization of thin porous silicon films formed on n+/p silicon junctions by spectroscopic ellipsometry,” J. Electrochem. Soc. 147, 636–641 (2000).
[CrossRef]

Tsang, L.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experimental and application to microwave remote sensing and polarimetry,” IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[CrossRef]

L. Tsang, J. A. Kong, K.-H. Ding, in Scattering of Electromagnetic Waves, J. A. Kong, ed. (Wiley, New York, 2001), Vol. 1.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

van Tiggelen, B. A.

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

Wen, B.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experimental and application to microwave remote sensing and polarimetry,” IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[CrossRef]

Winebrenner, D. P.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experimental and application to microwave remote sensing and polarimetry,” IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[CrossRef]

Wolf, E.

Wronski, C. R.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Zapien, J. A.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Larré, A. Halimaouì, F. Glowacki, F. Ferrieu, Y. Campidellì, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultrahigh vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Appl. Surf. Sci.

R. W. Collins, J. Koh, H. Fujiwara, P. I. Rovira, A. S. Ferlauto, J. A. Zapien, C. R. Wronski, R. Messier, “Recent progress in thin film growth analysis by multichannel spectroscopic ellipsometry,” Appl. Surf. Sci. 154-155, 217–228 (2000).
[CrossRef]

IEEE Trans. Antennas Propag.

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Figures (5)

Fig. 1
Fig. 1

Linearly polarized electromagnetic plane wave incident upon a slab of randomly distributed particles overlying a homogeneous half-space.

Fig. 2
Fig. 2

α e of PS determined by Eqs. (1) and (2). α of c-Si and αEMT of the PS are also displayed. In the Rayleigh scattering formalism, pores are scatterers and the c-Si skeleton is the surrounding material. In the EMT, f s means a void fraction.

Fig. 3
Fig. 3

Degree of polarization of the total Stokes vector in the specular reflection direction at three values of r.

Fig. 4
Fig. 4

Degree of polarization of the total Stokes vector in the specular reflection direction at four values of d.

Fig. 5
Fig. 5

Degree of polarization of the total Stokes vector in the specular reflection direction at four values of θ0i .

Equations (11)

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αs=2fs2πλ ns4r3εs-ε1εs+2ε12,
αe=αEMT+αs,
Iθ, ϕ, z=IpIsUV=EpEp*EsEs*2ReEpEs*2ImEpEs*,
I0iπ-θ0, ϕ0=1120δcos θ0-cos θ0iδϕ0,
cos θ ddzIz, θ, ϕ=-αeIz, θ, ϕ+0πdθ sin θ×02πdϕPθ, ϕ; θ, ϕ×Iz, θ, ϕ,
Iπ-θ, ϕ, z=0=T¯¯01θ0Ioiπ-θ0, ϕ0+R¯¯01θ˜Iθ, ϕ, z=0
Iθ, ϕ, z=-d=R¯¯12θ˜Iπ-θ, ϕ, z=-d,
R¯¯abθ˜=|Rpθ˜|20000|Rsθ˜|20000ReRpθ˜Rs*θ˜-ImRpθ˜Rs*θ˜00ImRpθ˜Rs*θ˜ReRpθ˜Rs*θ˜,
T¯¯abθ˜=εbεatpθ˜0000tsθ˜0000βθ˜ReTpθ˜Ts*θ˜-βθ˜ImTpθ˜Ts*θ˜00βθ˜ImTpθ˜Ts*θ˜βθ˜ReTpθ˜Ts*θ˜,
βθ˜=1-εa/εbsin2 θ˜1/2cos θ˜,
deg. pol.=Ip-Is2+U2+V21/2Ip+Is.

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