Abstract

A decomposition model with depolarization matrix is proposed to characterize the optical and physical properties of anisotropic thin films with rough surfaces. In the proposed approach, the refractive index and thickness of the thin film are inversely extracted using a pure polarization matrix, and the surface roughness of the film is characterized using a depolarization matrix. The validity of the proposed method is demonstrated by comparing the experimental results for the refractive index and thickness of a thin film with the analytical results obtained using the effective ellipsometric parameters of the film. The results show that the proposed method provides a reliable means of obtaining the optical and physical properties of thin films with fine or coarse rough surfaces. Importantly, the proposed method not only enables the coarse surface roughness of thin-film samples to be determined in a non-contact optical manner, but also provides a more versatile approach than the well-known effective medium approximation (EMA) model, which is restricted to the characterization of samples with low surface roughness.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Use of optical spacers to enhance infrared Mueller ellipsometry sensitivity: application to the characterization of organic thin films

Gerald Ndong, Angel Lizana, Enric Garcia-Caurel, Valerie Paret, Géraldine Melizzi, Denis Cattelan, Bernard Pelissier, and Jean-Hervé Tortai
Appl. Opt. 55(12) 3323-3332 (2016)

Ellipsometry of anisotropic thin films

D. J. De Smet
J. Opt. Soc. Am. 64(5) 631-638 (1974)

Improved determination of the optical constants of anisotropic thin films by ellipsometry using ant colony fitting algorithms

Jean-François Bisson, Gabriel Cormier, Ange Busungu, and Koffi N. Amouzou
J. Opt. Soc. Am. B 34(9) 1957-1964 (2017)

References

  • View by:
  • |
  • |
  • |

  1. K. Vedam, “Spectroscopy ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
    [Crossref]
  2. H. Fujiwara, Spectroscopic Ellipsometry Principle and Application (John Wiley & Sons, 2007).
  3. D. D. Engelsen, “Ellipsometry of anisotropic film,” J. Opt. Soc. Am. 61(11), 1461–1466 (1971).
  4. A. Malsi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
    [Crossref]
  5. T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
    [Crossref]
  6. H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
    [Crossref]
  7. M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
    [Crossref]
  8. P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
    [Crossref]
  9. R. H. Muller and J. C. Farmer, “Macroscopic optical model for the ellipsometry of an underpotential deposit: lead on copper and silver,” Surf. Sci. 135(1-3), 521–531 (1983).
    [Crossref]
  10. J. C. Farmer and R. H. Muller, “Effect of Rhodamine-B on the electrodeposition of lead on copper,” J. Electrochem. Soc. 132(2), 313–319 (1985).
    [Crossref]
  11. J. Qiu, W. J. Zhang, L. H. Liu, P. F. Hsu, and L. J. Liu, “Reflective properties of randomly rough surfaces under large incidence angles,” J. Opt. Soc. Am. A 31(6), 1251–1258 (2014).
    [Crossref] [PubMed]
  12. D. Nečas, I. Ohlídal, D. Franta, M. Ohlídal, V. Čudek, and J. Vodák, “Measurement of thickness distribution, optical constants, and roughness parameters of rough nonuniform ZnSe thin films,” Appl. Opt. 53(25), 5606–5614 (2014).
    [Crossref] [PubMed]
  13. L. M. S. Aas, P. G. Ellingsen, B. E. Fladmark, P. A. Letnes, and M. Kildemo, “Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms,” Opt. Express 21(7), 8753–8762 (2013).
    [Crossref] [PubMed]
  14. O. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and Ø. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards,” Opt. Express 20(14), 15045–15053 (2012).
    [Crossref] [PubMed]
  15. S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
    [Crossref] [PubMed]
  16. S. C. Siah, B. Hoex, and A. G. Aberle, “Accurate characterization of thin films on rough surfaces by spectroscopic ellipsometry,” Thin Solid Films 545, 451–457 (2013).
    [Crossref]
  17. X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using Mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
    [Crossref] [PubMed]
  18. H. T. Huang, W. Kong, and F. L. Terry., “Normal incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
    [Crossref]
  19. S. M. F. Nee and T. W. Nee, “Principle Mueller matrix of reflection and scattering measured for a one dimensional rough surface,” Opt. Eng. 41(5), 994–1001 (2002).
    [Crossref]
  20. P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
    [Crossref]
  21. S. R. Cloude, “Depolarization synthesis: understanding the optics of Mueller matrix depolarization,” J. Opt. Soc. Am. A 30(4), 691–700 (2013).
    [Crossref] [PubMed]
  22. M. W. Williams, “Depolarization and cross polarization in ellipsometry of rough surfaces,” Appl. Opt. 25(20), 3616–3622 (1986).
    [Crossref] [PubMed]
  23. Y. L. Lo, Y. F. Chung, and H. H. Lin, “Polarization scanning ellipsometry method for measuring effective ellipsometric parameters of isotropic and anisotropic thin film,” J. of Light. Tech. 31(14), 2361–2369 (2013).
    [Crossref]
  24. D. W. Berreman, “Optics in stratified and anisotropic media 4x4 matrix formulation,” J. Opt. Soc. Am. 62(4), 502–510 (1972).
    [Crossref]
  25. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B Condens. Matter 53(8), 4265–4274 (1996).
    [Crossref] [PubMed]
  26. M. Schubert, B. Rheinlander, J. A. Woollam, B. Johs, and C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from unaxial TiO2,” J. Opt. Soc. Am. A 13(4), 875–883 (1996).
    [Crossref]
  27. R. Barakat, “Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization thoery,” Opt. Commun. 38(3), 159–161 (1981).
    [Crossref]
  28. C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
    [Crossref]
  29. N. Nguyen-Huu, Y. L. Lo, Y. B. Chen, and T. Y. Yang, “Realization of integrated polarizer and color filters based on subwavelength metallic gratings using a hybrid numerical scheme,” Appl. Opt. 50(4), 415–426 (2011).
    [Crossref] [PubMed]

2014 (4)

2013 (5)

S. R. Cloude, “Depolarization synthesis: understanding the optics of Mueller matrix depolarization,” J. Opt. Soc. Am. A 30(4), 691–700 (2013).
[Crossref] [PubMed]

L. M. S. Aas, P. G. Ellingsen, B. E. Fladmark, P. A. Letnes, and M. Kildemo, “Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms,” Opt. Express 21(7), 8753–8762 (2013).
[Crossref] [PubMed]

Y. L. Lo, Y. F. Chung, and H. H. Lin, “Polarization scanning ellipsometry method for measuring effective ellipsometric parameters of isotropic and anisotropic thin film,” J. of Light. Tech. 31(14), 2361–2369 (2013).
[Crossref]

S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
[Crossref] [PubMed]

S. C. Siah, B. Hoex, and A. G. Aberle, “Accurate characterization of thin films on rough surfaces by spectroscopic ellipsometry,” Thin Solid Films 545, 451–457 (2013).
[Crossref]

2012 (2)

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
[Crossref]

O. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and Ø. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards,” Opt. Express 20(14), 15045–15053 (2012).
[Crossref] [PubMed]

2011 (1)

2002 (1)

S. M. F. Nee and T. W. Nee, “Principle Mueller matrix of reflection and scattering measured for a one dimensional rough surface,” Opt. Eng. 41(5), 994–1001 (2002).
[Crossref]

2001 (1)

H. T. Huang, W. Kong, and F. L. Terry., “Normal incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

2000 (1)

H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
[Crossref]

1998 (3)

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

K. Vedam, “Spectroscopy ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[Crossref]

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

1996 (2)

1990 (1)

P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
[Crossref]

1986 (1)

1985 (1)

J. C. Farmer and R. H. Muller, “Effect of Rhodamine-B on the electrodeposition of lead on copper,” J. Electrochem. Soc. 132(2), 313–319 (1985).
[Crossref]

1984 (1)

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

1983 (1)

R. H. Muller and J. C. Farmer, “Macroscopic optical model for the ellipsometry of an underpotential deposit: lead on copper and silver,” Surf. Sci. 135(1-3), 521–531 (1983).
[Crossref]

1981 (1)

R. Barakat, “Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization thoery,” Opt. Commun. 38(3), 159–161 (1981).
[Crossref]

1972 (1)

1971 (1)

D. D. Engelsen, “Ellipsometry of anisotropic film,” J. Opt. Soc. Am. 61(11), 1461–1466 (1971).

Aas, L. M. S.

Aberle, A. G.

S. C. Siah, B. Hoex, and A. G. Aberle, “Accurate characterization of thin films on rough surfaces by spectroscopic ellipsometry,” Thin Solid Films 545, 451–457 (2013).
[Crossref]

Alterovitz, S. A.

P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
[Crossref]

Aspnes, D. E.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

Barakat, R.

R. Barakat, “Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization thoery,” Opt. Commun. 38(3), 159–161 (1981).
[Crossref]

Berreman, D. W.

Chambon, P.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

Chen, X.

Chen, Y. B.

Chung, Y. F.

Y. L. Lo, Y. F. Chung, and H. H. Lin, “Polarization scanning ellipsometry method for measuring effective ellipsometric parameters of isotropic and anisotropic thin film,” J. of Light. Tech. 31(14), 2361–2369 (2013).
[Crossref]

Cloude, S. R.

Collins, R. W.

H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
[Crossref]

Cudek, V.

Ellingsen, P. G.

Engelsen, D. D.

D. D. Engelsen, “Ellipsometry of anisotropic film,” J. Opt. Soc. Am. 61(11), 1461–1466 (1971).

Erman, M.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

Farmer, J. C.

J. C. Farmer and R. H. Muller, “Effect of Rhodamine-B on the electrodeposition of lead on copper,” J. Electrochem. Soc. 132(2), 313–319 (1985).
[Crossref]

R. H. Muller and J. C. Farmer, “Macroscopic optical model for the ellipsometry of an underpotential deposit: lead on copper and silver,” Surf. Sci. 135(1-3), 521–531 (1983).
[Crossref]

Fladmark, B. E.

Franta, D.

Frette, Ø.

Fujiwara, H.

H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
[Crossref]

Garcia, H.

A. Malsi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

Goto, S.

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Gotoh, J.

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Hall, S. A.

S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
[Crossref] [PubMed]

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

M. Schubert, B. Rheinlander, J. A. Woollam, B. Johs, and C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from unaxial TiO2,” J. Opt. Soc. Am. A 13(4), 875–883 (1996).
[Crossref]

Hoex, B.

S. C. Siah, B. Hoex, and A. G. Aberle, “Accurate characterization of thin films on rough surfaces by spectroscopic ellipsometry,” Thin Solid Films 545, 451–457 (2013).
[Crossref]

Hore, D. K.

S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
[Crossref] [PubMed]

Hoyle, M. A.

S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
[Crossref] [PubMed]

Hsu, P. F.

Huang, H. T.

H. T. Huang, W. Kong, and F. L. Terry., “Normal incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

Jiang, H.

Johs, B.

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

M. Schubert, B. Rheinlander, J. A. Woollam, B. Johs, and C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from unaxial TiO2,” J. Opt. Soc. Am. A 13(4), 875–883 (1996).
[Crossref]

P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
[Crossref]

Kalyanaraman, R.

A. Malsi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

Kawata, M.

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Kelso, S. M.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

Kildemo, M.

Koh, J.

H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
[Crossref]

Kong, W.

H. T. Huang, W. Kong, and F. L. Terry., “Normal incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

Letnes, P. A.

L. M. S. Aas, P. G. Ellingsen, B. E. Fladmark, P. A. Letnes, and M. Kildemo, “Overdetermined broadband spectroscopic Mueller matrix polarimeter designed by genetic algorithms,” Opt. Express 21(7), 8753–8762 (2013).
[Crossref] [PubMed]

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
[Crossref]

Lin, H. H.

Y. L. Lo, Y. F. Chung, and H. H. Lin, “Polarization scanning ellipsometry method for measuring effective ellipsometric parameters of isotropic and anisotropic thin film,” J. of Light. Tech. 31(14), 2361–2369 (2013).
[Crossref]

Liu, L. H.

Liu, L. J.

Liu, S.

Lo, Y. L.

Y. L. Lo, Y. F. Chung, and H. H. Lin, “Polarization scanning ellipsometry method for measuring effective ellipsometric parameters of isotropic and anisotropic thin film,” J. of Light. Tech. 31(14), 2361–2369 (2013).
[Crossref]

N. Nguyen-Huu, Y. L. Lo, Y. B. Chen, and T. Y. Yang, “Realization of integrated polarizer and color filters based on subwavelength metallic gratings using a hybrid numerical scheme,” Appl. Opt. 50(4), 415–426 (2011).
[Crossref] [PubMed]

Ma, Z.

Malsi, A.

A. Malsi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

Maradudin, A. A.

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
[Crossref]

Maria, J.

Mcgahan, W. A.

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

Muller, R. H.

J. C. Farmer and R. H. Muller, “Effect of Rhodamine-B on the electrodeposition of lead on copper,” J. Electrochem. Soc. 132(2), 313–319 (1985).
[Crossref]

R. H. Muller and J. C. Farmer, “Macroscopic optical model for the ellipsometry of an underpotential deposit: lead on copper and silver,” Surf. Sci. 135(1-3), 521–531 (1983).
[Crossref]

Necas, D.

Nee, S. M. F.

S. M. F. Nee and T. W. Nee, “Principle Mueller matrix of reflection and scattering measured for a one dimensional rough surface,” Opt. Eng. 41(5), 994–1001 (2002).
[Crossref]

Nee, T. W.

S. M. F. Nee and T. W. Nee, “Principle Mueller matrix of reflection and scattering measured for a one dimensional rough surface,” Opt. Eng. 41(5), 994–1001 (2002).
[Crossref]

Nguyen-Huu, N.

Niwa, A.

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Nordam, T.

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
[Crossref]

Ohlídal, I.

Ohlídal, M.

Paulson, W.

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

Post, J. S.

S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
[Crossref] [PubMed]

Qiu, J.

Rheinlander, B.

Rovira, P. I.

H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
[Crossref]

Schubert, M.

Siah, S. C.

S. C. Siah, B. Hoex, and A. G. Aberle, “Accurate characterization of thin films on rough surfaces by spectroscopic ellipsometry,” Thin Solid Films 545, 451–457 (2013).
[Crossref]

Simonsen, I.

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
[Crossref]

Snyder, P. G.

P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
[Crossref]

Stamnes, J. J.

Sun, T.

Svensen, O.

Terry, F. L.

H. T. Huang, W. Kong, and F. L. Terry., “Normal incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

Theeten, J. B.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

Uchida, K.

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Vedam, K.

K. Vedam, “Spectroscopy ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[Crossref]

Vodák, J.

Williams, M. W.

Woollam, J. A.

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

M. Schubert, B. Rheinlander, J. A. Woollam, B. Johs, and C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from unaxial TiO2,” J. Opt. Soc. Am. A 13(4), 875–883 (1996).
[Crossref]

P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
[Crossref]

Xu, Z.

Yang, T.

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Yang, T. Y.

Zhang, C.

Zhang, W. J.

Anal. Chem. (1)

S. A. Hall, M. A. Hoyle, J. S. Post, and D. K. Hore, “Combined Stokes vector and Mueller matrix polarimetry for materials characterization,” Anal. Chem. 85(15), 7613–7619 (2013).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

H. T. Huang, W. Kong, and F. L. Terry., “Normal incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. 78(25), 3983–3985 (2001).
[Crossref]

J. Appl. Phys. (3)

C. M. Herzinger, B. Johs, W. A. Mcgahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[Crossref]

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56(10), 2664–2671 (1984).
[Crossref]

P. G. Snyder, J. A. Woollam, S. A. Alterovitz, and B. Johs, “Modeling Alx Ga1-x As optical constant as function of composition,” J. Appl. Phys. 6(11), 5925–5926 (1990).
[Crossref]

J. Electrochem. Soc. (1)

J. C. Farmer and R. H. Muller, “Effect of Rhodamine-B on the electrodeposition of lead on copper,” J. Electrochem. Soc. 132(2), 313–319 (1985).
[Crossref]

J. of Light. Tech. (1)

Y. L. Lo, Y. F. Chung, and H. H. Lin, “Polarization scanning ellipsometry method for measuring effective ellipsometric parameters of isotropic and anisotropic thin film,” J. of Light. Tech. 31(14), 2361–2369 (2013).
[Crossref]

J. Opt. (1)

A. Malsi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

J. Opt. Soc. Am. (2)

D. D. Engelsen, “Ellipsometry of anisotropic film,” J. Opt. Soc. Am. 61(11), 1461–1466 (1971).

D. W. Berreman, “Optics in stratified and anisotropic media 4x4 matrix formulation,” J. Opt. Soc. Am. 62(4), 502–510 (1972).
[Crossref]

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (1)

T. Yang, S. Goto, M. Kawata, K. Uchida, A. Niwa, and J. Gotoh, “Optical properties of Gan thin films on sapphire substrates characterized by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 37(2), 1105–1108 (1998).
[Crossref]

Opt. Commun. (1)

R. Barakat, “Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization thoery,” Opt. Commun. 38(3), 159–161 (1981).
[Crossref]

Opt. Eng. (1)

S. M. F. Nee and T. W. Nee, “Principle Mueller matrix of reflection and scattering measured for a one dimensional rough surface,” Opt. Eng. 41(5), 994–1001 (2002).
[Crossref]

Opt. Express (3)

Phys. Rev. A (1)

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two dimensional rough surfaces,” Phys. Rev. A 86(3), 031803 (2012).
[Crossref]

Phys. Rev. B (1)

H. Fujiwara, J. Koh, P. I. Rovira, and R. W. Collins, “Assessments of effective medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films,” Phys. Rev. B 61(16), 10832–10843 (2000).
[Crossref]

Phys. Rev. B Condens. Matter (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B Condens. Matter 53(8), 4265–4274 (1996).
[Crossref] [PubMed]

Surf. Sci. (1)

R. H. Muller and J. C. Farmer, “Macroscopic optical model for the ellipsometry of an underpotential deposit: lead on copper and silver,” Surf. Sci. 135(1-3), 521–531 (1983).
[Crossref]

Thin Solid Films (2)

K. Vedam, “Spectroscopy ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[Crossref]

S. C. Siah, B. Hoex, and A. G. Aberle, “Accurate characterization of thin films on rough surfaces by spectroscopic ellipsometry,” Thin Solid Films 545, 451–457 (2013).
[Crossref]

Other (1)

H. Fujiwara, Spectroscopic Ellipsometry Principle and Application (John Wiley & Sons, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 Optical equivalent model of thin film using in decomposition method.
Fig. 2
Fig. 2 Schematic illustration of the electric fields for two-layer thin film structure.
Fig. 3
Fig. 3 Correlation between input values and extracted values of effective ellipsometric parameters given ± 0.5% accuracy of output Stokes vectors with input value of: a) Ψ′pp = 50°, Ψ′ps = 20°, Ψ′sp = 20°, Δ′pp = 70°, Δ′ps = 80°, and Δ′sp = 80°; and b) Ψ′pp = 70°, Ψ′ps = 50°, Ψ′sp = 10°, Δ′pp = 50°, Δ′ps = 110°, and Δ′sp = 260°.
Fig. 4
Fig. 4 Simulation results by using decomposition model and GA fitting for normalized Stokes vectors (in four input polarized states of 0°, 90°, 45° and R-) of 215-nm thickness anisotropic thin film as function of the scanning angle θ given surface roughness values of: (a) 6 Å and (b) 200 Å.
Fig. 5
Fig. 5 Experimental setup used to characterize rough optical samples.
Fig. 6
Fig. 6 Experimental and GA curve-fitting results for normalized Stokes vectors (in four input polarized states of 0°, 90°, + 45° and R-) of 215 nm thickness anisotropic thin film as function of scanning angle θ given surface roughness values of: (a) Ra = 6 Å and (b) Ra = 197 Å, and (c) Ra = 2000 Å
Fig. 7
Fig. 7 Experimental and GA curve-fitting results for effective ellipsometric parameters of 215 nm thickness anisotropic thin film as function of scanning angle θ given surface roughness values of: (a) Ra = 6 Å and (b) Ra = 197 Å, and (c) Ra = 2000 Å

Tables (5)

Tables Icon

Table 1 Extracted values of MD, n0, ne and d for anisotropic thin film with surface roughness of 6 Å

Tables Icon

Table 2 Extracted values of MD, n0, ne and d for anisotropic thin film with surface roughness of 200 Å

Tables Icon

Table 3 Extracted values of MD, no, ne and d for thin film with Ra = 6 Å

Tables Icon

Table 4 Extracted values of MD, n0, ne and d for thin film with Ra = 197 Å

Tables Icon

Table 5 Extracted values of MD, n0, ne and d for thin film with Ra = 2000 Å

Equations (22)

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

S=( S 0 S 1 S 2 S 3 )=( I I 0° I 90° I 45° I 45° I R I L )
( S 0 S 1 S 2 S 3 ) output = ( m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 ) thinfilm ( S 0 S 1 S 2 S 3 ) input
M thinfilm = M D M R M D
[ E is E rs E ip E rp ]= T i 1 P(z) T t [ E ts 0 E tp 0 ]=T[ E ts 0 E tp 0 ]
J R =[ r pp r ps r sp r ss ]
M R =( R 11 R 12 0 0 R 12 R 11 0 0 0 0 R 33 R 34 0 0 R 34 R 33 )
M D =( 1 A 1 A 2 A 3 0 P 1 0 0 0 0 P 1 0 0 0 0 P 3 )
s 0° = ( m 11 + m 12 , m 21 + m 22 , m 31 + m 32 , m 41 + m 42 ) T
s 45° = ( m 11 + m 13 , m 21 + m 23 , m 31 + m 33 , m 41 + m 43 ) T
s 90° = ( m 11 m 12 , m 21 m 22 , m 31 m 32 , m 41 m 42 ) T
s R = ( m 11 + m 14 , m 21 + m 24 , m 31 + m 34 , m 41 + m 44 ) T
F Fitness = k=1 3 { abs[ ( S i,experiment (k) S i,theory (k) ) 2 ] } ,i=0°,45°,90°,R.
M Pure = M D 1 M thinfilm M D 1 = M D 1 M D M R M D M D 1
Ψ pp = tan 1 [ 1+ 1 2 ( M 12 + M 21 ) ] 1 2
Ψ sp = tan 1 [ 1+ 1 2 ( M 11 M 21 ) ] 1 2
Ψ ps = tan 1 [ 1+ 1 2 ( M 11 M 12 ) ] 1 2
Δ ps = tan 1 ( M 42 M 41 M 31 M 32 )
Δ pp = tan 1 ( M 34 M 43 M 33 + M 44 )
Δ sp = tan 1 ( M 14 M 24 M 13 M 23 )
F Fitness = j=1 6 { abs [ E Experiment (j) E Theory (j) ] 2 }
( s out ) P'S' 0,45,90,R =R(θ) M Pure ( s in ) XY 0+θ,45+θ,90+θ,R+θ
F Fitness = n=1 16 { abs [ M D (n) M EMA (n) ] 2 }

Metrics