Abstract

The simultaneous determination of t, n(λ), and κ(λ) of thin films can be a tough task for the high correlation of fit parameters. The strong assumptions about the type of dispersion relation are commonly used as a consequence to alleviate correlation concerns by reducing the free parameters before the nonlinear regression analysis. Here we present an angle-resolved spectral reflectometry for the simultaneous determination of weakly absorbing thin film parameters, where a reflectance interferogram is recorded in both angular and spectral domains in a single-shot measurement for the point of the sample being illuminated. The variations of the phase recovered from the interferogram as functions of t, n, and κ reveals that the unwrapped phase is monotonically related to t, n, and κ, thereby allowing the problem of correlation to be alleviated by multiple linear regression. After removing the 2π ambiguity of the unwrapped phase, the merit function based on the absolute unwrapped phase performs a 3D data cube with variables of t, n and κ at each wavelength. The unique solution of t, n, and κ can then be directly determined from the extremum of the 3D data cube at each wavelength with no need of dispersion relation. A sample of GaN thin film grown on a polished sapphire substrate is tested. The experimental data of t and [n(λ), κ(λ)] are confirmed by the scanning electron microscopy and the comparison with the results of other related works, respectively. The consistency of the results shows the proposed method provides a useful tool for the determination of the thickness and optical constants of weakly absorbing thin films.

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

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References

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    [Crossref]
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    [Crossref]

2017 (4)

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

M. Girtan, L. Hrostea, M. Boclinca, and B. Negulescu, “Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry,” AIMS Materials Science 4(3), 594–613 (2017).
[Crossref]

J. E. Park, J. Kim, and M. Cha, “Measurement of thickness profiles of glass plates by analyzing Haidinger fringes,” Appl. Opt. 56(7), 1855–1860 (2017).
[Crossref] [PubMed]

P. Nestler and C. A. Helm, “Determination of refractive index and layer thickness of nm-thin films via ellipsometry,” Opt. Express 25(22), 27077–27085 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (5)

S. T. Yen and P. K. Chung, “Extraction of optical constants from maxima of fringing reflectance spectra,” Appl. Opt. 54(4), 663–668 (2015).
[Crossref] [PubMed]

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

M. Quinten, F. Houta, and T. Fries, “Problems in thin film thickness measurement resolved: improvements of the fast Fourier transform analysis and consideration of the numerical aperture of microscope headers and collimators,” Proc. SPIE 9526, 95260R (2015).
[Crossref]

R. Casquel, J. A. Soler, M. Holgado, A. López, A. Lavín, J. de Vicente, F. J. Sanza, M. F. Laguna, M. J. Bañuls, and R. Puchades, “Sub-micrometric reflectometry for localized label-free biosensing,” Opt. Express 23(10), 12544–12554 (2015).
[Crossref] [PubMed]

B. Gralak, M. Lequime, M. Zerrad, and C. Amra, “Phase retrieval of reflection and transmission coefficients from Kramers-Kronig relations,” J. Opt. Soc. Am. A 32(3), 456–462 (2015).
[Crossref] [PubMed]

2014 (4)

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

N. Saigal, A. Mukherjee, V. Sugunakar, and S. Ghosh, “Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials,” Rev. Sci. Instrum. 85(7), 073105 (2014).
[Crossref] [PubMed]

K. Kim, S. Kim, S. Kwon, and H. J. Pahk, “Volumetric thin film thickness measurement using spectroscopic imaging reflectometer and compensation of reflectance modeling error,” Int. J. Precis. Eng. Manuf. 15(9), 1817–1822 (2014).
[Crossref]

P. K. Chung and S. T. Yen, “Extraction of infrared optical constants from fringing reflectance spectra,” J. Appl. Phys. 116(15), 153101 (2014).
[Crossref]

2010 (2)

B. Šantić, “Measurement of the refractive index and thickness of a transparent film from the shift of the interference pattern due to the sample rotation,” Thin Solid Films 518(14), 3619–3624 (2010).
[Crossref]

J. A. Pradeep and P. Agarwal, “Determination of thickness, refractive index, and spectral scattering of an inhomogeneous thin film with rough interfaces,” J. Appl. Phys. 108(4), 043515 (2010).
[Crossref]

2009 (2)

A. M. El-Naggar, S. Y. El-Zaiat, and S. M. Hassan, “Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum,” Opt. Laser Technol. 41(3), 334–338 (2009).
[Crossref]

J. Lunácek, P. Hlubina, and M. Lunácková, “Simple method for determination of the thickness of a nonabsorbing thin film using spectral reflectance measurement,” Appl. Opt. 48(5), 985–989 (2009).
[Crossref] [PubMed]

2008 (1)

W. D. Joo, J. You, Y. S. Ghim, and S. W. Kim, “Angle-resolved reflectometer for thickness measurement of multi-layered thin-film structures,” Proc. SPIE 7063, 70630Q (2008).
[Crossref]

2007 (1)

2006 (1)

R. P. Shukla, D. V. Udupa, N. C. Das, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38(7), 552–557 (2006).
[Crossref]

1997 (2)

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

1993 (1)

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

1989 (1)

1982 (1)

Adachi, S.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

Agarwal, P.

J. A. Pradeep and P. Agarwal, “Determination of thickness, refractive index, and spectral scattering of an inhomogeneous thin film with rough interfaces,” J. Appl. Phys. 108(4), 043515 (2010).
[Crossref]

Amra, C.

Bañuls, M. J.

Barshilia, H. C.

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Biswas, A.

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Boclinca, M.

M. Girtan, L. Hrostea, M. Boclinca, and B. Negulescu, “Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry,” AIMS Materials Science 4(3), 594–613 (2017).
[Crossref]

Böntgen, T.

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

Brown, S. J.

Bundesmann, C.

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

Casquel, R.

Cha, G.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Cha, M.

Chabinyc, M. L.

Choi, H.

Chung, P. K.

S. T. Yen and P. K. Chung, “Extraction of optical constants from maxima of fringing reflectance spectra,” Appl. Opt. 54(4), 663–668 (2015).
[Crossref] [PubMed]

P. K. Chung and S. T. Yen, “Extraction of infrared optical constants from fringing reflectance spectra,” J. Appl. Phys. 116(15), 153101 (2014).
[Crossref]

Das, N. C.

R. P. Shukla, D. V. Udupa, N. C. Das, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38(7), 552–557 (2006).
[Crossref]

de Oliveira, E. A.

de Vicente, J.

DeCrescent, R. A.

El-Naggar, A. M.

A. M. El-Naggar, S. Y. El-Zaiat, and S. M. Hassan, “Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum,” Opt. Laser Technol. 41(3), 334–338 (2009).
[Crossref]

El-Zaiat, S. Y.

A. M. El-Naggar, S. Y. El-Zaiat, and S. M. Hassan, “Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum,” Opt. Laser Technol. 41(3), 334–338 (2009).
[Crossref]

Fanton, J. T.

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

Frejlich, J.

Fricke, L.

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

Fries, T.

M. Quinten, F. Houta, and T. Fries, “Problems in thin film thickness measurement resolved: improvements of the fast Fourier transform analysis and consideration of the numerical aperture of microscope headers and collimators,” Proc. SPIE 9526, 95260R (2015).
[Crossref]

Fuke, S.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

Ghim, Y. S.

W. D. Joo, J. You, Y. S. Ghim, and S. W. Kim, “Angle-resolved reflectometer for thickness measurement of multi-layered thin-film structures,” Proc. SPIE 7063, 70630Q (2008).
[Crossref]

Ghosh, S.

N. Saigal, A. Mukherjee, V. Sugunakar, and S. Ghosh, “Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials,” Rev. Sci. Instrum. 85(7), 073105 (2014).
[Crossref] [PubMed]

Girtan, M.

M. Girtan, L. Hrostea, M. Boclinca, and B. Negulescu, “Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry,” AIMS Materials Science 4(3), 594–613 (2017).
[Crossref]

Gralak, B.

Grundmann, M.

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

Hassan, S. M.

A. M. El-Naggar, S. Y. El-Zaiat, and S. M. Hassan, “Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum,” Opt. Laser Technol. 41(3), 334–338 (2009).
[Crossref]

Helm, C. A.

Hlubina, P.

Holgado, M.

Houta, F.

M. Quinten, F. Houta, and T. Fries, “Problems in thin film thickness measurement resolved: improvements of the fast Fourier transform analysis and consideration of the numerical aperture of microscope headers and collimators,” Proc. SPIE 9526, 95260R (2015).
[Crossref]

Hrostea, L.

M. Girtan, L. Hrostea, M. Boclinca, and B. Negulescu, “Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry,” AIMS Materials Science 4(3), 594–613 (2017).
[Crossref]

Humphrey, S.

Ina, H.

Jin, J.

Joo, W. D.

W. D. Joo, J. You, Y. S. Ghim, and S. W. Kim, “Angle-resolved reflectometer for thickness measurement of multi-layered thin-film structures,” Proc. SPIE 7063, 70630Q (2008).
[Crossref]

Jyothi, J.

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Kawashima, T.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

Kelso, S. M.

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

Kim, J.

Kim, K.

K. Kim, S. Kim, S. Kwon, and H. J. Pahk, “Volumetric thin film thickness measurement using spectroscopic imaging reflectometer and compensation of reflectance modeling error,” Int. J. Precis. Eng. Manuf. 15(9), 1817–1822 (2014).
[Crossref]

Kim, S.

K. Kim, S. Kim, S. Kwon, and H. J. Pahk, “Volumetric thin film thickness measurement using spectroscopic imaging reflectometer and compensation of reflectance modeling error,” Int. J. Precis. Eng. Manuf. 15(9), 1817–1822 (2014).
[Crossref]

Kim, S. W.

W. D. Joo, J. You, Y. S. Ghim, and S. W. Kim, “Angle-resolved reflectometer for thickness measurement of multi-layered thin-film structures,” Proc. SPIE 7063, 70630Q (2008).
[Crossref]

Kobayashi, S.

Kwon, S.

K. Kim, S. Kim, S. Kwon, and H. J. Pahk, “Volumetric thin film thickness measurement using spectroscopic imaging reflectometer and compensation of reflectance modeling error,” Int. J. Precis. Eng. Manuf. 15(9), 1817–1822 (2014).
[Crossref]

Laguna, M. F.

Lavín, A.

Lee, B. H.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Lee, C.

Lee, S. I.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Leng, J. M.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Lequime, M.

López, A.

Lorbeer, J.

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

Lunácek, J.

Lunácková, M.

Majumdar, A.

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Mantravadi, M. V.

R. P. Shukla, D. V. Udupa, N. C. Das, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38(7), 552–557 (2006).
[Crossref]

Moon, J.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Mukherjee, A.

N. Saigal, A. Mukherjee, V. Sugunakar, and S. Ghosh, “Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials,” Rev. Sci. Instrum. 85(7), 073105 (2014).
[Crossref] [PubMed]

Nagaraja, H.

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Necas, D.

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Negulescu, B.

M. Girtan, L. Hrostea, M. Boclinca, and B. Negulescu, “Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry,” AIMS Materials Science 4(3), 594–613 (2017).
[Crossref]

Nestler, P.

Ohlídal, I.

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Ohlídal, M.

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Ohtsuka, K.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

Opsal, J.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

Pahk, H. J.

K. Kim, S. Kim, S. Kwon, and H. J. Pahk, “Volumetric thin film thickness measurement using spectroscopic imaging reflectometer and compensation of reflectance modeling error,” Int. J. Precis. Eng. Manuf. 15(9), 1817–1822 (2014).
[Crossref]

Park, J. E.

Pradeep, J. A.

J. A. Pradeep and P. Agarwal, “Determination of thickness, refractive index, and spectral scattering of an inhomogeneous thin film with rough interfaces,” J. Appl. Phys. 108(4), 043515 (2010).
[Crossref]

Puchades, R.

Quinten, M.

M. Quinten, F. Houta, and T. Fries, “Problems in thin film thickness measurement resolved: improvements of the fast Fourier transform analysis and consideration of the numerical aperture of microscope headers and collimators,” Proc. SPIE 9526, 95260R (2015).
[Crossref]

Rosencwaig, A.

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

Saigal, N.

N. Saigal, A. Mukherjee, V. Sugunakar, and S. Ghosh, “Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials,” Rev. Sci. Instrum. 85(7), 073105 (2014).
[Crossref] [PubMed]

Šantic, B.

B. Šantić, “Measurement of the refractive index and thickness of a transparent film from the shift of the interference pattern due to the sample rotation,” Thin Solid Films 518(14), 3619–3624 (2010).
[Crossref]

Sanza, F. J.

Sarkar, P.

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Schlitz, R. A.

Schmidt-Grund, R.

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

Schuller, J. A.

Shukla, R. P.

R. P. Shukla, D. V. Udupa, N. C. Das, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38(7), 552–557 (2006).
[Crossref]

Sidorowich, J. J.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Soler, J. A.

Soum-Glaude, A.

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Sugunakar, V.

N. Saigal, A. Mukherjee, V. Sugunakar, and S. Ghosh, “Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials,” Rev. Sci. Instrum. 85(7), 073105 (2014).
[Crossref] [PubMed]

Takeda, M.

Udupa, D. V.

R. P. Shukla, D. V. Udupa, N. C. Das, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38(7), 552–557 (2006).
[Crossref]

Vodák, J.

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Willenborg, D. L.

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

Yen, S. T.

S. T. Yen and P. K. Chung, “Extraction of optical constants from maxima of fringing reflectance spectra,” Appl. Opt. 54(4), 663–668 (2015).
[Crossref] [PubMed]

P. K. Chung and S. T. Yen, “Extraction of infrared optical constants from fringing reflectance spectra,” J. Appl. Phys. 116(15), 153101 (2014).
[Crossref]

Yoon, Y. D.

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

Yoshikawa, H.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

You, J.

W. D. Joo, J. You, Y. S. Ghim, and S. W. Kim, “Angle-resolved reflectometer for thickness measurement of multi-layered thin-film structures,” Proc. SPIE 7063, 70630Q (2008).
[Crossref]

Zajícková, L.

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Zerrad, M.

AIMS Materials Science (1)

M. Girtan, L. Hrostea, M. Boclinca, and B. Negulescu, “Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry,” AIMS Materials Science 4(3), 594–613 (2017).
[Crossref]

Appl. Opt. (6)

Appl. Phys., A Mater. Sci. Process. (1)

J. Jyothi, A. Biswas, P. Sarkar, A. Soum-Glaude, H. Nagaraja, and H. C. Barshilia, “Optical properties of TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber coatings by phase-modulated spectroscopic ellipsometry,” Appl. Phys., A Mater. Sci. Process. 123(7), 496 (2017).
[Crossref]

Appl. Surf. Sci. (1)

D. Nečas, J. Vodák, I. Ohlídal, M. Ohlídal, A. Majumdar, and L. Zajíčková, “Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry,” Appl. Surf. Sci. 350, 149–155 (2015).
[Crossref]

Int. J. Precis. Eng. Manuf. (1)

K. Kim, S. Kim, S. Kwon, and H. J. Pahk, “Volumetric thin film thickness measurement using spectroscopic imaging reflectometer and compensation of reflectance modeling error,” Int. J. Precis. Eng. Manuf. 15(9), 1817–1822 (2014).
[Crossref]

J. Appl. Phys. (5)

J. M. Leng, J. J. Sidorowich, Y. D. Yoon, J. Opsal, B. H. Lee, G. Cha, J. Moon, and S. I. Lee, “Simultaneous measurement of six layers in a silicon on insulator film stack using spectrophotometry and beam profile reflectometry,” J. Appl. Phys. 81(8), 3570–3578 (1997).
[Crossref]

J. T. Fanton, J. Opsal, D. L. Willenborg, S. M. Kelso, and A. Rosencwaig, “Multiparameter measurements of thin films using beam - profile reflectometry,” J. Appl. Phys. 73(11), 7035–7040 (1993).
[Crossref]

J. A. Pradeep and P. Agarwal, “Determination of thickness, refractive index, and spectral scattering of an inhomogeneous thin film with rough interfaces,” J. Appl. Phys. 108(4), 043515 (2010).
[Crossref]

P. K. Chung and S. T. Yen, “Extraction of infrared optical constants from fringing reflectance spectra,” J. Appl. Phys. 116(15), 153101 (2014).
[Crossref]

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Express (3)

Opt. Laser Technol. (2)

R. P. Shukla, D. V. Udupa, N. C. Das, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38(7), 552–557 (2006).
[Crossref]

A. M. El-Naggar, S. Y. El-Zaiat, and S. M. Hassan, “Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum,” Opt. Laser Technol. 41(3), 334–338 (2009).
[Crossref]

Proc. SPIE (2)

W. D. Joo, J. You, Y. S. Ghim, and S. W. Kim, “Angle-resolved reflectometer for thickness measurement of multi-layered thin-film structures,” Proc. SPIE 7063, 70630Q (2008).
[Crossref]

M. Quinten, F. Houta, and T. Fries, “Problems in thin film thickness measurement resolved: improvements of the fast Fourier transform analysis and consideration of the numerical aperture of microscope headers and collimators,” Proc. SPIE 9526, 95260R (2015).
[Crossref]

Rev. Sci. Instrum. (1)

N. Saigal, A. Mukherjee, V. Sugunakar, and S. Ghosh, “Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials,” Rev. Sci. Instrum. 85(7), 073105 (2014).
[Crossref] [PubMed]

Thin Solid Films (2)

L. Fricke, T. Böntgen, J. Lorbeer, C. Bundesmann, R. Schmidt-Grund, and M. Grundmann, “An extended Drude model for the in-situ spectroscopic ellipsometry analysis of ZnO thin layers and surface modifications,” Thin Solid Films 571, 437–441 (2014).
[Crossref]

B. Šantić, “Measurement of the refractive index and thickness of a transparent film from the shift of the interference pattern due to the sample rotation,” Thin Solid Films 518(14), 3619–3624 (2010).
[Crossref]

Other (3)

O. Stenzel, The physics of thin film optical spectra (Springer, 2005).

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping: theory, algorithms, and software (Wiley New York, 1998).

M. Quinten, A Practical Guide to Optical Metrology for Thin Films (John Wiley & Sons, 2012).

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic of optical path of angle-resolved spectral interference. (b) Reflectance fringe simulated in the image plane. (c) Cross-section profiles of the reflectance patterns for different wavelengths along the direction of p-polarization. L1, L2: lenses; Lobj: objective lens; f1, f2, fobj: focal lengths of L1, L2, Lobj; BS: beam splitter. Note that three discrete wavelengths of 400, 500, 700 nm are only shown for clarity in Fig. 1(b) and Fig. 1(c).
Fig. 2
Fig. 2 (a) Principle of single-shot measurement of 2D angle-resolved spectral interferogram. (b) The reflectance interferogram simulated in both angular and spectral domains. The angle of incidence and the wavelength range from −64° to 64° and from 400 nm to 920 nm, respectively. Cross-section profiles of reflectance patterns as functions of (c) angle of incidence at wavelength of 670 nm and (d) wavelength at angle of incidence of 0°, respectively. (e) The wrapped and unwrapped phase maps recovered from the reflectance interferogram.
Fig. 3
Fig. 3 Variations of reflectance as functions of (a) t1, (b) n1 and (c) κ1, respectively. Variations of wrapped phase as functions of (d) t1, (e) n1 and (f) κ1, respectively. Variations of unwrapped phase as functions of (g) t1, (h) n1 and (i) κ1, respectively. In the simulation, the angle of incidence and wavelength are arbitrary chosen to be θ0 = 52° and λ = 690 nm, respectively. The nominal values of the parameters are t1 = 1000 nm, n1 = 2.3, κ1 = 0.01, n0 = 1 and n2 = 4.9.
Fig. 4
Fig. 4 (a) Removal of the 2π ambiguity of the unwrapped phase map. Cross-section plots of the phase values along (b) the spectral domain and (c) the spectral domain. The green dot in Fig. 4(a) and 4(b) is the absolute phase value calculated by the extended KK relation at the angle of incidence of 0°and the wavelength of 720 nm.
Fig. 5
Fig. 5 3D data cube slices of the reciprocal of the low-dimensional merit function based on (a) the absolute unwrapped phase, (b) the wrapped phase and (c) the reflectance, respectively. In the simulation, the nominal values of the parameters are t1 = 1000 nm, n1 = 2.3, κ1 = 0.01, n0 = 1 and n2 = 4.9. The ranges of t1, n1 and κ1 are [800, 1200] nm, [1.6, 3.0] and [0, 0.1], respectively. The angle of incidence θ0 is in the range of [-64°, 64°] and the wavelength λ is 690 nm. The values of the 3D data cube slices are displayed in the logarithmic scale for clarity.
Fig. 6
Fig. 6 Flow chart of determination of thin film parameters.
Fig. 7
Fig. 7 Experimental results of (a) the absolute interferogram formed by the GaN layer, (b) the wrapped phase map and (c) the absolute unwrapped phase map. The angle of incidence and the wavelength range from −64.16° to 64.16° and from 400 to 920 nm, respectively.
Fig. 8
Fig. 8 Experimental results of (a) t1, (b) n1 and (c) κ1 of the GaN layer in the wavelength range from 400 to 920 nm.
Fig. 9
Fig. 9 (a) Fourier image of the interferogram. (b) Frequency spectrum in the spectral domain for different layer thicknesses.
Fig. 10
Fig. 10 Variations of reflectance, wrapped phase and unwrapped phase as functions of t1, n1, t2, n2, respectively. The nominal values of the parameters in the simulation are t1 = 500 nm, n1 = 1.455, t2 = 500 nm, n2 = 2.3 and n3 = 4.9, θ0 = 52°, λ = 690 nm.

Tables (1)

Tables Icon

Table 1 Error analysis of t1, n1 and κ1 with respect to Δλ, Δθ0, ΔR and Δψ

Equations (20)

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θ 0 , j = arc tan d [ j ( N + 1 ) / 2 ] f obj ,
r ˜ = r ˜ 01 + r ˜ 12 exp ( i γ ˜ 1 ) 1 + r ˜ 01 r ˜ 12 exp ( i γ ˜ 1 ) ,
γ ˜ 1 = 4 π t 1 λ n ˜ 1 cos θ ˜ 1 .
r ˜ 01 = ρ 01 exp ( i ψ 01 ) = n ˜ 1 cos θ 0 n 0 cos θ ˜ 1 n ˜ 1 cos θ 0 + n 0 cos θ ˜ 1 = n ˜ 1 2 cos θ 0 n 0 n ˜ 1 cos θ ˜ 1 n ˜ 1 2 cos θ 0 + n 0 n ˜ 1 cos θ ˜ 1 ,
r ˜ 12 = ρ 12 exp ( i ψ 12 ) = n 2 cos θ ˜ 1 n ˜ 1 cos θ 2 n 2 cos θ ˜ 1 + n ˜ 1 cos θ 2 = n 2 n ˜ 1 cos θ ˜ 1 n ˜ 1 2 cos θ 2 n 2 n ˜ 1 cos θ ˜ 1 + n ˜ 1 2 cos θ 2 .
n ˜ 1 cos θ ˜ 1 = u 1 i v 1 ,
u 1 = ( 1 / 2 ) { ( n 1 2 κ 1 2 n 0 2 sin 2 θ 0 ) + [ ( n 1 2 κ 1 2 n 0 2 sin 2 θ 0 ) 2 + 4 n 1 2 κ 1 2 ] 1 / 2 } 1 / 2 ,
v 1 = ( 1 / 2 ) { ( n 1 2 κ 1 2 n 0 2 sin 2 θ 0 ) + [ ( n 1 2 κ 1 2 n 0 2 sin 2 θ 0 ) 2 + 4 n 1 2 κ 1 2 ] 1 / 2 } 1 / 2 .
γ ˜ 1 = η ( u 1 i v 1 ) , η = 4 π t 1 λ ,
ρ 01 = { [ ( n 1 2 κ 1 2 ) cos θ 0 n 0 u 1 ] 2 + ( 2 n 1 k 1 cos θ 0 n 0 v 1 ) 2 [ ( n 1 2 κ 1 2 ) cos θ 0 + n 0 u 1 ] 2 + ( 2 n 1 k 1 cos θ 0 + n 0 v 1 ) 2 } 1 / 2 ,
ψ 01 = arc tan 2 n 0 cos θ 0 [ v 1 ( n 1 2 κ 1 2 ) 2 n 1 κ 1 u 1 ] ( n 1 2 + κ 1 2 ) 2 cos 2 θ 0 n 0 2 ( u 1 2 + v 1 2 ) ,
ρ 12 = { [ ( n 1 2 κ 1 2 ) cos θ 2 n 2 u 1 ] 2 + ( 2 n 1 κ 1 cos θ 2 n 2 v 1 ) 2 [ ( n 1 2 κ 1 2 ) cos θ 2 + n 2 u 1 ] 2 + ( 2 n 1 κ 1 cos θ 2 + n 2 v 1 ) 2 } 1 / 2 ,
ψ 12 = arc tan 2 n 2 cos θ 2 [ v 1 ( n 1 2 κ 1 2 ) 2 n 1 κ 1 u 1 ] ( n 1 2 + κ 1 2 ) 2 cos 2 θ 2 n 2 2 ( u 1 2 + v 1 2 ) .
r ˜ = ρ exp ( i ψ ) = ρ 01 exp ( i ψ 01 ) + ρ 12 exp ( η v 1 ) exp [ i ( ψ 12 η u 1 ) ] 1 + ρ 01 ρ 12 exp ( η v 1 ) exp [ i ( ψ 01 + ψ 12 η u 1 ) ] ,
R = | ρ | 2 = ρ 01 2 exp ( η v 1 ) + ρ 12 2 exp ( η v 1 ) + 2 ρ 01 ρ 12 cos ( ψ 12 ψ 01 η u 1 ) exp ( η v 1 ) + ρ 01 2 ρ 12 2 exp ( η v 1 ) + 2 ρ 01 ρ 12 cos ( ψ 12 + ψ 01 η u 1 ) .
ψ = arc tan ρ 12 ( 1 ρ 01 2 ) sin ( ψ 12 η u 1 ) + ρ 01 [ exp ( η v 1 ) ρ 12 2 exp ( η v 1 ) ] sin ψ 01 ρ 12 ( 1 + ρ 01 2 ) cos ( ψ 12 η u 1 ) + ρ 01 [ exp ( η v 1 ) + ρ 12 2 exp ( η v 1 ) ] cos ψ 01 .
χ 2 = q = 1 , j = 1 M , N { ψ th [ t 1 , n 1 ( λ ) , κ 1 ( λ ) , n 0 , n 2 , θ 0 , j , λ q ] ψ ex ( n 0 , n 2 , θ 0 , j , λ q ) } 2 .
χ λ 2 = j = 1 N [ ψ th ( t 1 , n 1 , κ 1 , n 0 , n 2 , θ 0 , j ) ψ ex ( n 0 , n 2 , θ 0 , j ) ] 2 | λ .
R film = ( I film / I ref ) R ref .
n 2 ( λ ) = A + B λ 2 λ 2 C ,

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